diff --git a/.cargo/config.toml b/.cargo/config.toml index 79760da5..dfcb7216 100644 --- a/.cargo/config.toml +++ b/.cargo/config.toml @@ -2,3 +2,6 @@ [build] # debug symbols https://pyo3.rs/main/debugging#common-setup rustflags = ["-g"] + +[net] +git-fetch-with-cli = true diff --git a/.gitignore b/.gitignore index 02661d9f..3cea3d40 100644 --- a/.gitignore +++ b/.gitignore @@ -87,3 +87,4 @@ visualizer.tgz package .mypy_cache/ *.json +python/egglog/exp/param_eq/trace/ diff --git a/AGENTS.md b/AGENTS.md index f8828ade..7a4b76d5 100644 --- a/AGENTS.md +++ b/AGENTS.md @@ -19,6 +19,9 @@ - Use the Context7 MCP server for egglog documentation instead of copying external doc summaries into this file. - Keep general workflows in the how-to guides, and keep Python-specific runtime/reference examples in `docs/reference/python-integration.md`. +- Before changing Python-facing `egglog` APIs or expression-inspection patterns, read `docs/reference/python-integration.md`. +- Before changing how egglog concepts map into Python declarations, relations, actions, or sort/function definitions, read `docs/reference/egglog-translation.md`. +- If a change touches both local Python ergonomics and egglog-language mapping, read `docs/reference/python-integration.md` first, then `docs/reference/egglog-translation.md`. - If a PR adds or updates a changelog entry in `docs/changelog.md`, keep it aligned with the final code changes. - For a clean docs rebuild, clear `docs/_build/`; the MyST-NB execution cache lives in `docs/_build/.jupyter_cache`. @@ -41,6 +44,7 @@ ## Verification - Prefer the minimal code change and the minimal diff that solves the task; only broaden the change if the smaller fix is not sufficient. +- For long-running profiling or trace probes, run them with explicit timeouts, check for lingering worker processes before and after, and inspect memory usage after any timeout or manual kill before starting the next experiment. - Run `make mypy` for typing changes. - Run targeted pytest for touched modules. - Run `make docs` for docs or public API changes. diff --git a/Cargo.lock b/Cargo.lock index fc8d1c58..78330bc6 100644 --- a/Cargo.lock +++ b/Cargo.lock @@ -4,9 +4,9 @@ version = 4 [[package]] name = "aho-corasick" -version = "1.1.3" +version = "1.1.4" source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "8e60d3430d3a69478ad0993f19238d2df97c507009a52b3c10addcd7f6bcb916" +checksum = "ddd31a130427c27518df266943a5308ed92d4b226cc639f5a8f1002816174301" dependencies = [ "memchr", ] @@ -19,9 +19,9 @@ checksum = "683d7910e743518b0e34f1186f92494becacb047c7b6bf616c96772180fef923" [[package]] name = "anstream" -version = "0.6.21" +version = "1.0.0" source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "43d5b281e737544384e969a5ccad3f1cdd24b48086a0fc1b2a5262a26b8f4f4a" +checksum = "824a212faf96e9acacdbd09febd34438f8f711fb84e09a8916013cd7815ca28d" dependencies = [ "anstyle", "anstyle-parse", @@ -34,50 +34,53 @@ dependencies = [ [[package]] name = "anstyle" -version = "1.0.13" +version = "1.0.14" source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "5192cca8006f1fd4f7237516f40fa183bb07f8fbdfedaa0036de5ea9b0b45e78" +checksum = "940b3a0ca603d1eade50a4846a2afffd5ef57a9feac2c0e2ec2e14f9ead76000" [[package]] name = "anstyle-parse" -version = "0.2.7" +version = "1.0.0" source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "4e7644824f0aa2c7b9384579234ef10eb7efb6a0deb83f9630a49594dd9c15c2" +checksum = "52ce7f38b242319f7cabaa6813055467063ecdc9d355bbb4ce0c68908cd8130e" dependencies = [ "utf8parse", ] [[package]] name = "anstyle-query" -version = "1.1.4" +version = "1.1.5" source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "9e231f6134f61b71076a3eab506c379d4f36122f2af15a9ff04415ea4c3339e2" +checksum = "40c48f72fd53cd289104fc64099abca73db4166ad86ea0b4341abe65af83dadc" dependencies = [ - "windows-sys 0.60.2", + "windows-sys", ] [[package]] name = "anstyle-wincon" -version = "3.0.10" +version = "3.0.11" source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "3e0633414522a32ffaac8ac6cc8f748e090c5717661fddeea04219e2344f5f2a" +checksum = "291e6a250ff86cd4a820112fb8898808a366d8f9f58ce16d1f538353ad55747d" dependencies = [ "anstyle", "once_cell_polyfill", - "windows-sys 0.60.2", + "windows-sys", ] [[package]] name = "anyhow" -version = "1.0.100" +version = "1.0.102" source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "a23eb6b1614318a8071c9b2521f36b424b2c83db5eb3a0fead4a6c0809af6e61" +checksum = "7f202df86484c868dbad7eaa557ef785d5c66295e41b460ef922eca0723b842c" [[package]] name = "arc-swap" -version = "1.7.1" +version = "1.9.1" source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "69f7f8c3906b62b754cd5326047894316021dcfe5a194c8ea52bdd94934a3457" +checksum = "6a3a1fd6f75306b68087b831f025c712524bcb19aad54e557b1129cfa0a2b207" +dependencies = [ + "rustversion", +] [[package]] name = "async-trait" @@ -87,7 +90,7 @@ checksum = "9035ad2d096bed7955a320ee7e2230574d28fd3c3a0f186cbea1ff3c7eed5dbb" dependencies = [ "proc-macro2", "quote", - "syn 2.0.107", + "syn 2.0.117", ] [[package]] @@ -110,9 +113,9 @@ checksum = "72b3254f16251a8381aa12e40e3c4d2f0199f8c6508fbecb9d91f575e0fbb8c6" [[package]] name = "bitflags" -version = "2.9.4" +version = "2.11.0" source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "2261d10cca569e4643e526d8dc2e62e433cc8aba21ab764233731f8d369bf394" +checksum = "843867be96c8daad0d758b57df9392b6d8d271134fce549de6ce169ff98a92af" [[package]] name = "bitmaps" @@ -134,9 +137,9 @@ dependencies = [ [[package]] name = "bumpalo" -version = "3.19.0" +version = "3.20.2" source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "46c5e41b57b8bba42a04676d81cb89e9ee8e859a1a66f80a5a72e1cb76b34d43" +checksum = "5d20789868f4b01b2f2caec9f5c4e0213b41e3e5702a50157d699ae31ced2fcb" [[package]] name = "bytes" @@ -161,9 +164,9 @@ dependencies = [ [[package]] name = "clap" -version = "4.5.51" +version = "4.6.0" source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "4c26d721170e0295f191a69bd9a1f93efcdb0aff38684b61ab5750468972e5f5" +checksum = "b193af5b67834b676abd72466a96c1024e6a6ad978a1f484bd90b85c94041351" dependencies = [ "clap_builder", "clap_derive", @@ -171,9 +174,9 @@ dependencies = [ [[package]] name = "clap_builder" -version = "4.5.51" +version = "4.6.0" source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "75835f0c7bf681bfd05abe44e965760fea999a5286c6eb2d59883634fd02011a" +checksum = "714a53001bf66416adb0e2ef5ac857140e7dc3a0c48fb28b2f10762fc4b5069f" dependencies = [ "anstream", "anstyle", @@ -183,27 +186,27 @@ dependencies = [ [[package]] name = "clap_derive" -version = "4.5.49" +version = "4.6.0" source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "2a0b5487afeab2deb2ff4e03a807ad1a03ac532ff5a2cee5d86884440c7f7671" +checksum = "1110bd8a634a1ab8cb04345d8d878267d57c3cf1b38d91b71af6686408bbca6a" dependencies = [ "heck", "proc-macro2", "quote", - "syn 2.0.107", + "syn 2.0.117", ] [[package]] name = "clap_lex" -version = "0.7.6" +version = "1.1.0" source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "a1d728cc89cf3aee9ff92b05e62b19ee65a02b5702cff7d5a377e32c6ae29d8d" +checksum = "c8d4a3bb8b1e0c1050499d1815f5ab16d04f0959b233085fb31653fbfc9d98f9" [[package]] name = "colorchoice" -version = "1.0.4" +version = "1.0.5" source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "b05b61dc5112cbb17e4b6cd61790d9845d13888356391624cbe7e41efeac1e75" +checksum = "1d07550c9036bf2ae0c684c4297d503f838287c83c53686d05370d0e139ae570" [[package]] name = "cpufeatures" @@ -272,9 +275,9 @@ checksum = "d0a5c400df2834b80a4c3327b3aad3a4c4cd4de0629063962b03235697506a28" [[package]] name = "crypto-common" -version = "0.1.6" +version = "0.1.7" source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "1bfb12502f3fc46cca1bb51ac28df9d618d813cdc3d2f25b9fe775a34af26bb3" +checksum = "78c8292055d1c1df0cce5d180393dc8cce0abec0a7102adb6c7b1eef6016d60a" dependencies = [ "generic-array", "typenum", @@ -333,7 +336,7 @@ checksum = "97369cbbc041bc366949bc74d34658d6cda5621039731c6310521892a3a20ae0" dependencies = [ "proc-macro2", "quote", - "syn 2.0.107", + "syn 2.0.117", ] [[package]] @@ -360,7 +363,7 @@ checksum = "d0881ea181b1df73ff77ffaaf9c7544ecc11e82fba9b5f27b262a3c73a332555" [[package]] name = "egglog" version = "2.0.0" -source = "git+https://github.com/saulshanabrook/egg-smol.git?branch=fix-container-fn-bug#114692b1812cafa18b118755c2c327f067169f4d" +source = "git+https://github.com/egraphs-good/egglog.git?rev=b5c211b9def133cad9540a11744e8a1e40bd2a29#b5c211b9def133cad9540a11744e8a1e40bd2a29" dependencies = [ "csv", "dyn-clone", @@ -371,7 +374,7 @@ dependencies = [ "egglog-numeric-id", "egglog-reports", "egraph-serialize", - "hashbrown 0.16.0", + "hashbrown 0.16.1", "im-rc", "indexmap", "log", @@ -387,16 +390,16 @@ dependencies = [ [[package]] name = "egglog-add-primitive" version = "2.0.0" -source = "git+https://github.com/saulshanabrook/egg-smol.git?branch=fix-container-fn-bug#114692b1812cafa18b118755c2c327f067169f4d" +source = "git+https://github.com/egraphs-good/egglog.git?rev=b5c211b9def133cad9540a11744e8a1e40bd2a29#b5c211b9def133cad9540a11744e8a1e40bd2a29" dependencies = [ "quote", - "syn 2.0.107", + "syn 2.0.117", ] [[package]] name = "egglog-ast" version = "2.0.0" -source = "git+https://github.com/saulshanabrook/egg-smol.git?branch=fix-container-fn-bug#114692b1812cafa18b118755c2c327f067169f4d" +source = "git+https://github.com/egraphs-good/egglog.git?rev=b5c211b9def133cad9540a11744e8a1e40bd2a29#b5c211b9def133cad9540a11744e8a1e40bd2a29" dependencies = [ "ordered-float", ] @@ -404,7 +407,7 @@ dependencies = [ [[package]] name = "egglog-bridge" version = "2.0.0" -source = "git+https://github.com/saulshanabrook/egg-smol.git?branch=fix-container-fn-bug#114692b1812cafa18b118755c2c327f067169f4d" +source = "git+https://github.com/egraphs-good/egglog.git?rev=b5c211b9def133cad9540a11744e8a1e40bd2a29#b5c211b9def133cad9540a11744e8a1e40bd2a29" dependencies = [ "anyhow", "dyn-clone", @@ -412,7 +415,7 @@ dependencies = [ "egglog-numeric-id", "egglog-reports", "egglog-union-find", - "hashbrown 0.16.0", + "hashbrown 0.16.1", "indexmap", "log", "num-rational", @@ -428,7 +431,7 @@ dependencies = [ [[package]] name = "egglog-concurrency" version = "2.0.0" -source = "git+https://github.com/saulshanabrook/egg-smol.git?branch=fix-container-fn-bug#114692b1812cafa18b118755c2c327f067169f4d" +source = "git+https://github.com/egraphs-good/egglog.git?rev=b5c211b9def133cad9540a11744e8a1e40bd2a29#b5c211b9def133cad9540a11744e8a1e40bd2a29" dependencies = [ "arc-swap", "egglog-numeric-id", @@ -439,7 +442,7 @@ dependencies = [ [[package]] name = "egglog-core-relations" version = "2.0.0" -source = "git+https://github.com/saulshanabrook/egg-smol.git?branch=fix-container-fn-bug#114692b1812cafa18b118755c2c327f067169f4d" +source = "git+https://github.com/egraphs-good/egglog.git?rev=b5c211b9def133cad9540a11744e8a1e40bd2a29#b5c211b9def133cad9540a11744e8a1e40bd2a29" dependencies = [ "anyhow", "bumpalo", @@ -452,7 +455,7 @@ dependencies = [ "egglog-reports", "egglog-union-find", "fixedbitset", - "hashbrown 0.16.0", + "hashbrown 0.16.1", "indexmap", "log", "num", @@ -469,7 +472,7 @@ dependencies = [ [[package]] name = "egglog-experimental" version = "0.1.0" -source = "git+https://github.com/egraphs-good/egglog-experimental?branch=main#eae9570d78105c53497fccdf0ff7fb1937592036" +source = "git+https://github.com/egraphs-good/egglog-experimental.git?rev=3f38efab7307b765bdb912b81e99736f27e00b1f#3f38efab7307b765bdb912b81e99736f27e00b1f" dependencies = [ "egglog", "egglog-ast", @@ -482,7 +485,7 @@ dependencies = [ [[package]] name = "egglog-numeric-id" version = "2.0.0" -source = "git+https://github.com/saulshanabrook/egg-smol.git?branch=fix-container-fn-bug#114692b1812cafa18b118755c2c327f067169f4d" +source = "git+https://github.com/egraphs-good/egglog.git?rev=b5c211b9def133cad9540a11744e8a1e40bd2a29#b5c211b9def133cad9540a11744e8a1e40bd2a29" dependencies = [ "rayon", ] @@ -490,10 +493,10 @@ dependencies = [ [[package]] name = "egglog-reports" version = "2.0.0" -source = "git+https://github.com/saulshanabrook/egg-smol.git?branch=fix-container-fn-bug#114692b1812cafa18b118755c2c327f067169f4d" +source = "git+https://github.com/egraphs-good/egglog.git?rev=b5c211b9def133cad9540a11744e8a1e40bd2a29#b5c211b9def133cad9540a11744e8a1e40bd2a29" dependencies = [ "clap", - "hashbrown 0.16.0", + "hashbrown 0.16.1", "indexmap", "rustc-hash", "serde", @@ -504,7 +507,7 @@ dependencies = [ [[package]] name = "egglog-union-find" version = "2.0.0" -source = "git+https://github.com/saulshanabrook/egg-smol.git?branch=fix-container-fn-bug#114692b1812cafa18b118755c2c327f067169f4d" +source = "git+https://github.com/egraphs-good/egglog.git?rev=b5c211b9def133cad9540a11744e8a1e40bd2a29#b5c211b9def133cad9540a11744e8a1e40bd2a29" dependencies = [ "crossbeam", "egglog-concurrency", @@ -576,14 +579,14 @@ source = "registry+https://github.com/rust-lang/crates.io-index" checksum = "39cab71617ae0d63f51a36d69f866391735b51691dbda63cf6f96d042b63efeb" dependencies = [ "libc", - "windows-sys 0.61.2", + "windows-sys", ] [[package]] name = "fastrand" -version = "2.3.0" +version = "2.4.0" source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "37909eebbb50d72f9059c3b6d82c0463f2ff062c9e95845c43a6c9c0355411be" +checksum = "a043dc74da1e37d6afe657061213aa6f425f855399a11d3463c6ecccc4dfda1f" [[package]] name = "fixedbitset" @@ -653,7 +656,7 @@ checksum = "e835b70203e41293343137df5c0664546da5745f82ec9b84d40be8336958447b" dependencies = [ "proc-macro2", "quote", - "syn 2.0.107", + "syn 2.0.117", ] [[package]] @@ -686,9 +689,9 @@ dependencies = [ [[package]] name = "generic-array" -version = "0.14.9" +version = "0.14.7" source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "4bb6743198531e02858aeaea5398fcc883e71851fcbcb5a2f773e2fb6cb1edf2" +checksum = "85649ca51fd72272d7821adaf274ad91c288277713d9c18820d8499a7ff69e9a" dependencies = [ "typenum", "version_check", @@ -713,10 +716,23 @@ checksum = "899def5c37c4fd7b2664648c28120ecec138e4d395b459e5ca34f9cce2dd77fd" dependencies = [ "cfg-if", "libc", - "r-efi", + "r-efi 5.3.0", "wasip2", ] +[[package]] +name = "getrandom" +version = "0.4.2" +source = "registry+https://github.com/rust-lang/crates.io-index" +checksum = "0de51e6874e94e7bf76d726fc5d13ba782deca734ff60d5bb2fb2607c7406555" +dependencies = [ + "cfg-if", + "libc", + "r-efi 6.0.0", + "wasip2", + "wasip3", +] + [[package]] name = "glob" version = "0.3.3" @@ -725,9 +741,9 @@ checksum = "0cc23270f6e1808e30a928bdc84dea0b9b4136a8bc82338574f23baf47bbd280" [[package]] name = "graphviz-rust" -version = "0.9.6" +version = "0.9.7" source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "db134cb611668917cabf340af9a39518426f9a10827b4cedcb4cdcf84443f6d0" +checksum = "7e3f0630e2e2d6bef34313acf63330e2ce87144f5dfef276abeeef9345dd5bf3" dependencies = [ "dot-generator", "dot-structures", @@ -756,14 +772,15 @@ dependencies = [ [[package]] name = "hashbrown" -version = "0.16.0" +version = "0.16.1" source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "5419bdc4f6a9207fbeba6d11b604d481addf78ecd10c11ad51e76c2f6482748d" +checksum = "841d1cc9bed7f9236f321df977030373f4a4163ae1a7dbfe1a51a2c1a51d9100" dependencies = [ "allocator-api2", "equivalent", "foldhash 0.2.0", "serde", + "serde_core", ] [[package]] @@ -813,9 +830,9 @@ checksum = "6dbf3de79e51f3d586ab4cb9d5c3e2c14aa28ed23d180cf89b4df0454a69cc87" [[package]] name = "hyper" -version = "1.8.1" +version = "1.9.0" source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "2ab2d4f250c3d7b1c9fcdff1cece94ea4e2dfbec68614f7b87cb205f24ca9d11" +checksum = "6299f016b246a94207e63da54dbe807655bf9e00044f73ded42c3ac5305fbcca" dependencies = [ "atomic-waker", "bytes", @@ -826,7 +843,6 @@ dependencies = [ "httparse", "itoa", "pin-project-lite", - "pin-utils", "smallvec", "tokio", "want", @@ -857,12 +873,13 @@ dependencies = [ [[package]] name = "icu_collections" -version = "2.1.1" +version = "2.2.0" source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "4c6b649701667bbe825c3b7e6388cb521c23d88644678e83c0c4d0a621a34b43" +checksum = "2984d1cd16c883d7935b9e07e44071dca8d917fd52ecc02c04d5fa0b5a3f191c" dependencies = [ "displaydoc", "potential_utf", + "utf8_iter", "yoke", "zerofrom", "zerovec", @@ -870,9 +887,9 @@ dependencies = [ [[package]] name = "icu_locale_core" -version = "2.1.1" +version = "2.2.0" source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "edba7861004dd3714265b4db54a3c390e880ab658fec5f7db895fae2046b5bb6" +checksum = "92219b62b3e2b4d88ac5119f8904c10f8f61bf7e95b640d25ba3075e6cac2c29" dependencies = [ "displaydoc", "litemap", @@ -883,9 +900,9 @@ dependencies = [ [[package]] name = "icu_normalizer" -version = "2.1.1" +version = "2.2.0" source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "5f6c8828b67bf8908d82127b2054ea1b4427ff0230ee9141c54251934ab1b599" +checksum = "c56e5ee99d6e3d33bd91c5d85458b6005a22140021cc324cea84dd0e72cff3b4" dependencies = [ "icu_collections", "icu_normalizer_data", @@ -897,15 +914,15 @@ dependencies = [ [[package]] name = "icu_normalizer_data" -version = "2.1.1" +version = "2.2.0" source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "7aedcccd01fc5fe81e6b489c15b247b8b0690feb23304303a9e560f37efc560a" +checksum = "da3be0ae77ea334f4da67c12f149704f19f81d1adf7c51cf482943e84a2bad38" [[package]] name = "icu_properties" -version = "2.1.2" +version = "2.2.0" source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "020bfc02fe870ec3a66d93e677ccca0562506e5872c650f893269e08615d74ec" +checksum = "bee3b67d0ea5c2cca5003417989af8996f8604e34fb9ddf96208a033901e70de" dependencies = [ "icu_collections", "icu_locale_core", @@ -917,15 +934,15 @@ dependencies = [ [[package]] name = "icu_properties_data" -version = "2.1.2" +version = "2.2.0" source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "616c294cf8d725c6afcd8f55abc17c56464ef6211f9ed59cccffe534129c77af" +checksum = "8e2bbb201e0c04f7b4b3e14382af113e17ba4f63e2c9d2ee626b720cbce54a14" [[package]] name = "icu_provider" -version = "2.1.1" +version = "2.2.0" source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "85962cf0ce02e1e0a629cc34e7ca3e373ce20dda4c4d7294bbd0bf1fdb59e614" +checksum = "139c4cf31c8b5f33d7e199446eff9c1e02decfc2f0eec2c8d71f65befa45b421" dependencies = [ "displaydoc", "icu_locale_core", @@ -936,6 +953,12 @@ dependencies = [ "zerovec", ] +[[package]] +name = "id-arena" +version = "2.3.0" +source = "registry+https://github.com/rust-lang/crates.io-index" +checksum = "3d3067d79b975e8844ca9eb072e16b31c3c1c36928edf9c6789548c524d0d954" + [[package]] name = "idna" version = "1.1.0" @@ -973,21 +996,24 @@ dependencies = [ [[package]] name = "indexmap" -version = "2.12.0" +version = "2.13.1" source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "6717a8d2a5a929a1a2eb43a12812498ed141a0bcfb7e8f7844fbdbe4303bba9f" +checksum = "45a8a2b9cb3e0b0c1803dbb0758ffac5de2f425b23c28f518faabd9d805342ff" dependencies = [ "equivalent", - "hashbrown 0.16.0", + "hashbrown 0.16.1", "serde", "serde_core", ] [[package]] name = "indoc" -version = "2.0.6" +version = "2.0.7" source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "f4c7245a08504955605670dbf141fceab975f15ca21570696aebe9d2e71576bd" +checksum = "79cf5c93f93228cf8efb3ba362535fb11199ac548a09ce117c9b1adc3030d706" +dependencies = [ + "rustversion", +] [[package]] name = "into-attr" @@ -1019,9 +1045,9 @@ checksum = "d98f6fed1fde3f8c21bc40a1abb88dd75e67924f9cffc3ef95607bad8017f8e2" [[package]] name = "iri-string" -version = "0.7.10" +version = "0.7.12" source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "c91338f0783edbd6195decb37bae672fd3b165faffb89bf7b9e6942f8b1a731a" +checksum = "25e659a4bb38e810ebc252e53b5814ff908a8c58c2a9ce2fae1bbec24cbf4e20" dependencies = [ "memchr", "serde", @@ -1044,16 +1070,18 @@ dependencies = [ [[package]] name = "itoa" -version = "1.0.15" +version = "1.0.18" source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "4a5f13b858c8d314ee3e8f639011f7ccefe71f97f96e50151fb991f267928e2c" +checksum = "8f42a60cbdf9a97f5d2305f08a87dc4e09308d1276d28c869c684d7777685682" [[package]] name = "js-sys" -version = "0.3.81" +version = "0.3.94" source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "ec48937a97411dcb524a265206ccd4c90bb711fca92b2792c407f268825b9305" +checksum = "2e04e2ef80ce82e13552136fabeef8a5ed1f985a96805761cbb9a2c34e7664d9" dependencies = [ + "cfg-if", + "futures-util", "once_cell", "wasm-bindgen", ] @@ -1074,23 +1102,29 @@ version = "1.5.0" source = "registry+https://github.com/rust-lang/crates.io-index" checksum = "bbd2bcb4c963f2ddae06a2efc7e9f3591312473c50c6685e1f298068316e66fe" +[[package]] +name = "leb128fmt" +version = "0.1.0" +source = "registry+https://github.com/rust-lang/crates.io-index" +checksum = "09edd9e8b54e49e587e4f6295a7d29c3ea94d469cb40ab8ca70b288248a81db2" + [[package]] name = "libc" -version = "0.2.177" +version = "0.2.184" source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "2874a2af47a2325c2001a6e6fad9b16a53b802102b528163885171cf92b15976" +checksum = "48f5d2a454e16a5ea0f4ced81bd44e4cfc7bd3a507b61887c99fd3538b28e4af" [[package]] name = "linux-raw-sys" -version = "0.11.0" +version = "0.12.1" source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "df1d3c3b53da64cf5760482273a98e575c651a67eec7f77df96b5b642de8f039" +checksum = "32a66949e030da00e8c7d4434b251670a91556f4144941d37452769c25d58a53" [[package]] name = "litemap" -version = "0.8.1" +version = "0.8.2" source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "6373607a59f0be73a39b6fe456b8192fcc3585f602af20751600e974dd455e77" +checksum = "92daf443525c4cce67b150400bc2316076100ce0b3686209eb8cf3c31612e6f0" [[package]] name = "lock_api" @@ -1103,15 +1137,15 @@ dependencies = [ [[package]] name = "log" -version = "0.4.28" +version = "0.4.29" source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "34080505efa8e45a4b816c349525ebe327ceaa8559756f0356cba97ef3bf7432" +checksum = "5e5032e24019045c762d3c0f28f5b6b8bbf38563a65908389bf7978758920897" [[package]] name = "memchr" -version = "2.7.6" +version = "2.8.0" source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "f52b00d39961fc5b2736ea853c9cc86238e165017a493d1d5c8eac6bdc4cc273" +checksum = "f8ca58f447f06ed17d5fc4043ce1b10dd205e060fb3ce5b979b8ed8e59ff3f79" [[package]] name = "memoffset" @@ -1124,13 +1158,13 @@ dependencies = [ [[package]] name = "mio" -version = "1.1.0" +version = "1.2.0" source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "69d83b0086dc8ecf3ce9ae2874b2d1290252e2a30720bea58a5c6639b0092873" +checksum = "50b7e5b27aa02a74bac8c3f23f448f8d87ff11f92d3aac1a6ed369ee08cc56c1" dependencies = [ "libc", "wasi", - "windows-sys 0.61.2", + "windows-sys", ] [[package]] @@ -1139,7 +1173,7 @@ version = "0.50.3" source = "registry+https://github.com/rust-lang/crates.io-index" checksum = "7957b9740744892f114936ab4a57b3f487491bbeafaf8083688b16841a4240e5" dependencies = [ - "windows-sys 0.61.2", + "windows-sys", ] [[package]] @@ -1217,9 +1251,9 @@ dependencies = [ [[package]] name = "once_cell" -version = "1.21.3" +version = "1.21.4" source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "42f5e15c9953c5e4ccceeb2e7382a716482c34515315f7b03532b8b4e8393d2d" +checksum = "9f7c3e4beb33f85d45ae3e3a1792185706c8e16d043238c593331cc7cd313b50" [[package]] name = "once_cell_polyfill" @@ -1322,9 +1356,9 @@ dependencies = [ [[package]] name = "ordered-float" -version = "5.1.0" +version = "5.3.0" source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "7f4779c6901a562440c3786d08192c6fbda7c1c2060edd10006b05ee35d10f2d" +checksum = "b7d950ca161dc355eaf28f82b11345ed76c6e1f6eb1f4f4479e0323b9e2fbd0e" dependencies = [ "num-traits", "rand 0.8.5", @@ -1352,9 +1386,9 @@ checksum = "9b4f627cb1b25917193a259e49bdad08f671f8d9708acfd5fe0a8c1455d87220" [[package]] name = "pest" -version = "2.8.3" +version = "2.8.6" source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "989e7521a040efde50c3ab6bbadafbe15ab6dc042686926be59ac35d74607df4" +checksum = "e0848c601009d37dfa3430c4666e147e49cdcf1b92ecd3e63657d8a5f19da662" dependencies = [ "memchr", "ucd-trie", @@ -1362,9 +1396,9 @@ dependencies = [ [[package]] name = "pest_derive" -version = "2.8.3" +version = "2.8.6" source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "187da9a3030dbafabbbfb20cb323b976dc7b7ce91fcd84f2f74d6e31d378e2de" +checksum = "11f486f1ea21e6c10ed15d5a7c77165d0ee443402f0780849d1768e7d9d6fe77" dependencies = [ "pest", "pest_generator", @@ -1372,22 +1406,22 @@ dependencies = [ [[package]] name = "pest_generator" -version = "2.8.3" +version = "2.8.6" source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "49b401d98f5757ebe97a26085998d6c0eecec4995cad6ab7fc30ffdf4b052843" +checksum = "8040c4647b13b210a963c1ed407c1ff4fdfa01c31d6d2a098218702e6664f94f" dependencies = [ "pest", "pest_meta", "proc-macro2", "quote", - "syn 2.0.107", + "syn 2.0.117", ] [[package]] name = "pest_meta" -version = "2.8.3" +version = "2.8.6" source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "72f27a2cfee9f9039c4d86faa5af122a0ac3851441a34865b8a043b46be0065a" +checksum = "89815c69d36021a140146f26659a81d6c2afa33d216d736dd4be5381a7362220" dependencies = [ "pest", "sha2", @@ -1422,7 +1456,7 @@ checksum = "d9b20ed30f105399776b9c883e68e536ef602a16ae6f596d2c473591d6ad64c6" dependencies = [ "proc-macro2", "quote", - "syn 2.0.107", + "syn 2.0.117", ] [[package]] @@ -1431,23 +1465,17 @@ version = "0.2.17" source = "registry+https://github.com/rust-lang/crates.io-index" checksum = "a89322df9ebe1c1578d689c92318e070967d1042b512afbe49518723f4e6d5cd" -[[package]] -name = "pin-utils" -version = "0.1.0" -source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "8b870d8c151b6f2fb93e84a13146138f05d02ed11c7e7c54f8826aaaf7c9f184" - [[package]] name = "portable-atomic" -version = "1.11.1" +version = "1.13.1" source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "f84267b20a16ea918e43c6a88433c2d54fa145c92a811b5b047ccbe153674483" +checksum = "c33a9471896f1c69cecef8d20cbe2f7accd12527ce60845ff44c153bb2a21b49" [[package]] name = "potential_utf" -version = "0.1.4" +version = "0.1.5" source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "b73949432f5e2a09657003c25bca5e19a0e9c84f8058ca374f49e0ebe605af77" +checksum = "0103b1cef7ec0cf76490e969665504990193874ea05c85ff9bab8b911d0a0564" dependencies = [ "zerovec", ] @@ -1461,11 +1489,21 @@ dependencies = [ "zerocopy", ] +[[package]] +name = "prettyplease" +version = "0.2.37" +source = "registry+https://github.com/rust-lang/crates.io-index" +checksum = "479ca8adacdd7ce8f1fb39ce9ecccbfe93a3f1344b3d0d97f20bc0196208f62b" +dependencies = [ + "proc-macro2", + "syn 2.0.117", +] + [[package]] name = "proc-macro2" -version = "1.0.101" +version = "1.0.106" source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "89ae43fd86e4158d6db51ad8e2b80f313af9cc74f5c0e03ccb87de09998732de" +checksum = "8fd00f0bb2e90d81d1044c2b32617f68fcb9fa3bb7640c23e9c748e53fb30934" dependencies = [ "unicode-ident", ] @@ -1490,14 +1528,14 @@ dependencies = [ "itertools", "proc-macro2", "quote", - "syn 2.0.107", + "syn 2.0.117", ] [[package]] name = "pyo3" -version = "0.27.1" +version = "0.27.2" source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "37a6df7eab65fc7bee654a421404947e10a0f7085b6951bf2ea395f4659fb0cf" +checksum = "ab53c047fcd1a1d2a8820fe84f05d6be69e9526be40cb03b73f86b6b03e6d87d" dependencies = [ "indexmap", "indoc", @@ -1516,18 +1554,18 @@ dependencies = [ [[package]] name = "pyo3-build-config" -version = "0.27.1" +version = "0.27.2" source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "f77d387774f6f6eec64a004eac0ed525aab7fa1966d94b42f743797b3e395afb" +checksum = "b455933107de8642b4487ed26d912c2d899dec6114884214a0b3bb3be9261ea6" dependencies = [ "target-lexicon", ] [[package]] name = "pyo3-ffi" -version = "0.27.1" +version = "0.27.2" source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "2dd13844a4242793e02df3e2ec093f540d948299a6a77ea9ce7afd8623f542be" +checksum = "1c85c9cbfaddf651b1221594209aed57e9e5cff63c4d11d1feead529b872a089" dependencies = [ "libc", "pyo3-build-config", @@ -1535,9 +1573,9 @@ dependencies = [ [[package]] name = "pyo3-log" -version = "0.13.2" +version = "0.13.3" source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "2f8bae9ad5ba08b0b0ed2bb9c2bdbaeccc69cafca96d78cf0fbcea0d45d122bb" +checksum = "26c2ec80932c5c3b2d4fbc578c9b56b2d4502098587edb8bef5b6bfcad43682e" dependencies = [ "arc-swap", "log", @@ -1546,34 +1584,34 @@ dependencies = [ [[package]] name = "pyo3-macros" -version = "0.27.1" +version = "0.27.2" source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "eaf8f9f1108270b90d3676b8679586385430e5c0bb78bb5f043f95499c821a71" +checksum = "0a5b10c9bf9888125d917fb4d2ca2d25c8df94c7ab5a52e13313a07e050a3b02" dependencies = [ "proc-macro2", "pyo3-macros-backend", "quote", - "syn 2.0.107", + "syn 2.0.117", ] [[package]] name = "pyo3-macros-backend" -version = "0.27.1" +version = "0.27.2" source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "70a3b2274450ba5288bc9b8c1b69ff569d1d61189d4bff38f8d22e03d17f932b" +checksum = "03b51720d314836e53327f5871d4c0cfb4fb37cc2c4a11cc71907a86342c40f9" dependencies = [ "heck", "proc-macro2", "pyo3-build-config", "quote", - "syn 2.0.107", + "syn 2.0.117", ] [[package]] name = "quote" -version = "1.0.41" +version = "1.0.45" source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "ce25767e7b499d1b604768e7cde645d14cc8584231ea6b295e9c9eb22c02e1d1" +checksum = "41f2619966050689382d2b44f664f4bc593e129785a36d6ee376ddf37259b924" dependencies = [ "proc-macro2", ] @@ -1584,6 +1622,12 @@ version = "5.3.0" source = "registry+https://github.com/rust-lang/crates.io-index" checksum = "69cdb34c158ceb288df11e18b4bd39de994f6657d83847bdffdbd7f346754b0f" +[[package]] +name = "r-efi" +version = "6.0.0" +source = "registry+https://github.com/rust-lang/crates.io-index" +checksum = "f8dcc9c7d52a811697d2151c701e0d08956f92b0e24136cf4cf27b57a6a0d9bf" + [[package]] name = "rand" version = "0.8.5" @@ -1603,7 +1647,7 @@ source = "registry+https://github.com/rust-lang/crates.io-index" checksum = "6db2770f06117d490610c7488547d543617b21bfa07796d7a12f6f1bd53850d1" dependencies = [ "rand_chacha 0.9.0", - "rand_core 0.9.3", + "rand_core 0.9.5", ] [[package]] @@ -1623,7 +1667,7 @@ source = "registry+https://github.com/rust-lang/crates.io-index" checksum = "d3022b5f1df60f26e1ffddd6c66e8aa15de382ae63b3a0c1bfc0e4d3e3f325cb" dependencies = [ "ppv-lite86", - "rand_core 0.9.3", + "rand_core 0.9.5", ] [[package]] @@ -1638,9 +1682,9 @@ dependencies = [ [[package]] name = "rand_core" -version = "0.9.3" +version = "0.9.5" source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "99d9a13982dcf210057a8a78572b2217b667c3beacbf3a0d8b454f6f82837d38" +checksum = "76afc826de14238e6e8c374ddcc1fa19e374fd8dd986b0d2af0d02377261d83c" dependencies = [ "getrandom 0.3.4", ] @@ -1685,9 +1729,9 @@ dependencies = [ [[package]] name = "regex-automata" -version = "0.4.13" +version = "0.4.14" source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "5276caf25ac86c8d810222b3dbb938e512c55c6831a10f3e6ed1c93b84041f1c" +checksum = "6e1dd4122fc1595e8162618945476892eefca7b88c52820e74af6262213cae8f" dependencies = [ "aho-corasick", "memchr", @@ -1696,9 +1740,9 @@ dependencies = [ [[package]] name = "regex-syntax" -version = "0.8.8" +version = "0.8.10" source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "7a2d987857b319362043e95f5353c0535c1f58eec5336fdfcf626430af7def58" +checksum = "dc897dd8d9e8bd1ed8cdad82b5966c3e0ecae09fb1907d58efaa013543185d0a" [[package]] name = "reqwest" @@ -1736,21 +1780,21 @@ dependencies = [ [[package]] name = "rustc-hash" -version = "2.1.1" +version = "2.1.2" source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "357703d41365b4b27c590e3ed91eabb1b663f07c4c084095e60cbed4362dff0d" +checksum = "94300abf3f1ae2e2b8ffb7b58043de3d399c73fa6f4b73826402a5c457614dbe" [[package]] name = "rustix" -version = "1.1.3" +version = "1.1.4" source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "146c9e247ccc180c1f61615433868c99f3de3ae256a30a43b49f67c2d9171f34" +checksum = "b6fe4565b9518b83ef4f91bb47ce29620ca828bd32cb7e408f0062e9930ba190" dependencies = [ "bitflags", "errno", "libc", "linux-raw-sys", - "windows-sys 0.61.2", + "windows-sys", ] [[package]] @@ -1761,9 +1805,9 @@ checksum = "b39cdef0fa800fc44525c84ccb54a029961a8215f9619753635a9c0d2538d46d" [[package]] name = "ryu" -version = "1.0.20" +version = "1.0.23" source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "28d3b2b1366ec20994f1fd18c3c594f05c5dd4bc44d8bb0c1c632c8d6829481f" +checksum = "9774ba4a74de5f7b1c1451ed6cd5285a32eddb5cccb8cc655a4e50009e06477f" [[package]] name = "scopeguard" @@ -1771,6 +1815,12 @@ version = "1.2.0" source = "registry+https://github.com/rust-lang/crates.io-index" checksum = "94143f37725109f92c262ed2cf5e59bce7498c01bcc1502d7b9afe439a4e9f49" +[[package]] +name = "semver" +version = "1.0.28" +source = "registry+https://github.com/rust-lang/crates.io-index" +checksum = "8a7852d02fc848982e0c167ef163aaff9cd91dc640ba85e263cb1ce46fae51cd" + [[package]] name = "serde" version = "1.0.228" @@ -1798,21 +1848,21 @@ checksum = "d540f220d3187173da220f885ab66608367b6574e925011a9353e4badda91d79" dependencies = [ "proc-macro2", "quote", - "syn 2.0.107", + "syn 2.0.117", ] [[package]] name = "serde_json" -version = "1.0.145" +version = "1.0.149" source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "402a6f66d8c709116cf22f558eab210f5a50187f702eb4d7e5ef38d9a7f1c79c" +checksum = "83fc039473c5595ace860d8c4fafa220ff474b3fc6bfdb4293327f1a37e94d86" dependencies = [ "indexmap", "itoa", "memchr", - "ryu", "serde", "serde_core", + "zmij", ] [[package]] @@ -1876,7 +1926,7 @@ source = "registry+https://github.com/rust-lang/crates.io-index" checksum = "3a766e1110788c36f4fa1c2b71b387a7815aa65f88ce0229841826633d93723e" dependencies = [ "libc", - "windows-sys 0.61.2", + "windows-sys", ] [[package]] @@ -1904,9 +1954,9 @@ dependencies = [ [[package]] name = "syn" -version = "2.0.107" +version = "2.0.117" source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "2a26dbd934e5451d21ef060c018dae56fc073894c5a7896f882928a76e6d081b" +checksum = "e665b8803e7b1d2a727f4023456bbbbe74da67099c585258af0ad9c5013b9b99" dependencies = [ "proc-macro2", "quote", @@ -1930,46 +1980,46 @@ checksum = "728a70f3dbaf5bab7f0c4b1ac8d7ae5ea60a4b5549c8a5914361c99147a709d2" dependencies = [ "proc-macro2", "quote", - "syn 2.0.107", + "syn 2.0.117", ] [[package]] name = "target-lexicon" -version = "0.13.3" +version = "0.13.5" source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "df7f62577c25e07834649fc3b39fafdc597c0a3527dc1c60129201ccfcbaa50c" +checksum = "adb6935a6f5c20170eeceb1a3835a49e12e19d792f6dd344ccc76a985ca5a6ca" [[package]] name = "tempfile" -version = "3.24.0" +version = "3.27.0" source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "655da9c7eb6305c55742045d5a8d2037996d61d8de95806335c7c86ce0f82e9c" +checksum = "32497e9a4c7b38532efcdebeef879707aa9f794296a4f0244f6f69e9bc8574bd" dependencies = [ "fastrand", - "getrandom 0.3.4", + "getrandom 0.4.2", "once_cell", "rustix", - "windows-sys 0.61.2", + "windows-sys", ] [[package]] name = "thiserror" -version = "2.0.17" +version = "2.0.18" source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "f63587ca0f12b72a0600bcba1d40081f830876000bb46dd2337a3051618f4fc8" +checksum = "4288b5bcbc7920c07a1149a35cf9590a2aa808e0bc1eafaade0b80947865fbc4" dependencies = [ "thiserror-impl", ] [[package]] name = "thiserror-impl" -version = "2.0.17" +version = "2.0.18" source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "3ff15c8ecd7de3849db632e14d18d2571fa09dfc5ed93479bc4485c7a517c913" +checksum = "ebc4ee7f67670e9b64d05fa4253e753e016c6c95ff35b89b7941d6b856dec1d5" dependencies = [ "proc-macro2", "quote", - "syn 2.0.107", + "syn 2.0.117", ] [[package]] @@ -1983,9 +2033,9 @@ dependencies = [ [[package]] name = "tinystr" -version = "0.8.2" +version = "0.8.3" source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "42d3e9c45c09de15d06dd8acf5f4e0e399e85927b7f00711024eb7ae10fa4869" +checksum = "c8323304221c2a851516f22236c5722a72eaa19749016521d6dff0824447d96d" dependencies = [ "displaydoc", "zerovec", @@ -1993,15 +2043,15 @@ dependencies = [ [[package]] name = "tokio" -version = "1.50.0" +version = "1.51.0" source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "27ad5e34374e03cfffefc301becb44e9dc3c17584f414349ebe29ed26661822d" +checksum = "2bd1c4c0fc4a7ab90fc15ef6daaa3ec3b893f004f915f2392557ed23237820cd" dependencies = [ "libc", "mio", "pin-project-lite", "socket2", - "windows-sys 0.61.2", + "windows-sys", ] [[package]] @@ -2100,7 +2150,7 @@ checksum = "7490cfa5ec963746568740651ac6781f701c9c5ea257c58e057f3ba8cf69e8da" dependencies = [ "proc-macro2", "quote", - "syn 2.0.107", + "syn 2.0.117", ] [[package]] @@ -2176,9 +2226,15 @@ checksum = "2896d95c02a80c6d6a5d6e953d479f5ddf2dfdb6a244441010e373ac0fb88971" [[package]] name = "unicode-ident" -version = "1.0.19" +version = "1.0.24" source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "f63a545481291138910575129486daeaf8ac54aee4387fe7906919f7830c7d9d" +checksum = "e6e4313cd5fcd3dad5cafa179702e2b244f760991f45397d14d4ebf38247da75" + +[[package]] +name = "unicode-xid" +version = "0.2.6" +source = "registry+https://github.com/rust-lang/crates.io-index" +checksum = "ebc1c04c71510c7f702b52b7c350734c9ff1295c464a03335b00bb84fc54f853" [[package]] name = "unindent" @@ -2212,11 +2268,11 @@ checksum = "06abde3611657adf66d383f00b093d7faecc7fa57071cce2578660c9f1010821" [[package]] name = "uuid" -version = "1.18.1" +version = "1.23.0" source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "2f87b8aa10b915a06587d0dec516c282ff295b475d94abf425d62b57710070a2" +checksum = "5ac8b6f42ead25368cf5b098aeb3dc8a1a2c05a3eee8a9a1a68c640edbfc79d9" dependencies = [ - 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"syn 2.0.107", + "syn 2.0.117", "synstructure", ] [[package]] name = "zerocopy" -version = "0.8.27" +version = "0.8.48" source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "0894878a5fa3edfd6da3f88c4805f4c8558e2b996227a3d864f47fe11e38282c" +checksum = "eed437bf9d6692032087e337407a86f04cd8d6a16a37199ed57949d415bd68e9" dependencies = [ "zerocopy-derive", ] [[package]] name = "zerocopy-derive" -version = "0.8.27" +version = "0.8.48" source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "88d2b8d9c68ad2b9e4340d7832716a4d21a22a1154777ad56ea55c51a9cf3831" +checksum = "70e3cd084b1788766f53af483dd21f93881ff30d7320490ec3ef7526d203bad4" dependencies = [ "proc-macro2", "quote", - "syn 2.0.107", + "syn 2.0.117", ] [[package]] name = "zerofrom" -version = "0.1.6" +version = "0.1.7" source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "50cc42e0333e05660c3587f3bf9d0478688e15d870fab3346451ce7f8c9fbea5" +checksum = "69faa1f2a1ea75661980b013019ed6687ed0e83d069bc1114e2cc74c6c04c4df" dependencies = [ "zerofrom-derive", ] [[package]] name = "zerofrom-derive" -version = "0.1.6" +version = "0.1.7" source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "d71e5d6e06ab090c67b5e44993ec16b72dcbaabc526db883a360057678b48502" +checksum = "11532158c46691caf0f2593ea8358fed6bbf68a0315e80aae9bd41fbade684a1" dependencies = [ "proc-macro2", "quote", - "syn 2.0.107", + "syn 2.0.117", "synstructure", ] [[package]] name = "zerotrie" -version = "0.2.3" +version = "0.2.4" source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "2a59c17a5562d507e4b54960e8569ebee33bee890c70aa3fe7b97e85a9fd7851" +checksum = "0f9152d31db0792fa83f70fb2f83148effb5c1f5b8c7686c3459e361d9bc20bf" dependencies = [ "displaydoc", "yoke", @@ -2527,9 +2617,9 @@ dependencies = [ [[package]] name = "zerovec" -version = "0.11.5" +version = "0.11.6" source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "6c28719294829477f525be0186d13efa9a3c602f7ec202ca9e353d310fb9a002" +checksum = "90f911cbc359ab6af17377d242225f4d75119aec87ea711a880987b18cd7b239" dependencies = [ "yoke", "zerofrom", @@ -2538,11 +2628,17 @@ dependencies = [ [[package]] name = "zerovec-derive" -version = "0.11.2" +version = "0.11.3" source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "eadce39539ca5cb3985590102671f2567e659fca9666581ad3411d59207951f3" +checksum = "625dc425cab0dca6dc3c3319506e6593dcb08a9f387ea3b284dbd52a92c40555" dependencies = [ "proc-macro2", "quote", - "syn 2.0.107", + "syn 2.0.117", ] + +[[package]] +name = "zmij" +version = "1.0.21" +source = "registry+https://github.com/rust-lang/crates.io-index" +checksum = "b8848ee67ecc8aedbaf3e4122217aff892639231befc6a1b58d29fff4c2cabaa" diff --git a/Cargo.toml b/Cargo.toml index e3741144..e1c997b9 100644 --- a/Cargo.toml +++ b/Cargo.toml @@ -18,19 +18,14 @@ opentelemetry = "0.28" opentelemetry-otlp = { version = "0.28", features = ["http-proto", "reqwest-blocking-client", "trace"] } opentelemetry-stdout = { version = "0.28", features = ["trace"] } opentelemetry_sdk = "0.28" -# egglog = { path = "../egg-smol", default-features = false } -# egglog-bridge = { path = "../egg-smol/egglog-bridge" } -# egglog-core-relations = { path = "../egg-smol/core-relations" } -# egglog-ast = { path = "../egg-smol/egglog-ast" } -# egglog-reports = { path = "../egg-smol/egglog-reports" } -egglog = { git = "https://github.com/saulshanabrook/egg-smol.git", branch = "fix-container-fn-bug", default-features = false } -egglog-ast = { git = "https://github.com/saulshanabrook/egg-smol.git", branch = "fix-container-fn-bug" } -egglog-core-relations = { git = "https://github.com/saulshanabrook/egg-smol.git", branch = "fix-container-fn-bug" } -egglog-reports = { git = "https://github.com/saulshanabrook/egg-smol.git", branch = "fix-container-fn-bug" } -egglog-bridge = { git = "https://github.com/saulshanabrook/egg-smol.git", branch = "fix-container-fn-bug" } +egglog = { git = "https://github.com/egraphs-good/egglog.git", default-features = false, rev = "b5c211b9def133cad9540a11744e8a1e40bd2a29" } +egglog-ast = { git = "https://github.com/egraphs-good/egglog.git", rev = "b5c211b9def133cad9540a11744e8a1e40bd2a29" } +egglog-core-relations = { git = "https://github.com/egraphs-good/egglog.git", rev = "b5c211b9def133cad9540a11744e8a1e40bd2a29" } +egglog-reports = { git = "https://github.com/egraphs-good/egglog.git", rev = "b5c211b9def133cad9540a11744e8a1e40bd2a29" } +egglog-bridge = { git = "https://github.com/egraphs-good/egglog.git", rev = "b5c211b9def133cad9540a11744e8a1e40bd2a29" } -egglog-experimental = { git = "https://github.com/egraphs-good/egglog-experimental", branch = "main", default-features = false } +egglog-experimental = { git = "https://github.com/egraphs-good/egglog-experimental.git", default-features = false, rev = "3f38efab7307b765bdb912b81e99736f27e00b1f" } egraph-serialize = { version = "0.3", features = ["serde", "graphviz"] } serde_json = "1" pyo3-log = "*" @@ -44,19 +39,6 @@ uuid = { version = "1.18", features = ["v4"] } rayon = "1.11" base64 = "0.22.1" -# Use patched version of egglog in experimental -[patch.'https://github.com/egraphs-good/egglog'] -# egglog = { path = "../egg-smol" } -# egglog-core-relations = { path = "../egg-smol/core-relations" } -# egglog-ast = { path = "../egg-smol/egglog-ast" } -# egglog-reports = { path = "../egg-smol/egglog-reports" } -# egglog-bridge = { path = "../egg-smol/egglog-bridge" } - -egglog = { git = "https://github.com/saulshanabrook/egg-smol.git", branch = "fix-container-fn-bug" } -egglog-ast = { git = "https://github.com/saulshanabrook/egg-smol.git", branch = "fix-container-fn-bug" } -egglog-core-relations = { git = "https://github.com/saulshanabrook/egg-smol.git", branch = "fix-container-fn-bug" } -egglog-bridge = { git = "https://github.com/saulshanabrook/egg-smol.git", branch = "fix-container-fn-bug" } -egglog-reports = { git = "https://github.com/saulshanabrook/egg-smol.git", branch = "fix-container-fn-bug" } # enable debug symbols for easier profiling [profile.release] diff --git a/docs/explanation/2026_02_containers.ipynb b/docs/explanation/2026_02_containers.ipynb new file mode 100644 index 00000000..2fe48111 --- /dev/null +++ b/docs/explanation/2026_02_containers.ipynb @@ -0,0 +1,3127 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "7c296c51", + "metadata": {}, + "source": [ + "```{post} 2026-03-13\n", + "```\n", + "\n", + "# Custom Data Structures in E-Graphs\n", + "\n", + "*Cross-posted on the [UW PLSE blog](https://uwplse.org/2026/02/24/egglog-containers.html).*\n", + "\n", + "[E-graphs](https://en.wikipedia.org/wiki/E-graph) are a data structure used to reason about program equivalence.\n", + "Combined with specialized algorithms they can be used to build optimizers or compilers. However,\n", + "their performance can struggle as the number of equivalent expressions explodes if we include on algebraic identities, such as\n", + "associativity, commutativity, and distributivity (A/C/D).\n", + "\n", + "Alternatively we can attempt to build these identities into our underlying data structure, such as Philip Zucker's explorations of\n", + "[Gröbner basis](https://www.philipzucker.com/multiset_rw/) and [bottom up e-matching](https://www.semanticscholar.org/paper/Omelets-Need-Onions%3A-E-graphs-Modulo-Theories-via-Zucker/b07bdef17fdbb7cf927a5a844fc587335864e89a).\n", + "For example, instead of representing a sequence of additions as say a tree of binary operations, we can instead represent it as a sorted list of terms being added\n", + "or a multiset mapping terms to their counts.\n", + "However, building entirely new e-graph systems to take advantage of this is a large engineering lift and splits the ecosystem of users,\n", + "reducing the possibility for code reuse between project that use e-graphs.\n", + "\n", + "Here, I explore how supporting custom data structures and higher order functions can\n", + "be used to build efficient algebraic representations without changing the internals of an e-graph system.\n", + "\n", + "## EGraphs in Egglog\n", + "\n", + "In this post we will be using, an e-graph framework built on top of a custom database. It's written in\n", + "[Rust](https://github.com/egraphs-good/egglog) with [bindings in Python](https://github.com/egraphs-good/egglog-python),\n", + "which I will be using here.\n", + "\n", + "First we start with an example where we define a language through a set of types, uninterpreted functions, and rewrite rules\n", + "to define equivalences between expressions.\n", + "\n", + "This lets us check things like if `2 * (x + 3) == 6 + 2 * x`, given distributivity and commutativity, along with constant folding rules:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "6c9489c3", + "metadata": {}, + "outputs": [ + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "b9a4b18d0a5840869508b030bb4555b9", + "version_major": 2, + "version_minor": 1 + }, + "text/plain": [ + "VisualizerWidget(egraphs=['{\"nodes\":{\"function-0-Num___mul__\":{\"op\":\"· * ·\",\"children\":[\"function-0-Num___init…" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from __future__ import annotations\n", + "\n", + "from egglog import *\n", + "\n", + "\n", + "# 1. Create a custom type\n", + "class Num(Expr):\n", + " # 2. Define constructors for this type from an integer,\n", + " # string, binary addition or multiplication\n", + " def __init__(self, value: i64Like) -> None: ...\n", + "\n", + " @classmethod\n", + " def var(cls, name: StringLike) -> Num: ...\n", + "\n", + " def __add__(self, other: Num) -> Num: ...\n", + "\n", + " def __mul__(self, other: Num) -> Num: ...\n", + "\n", + "\n", + "# 2. Define a set of rewrite rules that add equivalences\n", + "# They work by finding an expression that matches the LHS\n", + "# modulo the variables, then adding the RHS with the variables\n", + "# substituted, and setting them as equivalent to it\n", + "@ruleset\n", + "def comm_dist_fold(a: Num, b: Num, c: Num, i: i64, j: i64):\n", + " # commutativity\n", + " yield rewrite(a + b).to(b + a)\n", + " # distributivity\n", + " yield rewrite(a * (b + c)).to((a * b) + (a * c))\n", + " # constant folding\n", + " yield rewrite(Num(i) + Num(j)).to(Num(i + j))\n", + " yield rewrite(Num(i) * Num(j)).to(Num(i * j))\n", + "\n", + "\n", + "# 3. Create an empty e-graph\n", + "egraph = EGraph()\n", + "\n", + "# 4. Add our two initial expressions\n", + "expr1 = egraph.let(\"expr1\", Num(2) * (Num.var(\"x\") + Num(3)))\n", + "expr2 = egraph.let(\"expr2\", Num(6) + Num(2) * Num.var(\"x\"))\n", + "\n", + "\n", + "# 5. Run this ruleset until it is \"saturated\"\n", + "# meaning that further application will be no-ops\n", + "# as well as output a visualization showing the progress\n", + "egraph.saturate(comm_dist_fold)\n", + "# 6. Verify that our two expressions are now equivalent\n", + "egraph.check(expr1 == expr2)" + ] + }, + { + "cell_type": "markdown", + "id": "c00731f4", + "metadata": {}, + "source": [ + "The visualization shows the final state of the e-graph and allows us to step through it using the slider at the top:\n", + "\n", + "The arrows points a function to its arguments. When two expressions are equivalent they are placed in the same cluster,\n", + "called an e-class. The top e-class has labels `expr1` and `expr2` in it, meaning they are equivalent now.\n", + "\n", + "By dragging the top slide slider to the left it will show the initial state, before any of the rules were run,\n", + "when it just contains our two initial expressions. They are start in different e-classes, since we don't they are equal\n", + "until we run our rules. As you drag the slider to the right, you will see the state of the e-graph after each rule application.\n", + "\n", + "EGraphs can also be used for program optimization. By choosing a cost model, for example based on the total number of terms,\n", + "we can try to find an expression equivalent to our initial expression and extract it out.\n", + "\n", + "This is comparable to how term rewriting system can also be used for optimization or transformation. One way to look at\n", + "egraphs is as if we have use a term rewriting system but we remember all the previous terms we have encountered, and defer\n", + "picking the \"best' one till the end.\n", + "This lets us focus less on rule application order, but it does mean that our memory will increase over time, which\n", + "is what we will get to soon.\n", + "\n", + "For a more thorough introduction, check out the [egglog tutorial](https://egglog-python.readthedocs.io/latest/tutorials/tut_1_basics.html),\n", + "and for an example of how it can be used inside of a larger system see the [Numba v2 mini book](https://numba.pydata.org/numba-prototypes/sealir_tutorials/index.html).\n", + "More examples are collected [in the awesome e-graphs repo](https://github.com/philzook58/awesome-egraphs).\n", + "EGraphs also have [an active community](https://egraphs.org/) around them that [chat online](https://egraphs.zulipchat.com/) and\n", + "[meet in person](https://egraphs.org/workshop/).\n", + "\n", + "## Size Blow Up\n", + "\n", + "While e-graphs are powerful, they can \"blow up\", increasing in size drastically even when starting with small expression.\n", + "For example if we start with `2 + a + b + b + 3` and add A/C/D rules we can see it increase in size:" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "fe82287c", + "metadata": {}, + "outputs": [ + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "396ca2cfb54b467785dea46bdfb2a8fc", + "version_major": 2, + "version_minor": 1 + }, + "text/plain": [ + "VisualizerWidget(egraphs=['{\"nodes\":{\"primitive-String-0\":{\"op\":\"\\\\\"b\\\\\"\",\"children\":[],\"eclass\":\"String-0\",\"c…" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/html": [ + "
Num(5) + (Num.var("a") + Num.var("b") + Num.var("b"))\n",
+       "
\n" + ], + "text/latex": [ + "\\begin{Verbatim}[commandchars=\\\\\\{\\}]\n", + "\\PY{n}{Num}\\PY{p}{(}\\PY{l+m+mi}{5}\\PY{p}{)} \\PY{o}{+} \\PY{p}{(}\\PY{n}{Num}\\PY{o}{.}\\PY{n}{var}\\PY{p}{(}\\PY{l+s+s2}{\\PYZdq{}}\\PY{l+s+s2}{a}\\PY{l+s+s2}{\\PYZdq{}}\\PY{p}{)} \\PY{o}{+} \\PY{n}{Num}\\PY{o}{.}\\PY{n}{var}\\PY{p}{(}\\PY{l+s+s2}{\\PYZdq{}}\\PY{l+s+s2}{b}\\PY{l+s+s2}{\\PYZdq{}}\\PY{p}{)} \\PY{o}{+} \\PY{n}{Num}\\PY{o}{.}\\PY{n}{var}\\PY{p}{(}\\PY{l+s+s2}{\\PYZdq{}}\\PY{l+s+s2}{b}\\PY{l+s+s2}{\\PYZdq{}}\\PY{p}{)}\\PY{p}{)}\n", + "\\end{Verbatim}\n" + ], + "text/plain": [ + "Num(5) + (Num.var(\"a\") + Num.var(\"b\") + Num.var(\"b\"))" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "@ruleset\n", + "def assoc(a: Num, b: Num, c: Num):\n", + " yield birewrite(a + (b + c)).to((a + b) + c)\n", + "\n", + "\n", + "egraph = EGraph()\n", + "a, b = Num.var(\"a\"), Num.var(\"b\")\n", + "new_expr = egraph.let(\"new_expr\", Num(2) + a + b + b + Num(3))\n", + "\n", + "# run both the associativity and commutativity/distributivity\n", + "# rules together\n", + "egraph.saturate(assoc | comm_dist_fold)\n", + "egraph.extract(new_expr)" + ] + }, + { + "cell_type": "markdown", + "id": "e827591e", + "metadata": {}, + "source": [ + "As the number of e-nodes increases so does the memory usage and also the runtime, limiting the ability\n", + "to use these kinds of rules on large expressions. One way to work around this\n", + "is to limit the number of times we apply certain rules or limit the size of e-graphs, with the tradeoff that this\n", + "limits the size of our search space. What if instead we could maintain\n", + "an optimization like constant folding without an increasing blow-up size due to the other rules?\n", + "\n", + "We will look at how containers can be used to achieve this, but first some background on how Egglog handles primitives.\n", + "\n", + "## Primitives and Containers in Egglog\n", + "\n", + "Along with Egglog letting you define your own types, like `Num`, it also comes with a number of builtins/primitives like `i64` and `String`.\n", + "The core comes with a number of them, but they can also be written in Rust extensions as plugins. To define a new type in Rust\n", + "you must define how to compare them with equality and how to hash them.\n", + "Primitives are treated like opaque values, Egglog doesn't reason about their inner structure. Functions can also be defined\n", + "over primitives, again either in the core or as a Rust extension. Egglog doesn't know anything about their semantics, just that\n", + "they take in primitives and return other primitives.\n", + "\n", + "If we think of primitives as opaque values, what if we want to contain a primitive inside of another one? For example,\n", + "a `Vec` type that contains a number of items. To define such a type in Rust, we need the above properties around hashing\n", + "and equality, but we also need to make sure it respects congruence. Congruence is the property where if you have\n", + "two expression `f(a)` and `f(b)` in the e-graph, and then you make `a == b`, then `f(a)` should also equal `f(b)`. We want\n", + "this same property to hold for something like a vector, so if you have `Vec(a, c)` and `Vec(b, c)` in the e-graph, and you make `a == b`,\n", + "then these two vecs should also be equal `Vec(a, c) == Vec(b, c)`.\n", + "\n", + "We do this by implementing one additional operation on containers, rebuilding. This is called whenever we want to renormalize\n", + "the e-graph to preserve congruence. We defer it so we don't do it after every union operation, to reduce the amount of work.\n", + "Since containers \"contain\" references to other e-classes, we need to update those references. That what this rebuilding\n", + "operation does, so that when its time to rebuild, the `Vec` type calls rebuilding on each of its inner values, updating them with\n", + "new names for each e-class.\n", + "So then when we check for equality after that, it will preserve congruence.\n", + "\n", + "Egglog doesn't know anything more about the structures of containers besides how to rebuild them and any primitive functions you define on them.\n", + "This both makes them relatively easy to implement and add, but also limits the ability to \"match\" over them, which will see how to work around\n", + "in the next section.\n", + "\n", + "One use case for containers is to represent operations with more structure. I the above, we have defined\n", + "addition as a binary operation with two ordered arguments. However, we may decide that for our use case,\n", + "we not only wanna make `a + b` equal to `b + a`, but in fact indistinguishable. This effectively\n", + "replaces the commutative and associativity rules with instead a representation that maintains their invariants.\n", + "One way we could do that is with a container that represents all terms being added.\n", + "This would be a [multiset aka bag](https://en.wikipedia.org/wiki/Multiset), since\n", + "we want to know how many times a term is being added, but we don't care about the order.\n", + "\n", + "We can write this in the Python bindings like so:" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "dfd73580", + "metadata": {}, + "outputs": [], + "source": [ + "@function\n", + "def sum_(xs: MultiSet[Num]) -> Num: ..." + ] + }, + { + "cell_type": "markdown", + "id": "d123b8b4", + "metadata": {}, + "source": [ + "Now if we construct `sum_(MultiSet(a, b))` this will be equal to `sum_(MultiSet(b, a))` due to the implementation of multiset b\n", + "being order insensitive:" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "29c26ebd", + "metadata": {}, + "outputs": [], + "source": [ + "egraph = EGraph()\n", + "x = Num.var(\"x\")\n", + "y = Num.var(\"y\")\n", + "z = egraph.let(\"z\", sum_(MultiSet(x, y)))\n", + "egraph.check(z == sum_(MultiSet(y, x)))" + ] + }, + { + "cell_type": "markdown", + "id": "20b239e3", + "metadata": {}, + "source": [ + "We have the rebuilding property we talked about above as well, to maintain congruence. If we now union `x` with `y`,\n", + "the sum will reflect this to become `sum_(MultiSet(x, x))`:" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "7d74f69b", + "metadata": {}, + "outputs": [], + "source": [ + "egraph.register(union(x).with_(y))\n", + "egraph.check(z == sum_(MultiSet(x, x)))" + ] + }, + { + "cell_type": "markdown", + "id": "e04e08f6", + "metadata": {}, + "source": [ + "So we can see here we can represent a whole set of equal summations only with one multiset, instead of having to add\n", + "many terms to the e-graph.\n", + "\n", + "## Matching on Containers by Index\n", + "\n", + "Given this new implementation, how would we replicate the above constant folding example on it?\n", + "\n", + "Well first we can start by creating a new e-graph and adding the expression, this time using our `sum` function with multisets,\n", + "instead of binary addition:" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "0effdcd5", + "metadata": {}, + "outputs": [], + "source": [ + "egraph = EGraph()\n", + "new_expr = egraph.let(\"new_expr\", sum_(MultiSet(Num(2), a, b, b, Num(3))))" + ] + }, + { + "cell_type": "markdown", + "id": "c38c3c2b", + "metadata": {}, + "source": [ + "One way to think about a constant folding rule would be to \"Look for a sum that contains two constant numbers,\n", + "take them both out and add their sum back in\". However, we don't have the ability to match on the contents of a multiset directly,\n", + "since as we said above Egglog doesn't know anything about its inner structure.\n", + "\n", + "One way we can work around this is to build up an \"index\" function for the contents of the multiset. This maps\n", + "a multiset and an item inside of it, to the count of times it shows up in that multiset:" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "3705f64e", + "metadata": {}, + "outputs": [], + "source": [ + "@function\n", + "def ms_num_index(xs: MultiSet[Num], x: Num) -> i64: ..." + ] + }, + { + "cell_type": "markdown", + "id": "3afa7e4a", + "metadata": {}, + "source": [ + "It is similar to in a database if you need to do a join efficiently you have to build an index.\n", + "\n", + "Then we can add two rules, one that fills in the index whenever we have a sum and then another one that matches on that\n", + "to do the constant folding:" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "7af795ee", + "metadata": {}, + "outputs": [ + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "fb105cf2b45147cb8cd19d6823b56467", + "version_major": 2, + "version_minor": 1 + }, + "text/plain": [ + "VisualizerWidget(egraphs=['{\"nodes\":{\"primitive-egglog.builtins.MultiSet[Num]-4\":{\"op\":\"MultiSet\",\"children\":[…" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/html": [ + "
sum_(MultiSet(Num.var("a"), Num.var("b"), Num.var("b"), Num(5)))\n",
+       "
\n" + ], + "text/latex": [ + "\\begin{Verbatim}[commandchars=\\\\\\{\\}]\n", + "\\PY{n}{sum\\PYZus{}}\\PY{p}{(}\\PY{n}{MultiSet}\\PY{p}{(}\\PY{n}{Num}\\PY{o}{.}\\PY{n}{var}\\PY{p}{(}\\PY{l+s+s2}{\\PYZdq{}}\\PY{l+s+s2}{a}\\PY{l+s+s2}{\\PYZdq{}}\\PY{p}{)}\\PY{p}{,} \\PY{n}{Num}\\PY{o}{.}\\PY{n}{var}\\PY{p}{(}\\PY{l+s+s2}{\\PYZdq{}}\\PY{l+s+s2}{b}\\PY{l+s+s2}{\\PYZdq{}}\\PY{p}{)}\\PY{p}{,} \\PY{n}{Num}\\PY{o}{.}\\PY{n}{var}\\PY{p}{(}\\PY{l+s+s2}{\\PYZdq{}}\\PY{l+s+s2}{b}\\PY{l+s+s2}{\\PYZdq{}}\\PY{p}{)}\\PY{p}{,} \\PY{n}{Num}\\PY{p}{(}\\PY{l+m+mi}{5}\\PY{p}{)}\\PY{p}{)}\\PY{p}{)}\n", + "\\end{Verbatim}\n" + ], + "text/plain": [ + "sum_(MultiSet(Num.var(\"a\"), Num.var(\"b\"), Num.var(\"b\"), Num(5)))" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "@ruleset\n", + "def constant_fold_index(xs: MultiSet[Num], i: i64, k: i64):\n", + " # For all sums, fill in the index function\n", + " yield rule(sum_(xs)).then(xs.fill_index(ms_num_index))\n", + "\n", + " # Try replacing any sum with the folded version\n", + " yield rewrite(sum_(xs)).to(\n", + " # Replace the two numbers with their sum, by removing\n", + " # them and then inserting their sum back in\n", + " sum_(xs.remove(Num(i)).remove(Num(k)).insert(Num(i + k))),\n", + " # These are conditions for the rewrite to match:\n", + " # Look for a multiset that contains two numbers that\n", + " # are not the same one\n", + " ms_num_index(xs, Num(i)),\n", + " ms_num_index(xs, Num(k)),\n", + " i != k,\n", + " )\n", + "\n", + "\n", + "egraph = EGraph()\n", + "new_expr = egraph.let(\"new_expr\", sum_(MultiSet(Num(2), a, b, b, Num(3))))\n", + "egraph.saturate(constant_fold_index)\n", + "egraph.extract(new_expr)" + ] + }, + { + "cell_type": "markdown", + "id": "a4b2434a", + "metadata": {}, + "source": [ + "If we run this now we can see that we get back out the folded expression, without the blow-up from before:\n", + "\n", + "However, we still add a number of nodes to the e-graph to maintain the index. While this works in this small example,\n", + "if many intermediate multisets are generated, this can lead again to a blow-up in the e-graph size.\n", + "\n", + "So what if instead there was a way to express this rule without needing to maintain this index?\n", + "\n", + "## Matching on Containers with Higher Order Functions\n", + "\n", + "We can look at the rule above as trying to pull out two numbers from a sum and fold them in together. So if there were `n`\n", + "constants, it would trigger `n * (n - 1)` times, since we can choose any two of them to fold together. What if instead\n", + "we wanted to express a rule that selects *all* constants from a multiset and folds them together?\n", + "\n", + "The index approach won't work here, because we don't have a fixed number to match on. Instead, we can use higher order functions\n", + "to express this as a block wise operation. Effectively we want to say \"Pull out all constants in the multiset, add them together,\n", + "and then add that back into the multiset with all the non-constants\".\n", + "\n", + "But first we need to add a helper function that returns an `i64` for a `Num` if its a constant:" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "48c60d46", + "metadata": {}, + "outputs": [], + "source": [ + "@function\n", + "def get_i64(x: Num) -> i64: ...\n", + "\n", + "\n", + "@ruleset\n", + "def set_get_i64(i: i64):\n", + " yield rule(Num(i)).then(set_(get_i64(Num(i))).to(i))" + ] + }, + { + "cell_type": "markdown", + "id": "a6fc0049", + "metadata": {}, + "source": [ + "Then we can define the constant folding, using higher order `fold` and `map` operations" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "c5c70656", + "metadata": {}, + "outputs": [ + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "9146792eab264e4e856f42fd92cf77a0", + "version_major": 2, + "version_minor": 1 + }, + "text/plain": [ + "VisualizerWidget(egraphs=['{\"nodes\":{\"primitive-egglog.builtins.MultiSet[Num]-4\":{\"op\":\"MultiSet\",\"children\":[…" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/html": [ + "
sum_(MultiSet(Num.var("a"), Num.var("b"), Num.var("b"), Num(5)))\n",
+       "
\n" + ], + "text/latex": [ + "\\begin{Verbatim}[commandchars=\\\\\\{\\}]\n", + "\\PY{n}{sum\\PYZus{}}\\PY{p}{(}\\PY{n}{MultiSet}\\PY{p}{(}\\PY{n}{Num}\\PY{o}{.}\\PY{n}{var}\\PY{p}{(}\\PY{l+s+s2}{\\PYZdq{}}\\PY{l+s+s2}{a}\\PY{l+s+s2}{\\PYZdq{}}\\PY{p}{)}\\PY{p}{,} \\PY{n}{Num}\\PY{o}{.}\\PY{n}{var}\\PY{p}{(}\\PY{l+s+s2}{\\PYZdq{}}\\PY{l+s+s2}{b}\\PY{l+s+s2}{\\PYZdq{}}\\PY{p}{)}\\PY{p}{,} \\PY{n}{Num}\\PY{o}{.}\\PY{n}{var}\\PY{p}{(}\\PY{l+s+s2}{\\PYZdq{}}\\PY{l+s+s2}{b}\\PY{l+s+s2}{\\PYZdq{}}\\PY{p}{)}\\PY{p}{,} \\PY{n}{Num}\\PY{p}{(}\\PY{l+m+mi}{5}\\PY{p}{)}\\PY{p}{)}\\PY{p}{)}\n", + "\\end{Verbatim}\n" + ], + "text/plain": [ + "sum_(MultiSet(Num.var(\"a\"), Num.var(\"b\"), Num.var(\"b\"), Num(5)))" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "@ruleset\n", + "def constant_fold_sum(xs: MultiSet[Num]):\n", + " # Extract out all the constants from the sum\n", + " constants = xs.map(get_i64)\n", + " # Filter for the remaining values that are not constants\n", + " remaining = xs - constants.map(UnstableFn(Num))\n", + " # Sum all the constants to fold them together\n", + " folded = multiset_fold(i64.__add__, i64(0), constants)\n", + " yield rewrite(sum_(xs)).to(\n", + " # replace it with the non constants plus the folded\n", + " sum_(remaining.insert(Num(folded))),\n", + " # Only run this rule if there are more than one\n", + " # constant to fold together\n", + " constants.length() > 1,\n", + " )\n", + "\n", + "\n", + "egraph = EGraph()\n", + "new_expr = egraph.let(\"new_expr\", sum_(MultiSet(Num(2), a, b, b, Num(3))))\n", + "egraph.saturate(set_get_i64.saturate() + constant_fold_sum.saturate())\n", + "egraph.extract(new_expr)" + ] + }, + { + "cell_type": "markdown", + "id": "7b13a611", + "metadata": {}, + "source": [ + "Running the setting ruleset first, then the folding ruleset,\n", + "we can see that we get the same result as before,but without needing to maintain the index:\n", + "\n", + "Using higher order functions on containers, we can express efficient rewrite rules\n", + "that reduce the size of the e-graph compared to using binary operations. The container themselves preserves some of the core\n", + "identities that would lead to blow up, and the higher order functions support block wise operations to process an\n", + "arbitrary number of items as once.\n", + "\n", + "For a larger example that motivated this work, see the case study in Appendix 1, where we have a large polynomial expression with many terms that\n", + "we want to factor. That case study also demonstrates how we can convert from binary operations into containers as well. In the Appendix 2,\n", + "there are a few more examples that we could apply this approach to as well.\n", + "\n", + "## Takeaways\n", + "\n", + "Experimenting with using containers in this way explores how we can add more efficient representations in e-graphs\n", + "to an existing system like Egglog, by using custom data structures.\n", + "\n", + "It's also interesting that these representations can be not only more efficient but also more directly correspond\n", + "to the semantics of the your use case, compared to say a tree of binary operations.\n", + "\n", + "This work also highlights some of the current limitations of egglog.\n", + "\n", + "One issue is that composing functions of primitives is currently very limited. The only tool we have is currying, but\n", + "it is not possible to reorder arguments or compose them in more complicated manners. This inevitably leads to\n", + "creating more bespoke functions. For example, I had to add a `multiset_contains_swapped` function that swaps the order\n", + "of the `contains` method, since I needed to partially apply it with the second argument. Further exploring this line of\n", + "work might lead to trying out different ways of enriching primitive functions, possibly by allowing a way at runtime\n", + "to create new ones by composing others, either through a DSL/JIT or a higher order composition approach like the\n", + "[compiling to categories](http://conal.net/papers/compiling-to-categories/) work.\n", + "\n", + "Implementing these higher order functional primitives on containers is also challenging, due to the lack of built-in\n", + "generic type support in Egglog. Adding them currently is fiddly and requires careful thought over how to implement\n", + "their generic types. Adding built in support for generic types, both in primitives and user code, could make this more\n", + "scalable.\n", + "\n", + "Overall, I hope that this work shows that there is a design space here in Egglog to try out different\n", + "ways of representing new normalized forms of different domains and then designing algorithms over them. As opposed to\n", + "creating a whole new e-graph implementation, adding them as custom containers to Egglog supports reuse of the existing\n", + "engineering work and compositionality within the ecosystem. I am left wondering how further improvements to Egglog\n", + "can help extend this type of experimentation of how to efficiently represent different domains inside of e-graphs.\n", + "\n", + "## Appendix 1: Case Study from a Cloth Simulation Workload\n", + "\n", + "Here we start with an expression from the paper [\"Interactive design of periodic yarn-level cloth patterns\"](https://www.semanticscholar.org/paper/Interactive-design-of-periodic-yarn-level-cloth-Leaf-Wu/6350d7feb2dfc37d434da2839eacd5e8b025edda),\n", + "which is part of a larger program that does cloth simulation. It was recommended by my advisor, [Gilbert Bernstein](http://www.gilbertbernstein.com/),\n", + "since we can use their reference implementation in Mathematica to verify that our implementation matches theirs.\n", + "\n", + "![meme from tim and eric TV show with someone miming their mind being blown, with the text \"yarn = polynomials\" imposed](./2026_02_yarn-polynomials.gif)\n", + "\n", + "*Note that all code for this case study is reproducible in [this notebook](https://github.com/egraphs-good/egglog-python/blob/270a1876b6dbea37e441c132adbfdc8c11cbb319/docs/explanation/2026_02_containers_code.ipynb).*\n", + "*It is currently based on a branch of the Python bindings and Rust source, that adds additional multiset operations.*\n", + "For this docs version, the notebook content is reproduced later in this page in a folded appendix block.\n", + "\n", + "We define define a function to produce the amount of bending for a certain point over the [Python Array API Specification](https://data-apis.org/array-api/latest/API_specification/),\n", + "so that it works on both concrete NumPy arrays and symbolic arrays. It takes in a number of 1D arrays and returns a 0D array.\n", + "The details of what each argument represents and the underlying semantics are not important to this example, but our main objective\n", + "would be for a graphics researcher to be able to prototype a function like this. Then we would want our system\n", + "to \"optimize\" it in some way, before compiling it to something like CUDA to run on a GPU:" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "12bbeb82", + "metadata": {}, + "outputs": [], + "source": [ + "def bending_function(Q, Bp, Bpp):\n", + " xp = Q.__array_namespace__()\n", + " QM = xp.reshape(Q, (4, 3)).T\n", + "\n", + " yip = xp.vecdot(QM, Bp)\n", + " yipp = xp.vecdot(QM, Bpp)\n", + " num = xp.linalg.vector_norm(xp.cross(yip, yipp))\n", + " den = xp.linalg.vector_norm(yip) ** 3\n", + " return (num / den) ** 2" + ] + }, + { + "cell_type": "markdown", + "id": "8f0b2cac", + "metadata": {}, + "source": [ + "We symbolically evaluate the result of this function by using [an implementation of the Array API written in Egglog](https://github.com/egraphs-good/egglog-python/blob/cb263b163150181d164db25fbbac6e8a1e2da719/python/egglog/exp/array_api.py):" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "d2af639b", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
_Value_1 = Value.var("q2") * Value.var("bp1") + Value.var("q5") * Value.var("bp2") + Value.var("q8") * Value.var("bp3") + Value.var("q11") * Value.var("bp4")\n",
+       "_Value_2 = Value.var("q3") * Value.var("bpp1") + Value.var("q6") * Value.var("bpp2") + Value.var("q9") * Value.var("bpp3") + Value.var("q12") * Value.var("bpp4")\n",
+       "_Value_3 = Value.var("q3") * Value.var("bp1") + Value.var("q6") * Value.var("bp2") + Value.var("q9") * Value.var("bp3") + Value.var("q12") * Value.var("bp4")\n",
+       "_Value_4 = Value.var("q2") * Value.var("bpp1") + Value.var("q5") * Value.var("bpp2") + Value.var("q8") * Value.var("bpp3") + Value.var("q11") * Value.var("bpp4")\n",
+       "_Value_5 = Value.var("q1") * Value.var("bpp1") + Value.var("q4") * Value.var("bpp2") + Value.var("q7") * Value.var("bpp3") + Value.var("q10") * Value.var("bpp4")\n",
+       "_Value_6 = Value.var("q1") * Value.var("bp1") + Value.var("q4") * Value.var("bp2") + Value.var("q7") * Value.var("bp3") + Value.var("q10") * Value.var("bp4")\n",
+       "NDArray(\n",
+       "    RecursiveValue(\n",
+       "        (\n",
+       "            (_Value_1 * _Value_2 - _Value_3 * _Value_4) ** Value.from_int(Int(2))\n",
+       "            + (_Value_3 * _Value_5 - _Value_6 * _Value_2) ** Value.from_int(Int(2))\n",
+       "            + (_Value_6 * _Value_4 - _Value_1 * _Value_5) ** Value.from_int(Int(2))\n",
+       "        )\n",
+       "        / (_Value_6 ** Value.from_int(Int(2)) + _Value_1 ** Value.from_int(Int(2)) + _Value_3 ** Value.from_int(Int(2))) ** Value.from_int(Int(3))\n",
+       "    )\n",
+       ")\n",
+       "
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Value.var(\"q5\") * Value.var(\"bp2\") + Value.var(\"q8\") * Value.var(\"bp3\") + Value.var(\"q11\") * Value.var(\"bp4\")\n", + "_Value_2 = Value.var(\"q3\") * Value.var(\"bpp1\") + Value.var(\"q6\") * Value.var(\"bpp2\") + Value.var(\"q9\") * Value.var(\"bpp3\") + Value.var(\"q12\") * Value.var(\"bpp4\")\n", + "_Value_3 = Value.var(\"q3\") * Value.var(\"bp1\") + Value.var(\"q6\") * Value.var(\"bp2\") + Value.var(\"q9\") * Value.var(\"bp3\") + Value.var(\"q12\") * Value.var(\"bp4\")\n", + "_Value_4 = Value.var(\"q2\") * Value.var(\"bpp1\") + Value.var(\"q5\") * Value.var(\"bpp2\") + Value.var(\"q8\") * Value.var(\"bpp3\") + Value.var(\"q11\") * Value.var(\"bpp4\")\n", + "_Value_5 = Value.var(\"q1\") * Value.var(\"bpp1\") + Value.var(\"q4\") * Value.var(\"bpp2\") + Value.var(\"q7\") * Value.var(\"bpp3\") + Value.var(\"q10\") * Value.var(\"bpp4\")\n", + "_Value_6 = Value.var(\"q1\") * Value.var(\"bp1\") + Value.var(\"q4\") * Value.var(\"bp2\") + Value.var(\"q7\") * Value.var(\"bp3\") + Value.var(\"q10\") * Value.var(\"bp4\")\n", + "NDArray(\n", + " RecursiveValue(\n", + " (\n", + " (_Value_1 * _Value_2 - _Value_3 * _Value_4) ** Value.from_int(Int(2))\n", + " + (_Value_3 * _Value_5 - _Value_6 * _Value_2) ** Value.from_int(Int(2))\n", + " + (_Value_6 * _Value_4 - _Value_1 * _Value_5) ** Value.from_int(Int(2))\n", + " )\n", + " / (_Value_6 ** Value.from_int(Int(2)) + _Value_1 ** Value.from_int(Int(2)) + _Value_3 ** Value.from_int(Int(2))) ** Value.from_int(Int(3))\n", + " )\n", + ")" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import egglog\n", + "import egglog.exp.array_api as enp\n", + "\n", + "Bp = enp.NDArray([enp.Value.var(f\"bp{i}\") for i in range(1, 5)])\n", + "Bpp = enp.NDArray([enp.Value.var(f\"bpp{i}\") for i in range(1, 5)])\n", + "Q = enp.NDArray([enp.Value.var(f\"q{i}\") for i in range(1, 13)])\n", + "FunctionBending = enp.NDArray(bending_function(Q, Bp, Bpp).eval())\n", + "FunctionBending" + ] + }, + { + "cell_type": "markdown", + "id": "b0f21146", + "metadata": {}, + "source": [ + "We can also compute its gradient with respect to `Q`, to give us an even larger expression." + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "id": "1d4bd92b", + "metadata": {}, + "outputs": [], + "source": [ + "GradientBending = enp.NDArray(FunctionBending.diff(Q).eval())" + ] + }, + { + "cell_type": "markdown", + "id": "abdf0163", + "metadata": {}, + "source": [ + "Calling `eval` here will create the necessary e-graph with rewrites, add the expression, and reduce it to a simplified\n", + "form that only contains a rational expression with polynomial subexpressions.\n", + "\n", + "For the sake of this example, let's first fully \"distribute\" the polynomial we have. This means expanding it into a normal\n", + "form, by applying the distribute rule, so that `a(x + y)` becomes `ax + ay`. This is meant to simulate a worst-case scenario,\n", + "since the cost increases as we distribute, duplicating terms. This suffices to give us a large enough example to stress test our system:" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "id": "dee69d9e", + "metadata": {}, + "outputs": [], + "source": [ + "@egglog.ruleset\n", + "def remove_subtraction(a: enp.Value, b: enp.Value):\n", + " yield egglog.rewrite(a - b, subsume=True).to(a + (-1) * b)\n", + "\n", + "\n", + "@egglog.ruleset\n", + "def distribute(a: enp.Value, b: enp.Value, c: enp.Value):\n", + " yield egglog.rewrite((a + b) * c, subsume=True).to(a * c + b * c)\n", + " yield egglog.rewrite(c * (a + b), subsume=True).to(c * a + c * b)" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "id": "8b56437e", + "metadata": { + "tags": [ + "hide-output" + ] + }, + "outputs": [ + { + "data": { + "text/html": [ + "
_Value_1 = Value.var("q2") * Value.var("bp1")\n",
+       "_Value_2 = Value.var("q3") * Value.var("bpp1")\n",
+       "_Value_3 = Value.var("q6") * Value.var("bpp2")\n",
+       "_Value_4 = Value.var("q9") * Value.var("bpp3")\n",
+       "_Value_5 = Value.var("q12") * Value.var("bpp4")\n",
+       "_Value_6 = Value.var("q5") * Value.var("bp2")\n",
+       "_Value_7 = Value.var("q8") * Value.var("bp3")\n",
+       "_Value_8 = Value.var("q11") * Value.var("bp4")\n",
+       "_Value_9 = Value.from_int(Int(-1))\n",
+       "_Value_10 = Value.var("q3") * Value.var("bp1")\n",
+       "_Value_11 = Value.var("q2") * Value.var("bpp1")\n",
+       "_Value_12 = Value.var("q5") * Value.var("bpp2")\n",
+       "_Value_13 = Value.var("q8") * Value.var("bpp3")\n",
+       "_Value_14 = Value.var("q11") * Value.var("bpp4")\n",
+       "_Value_15 = Value.var("q6") * Value.var("bp2")\n",
+       "_Value_16 = Value.var("q9") * Value.var("bp3")\n",
+       "_Value_17 = Value.var("q12") * Value.var("bp4")\n",
+       "_Value_18 = Value.var("q1") * Value.var("bpp1")\n",
+       "_Value_19 = Value.var("q4") * Value.var("bpp2")\n",
+       "_Value_20 = Value.var("q7") * Value.var("bpp3")\n",
+       "_Value_21 = Value.var("q10") * Value.var("bpp4")\n",
+       "_Value_22 = Value.var("q1") * Value.var("bp1")\n",
+       "_Value_23 = Value.var("q4") * Value.var("bp2")\n",
+       "_Value_24 = Value.var("q7") * Value.var("bp3")\n",
+       "_Value_25 = Value.var("q10") * Value.var("bp4")\n",
+       "NDArray(\n",
+       "    RecursiveValue(\n",
+       "        (\n",
+       "            (\n",
+       "                _Value_1 * _Value_2\n",
+       "                + _Value_1 * _Value_3\n",
+       "                + _Value_1 * _Value_4\n",
+       "                + _Value_1 * _Value_5\n",
+       "                + (_Value_6 * _Value_2 + _Value_6 * _Value_3 + _Value_6 * _Value_4 + _Value_6 * _Value_5)\n",
+       "                + (_Value_7 * _Value_2 + _Value_7 * _Value_3 + _Value_7 * _Value_4 + _Value_7 * _Value_5)\n",
+       "                + (_Value_8 * _Value_2 + _Value_8 * _Value_3 + _Value_8 * _Value_4 + _Value_8 * _Value_5)\n",
+       "                + (\n",
+       "                    _Value_9 * (_Value_10 * _Value_11)\n",
+       "                    + _Value_9 * (_Value_10 * _Value_12)\n",
+       "                    + _Value_9 * (_Value_10 * _Value_13)\n",
+       "                    + _Value_9 * (_Value_10 * _Value_14)\n",
+       "                    + (_Value_9 * (_Value_15 * _Value_11) + _Value_9 * (_Value_15 * _Value_12) + _Value_9 * (_Value_15 * _Value_13) + _Value_9 * (_Value_15 * _Value_14))\n",
+       "                    + (_Value_9 * (_Value_16 * _Value_11) + _Value_9 * (_Value_16 * _Value_12) + _Value_9 * (_Value_16 * _Value_13) + _Value_9 * (_Value_16 * _Value_14))\n",
+       "                    + (_Value_9 * (_Value_17 * _Value_11) + _Value_9 * (_Value_17 * _Value_12) + _Value_9 * (_Value_17 * _Value_13) + _Value_9 * (_Value_17 * _Value_14))\n",
+       "                )\n",
+       "            )\n",
+       "            ** Value.from_int(Int(2))\n",
+       "            + (\n",
+       "                _Value_10 * _Value_18\n",
+       "                + _Value_10 * _Value_19\n",
+       "                + _Value_10 * _Value_20\n",
+       "                + _Value_10 * _Value_21\n",
+       "                + (_Value_15 * _Value_18 + _Value_15 * _Value_19 + _Value_15 * _Value_20 + _Value_15 * _Value_21)\n",
+       "                + (_Value_16 * _Value_18 + _Value_16 * _Value_19 + _Value_16 * _Value_20 + _Value_16 * _Value_21)\n",
+       "                + (_Value_17 * _Value_18 + _Value_17 * _Value_19 + _Value_17 * _Value_20 + _Value_17 * _Value_21)\n",
+       "                + (\n",
+       "                    _Value_9 * (_Value_22 * _Value_2)\n",
+       "                    + _Value_9 * (_Value_22 * _Value_3)\n",
+       "                    + _Value_9 * (_Value_22 * _Value_4)\n",
+       "                    + _Value_9 * (_Value_22 * _Value_5)\n",
+       "                    + (_Value_9 * (_Value_23 * _Value_2) + _Value_9 * (_Value_23 * _Value_3) + _Value_9 * (_Value_23 * _Value_4) + _Value_9 * (_Value_23 * _Value_5))\n",
+       "                    + (_Value_9 * (_Value_24 * _Value_2) + _Value_9 * (_Value_24 * _Value_3) + _Value_9 * (_Value_24 * _Value_4) + _Value_9 * (_Value_24 * _Value_5))\n",
+       "                    + (_Value_9 * (_Value_25 * _Value_2) + _Value_9 * (_Value_25 * _Value_3) + _Value_9 * (_Value_25 * _Value_4) + _Value_9 * (_Value_25 * _Value_5))\n",
+       "                )\n",
+       "            )\n",
+       "            ** Value.from_int(Int(2))\n",
+       "            + (\n",
+       "                _Value_22 * _Value_11\n",
+       "                + _Value_22 * _Value_12\n",
+       "                + _Value_22 * _Value_13\n",
+       "                + _Value_22 * _Value_14\n",
+       "                + (_Value_23 * _Value_11 + _Value_23 * _Value_12 + _Value_23 * _Value_13 + _Value_23 * _Value_14)\n",
+       "                + (_Value_24 * _Value_11 + _Value_24 * _Value_12 + _Value_24 * _Value_13 + _Value_24 * _Value_14)\n",
+       "                + (_Value_25 * _Value_11 + _Value_25 * _Value_12 + _Value_25 * _Value_13 + _Value_25 * _Value_14)\n",
+       "                + (\n",
+       "                    _Value_9 * (_Value_1 * _Value_18)\n",
+       "                    + _Value_9 * (_Value_1 * _Value_19)\n",
+       "                    + _Value_9 * (_Value_1 * _Value_20)\n",
+       "                    + _Value_9 * (_Value_1 * _Value_21)\n",
+       "                    + (_Value_9 * (_Value_6 * _Value_18) + _Value_9 * (_Value_6 * _Value_19) + _Value_9 * (_Value_6 * _Value_20) + _Value_9 * (_Value_6 * _Value_21))\n",
+       "                    + (_Value_9 * (_Value_7 * _Value_18) + _Value_9 * (_Value_7 * _Value_19) + _Value_9 * (_Value_7 * _Value_20) + _Value_9 * (_Value_7 * _Value_21))\n",
+       "                    + (_Value_9 * (_Value_8 * _Value_18) + _Value_9 * (_Value_8 * _Value_19) + _Value_9 * (_Value_8 * _Value_20) + _Value_9 * (_Value_8 * _Value_21))\n",
+       "                )\n",
+       "            )\n",
+       "            ** Value.from_int(Int(2))\n",
+       "        )\n",
+       "        / (\n",
+       "            (_Value_22 + _Value_23 + _Value_24 + _Value_25) ** Value.from_int(Int(2))\n",
+       "            + (_Value_1 + _Value_6 + _Value_7 + _Value_8) ** Value.from_int(Int(2))\n",
+       "            + (_Value_10 + _Value_15 + _Value_16 + _Value_17) ** Value.from_int(Int(2))\n",
+       "        )\n",
+       "        ** Value.from_int(Int(3))\n",
+       "    )\n",
+       ")\n",
+       "
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\\PY{n}{Value}\\PY{o}{.}\\PY{n}{from\\PYZus{}int}\\PY{p}{(}\\PY{n}{Int}\\PY{p}{(}\\PY{l+m+mi}{2}\\PY{p}{)}\\PY{p}{)}\n", + " \\PY{o}{+} \\PY{p}{(}\\PY{n}{\\PYZus{}Value\\PYZus{}1} \\PY{o}{+} \\PY{n}{\\PYZus{}Value\\PYZus{}6} \\PY{o}{+} \\PY{n}{\\PYZus{}Value\\PYZus{}7} \\PY{o}{+} \\PY{n}{\\PYZus{}Value\\PYZus{}8}\\PY{p}{)} \\PY{o}{*}\\PY{o}{*} \\PY{n}{Value}\\PY{o}{.}\\PY{n}{from\\PYZus{}int}\\PY{p}{(}\\PY{n}{Int}\\PY{p}{(}\\PY{l+m+mi}{2}\\PY{p}{)}\\PY{p}{)}\n", + " \\PY{o}{+} \\PY{p}{(}\\PY{n}{\\PYZus{}Value\\PYZus{}10} \\PY{o}{+} \\PY{n}{\\PYZus{}Value\\PYZus{}15} \\PY{o}{+} \\PY{n}{\\PYZus{}Value\\PYZus{}16} \\PY{o}{+} \\PY{n}{\\PYZus{}Value\\PYZus{}17}\\PY{p}{)} \\PY{o}{*}\\PY{o}{*} \\PY{n}{Value}\\PY{o}{.}\\PY{n}{from\\PYZus{}int}\\PY{p}{(}\\PY{n}{Int}\\PY{p}{(}\\PY{l+m+mi}{2}\\PY{p}{)}\\PY{p}{)}\n", + " \\PY{p}{)}\n", + " \\PY{o}{*}\\PY{o}{*} \\PY{n}{Value}\\PY{o}{.}\\PY{n}{from\\PYZus{}int}\\PY{p}{(}\\PY{n}{Int}\\PY{p}{(}\\PY{l+m+mi}{3}\\PY{p}{)}\\PY{p}{)}\n", + " \\PY{p}{)}\n", + "\\PY{p}{)}\n", + "\\end{Verbatim}\n" + ], + "text/plain": [ + "_Value_1 = Value.var(\"q2\") * Value.var(\"bp1\")\n", + "_Value_2 = Value.var(\"q3\") * Value.var(\"bpp1\")\n", + "_Value_3 = Value.var(\"q6\") * Value.var(\"bpp2\")\n", + "_Value_4 = Value.var(\"q9\") * Value.var(\"bpp3\")\n", + "_Value_5 = Value.var(\"q12\") * Value.var(\"bpp4\")\n", + "_Value_6 = Value.var(\"q5\") * Value.var(\"bp2\")\n", + "_Value_7 = Value.var(\"q8\") * Value.var(\"bp3\")\n", + "_Value_8 = Value.var(\"q11\") * Value.var(\"bp4\")\n", + "_Value_9 = Value.from_int(Int(-1))\n", + "_Value_10 = Value.var(\"q3\") * Value.var(\"bp1\")\n", + "_Value_11 = Value.var(\"q2\") * Value.var(\"bpp1\")\n", + "_Value_12 = Value.var(\"q5\") * Value.var(\"bpp2\")\n", + "_Value_13 = Value.var(\"q8\") * Value.var(\"bpp3\")\n", + "_Value_14 = Value.var(\"q11\") * Value.var(\"bpp4\")\n", + "_Value_15 = Value.var(\"q6\") * Value.var(\"bp2\")\n", + "_Value_16 = Value.var(\"q9\") * Value.var(\"bp3\")\n", + "_Value_17 = Value.var(\"q12\") * Value.var(\"bp4\")\n", + "_Value_18 = Value.var(\"q1\") * Value.var(\"bpp1\")\n", + "_Value_19 = Value.var(\"q4\") * Value.var(\"bpp2\")\n", + "_Value_20 = Value.var(\"q7\") * Value.var(\"bpp3\")\n", + "_Value_21 = Value.var(\"q10\") * Value.var(\"bpp4\")\n", + "_Value_22 = Value.var(\"q1\") * Value.var(\"bp1\")\n", + "_Value_23 = Value.var(\"q4\") * Value.var(\"bp2\")\n", + "_Value_24 = Value.var(\"q7\") * Value.var(\"bp3\")\n", + "_Value_25 = Value.var(\"q10\") * Value.var(\"bp4\")\n", + "NDArray(\n", + " RecursiveValue(\n", + " (\n", + " (\n", + " _Value_1 * _Value_2\n", + " + _Value_1 * _Value_3\n", + " + _Value_1 * _Value_4\n", + " + _Value_1 * _Value_5\n", + " + (_Value_6 * _Value_2 + _Value_6 * _Value_3 + _Value_6 * _Value_4 + _Value_6 * _Value_5)\n", + " + (_Value_7 * _Value_2 + _Value_7 * _Value_3 + _Value_7 * _Value_4 + _Value_7 * _Value_5)\n", + " + (_Value_8 * _Value_2 + _Value_8 * _Value_3 + _Value_8 * _Value_4 + _Value_8 * _Value_5)\n", + " + (\n", + " _Value_9 * (_Value_10 * _Value_11)\n", + " + _Value_9 * (_Value_10 * _Value_12)\n", + " + _Value_9 * (_Value_10 * _Value_13)\n", + " + _Value_9 * (_Value_10 * _Value_14)\n", + " + (_Value_9 * (_Value_15 * _Value_11) + _Value_9 * (_Value_15 * _Value_12) + _Value_9 * (_Value_15 * _Value_13) + _Value_9 * (_Value_15 * _Value_14))\n", + " + (_Value_9 * (_Value_16 * _Value_11) + _Value_9 * (_Value_16 * _Value_12) + _Value_9 * (_Value_16 * _Value_13) + _Value_9 * (_Value_16 * _Value_14))\n", + " + (_Value_9 * (_Value_17 * _Value_11) + _Value_9 * (_Value_17 * _Value_12) + _Value_9 * (_Value_17 * _Value_13) + _Value_9 * (_Value_17 * _Value_14))\n", + " )\n", + " )\n", + " ** Value.from_int(Int(2))\n", + " + (\n", + " _Value_10 * _Value_18\n", + " + _Value_10 * _Value_19\n", + " + _Value_10 * _Value_20\n", + " + _Value_10 * _Value_21\n", + " + (_Value_15 * _Value_18 + _Value_15 * _Value_19 + _Value_15 * _Value_20 + _Value_15 * _Value_21)\n", + " + (_Value_16 * _Value_18 + _Value_16 * _Value_19 + _Value_16 * _Value_20 + _Value_16 * _Value_21)\n", + " + (_Value_17 * _Value_18 + _Value_17 * _Value_19 + _Value_17 * _Value_20 + _Value_17 * _Value_21)\n", + " + (\n", + " _Value_9 * (_Value_22 * _Value_2)\n", + " + _Value_9 * (_Value_22 * _Value_3)\n", + " + _Value_9 * (_Value_22 * _Value_4)\n", + " + _Value_9 * (_Value_22 * _Value_5)\n", + " + (_Value_9 * (_Value_23 * _Value_2) + _Value_9 * (_Value_23 * _Value_3) + _Value_9 * (_Value_23 * _Value_4) + _Value_9 * (_Value_23 * _Value_5))\n", + " + (_Value_9 * (_Value_24 * _Value_2) + _Value_9 * (_Value_24 * _Value_3) + _Value_9 * (_Value_24 * _Value_4) + _Value_9 * (_Value_24 * _Value_5))\n", + " + (_Value_9 * (_Value_25 * _Value_2) + _Value_9 * (_Value_25 * _Value_3) + _Value_9 * (_Value_25 * _Value_4) + _Value_9 * (_Value_25 * _Value_5))\n", + " )\n", + " )\n", + " ** Value.from_int(Int(2))\n", + " + (\n", + " _Value_22 * _Value_11\n", + " + _Value_22 * _Value_12\n", + " + _Value_22 * _Value_13\n", + " + _Value_22 * _Value_14\n", + " + (_Value_23 * _Value_11 + _Value_23 * _Value_12 + _Value_23 * _Value_13 + _Value_23 * _Value_14)\n", + " + (_Value_24 * _Value_11 + _Value_24 * _Value_12 + _Value_24 * _Value_13 + _Value_24 * _Value_14)\n", + " + (_Value_25 * _Value_11 + _Value_25 * _Value_12 + _Value_25 * _Value_13 + _Value_25 * _Value_14)\n", + " + (\n", + " _Value_9 * (_Value_1 * _Value_18)\n", + " + _Value_9 * (_Value_1 * _Value_19)\n", + " + _Value_9 * (_Value_1 * _Value_20)\n", + " + _Value_9 * (_Value_1 * _Value_21)\n", + " + (_Value_9 * (_Value_6 * _Value_18) + _Value_9 * (_Value_6 * _Value_19) + _Value_9 * (_Value_6 * _Value_20) + _Value_9 * (_Value_6 * _Value_21))\n", + " + (_Value_9 * (_Value_7 * _Value_18) + _Value_9 * (_Value_7 * _Value_19) + _Value_9 * (_Value_7 * _Value_20) + _Value_9 * (_Value_7 * _Value_21))\n", + " + (_Value_9 * (_Value_8 * _Value_18) + _Value_9 * (_Value_8 * _Value_19) + _Value_9 * (_Value_8 * _Value_20) + _Value_9 * (_Value_8 * _Value_21))\n", + " )\n", + " )\n", + " ** Value.from_int(Int(2))\n", + " )\n", + " / (\n", + " (_Value_22 + _Value_23 + _Value_24 + _Value_25) ** Value.from_int(Int(2))\n", + " + (_Value_1 + _Value_6 + _Value_7 + _Value_8) ** Value.from_int(Int(2))\n", + " + (_Value_10 + _Value_15 + _Value_16 + _Value_17) ** Value.from_int(Int(2))\n", + " )\n", + " ** Value.from_int(Int(3))\n", + " )\n", + ")" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "egraph = egglog.EGraph()\n", + "egraph.register(FunctionBending)\n", + "egraph.run(remove_subtraction.saturate() + distribute.saturate())\n", + "FunctionBending_distributed = egraph.extract(FunctionBending)\n", + "\n", + "gradient_egraph = egglog.EGraph()\n", + "gradient_egraph.register(GradientBending)\n", + "gradient_egraph.run(remove_subtraction.saturate() + distribute.saturate())\n", + "GradientBending_distributed = gradient_egraph.extract(GradientBending)\n", + "FunctionBending_distributed" + ] + }, + { + "cell_type": "markdown", + "id": "8750436e", + "metadata": {}, + "source": [ + "We now have an expression that is mainly a sum of products, a multivariate polynomial.\n", + "\n", + "For some sense of their size, the `FunctionBending` has initial cost of 401 and the `GradientBending` has 20,570.\n", + "This cost is produced by the Egglog extractor, corresponding roughly to one node per op like `*` and one per variable as a tree.\n", + "This is meant to reflect roughly the cost to compute the expression, so a lower an expression with a lower cost would run faster.\n", + "\n", + "One way to lower the cost of a polynomial is to factor it, so that `ax + ay` becomes `a(x + y)`. This is the same as applying the distributivity rule in reverse.\n", + "There are however many equivalent factorizations, and some may be better than others.\n", + "One way to use egglog to optimize this space would be to add in the associativity, commutativity, and distributivity rules and run it until saturation, and extract\n", + "out the lowest cost:" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "id": "c4b47d4d", + "metadata": { + "tags": [ + "hide-output" + ] + }, + "outputs": [ + { + "data": { + "text/html": [ + "
_Value_1 = Value.var("q3") * Value.var("bpp1") + Value.var("q6") * Value.var("bpp2") + Value.var("q9") * Value.var("bpp3") + Value.var("q12") * Value.var("bpp4")\n",
+       "_Value_2 = Value.var("q2") * Value.var("bp1") + Value.var("q5") * Value.var("bp2") + Value.var("q8") * Value.var("bp3") + Value.var("q11") * Value.var("bp4")\n",
+       "_Value_3 = Value.var("q2") * Value.var("bpp1") + Value.var("q5") * Value.var("bpp2") + Value.var("q8") * Value.var("bpp3") + Value.var("q11") * Value.var("bpp4")\n",
+       "_Value_4 = Value.var("q3") * Value.var("bp1") + Value.var("q6") * Value.var("bp2") + Value.var("q9") * Value.var("bp3") + Value.var("q12") * Value.var("bp4")\n",
+       "_Value_5 = Value.var("q1") * Value.var("bpp1") + Value.var("q4") * Value.var("bpp2") + Value.var("q7") * Value.var("bpp3") + Value.var("q10") * Value.var("bpp4")\n",
+       "_Value_6 = Value.var("q1") * Value.var("bp1") + Value.var("q4") * Value.var("bp2") + Value.var("q7") * Value.var("bp3") + Value.var("q10") * Value.var("bp4")\n",
+       "NDArray(\n",
+       "    RecursiveValue(\n",
+       "        (\n",
+       "            (_Value_1 * _Value_2 + _Value_3 * _Value_4 * Value.from_int(Int(-1))) ** Value.from_int(Int(2))\n",
+       "            + (_Value_5 * _Value_4 + _Value_1 * _Value_6 * Value.from_int(Int(-1))) ** Value.from_int(Int(2))\n",
+       "            + (_Value_3 * _Value_6 + _Value_5 * _Value_2 * Value.from_int(Int(-1))) ** Value.from_int(Int(2))\n",
+       "        )\n",
+       "        / (_Value_6 ** Value.from_int(Int(2)) + _Value_2 ** Value.from_int(Int(2)) + _Value_4 ** Value.from_int(Int(2))) ** Value.from_int(Int(3))\n",
+       "    )\n",
+       ")\n",
+       "
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\\PY{p}{(}\n", + " \\PY{p}{(}\\PY{n}{\\PYZus{}Value\\PYZus{}1} \\PY{o}{*} \\PY{n}{\\PYZus{}Value\\PYZus{}2} \\PY{o}{+} \\PY{n}{\\PYZus{}Value\\PYZus{}3} \\PY{o}{*} \\PY{n}{\\PYZus{}Value\\PYZus{}4} \\PY{o}{*} \\PY{n}{Value}\\PY{o}{.}\\PY{n}{from\\PYZus{}int}\\PY{p}{(}\\PY{n}{Int}\\PY{p}{(}\\PY{o}{\\PYZhy{}}\\PY{l+m+mi}{1}\\PY{p}{)}\\PY{p}{)}\\PY{p}{)} \\PY{o}{*}\\PY{o}{*} \\PY{n}{Value}\\PY{o}{.}\\PY{n}{from\\PYZus{}int}\\PY{p}{(}\\PY{n}{Int}\\PY{p}{(}\\PY{l+m+mi}{2}\\PY{p}{)}\\PY{p}{)}\n", + " \\PY{o}{+} \\PY{p}{(}\\PY{n}{\\PYZus{}Value\\PYZus{}5} \\PY{o}{*} \\PY{n}{\\PYZus{}Value\\PYZus{}4} \\PY{o}{+} \\PY{n}{\\PYZus{}Value\\PYZus{}1} \\PY{o}{*} \\PY{n}{\\PYZus{}Value\\PYZus{}6} \\PY{o}{*} \\PY{n}{Value}\\PY{o}{.}\\PY{n}{from\\PYZus{}int}\\PY{p}{(}\\PY{n}{Int}\\PY{p}{(}\\PY{o}{\\PYZhy{}}\\PY{l+m+mi}{1}\\PY{p}{)}\\PY{p}{)}\\PY{p}{)} \\PY{o}{*}\\PY{o}{*} \\PY{n}{Value}\\PY{o}{.}\\PY{n}{from\\PYZus{}int}\\PY{p}{(}\\PY{n}{Int}\\PY{p}{(}\\PY{l+m+mi}{2}\\PY{p}{)}\\PY{p}{)}\n", + " \\PY{o}{+} \\PY{p}{(}\\PY{n}{\\PYZus{}Value\\PYZus{}3} \\PY{o}{*} \\PY{n}{\\PYZus{}Value\\PYZus{}6} \\PY{o}{+} \\PY{n}{\\PYZus{}Value\\PYZus{}5} \\PY{o}{*} \\PY{n}{\\PYZus{}Value\\PYZus{}2} \\PY{o}{*} \\PY{n}{Value}\\PY{o}{.}\\PY{n}{from\\PYZus{}int}\\PY{p}{(}\\PY{n}{Int}\\PY{p}{(}\\PY{o}{\\PYZhy{}}\\PY{l+m+mi}{1}\\PY{p}{)}\\PY{p}{)}\\PY{p}{)} \\PY{o}{*}\\PY{o}{*} \\PY{n}{Value}\\PY{o}{.}\\PY{n}{from\\PYZus{}int}\\PY{p}{(}\\PY{n}{Int}\\PY{p}{(}\\PY{l+m+mi}{2}\\PY{p}{)}\\PY{p}{)}\n", + " \\PY{p}{)}\n", + " \\PY{o}{/} \\PY{p}{(}\\PY{n}{\\PYZus{}Value\\PYZus{}6} \\PY{o}{*}\\PY{o}{*} \\PY{n}{Value}\\PY{o}{.}\\PY{n}{from\\PYZus{}int}\\PY{p}{(}\\PY{n}{Int}\\PY{p}{(}\\PY{l+m+mi}{2}\\PY{p}{)}\\PY{p}{)} \\PY{o}{+} \\PY{n}{\\PYZus{}Value\\PYZus{}2} \\PY{o}{*}\\PY{o}{*} \\PY{n}{Value}\\PY{o}{.}\\PY{n}{from\\PYZus{}int}\\PY{p}{(}\\PY{n}{Int}\\PY{p}{(}\\PY{l+m+mi}{2}\\PY{p}{)}\\PY{p}{)} \\PY{o}{+} \\PY{n}{\\PYZus{}Value\\PYZus{}4} \\PY{o}{*}\\PY{o}{*} \\PY{n}{Value}\\PY{o}{.}\\PY{n}{from\\PYZus{}int}\\PY{p}{(}\\PY{n}{Int}\\PY{p}{(}\\PY{l+m+mi}{2}\\PY{p}{)}\\PY{p}{)}\\PY{p}{)} \\PY{o}{*}\\PY{o}{*} \\PY{n}{Value}\\PY{o}{.}\\PY{n}{from\\PYZus{}int}\\PY{p}{(}\\PY{n}{Int}\\PY{p}{(}\\PY{l+m+mi}{3}\\PY{p}{)}\\PY{p}{)}\n", + " \\PY{p}{)}\n", + "\\PY{p}{)}\n", + "\\end{Verbatim}\n" + ], + "text/plain": [ + "_Value_1 = Value.var(\"q3\") * Value.var(\"bpp1\") + Value.var(\"q6\") * Value.var(\"bpp2\") + Value.var(\"q9\") * Value.var(\"bpp3\") + Value.var(\"q12\") * Value.var(\"bpp4\")\n", + "_Value_2 = Value.var(\"q2\") * Value.var(\"bp1\") + Value.var(\"q5\") * Value.var(\"bp2\") + Value.var(\"q8\") * Value.var(\"bp3\") + Value.var(\"q11\") * Value.var(\"bp4\")\n", + "_Value_3 = Value.var(\"q2\") * Value.var(\"bpp1\") + Value.var(\"q5\") * Value.var(\"bpp2\") + Value.var(\"q8\") * Value.var(\"bpp3\") + Value.var(\"q11\") * Value.var(\"bpp4\")\n", + "_Value_4 = Value.var(\"q3\") * Value.var(\"bp1\") + Value.var(\"q6\") * Value.var(\"bp2\") + Value.var(\"q9\") * Value.var(\"bp3\") + Value.var(\"q12\") * Value.var(\"bp4\")\n", + "_Value_5 = Value.var(\"q1\") * Value.var(\"bpp1\") + Value.var(\"q4\") * Value.var(\"bpp2\") + Value.var(\"q7\") * Value.var(\"bpp3\") + Value.var(\"q10\") * Value.var(\"bpp4\")\n", + "_Value_6 = Value.var(\"q1\") * Value.var(\"bp1\") + Value.var(\"q4\") * Value.var(\"bp2\") + Value.var(\"q7\") * Value.var(\"bp3\") + Value.var(\"q10\") * Value.var(\"bp4\")\n", + "NDArray(\n", + " RecursiveValue(\n", + " (\n", + " (_Value_1 * _Value_2 + _Value_3 * _Value_4 * Value.from_int(Int(-1))) ** Value.from_int(Int(2))\n", + " + (_Value_5 * _Value_4 + _Value_1 * _Value_6 * Value.from_int(Int(-1))) ** Value.from_int(Int(2))\n", + " + (_Value_3 * _Value_6 + _Value_5 * _Value_2 * Value.from_int(Int(-1))) ** Value.from_int(Int(2))\n", + " )\n", + " / (_Value_6 ** Value.from_int(Int(2)) + _Value_2 ** Value.from_int(Int(2)) + _Value_4 ** Value.from_int(Int(2))) ** Value.from_int(Int(3))\n", + " )\n", + ")" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "@egglog.ruleset\n", + "def factoring(a: enp.Value, b: enp.Value, c: enp.Value):\n", + " yield egglog.birewrite((a + b) * c).to(a * c + b * c)\n", + " yield egglog.rewrite(a * b).to(b * a)\n", + " yield egglog.rewrite(a + b).to(b + a)\n", + " yield egglog.birewrite(a * (b * c)).to((a * b) * c)\n", + "\n", + "\n", + "egraph.run(factoring.saturate())\n", + "egraph.extract(FunctionBending_distributed)" + ] + }, + { + "cell_type": "markdown", + "id": "63a9b173", + "metadata": {}, + "source": [ + "For the `FunctionBending` example, this works fine, taking about a tenth of a second to saturate and then extract out the smallest one.\n", + "\n", + "However, if we use the `GradientBending`, each iteration will take longer and longer. Cutting it off after 10 second per iteration,\n", + "we get through only three of them and the e-graph is not saturated. It will have decreased the cost to 2,126,268 from the original of\n", + "4,250,786. However, it will also have increased the number of nodes in the e-graph from 588,125 originally to\n", + "2,583,064. This blow is due to the evaluation of associativity and commutativity rules.\n", + "\n", + "The gradient is also only the first derivative of the function bending. In the real workload from the paper,\n", + "we also need to compute the second derivative and ideally consider it as part of a larger expression.\n", + "So at least if we fully distribute first, trying to naively explore the entire search space of factorization through\n", + "associativity, commutativity, and distributivity rules is not really feasible for this type of expression.\n", + "\n", + "### Representing Polynomials with Multisets\n", + "\n", + "Taking a step back, the main space we want to explore here is the different options for factoring the expression. We\n", + "don't really care about which expression to pick due to associativity or commutativity since the cost will be the same (at this\n", + "point we are not considering common sub expression elimination and constant folding doesn't apply in this example).\n", + "We add those rules so that we can explore the space of factorizations through the distributivity rule.\n", + "\n", + "So what if instead we choose to represent a polynomial such that the form is agnostic to ordering or association?\n", + "To represent just a product of values, we need a single multiset, storing the exponent of each term as the count of the number times\n", + "that expression shows up in the product. For example, the expression `a * b * b` would be represented as the multiset `{a: 1, b: 2}`.\n", + "To represent a sum of products (aka a polynomial), we need a multiset of multisets, where each inner multiset is a monomial, and the outer multiset is the sum of these monomials, with the counts holding the multiple of each.\n", + "For example, the expression `2 * a * b + 3 * a**2` would be represented as the multiset of multisets `{ {a: 1, b: 1}: 2, {a: 2}: 3}`.\n", + "\n", + "We can add a new function to construct values from this represent:\n", + "\n", + "```python\n", + "@function\n", + "def polynomial(x: MultiSet[MultiSet[Value]]) -> Value: ...\n", + "```\n", + "\n", + "Our first task then is to translate between our binary operations and this multiset form.\n", + "The first couple of rules are relatively straightforward, just converting addition, multiplication, and exponentiation to the\n", + "corresponding forms, along with saving some analysis on terms that we will use later. This is a one way translation, so\n", + "we can also delete the source terms once we match them, so extraction doesn't match them. We create a ruleset to do this translation:\n", + "\n", + "```python\n", + "@function(merge=lambda old, new: new)\n", + "def get_monomial(x: Value) -> MultiSet[Value]:\n", + " \"\"\"\n", + " Will be defined on all polynomials with exactly one monomial created in `to_polynomial_ruleset`:\n", + "\n", + " get_monomial(polynomial(MultiSet(xs))) => xs\n", + " \"\"\"\n", + "\n", + "\n", + "@function(merge=lambda old, new: new)\n", + "def get_sole_polynomial(xs: MultiSet[Value]) -> MultiSet[MultiSet[Value]]:\n", + " \"\"\"\n", + " Will be defined on all monomials that contain a single polynomial created in `to_polynomial_ruleset`:\n", + "\n", + " get_sole_polynomial(MultiSet(polynomial(xss))) => xss\n", + " \"\"\"\n", + "\n", + "@ruleset\n", + "def to_polynomial_ruleset(\n", + " n1: Value,\n", + " n2: Value,\n", + " n3: Value,\n", + " i: i64,\n", + " ms: MultiSet[Value],\n", + " mss: MultiSet[MultiSet[Value]],\n", + " mss1: MultiSet[MultiSet[Value]],\n", + "):\n", + " yield rule(\n", + " eq(n3).to(n1 + n2),\n", + " eq(mss).to(MultiSet(MultiSet(n1), MultiSet(n2))),\n", + " name=\"add\",\n", + " ).then(\n", + " union(n3).with_(polynomial(mss)),\n", + " set_(get_sole_polynomial(MultiSet(polynomial(mss)))).to(mss),\n", + " delete(n1 + n2),\n", + " )\n", + " yield rule(\n", + " eq(n3).to(n1 * n2),\n", + " eq(ms).to(MultiSet(n1, n2)),\n", + " name=\"mul\",\n", + " ).then(\n", + " union(n3).with_(polynomial(MultiSet(ms))),\n", + " set_(get_monomial(polynomial(MultiSet(ms)))).to(ms),\n", + " delete(n1 * n2),\n", + " )\n", + " yield rule(\n", + " eq(n3).to(n1**i),\n", + " i >= 0,\n", + " eq(ms).to(MultiSet.single(n1, i)),\n", + " name=\"pow\",\n", + " ).then(\n", + " union(n3).with_(polynomial(MultiSet(ms))),\n", + " set_(get_monomial(polynomial(MultiSet(ms)))).to(ms),\n", + " delete(n1**i),\n", + " )\n", + "```\n", + "\n", + "When applying this ruleset we will replace binary operations with multiset values, but they will be unnecessarily\n", + "nested. For example, we might end up with a term like `polynomial(MultiSet(MultiSet(polynomial(xs))))`, which should be replaced\n", + "with just `polynomial(xs)`. We define two additional rules to cover cases like this:\n", + "\n", + "```python\n", + " yield rule(\n", + " eq(n1).to(polynomial(mss)),\n", + " # For each monomial, if any of its terms is a polynomial with a single monomial, flatten\n", + " # that into the monomial, otherwise keep it as is\n", + " mss1 == mss.map(partial(multiset_flat_map, get_monomial)),\n", + " mss != mss1, # skip if this is a no-op\n", + " name=\"unwrap monomial\",\n", + " ).then(\n", + " union(n1).with_(polynomial(mss1)),\n", + " delete(polynomial(mss)),\n", + " set_(get_sole_polynomial(MultiSet(polynomial(mss1)))).to(mss1),\n", + " )\n", + " yield rule(\n", + " eq(n1).to(polynomial(mss)),\n", + " # If any of the monomials just has a single item which is a polynomial, then flatten that into the outer polynomial\n", + " mss1 == multiset_flat_map(UnstableFn(get_sole_polynomial), mss),\n", + " mss != mss1,\n", + " name=\"unwrap polynomial\",\n", + " ).then(\n", + " union(n1).with_(polynomial(mss1)),\n", + " delete(polynomial(mss)),\n", + " set_(get_sole_polynomial(MultiSet(polynomial(mss1)))).to(mss1),\n", + " )\n", + "```\n", + "\n", + "We have avoided the need to match inside of containers by instead using higher order functions to apply blockwise\n", + "operations that are executed in Rust during rule matching. We had to create the above analysis for the same reason,\n", + "we cannot create functions whose implementation is deferred until a later rewrite, they must be available at match time.\n", + "\n", + "After running these rulesets any subexpressions that contain only additions and multiplications will be turned into\n", + "flattened multisets, which is what we wanted to do in this section.\n", + "What's nice here is also if there are any other operations defined like `/`, this will work transparently\n", + "with them, making this type of analysis extensible as the system grows, since we only normalize polynomial subtrees. The\n", + "contents of their terms don't have to be limited to integers and variables:" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "id": "994d6edf", + "metadata": { + "tags": [ + "remove-input" + ] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "2144\n" + ] + }, + { + "data": { + "text/html": [ + "
_Value_1 = Value.var("bp1")\n",
+       "_Value_2 = Value.var("bpp1")\n",
+       "_Value_3 = Value.var("bpp2")\n",
+       "_Value_4 = Value.var("bpp3")\n",
+       "_Value_5 = Value.var("bpp4")\n",
+       "_Value_6 = Value.var("bp2")\n",
+       "_Value_7 = Value.var("bp3")\n",
+       "_Value_8 = Value.var("bp4")\n",
+       "_Value_9 = Value.from_int(Int(-1))\n",
+       "_Value_10 = polynomial(\n",
+       "    MultiSet(\n",
+       "        MultiSet(Value.var("q3"), _Value_1, Value.var("q2"), _Value_2),\n",
+       "        MultiSet(_Value_3, _Value_1, Value.var("q6"), Value.var("q2")),\n",
+       "        MultiSet(_Value_1, Value.var("q2"), _Value_4, Value.var("q9")),\n",
+       "        MultiSet(_Value_1, Value.var("q2"), Value.var("q12"), _Value_5),\n",
+       "        MultiSet(Value.var("q5"), Value.var("q3"), _Value_2, _Value_6),\n",
+       "        MultiSet(Value.var("q5"), _Value_3, Value.var("q6"), _Value_6),\n",
+       "        MultiSet(Value.var("q5"), _Value_6, _Value_4, Value.var("q9")),\n",
+       "        MultiSet(Value.var("q5"), _Value_6, Value.var("q12"), _Value_5),\n",
+       "        MultiSet(Value.var("q3"), _Value_2, _Value_7, Value.var("q8")),\n",
+       "        MultiSet(_Value_3, Value.var("q6"), _Value_7, Value.var("q8")),\n",
+       "        MultiSet(_Value_7, Value.var("q8"), _Value_4, Value.var("q9")),\n",
+       "        MultiSet(_Value_7, Value.var("q8"), Value.var("q12"), _Value_5),\n",
+       "        MultiSet(Value.var("q3"), _Value_2, _Value_8, Value.var("q11")),\n",
+       "        MultiSet(_Value_3, Value.var("q6"), _Value_8, Value.var("q11")),\n",
+       "        MultiSet(_Value_4, Value.var("q9"), _Value_8, Value.var("q11")),\n",
+       "        MultiSet(Value.var("q12"), _Value_5, _Value_8, Value.var("q11")),\n",
+       "        MultiSet(Value.var("q3"), _Value_1, _Value_9, Value.var("q2"), _Value_2),\n",
+       "        MultiSet(Value.var("q5"), _Value_3, Value.var("q3"), _Value_1, _Value_9),\n",
+       "        MultiSet(Value.var("q3"), _Value_1, _Value_9, Value.var("q8"), _Value_4),\n",
+       "        MultiSet(Value.var("q3"), _Value_1, _Value_9, _Value_5, Value.var("q11")),\n",
+       "        MultiSet(_Value_9, Value.var("q6"), Value.var("q2"), _Value_2, _Value_6),\n",
+       "        MultiSet(Value.var("q5"), _Value_3, _Value_9, Value.var("q6"), _Value_6),\n",
+       "        MultiSet(_Value_9, Value.var("q6"), _Value_6, Value.var("q8"), _Value_4),\n",
+       "        MultiSet(_Value_9, Value.var("q6"), _Value_6, _Value_5, Value.var("q11")),\n",
+       "        MultiSet(_Value_9, Value.var("q2"), _Value_2, _Value_7, Value.var("q9")),\n",
+       "        MultiSet(Value.var("q5"), _Value_3, _Value_9, _Value_7, Value.var("q9")),\n",
+       "        MultiSet(_Value_9, _Value_7, Value.var("q8"), _Value_4, Value.var("q9")),\n",
+       "        MultiSet(_Value_9, _Value_7, Value.var("q9"), _Value_5, Value.var("q11")),\n",
+       "        MultiSet(_Value_9, Value.var("q2"), _Value_2, Value.var("q12"), _Value_8),\n",
+       "        MultiSet(Value.var("q5"), _Value_3, _Value_9, Value.var("q12"), _Value_8),\n",
+       "        MultiSet(_Value_9, Value.var("q8"), _Value_4, Value.var("q12"), _Value_8),\n",
+       "        MultiSet(_Value_9, Value.var("q12"), _Value_5, _Value_8, Value.var("q11")),\n",
+       "    )\n",
+       ")\n",
+       "_Value_11 = polynomial(\n",
+       "    MultiSet(\n",
+       "        MultiSet(Value.var("q3"), _Value_1, _Value_2, Value.var("q1")),\n",
+       "        MultiSet(_Value_3, Value.var("q3"), _Value_1, Value.var("q4")),\n",
+       "        MultiSet(Value.var("q3"), _Value_1, Value.var("q7"), _Value_4),\n",
+       "        MultiSet(Value.var("q3"), _Value_1, _Value_5, Value.var("q10")),\n",
+       "        MultiSet(Value.var("q6"), _Value_2, Value.var("q1"), _Value_6),\n",
+       "        MultiSet(_Value_3, Value.var("q6"), Value.var("q4"), _Value_6),\n",
+       "        MultiSet(Value.var("q6"), Value.var("q7"), _Value_6, _Value_4),\n",
+       "        MultiSet(Value.var("q6"), _Value_6, _Value_5, Value.var("q10")),\n",
+       "        MultiSet(_Value_2, Value.var("q1"), _Value_7, Value.var("q9")),\n",
+       "        MultiSet(_Value_3, _Value_7, Value.var("q4"), Value.var("q9")),\n",
+       "        MultiSet(Value.var("q7"), _Value_7, _Value_4, Value.var("q9")),\n",
+       "        MultiSet(_Value_7, Value.var("q9"), _Value_5, Value.var("q10")),\n",
+       "        MultiSet(_Value_2, Value.var("q1"), Value.var("q12"), _Value_8),\n",
+       "        MultiSet(_Value_3, Value.var("q4"), Value.var("q12"), _Value_8),\n",
+       "        MultiSet(Value.var("q7"), _Value_4, Value.var("q12"), _Value_8),\n",
+       "        MultiSet(Value.var("q12"), _Value_5, Value.var("q10"), _Value_8),\n",
+       "        MultiSet(Value.var("q3"), _Value_1, _Value_9, _Value_2, Value.var("q1")),\n",
+       "        MultiSet(_Value_3, _Value_1, _Value_9, Value.var("q6"), Value.var("q1")),\n",
+       "        MultiSet(_Value_1, _Value_9, Value.var("q1"), _Value_4, Value.var("q9")),\n",
+       "        MultiSet(_Value_1, _Value_9, Value.var("q1"), Value.var("q12"), _Value_5),\n",
+       "        MultiSet(Value.var("q3"), _Value_9, _Value_2, Value.var("q4"), _Value_6),\n",
+       "        MultiSet(_Value_3, _Value_9, Value.var("q6"), Value.var("q4"), _Value_6),\n",
+       "        MultiSet(_Value_9, Value.var("q4"), _Value_6, _Value_4, Value.var("q9")),\n",
+       "        MultiSet(_Value_9, Value.var("q4"), _Value_6, Value.var("q12"), _Value_5),\n",
+       "        MultiSet(Value.var("q3"), _Value_9, _Value_2, Value.var("q7"), _Value_7),\n",
+       "        MultiSet(_Value_3, _Value_9, Value.var("q6"), Value.var("q7"), _Value_7),\n",
+       "        MultiSet(_Value_9, Value.var("q7"), _Value_7, _Value_4, Value.var("q9")),\n",
+       "        MultiSet(_Value_9, Value.var("q7"), _Value_7, Value.var("q12"), _Value_5),\n",
+       "        MultiSet(Value.var("q3"), _Value_9, _Value_2, Value.var("q10"), _Value_8),\n",
+       "        MultiSet(_Value_3, _Value_9, Value.var("q6"), Value.var("q10"), _Value_8),\n",
+       "        MultiSet(_Value_9, _Value_4, Value.var("q9"), Value.var("q10"), _Value_8),\n",
+       "        MultiSet(_Value_9, Value.var("q12"), _Value_5, Value.var("q10"), _Value_8),\n",
+       "    )\n",
+       ")\n",
+       "_Value_12 = polynomial(\n",
+       "    MultiSet(\n",
+       "        MultiSet(_Value_1, Value.var("q2"), _Value_2, Value.var("q1")),\n",
+       "        MultiSet(Value.var("q5"), _Value_3, _Value_1, Value.var("q1")),\n",
+       "        MultiSet(_Value_1, Value.var("q1"), Value.var("q8"), _Value_4),\n",
+       "        MultiSet(_Value_1, Value.var("q1"), _Value_5, Value.var("q11")),\n",
+       "        MultiSet(Value.var("q2"), _Value_2, Value.var("q4"), _Value_6),\n",
+       "        MultiSet(Value.var("q5"), _Value_3, Value.var("q4"), _Value_6),\n",
+       "        MultiSet(Value.var("q4"), _Value_6, Value.var("q8"), _Value_4),\n",
+       "        MultiSet(Value.var("q4"), _Value_6, _Value_5, Value.var("q11")),\n",
+       "        MultiSet(Value.var("q2"), _Value_2, Value.var("q7"), _Value_7),\n",
+       "        MultiSet(Value.var("q5"), _Value_3, Value.var("q7"), _Value_7),\n",
+       "        MultiSet(Value.var("q7"), _Value_7, Value.var("q8"), _Value_4),\n",
+       "        MultiSet(Value.var("q7"), _Value_7, _Value_5, Value.var("q11")),\n",
+       "        MultiSet(Value.var("q2"), _Value_2, Value.var("q10"), _Value_8),\n",
+       "        MultiSet(Value.var("q5"), _Value_3, Value.var("q10"), _Value_8),\n",
+       "        MultiSet(Value.var("q8"), _Value_4, Value.var("q10"), _Value_8),\n",
+       "        MultiSet(_Value_5, Value.var("q10"), _Value_8, Value.var("q11")),\n",
+       "        MultiSet(_Value_1, _Value_9, Value.var("q2"), _Value_2, Value.var("q1")),\n",
+       "        MultiSet(_Value_3, _Value_1, _Value_9, Value.var("q2"), Value.var("q4")),\n",
+       "        MultiSet(_Value_1, _Value_9, Value.var("q2"), Value.var("q7"), _Value_4),\n",
+       "        MultiSet(_Value_1, _Value_9, Value.var("q2"), _Value_5, Value.var("q10")),\n",
+       "        MultiSet(Value.var("q5"), _Value_9, _Value_2, Value.var("q1"), _Value_6),\n",
+       "        MultiSet(Value.var("q5"), _Value_3, _Value_9, Value.var("q4"), _Value_6),\n",
+       "        MultiSet(Value.var("q5"), _Value_9, Value.var("q7"), _Value_6, _Value_4),\n",
+       "        MultiSet(Value.var("q5"), _Value_9, _Value_6, _Value_5, Value.var("q10")),\n",
+       "        MultiSet(_Value_9, _Value_2, Value.var("q1"), _Value_7, Value.var("q8")),\n",
+       "        MultiSet(_Value_3, _Value_9, _Value_7, Value.var("q4"), Value.var("q8")),\n",
+       "        MultiSet(_Value_9, Value.var("q7"), _Value_7, Value.var("q8"), _Value_4),\n",
+       "        MultiSet(_Value_9, _Value_7, Value.var("q8"), _Value_5, Value.var("q10")),\n",
+       "        MultiSet(_Value_9, _Value_2, Value.var("q1"), _Value_8, Value.var("q11")),\n",
+       "        MultiSet(_Value_3, _Value_9, Value.var("q4"), _Value_8, Value.var("q11")),\n",
+       "        MultiSet(_Value_9, Value.var("q7"), _Value_4, _Value_8, Value.var("q11")),\n",
+       "        MultiSet(_Value_9, _Value_5, Value.var("q10"), _Value_8, Value.var("q11")),\n",
+       "    )\n",
+       ")\n",
+       "_Value_13 = polynomial(\n",
+       "    MultiSet(MultiSet(Value.var("q7"), _Value_7), MultiSet(Value.var("q4"), _Value_6), MultiSet(_Value_1, Value.var("q1")), MultiSet(Value.var("q10"), _Value_8))\n",
+       ")\n",
+       "_Value_14 = polynomial(\n",
+       "    MultiSet(MultiSet(_Value_1, Value.var("q2")), MultiSet(Value.var("q5"), _Value_6), MultiSet(_Value_8, Value.var("q11")), MultiSet(_Value_7, Value.var("q8")))\n",
+       ")\n",
+       "_Value_15 = polynomial(\n",
+       "    MultiSet(MultiSet(Value.var("q3"), _Value_1), MultiSet(Value.var("q6"), _Value_6), MultiSet(Value.var("q12"), _Value_8), MultiSet(_Value_7, Value.var("q9")))\n",
+       ")\n",
+       "_Value_16 = polynomial(MultiSet(MultiSet(_Value_13, _Value_13), MultiSet(_Value_14, _Value_14), MultiSet(_Value_15, _Value_15)))\n",
+       "NDArray(\n",
+       "    RecursiveValue(\n",
+       "        polynomial(MultiSet(MultiSet(_Value_10, _Value_10), MultiSet(_Value_11, _Value_11), MultiSet(_Value_12, _Value_12)))\n",
+       "        / polynomial(MultiSet(MultiSet(_Value_16, _Value_16, _Value_16)))\n",
+       "    )\n",
+       ")\n",
+       "
\n" + ], + "text/latex": [ + "\\begin{Verbatim}[commandchars=\\\\\\{\\}]\n", + "\\PY{n}{\\PYZus{}Value\\PYZus{}1} \\PY{o}{=} \\PY{n}{Value}\\PY{o}{.}\\PY{n}{var}\\PY{p}{(}\\PY{l+s+s2}{\\PYZdq{}}\\PY{l+s+s2}{bp1}\\PY{l+s+s2}{\\PYZdq{}}\\PY{p}{)}\n", + "\\PY{n}{\\PYZus{}Value\\PYZus{}2} \\PY{o}{=} \\PY{n}{Value}\\PY{o}{.}\\PY{n}{var}\\PY{p}{(}\\PY{l+s+s2}{\\PYZdq{}}\\PY{l+s+s2}{bpp1}\\PY{l+s+s2}{\\PYZdq{}}\\PY{p}{)}\n", + "\\PY{n}{\\PYZus{}Value\\PYZus{}3} \\PY{o}{=} \\PY{n}{Value}\\PY{o}{.}\\PY{n}{var}\\PY{p}{(}\\PY{l+s+s2}{\\PYZdq{}}\\PY{l+s+s2}{bpp2}\\PY{l+s+s2}{\\PYZdq{}}\\PY{p}{)}\n", + "\\PY{n}{\\PYZus{}Value\\PYZus{}4} \\PY{o}{=} \\PY{n}{Value}\\PY{o}{.}\\PY{n}{var}\\PY{p}{(}\\PY{l+s+s2}{\\PYZdq{}}\\PY{l+s+s2}{bpp3}\\PY{l+s+s2}{\\PYZdq{}}\\PY{p}{)}\n", + "\\PY{n}{\\PYZus{}Value\\PYZus{}5} \\PY{o}{=} \\PY{n}{Value}\\PY{o}{.}\\PY{n}{var}\\PY{p}{(}\\PY{l+s+s2}{\\PYZdq{}}\\PY{l+s+s2}{bpp4}\\PY{l+s+s2}{\\PYZdq{}}\\PY{p}{)}\n", + "\\PY{n}{\\PYZus{}Value\\PYZus{}6} \\PY{o}{=} 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\\PY{n}{MultiSet}\\PY{p}{(}\\PY{n}{\\PYZus{}Value\\PYZus{}7}\\PY{p}{,} \\PY{n}{Value}\\PY{o}{.}\\PY{n}{var}\\PY{p}{(}\\PY{l+s+s2}{\\PYZdq{}}\\PY{l+s+s2}{q9}\\PY{l+s+s2}{\\PYZdq{}}\\PY{p}{)}\\PY{p}{)}\\PY{p}{)}\n", + "\\PY{p}{)}\n", + "\\PY{n}{\\PYZus{}Value\\PYZus{}16} \\PY{o}{=} \\PY{n}{polynomial}\\PY{p}{(}\\PY{n}{MultiSet}\\PY{p}{(}\\PY{n}{MultiSet}\\PY{p}{(}\\PY{n}{\\PYZus{}Value\\PYZus{}13}\\PY{p}{,} \\PY{n}{\\PYZus{}Value\\PYZus{}13}\\PY{p}{)}\\PY{p}{,} \\PY{n}{MultiSet}\\PY{p}{(}\\PY{n}{\\PYZus{}Value\\PYZus{}14}\\PY{p}{,} \\PY{n}{\\PYZus{}Value\\PYZus{}14}\\PY{p}{)}\\PY{p}{,} \\PY{n}{MultiSet}\\PY{p}{(}\\PY{n}{\\PYZus{}Value\\PYZus{}15}\\PY{p}{,} \\PY{n}{\\PYZus{}Value\\PYZus{}15}\\PY{p}{)}\\PY{p}{)}\\PY{p}{)}\n", + "\\PY{n}{NDArray}\\PY{p}{(}\n", + " \\PY{n}{RecursiveValue}\\PY{p}{(}\n", + " \\PY{n}{polynomial}\\PY{p}{(}\\PY{n}{MultiSet}\\PY{p}{(}\\PY{n}{MultiSet}\\PY{p}{(}\\PY{n}{\\PYZus{}Value\\PYZus{}10}\\PY{p}{,} \\PY{n}{\\PYZus{}Value\\PYZus{}10}\\PY{p}{)}\\PY{p}{,} \\PY{n}{MultiSet}\\PY{p}{(}\\PY{n}{\\PYZus{}Value\\PYZus{}11}\\PY{p}{,} \\PY{n}{\\PYZus{}Value\\PYZus{}11}\\PY{p}{)}\\PY{p}{,} \\PY{n}{MultiSet}\\PY{p}{(}\\PY{n}{\\PYZus{}Value\\PYZus{}12}\\PY{p}{,} \\PY{n}{\\PYZus{}Value\\PYZus{}12}\\PY{p}{)}\\PY{p}{)}\\PY{p}{)}\n", + " \\PY{o}{/} \\PY{n}{polynomial}\\PY{p}{(}\\PY{n}{MultiSet}\\PY{p}{(}\\PY{n}{MultiSet}\\PY{p}{(}\\PY{n}{\\PYZus{}Value\\PYZus{}16}\\PY{p}{,} \\PY{n}{\\PYZus{}Value\\PYZus{}16}\\PY{p}{,} \\PY{n}{\\PYZus{}Value\\PYZus{}16}\\PY{p}{)}\\PY{p}{)}\\PY{p}{)}\n", + " \\PY{p}{)}\n", + "\\PY{p}{)}\n", + "\\end{Verbatim}\n" + ], + "text/plain": [ + "_Value_1 = Value.var(\"bp1\")\n", + "_Value_2 = Value.var(\"bpp1\")\n", + "_Value_3 = Value.var(\"bpp2\")\n", + "_Value_4 = Value.var(\"bpp3\")\n", + "_Value_5 = Value.var(\"bpp4\")\n", + "_Value_6 = Value.var(\"bp2\")\n", + "_Value_7 = Value.var(\"bp3\")\n", + "_Value_8 = Value.var(\"bp4\")\n", + "_Value_9 = Value.from_int(Int(-1))\n", + "_Value_10 = polynomial(\n", + " MultiSet(\n", + " MultiSet(Value.var(\"q3\"), _Value_1, Value.var(\"q2\"), _Value_2),\n", + " MultiSet(_Value_3, _Value_1, Value.var(\"q6\"), Value.var(\"q2\")),\n", + " MultiSet(_Value_1, Value.var(\"q2\"), _Value_4, Value.var(\"q9\")),\n", + " MultiSet(_Value_1, Value.var(\"q2\"), Value.var(\"q12\"), _Value_5),\n", + " MultiSet(Value.var(\"q5\"), Value.var(\"q3\"), _Value_2, _Value_6),\n", + " MultiSet(Value.var(\"q5\"), _Value_3, Value.var(\"q6\"), _Value_6),\n", + " MultiSet(Value.var(\"q5\"), _Value_6, _Value_4, Value.var(\"q9\")),\n", + " MultiSet(Value.var(\"q5\"), _Value_6, Value.var(\"q12\"), _Value_5),\n", + " MultiSet(Value.var(\"q3\"), _Value_2, _Value_7, Value.var(\"q8\")),\n", + " MultiSet(_Value_3, Value.var(\"q6\"), _Value_7, Value.var(\"q8\")),\n", + " MultiSet(_Value_7, Value.var(\"q8\"), _Value_4, Value.var(\"q9\")),\n", + " MultiSet(_Value_7, Value.var(\"q8\"), Value.var(\"q12\"), _Value_5),\n", + " MultiSet(Value.var(\"q3\"), _Value_2, _Value_8, Value.var(\"q11\")),\n", + " MultiSet(_Value_3, Value.var(\"q6\"), _Value_8, Value.var(\"q11\")),\n", + " MultiSet(_Value_4, Value.var(\"q9\"), _Value_8, Value.var(\"q11\")),\n", + " MultiSet(Value.var(\"q12\"), _Value_5, _Value_8, Value.var(\"q11\")),\n", + " MultiSet(Value.var(\"q3\"), _Value_1, _Value_9, Value.var(\"q2\"), _Value_2),\n", + " MultiSet(Value.var(\"q5\"), _Value_3, Value.var(\"q3\"), _Value_1, _Value_9),\n", + " MultiSet(Value.var(\"q3\"), _Value_1, _Value_9, Value.var(\"q8\"), _Value_4),\n", + " MultiSet(Value.var(\"q3\"), _Value_1, _Value_9, _Value_5, Value.var(\"q11\")),\n", + " MultiSet(_Value_9, Value.var(\"q6\"), Value.var(\"q2\"), _Value_2, _Value_6),\n", + " MultiSet(Value.var(\"q5\"), _Value_3, _Value_9, Value.var(\"q6\"), _Value_6),\n", + " MultiSet(_Value_9, Value.var(\"q6\"), _Value_6, Value.var(\"q8\"), _Value_4),\n", + " MultiSet(_Value_9, Value.var(\"q6\"), _Value_6, _Value_5, Value.var(\"q11\")),\n", + " MultiSet(_Value_9, Value.var(\"q2\"), _Value_2, _Value_7, Value.var(\"q9\")),\n", + " MultiSet(Value.var(\"q5\"), _Value_3, _Value_9, _Value_7, Value.var(\"q9\")),\n", + " MultiSet(_Value_9, _Value_7, Value.var(\"q8\"), _Value_4, Value.var(\"q9\")),\n", + " MultiSet(_Value_9, _Value_7, Value.var(\"q9\"), _Value_5, Value.var(\"q11\")),\n", + " MultiSet(_Value_9, Value.var(\"q2\"), _Value_2, Value.var(\"q12\"), _Value_8),\n", + " MultiSet(Value.var(\"q5\"), _Value_3, _Value_9, Value.var(\"q12\"), _Value_8),\n", + " MultiSet(_Value_9, Value.var(\"q8\"), _Value_4, Value.var(\"q12\"), _Value_8),\n", + " MultiSet(_Value_9, Value.var(\"q12\"), _Value_5, _Value_8, Value.var(\"q11\")),\n", + " )\n", + ")\n", + "_Value_11 = polynomial(\n", + " MultiSet(\n", + " MultiSet(Value.var(\"q3\"), _Value_1, _Value_2, Value.var(\"q1\")),\n", + " MultiSet(_Value_3, Value.var(\"q3\"), _Value_1, Value.var(\"q4\")),\n", + " MultiSet(Value.var(\"q3\"), _Value_1, Value.var(\"q7\"), _Value_4),\n", + " MultiSet(Value.var(\"q3\"), _Value_1, _Value_5, Value.var(\"q10\")),\n", + " MultiSet(Value.var(\"q6\"), _Value_2, Value.var(\"q1\"), _Value_6),\n", + " MultiSet(_Value_3, Value.var(\"q6\"), Value.var(\"q4\"), _Value_6),\n", + " MultiSet(Value.var(\"q6\"), Value.var(\"q7\"), _Value_6, _Value_4),\n", + " MultiSet(Value.var(\"q6\"), _Value_6, _Value_5, Value.var(\"q10\")),\n", + " MultiSet(_Value_2, Value.var(\"q1\"), _Value_7, Value.var(\"q9\")),\n", + " MultiSet(_Value_3, _Value_7, Value.var(\"q4\"), Value.var(\"q9\")),\n", + " MultiSet(Value.var(\"q7\"), _Value_7, _Value_4, Value.var(\"q9\")),\n", + " MultiSet(_Value_7, Value.var(\"q9\"), _Value_5, Value.var(\"q10\")),\n", + " MultiSet(_Value_2, Value.var(\"q1\"), Value.var(\"q12\"), _Value_8),\n", + " MultiSet(_Value_3, Value.var(\"q4\"), Value.var(\"q12\"), _Value_8),\n", + " MultiSet(Value.var(\"q7\"), _Value_4, Value.var(\"q12\"), _Value_8),\n", + " MultiSet(Value.var(\"q12\"), _Value_5, Value.var(\"q10\"), _Value_8),\n", + " MultiSet(Value.var(\"q3\"), _Value_1, _Value_9, _Value_2, Value.var(\"q1\")),\n", + " MultiSet(_Value_3, _Value_1, _Value_9, Value.var(\"q6\"), Value.var(\"q1\")),\n", + " MultiSet(_Value_1, _Value_9, Value.var(\"q1\"), _Value_4, Value.var(\"q9\")),\n", + " MultiSet(_Value_1, _Value_9, Value.var(\"q1\"), Value.var(\"q12\"), _Value_5),\n", + " MultiSet(Value.var(\"q3\"), _Value_9, _Value_2, Value.var(\"q4\"), _Value_6),\n", + " MultiSet(_Value_3, _Value_9, Value.var(\"q6\"), Value.var(\"q4\"), _Value_6),\n", + " MultiSet(_Value_9, Value.var(\"q4\"), _Value_6, _Value_4, Value.var(\"q9\")),\n", + " MultiSet(_Value_9, Value.var(\"q4\"), _Value_6, Value.var(\"q12\"), _Value_5),\n", + " MultiSet(Value.var(\"q3\"), _Value_9, _Value_2, Value.var(\"q7\"), _Value_7),\n", + " MultiSet(_Value_3, _Value_9, Value.var(\"q6\"), Value.var(\"q7\"), _Value_7),\n", + " MultiSet(_Value_9, Value.var(\"q7\"), _Value_7, _Value_4, Value.var(\"q9\")),\n", + " MultiSet(_Value_9, Value.var(\"q7\"), _Value_7, Value.var(\"q12\"), _Value_5),\n", + " MultiSet(Value.var(\"q3\"), _Value_9, _Value_2, Value.var(\"q10\"), _Value_8),\n", + " MultiSet(_Value_3, _Value_9, Value.var(\"q6\"), Value.var(\"q10\"), _Value_8),\n", + " MultiSet(_Value_9, _Value_4, Value.var(\"q9\"), Value.var(\"q10\"), _Value_8),\n", + " MultiSet(_Value_9, Value.var(\"q12\"), _Value_5, Value.var(\"q10\"), _Value_8),\n", + " )\n", + ")\n", + "_Value_12 = polynomial(\n", + " MultiSet(\n", + " MultiSet(_Value_1, Value.var(\"q2\"), _Value_2, Value.var(\"q1\")),\n", + " MultiSet(Value.var(\"q5\"), _Value_3, _Value_1, Value.var(\"q1\")),\n", + " MultiSet(_Value_1, Value.var(\"q1\"), Value.var(\"q8\"), _Value_4),\n", + " MultiSet(_Value_1, Value.var(\"q1\"), _Value_5, Value.var(\"q11\")),\n", + " MultiSet(Value.var(\"q2\"), _Value_2, Value.var(\"q4\"), _Value_6),\n", + " MultiSet(Value.var(\"q5\"), _Value_3, Value.var(\"q4\"), _Value_6),\n", + " MultiSet(Value.var(\"q4\"), _Value_6, Value.var(\"q8\"), _Value_4),\n", + " MultiSet(Value.var(\"q4\"), _Value_6, _Value_5, Value.var(\"q11\")),\n", + " MultiSet(Value.var(\"q2\"), _Value_2, Value.var(\"q7\"), _Value_7),\n", + " MultiSet(Value.var(\"q5\"), _Value_3, Value.var(\"q7\"), _Value_7),\n", + " MultiSet(Value.var(\"q7\"), _Value_7, Value.var(\"q8\"), _Value_4),\n", + " MultiSet(Value.var(\"q7\"), _Value_7, _Value_5, Value.var(\"q11\")),\n", + " MultiSet(Value.var(\"q2\"), _Value_2, Value.var(\"q10\"), _Value_8),\n", + " MultiSet(Value.var(\"q5\"), _Value_3, Value.var(\"q10\"), _Value_8),\n", + " MultiSet(Value.var(\"q8\"), _Value_4, Value.var(\"q10\"), _Value_8),\n", + " MultiSet(_Value_5, Value.var(\"q10\"), _Value_8, Value.var(\"q11\")),\n", + " MultiSet(_Value_1, _Value_9, Value.var(\"q2\"), _Value_2, Value.var(\"q1\")),\n", + " MultiSet(_Value_3, _Value_1, _Value_9, Value.var(\"q2\"), Value.var(\"q4\")),\n", + " MultiSet(_Value_1, _Value_9, Value.var(\"q2\"), Value.var(\"q7\"), _Value_4),\n", + " MultiSet(_Value_1, _Value_9, Value.var(\"q2\"), _Value_5, Value.var(\"q10\")),\n", + " MultiSet(Value.var(\"q5\"), _Value_9, _Value_2, Value.var(\"q1\"), _Value_6),\n", + " MultiSet(Value.var(\"q5\"), _Value_3, _Value_9, Value.var(\"q4\"), _Value_6),\n", + " MultiSet(Value.var(\"q5\"), _Value_9, Value.var(\"q7\"), _Value_6, _Value_4),\n", + " MultiSet(Value.var(\"q5\"), _Value_9, _Value_6, _Value_5, Value.var(\"q10\")),\n", + " MultiSet(_Value_9, _Value_2, Value.var(\"q1\"), _Value_7, Value.var(\"q8\")),\n", + " MultiSet(_Value_3, _Value_9, _Value_7, Value.var(\"q4\"), Value.var(\"q8\")),\n", + " MultiSet(_Value_9, Value.var(\"q7\"), _Value_7, Value.var(\"q8\"), _Value_4),\n", + " MultiSet(_Value_9, _Value_7, Value.var(\"q8\"), _Value_5, Value.var(\"q10\")),\n", + " MultiSet(_Value_9, _Value_2, Value.var(\"q1\"), _Value_8, Value.var(\"q11\")),\n", + " MultiSet(_Value_3, _Value_9, Value.var(\"q4\"), _Value_8, Value.var(\"q11\")),\n", + " MultiSet(_Value_9, Value.var(\"q7\"), _Value_4, _Value_8, Value.var(\"q11\")),\n", + " MultiSet(_Value_9, _Value_5, Value.var(\"q10\"), _Value_8, Value.var(\"q11\")),\n", + " )\n", + ")\n", + "_Value_13 = polynomial(\n", + " MultiSet(MultiSet(Value.var(\"q7\"), _Value_7), MultiSet(Value.var(\"q4\"), _Value_6), MultiSet(_Value_1, Value.var(\"q1\")), MultiSet(Value.var(\"q10\"), _Value_8))\n", + ")\n", + "_Value_14 = polynomial(\n", + " MultiSet(MultiSet(_Value_1, Value.var(\"q2\")), MultiSet(Value.var(\"q5\"), _Value_6), MultiSet(_Value_8, Value.var(\"q11\")), MultiSet(_Value_7, Value.var(\"q8\")))\n", + ")\n", + "_Value_15 = polynomial(\n", + " MultiSet(MultiSet(Value.var(\"q3\"), _Value_1), MultiSet(Value.var(\"q6\"), _Value_6), MultiSet(Value.var(\"q12\"), _Value_8), MultiSet(_Value_7, Value.var(\"q9\")))\n", + ")\n", + "_Value_16 = polynomial(MultiSet(MultiSet(_Value_13, _Value_13), MultiSet(_Value_14, _Value_14), MultiSet(_Value_15, _Value_15)))\n", + "NDArray(\n", + " RecursiveValue(\n", + " polynomial(MultiSet(MultiSet(_Value_10, _Value_10), MultiSet(_Value_11, _Value_11), MultiSet(_Value_12, _Value_12)))\n", + " / polynomial(MultiSet(MultiSet(_Value_16, _Value_16, _Value_16)))\n", + " )\n", + ")" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "polynomial_egraph = egglog.EGraph()\n", + "polynomial_egraph.register(FunctionBending_distributed)\n", + "polynomial_egraph.run(enp.to_polynomial_ruleset.saturate())\n", + "FunctionBending_polynomial_multisets, FunctionBending_polynomial_multisets_cost = polynomial_egraph.extract(\n", + " FunctionBending_distributed,\n", + " include_cost=True,\n", + ")\n", + "print(FunctionBending_polynomial_multisets_cost)\n", + "FunctionBending_polynomial_multisets" + ] + }, + { + "cell_type": "markdown", + "id": "c925788d", + "metadata": {}, + "source": [ + "### Greedy Multivariate Horner Factorization\n", + "\n", + "Now that we have our polynomial subterms represented as nested multisets, the next step here is to see if we can find a form\n", + "with lower cost. One of the ways to do this with polynomials is to try to find a factorization of them that minimizes the number\n", + "of multiplications. With univariate polynomials, we can use an optimal algorithm called [Horner's method](https://en.wikipedia.org/wiki/Horner%27s_method).\n", + "Extending this to multivariate polynomials, there isn't an efficient algorithm that is guaranteed to produce the optimal factoring, but\n", + "there is [a greedy algorithm that will often produce a good one](https://www.semanticscholar.org/paper/Greedy-algorithms-for-optimizing-multivariate-Ceberio-Kreinovich/96103f6f48bd15d40de43a716922d1177b2b5ea2).\n", + "\n", + "So instead of considering all possible factorizations and then waiting till extraction to pick out the best one,\n", + "we can try to implement this greedy algorithm. This is made easier by the fact that we have flattened the polynomial\n", + "into a multiset of multisets, so we can analysis it holistically.\n", + "\n", + "To implement this, we find the factor that shows up in the most monomials, then find the subset of monomials which contain it, take\n", + "the intersection of all of those (to find the largest factor we can pull out of all of them), factor that out, and add it to the remainder\n", + "that didn't include that factor:\n", + "\n", + "```python\n", + "@ruleset\n", + "def factor_ruleset(\n", + " n: Value,\n", + " mss: MultiSet[MultiSet[Value]],\n", + " counts: MultiSet[Value],\n", + " picked_term: Value,\n", + " picked: MultiSet[MultiSet[Value]],\n", + " divided: MultiSet[MultiSet[Value]],\n", + " factor: MultiSet[Value],\n", + " remainder: MultiSet[MultiSet[Value]],\n", + "):\n", + " yield rule(\n", + " eq(n).to(polynomial(mss)),\n", + " # Find factor that shows up in most monomials, at least two of them\n", + " counts == MultiSet.sum_multisets(mss.map(MultiSet.reset_counts)),\n", + " eq(picked_term).to(counts.pick_max()), # on ties pick an arbitrary one\n", + " # Only factor out if it appears in more than one monomial\n", + " counts.count(picked_term) > 1,\n", + " # The factor we choose is the largest intersection between all the monomials that have that that factored term\n", + " picked == mss.filter(partial(multiset_contains_swapped, picked_term)),\n", + " factor == multiset_fold(MultiSet.__and__, picked.pick(), picked), # intersection\n", + " divided == picked.map(partial(multiset_subtract_swapped, factor)),\n", + " # remainder is those monomials that do not contain the factor\n", + " remainder == mss.filter(partial(multiset_not_contains_swapped, picked_term)),\n", + " name=\"factor\",\n", + " ).then(\n", + " # factor * polynomial(divided) + remainder\n", + " union(n).with_(polynomial(MultiSet(factor.insert(polynomial(divided))) + remainder)),\n", + " delete(polynomial(mss)),\n", + " )\n", + "```\n", + "\n", + "If we apply this, we now have a factored form! We can see that this uses a similar technique to above, where we use higher order functions\n", + "to create a new polynomial based on the old one, and replace it." + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "id": "35a25ca7", + "metadata": { + "tags": [ + "remove-input" + ] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "2143\n" + ] + }, + { + "data": { + "text/html": [ + "
_Value_1 = Value.var("bp1")\n",
+       "_Value_2 = Value.var("bpp1")\n",
+       "_Value_3 = Value.var("bpp2")\n",
+       "_Value_4 = Value.var("bpp3")\n",
+       "_Value_5 = Value.var("bpp4")\n",
+       "_Value_6 = Value.var("bp2")\n",
+       "_Value_7 = Value.var("bp3")\n",
+       "_Value_8 = Value.var("bp4")\n",
+       "_Value_9 = Value.from_int(Int(-1))\n",
+       "_Value_10 = polynomial(\n",
+       "    MultiSet(\n",
+       "        MultiSet(Value.var("q3"), _Value_1, Value.var("q2"), _Value_2),\n",
+       "        MultiSet(_Value_3, _Value_1, Value.var("q6"), Value.var("q2")),\n",
+       "        MultiSet(_Value_1, Value.var("q2"), _Value_4, Value.var("q9")),\n",
+       "        MultiSet(_Value_1, Value.var("q2"), Value.var("q12"), _Value_5),\n",
+       "        MultiSet(Value.var("q5"), Value.var("q3"), _Value_2, _Value_6),\n",
+       "        MultiSet(Value.var("q5"), _Value_3, Value.var("q6"), _Value_6),\n",
+       "        MultiSet(Value.var("q5"), _Value_6, _Value_4, Value.var("q9")),\n",
+       "        MultiSet(Value.var("q5"), _Value_6, Value.var("q12"), _Value_5),\n",
+       "        MultiSet(Value.var("q3"), _Value_2, _Value_7, Value.var("q8")),\n",
+       "        MultiSet(_Value_3, Value.var("q6"), _Value_7, Value.var("q8")),\n",
+       "        MultiSet(_Value_7, Value.var("q8"), _Value_4, Value.var("q9")),\n",
+       "        MultiSet(_Value_7, Value.var("q8"), Value.var("q12"), _Value_5),\n",
+       "        MultiSet(Value.var("q3"), _Value_2, _Value_8, Value.var("q11")),\n",
+       "        MultiSet(_Value_3, Value.var("q6"), _Value_8, Value.var("q11")),\n",
+       "        MultiSet(_Value_4, Value.var("q9"), _Value_8, Value.var("q11")),\n",
+       "        MultiSet(Value.var("q12"), _Value_5, _Value_8, Value.var("q11")),\n",
+       "        MultiSet(Value.var("q3"), _Value_1, _Value_9, Value.var("q2"), _Value_2),\n",
+       "        MultiSet(Value.var("q5"), _Value_3, Value.var("q3"), _Value_1, _Value_9),\n",
+       "        MultiSet(Value.var("q3"), _Value_1, _Value_9, Value.var("q8"), _Value_4),\n",
+       "        MultiSet(Value.var("q3"), _Value_1, _Value_9, _Value_5, Value.var("q11")),\n",
+       "        MultiSet(_Value_9, Value.var("q6"), Value.var("q2"), _Value_2, _Value_6),\n",
+       "        MultiSet(Value.var("q5"), _Value_3, _Value_9, Value.var("q6"), _Value_6),\n",
+       "        MultiSet(_Value_9, Value.var("q6"), _Value_6, Value.var("q8"), _Value_4),\n",
+       "        MultiSet(_Value_9, Value.var("q6"), _Value_6, _Value_5, Value.var("q11")),\n",
+       "        MultiSet(_Value_9, Value.var("q2"), _Value_2, _Value_7, Value.var("q9")),\n",
+       "        MultiSet(Value.var("q5"), _Value_3, _Value_9, _Value_7, Value.var("q9")),\n",
+       "        MultiSet(_Value_9, _Value_7, Value.var("q8"), _Value_4, Value.var("q9")),\n",
+       "        MultiSet(_Value_9, _Value_7, Value.var("q9"), _Value_5, Value.var("q11")),\n",
+       "        MultiSet(_Value_9, Value.var("q2"), _Value_2, Value.var("q12"), _Value_8),\n",
+       "        MultiSet(Value.var("q5"), _Value_3, _Value_9, Value.var("q12"), _Value_8),\n",
+       "        MultiSet(_Value_9, Value.var("q8"), _Value_4, Value.var("q12"), _Value_8),\n",
+       "        MultiSet(_Value_9, Value.var("q12"), _Value_5, _Value_8, Value.var("q11")),\n",
+       "    )\n",
+       ")\n",
+       "_Value_11 = polynomial(\n",
+       "    MultiSet(\n",
+       "        MultiSet(Value.var("q3"), _Value_1, _Value_2, Value.var("q1")),\n",
+       "        MultiSet(_Value_3, Value.var("q3"), _Value_1, Value.var("q4")),\n",
+       "        MultiSet(Value.var("q3"), _Value_1, Value.var("q7"), _Value_4),\n",
+       "        MultiSet(Value.var("q3"), _Value_1, _Value_5, Value.var("q10")),\n",
+       "        MultiSet(Value.var("q6"), _Value_2, Value.var("q1"), _Value_6),\n",
+       "        MultiSet(_Value_3, Value.var("q6"), Value.var("q4"), _Value_6),\n",
+       "        MultiSet(Value.var("q6"), Value.var("q7"), _Value_6, _Value_4),\n",
+       "        MultiSet(Value.var("q6"), _Value_6, _Value_5, Value.var("q10")),\n",
+       "        MultiSet(_Value_2, Value.var("q1"), _Value_7, Value.var("q9")),\n",
+       "        MultiSet(_Value_3, _Value_7, Value.var("q4"), Value.var("q9")),\n",
+       "        MultiSet(Value.var("q7"), _Value_7, _Value_4, Value.var("q9")),\n",
+       "        MultiSet(_Value_7, Value.var("q9"), _Value_5, Value.var("q10")),\n",
+       "        MultiSet(_Value_2, Value.var("q1"), Value.var("q12"), _Value_8),\n",
+       "        MultiSet(_Value_3, Value.var("q4"), Value.var("q12"), _Value_8),\n",
+       "        MultiSet(Value.var("q7"), _Value_4, Value.var("q12"), _Value_8),\n",
+       "        MultiSet(Value.var("q12"), _Value_5, Value.var("q10"), _Value_8),\n",
+       "        MultiSet(Value.var("q3"), _Value_1, _Value_9, _Value_2, Value.var("q1")),\n",
+       "        MultiSet(_Value_3, _Value_1, _Value_9, Value.var("q6"), Value.var("q1")),\n",
+       "        MultiSet(_Value_1, _Value_9, Value.var("q1"), _Value_4, Value.var("q9")),\n",
+       "        MultiSet(_Value_1, _Value_9, Value.var("q1"), Value.var("q12"), _Value_5),\n",
+       "        MultiSet(Value.var("q3"), _Value_9, _Value_2, Value.var("q4"), _Value_6),\n",
+       "        MultiSet(_Value_3, _Value_9, Value.var("q6"), Value.var("q4"), _Value_6),\n",
+       "        MultiSet(_Value_9, Value.var("q4"), _Value_6, _Value_4, Value.var("q9")),\n",
+       "        MultiSet(_Value_9, Value.var("q4"), _Value_6, Value.var("q12"), _Value_5),\n",
+       "        MultiSet(Value.var("q3"), _Value_9, _Value_2, Value.var("q7"), _Value_7),\n",
+       "        MultiSet(_Value_3, _Value_9, Value.var("q6"), Value.var("q7"), _Value_7),\n",
+       "        MultiSet(_Value_9, Value.var("q7"), _Value_7, _Value_4, Value.var("q9")),\n",
+       "        MultiSet(_Value_9, Value.var("q7"), _Value_7, Value.var("q12"), _Value_5),\n",
+       "        MultiSet(Value.var("q3"), _Value_9, _Value_2, Value.var("q10"), _Value_8),\n",
+       "        MultiSet(_Value_3, _Value_9, Value.var("q6"), Value.var("q10"), _Value_8),\n",
+       "        MultiSet(_Value_9, _Value_4, Value.var("q9"), Value.var("q10"), _Value_8),\n",
+       "        MultiSet(_Value_9, Value.var("q12"), _Value_5, Value.var("q10"), _Value_8),\n",
+       "    )\n",
+       ")\n",
+       "_MultiSet_1 = MultiSet(_Value_1, _Value_9, Value.var("q2"), _Value_2, Value.var("q1"))\n",
+       "_MultiSet_2 = MultiSet(_Value_3, _Value_1, _Value_9, Value.var("q2"), Value.var("q4"))\n",
+       "_MultiSet_3 = MultiSet(_Value_1, _Value_9, Value.var("q2"), Value.var("q7"), _Value_4)\n",
+       "_MultiSet_4 = MultiSet(_Value_1, _Value_9, Value.var("q2"), _Value_5, Value.var("q10"))\n",
+       "_MultiSet_5 = MultiSet(Value.var("q5"), _Value_9, _Value_2, Value.var("q1"), _Value_6)\n",
+       "_MultiSet_6 = MultiSet(Value.var("q5"), _Value_3, _Value_9, Value.var("q4"), _Value_6)\n",
+       "_MultiSet_7 = MultiSet(Value.var("q5"), _Value_9, Value.var("q7"), _Value_6, _Value_4)\n",
+       "_MultiSet_8 = MultiSet(Value.var("q5"), _Value_9, _Value_6, _Value_5, Value.var("q10"))\n",
+       "_MultiSet_9 = MultiSet(_Value_9, _Value_2, Value.var("q1"), _Value_7, Value.var("q8"))\n",
+       "_MultiSet_10 = MultiSet(_Value_3, _Value_9, _Value_7, Value.var("q4"), Value.var("q8"))\n",
+       "_MultiSet_11 = MultiSet(_Value_9, _Value_7, Value.var("q8"), _Value_5, Value.var("q10"))\n",
+       "_MultiSet_12 = MultiSet(_Value_9, _Value_2, Value.var("q1"), _Value_8, Value.var("q11"))\n",
+       "_MultiSet_13 = MultiSet(_Value_3, _Value_9, Value.var("q4"), _Value_8, Value.var("q11"))\n",
+       "_MultiSet_14 = MultiSet(_Value_9, Value.var("q7"), _Value_4, _Value_8, Value.var("q11"))\n",
+       "_MultiSet_15 = MultiSet(_Value_9, _Value_5, Value.var("q10"), _Value_8, Value.var("q11"))\n",
+       "_Value_12 = polynomial(\n",
+       "    MultiSet(MultiSet(Value.var("q7"), _Value_7), MultiSet(Value.var("q4"), _Value_6), MultiSet(_Value_1, Value.var("q1")), MultiSet(Value.var("q10"), _Value_8))\n",
+       ")\n",
+       "_Value_13 = polynomial(\n",
+       "    MultiSet(MultiSet(_Value_1, Value.var("q2")), MultiSet(Value.var("q5"), _Value_6), MultiSet(_Value_8, Value.var("q11")), MultiSet(_Value_7, Value.var("q8")))\n",
+       ")\n",
+       "_Value_14 = polynomial(\n",
+       "    MultiSet(MultiSet(Value.var("q3"), _Value_1), MultiSet(Value.var("q6"), _Value_6), MultiSet(Value.var("q12"), _Value_8), MultiSet(_Value_7, Value.var("q9")))\n",
+       ")\n",
+       "_Value_15 = polynomial(MultiSet(MultiSet(_Value_12, _Value_12), MultiSet(_Value_13, _Value_13), MultiSet(_Value_14, _Value_14)))\n",
+       "NDArray(\n",
+       "    RecursiveValue(\n",
+       "        polynomial(\n",
+       "            MultiSet(\n",
+       "                MultiSet(_Value_10, _Value_10),\n",
+       "                MultiSet(_Value_11, _Value_11),\n",
+       "                MultiSet(\n",
+       "                    polynomial(\n",
+       "                        MultiSet(\n",
+       "                            MultiSet(_Value_1, Value.var("q2"), _Value_2, Value.var("q1")),\n",
+       "                            MultiSet(Value.var("q5"), _Value_3, _Value_1, Value.var("q1")),\n",
+       "                            MultiSet(_Value_1, Value.var("q1"), Value.var("q8"), _Value_4),\n",
+       "                            MultiSet(_Value_1, Value.var("q1"), _Value_5, Value.var("q11")),\n",
+       "                            MultiSet(Value.var("q2"), _Value_2, Value.var("q4"), _Value_6),\n",
+       "                            MultiSet(Value.var("q5"), _Value_3, Value.var("q4"), _Value_6),\n",
+       "                            MultiSet(Value.var("q4"), _Value_6, Value.var("q8"), _Value_4),\n",
+       "                            MultiSet(Value.var("q4"), _Value_6, _Value_5, Value.var("q11")),\n",
+       "                            MultiSet(Value.var("q2"), _Value_2, Value.var("q7"), _Value_7),\n",
+       "                            MultiSet(Value.var("q5"), _Value_3, Value.var("q7"), _Value_7),\n",
+       "                            MultiSet(Value.var("q7"), _Value_7, Value.var("q8"), _Value_4),\n",
+       "                            MultiSet(Value.var("q7"), _Value_7, _Value_5, Value.var("q11")),\n",
+       "                            MultiSet(Value.var("q2"), _Value_2, Value.var("q10"), _Value_8),\n",
+       "                            MultiSet(Value.var("q5"), _Value_3, Value.var("q10"), _Value_8),\n",
+       "                            MultiSet(Value.var("q8"), _Value_4, Value.var("q10"), _Value_8),\n",
+       "                            MultiSet(_Value_5, Value.var("q10"), _Value_8, Value.var("q11")),\n",
+       "                            _MultiSet_1,\n",
+       "                            _MultiSet_2,\n",
+       "                            _MultiSet_3,\n",
+       "                            _MultiSet_4,\n",
+       "                            _MultiSet_5,\n",
+       "                            _MultiSet_6,\n",
+       "                            _MultiSet_7,\n",
+       "                            _MultiSet_8,\n",
+       "                            _MultiSet_9,\n",
+       "                            _MultiSet_10,\n",
+       "                            _MultiSet_11,\n",
+       "                            _MultiSet_12,\n",
+       "                            _MultiSet_13,\n",
+       "                            _MultiSet_14,\n",
+       "                            _MultiSet_15,\n",
+       "                            MultiSet(Value.var("q7"), Value.var("q7"), _Value_7, Value.var("q8"), _Value_4),\n",
+       "                        )\n",
+       "                    ),\n",
+       "                    polynomial(\n",
+       "                        MultiSet(\n",
+       "                            MultiSet(_Value_1, Value.var("q2"), _Value_2, Value.var("q1")),\n",
+       "                            MultiSet(Value.var("q5"), _Value_3, _Value_1, Value.var("q1")),\n",
+       "                            MultiSet(_Value_1, Value.var("q1"), Value.var("q8"), _Value_4),\n",
+       "                            MultiSet(_Value_1, Value.var("q1"), _Value_5, Value.var("q11")),\n",
+       "                            MultiSet(Value.var("q2"), _Value_2, Value.var("q4"), _Value_6),\n",
+       "                            MultiSet(Value.var("q5"), _Value_3, Value.var("q4"), _Value_6),\n",
+       "                            MultiSet(Value.var("q4"), _Value_6, Value.var("q8"), _Value_4),\n",
+       "                            MultiSet(Value.var("q4"), _Value_6, _Value_5, Value.var("q11")),\n",
+       "                            MultiSet(Value.var("q2"), _Value_2, Value.var("q7"), _Value_7),\n",
+       "                            MultiSet(Value.var("q5"), _Value_3, Value.var("q7"), _Value_7),\n",
+       "                            MultiSet(Value.var("q7"), _Value_7, Value.var("q8"), _Value_4),\n",
+       "                            MultiSet(Value.var("q7"), _Value_7, _Value_5, Value.var("q11")),\n",
+       "                            MultiSet(Value.var("q2"), _Value_2, Value.var("q10"), _Value_8),\n",
+       "                            MultiSet(Value.var("q5"), _Value_3, Value.var("q10"), _Value_8),\n",
+       "                            MultiSet(Value.var("q8"), _Value_4, Value.var("q10"), _Value_8),\n",
+       "                            MultiSet(_Value_5, Value.var("q10"), _Value_8, Value.var("q11")),\n",
+       "                            _MultiSet_1,\n",
+       "                            _MultiSet_2,\n",
+       "                            _MultiSet_3,\n",
+       "                            _MultiSet_4,\n",
+       "                            _MultiSet_5,\n",
+       "                            _MultiSet_6,\n",
+       "                            _MultiSet_7,\n",
+       "                            _MultiSet_8,\n",
+       "                            _MultiSet_9,\n",
+       "                            _MultiSet_10,\n",
+       "                            MultiSet(_Value_9, Value.var("q7"), _Value_7, Value.var("q8"), _Value_4),\n",
+       "                            _MultiSet_11,\n",
+       "                            _MultiSet_12,\n",
+       "                            _MultiSet_13,\n",
+       "                            _MultiSet_14,\n",
+       "                            _MultiSet_15,\n",
+       "                        )\n",
+       "                    ),\n",
+       "                ),\n",
+       "            )\n",
+       "        )\n",
+       "        / polynomial(MultiSet(MultiSet(_Value_15, _Value_15, _Value_15)))\n",
+       "    )\n",
+       ")\n",
+       "
\n" + ], + "text/latex": [ + "\\begin{Verbatim}[commandchars=\\\\\\{\\}]\n", + "\\PY{n}{\\PYZus{}Value\\PYZus{}1} \\PY{o}{=} \\PY{n}{Value}\\PY{o}{.}\\PY{n}{var}\\PY{p}{(}\\PY{l+s+s2}{\\PYZdq{}}\\PY{l+s+s2}{bp1}\\PY{l+s+s2}{\\PYZdq{}}\\PY{p}{)}\n", + "\\PY{n}{\\PYZus{}Value\\PYZus{}2} \\PY{o}{=} \\PY{n}{Value}\\PY{o}{.}\\PY{n}{var}\\PY{p}{(}\\PY{l+s+s2}{\\PYZdq{}}\\PY{l+s+s2}{bpp1}\\PY{l+s+s2}{\\PYZdq{}}\\PY{p}{)}\n", + "\\PY{n}{\\PYZus{}Value\\PYZus{}3} \\PY{o}{=} \\PY{n}{Value}\\PY{o}{.}\\PY{n}{var}\\PY{p}{(}\\PY{l+s+s2}{\\PYZdq{}}\\PY{l+s+s2}{bpp2}\\PY{l+s+s2}{\\PYZdq{}}\\PY{p}{)}\n", + "\\PY{n}{\\PYZus{}Value\\PYZus{}4} \\PY{o}{=} \\PY{n}{Value}\\PY{o}{.}\\PY{n}{var}\\PY{p}{(}\\PY{l+s+s2}{\\PYZdq{}}\\PY{l+s+s2}{bpp3}\\PY{l+s+s2}{\\PYZdq{}}\\PY{p}{)}\n", + "\\PY{n}{\\PYZus{}Value\\PYZus{}5} \\PY{o}{=} \\PY{n}{Value}\\PY{o}{.}\\PY{n}{var}\\PY{p}{(}\\PY{l+s+s2}{\\PYZdq{}}\\PY{l+s+s2}{bpp4}\\PY{l+s+s2}{\\PYZdq{}}\\PY{p}{)}\n", + "\\PY{n}{\\PYZus{}Value\\PYZus{}6} \\PY{o}{=} 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\\PY{n}{MultiSet}\\PY{p}{(}\\PY{n}{\\PYZus{}Value\\PYZus{}5}\\PY{p}{,} \\PY{n}{Value}\\PY{o}{.}\\PY{n}{var}\\PY{p}{(}\\PY{l+s+s2}{\\PYZdq{}}\\PY{l+s+s2}{q10}\\PY{l+s+s2}{\\PYZdq{}}\\PY{p}{)}\\PY{p}{,} \\PY{n}{\\PYZus{}Value\\PYZus{}8}\\PY{p}{,} \\PY{n}{Value}\\PY{o}{.}\\PY{n}{var}\\PY{p}{(}\\PY{l+s+s2}{\\PYZdq{}}\\PY{l+s+s2}{q11}\\PY{l+s+s2}{\\PYZdq{}}\\PY{p}{)}\\PY{p}{)}\\PY{p}{,}\n", + " \\PY{n}{\\PYZus{}MultiSet\\PYZus{}1}\\PY{p}{,}\n", + " \\PY{n}{\\PYZus{}MultiSet\\PYZus{}2}\\PY{p}{,}\n", + " \\PY{n}{\\PYZus{}MultiSet\\PYZus{}3}\\PY{p}{,}\n", + " \\PY{n}{\\PYZus{}MultiSet\\PYZus{}4}\\PY{p}{,}\n", + " \\PY{n}{\\PYZus{}MultiSet\\PYZus{}5}\\PY{p}{,}\n", + " \\PY{n}{\\PYZus{}MultiSet\\PYZus{}6}\\PY{p}{,}\n", + " \\PY{n}{\\PYZus{}MultiSet\\PYZus{}7}\\PY{p}{,}\n", + " \\PY{n}{\\PYZus{}MultiSet\\PYZus{}8}\\PY{p}{,}\n", + " \\PY{n}{\\PYZus{}MultiSet\\PYZus{}9}\\PY{p}{,}\n", + " \\PY{n}{\\PYZus{}MultiSet\\PYZus{}10}\\PY{p}{,}\n", + " \\PY{n}{MultiSet}\\PY{p}{(}\\PY{n}{\\PYZus{}Value\\PYZus{}9}\\PY{p}{,} \\PY{n}{Value}\\PY{o}{.}\\PY{n}{var}\\PY{p}{(}\\PY{l+s+s2}{\\PYZdq{}}\\PY{l+s+s2}{q7}\\PY{l+s+s2}{\\PYZdq{}}\\PY{p}{)}\\PY{p}{,} \\PY{n}{\\PYZus{}Value\\PYZus{}7}\\PY{p}{,} \\PY{n}{Value}\\PY{o}{.}\\PY{n}{var}\\PY{p}{(}\\PY{l+s+s2}{\\PYZdq{}}\\PY{l+s+s2}{q8}\\PY{l+s+s2}{\\PYZdq{}}\\PY{p}{)}\\PY{p}{,} \\PY{n}{\\PYZus{}Value\\PYZus{}4}\\PY{p}{)}\\PY{p}{,}\n", + " \\PY{n}{\\PYZus{}MultiSet\\PYZus{}11}\\PY{p}{,}\n", + " \\PY{n}{\\PYZus{}MultiSet\\PYZus{}12}\\PY{p}{,}\n", + " \\PY{n}{\\PYZus{}MultiSet\\PYZus{}13}\\PY{p}{,}\n", + " \\PY{n}{\\PYZus{}MultiSet\\PYZus{}14}\\PY{p}{,}\n", + " \\PY{n}{\\PYZus{}MultiSet\\PYZus{}15}\\PY{p}{,}\n", + " \\PY{p}{)}\n", + " \\PY{p}{)}\\PY{p}{,}\n", + " \\PY{p}{)}\\PY{p}{,}\n", + " \\PY{p}{)}\n", + " \\PY{p}{)}\n", + " \\PY{o}{/} \\PY{n}{polynomial}\\PY{p}{(}\\PY{n}{MultiSet}\\PY{p}{(}\\PY{n}{MultiSet}\\PY{p}{(}\\PY{n}{\\PYZus{}Value\\PYZus{}15}\\PY{p}{,} \\PY{n}{\\PYZus{}Value\\PYZus{}15}\\PY{p}{,} \\PY{n}{\\PYZus{}Value\\PYZus{}15}\\PY{p}{)}\\PY{p}{)}\\PY{p}{)}\n", + " \\PY{p}{)}\n", + "\\PY{p}{)}\n", + "\\end{Verbatim}\n" + ], + "text/plain": [ + "_Value_1 = Value.var(\"bp1\")\n", + "_Value_2 = Value.var(\"bpp1\")\n", + "_Value_3 = Value.var(\"bpp2\")\n", + "_Value_4 = Value.var(\"bpp3\")\n", + "_Value_5 = Value.var(\"bpp4\")\n", + "_Value_6 = Value.var(\"bp2\")\n", + "_Value_7 = Value.var(\"bp3\")\n", + "_Value_8 = Value.var(\"bp4\")\n", + "_Value_9 = Value.from_int(Int(-1))\n", + "_Value_10 = polynomial(\n", + " MultiSet(\n", + " MultiSet(Value.var(\"q3\"), _Value_1, Value.var(\"q2\"), _Value_2),\n", + " MultiSet(_Value_3, _Value_1, Value.var(\"q6\"), Value.var(\"q2\")),\n", + " MultiSet(_Value_1, Value.var(\"q2\"), _Value_4, Value.var(\"q9\")),\n", + " MultiSet(_Value_1, Value.var(\"q2\"), Value.var(\"q12\"), _Value_5),\n", + " MultiSet(Value.var(\"q5\"), Value.var(\"q3\"), _Value_2, _Value_6),\n", + " MultiSet(Value.var(\"q5\"), _Value_3, Value.var(\"q6\"), _Value_6),\n", + " MultiSet(Value.var(\"q5\"), _Value_6, _Value_4, Value.var(\"q9\")),\n", + " MultiSet(Value.var(\"q5\"), _Value_6, Value.var(\"q12\"), _Value_5),\n", + " MultiSet(Value.var(\"q3\"), _Value_2, _Value_7, Value.var(\"q8\")),\n", + " MultiSet(_Value_3, Value.var(\"q6\"), _Value_7, Value.var(\"q8\")),\n", + " MultiSet(_Value_7, Value.var(\"q8\"), _Value_4, Value.var(\"q9\")),\n", + " MultiSet(_Value_7, Value.var(\"q8\"), Value.var(\"q12\"), _Value_5),\n", + " MultiSet(Value.var(\"q3\"), _Value_2, _Value_8, Value.var(\"q11\")),\n", + " MultiSet(_Value_3, Value.var(\"q6\"), _Value_8, Value.var(\"q11\")),\n", + " MultiSet(_Value_4, Value.var(\"q9\"), _Value_8, Value.var(\"q11\")),\n", + " MultiSet(Value.var(\"q12\"), _Value_5, _Value_8, Value.var(\"q11\")),\n", + " MultiSet(Value.var(\"q3\"), _Value_1, _Value_9, Value.var(\"q2\"), _Value_2),\n", + " MultiSet(Value.var(\"q5\"), _Value_3, Value.var(\"q3\"), _Value_1, _Value_9),\n", + " MultiSet(Value.var(\"q3\"), _Value_1, _Value_9, Value.var(\"q8\"), _Value_4),\n", + " MultiSet(Value.var(\"q3\"), _Value_1, _Value_9, _Value_5, Value.var(\"q11\")),\n", + " MultiSet(_Value_9, Value.var(\"q6\"), Value.var(\"q2\"), _Value_2, _Value_6),\n", + " MultiSet(Value.var(\"q5\"), _Value_3, _Value_9, Value.var(\"q6\"), _Value_6),\n", + " MultiSet(_Value_9, Value.var(\"q6\"), _Value_6, Value.var(\"q8\"), _Value_4),\n", + " MultiSet(_Value_9, Value.var(\"q6\"), _Value_6, _Value_5, Value.var(\"q11\")),\n", + " MultiSet(_Value_9, Value.var(\"q2\"), _Value_2, _Value_7, Value.var(\"q9\")),\n", + " MultiSet(Value.var(\"q5\"), _Value_3, _Value_9, _Value_7, Value.var(\"q9\")),\n", + " MultiSet(_Value_9, _Value_7, Value.var(\"q8\"), _Value_4, Value.var(\"q9\")),\n", + " MultiSet(_Value_9, _Value_7, Value.var(\"q9\"), _Value_5, Value.var(\"q11\")),\n", + " MultiSet(_Value_9, Value.var(\"q2\"), _Value_2, Value.var(\"q12\"), _Value_8),\n", + " MultiSet(Value.var(\"q5\"), _Value_3, _Value_9, Value.var(\"q12\"), _Value_8),\n", + " MultiSet(_Value_9, Value.var(\"q8\"), _Value_4, Value.var(\"q12\"), _Value_8),\n", + " MultiSet(_Value_9, Value.var(\"q12\"), _Value_5, _Value_8, Value.var(\"q11\")),\n", + " )\n", + ")\n", + "_Value_11 = polynomial(\n", + " MultiSet(\n", + " MultiSet(Value.var(\"q3\"), _Value_1, _Value_2, Value.var(\"q1\")),\n", + " MultiSet(_Value_3, Value.var(\"q3\"), _Value_1, Value.var(\"q4\")),\n", + " MultiSet(Value.var(\"q3\"), _Value_1, Value.var(\"q7\"), _Value_4),\n", + " MultiSet(Value.var(\"q3\"), _Value_1, _Value_5, Value.var(\"q10\")),\n", + " MultiSet(Value.var(\"q6\"), _Value_2, Value.var(\"q1\"), _Value_6),\n", + " MultiSet(_Value_3, Value.var(\"q6\"), Value.var(\"q4\"), _Value_6),\n", + " MultiSet(Value.var(\"q6\"), Value.var(\"q7\"), _Value_6, _Value_4),\n", + " MultiSet(Value.var(\"q6\"), _Value_6, _Value_5, Value.var(\"q10\")),\n", + " MultiSet(_Value_2, Value.var(\"q1\"), _Value_7, Value.var(\"q9\")),\n", + " MultiSet(_Value_3, _Value_7, Value.var(\"q4\"), Value.var(\"q9\")),\n", + " MultiSet(Value.var(\"q7\"), _Value_7, _Value_4, Value.var(\"q9\")),\n", + " MultiSet(_Value_7, Value.var(\"q9\"), _Value_5, Value.var(\"q10\")),\n", + " MultiSet(_Value_2, Value.var(\"q1\"), Value.var(\"q12\"), _Value_8),\n", + " MultiSet(_Value_3, Value.var(\"q4\"), Value.var(\"q12\"), _Value_8),\n", + " MultiSet(Value.var(\"q7\"), _Value_4, Value.var(\"q12\"), _Value_8),\n", + " MultiSet(Value.var(\"q12\"), _Value_5, Value.var(\"q10\"), _Value_8),\n", + " MultiSet(Value.var(\"q3\"), _Value_1, _Value_9, _Value_2, Value.var(\"q1\")),\n", + " MultiSet(_Value_3, _Value_1, _Value_9, Value.var(\"q6\"), Value.var(\"q1\")),\n", + " MultiSet(_Value_1, _Value_9, Value.var(\"q1\"), _Value_4, Value.var(\"q9\")),\n", + " MultiSet(_Value_1, _Value_9, Value.var(\"q1\"), Value.var(\"q12\"), _Value_5),\n", + " MultiSet(Value.var(\"q3\"), _Value_9, _Value_2, Value.var(\"q4\"), _Value_6),\n", + " MultiSet(_Value_3, _Value_9, Value.var(\"q6\"), Value.var(\"q4\"), _Value_6),\n", + " MultiSet(_Value_9, Value.var(\"q4\"), _Value_6, _Value_4, Value.var(\"q9\")),\n", + " MultiSet(_Value_9, Value.var(\"q4\"), _Value_6, Value.var(\"q12\"), _Value_5),\n", + " MultiSet(Value.var(\"q3\"), _Value_9, _Value_2, Value.var(\"q7\"), _Value_7),\n", + " MultiSet(_Value_3, _Value_9, Value.var(\"q6\"), Value.var(\"q7\"), _Value_7),\n", + " MultiSet(_Value_9, Value.var(\"q7\"), _Value_7, _Value_4, Value.var(\"q9\")),\n", + " MultiSet(_Value_9, Value.var(\"q7\"), _Value_7, Value.var(\"q12\"), _Value_5),\n", + " MultiSet(Value.var(\"q3\"), _Value_9, _Value_2, Value.var(\"q10\"), _Value_8),\n", + " MultiSet(_Value_3, _Value_9, Value.var(\"q6\"), Value.var(\"q10\"), _Value_8),\n", + " MultiSet(_Value_9, _Value_4, Value.var(\"q9\"), Value.var(\"q10\"), _Value_8),\n", + " MultiSet(_Value_9, Value.var(\"q12\"), _Value_5, Value.var(\"q10\"), _Value_8),\n", + " )\n", + ")\n", + "_MultiSet_1 = MultiSet(_Value_1, _Value_9, Value.var(\"q2\"), _Value_2, Value.var(\"q1\"))\n", + "_MultiSet_2 = MultiSet(_Value_3, _Value_1, _Value_9, Value.var(\"q2\"), Value.var(\"q4\"))\n", + "_MultiSet_3 = MultiSet(_Value_1, _Value_9, Value.var(\"q2\"), Value.var(\"q7\"), _Value_4)\n", + "_MultiSet_4 = MultiSet(_Value_1, _Value_9, Value.var(\"q2\"), _Value_5, Value.var(\"q10\"))\n", + "_MultiSet_5 = MultiSet(Value.var(\"q5\"), _Value_9, _Value_2, Value.var(\"q1\"), _Value_6)\n", + "_MultiSet_6 = MultiSet(Value.var(\"q5\"), _Value_3, _Value_9, Value.var(\"q4\"), _Value_6)\n", + "_MultiSet_7 = MultiSet(Value.var(\"q5\"), _Value_9, Value.var(\"q7\"), _Value_6, _Value_4)\n", + "_MultiSet_8 = MultiSet(Value.var(\"q5\"), _Value_9, _Value_6, _Value_5, Value.var(\"q10\"))\n", + "_MultiSet_9 = MultiSet(_Value_9, _Value_2, Value.var(\"q1\"), _Value_7, Value.var(\"q8\"))\n", + "_MultiSet_10 = MultiSet(_Value_3, _Value_9, _Value_7, Value.var(\"q4\"), Value.var(\"q8\"))\n", + "_MultiSet_11 = MultiSet(_Value_9, _Value_7, Value.var(\"q8\"), _Value_5, Value.var(\"q10\"))\n", + "_MultiSet_12 = MultiSet(_Value_9, _Value_2, Value.var(\"q1\"), _Value_8, Value.var(\"q11\"))\n", + "_MultiSet_13 = MultiSet(_Value_3, _Value_9, Value.var(\"q4\"), _Value_8, Value.var(\"q11\"))\n", + "_MultiSet_14 = MultiSet(_Value_9, Value.var(\"q7\"), _Value_4, _Value_8, Value.var(\"q11\"))\n", + "_MultiSet_15 = MultiSet(_Value_9, _Value_5, Value.var(\"q10\"), _Value_8, Value.var(\"q11\"))\n", + "_Value_12 = polynomial(\n", + " MultiSet(MultiSet(Value.var(\"q7\"), _Value_7), MultiSet(Value.var(\"q4\"), _Value_6), MultiSet(_Value_1, Value.var(\"q1\")), MultiSet(Value.var(\"q10\"), _Value_8))\n", + ")\n", + "_Value_13 = polynomial(\n", + " MultiSet(MultiSet(_Value_1, Value.var(\"q2\")), MultiSet(Value.var(\"q5\"), _Value_6), MultiSet(_Value_8, Value.var(\"q11\")), MultiSet(_Value_7, Value.var(\"q8\")))\n", + ")\n", + "_Value_14 = polynomial(\n", + " MultiSet(MultiSet(Value.var(\"q3\"), _Value_1), MultiSet(Value.var(\"q6\"), _Value_6), MultiSet(Value.var(\"q12\"), _Value_8), MultiSet(_Value_7, Value.var(\"q9\")))\n", + ")\n", + "_Value_15 = polynomial(MultiSet(MultiSet(_Value_12, _Value_12), MultiSet(_Value_13, _Value_13), MultiSet(_Value_14, _Value_14)))\n", + "NDArray(\n", + " RecursiveValue(\n", + " polynomial(\n", + " MultiSet(\n", + " MultiSet(_Value_10, _Value_10),\n", + " MultiSet(_Value_11, _Value_11),\n", + " MultiSet(\n", + " polynomial(\n", + " MultiSet(\n", + " MultiSet(_Value_1, Value.var(\"q2\"), _Value_2, Value.var(\"q1\")),\n", + " MultiSet(Value.var(\"q5\"), _Value_3, _Value_1, Value.var(\"q1\")),\n", + " MultiSet(_Value_1, Value.var(\"q1\"), Value.var(\"q8\"), _Value_4),\n", + " MultiSet(_Value_1, Value.var(\"q1\"), _Value_5, Value.var(\"q11\")),\n", + " MultiSet(Value.var(\"q2\"), _Value_2, Value.var(\"q4\"), _Value_6),\n", + " MultiSet(Value.var(\"q5\"), _Value_3, Value.var(\"q4\"), _Value_6),\n", + " MultiSet(Value.var(\"q4\"), _Value_6, Value.var(\"q8\"), _Value_4),\n", + " MultiSet(Value.var(\"q4\"), _Value_6, _Value_5, Value.var(\"q11\")),\n", + " MultiSet(Value.var(\"q2\"), _Value_2, Value.var(\"q7\"), _Value_7),\n", + " MultiSet(Value.var(\"q5\"), _Value_3, Value.var(\"q7\"), _Value_7),\n", + " MultiSet(Value.var(\"q7\"), _Value_7, Value.var(\"q8\"), _Value_4),\n", + " MultiSet(Value.var(\"q7\"), _Value_7, _Value_5, Value.var(\"q11\")),\n", + " MultiSet(Value.var(\"q2\"), _Value_2, Value.var(\"q10\"), _Value_8),\n", + " MultiSet(Value.var(\"q5\"), _Value_3, Value.var(\"q10\"), _Value_8),\n", + " MultiSet(Value.var(\"q8\"), _Value_4, Value.var(\"q10\"), _Value_8),\n", + " MultiSet(_Value_5, Value.var(\"q10\"), _Value_8, Value.var(\"q11\")),\n", + " _MultiSet_1,\n", + " _MultiSet_2,\n", + " _MultiSet_3,\n", + " _MultiSet_4,\n", + " _MultiSet_5,\n", + " _MultiSet_6,\n", + " _MultiSet_7,\n", + " _MultiSet_8,\n", + " _MultiSet_9,\n", + " _MultiSet_10,\n", + " _MultiSet_11,\n", + " _MultiSet_12,\n", + " _MultiSet_13,\n", + " _MultiSet_14,\n", + " _MultiSet_15,\n", + " MultiSet(Value.var(\"q7\"), Value.var(\"q7\"), _Value_7, Value.var(\"q8\"), _Value_4),\n", + " )\n", + " ),\n", + " polynomial(\n", + " MultiSet(\n", + " MultiSet(_Value_1, Value.var(\"q2\"), _Value_2, Value.var(\"q1\")),\n", + " MultiSet(Value.var(\"q5\"), _Value_3, _Value_1, Value.var(\"q1\")),\n", + " MultiSet(_Value_1, Value.var(\"q1\"), Value.var(\"q8\"), _Value_4),\n", + " MultiSet(_Value_1, Value.var(\"q1\"), _Value_5, Value.var(\"q11\")),\n", + " MultiSet(Value.var(\"q2\"), _Value_2, Value.var(\"q4\"), _Value_6),\n", + " MultiSet(Value.var(\"q5\"), _Value_3, Value.var(\"q4\"), _Value_6),\n", + " MultiSet(Value.var(\"q4\"), _Value_6, Value.var(\"q8\"), _Value_4),\n", + " MultiSet(Value.var(\"q4\"), _Value_6, _Value_5, Value.var(\"q11\")),\n", + " MultiSet(Value.var(\"q2\"), _Value_2, Value.var(\"q7\"), _Value_7),\n", + " MultiSet(Value.var(\"q5\"), _Value_3, Value.var(\"q7\"), _Value_7),\n", + " MultiSet(Value.var(\"q7\"), _Value_7, Value.var(\"q8\"), _Value_4),\n", + " MultiSet(Value.var(\"q7\"), _Value_7, _Value_5, Value.var(\"q11\")),\n", + " MultiSet(Value.var(\"q2\"), _Value_2, Value.var(\"q10\"), _Value_8),\n", + " MultiSet(Value.var(\"q5\"), _Value_3, Value.var(\"q10\"), _Value_8),\n", + " MultiSet(Value.var(\"q8\"), _Value_4, Value.var(\"q10\"), _Value_8),\n", + " MultiSet(_Value_5, Value.var(\"q10\"), _Value_8, Value.var(\"q11\")),\n", + " _MultiSet_1,\n", + " _MultiSet_2,\n", + " _MultiSet_3,\n", + " _MultiSet_4,\n", + " _MultiSet_5,\n", + " _MultiSet_6,\n", + " _MultiSet_7,\n", + " _MultiSet_8,\n", + " _MultiSet_9,\n", + " _MultiSet_10,\n", + " MultiSet(_Value_9, Value.var(\"q7\"), _Value_7, Value.var(\"q8\"), _Value_4),\n", + " _MultiSet_11,\n", + " _MultiSet_12,\n", + " _MultiSet_13,\n", + " _MultiSet_14,\n", + " _MultiSet_15,\n", + " )\n", + " ),\n", + " ),\n", + " )\n", + " )\n", + " / polynomial(MultiSet(MultiSet(_Value_15, _Value_15, _Value_15)))\n", + " )\n", + ")" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "polynomial_egraph.run(enp.factor_ruleset.saturate())\n", + "FunctionBending_polynomial_multisets_factored, FunctionBending_polynomial_multisets_factored_cost = (\n", + " polynomial_egraph.extract(\n", + " FunctionBending_polynomial_multisets,\n", + " include_cost=True,\n", + " )\n", + ")\n", + "print(FunctionBending_polynomial_multisets_factored_cost)\n", + "FunctionBending_polynomial_multisets_factored" + ] + }, + { + "cell_type": "markdown", + "id": "4a19a36b", + "metadata": {}, + "source": [ + "We can then turn this multiset form back into one with binary operations, giving us an end-end-end way to factor polynomials\n", + "in Egglog without exploring the full A/C/D space, reducing the size blowup.\n", + "\n", + "For the smaller expression of the bending function, this produces a result of the same cost as the full factorization\n", + "and takes half the time. It also produces many fewer nodes. While the full factored version has 13,040 in the e-graph,\n", + "this one only has 927, which is only slightly more than the original size after distributing (904 nodes).\n", + "\n", + "For the larger expression, of the gradient, the difference is even starker. This approach is able to factor it to a cost of 79,974,\n", + "whereas we stopped the full factorization after it reached 2,125,338. In terms of e-graph size we have 112,144 nodes at the end\n", + "compared to the 2,582,934 of the full factorization.\n", + "\n", + "So overall, this example shows a way to do a directed factorization to reduce the total cost of an expression,\n", + "without having to explore the full space of equivalent expressions. While this isolated use case might not be a good\n", + "fit for e-graphs, inside of a larger optimization pipeline this shows how we can capture this type of optimization in\n", + "a way that is composable.\n", + "\n", + "Moreover, it is an experiment in how we can build rules on top of containers that use higher order functions\n", + "to do more complicated analysis, without leading to a node blow up.\n", + "\n", + "## Appendix 2: Further Examples\n", + "\n", + "Above I presented a large example that comes from my current line of research. However, there are many\n", + "smaller examples that could also be used to explore the usefulness of this kind of technique. Due to limitations in my time\n", + "I haven't explored these deeply, but did want to mention them.\n", + "\n", + "[Yihong](https://effect.systems/) shared with me an example of how just having a simple associativity rule and a rule for multiplying by zero will lead\n", + "to never saturating:\n", + "\n", + "```clojure\n", + "(datatype Int (mul Int Int) (a) (zero))\n", + "\n", + "(birewrite (mul x (mul y z)) (mul (mul x y) z))\n", + "(rewrite (mul (zero) x) (zero))\n", + "\n", + "(mul (zero) (a))\n", + "(run-schedule (repeat 8 (run)))\n", + "```\n", + "\n", + "Instead, if we represented this as a product of a multiset, we could simply have a rule that looked for a zero element\n", + "in the multiset and replaced that with zero. Then there would be no associativity needed, and so no chance for this to blow up. A `product(MultiSet(...))`\n", + "operation can handle associativity and commutativity and the rebuilding handles merges.\n", + "\n", + "When I asked on the EGraph's Zulip for more examples, Sophia B also [shared another example with me](https://egraphs.zulipchat.com/#narrow/channel/328972-general/topic/A.2FC.20Blowup.20Example/near/573091425). If you have the rule `f(a + b) + 1 = f(a) + f(b)` plus A/C, you can derive equalities like `f(x) + (f(y) + f(z)) = f(x + (y + z)) + 2`, but it can take a large number of nodes.\n", + "Instead in this system, we would have to encode that rule over multisets and add constant propagation to the sum function, to see how it could be found more directly, through normalization.\n", + "\n", + "*I [used an LLM](https://chatgpt.com/share/69969a20-26d4-8011-879a-62a04adfed31) to get feedback on the draft and revised based on its suggestions to improve readability, organization, and consistency.*\n", + "*Thank you Oliver, Yihong, Gilbert and Alexandra also who gave feedback to me throughout this process and while drafting this post.*" + ] + } + ], + "metadata": { + "file_format": "mystnb", + "jupytext": { + "default_lexer": "python" + }, + "kernelspec": { + "display_name": "egglog (3.13.11)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.13.11" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/docs/reference/python-integration.md b/docs/reference/python-integration.md index 23f52d8f..e195fe48 100644 --- a/docs/reference/python-integration.md +++ b/docs/reference/python-integration.md @@ -90,6 +90,14 @@ match MyExpr("hello"): print(f"Matched MyExpr with value: {value}") ``` +This pattern also works well as a general alternative to `cast(...)`-heavy tuple destructuring from `get_callable_args`. If a custom `Expr` exposes preserved properties and `__match_args__`, later walkers can often match nested expressions directly: + +```python +match get_callable_args(expr, Math.__sub__): + case (Math(lhs), Math(rhs)): + ... +``` + ## Python Object Sort We define a custom "primitive sort" (i.e. a builtin type) for `PyObject`s. This allows us to store any Python object in the e-graph. @@ -250,6 +258,8 @@ Registering a conversion from A to B will also register all transitively reachab Math(2) + 30 + "x" ``` +When defining converters for a custom `Expr` sort, prefer registering conversions from egglog primitive sorts such as `i64`, `f64`, and `String` rather than directly from Python builtins like `int`, `float`, and `str`. The builtin promotions already handle those Python values transitively, so keeping the custom converters at the egglog-sort layer makes the promotion path clearer and usually leads to cleaner `...Like` aliases such as `Math | i64Like | f64Like | StringLike`. + If you want to have this work with the static type checker, you can define your own `Union` type, which MUST include the `Expr` class as the first item in the union. For example, in this case you could then define: diff --git a/pyproject.toml b/pyproject.toml index 6a8b3017..9fa0fb5b 100644 --- a/pyproject.toml +++ b/pyproject.toml @@ -52,6 +52,12 @@ test = [ "mypy", "syrupy>=5", "egglog[array]", + "pandas", + "altair", + "vl-convert-python", + "jupytext", + "nbclient", + "ipykernel", "opentelemetry-sdk", "opentelemetry-exporter-otlp-proto-http", "pytest-codspeed", @@ -65,8 +71,11 @@ docs = [ "sphinx-autodoc-typehints", "sphinx-gallery", "nbconvert", + "pandas", "matplotlib", "anywidget", + "altair", + "vl-convert-python", "seaborn", "egglog[array]", "line-profiler", @@ -227,6 +236,7 @@ preview = true [tool.ruff.lint.per-file-ignores] # Don't require annotations for tests "python/tests/**" = ["ANN001", "ANN201", "INP001"] +"python/egglog/exp/param_eq/test_*.py" = ["ANN001", "ANN201", "INP001"] "docs/**" = ["I001", "PLW0131"] # Disable these tests instead for now since ruff doesn't support including all method annotations of decorated class @@ -258,7 +268,7 @@ features = ["pyo3/extension-module"] [tool.pytest.ini_options] addopts = ["--import-mode=importlib", "--doctest-modules"] -testpaths = ["python"] +testpaths = ["python/tests", "python/egglog/exp/param_eq"] python_files = ["test_*.py", "test.py"] markers = ["slow: marks tests as slow (deselect with '-m \"not slow\"')"] norecursedirs = ["__snapshots__"] diff --git a/python/egglog/bindings.pyi b/python/egglog/bindings.pyi index 6c05af47..8d48cd03 100644 --- a/python/egglog/bindings.pyi +++ b/python/egglog/bindings.pyi @@ -175,6 +175,7 @@ class Value: def __gt__(self, other: object) -> bool: ... def __ge__(self, other: object) -> bool: ... +@final @final class EggSmolError(Exception): context: str @@ -515,6 +516,7 @@ class Function: class RunReport: iterations: list[IterationReport] updated: bool + can_stop: bool search_and_apply_time_per_rule: dict[str, timedelta] num_matches_per_rule: dict[str, int] search_and_apply_time_per_ruleset: dict[str, timedelta] @@ -525,6 +527,7 @@ class RunReport: cls, iterations: list[IterationReport], updated: bool, + can_stop: bool, search_and_apply_time_per_rule: dict[str, timedelta], num_matches_per_rule: dict[str, int], search_and_apply_time_per_ruleset: dict[str, timedelta], diff --git a/python/egglog/builtins.py b/python/egglog/builtins.py index 5f11934b..1138a496 100644 --- a/python/egglog/builtins.py +++ b/python/egglog/builtins.py @@ -366,6 +366,15 @@ def __rmod__(self, other: f64Like) -> f64: ... @method(egg_fn="abs") def __abs__(self) -> f64: ... + @method(egg_fn="exp") + def exp(self) -> f64: ... + + @method(egg_fn="log") + def log(self) -> f64: ... + + @method(egg_fn="sqrt") + def sqrt(self) -> f64: ... + @method(egg_fn="<") def __lt__(self, other: f64Like) -> Unit: # type: ignore[has-type] ... diff --git a/python/egglog/declarations.py b/python/egglog/declarations.py index 9a5d08e2..62b6e7a1 100644 --- a/python/egglog/declarations.py +++ b/python/egglog/declarations.py @@ -1065,6 +1065,8 @@ class BackOffDecl: id: UUID match_limit: int | None ban_length: int | None + fresh_rematch: bool = False + persistent: bool = False ## diff --git a/python/egglog/egraph.py b/python/egglog/egraph.py index 8fc6643b..ca9c4ed7 100644 --- a/python/egglog/egraph.py +++ b/python/egglog/egraph.py @@ -6,7 +6,7 @@ import tempfile from collections.abc import Callable, Generator, Iterable from contextvars import ContextVar, Token -from dataclasses import InitVar, dataclass, field +from dataclasses import InitVar, dataclass, field, replace from functools import partial from inspect import Parameter, currentframe, getmodule, signature from types import FrameType, FunctionType @@ -2063,7 +2063,9 @@ def to_runtime_expr(expr: BaseExpr) -> RuntimeExpr: return expr -def run(ruleset: Ruleset | None = None, *until: FactLike, scheduler: BackOff | None = None) -> Schedule: +def run( + ruleset: Ruleset | UnstableCombinedRuleset | None = None, *until: FactLike, scheduler: BackOff | None = None +) -> Schedule: """ Create a run configuration. """ @@ -2078,22 +2080,42 @@ def run(ruleset: Ruleset | None = None, *until: FactLike, scheduler: BackOff | N ) -def back_off(match_limit: None | int = None, ban_length: None | int = None) -> BackOff: +def back_off( + match_limit: None | int = None, + ban_length: None | int = None, + *, + fresh_rematch: bool = False, +) -> BackOff: """ Create a backoff scheduler configuration. ```python schedule = run(analysis_ruleset).saturate() + run(ruleset, scheduler=back_off(match_limit=1000, ban_length=5)) * 10 ``` - This will run the `analysis_ruleset` until saturation, then run `ruleset` 10 times, using a backoff scheduler. - """ - return BackOff(BackOffDecl(id=uuid4(), match_limit=match_limit, ban_length=ban_length)) + This will run the `analysis_ruleset` until saturation, then run `ruleset` 10 times, + using a backoff scheduler. Set `fresh_rematch=True` to use the fresh-rematch variant + that is closer to `egg`/`hegg`; the default keeps egglog's backlog behavior. + """ + return BackOff( + BackOffDecl( + id=uuid4(), + match_limit=match_limit, + ban_length=ban_length, + fresh_rematch=fresh_rematch, + ) + ) @dataclass(frozen=True) class BackOff: scheduler: BackOffDecl + def persistent(self) -> BackOff: + """ + Reuse this scheduler across repeated runs on the same egraph. + """ + return BackOff(replace(self.scheduler, persistent=True)) + def scope(self, schedule: Schedule) -> Schedule: """ Defines the scheduler to be created directly before the inner schedule, instead of the default which is at the diff --git a/python/egglog/egraph_state.py b/python/egglog/egraph_state.py index 1d65aeff..759466d6 100644 --- a/python/egglog/egraph_state.py +++ b/python/egglog/egraph_state.py @@ -30,6 +30,10 @@ _TRACER = trace.get_tracer(__name__) +def _normalize_global_let_name(name: str) -> str: + return name if name.startswith("$") else f"${name}" + + def span(frame_index: int = 0) -> bindings.RustSpan: """ Returns a span for the current file and line. @@ -44,10 +48,6 @@ def span(frame_index: int = 0) -> bindings.RustSpan: return bindings.RustSpan("", 0, 0) -def _normalize_global_let_name(name: str) -> str: - return name if name.startswith("$") else f"${name}" - - @dataclass class EGraphState: """ @@ -107,6 +107,14 @@ def copy(self) -> EGraphState: def _run_program(self, *commands: bindings._Command) -> list[bindings._CommandOutput]: return call_with_current_trace(self.egraph.run_program, *commands) + @staticmethod + def _persistent_scheduler_name(scheduler: BackOffDecl) -> str: + return f"_persistent_scheduler_{scheduler.id.hex}" + + @staticmethod + def _local_scheduler_name(index: int) -> str: + return f"_scheduler_{index}" + @_TRACER.start_as_current_span("run_schedule_to_egg") def run_schedule_to_egg(self, schedule: ScheduleDecl) -> bindings._Command: """ @@ -115,9 +123,11 @@ def run_schedule_to_egg(self, schedule: ScheduleDecl) -> bindings._Command: If there exists any custom schedulers in the schedule, it will be turned into a custom extract command otherwise will be a normal run command. """ - processed_schedule = self._process_schedule(schedule) + processed_schedule, persistent_schedulers = self._process_schedule(schedule) if processed_schedule is None: return bindings.RunSchedule(self._schedule_to_egg(schedule)) + for scheduler in persistent_schedulers: + self._run_program(self._persistent_scheduler_to_egg(scheduler)) top_level_schedules = self._schedule_with_scheduler_to_egg(processed_schedule, []) if len(top_level_schedules) == 1: schedule_expr = top_level_schedules[0] @@ -125,7 +135,7 @@ def run_schedule_to_egg(self, schedule: ScheduleDecl) -> bindings._Command: schedule_expr = bindings.Call(span(), "seq", top_level_schedules) return bindings.UserDefined(span(), "run-schedule", [schedule_expr]) - def _process_schedule(self, schedule: ScheduleDecl) -> ScheduleDecl | None: + def _process_schedule(self, schedule: ScheduleDecl) -> tuple[ScheduleDecl | None, tuple[BackOffDecl, ...]]: """ Processes a schedule to determine if it contains any custom schedulers. @@ -134,18 +144,22 @@ def _process_schedule(self, schedule: ScheduleDecl) -> ScheduleDecl | None: Also processes all rulesets in the schedule to make sure they are registered. """ - bound_schedulers: list[UUID] = [] + bound_schedulers: list[BackOffDecl] = [] unbound_schedulers: list[BackOffDecl] = [] + persistent_schedulers: dict[UUID, BackOffDecl] = {} def helper(s: ScheduleDecl) -> None: match s: case LetSchedulerDecl(scheduler, inner): - bound_schedulers.append(scheduler.id) + bound_schedulers.append(scheduler) return helper(inner) case RunDecl(ruleset_name, _, scheduler): self.ruleset_to_egg(ruleset_name) - if scheduler and scheduler.id not in bound_schedulers: - unbound_schedulers.append(scheduler) + if scheduler and scheduler.id not in {s.id for s in bound_schedulers}: + if scheduler.persistent: + persistent_schedulers[scheduler.id] = scheduler + else: + unbound_schedulers.append(scheduler) case SaturateDecl(inner) | RepeatDecl(inner, _): return helper(inner) case SequenceDecl(schedules): @@ -156,11 +170,11 @@ def helper(s: ScheduleDecl) -> None: return None helper(schedule) - if not bound_schedulers and not unbound_schedulers: - return None + if not bound_schedulers and not unbound_schedulers and not persistent_schedulers: + return None, () for scheduler in unbound_schedulers: schedule = LetSchedulerDecl(scheduler, schedule) - return schedule + return schedule, tuple(persistent_schedulers.values()) def _schedule_to_egg(self, schedule: ScheduleDecl) -> bindings._Schedule: msg = "Should never reach this, let schedulers should be handled by custom scheduler" @@ -184,7 +198,7 @@ def _schedule_to_egg(self, schedule: ScheduleDecl) -> bindings._Schedule: assert_never(schedule) def _schedule_with_scheduler_to_egg( # noqa: C901, PLR0912 - self, schedule: ScheduleDecl, bound_schedulers: list[UUID] + self, schedule: ScheduleDecl, bound_schedulers: list[BackOffDecl] ) -> list[bindings._Expr]: """ Turns a scheduler into an egg expression, to be used with a custom extract command. @@ -192,9 +206,12 @@ def _schedule_with_scheduler_to_egg( # noqa: C901, PLR0912 The bound_schedulers is a list of all the schedulers that have been bound. We can lookup their name as `_scheduler_{index}`. """ match schedule: - case LetSchedulerDecl(BackOffDecl(id, match_limit, ban_length), inner): - name = f"_scheduler_{len(bound_schedulers)}" - bound_schedulers.append(id) + case LetSchedulerDecl(scheduler, inner): + match_limit = scheduler.match_limit + ban_length = scheduler.ban_length + fresh_rematch = scheduler.fresh_rematch + name = self._local_scheduler_name(len(bound_schedulers)) + bound_schedulers.append(scheduler) args: list[bindings._Expr] = [] if match_limit is not None: args.append(bindings.Var(span(), ":match-limit")) @@ -202,14 +219,19 @@ def _schedule_with_scheduler_to_egg( # noqa: C901, PLR0912 if ban_length is not None: args.append(bindings.Var(span(), ":ban-length")) args.append(bindings.Lit(span(), bindings.Int(ban_length))) - back_off_decl = bindings.Call(span(), "back-off", args) + scheduler_name = "back-off-fresh" if fresh_rematch else "back-off" + back_off_decl = bindings.Call(span(), scheduler_name, args) let_decl = bindings.Call(span(), "let-scheduler", [bindings.Var(span(), name), back_off_decl]) return [let_decl, *self._schedule_with_scheduler_to_egg(inner, bound_schedulers)] case RunDecl(ruleset_ident, until, scheduler): args = [bindings.Var(span(), str(ruleset_ident))] if scheduler: name = "run-with" - scheduler_name = f"_scheduler_{bound_schedulers.index(scheduler.id)}" + scheduler_name = self._persistent_scheduler_name(scheduler) + for i, bound in enumerate(bound_schedulers): + if bound.id == scheduler.id: + scheduler_name = self._local_scheduler_name(i) + break args.insert(0, bindings.Var(span(), scheduler_name)) else: name = "run" @@ -225,9 +247,8 @@ def _schedule_with_scheduler_to_egg( # noqa: C901, PLR0912 args.append(fact_egg.expr) return [bindings.Call(span(), name, args)] case SaturateDecl(inner): - return [ - bindings.Call(span(), "saturate", self._schedule_with_scheduler_to_egg(inner, bound_schedulers)) - ] + args = self._schedule_with_scheduler_to_egg(inner, bound_schedulers) + return [bindings.Call(span(), "saturate", args)] case RepeatDecl(inner, times): return [ bindings.Call( @@ -247,6 +268,22 @@ def _schedule_with_scheduler_to_egg( # noqa: C901, PLR0912 case _: assert_never(schedule) + def _persistent_scheduler_to_egg(self, scheduler: BackOffDecl) -> bindings._Command: + args: list[bindings._Expr] = [] + if scheduler.match_limit is not None: + args.append(bindings.Var(span(), ":match-limit")) + args.append(bindings.Lit(span(), bindings.Int(scheduler.match_limit))) + if scheduler.ban_length is not None: + args.append(bindings.Var(span(), ":ban-length")) + args.append(bindings.Lit(span(), bindings.Int(scheduler.ban_length))) + scheduler_name = "back-off-fresh" if scheduler.fresh_rematch else "back-off" + back_off_decl = bindings.Call(span(), scheduler_name, args) + return bindings.UserDefined( + span(), + "let-scheduler", + [bindings.Var(span(), self._persistent_scheduler_name(scheduler)), back_off_decl], + ) + def ruleset_to_egg(self, ident: Ident) -> None: """ Registers a ruleset if it's not already registered. diff --git a/python/egglog/exp/param_eq/Makefile b/python/egglog/exp/param_eq/Makefile new file mode 100644 index 00000000..f60fcb93 --- /dev/null +++ b/python/egglog/exp/param_eq/Makefile @@ -0,0 +1,66 @@ +# Canonical local workflow for the retained param-eq replication package. +# The file dependencies document the expected order: +# 1. normalize archived Haskell outputs +# 2. run the current local Haskell pipeline across the same rows +# 3. run the retained Egglog corpus baseline against those rows +# 4. refresh the golden cases and notebook +# 5. run the replication-local tests + +PARAM_EQ_DIR := $(abspath $(dir $(lastword $(MAKEFILE_LIST)))) +REPO_ROOT := $(abspath $(PARAM_EQ_DIR)/../../../..) +EGGLOG_PARAM_EQ_DATA_DIR ?= $(REPO_ROOT)/../param-eq-haskell +export EGGLOG_PARAM_EQ_DATA_DIR + +ARTIFACT_DIR := $(PARAM_EQ_DIR)/artifacts +GOLDEN := $(PARAM_EQ_DIR)/haskell_golden.json +NOTEBOOK := $(PARAM_EQ_DIR)/replication.ipynb +ARCHIVED_HASKELL_ROWS := $(ARTIFACT_DIR)/haskell_paper_rows.csv +LIVE_HASKELL_ROWS := $(ARTIFACT_DIR)/haskell_live_rows.csv +ARCHIVED_RUNTIME_ROWS := $(ARTIFACT_DIR)/pagie_runtime_scatter.csv +RUNTIME_COMPARE_ROWS := $(ARTIFACT_DIR)/pagie_runtime_compare.csv +EGGLOG_ROWS := $(ARTIFACT_DIR)/egglog_paper_rows.csv +HASKELL_FIXTREE := $(EGGLOG_PARAM_EQ_DATA_DIR)/src/FixTree.hs +HASKELL_MAIN := $(EGGLOG_PARAM_EQ_DATA_DIR)/src/Main.hs +HASKELL_RESULTS := $(EGGLOG_PARAM_EQ_DATA_DIR)/results +HASKELL_RUNTIME := $(EGGLOG_PARAM_EQ_DATA_DIR)/runtimes +HASKELL_TABLES := \ + $(HASKELL_RESULTS)/pagie_table_counts.csv \ + $(HASKELL_RESULTS)/kotanchek_table_counts.csv +HASKELL_EXPRS := \ + $(wildcard $(HASKELL_RESULTS)/exprs/*_exprs_*) \ + $(wildcard $(HASKELL_RESULTS)/exprs_simpl/*_exprs_*) + +.PHONY: golden archived-artifacts live-haskell artifacts notebook test all + +$(ARCHIVED_HASKELL_ROWS) $(ARCHIVED_RUNTIME_ROWS): $(PARAM_EQ_DIR)/normalize_archives.py $(PARAM_EQ_DIR)/paths.py $(HASKELL_TABLES) $(HASKELL_EXPRS) $(HASKELL_RUNTIME) + cd $(REPO_ROOT) && uv run python -m egglog.exp.param_eq.normalize_archives + +$(RUNTIME_COMPARE_ROWS): $(PARAM_EQ_DIR)/run_runtime_compare.py $(PARAM_EQ_DIR)/run_egglog_corpus.py $(ARCHIVED_RUNTIME_ROWS) $(HASKELL_MAIN) $(HASKELL_FIXTREE) + cd $(REPO_ROOT) && uv run python -m egglog.exp.param_eq.run_runtime_compare + +$(LIVE_HASKELL_ROWS): $(PARAM_EQ_DIR)/run_haskell_corpus.py $(PARAM_EQ_DIR)/generate_haskell_golden.py $(PARAM_EQ_DIR)/pipeline.py $(PARAM_EQ_DIR)/paths.py $(ARCHIVED_HASKELL_ROWS) $(HASKELL_FIXTREE) $(HASKELL_MAIN) + cd $(REPO_ROOT) && uv run python -m egglog.exp.param_eq.run_haskell_corpus + +$(EGGLOG_ROWS): $(PARAM_EQ_DIR)/run_egglog_corpus.py $(PARAM_EQ_DIR)/pipeline.py $(ARCHIVED_HASKELL_ROWS) $(ARCHIVED_RUNTIME_ROWS) + cd $(REPO_ROOT) && uv run python -m egglog.exp.param_eq.run_egglog_corpus + +$(GOLDEN): $(PARAM_EQ_DIR)/generate_haskell_golden.py $(PARAM_EQ_DIR)/pipeline.py $(PARAM_EQ_DIR)/paths.py $(HASKELL_FIXTREE) $(HASKELL_MAIN) $(ARCHIVED_HASKELL_ROWS) + cd $(REPO_ROOT) && uv run python -m egglog.exp.param_eq.generate_haskell_golden + +$(NOTEBOOK): $(PARAM_EQ_DIR)/replication.py $(ARCHIVED_HASKELL_ROWS) $(LIVE_HASKELL_ROWS) $(EGGLOG_ROWS) $(RUNTIME_COMPARE_ROWS) + cd $(REPO_ROOT) && uv run python python/egglog/exp/param_eq/replication.py + +archived-artifacts: $(ARCHIVED_HASKELL_ROWS) $(ARCHIVED_RUNTIME_ROWS) + +live-haskell: $(LIVE_HASKELL_ROWS) + +golden: $(GOLDEN) + +artifacts: $(ARCHIVED_HASKELL_ROWS) $(ARCHIVED_RUNTIME_ROWS) $(LIVE_HASKELL_ROWS) $(EGGLOG_ROWS) $(RUNTIME_COMPARE_ROWS) + +notebook: $(NOTEBOOK) + +test: $(GOLDEN) $(EGGLOG_ROWS) $(NOTEBOOK) + cd $(REPO_ROOT) && uv run pytest python/egglog/exp/param_eq/test_pipeline.py python/egglog/exp/param_eq/test_replication_notebook.py -q + +all: test diff --git a/python/egglog/exp/param_eq/README.md b/python/egglog/exp/param_eq/README.md new file mode 100644 index 00000000..758c7557 --- /dev/null +++ b/python/egglog/exp/param_eq/README.md @@ -0,0 +1,206 @@ +# Param-Eq Replication + +This directory is the canonical retained `param_eq` package for the symbolic +regression simplification replication. + +It keeps one baseline: + +- archived Haskell paper rows as the published reference +- live Haskell reruns as the primary behavioral baseline +- Egglog as the retained replication implementation + +The notebook and checked-in artifacts are meant to answer one practical +question: + +- do archived Haskell, live Haskell, and Egglog support the same qualitative + conclusions on the retained paper metrics? + +## What This Package Contains + +### Source files + +- [pipeline.py](pipeline.py) + - the retained Egglog translation of the simplification pipeline +- [run_haskell_corpus.py](run_haskell_corpus.py) + - reruns the local Haskell implementation across the retained corpus rows +- [run_egglog_corpus.py](run_egglog_corpus.py) + - runs the retained Egglog baseline across the same rows +- [normalize_archives.py](normalize_archives.py) + - converts the archived Haskell paper outputs into the checked-in CSV + artifacts used by the notebook +- [generate_haskell_golden.py](generate_haskell_golden.py) + - regenerates the reduced Haskell-backed golden cases used in tests +- [replication.py](replication.py) + - jupytext notebook source for the thesis/check notebook +- [paths.py](paths.py) + - shared local path helpers for this package +- [__main__.py](__main__.py) + - one-off CLI entrypoint for simplifying a single expression + +### Tests + +- [test_pipeline.py](test_pipeline.py) + - replication-local behavioral tests for the retained baseline +- [test_replication_notebook.py](test_replication_notebook.py) + - smoke test that the notebook source runs and writes an executed notebook + +### Checked-in artifacts + +- [artifacts/haskell_paper_rows.csv](artifacts/haskell_paper_rows.csv) + - archived paper-era Haskell results for the retained rows +- [artifacts/haskell_live_rows.csv](artifacts/haskell_live_rows.csv) + - current local Haskell rerun on the same retained rows +- [artifacts/egglog_paper_rows.csv](artifacts/egglog_paper_rows.csv) + - current Egglog results on the same retained rows +- [artifacts/pagie_runtime_scatter.csv](artifacts/pagie_runtime_scatter.csv) + - archived Haskell Figure 9 benchmark sweep, normalized from the original + Criterion output +- [artifacts/pagie_runtime_compare.csv](artifacts/pagie_runtime_compare.csv) + - apples-to-apples Pagie runtime sweep used by the notebook for archived + Haskell, live Haskell, and Egglog +- [haskell_golden.json](haskell_golden.json) + - reduced Haskell-backed golden cases used by + [test_pipeline.py](test_pipeline.py) +- [replication.ipynb](replication.ipynb) + - executed notebook artifact generated from [replication.py](replication.py) + +## Problem And Data Overview + +This replication is about simplifying formulas that were already produced by +symbolic-regression systems. It is not about training or rerunning those +regressors. + +The retained benchmark families are: + +- `Pagie` +- `Kotanchek` + +The formulas in those datasets were originally produced by several older +symbolic-regression systems: + +- `Bingo` +- `EPLEX` +- `GOMEA` +- `Operon` +- `SBP` +- `SRjl` + +In the notebook displays, those names are normalized to the paper-facing +labels: + +- `GOMEA -> GP-GOMEA` +- `SRjl -> PySR` + +Useful columns in the row artifacts: + +- `original_expr` + - archived benchmark formula for the row +- `sympy_expr` + - archived Sympy-normalized variant of that formula +- `orig_params` + - parameter count before simplification +- `simpl_params` + - parameter count after simplification +- `n_rank` + - the paper's rank target for the row +- `dataset`, `algorithm`, `algo_row` + - stable identifiers for matching the same row across artifacts + +## Artifact Roles + +The three main row artifacts serve different purposes: + +- [artifacts/haskell_paper_rows.csv](artifacts/haskell_paper_rows.csv) + - the published paper reference +- [artifacts/haskell_live_rows.csv](artifacts/haskell_live_rows.csv) + - the current local Haskell behavior +- [artifacts/egglog_paper_rows.csv](artifacts/egglog_paper_rows.csv) + - the current Egglog behavior + +The notebook compares all three side by side. In practice: + +- archived Haskell is the published reference +- live Haskell is the primary comparison target for current behavior +- Egglog is the retained replication being evaluated + +## Where To Find The Formulas + +For the exact formulas used by the notebook and corpus runners, start with the +checked-in row artifacts: + +- [artifacts/haskell_paper_rows.csv](artifacts/haskell_paper_rows.csv) +- [artifacts/haskell_live_rows.csv](artifacts/haskell_live_rows.csv) +- [artifacts/egglog_paper_rows.csv](artifacts/egglog_paper_rows.csv) + +For the raw Haskell-side inputs and expression dumps, look in the sibling +`param-eq-haskell` checkout: + +- `../param-eq-haskell/results/exprs/` +- `../param-eq-haskell/results/exprs_simpl/` +- `../param-eq-haskell/results/dataset/Pagie.csv` +- `../param-eq-haskell/results/dataset/Kotanchek.csv` + +## Workflow + +The local [Makefile](Makefile) is the canonical entrypoint for this package: + +```bash +cd python/egglog/exp/param_eq +make all +``` + +Useful targets: + +- `make archived-artifacts` + - regenerate the normalized archived paper artifacts +- `make live-haskell` + - regenerate [artifacts/haskell_live_rows.csv](artifacts/haskell_live_rows.csv) +- `make golden` + - regenerate [haskell_golden.json](haskell_golden.json) +- `make artifacts` + - regenerate all checked-in CSV artifacts +- `make notebook` + - execute [replication.py](replication.py) and refresh + [replication.ipynb](replication.ipynb) +- `make test` + - run the replication-local pytest targets + +One-off CLI use: + +```bash +uv run python -m egglog.exp.param_eq --expr='...' +``` + +After local engine changes, rebuild the package with: + +```bash +uv sync --reinstall-package egglog --all-extras +``` + +## Data Root + +By default the live Haskell checkout is expected at the sibling path +`../param-eq-haskell` relative to the `egg-smol-python` repository root. + +Override it with: + +```bash +export EGGLOG_PARAM_EQ_DATA_DIR=/path/to/param-eq-haskell +``` + +The notebook and tests do not shell out to Haskell during normal execution. +They use the checked-in artifacts in [artifacts/](artifacts/) and +[haskell_golden.json](haskell_golden.json). + +## Notebook Scope + +The notebook in [replication.ipynb](replication.ipynb) is comparison-first. + +Its job is to show, using the same plots and the same table layouts, that: + +- archived Haskell, live Haskell, and Egglog can be compared directly from one + shared data pipeline +- the three result sets support similar qualitative conclusions on the retained + paper metrics +- the remaining archive drift is modest but should still be reported + explicitly, rather than silently folded into Egglog-vs-Haskell comparisons diff --git a/python/egglog/exp/param_eq/__init__.py b/python/egglog/exp/param_eq/__init__.py new file mode 100644 index 00000000..10d90f73 --- /dev/null +++ b/python/egglog/exp/param_eq/__init__.py @@ -0,0 +1 @@ +"""Retained param-eq paper-replication baseline for egglog Python.""" diff --git a/python/egglog/exp/param_eq/__main__.py b/python/egglog/exp/param_eq/__main__.py new file mode 100644 index 00000000..cf400b31 --- /dev/null +++ b/python/egglog/exp/param_eq/__main__.py @@ -0,0 +1,8 @@ +"""Run the retained param-eq replication CLI as ``python -m egglog.exp.param_eq``.""" + +from __future__ import annotations + +from .pipeline import _cli + +if __name__ == "__main__": + _cli() diff --git a/python/egglog/exp/param_eq/__new_plan.md b/python/egglog/exp/param_eq/__new_plan.md new file mode 100644 index 00000000..227b5657 --- /dev/null +++ b/python/egglog/exp/param_eq/__new_plan.md @@ -0,0 +1,58 @@ +pre: + +use a local folder path for experimental and egglog +so we can modify them easier. + +use `uv sync --reinstall-package egglog --all-extras` to update based on egglog experimental + +rename egg_like to fresh_rematch or something + +try removing haskell backoff and compensating by decreasing backoff size? + +use sum of all_function_sizes instead of serialized sum of counts for performance? + +perm scheduler add to egglog experimental, return new ExperminetalEgraph struct so we can store extra data like perminent schedulers. Make all of them perm by default. +expose in Python by default, by adding a top level scope somehow, +like `.global()` or something...? that way we dont need a custom scheduler in egglog +python. + +Remove `stop-when-no-updates` in experimental that we added... since dont use it anymore + + +replace `is_const(a, ca)` with `is_const(a)` where `ca` + is generated as a new var like `_ca` inside the function since it isn't referenced elsewhere. + +once all that is done if things still work, we are ready to package the repo up +to a stable place. So remove all extra code for checking different versions, review +the code as a whole and make any simplifications/remove dead code. We are done trying to fix the schedules and rules to match baseline, we now want a clean part to build off of for multisets, with the replication notebook just showing that we hit +the baseline basically. + +--- + +Overall goal: See how replacing binary ops with containers +can get us closer to saturation or at least decrease the number +of nodes and reduce need for backoff which is not complete. + + + +We want to remove +, -, /, *, and replace with `polynomial(Map[Map[Expr, i64], i64])`. Input into the e-graph with that and after extract out in that form. + + +First, we want to make a plan by going through and leaving a comment next to each rewrite to see how it would change under the new plan. We can imagine we have any functional operations over +maps that we want at this time, and then once we settle on our design, we can go and actually add those. + +Many rewrites will be simply deleted, like `a*b -> b*a`, and many others can be collapsed into one, like + +``` + yield rewrite((x / a) + (y / b)).to( + (x + (y / (b * a))) / a, + *is_const(a, ca), + *is_const(b, cb), + *is_not_const(x), + *is_not_const(y), + ) +``` + +is just a directed rewrite so that if we have a constant term in one of the monomials, we try factoring it out. + +Stop after adding comments before each rule so I can manually inspect and see what makes sense before trying to implement it. diff --git a/python/egglog/exp/param_eq/artifacts/egglog_paper_rows.csv b/python/egglog/exp/param_eq/artifacts/egglog_paper_rows.csv new file mode 100644 index 00000000..eec96c7b --- /dev/null +++ b/python/egglog/exp/param_eq/artifacts/egglog_paper_rows.csv @@ -0,0 +1,342 @@ +dataset,raw_index,algorithm_raw,algorithm,algo_row,is_paper_row,drop_reason,n_params,n_rank,original_expr,sympy_expr,orig_status,orig_runtime_ms,orig_nodes,orig_params,simpl_nodes,simpl_params,orig_total_size,orig_egraph_nodes,orig_eclass_count,orig_passes,orig_extracted_cost,orig_rendered,sympy_status,sympy_runtime_ms,orig_nodes_sympy,orig_params_sympy,simpl_nodes_sympy,simpl_params_sympy,sympy_total_size,sympy_egraph_nodes,sympy_eclass_count,sympy_passes,sympy_extracted_cost,sympy_rendered +pagie,3,Bingo,Bingo,4,1,kept,9.0,6.0,(321.50462762611204)*((((-2588.281378882496)^(-1))*((x0)*(x1)) + plog((3323.2144588507704)*((x0)*(x1))) - (3.834139037636267))*(((((-2588.281378882496)^(-1))*((x0)*(x1)) + plog((3323.2144588507704)*((x0)*(x1))) - (-2588.281378882496 + 3.834139037636267 + plog(-2588.281378882496)))^(-1))*(plog(plog((3323.2144588507704)*((x0)*(x1))))))),321.50462762611204*(0.0003863567570971573*x0*x1 - log(x0*x1) - 4.2745487663580279)*log(log(x0*x1) + 8.1086878039942949)/(0.0003863567570971573*x0*x1 - log(x0*x1) - 2584.6971782746911 + I*pi),saturated,357.475625,55,10,41,6,197,208,70,2,86,(321.50462762611204 * (((4.274548766358028 + (-0.00038635675709715734 * (x0 * x1))) + log(abs((x0 * x1)))) * ((((2584.697178274691 + (-0.00038635675709715734 * (x0 * x1))) + log(abs((x0 * x1)))) ** -1.0) * log(abs((8.108687803994295 + log(abs((x0 * x1))))))))),saturated,250.124167,39,6,39,6,136,148,58,1,81,(((321.50462762611204 * ((((0.0003863567570971573 * x0) * x1) - log((x0 * x1))) - 4.274548766358028)) * log((log((x0 * x1)) + 8.108687803994295))) / (((((0.0003863567570971573 * x0) * x1) - log((x0 * x1))) - 2584.697178274691) + (I * pi))) +pagie,1,Bingo,Bingo,2,1,kept,4.0,4.0,0.04547093390683249 + (0.17516554602688977)*(plog((34.093055726490284)*((x0)*(x0)) + x1 + (-428.9738000218307)*(((x0)*(x0))*((x1)*(x1))))),0.17516554602688977*log(-428.9738000218307*x0**2*x1**2 + 34.093055726490284*x0**2 + x1) + 0.04547093390683249,saturated,342.399583,23,4,19,4,95,103,41,2,44,(0.04547093390683249 + (0.17516554602688977 * log(abs((((x0 * x0) * (34.093055726490284 + (-428.9738000218307 * (x1 * x1)))) + x1))))),saturated,281.876459,22,4,18,4,70,79,39,2,51,((0.17516554602688977 * log((((x0 ** 2.0) * (((x1 ** 2.0) * -428.9738000218307) + 34.093055726490284)) + x1))) + 0.04547093390683249) +pagie,0,Bingo,Bingo,1,1,kept,6.0,4.0,0.5240322255066139 + (-0.45351118068033663)*(plog(-54.93119319072758 + (755.3723998652232)*((plog((-2)*((x0)*((x1)^(-1))) + (-66438756992.645454)*((x0)*(x1))))^(-1)) + plog((-2)*((x0)*((x1)^(-1))) + (-66438756992.645454)*((x0)*(x1))))),0.52403222550661389 - 0.45351118068033663*log(log(-x0*(66438756992.645454*x1 + 2/x1)) - 54.93119319072758 + 755.3723998652232/log(-x0*(66438756992.645454*x1 + 2/x1))),saturated,364.997125,43,8,37,7,191,208,87,2,93,(0.5240322255066139 + (-0.45351118068033663 * log(abs(((-54.238046010167636 + log(abs((x0 * ((x1 ** -1.0) + (33219378496.322727 * x1)))))) + (755.3723998652232 * ((log(abs((x0 * ((x1 ** -1.0) + (33219378496.322727 * x1))))) + 0.6931471805599453) ** -1.0))))))),saturated,413.185334,34,10,28,7,92,102,49,2,69,(0.5240322255066139 + (-0.45351118068033663 * log(((-30.011646777931055 + log((((-3.010291117007793e-11 / x1) - x1) * x0))) + (755.3723998652232 / log((-66438756992.645454 * (x0 * (x1 + (3.010291117007793e-11 / x1)))))))))) +pagie,4,Bingo,Bingo,5,1,kept,3.0,3.0,-0.7617093798419142 + (0.3424256684358176)*(plog((x1)*((249.92555522398015)*(x0) + ((x1)^(-2))*(plog(x0)) - (x0 + x1)))),0.3424256684358176*log((x1**2*(248.92555522398015*x0 - x1) + log(x0))/x1) - 0.7617093798419142,saturated,238.088541,23,3,23,3,70,77,38,1,49,(-0.7617093798419142 + (0.3424256684358176 * log(abs((x1 * (((249.92555522398015 * x0) + ((x1 ** -2.0) * log(abs(x0)))) - (x0 + x1))))))),saturated,268.909167,19,3,19,3,61,71,40,1,44,((0.3424256684358176 * log(((((x1 ** 2.0) * ((248.92555522398015 * x0) - x1)) + log(x0)) / x1))) - 0.7617093798419142) +pagie,6,Bingo,Bingo,7,1,kept,6.0,4.0,(0.33963694568414915)*(plog((-35.167844692926785)*(((-1)*(((2)^(-1))*((1.1727867299483856)^(-1))))*((x0)*((58.20319882282552 + x0)*(x1))) + plog(x1)))) - (1.1727867299483856),0.33963694568414915*log(14.993282152192549*x0*x1*(x0 + 58.20319882282552) - 35.167844692926785*log(x1)) - 1.1727867299483856,saturated,289.170917,29,7,19,4,98,104,36,2,43,(0.33963694568414915 * (0.10707222600206379 + log(abs(((-0.42633497398286985 * (x0 * ((58.20319882282552 + x0) * x1))) + log(abs(x1))))))),saturated,276.775708,19,5,17,4,62,70,35,2,41,(0.33963694568414915 * (-0.7454576917979261 + log(((((x0 + 58.20319882282552) * x1) * x0) + (-2.3455734598967712 * log(x1)))))) +pagie,7,Bingo,Bingo,8,1,kept,5.0,5.0,(0.3219453819768659)*(4.881341193040894 + (0.006998797255225593)*(x0) + (-3.3010592991000216)*(exp((-0.7560873364652252)*((x0)*(x0)))) + plog(x1)),0.002253230455712244*x0 + 0.3219453819768659*log(x1) + 1.571525254952961 - 1.0627607969770417*exp(-0.7560873364652252*x0**2),saturated,269.242458,20,5,20,5,104,114,50,2,49,(0.3219453819768659 * (((0.006998797255225593 * (x0 + 697.4542932210649)) + (-3.3010592991000216 * exp((-0.7560873364652252 * (x0 * x0))))) + log(abs(x1)))),saturated,315.563708,19,5,19,5,762,790,203,1,52,((((0.002253230455712244 * x0) + (0.3219453819768659 * log(x1))) + 1.571525254952961) - (1.0627607969770416 * exp((-0.7560873364652252 * (x0 ** 2.0))))) +pagie,5,Bingo,Bingo,6,1,kept,8.0,5.0,0.2033733319566922 + (0.0885895005060784)*(plog(((520439.72713022487)*(((x0)*(x0))*((28890.10432966032 + x0)^(-1))) + (-165.43872587343168)*(((x0)*(x0))*((x1)*(x1))) - (x1))*((520439.72713022487)*(((x0)*(x0))*((28890.10432966032 + x0)^(-1))) + (-165.43872587343168)*(((x0)*(x0))*((x1)*(x1))) - (x1)))),0.0885895005060784*log((-x0**2 + x1*(x0 + 28890.10432966032)*(0.00031788258514714704*x0**2*x1 + 1.9214520872842191e-6))**2/(3.461392830531733e-5*x0 + 1)**2) + 0.71562882269299686,saturated,337.813709,53,8,45,8,158,169,63,2,107,(0.2033733319566922 + (0.0885895005060784 * log(abs(((((x0 * x0) * ((520439.72713022487 * ((28890.10432966032 + x0) ** -1.0)) + (-165.43872587343168 * (x1 * x1)))) - x1) * (((x0 * x0) * ((520439.72713022487 * ((28890.10432966032 + x0) ** -1.0)) + (-165.43872587343168 * (x1 * x1)))) - x1)))))),saturated,798.467417,36,8,34,7,154,167,66,2,95,((0.0885895005060784 * log((((((x1 * (x0 + 28890.10432966032)) * (((0.00031788258514714706 * (x0 ** 2.0)) * x1) + 1.921452087284219e-06)) - (x0 ** 2.0)) ** 2.0) / (((3.461392830531733e-05 * x0) + 1.0) ** 2.0)))) + 0.7156288226929969) +pagie,8,Bingo,Bingo,9,1,kept,7.0,5.0,(-0.0016845463969705932)*((plog(x1 + (-5504.7494866201905)*((x0)*(x1))))*(35.98329321843688 + (-0.17812022427202742)*(35.98329321843688 + x0) + (-12.262360262937122)*(plog(x1 + (-5504.7494866201905)*((x0)*(x1)))))),(0.00030005178202503779*x0 + 0.020656514799286105*log(x1*(1 - 5504.7494866201905*x0)) - 0.049818675688932783)*log(x1*(1 - 5504.7494866201905*x0)),saturated,290.009917,31,7,27,5,65,71,31,2,59,((0.020656514799286103 * (log(abs((x1 + (-5504.7494866201905 * (x0 * x1))))) + (0.014525769953961822 * (-166.03359377740895 + x0)))) * log(abs((x1 + (-5504.7494866201905 * (x0 * x1)))))),saturated,319.691417,25,7,23,6,94,103,45,2,58,((0.020656514799286103 * ((6.2016007537634605 + log((x1 * (0.00018166130946205522 - x0)))) + (0.014525769953961822 * x0))) * log((x1 * (-5504.7494866201905 * (x0 + -0.00018166130946205522))))) +pagie,9,Bingo,Bingo,10,1,kept,5.0,4.0,(-1647.7560776017172)*((plog(x1 + (-5504.7201863492755)*((x0)*(x1))))*(3.021827100299453e-05 + (-1.2535194814297265e-05)*(plog(x1 + (-5504.7201863492755)*((x0)*(x1)))))),(0.020654943439179847*log(x1*(1 - 5504.7201863492755*x0)) - 0.049792339699799975)*log(x1*(1 - 5504.7201863492755*x0)),saturated,335.017042,25,5,23,4,56,61,26,2,49,((0.020654943439179847 * (log(abs((x1 + (-5504.7201863492755 * (x0 * x1))))) + -2.410674221714407)) * log(abs((x1 + (-5504.7201863492755 * (x0 * x1)))))),saturated,396.142750,21,6,19,5,67,74,34,2,48,((0.020654943439179847 * (6.202686997149495 + log((x1 * (0.0001816622764005011 - x0))))) * log((x1 * (-5504.7201863492755 * (x0 + -0.0001816622764005011))))) +pagie,10,Bingo,Bingo,11,1,kept,5.0,5.0,1.1892515725526536 + (-1.529035305818532 + exp(plog((x0)*(x1))))*(0.2778146070096167 + (6.532680622052586e-05)*(x0) + (-0.07902303898937542)*(plog((x0)*(x1)))),(x0*x1 - 1.529035305818532)*(6.532680622052586e-5*x0 - 0.07902303898937542*log(x0*x1) + 0.2778146070096167) + 1.1892515725526536,saturated,356.751542,24,5,22,5,162,175,68,2,52,(1.1892515725526536 + ((-1.529035305818532 + abs((x0 * x1))) * ((0.2778146070096167 + (6.532680622052586e-05 * x0)) + (-0.07902303898937542 * log(abs((x0 * x1))))))),saturated,377.662792,20,5,20,5,158,171,65,2,50,((((x0 * x1) + -1.529035305818532) * (((6.532680622052586e-05 * x0) + (-0.07902303898937542 * log((x0 * x1)))) + 0.2778146070096167)) + 1.1892515725526536) +pagie,11,Bingo,Bingo,12,1,kept,4.0,4.0,(0.32709300308221473)*(plog((2.8938067344221365)*(x0) + (33.37981491587227)*((x0)*(x1)) - (exp(0.32709300308221473)))),0.32709300308221473*log(33.37981491587227*x0*x1 + 2.8938067344221365*x0 - 1.3869304599899063),saturated,407.256041,16,4,13,4,84,96,48,2,35,(0.32709300308221473 * log(abs(((x0 * (33.37981491587227 * (x1 + 0.0866933127614832))) - 1.3869304599899064)))),saturated,344.217834,14,4,12,4,70,81,42,2,34,(0.32709300308221473 * log(((x0 * (33.37981491587227 * (x1 + 0.0866933127614832))) - 1.3869304599899064))) +pagie,12,Bingo,Bingo,13,1,kept,5.0,5.0,0.46055102457050884 + (-11903.1935774518 + ((x0)^(-1))*(exp(x1)))*((-9960.615166624408 + (-8736.856642285593)*((x1)^(-2)) + ((x0)^(-1))*(exp(x1)))^(-1)) + (0.3353899762817782)*(plog(x0)),(11903.1935774518 - exp(x1)/x0)/(9960.615166624408 + 8736.856642285593/x1**2 - exp(x1)/x0) + 0.3353899762817782*log(x0) + 0.46055102457050884,saturated,306.501291,33,5,33,5,83,93,47,2,84,((0.46055102457050884 + ((-11903.1935774518 + ((x0 ** -1.0) * exp(x1))) * (((-8736.856642285593 * ((x1 ** -2.0) + 1.1400685137050246)) + ((x0 ** -1.0) * exp(x1))) ** -1.0))) + (0.3353899762817782 * log(abs(x0)))),saturated,362.999667,26,5,26,5,69,78,41,1,62,((((11903.1935774518 - (exp(x1) / x0)) / ((9960.615166624408 + (8736.856642285593 / (x1 ** 2.0))) - (exp(x1) / x0))) + (0.3353899762817782 * log(x0))) + 0.46055102457050884) +pagie,2,Bingo,Bingo,3,1,kept,5.0,5.0,((plog(1 - ((-4.620613175155346)*(-4.620613175155346))))^(-1))*(plog(1 + ((-0.7045923450774843)^(-1))*((x1)*(x0 + ((-4.620613175155346)*(-4.620613175155346) - (-0.7045923450774843))*(x0) + plog(-0.5941007048060543 + x0))) - (x0))),log(-x0 - 1.419260380823509*x1*(23.05465845949665*x0 + log(x0 - 0.5941007048060543)) + 1)/(3.013084160749133 + I*pi),saturated,304.649417,37,9,23,5,82,90,41,2,53,(0.331885850726245 * log(abs(((1.0 + (-1.4192603808235096 * (x1 * ((x0 + (22.05465845949665 * x0)) + log(abs((-0.5941007048060543 + x0))))))) - x0)))),saturated,3295.653708,25,6,23,5,66,75,38,2,54,(log(((1.0 - x0) + (-1.419260380823509 * (((23.05465845949665 * x0) + log((x0 + -0.5941007048060543))) * x1)))) / (3.013084160749133 + (I * pi))) +pagie,14,Bingo,Bingo,15,1,kept,13.0,6.0,-0.3615909827079473 - ((-0.3615909827079473 + (-0.15940944833036993 + (0.7495558385988832 + (-0.052282035688047096)*((x0)*(x0)))*(0.7495558385988832 + (-0.052282035688047096)*((x0)*(x0))))*(-0.15940944833036993 + (0.7495558385988832 + (-0.052282035688047096)*((x0)*(x0)))*(0.7495558385988832 + (-0.052282035688047096)*((x0)*(x0)))))*(plog((-242.5021661422168)*(x1)))),-(0.3156573931905898*((0.069750688335342645*x0**2 - 1)**2 - 0.28373053437106359)**2 - 0.3615909827079473)*(log(-x1) + 5.491010642882867) - 0.3615909827079473,saturated,874.506625,45,13,39,10,113,125,57,2,98,(-0.3615909827079473 - ((-0.3615909827079473 + (7.471537092712174e-06 * (((((x0 * x0) + -14.336776078714344) * ((x0 * x0) + -14.336776078714344)) + -58.318867312320975) * ((((x0 * x0) + -14.336776078714344) * ((x0 * x0) + -14.336776078714344)) + -58.318867312320975)))) * log((242.5021661422168 * abs(x1))))),saturated,321.240959,28,9,26,8,113,129,65,2,83,(((-5.491010642882867 - log((-1.0 * x1))) * ((0.3156573931905898 * (((((0.06975068833534265 * (x0 ** 2.0)) - 1.0) ** 2.0) - 0.2837305343710636) ** 2.0)) - 0.3615909827079473)) - 0.3615909827079473) +pagie,15,Bingo,Bingo,16,1,kept,8.0,7.0,(-0.0016724665952508537)*(292.42415431458545 + x1 + ((-1)*((-314.9892428270721)^(-1)))*((((x0)^(-1))*((x1)^(-1)))*((39.54832653926522 + x1)*(plog((-314.9892428270721)*((x0)*(x1)))))) + (-240.49898207944213)*(plog((-314.9892428270721)*((x0)*((x1)*((plog((-314.9892428270721)*((x0)*(x1))))^(-1))))))),(x0*x1*(-0.0016724665952508537*x1 + 0.40222651371970066*log(-x0*x1/(log(-x0*x1) + 5.75253848848719)) + 1.8247538715269739) - 5.3095990842107314e-6*(x1 + 39.54832653926522)*(log(-x0*x1) + 5.75253848848719))/(x0*x1),saturated,683.382375,51,9,45,7,533,547,119,2,105,(-0.0016724665952508537 * (((-240.49898207944213 * (4.536632492602386 + log(abs((x0 * (x1 * (log(abs((-314.9892428270721 * (x0 * x1)))) ** -1.0))))))) + x1) + (0.0031747115902272137 * (((x0 ** -1.0) * (x1 ** -1.0)) * ((39.54832653926522 + x1) * log(abs((-314.9892428270721 * (x0 * x1))))))))),saturated,373.990542,46,10,46,10,194,204,66,2,108,((((log(((-1.0 * x0) * x1)) + 5.75253848848719) * (x1 + 39.54832653926522)) + (314.9892428270721 * ((x0 * x1) * ((x1 + (-240.49898207944213 * log((((-1.0 * x0) * x1) / (log(((-1.0 * x0) * x1)) + 5.75253848848719))))) + -1091.0554965393965)))) * (-5.309599084210731e-06 / (x0 * x1))) +pagie,17,Bingo,Bingo,18,1,kept,5.0,4.0,(7.051978434353006)*(0.1577598589609299 + (-0.001006011746264326)*((-8.107154770143312 + x0)*((6.507788542716649 + x0 + plog(x0))*(plog((x0)*(x1)))))),-0.007094373139361835*(x0 - 8.107154770143312)*(x0 + log(x0) + 6.507788542716649)*log(x0*x1) + 1.112519123199049,saturated,299.146750,23,5,21,4,73,79,34,2,46,(-0.007094373139361835 * (((-8.107154770143312 + x0) * (((6.507788542716649 + x0) + log(abs(x0))) * log(abs((x0 * x1))))) + -156.8171142600944)),saturated,320.369417,19,4,19,4,115,122,41,2,44,((((-0.007094373139361835 * (x0 + -8.107154770143312)) * ((x0 + log(x0)) + 6.507788542716649)) * log((x0 * x1))) + 1.112519123199049) +pagie,20,Bingo,Bingo,21,1,kept,7.0,3.0,plog(plog(5.852257156264611 + ((exp(plog((0.0004240447616209535)*((x0)*(x1)))))*(exp(plog((0.0004240447616209535)*((x0)*(x1))))))*((7480.0610581772835 + plog((0.0004240447616209535)*((x0)*(x1))))*(7480.0610581772835 + plog((0.0004240447616209535)*((x0)*(x1))))))),log(log(10.039948113913963*x0**2*x1**2*(0.00013382768590600596*log(x0*x1) + 1)**2 + 5.852257156264611)),saturated,880.901500,43,7,33,4,551,558,97,2,61,log(abs(log(abs((5.852257156264611 + ((1.7981395985817125e-07 * (abs((x0 * x1)) * abs((x0 * x1)))) * ((7472.29538663884 + log(abs((x0 * x1)))) * (7472.29538663884 + log(abs((x0 * x1))))))))))),saturated,370.895000,24,4,24,4,128,138,53,1,63,log(log(((((10.039948113913963 * (x0 ** 2.0)) * (x1 ** 2.0)) * (((0.00013382768590600595 * log((x0 * x1))) + 1.0) ** 2.0)) + 5.852257156264611))) +pagie,19,Bingo,Bingo,20,1,kept,6.0,5.0,(-0.00010507476032088567)*((-819.22982975795 + ((x0)^(-1))*(1.9180501896236644 - (x1)))*(plog((-61.64925975453745)*((-9.235869766393078)*((x0)*(x1)) + ((-1)*(((-9.235869766393078)*(-9.235869766393078))*((-9.235869766393078)*(-9.235869766393078))))*((((x0)*(x0))*((x0)*(x0)))*(((x1)*(x1))*((x1)*(x1)))))))),0.00010507476032088567*(819.22982975795*x0 + x1 - 1.9180501896236644)*log(x0*x1*(448579.1335037871*x0**3*x1**3 + 569.384534287446))/x0,saturated,1133.773916,47,10,33,5,227,236,67,2,73,(-0.00010507476032088567 * ((-819.22982975795 + ((x0 ** -1.0) * (1.9180501896236644 - x1))) * log((448579.133503787 * abs((x0 * (x1 * ((((x0 * x0) * x0) * ((x1 * x1) * x1)) + 0.0012693067772458905)))))))),saturated,304.077750,28,5,28,5,209,222,75,1,70,(((0.00010507476032088567 * (((819.22982975795 * x0) + x1) - 1.9180501896236644)) * log(((x0 * x1) * (((448579.1335037871 * (x0 ** 3.0)) * (x1 ** 3.0)) + 569.384534287446)))) / x0) +pagie,22,Bingo,Bingo,23,1,kept,5.0,4.0,-5.64393372152411 + (0.002708862303985314)*((x1)^(-1)) + (-0.06435725235582418)*((-2311.5964730737646 - (x0))*((plog((3566206920.7839065)*(((x0)^(-1))*((x1)^(-1)))))^(-1))),0.06435725235582418*x0/log(3566206920.7839065/(x0*x1)) - 5.64393372152411 + 148.7679975624414/log(3566206920.7839065/(x0*x1)) + 0.002708862303985314/x1,saturated,271.417666,27,5,27,5,219,234,87,1,76,((-5.64393372152411 + (0.002708862303985314 * (x1 ** -1.0))) + (-0.06435725235582418 * ((-2311.5964730737646 - x0) * (log(abs((3566206920.7839065 * ((x0 ** -1.0) * (x1 ** -1.0))))) ** -1.0)))),saturated,301.426708,25,6,25,6,199,210,66,2,61,(((0.002708862303985314 / x1) + (((0.06435725235582418 * x0) / log((3566206920.7839065 / (x0 * x1)))) + -5.64393372152411)) + (148.7679975624414 / log((3566206920.7839065 / (x0 * x1))))) +pagie,21,Bingo,Bingo,22,1,kept,4.0,4.0,(0.3407158075111429)*(plog(0.39963452583999787 + (0.07297318016992407)*((x0)*((x1)*(401.296952200405 + x0 + (2)*(x1) - (exp(x0) + exp(x1)))) - (x0)))),0.3407158075111429*log(0.07297318016992407*x0*x1*(x0 + 2*x1 - exp(x0) - exp(x1) + 401.296952200405) - 0.07297318016992407*x0 + 0.39963452583999787),saturated,262.818500,27,5,27,5,112,122,54,1,59,(0.3407158075111429 * log(abs((0.39963452583999787 + (0.07297318016992407 * ((x0 * (x1 * (((401.296952200405 + x0) + (2.0 * x1)) - (exp(x0) + exp(x1))))) - x0)))))),saturated,570.987750,28,6,26,5,73,81,40,2,58,(0.3407158075111429 * log((0.07297318016992407 * ((5.47645758221604 - x0) + ((((((x0 + (2.0 * x1)) - exp(x0)) - exp(x1)) + 401.296952200405) * x1) * x0))))) +pagie,13,Bingo,Bingo,14,1,kept,6.0,6.0,-3.6628323446084137 + (-140960.10336012763)*(((-1951.8497630927013 + x0)^(-1))*((plog(((x0)^(-1))*(-38271.243311540704 + (-3434828.851252485)*((x1)^(-1)) + (-66329.49759041717)*(x1))))^(-1))),-3.6628323446084137 - 140960.10336012763/((x0 - 1951.8497630927013)*log(-(66329.49759041717*x1 + 38271.243311540704 + 3434828.851252485/x1)/x0)),saturated,318.583250,29,6,29,6,274,293,107,1,83,(-3.6628323446084137 + (-140960.10336012763 * (((-1951.8497630927013 + x0) ** -1.0) * (log(abs(((x0 ** -1.0) * ((-38271.243311540704 + (-3434828.851252485 * (x1 ** -1.0))) + (-66329.49759041717 * x1))))) ** -1.0)))),saturated,3856.909750,22,7,20,6,87,101,56,2,54,(-3.6628323446084137 - (140960.10336012763 / ((x0 - 1951.8497630927013) * log(((((-66329.49759041717 * x1) - 38271.243311540704) - (3434828.851252485 / x1)) / x0))))) +pagie,23,Bingo,Bingo,24,1,kept,5.0,4.0,(plog(0.8889056731853394))*(-25.375926540572554 + (-2.4339755472913582)*(plog((x0)*(x1))) + plog((-4625426.158330705)*((plog((plog(0.8889056731853394 + (0.8889056731853394)*(0.8889056731853394)))*((x1)^(-1))))^(-1)))),0.28663506996925448*log(x0*x1) - 0.1177641535011456*log(-4625426.158330705/log(0.5182334989833757/x1)) + 2.9883745083577819,saturated,307.120791,33,7,23,4,71,79,41,2,56,(-0.11776415350114562 * ((-2.4339755472913582 * (4.120356708064521 + log(abs((x0 * x1))))) + log(abs((log(abs((0.5182334989833758 * (x1 ** -1.0)))) ** -1.0))))),saturated,324.951500,18,5,18,5,121,132,54,2,46,(((0.2866350699692545 * log((x0 * x1))) + (-0.1177641535011456 * log((-4625426.158330705 / (-0.65732936805086 - log(x1)))))) + 2.988374508357782) +pagie,24,Bingo,Bingo,25,1,kept,4.0,3.0,exp((-2.377396411352944)*(((-10.503285479940024 - (plog((0.14985143797609368)*(x0))))^(-1))*(plog((1.4308910409656768)*((x0)*(x1)))))),exp(2.377396411352944*(log(x0*x1) + 0.3582973557925481)/(log(x0) + 8.6051745907779115)),saturated,311.917834,20,4,18,3,90,97,40,2,41,exp((-2.377396411352944 * (((-8.605174590777912 - log(abs(x0))) ** -1.0) * log((1.4308910409656768 * abs((x0 * x1))))))),saturated,254.792625,14,3,14,3,42,47,24,1,32,exp(((2.377396411352944 * (log((x0 * x1)) + 0.3582973557925481)) / (log(x0) + 8.605174590777912))) +pagie,25,Bingo,Bingo,26,1,kept,3.0,2.0,-1668.413725381717 + (0.35562720568200606)*(4695.7060144269335 + plog(x1) - (exp(1 - ((x0)*(x0))))),-0.35562720568200606*exp(1 - x0**2) + 0.35562720568200606*log(x1) + 1.5070832331229962,saturated,261.567709,16,4,16,4,46,53,30,1,39,(-1668.413725381717 + (0.35562720568200606 * ((4695.7060144269335 + log(abs(x1))) - exp((1.0 - (x0 * x0)))))),saturated,320.907541,15,4,13,3,41,48,28,2,35,((-0.35562720568200606 * (exp((1.0 - (x0 ** 2.0))) - log(x1))) + 1.5070832331229962) +pagie,18,Bingo,Bingo,19,1,kept,6.0,5.0,3.5993169689720506 + (-4.508737153066167e-07)*((521.6683948517077 + (23.730684923841224)*(plog((x0)*(x1))) - (x0))*(10602.124752119917 + (-1792.3707483707349)*(plog((x0)*(x1))))),4.508737153066167e-7*(1792.3707483707349*log(x0*x1) - 10602.124752119917)*(-x0 + 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0.644) + 0.203*exp(1.51740251293508*exp(plog(0.277729*exp(1.09526900525847*exp(plog(0.357*x1)**3)))**3)) + 0.0618744,saturated,308.582250,73,17,57,11,164,180,91,2,132,(((-0.4 * (0.5585066205818874 - log(abs(x1)))) + (exp(exp(((log(abs((exp(exp((((log(abs(x1)) + -1.030019497202498) ** 3.0) + 0.091))) * 0.277729))) ** 3.0) + 0.417))) + log(abs(((-0.372111067156366 + log(abs(log(abs((0.423 + abs((x0 ** 3.0)))))))) - exp((2.596 + log(abs(((x0 + -0.142) * x0)))))))))) * 0.203),saturated,2777.964833,65,14,55,11,240,260,115,2,130,((0.0812 * (-0.5585066205818873 + log(abs(x1)))) + (0.203 * (exp((1.51740251293508 * exp((log(abs((0.277729 * exp((1.09526900525847 * exp(((-1.030019497202498 + log(abs(x1))) ** 3.0))))))) ** 3.0)))) + log(abs(((-0.372111067156366 + log(abs(log(abs((abs((x0 ** 3.0)) + 0.423)))))) + (-13.4099906492963 * abs((x0 * (x0 + -0.142)))))))))) 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(0.16456659200000004 / (x1 ** 2.0)))) ** 3.0)),saturated,352.484208,55,10,53,9,157,171,75,2,155,(exp((((x1 ** 2.0) + 1.2854814793967273) * (-0.304612761792 / (x1 ** 4.0)))) + exp((((0.10536832436291177 * ((x0 ** 2.0) + -6.850597671733092)) * (((0.108837568328275 * (x0 ** 6.0)) + 1.0) ** 4.0)) / ((x0 ** 2.0) * (((0.00954923344395646 * (x0 ** 12.0)) + (((0.108837568328275 * (x0 ** 6.0)) + 1.0) ** 2.0)) ** 2.0))))) +pagie,48,EPLEX,EPLEX,19,1,kept,6.0,4.0,(exp(((plog((x0*(-0.382)))^3)^3))-(((-0.438/(0.616^2))*exp(((plog((x1*(-0.327)))*exp(-0.212))^3)))*0.821)),exp(plog(-0.382*x0)**9) + 0.947667186709394*exp(0.529405817708694*plog(-0.327*x1)**3),saturated,329.046667,30,6,23,4,91,104,57,2,60,(exp(((log(abs((x0 * -0.382))) ** 3.0) ** 3.0)) - (-0.9476671867093944 * exp(((log(abs((x1 * -0.327))) * 0.8089646975664998) ** 3.0)))),saturated,292.558334,21,4,21,4,82,94,52,1,53,(exp((log(abs((-0.382 * x0))) ** 9.0)) + (0.947667186709394 * exp((0.529405817708694 * (log(abs((-0.327 * x1))) ** 3.0))))) 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exp(((-1.1469630327669542 + (3.0 * exp((-0.5816058058270378 * abs((x1 ** 2.0)))))) - (2.44919517166754 * exp((-1.0 * exp((-0.18496503345507379 - (2.0 * log(abs((x0 ** 2.0))))))))))))))))) +pagie,56,EPLEX,EPLEX,27,1,kept,8.0,4.0,(exp((-0.777/(((x1*(exp((-0.306+x1))-x1))^2)*1.032)))-(exp((((0.351/((x0*0.3)^2))/(-2.161))*exp(-0.942)))/(-0.958))),exp(-0.752906976744186/(x1**2*(x1 - 0.7363866194561*exp(x1))**2)) + 1.04384133611691*exp(-0.703565342734522/x0**2),saturated,342.102666,31,8,24,5,52,60,36,2,63,(exp((-0.752906976744186 / ((x1 * (exp((-0.306 + x1)) - x1)) ** 2.0))) - (exp((-0.06332088084610697 / ((x0 * 0.3) ** 2.0))) / -0.958)),saturated,317.287417,24,4,24,4,51,58,33,2,63,(exp((-0.752906976744186 / ((x1 ** 2.0) * ((x1 + (-0.7363866194561 * exp(x1))) ** 2.0)))) + (1.04384133611691 * exp((-0.703565342734522 / (x0 ** 2.0))))) 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((exp((1.48145233407848 * exp((-0.658 / (x1 ** 2.0))))) * 0.006968016239569429) * (log(abs((-0.155 - exp((log(abs(log(abs((0.164047378003738 * (5.467932562625664 - abs((-0.003 - (0.276544027789322 / x1))))))))) - (x0 ** 2.0)))))) ** 4.0))))) ** 2.0)) +pagie,59,EPLEX,EPLEX,30,1,kept,13.0,6.0,exp(plog(plog(plog(((exp(plog((plog((x0/(-1.206/x1)))-(0.02*(-0.823)))))+((-1.052^2)^2))/(exp(plog(plog(plog(plog(plog((-0.892/(-0.928/(exp(plog(plog(plog((-0.621/(-0.463/(x1/(-0.848))))))))/(x1/(plog(plog((-0.985/(x0/(-0.606)))))/(x0/0.057))))))))))))/(x1/(-1.265/(x0/0.06))))))))),exp(plog(plog(plog(-13.1752305665349*x0*x1*(exp(plog(plog(-0.829187396351575*x0*x1) + 0.01646)) + 1.224793743616)*exp(-plog(plog(plog(plog(plog(0.0547887931034483*plog(plog(0.59691/x0))*exp(plog(plog(plog(-1.58166591955662*x1))))/(x0*x1))))))))))),saturated,302.884041,83,15,67,13,138,153,90,2,140,abs(log(abs(log(abs(((abs((log(abs((x0 / (-1.206 / x1)))) + 0.01646)) + 1.2247937436160004) / (abs(log(abs(log(abs(log(abs(log(abs((-0.892 / (-0.928 / (abs(log(abs(log(abs((-0.621 / (-0.463 / (x1 / -0.848)))))))) / (x1 / (log(abs(log(abs((-0.985 / (x0 / -0.606)))))) / (x0 / 0.057))))))))))))))) / (x1 / (-1.265 / (x0 / 0.06)))))))))),saturated,514.921375,65,8,57,7,673,687,153,2,100,abs(log(abs(log(abs(((((-13.1752305665349 * x0) * x1) * (abs((-0.17084909830499423 + log(abs((x0 * x1))))) + 1.224793743616)) * exp((-1.0 * log(abs(log(abs(log(abs(log(abs(log(abs(((abs(log(abs((0.4584786710374761 + log(abs(x1)))))) * log(abs(log(abs((0.59691 / x0)))))) * (0.0547887931034483 / (x0 * x1))))))))))))))))))))) +pagie,57,EPLEX,EPLEX,28,1,kept,7.0,6.0,exp((exp(plog((exp(plog(exp(plog(exp(plog(exp(plog(exp(exp(plog((exp((-0.231*((plog(exp(plog(x1)))-plog(x0))^2)))*exp((-0.176-((x1*exp(plog(-0.292)))^2)))))))))))))))*(0.496^2))))*plog((exp(plog(x1))*(exp(plog((-0.994*(-1.255*x0))))-((-0.386*x0)^2)))))),exp(plog((-0.148996*x0**2 + exp(plog(1.24747*x0)))*exp(plog(x1)))*exp(plog(0.246016*exp(plog(exp(plog(exp(plog(exp(plog(exp(exp(plog(0.838617983337074*exp(-x1**2*exp(2*plog(-0.292)) - 0.231*(plog(x0) - plog(exp(plog(x1))))**2))))))))))))))),saturated,359.385000,73,7,48,6,120,129,63,2,99,exp(((abs(abs(abs(abs(abs(exp(abs((exp((-0.231 * ((log(abs(abs(x1))) - log(abs(x0))) ** 2.0))) * exp((-0.176 - ((x1 * 0.292) ** 2.0))))))))))) * 0.24601599999999998) * log(abs((abs(x1) * (abs((1.2474699999999999 * x0)) - ((-0.386 * x0) ** 2.0))))))),saturated,1709.296000,72,8,47,6,209,223,92,2,98,exp((log(abs((((-0.148996 * (x0 ** 2.0)) + abs((1.24747 * x0))) * abs(x1)))) * (0.246016 * abs(abs(abs(abs(abs(exp(abs((0.838617983337074 * exp((-0.231 * (((log(abs(x0)) - log(abs(abs(x1)))) ** 2.0) + (0.3691082251082251 * (x1 ** 2.0)))))))))))))))) +pagie,90,GOMEA,GOMEA,1,1,kept,3.0,3.0,1.950385-1.107514*((exp(((x1-x1)-(x1*x1)))+exp((exp(-5.436000)-(x0*x0))))),1.950385 - 1.107514*exp(-x1**2) - 1.11234982803047*exp(-x0**2),saturated,303.810125,20,3,17,4,46,53,30,2,41,(1.107514 * ((1.7610477158753748 - exp((-1.0 * (x1 * x1)))) - exp((0.004356875966022165 - (x0 * x0))))),saturated,268.752500,19,5,19,5,181,198,82,1,56,((1.950385 - (1.107514 * exp((-1.0 * (x1 ** 2.0))))) - (1.11234982803047 * exp((-1.0 * (x0 ** 2.0))))) +pagie,91,GOMEA,GOMEA,2,1,kept,4.0,4.0,1.993812-1.064938*((exp(((-9.935000+9.358000)*(x0*x0)))+exp((exp(-11.329000)-(x1*x1))))),1.993812 - 1.06495079984612*exp(-x1**2) - 1.064938*exp(-0.577*x0**2),saturated,294.647250,20,5,17,4,42,48,27,2,41,(1.064938 * ((1.872232937504343 - exp((-0.577 * (x0 * x0)))) - exp((1.2019262341499391e-05 - (x1 * x1))))),saturated,286.127084,19,5,19,5,177,194,82,1,56,((1.993812 - (1.06495079984612 * exp((-1.0 * (x1 ** 2.0))))) - (1.064938 * exp((-0.577 * (x0 ** 2.0))))) +pagie,92,GOMEA,GOMEA,3,1,kept,4.0,3.0,1.950381-42823.103036*((exp(((11.065000-21.622000)-(x0*x0)))+exp(((-3.089000-7.475000)-(x1*x1))))),1.950381 - 1.10609193829701*exp(-x1**2) - 1.11386174445997*exp(-x0**2),saturated,312.266959,21,6,17,4,36,42,26,2,41,(42823.103036 * ((4.554506473667678e-05 - exp((-10.557 - (x0 * x0)))) - exp((-10.564 - (x1 * x1))))),saturated,277.749833,19,5,19,5,174,190,79,1,56,((1.950381 - (1.10609193829701 * exp((-1.0 * (x1 ** 2.0))))) - (1.11386174445997 * exp((-1.0 * (x0 ** 2.0))))) +pagie,93,GOMEA,GOMEA,4,1,kept,3.0,3.0,1.950390-1.109745*((exp(((x0-x0)-(x1*x1)))+exp((exp(-8.548000)-(x0*x0))))),1.95039 - 1.109745*exp(-x1**2) - 1.1099602365778*exp(-x0**2),saturated,309.265166,20,3,17,4,46,53,30,2,41,(1.109745 * ((1.7575118608328941 - exp((-1.0 * (x1 * x1)))) - exp((0.00019393257710559848 - (x0 * x0))))),saturated,279.002834,19,5,19,5,174,190,79,1,56,((1.95039 - (1.109745 * exp((-1.0 * (x1 ** 2.0))))) - (1.1099602365778 * exp((-1.0 * (x0 ** 2.0))))) +pagie,94,GOMEA,GOMEA,5,1,kept,3.0,3.0,1.950365-1.102849*((exp(((x1-x1)-(x1*x1)))+exp(((4.752000-4.739000)-(x0*x0))))),1.950365 - 1.102849*exp(-x1**2) - 1.1172796328829*exp(-x0**2),saturated,299.192208,21,4,17,4,46,53,30,2,41,(1.102849 * ((1.7684787309958117 - exp((-1.0 * (x1 * x1)))) - exp((0.0129999999999999 - (x0 * x0))))),saturated,299.725958,19,5,19,5,174,190,79,1,56,((1.950365 - (1.102849 * exp((-1.0 * (x1 ** 2.0))))) - (1.1172796328829 * exp((-1.0 * (x0 ** 2.0))))) +pagie,95,GOMEA,GOMEA,6,1,kept,4.0,4.0,1.974644-1.060379*((exp((exp(-3.066000)-(x0*x0)))+exp(((-0.726000*x1)*x1)))),1.974644 - 1.060379*exp(-0.726*x1**2) - 1.11097010569563*exp(-x0**2),saturated,328.659209,18,4,17,4,42,48,27,2,41,(1.060379 * ((1.8622058716741845 - exp((0.0466072113417544 - (x0 * x0)))) - exp(((-0.726 * x1) * x1)))),saturated,286.907417,19,5,19,5,184,202,85,1,56,((1.974644 - (1.060379 * exp((-0.726 * (x1 ** 2.0))))) - (1.11097010569563 * exp((-1.0 * (x0 ** 2.0))))) +pagie,96,GOMEA,GOMEA,7,1,kept,4.0,3.0,1.918745-23802.792114*((exp((-10.432000-(x0*x0)))+exp(((2.700000-12.507000)-(x1*x1))))),1.918745 - 1.31069583571551*exp(-x1**2) - 0.701564925378973*exp(-x0**2),saturated,317.230666,19,5,17,4,36,42,26,2,41,(23802.792114 * ((8.061008098589655e-05 - exp((-10.432 - (x0 * x0)))) - exp((-9.806999999999999 - (x1 * x1))))),saturated,312.946291,19,5,19,5,174,190,79,1,56,((1.918745 - (1.31069583571551 * exp((-1.0 * (x1 ** 2.0))))) - (0.701564925378973 * exp((-1.0 * (x0 ** 2.0))))) +pagie,97,GOMEA,GOMEA,8,1,kept,4.0,3.0,1.942860-1.152683*(exp((((-2.509000-10.440000)*(x1*x1))*(exp(-4.814000)*(x0*x0))))),1.94286 - 1.152683*exp(-0.105085451613159*x0**2*x1**2),saturated,375.796916,19,5,14,3,134,143,46,2,33,(1.94286 - (1.152683 * exp((-0.1050854516131593 * ((x1 * x1) * (x0 * x0)))))),saturated,346.685250,14,3,14,3,70,80,41,1,41,(1.94286 - (1.152683 * exp(((-0.105085451613159 * (x0 ** 2.0)) * (x1 ** 2.0))))) +pagie,99,GOMEA,GOMEA,10,1,kept,4.0,3.0,1.844910-1.211361*(exp((((12.665000-12.944000)+exp(-7.863000))*((x0*x0)*(x1*x1))))),1.84491 - 1.211361*exp(-0.278615282015546*x0**2*x1**2),saturated,295.292792,19,5,14,3,134,143,46,2,33,(1.84491 - (1.211361 * exp((-0.2786152820155465 * ((x0 * x0) * (x1 * x1)))))),saturated,270.522333,14,3,14,3,70,80,41,1,41,(1.84491 - (1.211361 * exp(((-0.278615282015546 * (x0 ** 2.0)) * (x1 ** 2.0))))) +pagie,26,Bingo,Bingo,27,1,kept,11.0,8.0,(0.3423580139257516)*(plog(0.45123069569900626 + (x0)*(((-1)*(-0.4457591552950685))*(((x1)^(-1))*((24.139650704131938 + (-0.8538385588541292)*((x1)*(x1)) + (-6.699001432126425)*(plog((-0.4457591552950685)*((x1)^(-1)))))^(-1))) + (x1)*(24.139650704131938 + (-0.8538385588541292)*((x1)*(x1)) + (-6.699001432126425)*(plog((-0.4457591552950685)*((x1)^(-1)))))))),0.3423580139257516*log((-x0*(873.33762693716456*x1**2*(0.028892470433989278*x1**2 + 0.22668301730799557*log(-1/x1) - 1)**2 + 0.4457591552950685) + 0.45123069569900626*x1*(0.8538385588541292*x1**2 + 6.699001432126425*log(-1/x1) - 29.552286323348394))/(x1*(0.8538385588541292*x1**2 + 6.699001432126425*log(-1/x1) - 29.552286323348394))),saturated,454.545917,55,12,49,9,347,371,138,2,123,(0.3423580139257516 * log(abs((0.45123069569900626 + (x0 * ((0.4457591552950685 * ((x1 ** -1.0) * (((-6.699001432126425 * (-4.411446485385776 + log(abs((x1 ** -1.0))))) + (-0.8538385588541292 * (x1 * x1))) ** -1.0))) + (x1 * ((-6.699001432126425 * (-4.411446485385776 + log(abs((x1 ** -1.0))))) + (-0.8538385588541292 * (x1 * x1)))))))))),saturated,14279.642792,67,17,61,14,317,342,132,2,166,(0.3423580139257516 * log((((-1022.8369495390365 * (x0 * ((((((0.02889247043398928 * (x1 ** 2.0)) + (0.22668301730799556 * log((-1.0 / x1)))) - 1.0) ** 2.0) * (x1 ** 2.0)) - -0.0005104087371780447))) - ((-0.45123069569900626 * x1) * (((x1 ** 2.0) - 34.61109365101552) - (-7.845747141141808 * log((-1.0 / x1)))))) / (x1 * (((x1 ** 2.0) - 34.61109365101552) - (-7.845747141141808 * log((-1.0 / x1)))))))) +pagie,100,GOMEA,GOMEA,11,1,kept,4.0,3.0,1.950391-0.000021*((exp(((13.012000-2.124000)-(x0*x0)))+exp(((-1.572000+12.461000)-(x1*x1))))),1.950391 - 1.12525747907577*exp(-x1**2) - 1.12413278403794*exp(-x0**2),saturated,275.014750,21,6,17,4,36,42,26,2,41,(2.1e-05 * ((92875.76190476191 - exp((10.888 - (x0 * x0)))) - exp((10.889 - (x1 * x1))))),saturated,287.978875,19,5,19,5,181,198,82,1,56,((1.950391 - (1.12525747907577 * exp((-1.0 * (x1 ** 2.0))))) - (1.12413278403794 * exp((-1.0 * (x0 ** 2.0))))) +pagie,101,GOMEA,GOMEA,12,1,kept,4.0,3.0,1.884443-1.188614*(exp((((-3.546000+x1)-(x1-3.362000))*((x0*x0)*(x1*x1))))),1.884443 - 1.188614*exp(-0.184*x0**2*x1**2),saturated,252.188584,20,4,20,4,159,170,57,1,46,(1.884443 - (1.188614 * exp((((-3.546 + x1) - (x1 - 3.362)) * ((x0 * x0) * (x1 * x1)))))),saturated,252.172250,14,3,14,3,70,80,41,1,41,(1.884443 - (1.188614 * exp(((-0.184 * (x0 ** 2.0)) * (x1 ** 2.0))))) +pagie,102,GOMEA,GOMEA,13,1,kept,3.0,3.0,1.926897-1.163077*(exp((x0*((-0.122000*x1)*(x0*x1))))),1.926897 - 1.163077*exp(-0.122*x0**2*x1**2),saturated,249.270708,14,3,14,3,134,143,46,1,33,(1.926897 - (1.163077 * exp((x0 * ((-0.122 * x1) * (x0 * x1)))))),saturated,248.709458,14,3,14,3,70,80,41,1,41,(1.926897 - (1.163077 * exp(((-0.122 * (x0 ** 2.0)) * (x1 ** 2.0))))) +pagie,104,GOMEA,GOMEA,15,1,kept,3.0,3.0,1.950390-1.109582*((exp((exp(-7.605000)-(x0*x0)))+exp(((x1-x1)-(x1*x1))))),1.95039 - 1.109582*exp(-x1**2) - 1.11013465996109*exp(-x0**2),saturated,280.206000,20,3,17,4,46,53,30,2,41,(1.109582 * ((1.75777004313336 - exp((0.0004979554215032735 - (x0 * x0)))) - exp((-1.0 * (x1 * x1))))),saturated,248.132833,19,5,19,5,174,190,79,1,56,((1.95039 - (1.109582 * exp((-1.0 * (x1 ** 2.0))))) - (1.11013465996109 * exp((-1.0 * (x0 ** 2.0))))) +pagie,105,GOMEA,GOMEA,16,1,kept,3.0,3.0,1.950383-1.106588*((exp((exp(-5.103000)-(x0*x0)))+exp(((x0-x0)-(x1*x1))))),1.950383 - 1.106588*exp(-x1**2) - 1.11333486172906*exp(-x0**2),saturated,281.581625,20,3,17,4,46,53,30,2,41,(1.106588 * ((1.762519564643752 - exp((0.0060784837337638405 - (x0 * x0)))) - exp((-1.0 * (x1 * x1))))),saturated,264.661625,19,5,19,5,181,198,82,1,56,((1.950383 - (1.106588 * exp((-1.0 * (x1 ** 2.0))))) - (1.11333486172906 * exp((-1.0 * (x0 ** 2.0))))) +pagie,98,GOMEA,GOMEA,9,1,kept,3.0,3.0,2.007440-1.043210*((exp(((x1*x1)*(23.561000-24.049000)))+exp(((x1-x1)-(x0*x0))))),2.00744 - 1.04321*exp(-0.488*x1**2) - 1.04321*exp(-x0**2),saturated,383.510750,21,4,17,4,52,59,31,2,41,(1.04321 * ((1.9242913699063466 - exp(((x1 * x1) * -0.48799999999999955))) - exp((-1.0 * (x0 * x0))))),saturated,4127.474000,19,5,17,4,41,48,29,2,49,(1.04321 * ((1.9242913699063466 - exp((-0.488 * (x1 ** 2.0)))) - exp((-1.0 * (x0 ** 2.0))))) +pagie,103,GOMEA,GOMEA,14,1,kept,4.0,4.0,1.993304-1.068007*((exp(((17.091000-17.877000)*(x1*x1)))+exp(((-0.722000*x0)*x0)))),1.993304 - 1.068007*exp(-0.785999999999998*x1**2) - 1.068007*exp(-0.722*x0**2),saturated,279.976291,19,5,17,4,48,54,28,2,41,(1.068007 * ((1.8663772802987246 - exp((-0.7859999999999978 * (x1 * x1)))) - exp(((-0.722 * x0) * x0)))),saturated,5780.491667,19,5,17,4,41,48,29,2,49,(1.068007 * ((1.8663772802987246 - exp((-0.785999999999998 * (x1 ** 2.0)))) - exp((-0.722 * (x0 ** 2.0))))) +pagie,108,GOMEA,GOMEA,19,1,kept,4.0,4.0,1.942097-1.116958*((exp((exp(-18.411000)-(x1*x1)))+exp(((-0.561000*x0)*(x0+x0))))),1.942097 - 1.11695801127823*exp(-x1**2) - 1.116958*exp(-1.122*x0**2),saturated,306.295750,20,4,19,4,50,56,29,2,44,(1.116958 * ((1.7387377143992881 - exp((1.009727753928824e-08 - (x1 * x1)))) - exp(((-0.561 * x0) * (x0 + x0))))),saturated,335.188459,19,5,19,5,177,194,82,1,56,((1.942097 - (1.11695801127823 * exp((-1.0 * (x1 ** 2.0))))) - (1.116958 * exp((-1.122 * (x0 ** 2.0))))) +pagie,109,GOMEA,GOMEA,20,1,kept,4.0,3.0,1.949837-0.000010*((exp(((9.658000+1.885000)-(x1*x1)))+exp(((10.589000+1.026000)-(x0*x0))))),1.949837 - 1.03053134177528*exp(-x1**2) - 1.10746601366406*exp(-x0**2),saturated,325.932000,21,6,17,4,36,42,26,2,41,(1e-05 * ((194983.69999999998 - exp((11.543 - (x1 * x1)))) - exp((11.615 - (x0 * x0))))),saturated,363.476791,19,5,19,5,174,190,79,1,56,((1.949837 - (1.03053134177528 * exp((-1.0 * (x1 ** 2.0))))) - (1.10746601366406 * exp((-1.0 * (x0 ** 2.0))))) +pagie,110,GOMEA,GOMEA,21,1,kept,4.0,3.0,1.950389-1.108799*((exp((exp(-6.234000)-(x0*x0)))+exp((exp(-24.872000)-(x1*x1))))),1.950389 - 1.1087990000175*exp(-x1**2) - 1.11097614346804*exp(-x0**2),saturated,375.266792,19,4,17,4,36,42,26,2,41,(1.108799 * ((1.7590104247929514 - exp((0.0019615898236818204 - (x0 * x0)))) - exp((1.5784384301013077e-11 - (x1 * x1))))),saturated,332.094167,19,5,19,5,195,213,88,1,56,((1.950389 - (1.1087990000175 * exp((-1.0 * (x1 ** 2.0))))) - (1.11097614346804 * exp((-1.0 * (x0 ** 2.0))))) +pagie,106,GOMEA,GOMEA,17,1,kept,2.0,2.0,1.950390-1.109849*((exp(((x1-x1)-(x0*x0)))+exp(((x0-x0)-(x1*x1))))),1.95039 - 1.109849*exp(-x1**2) - 1.109849*exp(-x0**2),saturated,279.294542,21,2,17,4,50,56,28,2,41,(1.109849 * ((1.7573471706511425 - exp((-1.0 * (x0 * x0)))) - exp((-1.0 * (x1 * x1))))),saturated,6703.228041,19,5,17,4,38,44,26,2,49,(1.109849 * ((1.7573471706511425 - exp((-1.0 * (x1 ** 2.0)))) - exp((-1.0 * (x0 ** 2.0))))) +pagie,111,GOMEA,GOMEA,22,1,kept,4.0,3.0,1.938930-5.446100*((exp(((-0.454000-1.011000)-(x1*x1)))+exp(((-1.344000-0.479000)-(x0*x0))))),1.93893 - 1.25847384938469*exp(-x1**2) - 0.879765183704653*exp(-x0**2),saturated,405.483500,21,6,17,4,36,42,26,2,41,(5.4461 * ((0.3560217403279411 - exp((-1.4649999999999999 - (x1 * x1)))) - exp((-1.823 - (x0 * x0))))),saturated,327.058958,19,5,19,5,174,190,79,1,56,((1.93893 - (1.25847384938469 * exp((-1.0 * (x1 ** 2.0))))) - (0.879765183704653 * exp((-1.0 * (x0 ** 2.0))))) +pagie,113,GOMEA,GOMEA,24,1,kept,4.0,3.0,1.961773-1.139885*(exp(((-4.331000*(x1*x0))*((x1*x0)*exp(-3.893000))))),1.961773 - 1.139885*exp(-0.0882835453806378*x0**2*x1**2),saturated,350.484416,17,4,14,3,134,143,46,2,33,(1.961773 - (1.139885 * exp((-0.0882835453806378 * ((x1 * x0) * (x1 * x0)))))),saturated,312.781583,14,3,14,3,70,80,41,1,41,(1.961773 - (1.139885 * exp(((-0.0882835453806378 * (x0 ** 2.0)) * (x1 ** 2.0))))) +pagie,107,GOMEA,GOMEA,18,1,kept,2.0,2.0,1.950390-1.109849*((exp(((x1-x1)-(x0*x0)))+exp(((x0-x0)-(x1*x1))))),1.95039 - 1.109849*exp(-x1**2) - 1.109849*exp(-x0**2),saturated,298.375292,21,2,17,4,50,56,28,2,41,(1.109849 * ((1.7573471706511425 - exp((-1.0 * (x0 * x0)))) - exp((-1.0 * (x1 * x1))))),saturated,6959.886875,19,5,17,4,38,44,26,2,49,(1.109849 * ((1.7573471706511425 - exp((-1.0 * (x1 ** 2.0)))) - exp((-1.0 * (x0 ** 2.0))))) +pagie,114,GOMEA,GOMEA,25,1,kept,3.0,3.0,2.015663-2.611492*((exp((x1-exp(x1)))+exp(((1.434000-2.275000)-(x0*x0))))),-2.611492*exp(x1 - exp(x1)) + 2.015663 - 1.12628173318904*exp(-x0**2),saturated,345.393792,18,4,16,3,33,38,23,2,35,(2.611492 * ((0.7718434519424144 - exp((x1 - exp(x1)))) - exp((-0.841 - (x0 * x0))))),saturated,254.912666,18,4,18,4,149,163,68,1,46,(((-2.611492 * exp((x1 - exp(x1)))) + 2.015663) - (1.12628173318904 * exp((-1.0 * (x0 ** 2.0))))) +pagie,115,GOMEA,GOMEA,26,1,kept,4.0,2.0,1.950387-0.000000*((exp((19.402000-(x1*x1)))+exp(((18.128000+1.277000)-(x0*x0))))),1.95038700000000,saturated,266.552500,19,5,1,1,3,4,3,2,6,1.950387,saturated,249.720417,1,1,1,1,3,4,3,1,6,1.950387 +pagie,116,GOMEA,GOMEA,27,1,kept,4.0,2.0,2.013362-0.000000*((exp(((x0+22.086000)-exp(x0)))+exp(((6.546000+14.636000)-(x1*x1))))),2.01336200000000,saturated,281.860958,20,5,1,1,3,4,3,2,6,2.013362,saturated,244.427291,1,1,1,1,3,4,3,1,6,2.013362 +pagie,118,GOMEA,GOMEA,29,1,kept,4.0,3.0,2.072676-0.000520*((exp(((x1+8.426000)-exp(x1)))+exp(((8.611000+x0)-exp(x0))))),-2.85570358866897*exp(x0 - exp(x0)) - 2.37338748595467*exp(x1 - exp(x1)) + 2.072676,saturated,341.177917,19,4,19,4,42,48,28,2,43,(0.00052 * ((3985.915384615385 - exp(((x1 + 8.426) - exp(x1)))) - exp(((8.611 + x0) - exp(x0))))),saturated,333.581542,17,3,17,3,114,123,48,2,36,(((-2.85570358866897 * exp((x0 - exp(x0)))) + (-2.37338748595467 * exp((x1 - exp(x1))))) + 2.072676) +pagie,112,GOMEA,GOMEA,23,1,kept,3.0,3.0,1.967245-1.093740*((exp(((-3.351000+2.551000)*(x0*x0)))+exp(((x1-x1)-(x1*x1))))),1.967245 - 1.09374*exp(-x1**2) - 1.09374*exp(-0.8*x0**2),saturated,413.953041,21,4,17,4,52,59,31,2,41,(1.09374 * ((1.7986404447126374 - exp((-0.7999999999999998 * (x0 * x0)))) - exp((-1.0 * (x1 * x1))))),saturated,4535.272250,19,5,17,4,41,48,29,2,49,(1.09374 * ((1.7986404447126374 - exp((-1.0 * (x1 ** 2.0)))) - exp((-0.8 * (x0 ** 2.0))))) +pagie,120,Operon,Operon,1,1,kept,12.0,7.0,(0.0000018283429881 + (1.0000038146972656 * (((exp((((0.0879114493727684 * x0) * ((-110.2642364501953125) * x0)) + (-1.4756100177764893))) + 1.6358861923217773) / exp(exp((((-1.3751174211502075) * x1) * (0.7306602597236633 * x1))))) - (exp((((0.0290526524186134 * x0) * ((-29.7418365478515625) * x0)) + 0.1625563055276871)) + (-0.3440066277980804))))),0.22864008270232224*exp(-9.693488840318309485*x0**2 - exp(-1.0047436520881447*x1**2)) + 0.34400976842221091 + 1.635892432732362*exp(-exp(-1.0047436520881447*x1**2)) - 1.1765190489038249*exp(-0.8640792395159440872*x0**2),saturated,460.325584,39,12,31,8,100,112,56,2,77,(1.0000038146972656 * (0.3440084561340939 + (((exp(((-9.69348884031831 * (x0 * x0)) + -1.4756100177764893)) + 1.6358861923217773) / exp(exp((-1.0047436520881448 * (x1 * x1))))) - exp(((-0.8640792395159441 * (x0 * x0)) + 0.1625563055276871))))),saturated,417.383875,38,9,38,9,719,750,203,1,107,((((0.22864008270232225 * exp(((-9.69348884031831 * (x0 ** 2.0)) - exp((-1.0047436520881448 * (x1 ** 2.0)))))) + 0.3440097684222109) + (1.635892432732362 * exp((-1.0 * exp((-1.0047436520881448 * (x1 ** 2.0))))))) - (1.1765190489038249 * exp((-0.8640792395159441 * (x0 ** 2.0))))) +pagie,54,EPLEX,EPLEX,25,1,kept,11.0,7.0,(exp((-0.772^2))-(-0.16+(exp((plog(-0.598)*((x1-(x1-(exp(plog((plog((plog((x0*(-0.413^3)))*(-0.543^3)))+(exp((-0.33*((0.032+((x1-(x1*(exp(plog((exp(plog(exp(plog((x0*(-0.371^2))))))*(-0.774^2))))*(-0.543^2))))^2))-plog((x0*(-0.735^3))))))^2))))^2)))^2)))^3))),0.711020095242334 - 1.0*exp(3*plog(-0.598)*exp(4*plog(plog(-0.160103007*plog(-0.070444997*x0)) + 0.979101465343806*exp(-0.05737771564866*x1**2*exp(2*plog(-0.599076*exp(plog(exp(plog(-0.137641*x0)))))) - 0.38920068*x1**2*exp(plog(-0.599076*exp(plog(exp(plog(-0.137641*x0)))))) - 0.66*x1**2 + 0.66*plog(-0.397065375*x0))))),saturated,4105.166291,96,18,45,7,152,168,82,2,110,(0.7110200952423344 - (exp((-0.5141645250315053 * ((abs((log((abs(log(abs((x0 * -0.070444997)))) * 0.16010300700000005)) + (exp((-0.33 * ((0.9556543393079011 + ((x1 - (x1 * (-0.024312487745842885 * abs(abs(abs(x0)))))) ** 2.0)) - log(abs(x0))))) ** 2.0))) ** 2.0) ** 2.0))) ** 3.0)),saturated,18881.266708,86,18,56,13,182,204,105,2,131,(0.711020095242334 - exp((-1.542493575094516 * exp((4.0 * log(abs((log((0.160103007 * abs(log(abs((-0.070444997 * x0)))))) + (0.979101465343806 * exp((-0.05737771564866 * (((x1 ** 2.0) * (exp((2.0 * log((0.08245741971600001 * abs(abs(abs(x0))))))) + (0.5593196498275389 * (abs(abs(abs(x0))) + 20.565563064828417)))) + (-11.502723531925998 * log(abs((-0.397065375 * x0)))))))))))))))) +pagie,119,GOMEA,GOMEA,30,1,kept,4.0,4.0,1.983784-1.077004*((exp(((x1*x1)*(-17.973000+17.206000)))+exp(((-1.143000+0.306000)*(x0*x0))))),1.983784 - 1.077004*exp(-0.766999999999999*x1**2) - 1.077004*exp(-0.837*x0**2),saturated,274.734209,21,6,17,4,48,54,28,2,41,(1.077004 * ((1.8419467337168662 - exp(((x1 * x1) * -0.7669999999999995))) - exp((-0.837 * (x0 * x0))))),saturated,5095.197250,19,5,17,4,41,48,29,2,49,(1.077004 * ((1.8419467337168662 - exp((-0.766999999999999 * (x1 ** 2.0)))) - exp((-0.837 * (x0 ** 2.0))))) +pagie,117,GOMEA,GOMEA,28,1,kept,2.0,2.0,1.950390-1.109849*((exp(((x0-x0)-(x1*x1)))+exp(((x0-x0)-(x0*x0))))),1.95039 - 1.109849*exp(-x1**2) - 1.109849*exp(-x0**2),saturated,293.231833,21,2,17,4,50,56,28,2,41,(1.109849 * ((1.7573471706511425 - exp((-1.0 * (x1 * x1)))) - exp((-1.0 * (x0 * x0))))),saturated,6202.910917,19,5,17,4,38,44,26,2,49,(1.109849 * ((1.7573471706511425 - exp((-1.0 * (x1 ** 2.0)))) - exp((-1.0 * (x0 ** 2.0))))) +pagie,123,Operon,Operon,4,1,kept,13.0,8.0,(0.0130726965144277 + (0.9919041991233826 * (exp(((((58.9215812683105469 * x0) * exp((((-5.0386314392089844) * x1) * (2.4705743789672852 * x1)))) + (log(((0.4419521391391754 * x0) * (0.1393797099590302 * x0))) / (0.0113436263054609 * x0))) / (381.6167297363281250 * x0))) - (exp(((((-0.8848519921302795) * x1) * (0.9313139915466309 * x1)) + 0.1248256787657738)) + (-0.9970148205757141))))),0.9919041991233826*exp(0.1543998904582130231*exp(-12.448313738768775*x1**2) + 0.2310046294243750492*log(x0**2)/x0**2 - 0.6438346264391826885/x0**2) + 1.002015883631724 - 1.123778793245288*exp(-0.8240750407188386*x1**2),saturated,353.862125,47,13,37,8,123,135,63,2,86,(0.9919041991233826 * (1.0101942148417944 + (exp(((0.154399890458213 / x0) * ((exp((-12.448313738768775 * (x1 * x1))) * x0) + (log((0.061599160968991234 * (x0 * x0))) * (1.4961450344221223 / x0))))) - exp(((-0.8240750407188386 * (x1 * x1)) + 0.1248256787657738))))),saturated,309.693375,39,8,39,8,226,248,109,2,109,(((0.9919041991233826 * exp((((0.15439989045821303 * exp((-12.448313738768775 * (x1 ** 2.0)))) + (log((x0 ** 2.0)) * (0.23100462942437505 / (x0 ** 2.0)))) - (0.6438346264391827 / (x0 ** 2.0))))) + 1.002015883631724) - (1.123778793245288 * exp((-0.8240750407188386 * (x1 ** 2.0))))) +pagie,122,Operon,Operon,3,1,kept,13.0,7.0,(0.0000011243114386 + (0.9999998211860657 * (((((-1.5812002420425415) + exp((((-0.1428712755441666) * x1) * (6.4702811241149902 * x1)))) + exp(((0.0134312557056546 * x0) * ((-68.7404861450195312) * x0)))) * (-1.2517620325088501)) - ((exp((((-0.0396961532533169) * x1) * (152.2495422363281250 * x1))) + exp(((1.0955569744110107 * x0) * ((-5.6038808822631836) * x0)))) * (-0.2742688059806824))))),1.9792871991701026 + 0.2742687569375981*exp(-6.043721161360625488*x1**2) - 1.2517618086763563*exp(-0.9244173173316527744*x1**2) + 0.2742687569375981*exp(-6.1393707843319587*x0**2) - 1.2517618086763563*exp(-0.923271046744764579*x0**2),saturated,346.624125,45,13,33,7,158,168,60,2,76,(-1.2517618086763562 * ((-1.5812011402257509 + (exp((-0.9232710467447646 * (x0 * x0))) + exp((-0.9244173173316528 * (x1 * x1))))) + (-0.21910618700503146 * (exp((-6.043721161360626 * (x1 * x1))) + exp((-6.139370784331959 * (x0 * x0))))))),saturated,2501.335125,37,9,33,7,173,186,71,2,92,((-1.2517618086763562 * (exp((-0.9232710467447646 * (x0 ** 2.0))) + exp((-0.9244173173316528 * (x1 ** 2.0))))) + (0.2742687569375981 * (exp((-6.139370784331959 * (x0 ** 2.0))) + (exp((-6.043721161360626 * (x1 ** 2.0))) + 7.216597403474695)))) +pagie,126,Operon,Operon,7,1,kept,12.0,7.0,(0.0028247879818082 + (0.9984024167060852 * (0.7176343202590942 - ((exp(((4.5870537757873535 * x1) * ((-0.0708576515316963) * x1))) / ((((-2.5320065021514893) * x1) * ((-0.5026428699493408) * x1)) + exp((((-1.5353101491928101) * x1) * (1.0705516338348389 * x1))))) + ((-3.4508912563323975) / exp(exp(exp(((1.6964559555053711 * x0) * ((-0.5267499089241028) * x0)))))))))),0.7193126276397166 + 3.4453781701121642*exp(-exp(exp(-0.89360802005620601*x0**2))) - 0.9984024167060852*exp(-0.32502785800189209*x1**2)/(1.2726950149718163*x1**2 + exp(-1.6436287886615731*x1**2)),saturated,373.768917,44,12,36,8,107,118,57,2,84,(0.0028247879818082 + (0.9984024167060852 * (0.7176343202590942 - ((exp((-0.3250278580018921 * (x1 * x1))) / ((1.2726950149718164 * (x1 * x1)) + exp((-1.643628788661573 * (x1 * x1))))) + (-3.4508912563323975 / exp(exp(exp((-0.893608020056206 * (x0 * x0)))))))))),saturated,306.157458,36,8,36,8,200,217,90,1,100,((0.7193126276397166 + (3.445378170112164 * exp((-1.0 * exp(exp((-0.893608020056206 * (x0 ** 2.0)))))))) - ((0.9984024167060852 * exp((-0.3250278580018921 * (x1 ** 2.0)))) / ((1.2726950149718164 * (x1 ** 2.0)) + exp((-1.643628788661573 * (x1 ** 2.0)))))) +pagie,121,Operon,Operon,2,1,kept,13.0,6.0,((-0.0615618973970413) + (1.0497297048568726 * (((((3.4508244991302490 * x0) * (exp(((2.5524139404296875 * x0) * ((-1.6356614828109741) * x0))) * (((2.4663076400756836 * x0) * ((-0.0845688283443451) * x0)) * (3.5071039199829102 * x0)))) - exp(((3.0741317272186279 * x0) * ((-0.2599562704563141) * x0)))) - exp(((0.0030150315724313 * x1) * ((-247.1376800537109375) * x1)))) + 1.9547927379608154))),-2.6497601004867348*x0**4*exp(-4.174885170550624*x0**2) + 1.9904421064789234 - 1.0497297048568726*exp(-0.745127908099363587*x1**2) - 1.0497297048568726*exp(-0.79913981869918164*x0**2),saturated,1326.550875,48,13,34,6,177,185,53,2,74,(1.0497297048568726 * (1.8961472627378055 + (((((-2.524230845547065 * (x0 * (x0 * x0))) * x0) * exp((-4.174885170550624 * (x0 * x0)))) - exp((-0.7991398186991816 * (x0 * x0)))) - exp((-0.7451279080993636 * (x1 * x1)))))),saturated,5280.702875,32,7,30,6,322,344,122,2,84,(((-2.6497601004867346 * (x0 ** 4.0)) * exp((-4.174885170550624 * (x0 ** 2.0)))) - (-1.9904421064789235 - (-1.0497297048568726 * (exp((-0.7991398186991816 * (x0 ** 2.0))) + exp((-0.7451279080993636 * (x1 ** 2.0))))))) +pagie,125,Operon,Operon,6,1,kept,13.0,8.0,(0.0004403672355693 + (0.9997187852859497 * (exp((((-13.4114389419555664) * x0) * (0.2287123352289200 * x0))) - ((-3.1294746398925781) + (exp((exp((((-3.3788871765136719) * x0) * (0.2795567214488983 * x0))) - (-0.1448028236627579))) + ((1.0040752887725830 + ((1.8763431310653687 * x1) * (0.6411635279655457 * x1))) / exp(((1.1580088138580322 * x1) * (1.2662296295166016 * x1))))))))),-1.2027044682559756*x1**2*exp(-1.4663050713484154*x1**2) - 1.155486617848524*exp(exp(-0.94459062121188704*x0**2)) + 3.1290349528121623 - 1.0037929280273658*exp(-1.4663050713484154*x1**2) + 0.9997187852859497*exp(-3.06736151919473366*x0**2),saturated,757.400917,45,13,35,8,140,153,68,2,83,(0.9997187852859497 * (3.1299151310007285 + (exp((-3.067361519194734 * (x0 * x0))) - (exp((exp((-0.9445906212118871 * (x0 * x0))) + 0.1448028236627579)) + (((x1 * x1) + 0.8346131194498276) * (1.20304278158779 / exp((1.4663050713484154 * (x1 * x1))))))))),saturated,3420.028167,42,9,35,8,587,612,167,2,99,(((0.9997187852859497 * exp((-3.067361519194734 * (x0 ** 2.0)))) + ((exp((-1.4663050713484154 * (x1 ** 2.0))) * (-1.0037929280273659 + (-1.2027044682559755 * (x1 ** 2.0)))) + (-1.155486617848524 * exp(exp((-0.9445906212118871 * (x0 ** 2.0))))))) + 3.1290349528121624) +pagie,124,Operon,Operon,5,1,kept,13.0,7.0,((-0.0197761859744787) + (1.0117771625518799 * ((exp(((1.6896657943725586 * x1) * ((-1.6174912452697754) * x1))) * ((0.0575970448553562 * x1) * ((-14.7621564865112305) * x1))) - (exp(((0.4481753110885620 * x1) * ((-1.8585087060928345) * x1))) - (1.9719880819320679 - exp((((0.2870940864086151 * x0) * ((-1.9049599170684814) * x0)) / exp((((-0.2803071439266205) * x0) * (0.7164036631584167 * x0)))))))))),-0.860270199378549024*x1**2*exp(-2.7330196298294141*x1**2) + 1.975436320148873 - 1.0117771625518799*exp(-0.54690272703580685*x0**2*exp(0.2008130647185045*x0**2)) - 1.0117771625518799*exp(-0.83293771751395694*x1**2),saturated,354.351958,49,13,37,7,148,157,58,2,82,(1.0117771625518799 * (1.9524420922552503 + ((exp((-2.733019629829414 * (x1 * x1))) * (-0.8502565893153748 * (x1 * x1))) - (exp(((-0.5469027270358069 * (x0 * x0)) / exp((-0.20081306471850446 * (x0 * x0))))) + exp((-0.832937717513957 * (x1 * x1))))))),saturated,4310.727375,39,8,37,7,267,286,103,2,102,(((-1.0117771625518799 * (exp((-0.832937717513957 * (x1 ** 2.0))) + exp(((-0.5469027270358069 * (x0 ** 2.0)) * exp((0.2008130647185045 * (x0 ** 2.0))))))) - -1.975436320148873) - (0.860270199378549 * (exp((-2.733019629829414 * (x1 ** 2.0))) * (x1 ** 2.0)))) +pagie,129,Operon,Operon,10,1,kept,14.0,8.0,(0.0000002913372725 + (1.0000000000000000 * ((1.0092900991439819 / ((((-9.8911437988281250) * x0) * ((-0.0619828216731548) * x0)) - exp((((-5.2376017570495605) * x0) * ((-0.1814788132905960) * x0))))) + ((2.9227268695831299 / ((-1.9528466463088989) - exp((((-1044.4626464843750000) * x1) * ((-0.0013573808828369) * x1))))) + (((241.8676300048828125 * x1) * (0.0000091869978860 * x1)) - (-1.9428678750991821)))))),0.002222037405546688681*x1**2 + 1.9428681664364546 - 2.9227268695831299/(exp(1.4177336291751259086*x1**2) + 1.9528466463088989) + 1.0092900991439819/(0.61308100222629464*x0**2 - exp(0.95051375135809475*x0**2)),saturated,1756.658083,45,14,33,8,226,239,78,2,81,(((1.9428681664364547 + (0.0022220374055466887 * (x1 * x1))) + (2.92272686958313 / (-1.952846646308899 - exp((1.417733629175126 * (x1 * x1)))))) + (1.009290099143982 / ((0.6130810022262947 * (x0 * x0)) - exp((0.9505137513580948 * (x0 * x0)))))),saturated,242.356000,33,8,33,8,96,110,61,1,97,((((0.0022220374055466887 * (x1 ** 2.0)) + 1.9428681664364547) - (2.92272686958313 / (exp((1.417733629175126 * (x1 ** 2.0))) + 1.952846646308899))) + (1.009290099143982 / ((0.6130810022262947 * (x0 ** 2.0)) - exp((0.9505137513580948 * (x0 ** 2.0)))))) +pagie,128,Operon,Operon,9,1,kept,13.0,7.0,((-0.0000084446337496) + (1.0000045299530029 * ((((exp(((1.8677622079849243 * x1) * ((-3.2215218544006348) * x1))) + exp(((4.2088832855224609 * x0) * ((-1.4519027471542358) * x0)))) * 0.2748067975044250) - ((exp(((0.5492876768112183 * x1) * ((-1.6836870908737183) * x1))) + exp(((1.3932512998580933 * x0) * ((-0.6629599928855896) * x0)))) * 1.2524310350418091)) + 1.9792671203613281))),1.9792676417146139 + 0.27480804236630257*exp(-6.0170367718470175*x1**2) - 1.2524367084955372*exp(-0.92482857062306332*x1**2) + 0.27480804236630257*exp(-6.1108892047016068*x0**2) - 1.2524367084955372*exp(-0.92366987184176*x0**2),saturated,366.103416,45,13,33,7,158,168,60,2,76,(0.2748080423663026 * (7.20236432919372 + ((exp((-6.0170367718470175 * (x1 * x1))) + exp((-6.110889204701607 * (x0 * x0)))) + (-4.5574965627320125 * (exp((-0.9248285706230632 * (x1 * x1))) + exp((-0.92366987184176 * (x0 * x0)))))))),saturated,3183.026375,37,9,33,7,173,186,71,2,92,((-1.2524367084955372 * (exp((-0.92366987184176 * (x0 ** 2.0))) + exp((-0.9248285706230633 * (x1 ** 2.0))))) + (0.2748080423663026 * (exp((-6.110889204701607 * (x0 ** 2.0))) + (exp((-6.0170367718470175 * (x1 ** 2.0))) + 7.20236432919372)))) +pagie,131,Operon,Operon,12,1,kept,14.0,6.0,((-0.0001345924683847) + (1.0000907182693481 * (((0.0052004987373948 * x0) * ((-5.5132131576538086) * x0)) - (log((((-29.4069671630859375) * x1) * (((-0.0669591948390007) + (((7.1831178665161133 * x0) * ((-12.8945026397705078) * x0)) * (((-0.0048121302388608) * x0) * ((-3.7251195907592773) * x0)))) * (11.7470531463623047 * x1)))) * ((-0.1758960038423538) + ((5.9699630737304688 * x1) * (0.0000638487472315 * x1))))))),-0.028674059090422408*x0**2 - 1.0000907182693481*(0.0003811746632760055*x1**2 - 0.1758960038423538)*log(x1**2*(573.554050429521172*x0**4 + 23.1307328639999089)) - 0.0001345924683847,saturated,887.406916,48,14,32,6,351,376,132,2,72,(-0.02867405909042241 * (((x0 * x0) + (0.013294568501084911 * (log(((573.5540504295212 * (x1 * (((x0 * x0) * (x0 * x0)) + 0.04032877607032475))) * x1)) * ((x1 * x1) + -461.4577535941546)))) + 0.004693875672093318)),saturated,807.212500,30,7,28,6,244,267,109,2,82,(((-0.028674059090422407 * (x0 ** 2.0)) - ((0.00038120924278177724 * ((x1 ** 2.0) - 461.4577535941546)) * log(((x1 ** 2.0) * (573.5540504295212 * ((x0 ** 4.0) + 0.04032877607032475)))))) - 0.0001345924683847) +pagie,132,Operon,Operon,13,1,kept,12.0,8.0,((-0.0000847672417876) + (1.0000656843185425 * ((exp((((-1.8279364109039307) * x1) * (2.2386462688446045 * x1))) - ((-1.5547065734863281) + ((-1.6497515439987183) / exp(exp(((0.0022635490167886 * x0) * ((-443.1721801757812500) * x0))))))) - exp(exp(((-1.6148645877838135) + exp((0.5693863630294800 + ((0.0016070556594059 * x1) * ((-348.2632751464843750) * x1)))))))))),-1.0000656843185425*exp(0.19891760449084139*exp(1.767182310249908*exp(-0.5596784672873918045*x1**2))) + 1.5547239260863535 + 1.6498599068046503*exp(-exp(-1.003141952704949999*x0**2)) + 1.0000656843185425*exp(-4.0921030259552823*x1**2),saturated,288.698792,41,12,35,9,125,140,70,2,86,(-8.47672417876e-05 + (1.0000656843185425 * ((exp((-4.092103025955282 * (x1 * x1))) - (-1.5547065734863281 + (-1.6497515439987183 / exp(exp((-1.00314195270495 * (x0 * x0))))))) - exp(exp((-1.6148645877838135 + exp((0.56938636302948 + (-0.5596784672873918 * (x1 * x1)))))))))),saturated,1459.099167,37,10,35,9,115,129,66,2,98,((1.0000656843185425 * (exp((-4.092103025955282 * (x1 ** 2.0))) + (1.5546218118120534 - exp((0.1989176044908414 * exp((1.767182310249908 * exp((-0.5596784672873918 * (x1 ** 2.0)))))))))) + (1.6498599068046502 * exp((-1.0 * exp((-1.00314195270495 * (x0 ** 2.0))))))) +pagie,127,Operon,Operon,8,1,kept,13.0,7.0,((-0.0218773111701012) + (1.0134590864181519 * ((((((-0.3641613721847534) * x0) * (2.2286646366119385 * x0)) * exp((((-2.4582626819610596) * x0) * (1.0862829685211182 * x0)))) + (1.9716572761535645 - exp(((((-2.4894037246704102) * x1) * (0.2193875461816788 * x1)) * exp((((-0.4357891678810120) * x1) * ((-0.4778871238231659) * x1))))))) - exp((((-1.3948150873184204) * x0) * (0.5922598838806152 * x0)))))),-0.8225168802330056*x0**2*exp(-2.6703688835653453*x0**2) + 1.9763166706501921 - 1.0134590864181519*exp(-0.54614417461097283*x1**2*exp(0.2082580320319476*x1**2)) - 1.0134590864181519*exp(-0.82609302165013783*x0**2),saturated,323.622667,49,13,39,8,160,171,64,2,89,(-0.0218773111701012 + (1.0134590864181519 * ((((-0.8115935722082384 * (x0 * x0)) * exp((-2.670368883565345 * (x0 * x0)))) + (1.9716572761535645 - exp(((-0.5461441746109729 * (x1 * x1)) * exp((0.20825803203194762 * (x1 * x1))))))) - exp((-0.8260930216501379 * (x0 * x0)))))),saturated,6335.663458,39,8,37,7,291,311,111,2,102,(((-1.0134590864181519 * (exp((-0.8260930216501379 * (x0 ** 2.0))) + exp(((-0.5461441746109729 * (x1 ** 2.0)) * exp((0.2082580320319476 * (x1 ** 2.0))))))) - -1.976316670650192) - (0.8225168802330056 * (exp((-2.670368883565345 * (x0 ** 2.0))) * (x0 ** 2.0)))) +pagie,130,Operon,Operon,11,1,kept,13.0,8.0,((-0.0000135196241899) + (1.0000069141387939 * ((1.2255471944808960 * exp(((-1.7740323543548584) * exp(((2.9035081863403320 * x1) * ((-0.4098204970359802) * x1)))))) - ((1.2498761415481567 * exp(((0.1515025645494461 * x0) * ((-6.0828857421875000) * x0)))) + ((-0.7505750060081482) - (0.2749604582786560 * exp(((1.1432402133941650 * x0) * ((-5.4770793914794922) * x0))))))))),0.75056667596372507 + 1.2255556680842971*exp(-1.7740323543548584*exp(-1.1899171680740323*x1**2)) + 0.27496235939342737*exp(-6.261617412291798*x0**2) - 1.2498847833652745*exp(-0.92157278980266706*x0**2),saturated,3995.032334,41,13,31,8,204,218,78,2,77,(1.2255556680842972 * ((0.6124296884342744 + (0.22435729894116463 * exp((-6.261617412291798 * (x0 * x0))))) + (exp((-1.7740323543548584 * exp((-1.1899171680740324 * (x1 * x1))))) + (-1.0198514974999113 * exp((-0.9215727898026671 * (x0 * x0))))))),saturated,356.107916,31,8,31,8,695,727,206,1,89,(((0.7505666759637251 + (1.2255556680842972 * exp((-1.7740323543548584 * exp((-1.1899171680740324 * (x1 ** 2.0))))))) + (0.2749623593934274 * exp((-6.261617412291798 * (x0 ** 2.0))))) - (1.2498847833652744 * exp((-0.9215727898026671 * (x0 ** 2.0))))) +pagie,134,Operon,Operon,15,1,kept,15.0,7.0,((-0.0000022516087483) + (1.0000016689300537 * (((((51.6682472229003906 * x0) * ((-0.0001894439337775) * x0)) + 2.5324115753173828) + ((-46.3591499328613281) / (((13.0968494415283203 * x0) * (2.1884925365447998 * x0)) + 34.0089225769042969))) + (((-1351.7908935546875000) / (((17.2840843200683594 * x1) * (47.4518127441406250 * x1)) + 990.7814331054687500)) + ((0.0012052881065756 * x1) * ((-8.2380609512329102) * x1)))))),-0.00978825234117588218*x0**2 - 0.0099292534569677497*x1**2 + 2.5324135501264209 - 1351.7931495991360721/(820.161132609820926*x1**2 + 990.78143310546875) - 46.3592273030399151/(28.6623572550356584*x0**2 + 34.0089225769042969),saturated,2520.009625,45,15,29,7,842,862,160,2,72,(-0.009788252341175882 * (((x0 * x0) + -258.7196837451166) + (1.0144051369822908 * (((x1 * x1) + (165.99479114520634 / ((x1 * x1) + 1.2080326581103884))) + (162.89497489770397 / ((x0 * x0) + 1.186536134285651)))))),saturated,323.091458,33,9,29,7,188,209,96,2,88,(((((-0.009788252341175882 * (x0 ** 2.0)) - (0.009929253456967749 * (x1 ** 2.0))) + 2.532413550126421) - (1.6482043538171796 / ((x1 ** 2.0) + 1.2080326581103884))) - (1.6174254926257021 / ((x0 ** 2.0) + 1.186536134285651))) +pagie,135,Operon,Operon,16,1,kept,13.0,8.0,(0.0071523520164192 + (0.9955711960792542 * (((exp(((0.0195227134972811 * x1) * ((-151.1385955810546875) * x1))) * ((396057.1250000000000000 * x1) * ((-0.0000024948039936) * x1))) + ((85.4024658203125000 * x1) / ((43.1343650817871094 * x1) - (((-47.3760452270507812) * x1) * exp(((0.9379857182502747 * x0) * ((-1.2238332033157349) * x0))))))) - exp(((185448.0000000000000000 * x1) * ((-0.0000044009234443) * x1)))))),-0.9837088628772344519805*x1**2*exp(-2.950635499910365785*x1**2) + 85.0242350448461413*x1/(43.1343650817871094*x1 + 47.3760452270507812*x1*exp(-1.1479380662306441*x0**2)) + 0.0071523520164192 - 0.9955711960792542*exp(-0.816142450898546401501*x1**2),saturated,1149.035292,50,13,36,8,126,138,62,2,85,(0.0071523520164192 + (0.9955711960792542 * ((x1 * ((exp((-2.9506354999103657 * (x1 * x1))) * (-0.9880848971437344 * x1)) + (1.8026507998086212 / (x1 * (exp((-1.147938066230644 * (x0 * x0))) + 0.9104678297874944))))) - exp((-0.8161424508985464 * (x1 * x1)))))),saturated,4032.805375,42,9,38,8,678,707,194,2,104,(((((-0.9837088628772345 * (x1 ** 2.0)) * exp((-2.9506354999103657 * (x1 ** 2.0)))) + (x1 * (1.7946672128786931 / (x1 * (exp((-1.1479380662306442 * (x0 ** 2.0))) + 0.9104678297874944))))) + 0.0071523520164192) - (0.9955711960792542 * exp((-0.8161424508985464 * (x1 ** 2.0))))) +pagie,138,Operon,Operon,19,1,kept,12.0,9.0,((-0.0000098704376796) + (1.0000013113021851 * ((exp(exp(((-0.1284630000591278) - exp((((-1.7482314109802246) * x0) * (0.6576864719390869 * x0)))))) - exp((0.2162327617406845 + (((-0.0238646697252989) * x1) * (38.5694580078125000 * x1))))) - exp((((-0.9399499893188477) - exp(((1.4266452789306641 * x1) * ((-5.3529791831970215) * x1)))) * 0.8908159136772156))))),1.0000013113021851*exp(0.8794461012701917*exp(-exp(-1.1497881488206758*x0**2))) - 9.8704376796e-6 - 0.4328685844136254*exp(-0.8908159136772156*exp(-7.6368024799221532*x1**2)) - 1.24139292161274*exp(-0.92044737684023015*x1**2),saturated,285.037125,41,12,35,9,108,121,62,2,86,(-9.8704376796e-06 + (1.000001311302185 * ((exp(exp((-0.1284630000591278 - exp((-1.1497881488206758 * (x0 * x0)))))) - exp((0.2162327617406845 + (-0.9204473768402301 * (x1 * x1))))) - exp(((-0.9399499893188477 - exp((-7.636802479922153 * (x1 * x1)))) * 0.8908159136772156))))),saturated,301.281041,37,10,37,10,548,579,175,1,105,((((1.000001311302185 * exp((0.8794461012701917 * exp((-1.0 * exp((-1.1497881488206758 * (x0 ** 2.0)))))))) - 9.8704376796e-06) - (0.4328685844136254 * exp((-0.8908159136772156 * exp((-7.636802479922153 * (x1 ** 2.0))))))) - (1.24139292161274 * exp((-0.9204473768402301 * (x1 ** 2.0))))) +pagie,136,Operon,Operon,17,1,kept,13.0,8.0,(0.0005329695995897 + (0.9996598958969116 * (((2.9738872051239014 + exp(((100.4859924316406250 * x1) * ((-0.0308157186955214) * x1)))) - ((((0.7702111005783081 * x0) * (1.5427883863449097 * x0)) + 1.0054689645767212) * exp((((-1.7126119136810303) * x0) * (0.8499408960342407 * x0))))) - exp(exp((((100.9902267456054688 * x1) * ((-0.0091333612799644) * x1)) + 0.0902468413114548)))))),-1.1878686045713406*x0**2*exp(-1.4556189044729706*x0**2) - 0.9996598958969116*exp(1.09444440445747*exp(-0.9223802266131381654*x1**2)) + 2.9734087434829063 + 0.9996598958969116*exp(-3.096548075613729891*x1**2) - 1.0051270004563406*exp(-1.4556189044729706*x0**2),saturated,405.284875,45,13,37,9,138,152,69,2,90,(0.0005329695995897 + (0.9996598958969116 * (((2.9738872051239014 + exp((-3.09654807561373 * (x1 * x1)))) + (-1.1882727410061449 * (exp((-1.4556189044729706 * (x0 * x0))) * ((x0 * x0) + 0.8461600858783999)))) - exp(exp(((-0.9223802266131381 * (x1 * x1)) + 0.0902468413114548)))))),saturated,10204.511375,44,10,35,8,186,204,87,2,99,(-0.9996598958969116 * ((exp((1.09444440445747 * exp((-0.9223802266131381 * (x1 ** 2.0))))) - (exp((-3.09654807561373 * (x1 ** 2.0))) - (exp((-1.4556189044729706 * (x0 ** 2.0))) * (1.0054689645767212 - (-1.1882727410061449 * (x0 ** 2.0)))))) - 2.9744203560503086)) +pagie,140,Operon,Operon,21,1,kept,13.0,8.0,(0.0056000440381467 + (0.9965137243270874 * ((0.7391300201416016 + (exp((((-26.2499160766601562) * x1) * (0.1143757924437523 * x1))) * (((-49.5787200927734375) * x1) * (0.0202242378145456 * x1)))) - (exp(((2.2524499893188477 * x1) * ((-0.3599792122840881) * x1))) + (exp((exp((((-0.7799134254455566) * x0) * (1.5038967132568359 * x0))) * (-1.7264224290847778))) * (-1.2398984432220459)))))),-0.999196165577684391*x1**2*exp(-3.00235495284999869*x1**2) + 0.7421532531714092 + 1.2355758154425587*exp(-1.7264224290847778*exp(-1.1729092371524529*x0**2)) - 0.9965137243270874*exp(-0.810835172864301451*x1**2),saturated,891.717667,45,13,37,9,159,173,72,2,90,(0.9965137243270874 * ((((0.7391300201416016 + (exp((-3.002354952849999 * (x1 * x1))) * (-1.0026918256970403 * (x1 * x1)))) - exp((-0.8108351728643014 * (x1 * x1)))) + (1.239898443222046 * exp((exp((-1.172909237152453 * (x0 * x0))) * -1.7264224290847778)))) + 0.005619635637159161)),saturated,392.932209,35,8,35,8,736,767,211,1,99,(((((-0.9991961655776844 * (x1 ** 2.0)) * exp((-3.002354952849999 * (x1 ** 2.0)))) + 0.7421532531714092) + (1.2355758154425587 * exp((-1.7264224290847778 * exp((-1.172909237152453 * (x0 ** 2.0))))))) - (0.9965137243270874 * exp((-0.8108351728643014 * (x1 ** 2.0))))) +pagie,141,Operon,Operon,22,1,kept,12.0,7.0,(0.0059260418638587 + (0.9963514208793640 * (((1.9877398014068604 + ((((-0.0255243461579084) * x1) * (39.2693595886230469 * x1)) * exp((((-0.0006980864563957) * x1) * (4245.9946289062500000 * x1))))) - exp((((-0.0209862142801285) * x1) * (38.7934265136718750 * x1)))) - exp((exp((-2.6416935920715332)) + ((0.0101619474589825 * x0) * ((-75.6802444458007812) * x0))))))),-0.998667666466396711*x1**2*exp(-2.9640713443683392264*x1**2) + 1.9864134173340489 - 0.996351420879364*exp(-0.81412716147633626667*x1**2) - 1.0699214810013096*exp(-0.769058667741179754*x0**2),saturated,366.287583,43,12,34,8,140,153,65,2,82,(0.0059260418638587 + (0.996351420879364 * (((1.9877398014068604 + ((-1.002324727539394 * (x1 * x1)) * exp((-2.9640713443683393 * (x1 * x1))))) - exp((-0.8141271614763362 * (x1 * x1)))) - exp((0.07124051495942774 + (-0.7690586677411797 * (x0 * x0))))))),saturated,418.838750,32,7,32,7,762,793,204,1,91,(((((-0.9986676664663967 * (x1 ** 2.0)) * exp((-2.9640713443683393 * (x1 ** 2.0)))) + 1.9864134173340489) - (0.996351420879364 * exp((-0.8141271614763362 * (x1 ** 2.0))))) - (1.0699214810013096 * exp((-0.7690586677411797 * (x0 ** 2.0))))) +pagie,139,Operon,Operon,20,1,kept,14.0,8.0,((-0.0000002506655221) + (1.0000001192092896 * (((((-0.0002352308656555) * x0) + 1.9712915420532227) - (exp((((-0.0005102988216095) * x1) * (2861.8625488281250000 * x1))) * (1.0045522451400757 + ((0.0003667365817819 * x1) * (3236.1384277343750000 * x1))))) + (exp((((-0.0249317195266485) * x0) * (58.4497108459472656 * x0))) * ((-1.0050251483917236) + (((-0.0338098518550396) * x0) * (35.2732009887695312 * x0))))))),-1.1925818420501513*x0**2*exp(-1.45725179722486209*x0**2) - 0.0002352308936972044*x0 - 1.1868104866391750118*x1**2*exp(-1.4604050862753523738*x1**2) + 1.9712915263839649 - 1.0045523648920352*exp(-1.4604050862753523738*x1**2) - 1.0050252682000576*exp(-1.45725179722486209*x0**2),saturated,5213.757334,47,14,35,8,255,270,91,2,84,(-0.00023523089369720438 * (((-8380.240772801997 + x0) + (5045.300249408862 * (exp((-1.4604050862753524 * (x1 * x1))) * ((x1 * x1) + 0.8464303072824536)))) + (5069.835102464369 * (exp((-1.4572517972248622 * (x0 * x0))) * ((x0 * x0) + 0.842730647711634))))),saturated,3099.478417,49,10,35,8,813,843,221,2,100,((((exp((-1.4572517972248622 * (x0 ** 2.0))) * (-1.0050252682000576 + (-1.1925818420501513 * (x0 ** 2.0)))) + (-0.0002352308936972044 * x0)) + 1.971291526383965) + (exp((-1.4604050862753524 * (x1 ** 2.0))) * (-1.0045523648920351 + (-1.186810486639175 * (x1 ** 2.0))))) +pagie,143,Operon,Operon,24,1,kept,13.0,9.0,(0.0049892361275852 + (0.9968150258064270 * (exp(((-0.7375680804252625) / (exp((((-7.8003888130187988) * x1) * ((-0.0912654846906662) * x1))) - 0.9434194564819336))) - (exp(((((-11.2235412597656250) * x0) * (0.0819300860166550 * x0)) - (exp(((((-56.8530616760253906) * x0) * (0.1006406396627426 * x0)) - 1.4147840738296509)) - 0.2206120193004608))) - 0.9837305545806885)))),-1.242868435105807*exp(-0.919545700824074031*x0**2 - 0.24297807310963717*exp(-5.72172849386055215*x0**2)) + 0.985586634278505 + 0.996815025806427*exp(-0.7375680804252625/(exp(0.71190626579581106*x1**2) - 0.9434194564819336)),saturated,292.452750,41,13,33,9,125,141,71,2,84,(0.996815025806427 * (0.9887357320694095 + (exp((-0.7375680804252625 / (exp((0.7119062657958111 * (x1 * x1))) + -0.9434194564819336))) - exp(((-0.919545700824074 * (x0 * x0)) - (exp(((-5.721728493860552 * (x0 * x0)) + -1.4147840738296509)) + -0.2206120193004608)))))),saturated,299.290375,33,9,33,9,191,210,92,2,96,(((-1.242868435105807 * exp(((-0.919545700824074 * (x0 ** 2.0)) + (-0.24297807310963718 * exp((-5.721728493860552 * (x0 ** 2.0))))))) + 0.985586634278505) + (0.996815025806427 * exp((-0.7375680804252625 / (exp((0.7119062657958111 * (x1 ** 2.0))) + -0.9434194564819336))))) +pagie,142,Operon,Operon,23,1,kept,13.0,8.0,(0.0007810645620339 + (0.9995014071464539 * (((((-1.0057448148727417) + ((0.7655488848686218 * x0) * ((-1.5458080768585205) * x0))) * exp(((0.4586827158927917 * x0) * ((-3.1686115264892578) * x0)))) + (2.9749636650085449 + exp(((-0.3110347986221313) + ((3.0109248161315918 * x1) * ((-1.1550782918930054) * x1)))))) - exp(exp(((23.0867309570312500 * x1) * ((-0.0377156287431717) * x1))))))),-1.1828016188405823*x0**2*exp(-1.4533873405792973*x0**2) - 0.9995014071464539*exp(exp(-0.870730573668879675*x1**2)) + 2.9742614339476462 + 0.7323230656900827*exp(-3.4778538936355404*x1**2) - 1.0052433576955551*exp(-1.4533873405792973*x0**2),saturated,360.510416,45,13,37,9,151,166,74,2,90,(0.0007810645620339 + (0.9995014071464539 * ((((-1.0057448148727417 + (-1.1833916494599492 * (x0 * x0))) * exp((-1.4533873405792972 * (x0 * x0)))) + (2.974963665008545 + exp((-0.3110347986221313 + (-3.4778538936355403 * (x1 * x1)))))) - exp(exp((-0.8707305736688796 * (x1 * x1))))))),saturated,4766.418708,42,9,35,8,671,698,187,2,99,((((exp((-1.4533873405792972 * (x0 ** 2.0))) * (-1.005243357695555 + (-1.1828016188405823 * (x0 ** 2.0)))) + (-0.9995014071464539 * exp(exp((-0.8707305736688796 * (x1 ** 2.0)))))) + 2.974261433947646) + (0.7323230656900827 * exp((-3.4778538936355403 * (x1 ** 2.0))))) +pagie,137,Operon,Operon,18,1,kept,14.0,7.0,(0.0000816054744064 + (1.0001157522201538 * (((((-0.0021946807391942) * x0) * (13.7494821548461914 * x0)) + (-8.4071483612060547)) + ((log((((6955.1982421875000000 * x1) * (16.8089103698730469 * x1)) + 27880.0878906250000000)) + log((((85251.5703125000000000 * x0) * (3.5084772109985352 * x0)) + 63949.3125000000000000))) * (((1.2129596471786499 * x1) * ((-0.0008703975472599) * x1)) + 0.3835373818874359))))),-0.0301792165661435915*x0**2 - 1.0001157522201538*(0.0010557571018295306*x1**2 - 0.3835373818874359)*(log(299103.191643245522053*x0**2 + 63949.3125) + log(116909.30385762825625*x1**2 + 27880.087890625)) - 8.4080399018196203,saturated,14807.595250,45,14,31,7,74,83,42,2,74,(-0.0010558793080580105 * ((((24.277697647852335 + log(((x1 * x1) + 0.23847621165016322))) + log(((x0 * x0) + 0.213803510917648))) * ((x1 * x1) + -363.2818393765012)) + (28.582070257300217 * (278.60365040927337 + (x0 * x0))))),saturated,800.991250,35,9,31,7,226,247,100,2,90,(((-0.030179216566143592 * (x0 ** 2.0)) - ((0.0010558793080580105 * ((x1 ** 2.0) - 363.2818393765012)) * ((24.277697647852335 + log(((x1 ** 2.0) + 0.23847621165016322))) + log(((x0 ** 2.0) + 0.213803510917648))))) - 8.40803990181962) +pagie,145,Operon,Operon,26,1,kept,12.0,8.0,((-0.0001599656243343) + (1.0001020431518555 * ((exp(((25.9337768554687500 * x1) * ((-0.1575351804494858) * x1))) - (exp(exp(exp(((17.7164573669433594 * x1) * ((-0.0314616635441780) * x1))))) * 0.1594999134540558)) - ((-1.1739871501922607) - (exp((exp((((-0.3572374880313873) * x0) * (3.2828271389007568 * x0))) * (-1.7236351966857910))) * 1.2407730817794800))))),-0.15951618932794533*exp(exp(exp(-0.557389220873545688*x1**2))) + 1.1739469819169699 + 1.2408996941754822*exp(-1.723635196685791*exp(-1.1727489207421725*x0**2)) + 1.0001020431518555*exp(-4.08548221666296794*x1**2),saturated,524.113875,41,12,33,8,236,252,92,2,79,(1.0001020431518555 * ((1.1738272008896573 + (exp((-4.085482216662968 * (x1 * x1))) + (-0.1594999134540558 * exp(exp(exp((-0.5573892208735457 * (x1 * x1)))))))) + (exp((exp((-1.1727489207421724 * (x0 * x0))) * -1.723635196685791)) * 1.24077308177948))),saturated,316.884625,33,8,33,8,471,492,134,1,91,((((-0.15951618932794534 * exp(exp(exp((-0.5573892208735457 * (x1 ** 2.0)))))) + 1.17394698191697) + (1.2408996941754822 * exp((-1.723635196685791 * exp((-1.1727489207421724 * (x0 ** 2.0))))))) + (1.0001020431518555 * exp((-4.085482216662968 * (x1 ** 2.0))))) +pagie,144,Operon,Operon,25,1,kept,13.0,7.0,((-0.0000055456266637) + (1.0000027418136597 * ((((exp((((-4.2250251770019531) * x1) * (1.4258037805557251 * x1))) + exp((((-1.1716369390487671) * x0) * (5.2204809188842773 * x0)))) * 0.2746707499027252) - (-1.9792732000350952)) - ((exp((((-1.7990413904190063) * x1) * (0.5140095949172974 * x1))) + exp(((1.8088867664337158 * x0) * ((-0.5105684995651245) * x0)))) * 1.2522673606872559)))),1.9792730812067276 + 0.2746715029987392*exp(-6.0240568703125063*x1**2) - 1.252270794171011*exp(-0.92472453632872492*x1**2) + 0.2746715029987392*exp(-6.1165082841640697*x0**2) - 1.252270794171011*exp(-0.92356060222127209*x0**2),saturated,427.607125,45,13,33,7,158,168,60,2,76,(0.2746715029987392 * ((7.205964432414428 + (exp((-6.024056870312506 * (x1 * x1))) + exp((-6.11650828416407 * (x0 * x0))))) + (-4.559158050614224 * (exp((-0.9247245363287249 * (x1 * x1))) + exp((-0.9235606022212721 * (x0 * x0))))))),saturated,5349.019417,37,9,33,7,173,186,71,2,92,((-1.252270794171011 * (exp((-0.9235606022212721 * (x0 ** 2.0))) + exp((-0.9247245363287249 * (x1 ** 2.0))))) + (0.2746715029987392 * (exp((-6.11650828416407 * (x0 ** 2.0))) + (exp((-6.024056870312506 * (x1 ** 2.0))) + 7.205964432414428)))) +pagie,147,Operon,Operon,28,1,kept,13.0,7.0,((-0.0000072608104347) + (1.0000052452087402 * (((-1.2524669170379639) * (exp((((-0.8438813686370850) * x0) * (1.0945762395858765 * x0))) + (exp((((-0.6344506740570068) * x1) * (1.4577195644378662 * x1))) + (-1.5802922248840332)))) + (0.2748360037803650 * (exp(((19.0184898376464844 * x0) * ((-0.3212499320507050) * x0))) + exp((((-0.8187244534492493) * x1) * (7.3472332954406738 * x1)))))))),1.9792668517605557 + 0.27483744535257415*exp(-6.0153595641737924*x1**2) - 1.252473486488384*exp(-0.92485116024369056*x1**2) + 0.27483744535257415*exp(-6.10968856805095664*x0**2) - 1.252473486488384*exp(-0.92369249513936332*x0**2),saturated,397.375208,45,13,33,7,158,168,60,2,76,(-1.252473486488384 * ((-1.5802864277070765 + (exp((-0.9236924951393632 * (x0 * x0))) + exp((-0.9248511602436906 * (x1 * x1))))) + (-0.2194357392132493 * (exp((-6.109688568050957 * (x0 * x0))) + exp((-6.015359564173792 * (x1 * x1))))))),saturated,2251.142250,37,9,33,7,173,186,71,2,92,((-1.252473486488384 * (exp((-0.9236924951393634 * (x0 ** 2.0))) + exp((-0.9248511602436905 * (x1 ** 2.0))))) + (0.27483744535257415 * (exp((-6.109688568050957 * (x0 ** 2.0))) + (exp((-6.015359564173792 * (x1 ** 2.0))) + 7.201590923032561)))) +pagie,149,Operon,Operon,30,1,kept,13.0,7.0,((-0.0166908428072929) + (1.0103557109832764 * ((-1.0929064750671387) * ((((-1.8171284198760986) + exp(((0.4634887576103210 * x0) * ((-1.7064006328582764) * x0)))) + ((exp((((-0.0545985996723175) * x1) * (290.8274841308593750 * x1))) + exp((((-6.8895225524902344) * x0) * (4.0632553100585938 * x0)))) * (-0.0849393755197525))) + exp((((-0.0165483560413122) * x1) * (47.9090309143066406 * x1))))))),1.9898265121958887 + 0.093792122361465658*exp(-15.87877337976806101*x1**2) - 1.1042242986546854*exp(-0.7928157011641792664*x1**2) + 0.093792122361465658*exp(-27.993889095174382*x0**2) - 1.1042242986546854*exp(-0.79089750930894803*x0**2),saturated,323.268959,45,13,33,7,148,158,58,2,76,(-1.1042242986546853 * (((-1.802012973831642 + exp((-0.790897509308948 * (x0 * x0)))) + exp((-0.7928157011641793 * (x1 * x1)))) + ((exp((-15.878773379768061 * (x1 * x1))) + exp((-27.99388909517438 * (x0 * x0)))) * -0.0849393755197525))),saturated,1357.108833,37,9,33,7,173,186,71,2,92,((-1.1042242986546853 * (exp((-0.790897509308948 * (x0 ** 2.0))) + exp((-0.7928157011641793 * (x1 ** 2.0))))) + (0.09379212236146565 * (exp((-27.99388909517438 * (x0 ** 2.0))) + (exp((-15.878773379768061 * (x1 ** 2.0))) + 21.21528399290606)))) +pagie,150,SBP,SBP,1,1,kept,5.0,2.0,0.004376-0.000000*((((exp(4.787000)+((exp(x1)-exp(((x0-(x0*x0))+(15.039000-x1))))*x1))*15.260000)*(exp(x0)*x1))),0.00437600000000000,saturated,405.280875,29,5,1,1,3,4,3,2,6,0.004376,saturated,274.399708,1,1,1,1,3,4,3,1,6,0.004376 +pagie,151,SBP,SBP,2,1,kept,5.0,2.0,0.166642-0.018385*(((((x0*x1)+((((-5.488000+x1)*(x1+0.546000))+x1)*x1))+(x0*x0))+exp((-13.828000*x0)))),-0.018385*x0**2 - 0.018385*x0*x1 - 0.018385*x1**3 + 0.07247367*x1**2 + 0.05508969648*x1 + 0.166642 - 0.018385*exp(-13.828*x0),saturated,287.218250,28,5,26,5,168,179,64,2,59,(0.166642 - (0.018385 * (((x1 * (x0 + (((-5.488 + x1) * (x1 + 0.546)) + x1))) + (x0 * x0)) + exp((-13.828 * x0))))),saturated,3900.609667,36,8,28,5,1563,1586,308,2,74,(((-0.018385 * ((x1 * (-2.996448 + x0)) + ((exp((-13.828 * x0)) + (x1 ** 3.0)) + (x0 ** 2.0)))) + 0.166642) + (0.07247367 * (x1 ** 2.0))) +pagie,133,Operon,Operon,14,1,kept,13.0,8.0,(0.0049303476698697 + (0.9968529939651489 * ((((exp((((-0.1228989660739899) * x1) * (28.5782623291015625 * x1))) - (0.0001418351894245 * x0)) - exp((((-0.9014899730682373) * x1) * (0.9040312170982361 * x1)))) - exp((((-0.1503573954105377) * x1) * (16.6330261230468750 * x1)))) + (((-1.0727374553680420) * exp((((-0.1865450739860535) * x0) * (4.1227397918701172 * x0)))) - (-1.9877362251281738))))),-0.0001413888332274268*x0 + 1.986411154901873 + 0.9968529939651489*exp(-3.51223889243783649*x1**2) - 0.9968529939651489*exp(-2.50089848565676186*x1**2) - 0.9968529939651489*exp(-0.814975077554734653*x1**2) - 1.069361544122188*exp(-0.76907679949965783*x0**2),saturated,306.696875,47,13,37,8,113,124,57,2,86,(0.9968529939651489 * ((1.9926821376144859 + (-1.072737455368042 * exp((-0.7690767994996578 * (x0 * x0))))) + (((exp((-3.5122388924378365 * (x1 * x1))) + (-0.0001418351894245 * x0)) - exp((-0.8149750775547346 * (x1 * x1)))) - exp((-2.5008984856567618 * (x1 * x1)))))),saturated,28319.784375,41,10,37,8,456,479,136,2,102,((-0.9968529939651489 * (exp((-0.8149750775547346 * (x1 ** 2.0))) - ((exp((-3.5122388924378365 * (x1 ** 2.0))) - ((0.00014183518942449994 * x0) - 1.9926821376144856)) - exp((-2.5008984856567618 * (x1 ** 2.0)))))) - (1.069361544122188 * exp((-0.7690767994996578 * (x0 ** 2.0))))) +pagie,153,SBP,SBP,4,1,kept,3.0,3.0,-0.000465+0.164361*(exp((x0*(2.011000-x0)))),0.164361*exp(-x0**2 + 2.011*x0) - 0.000465,saturated,287.972583,10,3,10,3,33,38,21,1,27,(-0.000465 + (0.164361 * exp((x0 * (2.011 - x0))))),saturated,315.215250,14,4,12,3,49,58,34,2,34,((0.164361 * exp(((2.011 * x0) - (x0 ** 2.0)))) - 0.000465) +pagie,148,Operon,Operon,29,1,kept,13.0,7.0,((-0.0000072977472882) + (1.0000039339065552 * ((0.2748106420040131 * (exp(((0.8403434157371521 * x1) * ((-7.1597433090209961) * x1))) + exp(((2.1294348239898682 * x0) * ((-2.8703227043151855) * x0))))) - ((-1.9792662858963013) + (1.2524309158325195 * (exp(((1.7403106689453125 * x1) * ((-0.5314179658889771) * x1))) + exp(((0.6934723854064941 * x0) * ((-1.3319598436355591) * x0))))))))),1.9792667743976297 + 0.27481172308339912*exp(-6.016643148103924*x1**2) - 1.2524358427787092*exp(-0.92483235570580301*x1**2) + 0.27481172308339912*exp(-6.1121651226575295*x0**2) - 1.2524358427787092*exp(-0.92367737003161206*x0**2),saturated,384.414416,45,13,33,7,158,168,60,2,76,(0.27481172308339913 * ((7.202264707597524 + (exp((-6.016643148103924 * (x1 * x1))) + exp((-6.1121651226575295 * (x0 * x0))))) + (-4.557432371247945 * (exp((-0.9248323557058029 * (x1 * x1))) + exp((-0.9236773700316121 * (x0 * x0))))))),saturated,8702.087625,37,9,33,7,173,186,71,2,92,((-1.2524358427787092 * (exp((-0.9236773700316121 * (x0 ** 2.0))) + exp((-0.924832355705803 * (x1 ** 2.0))))) + (0.27481172308339913 * (exp((-6.1121651226575295 * (x0 ** 2.0))) + (exp((-6.016643148103924 * (x1 ** 2.0))) + 7.202264707597526)))) +pagie,155,SBP,SBP,6,1,kept,6.0,1.0,0.012711-0.000000*((x1-(((16.817000*((16.817000*x1)-exp(x1)))-exp(x1))*exp(((19.315000-x0)*(17.099000+x0)))))),0.0127110000000000,saturated,299.134875,26,6,1,1,3,4,3,2,6,0.012711,saturated,246.090375,1,1,1,1,3,4,3,1,6,0.012711 +pagie,146,Operon,Operon,27,1,kept,13.0,6.0,((-0.0639297738671303) + (1.0392827987670898 * ((1.9780735969543457 + ((exp((((-2.4385366439819336) * x1) * (2.2576689720153809 * x1))) * ((((-10.0973072052001953) * x1) * (391.6708374023437500 * x1)) * (((-0.0011133030056953) * x1) * ((-1.3449389934539795) * x1)))) - exp((((-1.7093311548233032) * x1) * (0.4650919437408447 * x1))))) - exp((((-1.2320897579193115) * x0) * (0.5889392495155334 * x0)))))),-6.154269525587394387*x1**4*exp(-5.5054085182405289*x1**2) + 1.9918480901428665 - 1.0392827987670898*exp(-0.79499614929355283*x1**2) - 1.0392827987670898*exp(-0.72562601736477455*x0**2),saturated,1298.449750,48,13,36,7,191,201,61,2,81,(-0.0639297738671303 + (1.0392827987670898 * ((1.9780735969543457 + ((exp((-5.505408518240529 * (x1 * x1))) * (-5.921650519847204 * ((x1 * x1) * (x1 * x1)))) - exp((-0.7949961492935529 * (x1 * x1))))) - exp((-0.7256260173647746 * (x0 * x0)))))),saturated,13317.808167,32,7,30,6,322,344,122,2,84,(((-6.154269525587394 * (x1 ** 4.0)) * exp((-5.505408518240529 * (x1 ** 2.0)))) - (-1.9918480901428666 - (-1.0392827987670898 * (exp((-0.7256260173647745 * (x0 ** 2.0))) + exp((-0.7949961492935528 * (x1 ** 2.0))))))) +pagie,152,SBP,SBP,3,1,kept,5.0,5.0,0.084583-0.012464*((((exp(x1)-(x0*(x1-1.179000)))+x1)+(x1*((-17.342000-(x0*(x1-3.045000)))+(x0*x0))))),0.012464*x0*(x1 - 1.179) + 0.012464*x1*(-x0**2 + x0*(x1 - 3.045) + 17.342) - 0.012464*x1 - 0.012464*exp(x1) + 0.084583,saturated,299.854708,28,5,28,5,183,196,73,1,62,(0.084583 - (0.012464 * (((exp(x1) - (x0 * (x1 - 1.179))) + x1) + (x1 * ((-17.342 - (x0 * (x1 - 3.045))) + (x0 * x0)))))),saturated,5824.929250,36,9,26,5,118,126,46,2,63,(-0.012464 * ((exp(x1) + -6.786184210526317) + ((x1 * (-16.342 + (((3.045 - x1) * x0) + (x0 ** 2.0)))) + ((1.179 - x1) * x0)))) +pagie,158,SBP,SBP,9,1,kept,6.0,4.0,-0.135470+0.008287*((((x1*15.772000)-exp(x1))+exp(((x0-(9.538000-(4.169000-((x0*x0)-((x0+8.367000)+x1)))))-x1)))),0.130702564*x1 - 0.008287*exp(x1) + 0.16611627946936*exp(-x0**2 + 2*x0) - 0.13547,saturated,362.140750,29,6,25,4,81,88,39,2,53,(-0.13547 + (0.008287 * (((x1 * 15.772) - exp(x1)) + exp(((((x0 + 2.998) - ((x0 * x0) - x0)) + x1) - x1))))),saturated,605.834625,23,6,21,5,698,728,196,2,55,((((0.130702564 * x1) - (0.008287 * exp(x1))) + (0.16611627946936 * exp(((2.0 * x0) - (x0 ** 2.0))))) - 0.13547) +pagie,157,SBP,SBP,8,1,kept,4.0,3.0,0.230781+0.006661*((((x1*x1)*(x0-x1))-((((x0*x0)-(19.670000+x0))+4.294000)*((x1+x0)-(x0*x0))))),0.006661*x1**2*(x0 - x1) + 0.006661*(-x0**2 + x0 + 15.376)*(-x0**2 + x0 + x1) + 0.230781,saturated,289.366375,29,4,27,3,57,63,31,2,53,(0.230781 + (0.006661 * (((x1 * x1) * (x0 - x1)) - ((-15.376000000000001 + ((x0 * x0) - x0)) * ((x1 + x0) - (x0 * x0)))))),saturated,2840.663209,33,6,27,3,64,71,34,2,65,((0.006661 * (((x0 - x1) * (x1 ** 2.0)) + (((x0 - (x0 ** 2.0)) + x1) * ((x0 - (x0 ** 2.0)) + 15.376)))) + 0.230781) +pagie,159,SBP,SBP,10,1,kept,6.0,5.0,0.154306-0.001732*((((-20.410000+(((exp(11.767000)*(x0+(x0+(x0+x1))))*(-1.883000+x0))*exp((-7.374000-x0))))*x0)-x1)),(-0.001732*x0*(0.000627353738614736*(x0 - 1.883)*(386780.368892305*x0 + 128926.789630768*x1) - 20.41*exp(x0)) + (0.001732*x1 + 0.154306)*exp(x0))*exp(-x0),saturated,354.581417,29,6,28,6,215,231,85,2,66,(0.154306 - (0.001732 * (((-20.41 + (((128926.78963076824 * (x0 + (x0 + (x0 + x1)))) * (-1.883 + x0)) * exp((-7.374 - x0)))) * x0) - x1))),saturated,5668.998708,36,9,32,7,164,175,66,2,75,((((0.03535012 * x0) * (exp(x0) + ((-11.888687430052634 * (x0 + -1.883)) * (x0 + (0.3333333333333325 * x1))))) + ((0.001732 * (x1 + 89.09122401847574)) * exp(x0))) * exp((-1.0 * x0))) +pagie,161,SBP,SBP,12,1,kept,6.0,5.0,0.667683-0.006309*((((x0*x0)-(x0-exp(exp((exp(((exp(x1)+0.069000)-x1))*(-0.069000))))))*((-6.657000+x0)*(-6.908000+x0)))),-0.006309*(x0 - 6.908)*(x0 - 6.657)*(x0**2 - x0 + exp(exp(-0.0739290984312359*exp(-x1 + exp(x1))))) + 0.667683,saturated,321.502334,29,6,29,6,183,195,68,2,66,(0.667683 - (0.006309 * ((((x0 * x0) - x0) + exp(exp((exp(((exp(x1) + 0.069) - x1)) * -0.069)))) * ((-6.657 + x0) * (-6.908 + x0))))),saturated,562.083250,29,6,27,5,121,130,50,2,63,((((-0.006309 * (x0 + -6.908)) * (x0 + -6.657)) * (((x0 ** 2.0) - x0) + exp(exp((-0.0739290984312359 * exp((exp(x1) - x1))))))) + 0.667683) +pagie,160,SBP,SBP,11,1,kept,5.0,4.0,-0.056784-0.009562*((((-18.680000-((x0+(((x0+x0)-(x0*x0))-16.065000))+x0))+x0)*((x1+8.713000)-(x0*x0)))),0.009562*(-x0**2 + 3*x0 + 2.615)*(-x0**2 + x1 + 8.713) - 0.056784,saturated,541.907375,29,5,27,4,98,108,50,2,57,(-0.056784 - (0.009562 * (((((-2.6149999999999984 - ((x0 + x0) - (x0 * x0))) - x0) - x0) + x0) * ((x1 + 8.713) - (x0 * x0))))),saturated,5364.551958,25,7,21,5,84,98,53,2,60,(((0.009562 * ((3.0 * (x0 - -0.8716666666666667)) - (x0 ** 2.0))) * ((x1 - (x0 ** 2.0)) - -8.713)) - 0.056784) +pagie,154,SBP,SBP,5,1,kept,8.0,7.0,0.018176+0.001712*((((((-8.935000*x0)+18.954000)*((x0*(x0-5.120000))*(x0-4.881000)))+x1)-((x1*18.328000)*(x1-4.881000)))),-0.001712*x0*(x0 - 5.12)*(x0 - 4.881)*(8.935*x0 - 18.954) - 0.031377536*x1*(x1 - 4.881) + 0.001712*x1 + 0.018176,saturated,618.034292,29,8,29,8,569,585,123,2,76,(0.018176 + (0.001712 * (((((-8.935 * x0) + 18.954) * ((x0 * (x0 + -5.12)) * (x0 + -4.881))) + x1) + (-18.328 * ((x1 + -4.881) * x1))))),saturated,13993.262375,31,9,25,7,494,507,102,2,66,(((x1 * (-0.031377536 * (-4.935561326931471 + x1))) + (((-0.015296720000000001 * ((x0 + -2.1213206491326244) * x0)) * (x0 + -5.12)) * (x0 + -4.881))) + 0.018176) +pagie,163,SBP,SBP,14,1,kept,5.0,4.0,0.001352+0.001458*((exp(((x0+(x0+2.705000))-(x0*x0)))*((exp(-11.964000)-(((x1+x1)-10.429000)*x1))-x1))),(-0.021803393734787*x1*(2*x1 - 10.429) - 0.021803393734787*x1 + 0.001352*exp(x0*(x0 - 2)) + 1.38875269916455e-7)*exp(x0*(2 - x0)),saturated,475.411250,27,5,26,5,80,88,41,2,59,(0.001352 + (0.001458 * (exp(((x0 + (x0 + 2.705)) - (x0 * x0))) * ((6.369433658159443e-06 - (((x1 + x1) + -10.429) * x1)) - x1)))),saturated,2987.053666,31,8,25,6,175,187,68,2,61,((((x1 * (-0.043606787469574 * (-4.7145 + x1))) + (0.001352 * exp((x0 * (x0 + -2.0))))) + 1.38875269916455e-07) * exp((x0 * (2.0 - x0)))) +pagie,156,SBP,SBP,7,1,kept,3.0,3.0,0.112902-0.007452*(((((x0*(x1*x0))+((((x0-x1)+x0)*x0)+(x1*(-20.819000))))-(x0-exp(x1)))+x1)),-0.007452*x0**2*x1 - 0.007452*x0*(2*x0 - x1) + 0.007452*x0 + 0.147691188*x1 - 0.007452*exp(x1) + 0.112902,saturated,316.557167,28,3,26,3,148,157,58,2,51,(0.007452 * ((((15.150563607085346 - (x0 * ((x1 * x0) + ((x0 - x1) + x0)))) - (x1 * -20.819)) + (x0 - exp(x1))) - x1)),saturated,16173.561166,32,7,24,4,101,107,37,2,56,(-0.007452 * ((exp(x1) + ((x1 * (-19.819 + (x0 ** 2.0))) + (((2.0 * x0) - x1) * x0))) + (-15.150563607085346 - x0))) +pagie,165,SBP,SBP,16,1,kept,5.0,4.0,0.040499-0.003093*((x0-exp((((((((exp(1.871000)-1.708000)+(x1*(-1.785000)))+x1)*x1)+(x0-x1))-(x0*x0))+x0)))),-0.003093*x0 + 0.003093*exp(-x0**2 + 2*x0 - 0.785*x1**2 + 3.78678794091585*x1) + 0.040499,saturated,506.637000,29,5,26,4,98,109,52,2,55,(0.040499 - (0.003093 * (x0 - exp(((((((4.7867879409158505 + (x1 * -1.785)) + x1) * x1) + (x0 - x1)) - (x0 * x0)) + x0))))),saturated,3844.703708,28,7,24,5,91,101,48,2,64,((-0.003093 * (x0 - exp(((((2.0 * x0) - (x0 ** 2.0)) + (-0.785 * (x1 ** 2.0))) + (3.78678794091585 * x1))))) + 0.040499) +pagie,166,SBP,SBP,17,1,kept,4.0,4.0,-0.065845-0.048266*(((x0-(x1+x1))-(x1+((x1+(x1+((3.579000-x0)*((3.247000-x0)*x0))))-(x1*x1))))),0.048266*x0*(x0 - 3.579)*(x0 - 3.247) - 0.048266*x0 - 0.048266*x1**2 + 0.24133*x1 - 0.065845,saturated,476.822000,29,4,29,4,456,466,92,2,60,(-0.065845 - (0.048266 * ((((x0 - x1) - x1) - x1) - ((x1 + (x1 + ((3.579 - x0) * ((3.247 - x0) * x0)))) - (x1 * x1))))),saturated,2485.784917,27,7,23,5,95,107,52,2,59,(-0.048266 * ((-4.999999999999999 * (x1 - 0.2728421663282642)) - (((((x0 - 3.247) * (x0 - 3.579)) * x0) - (x1 ** 2.0)) - x0))) +pagie,168,SBP,SBP,19,1,kept,5.0,5.0,0.012782+0.160826*((exp(((x0*x0)-exp(x0)))*((x0-(((-13.585000-x0)+exp((2.825000-(x1*x1))))*x0))+2.825000))),((0.160826*x0*((x0 + 13.585)*exp(x1**2) - 16.860944986089) + (0.160826*x0 + 0.45433345)*exp(x1**2))*exp(x0**2 - exp(x0)) + 0.012782*exp(x1**2))*exp(-x1**2),saturated,405.550542,28,5,28,5,71,78,38,1,61,(0.012782 + (0.160826 * (exp(((x0 * x0) - exp(x0))) * ((x0 - (((-13.585 - x0) + exp((2.825 - (x1 * x1)))) * x0)) + 2.825)))),saturated,996.679791,47,7,45,6,141,152,64,2,109,((((0.160826 * (((((x0 + 13.585) * exp((x1 ** 2.0))) + -16.860944986089) * x0) + (exp((x1 ** 2.0)) * (x0 + 2.825)))) * exp(((x0 ** 2.0) - exp(x0)))) + (0.012782 * exp((x1 ** 2.0)))) * exp((-1.0 * (x1 ** 2.0)))) +pagie,169,SBP,SBP,20,1,kept,7.0,4.0,0.000053-0.001570*((exp((x0-(x0*x0)))*(exp(x0)*((-10.978000+((15.694000-(exp(x1)+exp(-0.624000)))+(x1*15.599000)))*(-5.236000))))),((0.12823189148*x1 - 0.00822052*exp(x1) + 0.0343634427135555)*exp(x0) + 5.3e-5*exp(x0*(x0 - 1)))*exp(x0*(1 - x0)),saturated,600.169541,29,7,24,5,190,202,68,2,55,(5.3e-05 - ((-0.00822052 * (exp((x0 - (x0 * x0))) * (-10.978 + ((15.158203042332545 - exp(x1)) + (x1 * 15.599))))) * exp(x0))),saturated,383.544500,29,6,29,6,318,335,111,2,66,((((((0.12823189148 * x1) + (-0.00822052 * exp(x1))) + 0.0343634427135555) * exp(x0)) + (5.3e-05 * exp((x0 * (x0 + -1.0))))) * exp((x0 * (1.0 - x0)))) +pagie,170,SBP,SBP,21,1,kept,4.0,4.0,0.028119+0.006351*(exp((((x0+x0)-(x0*x0))-(((x1+x0)+(-4.674000-x0))*((x0-(x1*(-0.703000)))-x0))))),0.006351*exp(-x0**2 + 2*x0 - 0.703*x1**2 + 3.285822*x1) + 0.028119,saturated,292.899250,28,4,28,4,70,77,37,2,58,(0.028119 + (0.006351 * exp((((x0 + x0) - (x0 * x0)) - (((x1 + x0) + (-4.674 - x0)) * ((x0 + (0.703 * x1)) - x0)))))),saturated,2919.336000,24,6,22,5,89,99,47,2,61,((0.006351 * exp(((((2.0 * x0) - (x0 ** 2.0)) + (-0.703 * (x1 ** 2.0))) + (3.285822 * x1)))) + 0.028119) +pagie,167,SBP,SBP,18,1,kept,5.0,3.0,-8343620.960004+0.024527*((x0-((x0*x0)+(((20.791000-(x0-(x1*x0)))+((x1*x1)*(x1-4.494000)))-exp(19.645000))))),-0.024527*x0**2 - 0.024527*x0*x1 + 0.049054*x0 + x1**2*(0.110224338 - 0.024527*x1) + 94.8131869230419,saturated,467.621459,28,5,21,3,56,61,27,2,44,(0.024527 * ((3865.6658752646445 + ((x0 - (x0 * (x0 + x1))) - ((x1 * x1) * (x1 + -4.494)))) + x0)),saturated,7008.125250,27,6,21,4,60,67,33,2,56,((0.024527 * (((x1 ** 2.0) * (4.494 - x1)) + (((2.0 - x1) * x0) - (x0 ** 2.0)))) + 94.8131869230419) +pagie,173,SBP,SBP,24,1,kept,5.0,4.0,0.036923-0.004153*((((((x1*(-2.331000))+(14.536000-4.614000))*x1)*(x1*(-7.835000+x1)))*exp(((x0+(x0+x0))-exp(x0))))),0.004153*x1**2*(x1 - 7.835)*(2.331*x1 - 9.922)*exp(3*x0 - exp(x0)) + 0.036923,saturated,816.062208,29,6,25,4,565,575,96,2,53,(0.036923 - ((((-0.009680643 * (x1 * x1)) * (x1 + -4.256542256542257)) * (-7.835 + x1)) * exp(((x0 + (x0 + x0)) - exp(x0))))),saturated,431.225208,25,6,23,5,257,266,61,2,58,((((0.009680643 * ((x1 + -4.256542256542257) * (x1 ** 2.0))) * (x1 + -7.835)) * exp(((3.0 * x0) - exp(x0)))) + 0.036923) +pagie,164,SBP,SBP,15,1,kept,6.0,5.0,1.139001+0.010850*(((((x0*x0)-(-6.659000+x0))*(-12.488000+x0))-((13.571000-(exp(x0)-x0))-((x1*14.814000)-exp(x1))))),0.01085*x0**3 - 0.1463448*x0**2 + 0.19689495*x0 + 0.1607319*x1 + 0.01085*exp(x0) - 0.01085*exp(x1) + 0.0894957768,saturated,647.748500,29,6,27,5,108,115,42,2,60,(0.01085 * ((91.40605069124423 + ((exp(x0) - x0) + ((((x0 * x0) + 6.659) - x0) * (-12.488 + x0)))) + ((x1 * 14.814) - exp(x1)))),saturated,12675.696916,31,7,27,5,452,470,120,2,68,(((-0.01085 * (exp(x1) + ((((-18.147000000000002 * x0) - exp(x0)) - (x0 ** 3.0)) + (13.488 * (x0 ** 2.0))))) + (0.1607319 * x1)) + 0.0894957768) +pagie,174,SBP,SBP,25,1,kept,5.0,4.0,0.015024+291401.986945*((((exp((-17.803000+x0))*((x1-6.944000)*x1))*(((x1-5.300000)*x1)+x1))*exp((x0-(x0*x0))))),(0.00540440450573385*x1**2*(x1 - 6.944)*(x1 - 4.3)*exp(x0) + 0.015024*exp(x0*(x0 - 1)))*exp(x0*(1 - x0)),saturated,448.326584,29,5,29,5,720,728,100,2,63,(0.015024 + (291401.986945 * (((exp((-17.803 + x0)) * ((x1 + -6.944) * x1)) * (((x1 + -5.3) * x1) + x1)) * exp((x0 - (x0 * x0)))))),saturated,360.147917,32,6,32,6,450,461,93,2,75,((((((0.00540440450573385 * (x1 ** 2.0)) * (x1 + -6.944)) * (x1 + -4.3)) * exp(x0)) + (0.015024 * exp((x0 * (x0 + -1.0))))) * exp((x0 * (1.0 - x0)))) +pagie,176,SBP,SBP,27,1,kept,6.0,4.0,-0.000040+0.007900*(((((((x1+2.278000)*15.139000)-(exp(x1)-(-18.519000-2.538000)))-9.513000)+x1)*exp(((x0+x0)-(x0*x0))))),(0.1274981*x1 - 0.0079*exp(x1) - 4.0e-5*exp(x0*(x0 - 2)) + 0.0309414718)*exp(x0*(2 - x0)),saturated,302.205625,29,7,25,5,81,89,41,2,57,(-4e-05 + (0.0079 * (((((15.139 * (0.88708910760288 + x1)) - exp(x1)) + -9.513) + x1) * exp(((x0 + x0) - (x0 * x0)))))),saturated,487.719750,26,6,26,6,560,580,146,2,62,(((((0.1274981 * x1) + (-0.0079 * exp(x1))) + (-4e-05 * exp((x0 * (x0 + -2.0))))) + 0.0309414718) * exp((x0 * (2.0 - x0)))) +pagie,172,SBP,SBP,23,1,kept,4.0,4.0,0.008754-0.000016*((exp(x1)+((exp(x1)-exp(((10.503000-(exp(exp(((0.239000-x1)*x1)))+(x0*x0)))+x0)))*exp(x0)))),-1.6e-5*exp(x1) - 1.6e-5*exp(x0 + x1) + 0.582793804249181*exp(-x0**2 + 2*x0 - exp(exp(-x1**2 + 0.239*x1))) + 0.008754,saturated,412.020750,29,4,29,4,96,106,52,2,57,(0.008754 - (1.6e-05 * (exp(x1) + ((exp(x1) - exp((((10.503 - exp(exp(((0.239 - x1) * x1)))) - (x0 * x0)) + x0))) * exp(x0))))),saturated,13531.552500,38,8,32,5,182,193,68,2,74,(((-1.6e-05 * (exp(x1) + exp((x0 + x1)))) + (0.582793804249181 * exp((((2.0 * x0) - (x0 ** 2.0)) - exp(exp(((0.239 * x1) - (x1 ** 2.0)))))))) + 0.008754) +pagie,178,SBP,SBP,29,1,kept,6.0,6.0,0.105238-0.004516*((x0-(((x0*(((x1-5.432000)*x1)+x1))*((x0-x1)-3.749000))*(exp((2.638000-x0))-1.033000)))),(0.004516*x0*x1*(x1 - 4.432)*(1.033*exp(x0) - 13.9852052082504)*(-x0 + x1 + 3.749) + (0.105238 - 0.004516*x0)*exp(x0))*exp(-x0),saturated,235.400209,28,6,28,6,154,169,70,1,66,(0.105238 - (0.004516 * (x0 - (((x0 * (((x1 - 5.432) * x1) + x1)) * ((x0 - x1) - 3.749)) * (exp((2.638 - x0)) - 1.033))))),saturated,2129.606875,38,9,34,7,777,788,125,2,78,((((((0.004665028 * ((exp(x0) + -13.538436794046856) * x0)) * x1) * (x1 + -4.432)) * ((x1 - x0) + 3.749)) + ((0.004516 * (23.303365810451727 - x0)) * exp(x0))) * exp((-1.0 * x0))) +pagie,175,SBP,SBP,26,1,kept,6.0,2.0,-0.068550+0.001527*(((x0*exp(((x0+5.699000)-(x0*x0))))+((9.142000+(exp(3.890000)-(exp(x1)-exp((x0*(-16.248000))))))*x1))),0.455914378864642*x0*exp(-x0**2 + 1.0*x0) - 0.001527*x1*exp(x1) + 0.0886467577217386*x1 + 0.001527*x1*exp(-16.248*x0) - 0.06855,saturated,269.933583,29,6,28,6,93,102,47,2,65,(-0.06855 + (0.001527 * ((x0 * exp(((x0 + 5.699) - (x0 * x0)))) + ((9.142 + (48.91088652373189 - (exp(x1) - exp((x0 * -16.248))))) * x1)))),saturated,12840.148375,36,8,26,5,238,257,99,2,62,(((x1 * (0.001527 * ((exp((-16.248 * x0)) - exp(x1)) + 58.0528865237319))) - ((-0.455914378864642 * x0) * exp((x0 - (x0 ** 2.0))))) - 0.06855) +pagie,179,SBP,SBP,30,1,kept,7.0,4.0,0.001726+7916541148486.587891*(((((19.413000-x1)-14.742000)*exp(((x0+((x0-14.602000)-20.496000))-(x0*x0))))*((x1+7.517000)*x1))),(-0.004525512279437932278*x1*(x1 - 4.671)*(x1 + 7.517) + 0.001726*exp(x0*(x0 - 2)))*exp(x0*(2 - x0)),saturated,306.795958,28,7,26,6,264,273,63,2,63,(0.001726 + (7916541148486.588 * ((((19.413 - x1) + -14.742) * exp(((x0 + (-35.098 + x0)) - (x0 * x0)))) * ((x1 + 7.517) * x1)))),saturated,274.395791,27,6,27,6,198,208,65,2,64,(((((-0.004525512279437933 * x1) * (x1 + -4.671)) * (x1 + 7.517)) + (0.001726 * exp((x0 * (x0 + -2.0))))) * exp((x0 * (2.0 - x0)))) +pagie,181,SRjl,SRjl,2,1,kept,9.0,8.0,((((exp((x0 / (((x0 * -0.0022067561107765228) * x0) * x0)) * 0.001500675632471371) - exp((x1 * ((0.031646250254694995 / x1) - x1)) * 0.7356976269859291)) / 0.9595286921357497) - ((exp((0.04424753013408821 - 1.2094507170296283) * x0) + (exp(x0) / 0.3577168125819259)) * 9.500013495936925e-5)) - -1.0189821492909057),-0.0002655735811623668*exp(1.0*x0) + 1.0189821492909057 - 1.066727053275426*exp(-0.7356976269859291*x1**2) - 9.500013495936925e-5*exp(-1.1652031868955401*x0) + 1.0421783196229057*exp(-0.68003692168017009/x0**2),saturated,322.310375,41,10,37,8,186,205,93,2,86,((((exp((x0 * (-0.6800369216801702 / ((x0 * x0) * x0)))) - exp(((x1 * ((0.031646250254694995 / x1) - x1)) * 0.7356976269859291))) / 0.9595286921357497) - ((exp((-1.1652031868955401 * x0)) + (exp(x0) / 0.3577168125819259)) * 9.500013495936925e-05)) - -1.0189821492909057),saturated,9608.051292,33,9,31,8,4356,4398,1206,2,85,(((((-0.0002655735811623668 * exp(x0)) + 1.0189821492909057) + (-1.066727053275426 * exp((-0.7356976269859291 * (x1 ** 2.0))))) + (-9.500013495936925e-05 * exp((-1.1652031868955401 * x0)))) + (1.0421783196229057 * exp((-0.68003692168017 / (x0 ** 2.0))))) +pagie,177,SBP,SBP,28,1,kept,6.0,5.0,0.353732-0.011340*(((exp(((4.034000-exp(x0))-(-0.257000+x0)))+(exp(x1)+(((x0-12.363000)-x1)*x1)))+(x0*11.508000))),-0.01134*x0*x1 - 0.13050072*x0 + 0.01134*x1**2 + 0.14019642*x1 - 0.01134*exp(x1) - 0.828267606396439*exp(-x0 - exp(x0)) + 0.353732,saturated,309.334041,28,6,28,6,143,157,69,2,65,(0.01134 * ((((11.508 * (2.7105750834171647 - x0)) - exp(x1)) - (((x0 - 12.363) - x1) * x1)) - exp(((4.034 - exp(x0)) - (-0.257 + x0))))),saturated,21786.738291,36,8,30,6,1052,1077,220,2,72,((((-0.01134 * ((exp(x1) - (x1 ** 2.0)) + (x0 * (x1 + 11.508)))) + (0.14019642 * x1)) + (-0.828267606396439 * exp(((-1.0 * x0) - exp(x0))))) + 0.353732) +pagie,182,SRjl,SRjl,3,1,kept,10.0,5.0,(((exp(((x1 / -1.1526895432904412) * x1) - ((0.1560929128293564 + 0.04873876471741229) + -0.10767615949898787)) * -0.7499061083076463) - -1.1526895432904412) * ((exp((log(x1 * x1) - 78.41442075024227) + 1.0254454456547013) + ((log(x0 * (x0 + 0.0034420466463509335)) - 0.6739116903430199) * 0.1560929128293564)) + 1.4227637491659069)),(1.1526895432904412*exp(0.86753628140446462*x1**2) - 0.68047595810869021)*(2.4569429090028012e-34*x1**2 + 0.1560929128293564*log(x0*(x0 + 0.0034420466463509335)) + 1.3175709104305097)*exp(-0.86753628140446462*x1**2),saturated,294.352250,39,12,31,8,107,122,64,2,77,((-0.7499061083076463 * (exp((((x1 / -1.1526895432904412) * x1) - 0.0971555180477808)) - 1.537111820427464)) * ((0.1560929128293564 * (8.440939992393519 + log((x0 * (x0 + 0.0034420466463509335))))) + exp((-77.38897530458758 + log((x1 * x1)))))),saturated,337.112333,34,8,32,7,147,160,64,2,87,(((2.832092399669127e-34 * (exp((0.8675362814044646 * (x1 ** 2.0))) - 0.5903375822827533)) * (((x1 ** 2.0) + (635313552697525949805350164103168.0 * log((x0 * (x0 + 0.0034420466463509335))))) + 5362643574674154744724234929438720.0)) * exp((-0.8675362814044646 * (x1 ** 2.0)))) +pagie,184,SRjl,SRjl,5,1,kept,10.0,6.0,(((((1.2970116211177067 - exp(0.09432994685391581 - (((x1 * (x0 * x0)) * 0.7382751656820474) / x1))) + (((log((x0 * x0) * (x1 * x1)) + 0.7382751656820474) * -0.0021496742064029224) / 0.4593468932730417)) - exp(0.07743331735052479 - ((x1 * x1) / 1.2970116211177067))) + 0.7157260145245514) / 0.9972373150183798),-0.0046928140002785499*log(x0**2*x1**2) + 2.0148490122804748 - 1.0835035577813302*exp(-0.77100311494375405*x1**2) - 1.1019666587915574*exp(-0.7382751656820474*x0**2),saturated,917.117459,42,10,36,9,111,123,59,2,89,(((((1.2970116211177067 - exp((0.09432994685391581 + (-0.7382751656820474 * (x0 * x0))))) + ((log(((x0 * x0) * (x1 * x1))) + 0.7382751656820474) * -0.004679849233518443)) - exp((0.07743331735052479 - ((x1 * x1) / 1.2970116211177067)))) + 0.7157260145245514) / 0.9972373150183798),saturated,386.232000,30,6,30,6,646,676,184,1,84,((((-0.00469281400027855 * log(((x0 ** 2.0) * (x1 ** 2.0)))) + 2.0148490122804747) - (1.0835035577813301 * exp((-0.7710031149437541 * (x1 ** 2.0))))) - (1.1019666587915573 * exp((-0.7382751656820474 * (x0 ** 2.0))))) +pagie,180,SRjl,SRjl,1,1,kept,12.0,5.0,(((((exp(-5.8345976856156 / ((x1 / 0.24351267979731375) * (x1 + x1))) - ((exp((((x0 / 1.766673822805128) + x0) * -0.49092178828863786) * x0) + (((((exp(x1) + x1) * -0.008401864666152042) * x1) / 0.9570866462661449) * -0.008401864666152042)) + 0.2591798019283134)) + 1.310080342754076) * 1.059245011980159) - 0.12992279845402313) + 0.020457225936674983),-7.8126170022109049e-5*x1**2 - 7.8126170022109049e-5*x1*exp(x1) + 1.0036955834395923 + 1.059245011980159*exp(-0.71039925898172978/x1**2) - 1.059245011980159*exp(-0.76880092022095535*x0**2),saturated,9607.477916,44,12,34,7,147,159,67,2,78,(1.059245011980159 * (0.9475575264341134 + (exp((-5.8345976856156 / ((x1 / 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0.01298849338900694*log(0.20268567846152597*exp(x0**2) + 2.038057969841441) + 1.5507417499535017 - 1.08052508179534*exp(-0.7571275768495004*x1**2),saturated,2944.202167,40,11,31,8,237,258,101,2,77,(((log(((x0 * x0) - -0.04513019797782104)) * 0.2138739307078718) - ((exp(((x1 * -0.7571275768495004) * x1)) + -1.4351742278641733) - (-0.01202053853986061 * log((exp(((x0 * x0) + -1.5960988818854747)) + 2.038057969841441))))) / 0.925475971680782),saturated,473.705666,31,8,29,7,225,244,95,2,82,((-0.01298849338900694 * ((-120.98960384882812 + (-17.792375108540842 * log(((x0 ** 2.0) + 0.04513019797782104)))) + log((exp((x0 ** 2.0)) + 10.055263821850678)))) - (1.08052508179534 * exp((-0.7571275768495004 * (x1 ** 2.0))))) +pagie,190,SRjl,SRjl,11,1,kept,11.0,5.0,((((((((exp((x1 * x1) * (-0.8539670752898669 - -0.06861288831350038)) / -0.19259636770415733) / -0.19259636770415733) + 3.1444526030898876) * 1.076497237488826) - (log(((x0 + x0) * (x0 / 2.091840775928573)) + 0.033936636251736194) / 0.18658509602397805)) * -0.0338639205428945) - -1.5240792477436123) * 1.0741028792241336),0.19494233640325661*log(0.9560957138873036*x0**2 + 0.033936636251736194) + 1.513894369267021 - 1.0556011444784045*exp(-0.7853541869763665*x1**2),saturated,280.946625,35,12,27,8,102,117,63,2,72,(-0.036373334556940265 * ((((exp(((x1 * x1) * -0.7853541869763665)) + 0.11663831509104948) * 29.02129148555034) - (log((((x0 + x0) * (x0 / 2.091840775928573)) + 0.033936636251736194)) / 0.18658509602397805)) - 45.005989363018465)),saturated,306.071834,21,6,19,5,106,120,60,2,56,((0.19494233640325662 * (7.720960063733485 + log(((x0 ** 2.0) + 0.03549501975461879)))) - (1.0556011444784046 * exp((-0.7853541869763665 * (x1 ** 2.0))))) +pagie,189,SRjl,SRjl,10,1,kept,9.0,6.0,((exp((-1.2342630257966531 / (x0 * x0)) / ((x0 * x0) + 0.9482559484212596)) - (exp((x1 * (x1 * (0.8761146826522526 * 0.9587448440316082))) / -1.0837327603551368) - (((exp((x1 * x1) * -0.9557223147859552) * exp(0.492006378174328 / (1.588437324004253 + -0.9292660969299782))) + (-2.960691001121504 - 0.5190971040162952)) * -0.031172251360838864))) + 0.8817821046110705),0.99025493410688315 + 1.0*exp(-1.2342630257966531/(x0**2*(x0**2 + 0.9482559484212596))) - 0.065754610986397446*exp(-0.95572231478595519*x1**2) - 1.0*exp(-0.77507155407757481*x1**2),saturated,306.574667,45,13,30,6,67,75,39,2,68,((-0.06575461098639744 * (-15.059855411687186 + exp(((x1 * x1) * -0.9557223147859552)))) + (exp(((-1.2342630257966531 / (x0 * x0)) / ((x0 * x0) + 0.9482559484212596))) - exp(((x1 * x1) * -0.7750715540775749)))),saturated,1133.689000,34,8,30,6,81,92,49,2,84,((((-0.06575461098639744 * exp((-0.9557223147859552 * (x1 ** 2.0)))) - exp((-0.7750715540775748 * (x1 ** 2.0)))) - -0.9902549341068831) + exp((-1.2342630257966531 / ((x0 ** 2.0) * ((x0 ** 2.0) + 0.9482559484212596))))) +pagie,192,SRjl,SRjl,13,1,kept,13.0,7.0,(((((exp((-0.7138528763883562 / (x0 * x0)) + 0.6575814106270943) - 0.5583647924168882) + 2.5240588769642627) - (((exp(((x1 * x1) * (-0.7420809685476653 * 1.0343924978284673)) + 2.722416367428707) / 0.4579119827966314) - ((1.7325139467565818 - exp(x0 * ((0.06237773186828809 * x0) - x0))) * 1.1857194316753739)) * 0.06237773186828809)) / 1.8907855438451246) + -0.0595161601319482),1.047872847950701 - 1.0963158762930161*exp(-0.76760298664698778*x1**2) - 0.039117333544688729*exp(-0.9376222681317119*x0**2) + 1.0208024526117151*exp(-0.7138528763883562/x0**2),saturated,709.718416,44,14,36,10,132,147,71,2,93,(((1.8531617893447152 + exp(((-0.7138528763883562 / (x0 * x0)) + 0.6575814106270943))) + ((exp((((x1 * x1) * -0.7676029866469878) + 2.722416367428707)) + (-0.5429551359989654 * (1.7325139467565818 - exp((x0 * ((0.06237773186828809 * x0) - x0)))))) * -0.13622209990515008)) / 1.8907855438451246),saturated,517.574292,28,7,28,7,715,745,195,2,81,(((1.047872847950701 - (1.096315876293016 * exp((-0.7676029866469878 * (x1 ** 2.0))))) + (-0.03911733354468873 * exp((-0.9376222681317119 * (x0 ** 2.0))))) + 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1.0664521063252117*exp(-0.10404642108656967*x0**2*x1**2) - 0.48069483321790738*exp(-x0**2),saturated,902.997583,45,8,39,8,252,265,83,2,90,(((-1.0664521063252117 / exp(((x0 * (x0 * (x1 * x1))) * 0.10404642108656967))) + 1.944047815133558) + ((((((x1 * 0.8979952519492354) - x1) * x1) + 1.0286004868903225) / exp(((x0 * x0) + 1.294289683924389))) * (((x1 * 0.13355299915112226) * x1) + -1.7050047618728166))),saturated,6639.067000,49,9,35,7,349,372,130,2,100,(((exp((-1.0 * (x0 ** 2.0))) * (-0.4806948332179074 + ((-0.003733972929107801 * (x1 ** 4.0)) + (0.08532259609581337 * (x1 ** 2.0))))) + 1.944047815133558) + (-1.0664521063252117 * exp(((-0.10404642108656967 * (x0 ** 2.0)) * (x1 ** 2.0))))) +pagie,204,SRjl,SRjl,25,1,kept,12.0,5.0,(((((x1 / 0.6289404449426587) / x1) + ((exp((x1 * ((x0 - x0) - (x1 * 0.7129831793049115))) - -0.09328282342059575) * 1.950745841766394) / -1.9881017574797382)) - ((((log(((x0 * x0) - -0.012659920175938618) * 0.74536250005349) * 1.1684223581358428) + -0.06564012561915462) / 0.44888855366171493) * -0.06798257267019443)) + 0.026976315382705767),0.17695340463350413*log(0.74536250005349*x0**2 + 0.0094362297528152276) + 1.6070110136575641 - 1.0771453131190881*exp(-0.7129831793049115*x1**2),saturated,9996.834417,41,12,27,7,125,138,63,2,68,((0.17695340463350415 * (-0.19761433110752527 + log(((x0 * x0) + 0.012659920175938618)))) + (((x1 / 0.6289404449426587) / x1) + (exp(((x1 * (-0.7129831793049115 * x1)) + 0.09328282342059575)) * -0.9812102596998359))),saturated,306.008834,21,6,19,5,106,120,60,2,56,((0.17695340463350412 * (8.787664391311479 + log(((x0 ** 2.0) + 0.012659920175938618)))) - (1.077145313119088 * exp((-0.7129831793049115 * (x1 ** 2.0))))) +kotanchek,2,Bingo,Bingo,3,1,kept,6.0,5.0,-0.01768299095097286 + (-0.002127834025158428)*(((x0)*(x0))*((-120.62183607997726 + (375.5222524620757)*((x1)*(-4.734655034994491 + x1)))*((exp((2)*(x0)))^(-1)))),(x0**2*(-0.7990490259929379*x1*(x1 - 4.734655034994491) + 0.25666324698805811) - 0.01768299095097286*exp(2*x0))*exp(-2*x0),saturated,418.495000,24,6,22,5,184,193,53,2,57,(-0.01768299095097286 + (((-0.799049025992938 * (x0 * x0)) * ((x1 * (-4.734655034994491 + x1)) + -0.3212108877413568)) * (exp((2.0 * x0)) ** -1.0))),saturated,287.764250,25,6,25,6,160,175,74,1,65,((((x0 ** 2.0) * (((-0.7990490259929379 * x1) * (x1 - 4.734655034994491)) + 0.2566632469880581)) - (0.01768299095097286 * exp((2.0 * x0)))) * exp((-2.0 * x0))) +pagie,171,SBP,SBP,22,1,kept,6.0,2.0,0.179028-0.009630*((exp((x0*(-15.767000)))+((exp(x1)-(((((x0+(x0+x0))-18.776000)*x0)+18.776000)*x0))+(-14.972000*x1)))),0.02889*x0**3 - 0.18081288*x0**2 + 0.18081288*x0 + 0.14418036*x1 - 0.00963*exp(x1) + 0.179028 - 0.00963*exp(-15.767*x0),saturated,452.049042,29,6,29,6,86,96,47,2,67,(0.00963 * ((((18.590654205607475 - exp((x0 * -15.767))) + (14.972 * x1)) - exp(x1)) + (((((x0 + (x0 + x0)) + -18.776) * x0) + 18.776) * x0))),saturated,55452.304792,33,8,29,6,4858,4891,1479,2,75,(((-0.00963 * (exp((-15.767 * x0)) + exp(x1))) + (((0.18081288 * (x0 - (x0 ** 2.0))) + (0.02889 * (x0 ** 3.0))) + (0.14418036 * x1))) + 0.179028) +kotanchek,3,Bingo,Bingo,4,1,kept,4.0,4.0,(-0.03144312866911644)*(-3.0969157782045578 + (-31.196859437348742)*((-0.044758903858526766)*(x0) + ((x0)*(x0))*((exp((x0)*(x0)))^(-1))) - (x1)),0.980926865360896*x0**2*exp(-x0**2) - 0.043905211258934374*x0 + 0.03144312866911644*x1 + 0.097376721291502782,saturated,307.034208,22,4,20,4,64,72,36,2,50,(-0.03144312866911644 * ((-3.0969157782045578 + (-31.196859437348742 * (x0 * (-0.044758903858526766 + ((exp((x0 * x0)) ** -1.0) * x0))))) - x1)),saturated,648.519625,22,5,22,5,705,728,171,2,61,((0.09737672129150278 + (((0.980926865360896 * (x0 ** 2.0)) * exp((-1.0 * (x0 ** 2.0)))) + (-0.043905211258934373 * x0))) + (0.03144312866911644 * x1)) +kotanchek,5,Bingo,Bingo,6,1,kept,7.0,5.0,(x0)*((-0.708264064344585 + (0.22602214542380888)*(x0))*(-0.708264064344585 + (0.22602214542380888)*(x0))) + ((0.3286374849396323)*((x0 - ((x0)*(x0)))*(x1)) + (x1)*(x1))*(0.07900418526719069 + (-0.004875727623836811)*((x1)*(x1))),0.50163798484191*x0*(0.31912129501157985*x0 - 1)**2 - x1*(0.004875727623836811*x1**2 - 0.07900418526719069)*(-0.3286374849396323*x0*(x0 - 1) + x1),saturated,351.532292,35,7,31,6,241,251,71,2,71,((x0 * (0.051086010221981414 * ((x0 + -3.1336047315918334) * (x0 + -3.1336047315918334)))) + ((x1 * ((0.3286374849396323 * (x0 - (x0 * x0))) + x1)) * (0.07900418526719069 + (-0.004875727623836811 * (x1 * x1))))),saturated,332.844166,31,7,31,7,346,365,111,2,83,(((0.50163798484191 * x0) * (((0.3191212950115799 * x0) - 1.0) ** 2.0)) - (((((-0.3286374849396323 * x0) * (x0 - 1.0)) + x1) * x1) * ((0.004875727623836811 * (x1 ** 2.0)) - 0.07900418526719069))) +kotanchek,0,Bingo,Bingo,1,1,kept,4.0,4.0,0.11064466475608078 + (-0.010036545250561161)*((2)*(x0) + (2)*(x1)) + (0.713072197849276)*((0.022522799045566234 + (x0)*(x0))*(((x0)*(x0) + ((2)^(-1))*(((x1)^(-1))*(exp((x0)*(x0)))))^(-1))),(1.42614439569855*x1*(x0**2 + 0.022522799045566234) + (2*x0**2*x1 + exp(x0**2))*(-0.020073090501122322*x0 - 0.020073090501122322*x1 + 0.11064466475608078))/(2*x0**2*x1 + exp(x0**2)),saturated,3807.736875,38,7,32,5,173,184,65,2,76,((-0.020073090501122322 * ((x0 + x1) + -5.5120891698213805)) + (0.713072197849276 * ((0.022522799045566234 + (x0 * x0)) * (((x0 * x0) + (0.5 * ((x1 ** -1.0) * exp((x0 * x0))))) ** -1.0)))),saturated,800.381541,45,7,43,6,97,104,42,2,108,(((((x0 ** 2.0) + 0.022522799045566234) * x1) + (-0.014075075820979669 * ((((2.0 * (x0 ** 2.0)) * x1) + exp((x0 ** 2.0))) * ((x0 + x1) + -5.5120891698213805)))) * (1.42614439569855 / (((2.0 * (x0 ** 2.0)) * x1) + exp((x0 ** 2.0))))) +kotanchek,4,Bingo,Bingo,5,1,kept,7.0,5.0,-0.00021014784984354508 + (-79102.81028278018 + (9.442859863771085)*(8377.090142621715 + (x1)*(4.739077949578231 - (x1))))*((1.3508252037586896e-06)*(x0) + (0.004486719103561921)*(exp((2)*(x0) - ((x0)*(x0))))),(-(1.3508252037586896e-6*x0*exp(x0*(x0 - 2)) + 0.004486719103561921)*(9.442859863771085*x1*(x1 - 4.739077949578231) - 0.8780001748054929) - 0.00021014784984354508*exp(x0*(x0 - 2)))*exp(x0*(2 - x0)),saturated,307.843625,28,8,24,6,73,82,41,2,60,(-0.00021014784984354508 + ((0.04236745974303985 * (exp(((2.0 * x0) - (x0 * x0))) + (0.00030107193532269384 * x0))) * (0.0929803245489893 + (x1 * (4.739077949578231 - x1))))),saturated,1049.783667,40,10,36,8,158,174,77,2,85,((((1.275565309954333e-05 * (((x1 - 4.739077949578231) * x1) - 0.092980324549141)) * (-3321.465346573016 - (exp((x0 * (x0 - 2.0))) * x0))) - (0.00021014784984354508 * exp((x0 * (x0 - 2.0))))) * exp((x0 * (2.0 - x0)))) +kotanchek,7,Bingo,Bingo,8,1,kept,6.0,5.0,(0.11720391936222797)*((x1)*((0.6931234338478329 + (x0)*(6.4849819024041455 + (-0.6667403548542734)*((-1.3864562418418644 + x1)*(-1.3864562418418644 + x1)) - (x0)))*((exp(x0))^(-1)))),-0.11720391936222797*x1*(x0*(x0 + 1.2816489216174494*(0.72126329690112023*x1 - 1)**2 - 6.4849819024041455) - 0.6931234338478329)*exp(-x0),saturated,253.746083,26,6,26,6,120,129,48,1,67,(0.11720391936222797 * (x1 * ((0.6931234338478329 + (x0 * ((6.4849819024041455 + (-0.6667403548542734 * ((-1.3864562418418644 + x1) * (-1.3864562418418644 + x1)))) - x0))) * (exp(x0) ** -1.0)))),saturated,341.619875,26,7,26,7,148,162,65,2,71,(((-0.11720391936222797 * x1) * ((x0 * ((x0 + (1.2816489216174494 * ((0.7212632969011202 * (x1 - 1.3864562418418644)) ** 2.0))) - 6.4849819024041455)) - 0.6931234338478329)) * exp((-1.0 * x0))) +kotanchek,8,Bingo,Bingo,9,1,kept,2.0,2.0,(exp(x0))*((3.396536372521252 + ((0.4137631538437465 + x1)^(-1))*(((exp(x0))^(-1))*(exp(exp(x0)))))^(-1)),(x1 + 0.4137631538437465)*exp(2*x0)/(3.396536372521252*(x1 + 0.4137631538437465)*exp(x0) + exp(exp(x0))),saturated,240.479792,21,2,21,2,49,54,26,1,50,(exp(x0) * ((3.396536372521252 + (((0.4137631538437465 + x1) ** -1.0) * ((exp(x0) ** -1.0) * exp(exp(x0))))) ** -1.0)),saturated,314.495750,21,4,21,4,58,63,28,1,46,(((x1 + 0.4137631538437465) * exp((2.0 * x0))) / (((3.396536372521252 * (x1 + 0.4137631538437465)) * exp(x0)) + exp(exp(x0)))) +kotanchek,10,Bingo,Bingo,11,1,kept,4.0,4.0,0.2306440753250631 + (0.03139967317000205)*(x1) + (-1.1634241022901022 + (exp(exp(-1 + x0)))^(-1))*(1.2522488356336676 - (exp((x0)*((exp(exp(-1 + x0)))^(-1))))),((0.03139967317000205*x1 + 0.2306440753250631)*exp(exp(x0 - 1)) + (exp(x0*exp(-exp(x0 - 1))) - 1.2522488356336676)*(1.1634241022901022*exp(exp(x0 - 1)) - 1))*exp(-exp(x0 - 1)),saturated,258.111875,28,6,28,6,69,77,38,1,72,((0.2306440753250631 + (0.03139967317000205 * x1)) + ((-1.1634241022901022 + (exp(exp((-1.0 + x0))) ** -1.0)) * (1.2522488356336676 - exp((x0 * (exp(exp((-1.0 + x0))) ** -1.0)))))),saturated,288.804208,42,11,42,11,167,180,71,2,103,((((0.03139967317000205 * (x1 + 7.34542917298295)) * exp(exp((x0 - 1.0)))) + ((exp((x0 * exp((-1.0 * exp((x0 - 1.0)))))) - 1.2522488356336676) * ((1.1634241022901022 * exp(exp((x0 - 1.0)))) - 1.0))) * exp((-1.0 * exp((x0 - 1.0))))) +kotanchek,9,Bingo,Bingo,10,1,kept,3.0,3.0,(0.03943336488999562)*((x1)*(((x0)*(x0) + x1)*((0.12426947579595604 + (0.046906498950706255)*(x1 + (4)*((x1)*(x1)) + exp((x0)*(x0))) - (plog(x1)))^(-1)))),0.03943336488999562*x1*(x0**2 + x1)/(0.18762599580282502*x1**2 + 0.046906498950706255*x1 + 0.046906498950706255*exp(x0**2) - log(x1) + 0.12426947579595604),saturated,346.376583,32,4,32,4,178,186,57,2,67,(0.03943336488999562 * (x1 * (((x0 * x0) + x1) * (((0.046906498950706255 * (((x1 + (4.0 * (x1 * x1))) + exp((x0 * x0))) + 2.649301878755651)) - log(abs(x1))) ** -1.0)))),saturated,714.287833,31,5,29,4,112,119,44,2,71,(((0.03943336488999562 * x1) * ((x0 ** 2.0) + x1)) / (((0.046906498950706255 * (exp((x0 ** 2.0)) + (x1 + (4.0 * (x1 ** 2.0))))) - log(x1)) + 0.12426947579595604)) +kotanchek,11,Bingo,Bingo,12,1,kept,6.0,5.0,(-0.04106910574307527)*(78.09907550417113 + x0 + (1.0611956406287764)*((x1)*(-4.735723943783631 + x1))) + (0.00822065460724008 + (x0)*(x0))*((exp((x0)*(x0)))^(-1)) - (plog(-0.04106910574307527)),(x0**2 - (0.04106910574307527*x0 + 0.043582355979073722*x1*(x1 - 4.735723943783631) + 0.01496006509706177 + I*pi)*exp(x0**2) + 0.00822065460724008)*exp(-x0**2),saturated,285.683333,30,6,26,5,84,93,43,2,63,((-0.04106910574307527 * ((0.36426566457643617 + x0) + (1.0611956406287764 * (x1 * (-4.735723943783631 + x1))))) + ((0.00822065460724008 + (x0 * x0)) * (exp((x0 * x0)) ** -1.0))),saturated,322.690458,35,6,35,6,240,257,92,2,88,((((x0 ** 2.0) - (((((0.04106910574307527 * x0) + ((0.04358235597907372 * x1) * (x1 + -4.735723943783631))) + 0.01496006509706177) + (I * pi)) * exp((x0 ** 2.0)))) + 0.00822065460724008) * exp((-1.0 * (x0 ** 2.0)))) +kotanchek,12,Bingo,Bingo,13,1,kept,9.0,5.0,((69920813446.957 + (3837.522818140268)*((-6411.945978052463 + (5614.613323813786)*(x0))*(-6411.945978052463 + (5614.613323813786)*(x0))))^(-1))*(32356483533.402588 + (-10343913179.625605)*(x0) + (5885307060.08351)*(x1)),(-10343913179.625605*x0 + 5885307060.08351*x1 + 32356483533.402588)/(157772272201.0846*(0.8756488814834252*x0 - 1)**2 + 69920813446.957),saturated,320.074000,27,9,23,7,184,199,76,2,67,(((69920813446.957 + (120973619469.07672 * ((x0 + -1.142010252221088) * (x0 + -1.142010252221088)))) ** -1.0) * ((32356483533.402588 + (-10343913179.625605 * x0)) + (5885307060.08351 * x1))),saturated,502.721708,21,7,19,6,85,96,47,2,57,((-0.065562300874022 * ((x0 + (-0.5689633079747608 * x1)) + -3.1280699065741504)) / (((0.8756488814834252 * (x0 + -1.142010252221088)) ** 2.0) + 0.4431755496164828)) +kotanchek,14,Bingo,Bingo,15,1,kept,3.0,3.0,-0.009079799107138235 + (0.973619601464109)*((-1.1573239810414302 + (x1)^(-2) + exp(x0) + (-2)*(plog(x0)))^(-1)),-0.009079799107138235 + 0.973619601464109/(exp(x0) - 2*log(x0) - 1.1573239810414302 + x1**(-2)),saturated,343.495584,20,4,20,4,116,125,47,1,53,(-0.009079799107138235 + (0.973619601464109 * ((((-1.1573239810414302 + (x1 ** -2.0)) + exp(x0)) + (-2.0 * log(abs(x0)))) ** -1.0))),saturated,391.646542,17,4,17,4,100,107,38,2,45,(-0.009079799107138235 + (0.973619601464109 / (((exp(x0) + (-2.0 * log(x0))) + -1.1573239810414302) + (x1 ** -2.0)))) +kotanchek,15,Bingo,Bingo,16,1,kept,5.0,4.0,-5.9611827480310925e-05 + (-8.813638500217107e-05)*((-119.17342611160666 + (1306.8992589231564)*((x1)*(-4.739082076972427 + x1)))*((exp((-1 + x0)*(-1 + x0)))^(-1))),(-0.11518537624350337*x1*(x1 - 4.739082076972427) - 5.9611827480310925e-5*exp((x0 - 1)**2) + 0.010503514965800351)*exp(-(x0 - 1)**2),saturated,311.857000,24,7,22,6,65,73,36,2,61,(-5.9611827480310925e-05 + ((-0.11518537624350336 * ((x1 * (-4.739082076972427 + x1)) + -0.09118792079643674)) * (exp(((-1.0 + x0) * (-1.0 + x0))) ** -1.0))),saturated,265.082667,27,7,27,7,215,232,88,1,76,(((((-0.11518537624350338 * x1) * (x1 - 4.739082076972427)) - (5.9611827480310925e-05 * exp(((x0 - 1.0) ** 2.0)))) + 0.010503514965800351) * exp((-1.0 * ((x0 - 1.0) ** 2.0)))) 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- (x0)))^(-1)) - ((x1)*(x1)))),0.004874455021822982*(x1 + 0.6623280966084486)*(x0 + (9.896181203737148 - x1**2)*exp(x0*(x0 - 2)) + 10.524866972388967)*exp(x0*(2 - x0)),saturated,249.114250,26,5,26,5,64,71,35,1,63,(0.004874455021822982 * ((0.6623280966084486 + x1) * ((9.896181203737148 + ((10.524866972388967 + x0) * (exp(((x0 * (-1.0 + x0)) - x0)) ** -1.0))) - (x1 * x1)))),saturated,290.247875,29,6,29,6,125,133,48,2,71,(((0.004874455021822982 * (x1 + 0.6623280966084486)) * ((x0 + ((9.896181203737148 - (x1 ** 2.0)) * exp((x0 * (x0 + -2.0))))) + 10.524866972388967)) * exp((x0 * (2.0 - x0)))) +kotanchek,20,Bingo,Bingo,21,1,kept,4.0,4.0,((2)*(0.17850583364543127))*((x0 + exp(x0))*((((-1)*(0.17850583364543127))*((x0)*(exp(x0))) + exp(((2)*(0.17850583364543127))*(x0 + exp(x0))) - (plog(((2)*(0.17850583364543127))*(x0 + exp(x0)))))^(-1))),0.35701166729086254*(-x0 - exp(x0))/(0.17850583364543127*x0*exp(x0) - exp(0.35701166729086254*x0 + 0.35701166729086254*exp(x0)) + log(x0 + exp(x0)) - 1.0299868162495162),saturated,300.794000,40,8,32,4,103,110,44,2,65,(0.35701166729086253 * ((x0 + exp(x0)) * ((((-0.17850583364543127 * (x0 * exp(x0))) + exp((0.35701166729086253 * (x0 + exp(x0))))) - log((0.35701166729086253 * abs((x0 + exp(x0)))))) ** -1.0))),saturated,286.292583,33,6,31,5,83,89,38,2,64,((0.35701166729086253 * ((-1.0 * x0) - exp(x0))) / (((((0.17850583364543127 * x0) * exp(x0)) - exp((0.35701166729086253 * (x0 + exp(x0))))) + log((x0 + exp(x0)))) + -1.0299868162495163)) +kotanchek,19,Bingo,Bingo,20,1,kept,5.0,5.0,(-0.03309619870833754)*(-3.819150332778322 + x0 + (0.03907279509253594 + (x0)*(x0))*((-15.272972634101004 + (-7.53747357012547)*(x1))*((exp((x0)*(x0)))^(-1)))),((0.1263993583106448 - 0.03309619870833754*x0)*exp(x0**2) + 0.03309619870833754*(x0**2 + 0.03907279509253594)*(7.53747357012547*x1 + 15.272972634101004))*exp(-x0**2),saturated,293.134333,24,5,24,5,123,132,48,2,60,(-0.03309619870833754 * ((-3.819150332778322 + x0) + ((0.03907279509253594 + (x0 * x0)) * ((-7.53747357012547 * (x1 + 2.026272131107024)) * (exp((x0 * x0)) ** -1.0))))),saturated,924.317291,31,7,29,6,152,164,65,2,79,((((0.1263993583106448 + (-0.03309619870833754 * x0)) * exp((x0 ** 2.0))) + ((0.24946172303571493 * (x1 + 2.026272131107024)) * ((x0 ** 2.0) + 0.03907279509253594))) * exp((-1.0 * (x0 ** 2.0)))) +kotanchek,13,Bingo,Bingo,14,1,kept,5.0,5.0,(-0.008870475378536939 + (-0.0506336679649604)*(x1))*(((x0 + (-0.3460574947000204)*(1.0326587094648079 + exp(x0)))^(-1))*(plog(-9.541496629390634 + (2)*(x1)))),(0.0506336679649604*x1 + 0.008870475378536939)*log(2*x1 - 9.541496629390634)/(-x0 + 0.3460574947000204*exp(x0) + 0.35735928587754767),saturated,302.615542,24,6,24,6,140,152,60,1,63,((-0.008870475378536939 + (-0.0506336679649604 * x1)) * (((x0 + (-0.3460574947000204 * (1.0326587094648079 + exp(x0)))) ** -1.0) * log(abs((-9.541496629390634 + (2.0 * x1)))))),saturated,2623.756333,23,7,21,6,105,114,46,2,55,(((0.0506336679649604 * (x1 + 0.1751892709940647)) * (0.6931471805599453 + log((x1 + -4.770748314695317)))) / ((0.35735928587754767 - x0) + (0.3460574947000204 * exp(x0)))) +kotanchek,21,Bingo,Bingo,22,1,kept,3.0,3.0,(0.6877488188414488)*(exp((2)*(x0) - ((x0)*(x0) + (-0.8494111690013563 - (x1))*((-0.2000198424296049 - (x1))^(-1))))),0.6877488188414488*exp(-(-x0*(2 - x0)*(x1 + 0.2000198424296049) + x1 + 0.8494111690013563)/(x1 + 0.2000198424296049)),saturated,272.515709,20,4,20,4,43,50,30,2,50,(0.6877488188414488 * exp((((2.0 * x0) - (x0 * x0)) - ((-0.8494111690013563 - x1) * ((-0.2000198424296049 - x1) ** -1.0))))),saturated,337.754666,24,7,20,5,56,63,32,2,50,(0.6877488188414488 * exp((((((-2.0 + x0) * ((-0.2000198424296049 - x1) * x0)) - x1) + -0.8494111690013563) / (x1 + 0.2000198424296049)))) +kotanchek,22,Bingo,Bingo,23,1,kept,7.0,6.0,(2.5131784365055503)*(((exp(x0))^(-1))*(20.83283257582063 + x0 + (0.029475689425325854)*(x1) + (-0.6569808069960112)*((5.186033678881531 - (x0))*(5.714201897136322 + x0 + ((2.5131784365055503)^(-1))*(exp(x0)))))),(2.5131784365055503*x0 + 0.074077667064863612*x1 + 1.6511099973403901*(x0 - 5.186033678881531)*(x0 + 0.39790250683132961*exp(x0) + 5.714201897136322) + 52.356625600882787)*exp(-x0),saturated,311.269500,31,7,29,7,234,249,85,2,75,(2.5131784365055503 * ((exp(x0) ** -1.0) * (((20.83283257582063 + x0) + (0.029475689425325854 * x1)) + (-0.6569808069960112 * ((5.186033678881531 - x0) * ((5.714201897136322 + x0) + (0.3979025068313296 * exp(x0)))))))),saturated,534.865583,29,8,29,8,582,604,156,2,75,(((((2.5131784365055503 * x0) + (0.07407766706486361 * x1)) + ((1.65110999734039 * (x0 + -5.186033678881531)) * ((x0 + (0.3979025068313296 * exp(x0))) + 5.714201897136322))) + 52.356625600882786) * exp((-1.0 * x0))) +kotanchek,23,Bingo,Bingo,24,1,kept,8.0,8.0,0.006514843839523813 + (0.012790360845057828 + (-0.13720269441638683)*((x0 + (x0)*(x0))*(2.4024045089083383 + x1)))*((-1.5068813313136211 + (-0.32506758388128154)*(exp((x0)*(x0))) - ((x0)*(x0)))^(-1)) + exp(-1.5068813313136211 + (-0.32506758388128154)*(exp((x0)*(x0)))),(0.13720269441638683*(x0**2 + x0)*(x1 + 2.4024045089083383) - 0.012790360845057828)/(x0**2 + 0.32506758388128154*exp(x0**2) + 1.5068813313136211) + 0.006514843839523813 + 0.22159999840345781*exp(-0.32506758388128154*exp(x0**2)),saturated,266.559750,40,8,40,8,120,132,59,1,95,((0.006514843839523813 + ((0.012790360845057828 + (-0.13720269441638683 * ((x0 + (x0 * x0)) * (2.4024045089083383 + x1)))) * (((-1.5068813313136211 + (-0.32506758388128154 * exp((x0 * x0)))) - (x0 * x0)) ** -1.0))) + exp((-1.5068813313136211 + (-0.32506758388128154 * exp((x0 * x0)))))),saturated,331.451292,38,8,38,8,204,221,88,2,104,((((((0.13720269441638683 * ((x0 ** 2.0) + x0)) * (x1 + 2.4024045089083383)) + -0.012790360845057828) / (((x0 ** 2.0) + (0.32506758388128154 * exp((x0 ** 2.0)))) + 1.5068813313136211)) + 0.006514843839523813) + (0.22159999840345782 * exp((-0.32506758388128154 * exp((x0 ** 2.0)))))) 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+ (2.057897964881403)*(x1) - (x0))^(-1))*(0.20556825888097427 + (-2.9052829962789213)*(x0) + exp(plog(x0)) - (x1))),(3.678253204741038*x0 + 1.9305547847352778*x1 - 0.39686078577236514)/(x0**6 - x0 + 2.057897964881403*x1 + 10.665734721501936),saturated,308.939958,36,5,34,5,103,112,48,2,75,(-1.9305547847352778 * (((((10.665734721501936 + ((x0 * (x0 * x0)) * (x0 * (x0 * x0)))) + (2.057897964881403 * x1)) - x0) ** -1.0) * (((-2.9052829962789213 * (x0 + -0.07075670739968036)) + abs(x0)) - x1))),saturated,273.490750,21,5,21,5,195,213,86,1,56,((((3.678253204741038 * x0) + (1.9305547847352778 * x1)) - 0.39686078577236517) / ((((x0 ** 6.0) - x0) + (2.057897964881403 * x1)) + 10.665734721501936)) +kotanchek,27,Bingo,Bingo,28,1,kept,4.0,4.0,(0.20913305449088818 + (0.62938832186819)*(x0))*(exp((2.665810272148384)*(((-12.800195782530425 + (3)*(x0) - (x1))^(-1))*(exp(x0))))),(0.62938832186819*x0 + 0.20913305449088818)*exp(-2.665810272148384*exp(x0)/(-3*x0 + x1 + 12.800195782530425)),saturated,276.466875,21,5,21,5,88,98,46,1,55,((0.20913305449088818 + (0.62938832186819 * x0)) * exp((2.665810272148384 * ((((-12.800195782530425 + (3.0 * x0)) - x1) ** -1.0) * exp(x0))))),saturated,259.932500,19,5,19,5,91,100,44,1,48,(((0.62938832186819 * x0) + 0.20913305449088818) * exp(((-2.665810272148384 * exp(x0)) / (((-3.0 * x0) + x1) + 12.800195782530425)))) +kotanchek,25,Bingo,Bingo,26,1,kept,6.0,6.0,0.2497806421525048 + (-0.6964203985908678 + (2)*(((exp(x0))^(-1))*(plog(x0 + exp(x0)))))*(0.11848913269441189 + (0.13470217521610287 + (0.5185123293134022)*(x0))*(-0.0008622481242864235 + (2)*(((exp(x0))^(-1))*(plog(x0 + exp(x0)))))),(((0.5185123293134022*x0 + 0.13470217521610287)*(0.0008622481242864235*exp(x0) - 2*log(x0 + exp(x0))) - 0.11848913269441189*exp(x0))*(0.6964203985908678*exp(x0) - 2*log(x0 + exp(x0))) + 0.2497806421525048*exp(2*x0))*exp(-2*x0),saturated,356.042125,41,8,37,6,80,89,44,2,84,(0.2497806421525048 + ((2.0740493172536087 * (((exp(x0) ** -1.0) * log(abs((x0 + exp(x0))))) + -0.3482101992954339)) * (((((exp(x0) ** -1.0) * log(abs((x0 + exp(x0))))) + -0.00043112406214321176) * (x0 + 0.25978586737652176)) + 0.11425874178470499))),saturated,1040.189458,48,10,44,8,155,166,67,2,94,((((-0.08251824901972855 * (exp(x0) + (-2.8718285737275733 * log((x0 + exp(x0)))))) * (exp(x0) + (-0.0037732260605107 * ((x0 + 0.25978586737652176) * (exp(x0) + (-2319.517948102414 * log((x0 + exp(x0))))))))) + (0.2497806421525048 * exp((2.0 * x0)))) * exp((-2.0 * x0))) +kotanchek,28,Bingo,Bingo,29,1,kept,6.0,6.0,(1.550707023441505e-05 + (6.656270926980652e-05)*(x1))*((-52.61627831646421 + exp(x0))*((35.56866639996601)*((x1)*((6.784280947796324 - (x1))^(-1))) + (exp(x0))*((-52.61627831646421 + exp(x0))*((exp(x0) - (x0))^(-1))))),-(6.656270926980652e-5*x1 + 1.550707023441505e-5)*(35.56866639996601*x1*(x0 - exp(x0)) + (x1 - 6.784280947796324)*(exp(x0) - 52.61627831646421)*exp(x0))*(exp(x0) - 52.61627831646421)/((x0 - exp(x0))*(x1 - 6.784280947796324)),saturated,250.100375,35,6,35,6,143,152,54,1,83,((1.550707023441505e-05 + (6.656270926980652e-05 * x1)) * ((-52.61627831646421 + exp(x0)) * ((35.56866639996601 * (x1 * ((6.784280947796324 - x1) ** -1.0))) + (exp(x0) * ((-52.61627831646421 + exp(x0)) * ((exp(x0) - x0) ** -1.0)))))),saturated,859.808208,42,8,40,7,306,320,86,2,86,(((((-6.656270926980652e-05 * x1) - 1.550707023441505e-05) * ((((x1 - 6.784280947796324) * (exp(x0) - 52.61627831646421)) * exp(x0)) - ((-35.56866639996601 * x1) * (x0 - exp(x0))))) * (exp(x0) - 52.61627831646421)) / ((x0 - exp(x0)) * (x1 - 6.784280947796324))) +kotanchek,32,EPLEX,EPLEX,3,1,kept,3.0,3.0,(0.414/exp(((-0.896^2)*((x0-0.8)^2)))),0.414*exp(0.802816*(x0 - 0.8)**2),saturated,365.444792,14,4,10,3,34,41,26,2,31,(0.414 / exp((-0.8028160000000001 * ((x0 - 0.8) ** 2.0)))),saturated,266.342167,10,3,10,3,35,42,26,1,31,(0.414 * exp((0.802816 * ((x0 - 0.8) ** 2.0)))) +kotanchek,33,EPLEX,EPLEX,4,1,kept,10.0,7.0,((0.002+((0.192*(-1.412+plog(((x0*0.268)-exp(-1.569)))))^2))*(((x1*(-0.008+plog(((x1*0.384)-exp(exp(-0.001))))))*0.4)+0.096)),(0.4*x1*(plog(0.384*x1 - 2.71556626264888) - 0.008) + 0.096)*(0.073497378816*(0.708215297450425*plog(0.268*x0 - 0.208253331596652) - 1)**2 + 0.002),saturated,321.391167,34,10,27,8,100,112,55,2,75,((0.002 + ((0.192 * (-2.72876829847128 + log(abs((x0 + -0.7770646701367595))))) ** 2.0)) * (((x1 * (-0.9651127263944101 + log(abs((x1 + -7.071787142314785))))) * 0.4) + 0.096)),saturated,300.124042,33,11,27,8,82,93,49,2,75,((0.029398951526400003 * (((-0.9651127263944101 + log(abs((x1 + -7.0717871423147916)))) * x1) + 0.24)) * (((0.708215297450425 * (-2.72876829847128 + log(abs((x0 + -0.7770646701367612))))) ** 2.0) + 0.02721185479290331)) +kotanchek,29,Bingo,Bingo,30,1,kept,7.0,6.0,0.042494906292620545 + (-0.03269369442908581)*(((2)^(-1))*((x0)*(((exp(x0))^(-1))*((-9.993015936395594)*(x1 - (-3.303202526637662)) + 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0.115))))) + ((x0 - exp((0.288 - (x1 ** 2.0)))) - (x0 ** 2.0))) + x0)),saturated,8944.307916,46,9,44,8,140,154,72,2,116,(0.435642283097052 * exp((((((((2.0 * x0) - (x0 ** 2.0)) - (0.0269776062506729 * exp(x1))) - (0.783533093999475 * exp(((0.115 * (x1 ** 2.0)) * (2.0 - (x1 ** 2.0)))))) * exp((x1 ** 2.0))) - 1.33375730412338) * exp((-1.0 * (x1 ** 2.0)))))) +kotanchek,97,GOMEA,GOMEA,8,1,kept,3.0,3.0,0.040188-0.167339*((exp((exp(-4.145000)-(x1*x1)))-exp(((x0+x0)-(x0*x0))))),0.167339*exp(-x0**2 + 2*x0) + 0.040188 - 0.170011338339925*exp(-x1**2),saturated,301.115500,20,3,19,3,65,74,40,2,40,(0.040188 - (0.167339 * (exp((0.015843435951321115 - (x1 * x1))) - exp(((x0 + x0) - (x0 * x0)))))),saturated,433.569291,23,6,21,5,152,166,69,2,59,(((0.167339 * exp(((2.0 * x0) - (x0 ** 2.0)))) + 0.040188) - (0.170011338339925 * exp((-1.0 * (x1 ** 2.0))))) +kotanchek,95,GOMEA,GOMEA,6,1,kept,3.0,3.0,0.041578+0.022505*(((((x0+x1)-exp(x0))+((4.360000-x1)*(x1+x1)))*exp(((x0+x0)-(x0*x0))))),(0.022505*x0 - 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x0) - (x0 * x0))) * ((exp(x1) - (x1 * 16.705)) * ((x0 - x1) + (18.607 - x0)))))),saturated,329.716000,28,6,28,6,125,135,56,2,65,((((-0.000529 * (x1 + -18.607)) * ((16.705 * x1) - exp(x1))) + (0.010331 * exp((x0 * (x0 + -2.0))))) * exp((x0 * (2.0 - x0)))) +kotanchek,103,GOMEA,GOMEA,14,1,kept,4.0,4.0,0.002398-0.008408*(((((x1*(-16.678000))+exp(x1))+((x1+x0)-(x0+3.300000)))*exp(((x0+x0)-(x0*x0))))),(0.131820624*x1 - 0.008408*exp(x1) + 0.002398*exp(x0*(x0 - 2)) + 0.0277464)*exp(x0*(2 - x0)),saturated,269.875542,27,4,27,4,181,193,69,1,56,(0.002398 - (0.008408 * ((((x1 * -16.678) + exp(x1)) + ((x1 + x0) - (x0 + 3.3))) * exp(((x0 + x0) - (x0 * x0)))))),saturated,622.745292,26,6,26,6,629,651,159,2,62,(((((0.131820624 * x1) + (-0.008408 * exp(x1))) + (0.002398 * exp((x0 * (x0 + -2.0))))) + 0.0277464) * exp((x0 * (2.0 - x0)))) 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x0)),saturated,316.288917,27,6,23,4,160,172,64,2,50,(0.001058 - (0.008482 * (exp(((x0 + x0) - (x0 * x0))) * ((-4.062000000000001 + (x1 + exp(x1))) - (x1 * 16.294))))),saturated,546.805291,26,6,26,6,612,633,158,2,62,(((((0.129723708 * x1) + (-0.008482 * exp(x1))) + (0.001058 * exp((x0 * (x0 + -2.0))))) + 0.034453884) * exp((x0 * (2.0 - x0)))) +kotanchek,96,GOMEA,GOMEA,7,1,kept,5.0,4.0,-0.002373+0.007876*((exp(((x0+x0)-(x0*x0)))*(((x1-0.327000)+(x1*14.509000))-(exp(x1)+(x0-6.946000))))),(-0.007876*x0 + 0.122148884*x1 - 0.007876*exp(x1) - 0.002373*exp(x0*(x0 - 2)) + 0.052131244)*exp(x0*(2 - x0)),saturated,339.307500,27,5,25,4,85,93,42,2,53,(-0.002373 + (0.007876 * (exp(((x0 + x0) - (x0 * x0))) * (((6.619 + ((x1 * 14.509) + x1)) - x0) - exp(x1))))),saturated,8702.061375,30,7,28,6,493,510,125,2,65,((((-0.007876 * ((x0 + (-15.509000000000002 * x1)) + exp(x1))) + (-0.002373 * exp((x0 * (x0 + -2.0))))) + 0.052131244) * exp((x0 * (2.0 - x0)))) +kotanchek,105,GOMEA,GOMEA,16,1,kept,4.0,3.0,0.007824-0.012740*((exp(((x0+x0)-(x0*x0)))*(((x1-8.411000)+4.098000)*((x1*x1)+(x1+x1))))),(-0.01274*x1*(x1 - 4.313)*(x1 + 2) + 0.007824*exp(x0*(x0 - 2)))*exp(x0*(2 - x0)),saturated,329.919792,26,4,24,3,168,177,56,2,48,(0.007824 - (0.01274 * (exp(((x0 + x0) - (x0 * x0))) * ((-4.313 + x1) * ((x1 * x1) + (x1 + x1)))))),saturated,345.815250,27,6,27,6,195,204,62,2,64,(((((-0.01274 * x1) * (x1 + -4.313)) * (x1 + 2.0)) + (0.007824 * exp((x0 * (x0 + -2.0))))) * exp((x0 * (2.0 - x0)))) +kotanchek,106,GOMEA,GOMEA,17,1,kept,5.0,5.0,0.002551-0.007740*((exp(((x0+x0)-(x0*x0)))*(((0.548000+x1)*(x1-4.287000))*(x1-(-1.260000-x1))))),(-0.00774*(x1 - 4.287)*(x1 + 0.548)*(2*x1 + 1.26) + 0.002551*exp(x0*(x0 - 2)))*exp(x0*(2 - x0)),saturated,321.370584,26,5,26,5,431,444,92,1,59,(0.002551 - (0.00774 * (exp(((x0 + x0) - (x0 * x0))) * (((0.548 + x1) * (x1 - 4.287)) * (x1 - (-1.26 - x1)))))),saturated,419.055792,31,8,29,7,204,215,69,2,71,((((-0.01548 * ((x1 + 0.63) * (x1 + -4.287))) * (x1 + 0.548)) + (0.002551 * exp((x0 * (x0 + -2.0))))) * exp((x0 * (2.0 - x0)))) +kotanchek,107,GOMEA,GOMEA,18,1,kept,3.0,3.0,0.002206+0.022640*(((((x0*x0)-(x0*x0))-((-4.636000+x1)*(x1+x1)))*exp(((x0+x0)-(x0*x0))))),(-0.04528*x1*(x1 - 4.636) + 0.002206*exp(x0*(x0 - 2)))*exp(x0*(2 - x0)),saturated,305.603292,28,3,20,3,99,105,36,2,42,(0.002206 + ((-0.02264 * ((-4.636 + x1) * (x1 + x1))) * exp(((x0 + x0) - (x0 * x0))))),saturated,322.099458,23,5,23,5,115,124,50,2,54,((((-0.04528 * x1) * (x1 + -4.636)) + (0.002206 * exp((x0 * (x0 + -2.0))))) * exp((x0 * (2.0 - x0)))) +kotanchek,108,GOMEA,GOMEA,19,1,kept,5.0,5.0,0.014415+0.001055*((exp(((x0+x0)-(x0*x0)))*(((x1*x1)*(-4.670000+x1))*((5.882000+x1)*(-4.779000+x1))))),(0.001055*x1**2*(x1 - 4.779)*(x1 - 4.67)*(x1 + 5.882) + 0.014415*exp(x0*(x0 - 2)))*exp(x0*(2 - x0)),saturated,369.912167,28,5,28,5,815,823,154,1,62,(0.014415 + (0.001055 * (exp(((x0 + x0) - (x0 * x0))) * (((x1 * x1) * (-4.67 + x1)) * ((5.882 + x1) * (-4.779 + x1)))))),saturated,424.742208,33,7,33,7,451,462,93,2,81,((((((0.001055 * (x1 ** 2.0)) * (x1 + -4.779)) * (x1 + -4.67)) * (x1 + 5.882)) + (0.014415 * exp((x0 * (x0 + -2.0))))) * exp((x0 * (2.0 - x0)))) +kotanchek,109,GOMEA,GOMEA,20,1,kept,5.0,4.0,0.001729-0.008336*((exp(((x0+x0)-(x0*x0)))*(((x1-3.517000)-(18.874000*x1))+((2.182000*x1)+exp(x1))))),(0.130808512*x1 - 0.008336*exp(x1) + 0.001729*exp(x0*(x0 - 2)) + 0.029317712)*exp(x0*(2 - x0)),saturated,349.008875,27,5,23,4,157,169,63,2,50,(0.001729 - (0.008336 * (exp(((x0 + x0) - (x0 * x0))) * (((x1 * -16.692) + (x1 - 3.517)) + exp(x1))))),saturated,615.170417,26,6,26,6,787,814,209,2,62,(((((0.130808512 * x1) + (-0.008336 * exp(x1))) + (0.001729 * exp((x0 * (x0 + -2.0))))) + 0.029317712) * exp((x0 * (2.0 - x0)))) +kotanchek,110,GOMEA,GOMEA,21,1,kept,4.0,4.0,-0.000234-0.008008*((exp(((x0+x0)-(x0*x0)))*(((-15.725000+11.634000)+(x1+x1))+((x1*(-17.925000))+exp(x1))))),(0.1275274*x1 - 0.008008*exp(x1) - 0.000234*exp(x0*(x0 - 2)) + 0.032760728)*exp(x0*(2 - x0)),saturated,335.413791,27,5,25,4,226,237,68,2,53,(-0.000234 - (0.008008 * (exp(((x0 + x0) - (x0 * x0))) * ((-4.090999999999999 + (x1 + x1)) + ((x1 * -17.925) + exp(x1)))))),saturated,669.062667,26,6,26,6,771,794,189,2,62,(((((0.1275274 * x1) + (-0.008008 * exp(x1))) + (-0.000234 * exp((x0 * (x0 + -2.0))))) + 0.032760728) * exp((x0 * (2.0 - x0)))) +kotanchek,112,GOMEA,GOMEA,23,1,kept,3.0,3.0,0.027028+0.108127*((((exp(x0)*exp(x0))*((x1*x1)*(x1+6.423000)))*exp(((x0-x1)-exp(x0))))),(x1**2*(0.108127*x1 + 0.694499721)*exp(2*x0) + 0.027028*exp(-x0 + x1 + exp(x0)))*exp(x0 - x1 - exp(x0)),saturated,435.856291,25,3,25,3,919,925,131,1,48,(0.027028 + (0.108127 * (((exp(x0) * exp(x0)) * ((x1 * x1) * (x1 + 6.423))) * exp(((x0 - x1) - exp(x0)))))),saturated,331.804708,34,5,32,4,204,213,66,2,66,(((((x1 ** 2.0) * ((0.108127 * x1) + 0.694499721)) * exp((2.0 * x0))) + (0.027028 * exp(((x1 - x0) + exp(x0))))) * exp(((x0 - x1) - exp(x0)))) +kotanchek,113,GOMEA,GOMEA,24,1,kept,5.0,4.0,0.014790+0.002199*((exp(((x0+x0)-(x0*x0)))*(((-8.382000+x1)-(0.249000-x1))*((x1*x1)*(-7.883000+x1))))),(0.002199*x1**2*(x1 - 7.883)*(2*x1 - 8.631) + 0.01479*exp(x0*(x0 - 2)))*exp(x0*(2 - x0)),saturated,424.112292,28,5,26,4,493,500,77,2,55,(0.01479 + (0.002199 * (exp(((x0 + x0) - (x0 * x0))) * (((-8.631 + x1) + x1) * ((x1 * x1) * (-7.883 + x1)))))),saturated,431.883791,31,7,29,6,200,210,66,2,71,((((0.004398 * ((x1 + -4.3155) * (x1 ** 2.0))) * (x1 + -7.883)) + (0.01479 * exp((x0 * (x0 + -2.0))))) * exp((x0 * (2.0 - x0)))) +kotanchek,114,GOMEA,GOMEA,25,1,kept,4.0,3.0,0.010559+0.013455*(((((4.203000-x1)+exp(-3.785000))*((x1*x1)+(x1+x1)))*exp(((x0+x0)-(x0*x0))))),(-0.013455*x1*(x1 - 4.22570886277673)*(x1 + 2) + 0.010559*exp(x0*(x0 - 2)))*exp(x0*(2 - x0)),saturated,326.248625,27,4,26,4,114,121,43,2,55,(0.010559 + (0.013455 * ((((4.203 - x1) + 0.022708862776731332) * ((x1 * x1) + (x1 + x1))) * exp(((x0 + x0) - (x0 * x0)))))),saturated,364.942000,27,6,27,6,195,204,62,2,64,(((((-0.013455 * x1) * (x1 + -4.22570886277673)) * (x1 + 2.0)) + (0.010559 * exp((x0 * (x0 + -2.0))))) * exp((x0 * (2.0 - x0)))) +kotanchek,115,GOMEA,GOMEA,26,1,kept,5.0,4.0,-0.002850-0.007989*((exp(((x0+x0)-(x0*x0)))*((0.141000+exp(x1))-((5.595000-x1)+(x1*16.435000))))),(0.123310215*x1 - 0.007989*exp(x1) - 0.00285*exp(x0*(x0 - 2)) + 0.043572006)*exp(x0*(2 - x0)),saturated,350.830375,25,5,23,4,160,172,64,2,50,(-0.00285 - (0.007989 * (exp(((x0 + x0) - (x0 * x0))) * (((-5.454 + exp(x1)) + x1) - (x1 * 16.435))))),saturated,814.101208,26,6,26,6,812,837,202,2,62,(((((0.123310215 * x1) + (-0.007989 * exp(x1))) + (-0.00285 * exp((x0 * (x0 + -2.0))))) + 0.043572006) * exp((x0 * (2.0 - x0)))) +kotanchek,111,GOMEA,GOMEA,22,1,kept,4.0,4.0,0.005151-0.019625*((exp(((x0+x0)-(x0*x0)))*(((x1-4.022000)*(x1*x1))+((-1.303000-0.050000)-x1)))),(x1**2*(0.07893175 - 0.019625*x1) + 0.019625*x1 + 0.005151*exp(x0*(x0 - 2)) + 0.026552625)*exp(x0*(2 - x0)),saturated,317.139625,26,5,24,4,101,112,52,2,52,(0.005151 - (0.019625 * (exp(((x0 + x0) - (x0 * x0))) * (((x1 - 4.022) * (x1 * x1)) + (-1.353 - x1))))),saturated,2594.989875,31,7,29,6,232,245,81,2,71,((((0.019625 * (x1 + ((x1 ** 2.0) * (4.021999999999999 - x1)))) + (0.005151 * exp((x0 * (x0 + -2.0))))) + 0.026552625) * exp((x0 * (2.0 - x0)))) +kotanchek,117,GOMEA,GOMEA,28,1,kept,5.0,4.0,-0.002065-0.007572*((exp(((x0+x0)-(x0*x0)))*(((x1+2.326000)-(7.014000-x1))+(exp(x1)-(18.337000*x1))))),(0.123703764*x1 - 0.007572*exp(x1) - 0.002065*exp(x0*(x0 - 2)) + 0.035497536)*exp(x0*(2 - x0)),saturated,350.946542,27,5,25,4,233,245,72,2,53,(-0.002065 - (0.007572 * (exp(((x0 + x0) - (x0 * x0))) * (((-4.688000000000001 + x1) + x1) + (exp(x1) - (18.337 * x1)))))),saturated,571.819917,26,6,26,6,582,603,152,2,62,(((((0.123703764 * x1) + (-0.007572 * exp(x1))) + (-0.002065 * exp((x0 * (x0 + -2.0))))) + 0.035497536) * exp((x0 * (2.0 - x0)))) +kotanchek,118,GOMEA,GOMEA,29,1,kept,5.0,4.0,0.000258-0.008126*((exp(((x0+x0)-(x0*x0)))*(((1.637000-17.444000)*(-1.529000+x1))-((20.873000+7.266000)-exp(x1))))),(0.128447682*x1 - 0.008126*exp(x1) + 0.000258*exp(x0*(x0 - 2)) + 0.0322610082220001)*exp(x0*(2 - x0)),saturated,351.297250,27,7,21,4,90,100,47,2,47,(0.000258 - (0.008126 * (exp(((x0 + x0) - (x0 * x0))) * ((-15.806999999999999 * (0.25116068830265115 + x1)) + exp(x1))))),saturated,551.404708,26,6,26,6,647,669,167,2,62,(((((0.128447682 * x1) + (-0.008126 * exp(x1))) + (0.000258 * exp((x0 * (x0 + -2.0))))) + 0.0322610082220001) * exp((x0 * (2.0 - x0)))) +kotanchek,116,GOMEA,GOMEA,27,1,kept,4.0,3.0,0.013200-0.015123*(((((-5.053000*x1)*(5.158000-x1))*(exp(x0)*(x1*x1)))*exp(((x0-x1)-(x0*x0))))),(x1**3*(0.394156405002 - 0.076416519*x1)*exp(x0) + 0.0132*exp(x0**2 - x0 + x1))*exp(-x0**2 + x0 - x1),saturated,2406.856417,27,4,25,3,874,883,130,2,49,(0.0132 - ((((-0.076416519 * x1) * (5.158 - x1)) * (exp(x0) * (x1 * x1))) * exp(((x0 - x1) - (x0 * x0))))),saturated,361.385125,34,4,32,3,195,204,64,2,71,(((((x1 ** 3.0) * (0.076416519 * (5.1579999999999995 - x1))) * exp(x0)) + (0.0132 * exp((((x0 ** 2.0) - x0) + x1)))) * exp(((x0 - (x0 ** 2.0)) - x1))) +kotanchek,119,GOMEA,GOMEA,30,1,kept,6.0,5.0,0.004369-0.000167*((exp(((x0+x0)-(x0*x0)))*(((x1*(-8.637000))*(4.502000-x1))*((11.197000-x1)*(1.581000+x1))))),(0.001442379*x1*(x1 - 11.197)*(x1 - 4.502)*(x1 + 1.581) + 0.004369*exp(x0*(x0 - 2)))*exp(x0*(2 - x0)),saturated,2219.957917,28,6,26,5,704,715,118,2,59,(0.004369 - (((-0.001442379 * ((4.502 - x1) * x1)) * ((11.197 - x1) * (1.581 + x1))) * exp(((x0 + x0) - (x0 * x0))))),saturated,412.945042,31,7,31,7,449,460,92,2,74,((((((0.001442379 * x1) * (x1 + -11.197)) * (x1 + -4.502)) * (x1 + 1.581)) + (0.004369 * exp((x0 * (x0 + -2.0))))) * exp((x0 * (2.0 - x0)))) +kotanchek,121,Operon,Operon,2,1,kept,13.0,10.0,(0.0019190539605916 + (0.9954085946083069 * ((exp((3.0602750778198242 * x0)) / exp(((exp(((0.4211926460266113 * x0) + 1.6726008653640747)) - ((1.3422309160232544 * x1) - exp(((-1.2979059219360352) * x0)))) + ((0.0003775433578994 * x1) * (1131.5198974609375000 * x1))))) * ((((-0.0027062874287367) * x1) * ((-6793.8808593750000000) * x1)) + (((-24.5153598785400391) * x1) - (-29.1849021911621094)))))),(18.30177589013476524*x1**2 - 24.4027999230144136*x1 + 29.0509024738855719)*exp(3.0602750778198242*x0 + ((-0.42719782161738710485*x1**2 + 1.3422309160232544*x1 - 5.3260020130810325*exp(0.4211926460266113*x0))*exp(1.2979059219360352*x0) - 1)*exp(-1.2979059219360352*x0)) + 0.0019190539605916,saturated,934.367375,47,13,37,10,177,192,78,2,94,(0.0019190539605916 + ((18.301775890134767 * ((x1 * (x1 + -1.3333569413975992)) + 1.5873269702501889)) * (exp((3.060275077819824 * x0)) / exp((((x1 * ((0.4271978216173871 * x1) + -1.3422309160232544)) + exp(((0.4211926460266113 * x0) + 1.6726008653640747))) + exp((-1.2979059219360352 * x0))))))),saturated,649.280583,47,12,47,12,691,731,246,2,125,(((((18.301775890134767 * (x1 ** 2.0)) + (-24.402799923014413 * x1)) + 29.05090247388557) * exp(((3.060275077819824 * x0) + ((((((-0.4271978216173871 * (x1 ** 2.0)) + (1.3422309160232544 * x1)) + (-5.326002013081032 * exp((0.4211926460266113 * x0)))) * exp((1.2979059219360352 * x0))) + -1.0) * exp((-1.2979059219360352 * x0)))))) + 0.0019190539605916) +kotanchek,122,Operon,Operon,3,1,kept,11.0,10.0,((-0.0000014371197494) + (1.0000287294387817 * ((((((0.0082893725484610 * x1) - (-0.0444908216595650)) / exp(log((exp((0.3769945502281189 * x1)) + ((-0.9402246475219727) * x1))))) - (exp((0.0002179348812206 * x1)) + (-1.0048899650573730))) / exp(((0.3332124650478363 * x0) * (3.0010888576507568 * x0)))) / exp(((-2.0000004768371582) * x0))))),((-1.351215409826481e-6*x1 + 1.4371197494e-6*exp(0.3769945502281189*x1))*exp(1.0000002160854038*x0**2) - (0.00828961069748217*x1 + 1.0000287294387817*(0.9402246475219727*x1 - exp(0.3769945502281189*x1))*(exp(0.0002179348812206*x1) - 1.004889965057373) + 0.044492099855902216)*exp(2.0000004768371582*x0))*exp(-1.0000002160854038*x0**2)/(0.9402246475219727*x1 - exp(0.3769945502281189*x1)),saturated,380.096875,41,11,37,10,187,205,91,2,94,(-1.4371197494e-06 + (((((0.008289372548461 * x1) + 0.044490821659565) / (exp((0.3769945502281189 * x1)) + (-0.9402246475219727 * x1))) - (exp((0.0002179348812206 * x1)) + -1.004889965057373)) * ((1.0000287294387817 / exp((1.0000002160854038 * (x0 * x0)))) / exp((-2.000000476837158 * x0))))),saturated,621.935834,62,15,62,15,552,581,186,2,158,((((1.4371197494e-06 * (exp((0.3769945502281189 * x1)) + (-0.9402246475219729 * x1))) * exp((1.0000002160854038 * (x0 ** 2.0)))) - ((((0.00828961069748217 * x1) + ((1.0000287294387817 * ((0.9402246475219727 * x1) - exp((0.3769945502281189 * x1)))) * (exp((0.0002179348812206 * x1)) - 1.004889965057373))) + 0.04449209985590222) * exp((2.000000476837158 * x0)))) * (exp((-1.0000002160854038 * (x0 ** 2.0))) / ((0.9402246475219727 * x1) - exp((0.3769945502281189 * x1))))) +kotanchek,123,Operon,Operon,4,1,kept,12.0,10.0,(0.0000182324292837 + (0.9999566078186035 * ((((exp(((-1.0928704738616943) * x0)) + (2.6822447776794434 * x0)) / (7.4495120048522949 - ((((-3.5652680397033691) * x1) - (-17.8263320922851562)) * (0.2804658412933350 * x1)))) / (exp(exp((0.5965437889099121 * x0))) + ((-1.4266524314880371) * x0))) / (exp((0.4577265381813049 * x0)) + ((-0.9410613179206848) * x0))))),1.82324292837e-5 + 0.9999566078186035*(2.6822447776794434*x0 + exp(-1.0928704738616943*x0))/((0.9410613179206848*x0 - exp(0.4577265381813049*x0))*(1.4266524314880371*x0 - exp(exp(0.5965437889099121*x0)))*(0.280465841293335*x1*(3.5652680397033691*x1 - 17.8263320922851562) + 7.4495120048522949)),saturated,2207.063833,43,12,39,10,292,305,99,2,97,(1.82324292837e-05 + ((-1.0000207089543987 / (-7.449989547754554 - (x1 * (x1 + -4.999997726333168)))) * (((exp((-1.0928704738616943 * x0)) + (2.6822447776794434 * x0)) / (exp(exp((0.5965437889099121 * x0))) + (-1.426652431488037 * x0))) / (exp((0.4577265381813049 * x0)) + (-0.9410613179206848 * x0))))),saturated,520.068000,43,12,39,10,117,130,64,2,97,(1.82324292837e-05 + ((1.0000207089543989 * ((2.6822447776794434 * x0) + exp((-1.0928704738616943 * x0)))) / ((((0.9410613179206848 * x0) - exp((0.4577265381813049 * x0))) * ((1.426652431488037 * x0) - exp(exp((0.5965437889099121 * x0))))) * ((x1 * (x1 + -4.999997726333168)) + 7.449989547754554)))) +kotanchek,120,Operon,Operon,1,1,kept,14.0,8.0,((-0.0000644577157800) + (1.0001556873321533 * ((((-0.0006379182450473) - (0.0003036445996258 * x1)) + (((1.0098193883895874 * x1) * ((-2.1118876934051514) * x1)) * (0.0005665634525940 * x1))) * (exp((1.9995476007461548 * x0)) * ((((2.9050014019012451 * x1) * ((-1.6316955089569092) * x1)) + ((-83.5919265747070312) - ((-39.5477447509765625) * x1))) / exp(((0.0681112110614777 * x0) * (14.6775512695312500 * x0)))))))),(1.0001556873321533*(4.7400777409957869*x1**2 - 39.5477447509765625*x1 + 83.5919265747070312)*(0.0012082674617850116*x1**3 + 0.0003036445996258*x1 + 0.0006379182450473)*exp(1.9995476007461548*x0) - 6.445771578e-5*exp(0.999705792384702974*x0**2))*exp(-0.999705792384702974*x0**2),saturated,1616.727458,49,14,35,8,884,902,158,2,84,(-6.445771578e-05 + (((0.047791692572478874 * ((2.113696421908935 - x1) + (0.11985709351678615 * (x1 * x1)))) * (exp((1.9995476007461548 * x0)) / exp((0.999705792384703 * (x0 * x0))))) * ((x1 * ((x1 * x1) + 0.25130578222905736)) + 0.5279611222045848))),saturated,4502.503542,46,11,42,9,291,312,114,2,114,((((0.005728173365985095 * ((((x1 ** 2.0) - (8.343269227198043 * x1)) + 17.63513831255143) * (((x1 ** 3.0) + (0.25130578222905736 * x1)) + 0.5279611222045848))) * exp((1.9995476007461548 * x0))) - (6.445771578e-05 * exp((0.999705792384703 * (x0 ** 2.0))))) * exp((-0.999705792384703 * (x0 ** 2.0)))) +kotanchek,126,Operon,Operon,7,1,kept,12.0,10.0,((-0.0000124719463201) + (0.9946426749229431 * (exp(((exp(exp(((1.1653105020523071 * x1) - exp((0.4197142422199249 * x1))))) - ((0.9311969876289368 * x0) * (1.0738922357559204 * x0))) - (((-1.9999958276748657) * x0) - (-5.5033035278320312)))) * (exp((0.2837287485599518 * x1)) - ((-2.8964312076568604) - (((-0.2071333527565002) * x1) - exp(((-0.6339063644409180) * x1)))))))),(((-0.00083919477106758292*x1 + 0.0040514709963398087*exp(0.2837287485599518*x1) + 0.011734807030715255)*exp(0.633906364440918*x1) - 0.0040514709963398087)*exp(-1.0000052149740171*x0**2 + 1.9999958276748657*x0 + exp(exp(1.1653105020523071*x1 - exp(0.4197142422199249*x1)))) - 1.24719463201e-5*exp(0.633906364440918*x1))*exp(-0.633906364440918*x1),saturated,1146.160208,45,12,41,11,259,280,109,2,103,(-1.24719463201e-05 + (0.9946426749229431 * (exp((((x0 * (1.9999958276748657 + (-1.000005214974017 * x0))) + exp(exp(((1.1653105020523071 * x1) - exp((0.4197142422199249 * x1)))))) + -5.503303527832031)) * (exp((0.2837287485599518 * x1)) - (-2.8964312076568604 - ((-0.2071333527565002 * x1) - exp((-0.633906364440918 * x1)))))))),saturated,324.412458,53,13,53,13,411,442,170,1,132,((((((((-0.000839194771067583 * x1) + (0.004051470996339809 * exp((0.2837287485599518 * x1)))) + 0.011734807030715255) * exp((0.633906364440918 * x1))) - 0.004051470996339809) * exp((((-1.000005214974017 * (x0 ** 2.0)) + (1.9999958276748657 * x0)) + exp(exp(((1.1653105020523071 * x1) - exp((0.4197142422199249 * x1)))))))) - (1.24719463201e-05 * exp((0.633906364440918 * x1)))) * exp((-0.633906364440918 * x1))) +kotanchek,127,Operon,Operon,8,1,kept,14.0,9.0,((-0.0148077905178070) + (1.0382655858993530 * (((((0.0000003963598942 * x0) * (1793.5753173828125000 * x0)) + (0.0000325083929056 * x1)) * ((((68.1199569702148438 * x0) + 50.2617149353027344) + ((0.1230096146464348 * x1) * (355.7100830078125000 * x0))) * (exp(((-2.7948594093322754) * x0)) * (exp(((-3.0556442737579346) * x1)) + (2.6853957176208496 * x1))))) * (((-5.3364686965942383) * x1) + 22.9583053588867188)))),(-1.038265585899353*(0.00071090132303758300646*x0**2 + 3.25083929056e-5*x1)*(5.3364686965942383*x1 - 22.9583053588867188)*(2.6853957176208496*x1*exp(3.0556442737579346*x1) + 1)*(43.75576023664235082*x0*x1 + 68.1199569702148438*x0 + 50.2617149353027344) - 0.014807790517807*exp(2.7948594093322754*x0 + 3.0556442737579346*x1))*exp(-2.7948594093322754*x0 - 3.0556442737579346*x1),saturated,1853.466458,49,14,37,9,663,675,114,2,91,(-0.014807790517807 + ((-0.007881214714052953 * (((x1 + -4.302153102395002) * (x1 + (21.868239537461754 * (x0 * x0)))) * ((x0 * (x1 + 1.556822612652704)) + 1.1486879593332286))) * (exp((-2.7948594093322754 * x0)) * (exp((-3.0556442737579346 * x1)) + (2.6853957176208496 * x1))))),saturated,789.683833,60,16,50,12,1072,1106,246,2,126,((((-0.021164180242768227 * ((x0 * (x1 + 1.556822612652704)) + 1.1486879593332286)) * (((x1 - 4.302153102395002) * (x1 + (21.868239537461754 * (x0 ** 2.0)))) * ((exp((3.0556442737579346 * x1)) * x1) + 0.37238459622105863))) - (0.014807790517807 * exp((2.7948594093322754 * (x0 - (-1.0933087594871056 * x1)))))) * exp((-2.7948594093322754 * (x0 - (-1.0933087594871056 * x1))))) +kotanchek,128,Operon,Operon,9,1,kept,12.0,11.0,(0.0000034507245346 + (0.9999927282333374 * exp(((((2.4630110263824463 * x0) * (((-0.4060201048851013) * x0) + 0.8120366930961609)) - ((((-0.8767948746681213) * x1) / (((-0.3692416250705719) * x1) + exp((0.4968747496604919 * x1)))) + (0.7100588083267212 * x1))) - exp(((1.4052648544311523 - exp((0.1799458712339401 * x1))) * exp(exp((0.2937204837799072 * x1))))))))),0.9999927282333374*exp(-2.4630110263824463*x0*(0.4060201048851013*x0 - 0.8120366930961609) - 0.7100588083267212*x1 - 0.8767948746681213*x1/(0.3692416250705719*x1 - exp(0.4968747496604919*x1)) - exp(-(exp(0.1799458712339401*x1) - 1.4052648544311523)*exp(exp(0.2937204837799072*x1)))) + 3.4507245346e-6,saturated,1354.188125,45,12,41,11,116,130,67,2,103,(3.4507245346e-06 + (0.9999927282333374 * exp(((((-1.000031995264962 * x0) * (x0 + -1.9999913386701804)) + (x1 * (-0.7100588083267212 + (0.8767948746681213 / ((-0.3692416250705719 * x1) + exp((0.4968747496604919 * x1))))))) - exp(((1.4052648544311523 - exp((0.1799458712339401 * x1))) * exp(exp((0.2937204837799072 * x1))))))))),saturated,1433.899625,47,13,41,11,115,129,67,2,103,((0.9999927282333374 * exp((((x1 * (-0.7100588083267212 + (-0.8767948746681213 / ((0.3692416250705719 * x1) - exp((0.4968747496604919 * x1)))))) + (-1.000031995264962 * (x0 * (x0 + -1.9999913386701804)))) - exp(((1.4052648544311523 - exp((0.1799458712339401 * x1))) * exp(exp((0.2937204837799072 * x1)))))))) + 3.4507245346e-06) +kotanchek,125,Operon,Operon,6,1,kept,12.0,11.0,(0.0015015223762020 + (0.9966979622840881 * ((exp(1.7057397365570068) + ((2.2468583583831787 * x1) + (((2.7354996204376221 * x1) + ((-5.6414661407470703) * exp((0.1865983307361603 * x1)))) / exp(((-0.6834985017776489) * x1))))) * (((0.0036516967229545 * x1) - exp((1.9130901098251343 * x0))) / (exp(exp((0.7873576283454895 * x0))) + ((-2.2153601646423340) * x0)))))),(0.0033264128585570114*x0 - 0.9966979622840881*(0.0036516967229545*x1 - exp(1.9130901098251343*x0))*(2.2468583583831787*x1 + (2.7354996204376221*x1 - 5.6414661407470703*exp(0.1865983307361603*x1))*exp(0.6834985017776489*x1) + 5.5054567488820503) - 0.001501522376202*exp(exp(0.7873576283454895*x0)))/(2.215360164642334*x0 - exp(exp(0.7873576283454895*x0))),saturated,575.912041,45,12,42,11,153,167,73,2,105,(0.001501522376202 + ((-5.622837806777284 * (((exp((0.1865983307361603 * x1)) + (-0.48489161366753747 * x1)) / exp((-0.6834985017776489 * x1))) + (-0.3982756082066352 * (x1 + 2.4502909710978544)))) * (((0.0036516967229545 * x1) - exp((1.9130901098251343 * x0))) / (exp(exp((0.7873576283454895 * x0))) + (-2.215360164642334 * x0))))),saturated,7280.360042,54,14,52,13,375,402,152,2,127,((((0.0033264128585570115 * x0) - ((2.2394391473414856 * ((0.0036516967229545 * x1) - exp((1.9130901098251343 * x0)))) * ((x1 + 2.4502909710978544) + (-2.5108241112299683 * (exp((0.6834985017776489 * x1)) * (exp((0.1865983307361603 * x1)) + (-0.48489161366753747 * x1))))))) - (0.001501522376202 * exp(exp((0.7873576283454895 * x0))))) / ((2.215360164642334 * x0) - exp(exp((0.7873576283454895 * x0))))) +kotanchek,130,Operon,Operon,11,1,kept,13.0,10.0,(0.0006644097738899 + (0.9983761310577393 * ((((exp((0.3564732372760773 * x1)) * ((2.8750302791595459 * x1) + (-16.9938793182373047))) + (8.4957685470581055 + 8.5495948791503906)) + (3.2266986370086670 * x1)) / exp((((((-0.4841774106025696) * x0) + 0.9682721495628357) * ((-2.0647206306457520) * x0)) + ((0.0918822064995766 * x1) * ((3.7386786937713623 * x1) + (-3.2311415672302246)))))))),(3.2214589013059937*x1 + (2.8703616067811596*x1 - 16.9662834854038927)*exp(0.3564732372760773*x1) + 0.0006644097738899*exp(2.064720630645752*x0*(0.4841774106025696*x0 - 0.9682721495628357) + 0.0918822064995766*x1*(3.7386786937713623*x1 - 3.2311415672302246)) + 17.01768398993113)*exp(-2.064720630645752*x0*(0.4841774106025696*x0 - 0.9682721495628357) - 0.0918822064995766*x1*(3.7386786937713623*x1 - 3.2311415672302246)),saturated,964.767708,43,14,35,10,192,208,85,2,92,(0.0006644097738899 + ((3.2214589013059935 * ((x1 + 5.282601613521155) + (0.8910129524289453 * (exp((0.3564732372760773 * x1)) * (x1 + -5.9108522930774505))))) / exp((((0.9996910885637647 * x0) * (x0 + -1.999829253408992)) + ((0.3435180477766676 * x1) * (x1 + -0.8642469256888284)))))),saturated,2557.382708,60,18,52,14,883,921,256,2,133,(((((3.2214589013059935 * x1) + ((2.8703616067811595 * (x1 - 5.9108522930774505)) * exp((0.3564732372760773 * x1)))) + (0.0006644097738899 * exp((0.9996910885637647 * ((x0 * (x0 - 1.999829253408992)) - (-0.34362419722095633 * (x1 * (x1 - 0.8642469256888284)))))))) + 17.01768398993113) * exp(((-0.9996910885637647 * (x0 * (x0 - 1.999829253408992))) - (0.3435180477766676 * (x1 * (x1 - 0.8642469256888284)))))) +kotanchek,131,Operon,Operon,12,1,kept,14.0,12.0,((-0.0007296766270883) + (1.0011714696884155 * (((((-796.1662597656250000) * x0) - (-3327.3220214843750000)) + ((((-416.2025756835937500) * x0) + 5066.6352539062500000) / ((1.3030259609222412 * x0) - exp((0.6703483462333679 * x0))))) / (((-34525.6953125000000000) - exp((2.9498600959777832 * x0))) - ((((-0.1925518661737442) * x0) + ((-19.2132587432861328) * x1)) * (((-239.9505157470703125) * x1) + 1202.1625976562500000)))))),1.0011714696884155*(796.166259765625*x0 - 3327.322021484375 + (416.20257568359375*x0 - 5066.63525390625)/(1.3030259609222412*x0 - exp(0.6703483462333679*x0)))/((0.1925518661737442*x0 + 19.2132587432861328*x1)*(239.9505157470703125*x1 - 1202.16259765625) + exp(2.9498600959777832*x0) + 34525.6953125) - 0.0007296766270883,saturated,424.885083,45,14,41,12,150,166,78,2,109,(-0.0007296766270883 + ((-797.0989444058796 / ((-34525.6953125 - exp((2.949860095977783 * x0))) + (-46.20291959645078 * ((x1 + -5.010043816381869) * (x0 + (99.7822515308657 * x1)))))) * ((x0 + -4.179179889466643) + (0.522758369346266 * ((x0 + -12.173483658971914) / ((1.3030259609222412 * x0) - exp((0.6703483462333679 * x0)))))))),saturated,423.528417,45,14,41,12,192,215,102,2,109,(((797.0989444058796 * ((x0 - 4.179179889466643) + ((0.522758369346266 * (x0 - 12.173483658971914)) / ((1.3030259609222412 * x0) - exp((0.6703483462333679 * x0)))))) / ((((46.20291959645078 * (x1 - 5.010043816381869)) * (x0 + (99.7822515308657 * x1))) + exp((2.949860095977783 * x0))) + 34525.6953125)) - 0.0007296766270883) +kotanchek,132,Operon,Operon,13,1,kept,12.0,10.0,(0.0036648171953857 + (0.9917431473731995 * (((0.7433260083198547 * x1) / ((exp(exp((0.5352578163146973 * x0))) * (exp((2.5961806774139404 * x1)) - (1.9263886213302612 - (297.5476074218750000 * x1)))) * exp(((-1.0667701959609985) * x1)))) / exp(((exp(((-0.1313982456922531) * x0)) * ((-6.9308919906616211) * x0)) - (((-4.3688435554504395) * x0) + 3.7469267845153809)))))),(31.249866299263655*x1*exp(x0*(6.9308919906616211 - 4.3688435554504395*exp(0.1313982456922531*x0))*exp(-0.1313982456922531*x0) + 1.0667701959609985*x1) + (1.090457588125561273*x1 + 0.0036648171953857*exp(2.5961806774139404*x1) - 0.0070598621444464934)*exp(exp(0.5352578163146973*x0)))*exp(-exp(0.5352578163146973*x0))/(297.547607421875*x1 + exp(2.5961806774139404*x1) - 1.9263886213302612),saturated,409.750500,45,12,41,11,227,247,104,2,103,(0.0036648171953857 + (((0.7371884750154898 * x1) / ((exp(exp((0.5352578163146973 * x0))) * ((exp((2.5961806774139404 * x1)) + -1.9263886213302612) + (297.547607421875 * x1))) * exp((-1.0667701959609985 * x1)))) / exp(((x0 * ((exp((-0.1313982456922531 * x0)) * -6.930891990661621) + 4.3688435554504395)) + -3.746926784515381)))),saturated,687.828417,62,16,62,16,699,727,205,2,153,((((31.249866299263655 * x1) * exp((((x0 * (6.930891990661621 + (-4.3688435554504395 * exp((0.1313982456922531 * x0))))) * exp((-0.1313982456922531 * x0))) + (1.0667701959609985 * x1)))) + ((((1.0904575881255614 * x1) + (0.0036648171953857 * exp((2.5961806774139404 * x1)))) + -0.007059862144446493) * exp(exp((0.5352578163146973 * x0))))) * (exp((-1.0 * exp((0.5352578163146973 * x0)))) / (((297.547607421875 * x1) + exp((2.5961806774139404 * x1))) + -1.9263886213302612))) +kotanchek,133,Operon,Operon,14,1,kept,14.0,11.0,((-0.0022257824894041) + (1.0057435035705566 * (((exp(((((-0.7701046466827393) * x1) - (-3.8445262908935547)) * (1.3931946754455566 * x1))) + (((15.1122426986694336 * x1) - (-13.2947568893432617)) * (((-2.5437910556793213) * x1) - (-15.1461124420166016)))) / (exp((2.8625166416168213 * x0)) + (((-3.6063053607940674) * x0) + 62.3201675415039062))) * ((0.0344910286366940 * x0) + 0.0158514883369207)))),-1.0057435035705566*(0.034491028636694*x0 + 0.0158514883369207)*((2.5437910556793213*x1 - 15.1461124420166016)*(15.1122426986694336*x1 + 13.2947568893432617) - exp(-1.3931946754455566*x1*(0.7701046466827393*x1 - 3.8445262908935547)))/(-3.6063053607940674*x0 + exp(2.8625166416168213*x0) + 62.3201675415039062) - 0.0022257824894041,saturated,355.063625,43,14,37,11,184,199,79,2,99,(-0.0022257824894041 + ((exp(((-1.072905693294274 * x1) * (x1 + -4.992212821275688))) + (-38.442387808130434 * ((x1 + 0.87973420983464) * (x1 + -5.954149578520246)))) * (0.034689127982821026 * ((x0 + 0.4595829397809482) / (exp((2.8625166416168213 * x0)) + ((-3.6063053607940674 * x0) + 62.320167541503906)))))),saturated,356.615458,43,14,37,11,202,222,94,2,99,((((-0.034689127982821026 * (x0 + 0.4595829397809482)) * ((38.442387808130434 * ((x1 + 0.87973420983464) * (x1 - 5.954149578520246))) - exp((-1.072905693294274 * (x1 * (x1 - 4.992212821275688)))))) / (((-3.6063053607940674 * x0) + exp((2.8625166416168213 * x0))) + 62.320167541503906)) - 0.0022257824894041) +kotanchek,134,Operon,Operon,15,1,kept,13.0,12.0,(0.0003700088418555 + (0.9992044568061829 * (((exp((0.1231540888547897 * x1)) * (((((-2.6712670326232910) * x0) - 1.5445685386657715) * ((1.0232990980148315 * x0) - exp(((-4.9796590805053711) * x0)))) - (((-10.8486871719360352) * x0) - 0.5861128568649292))) / (exp((2.4178924560546875 * x0)) - (-42.5792884826660156))) / (exp((0.3763327002525330 * x1)) - (0.9377985596656799 * x1))))),0.0003700088418555 - 0.9992044568061829*(10.8486871719360352*x0 - (1.0232990980148315*x0 - exp(-4.9796590805053711*x0))*(2.671267032623291*x0 + 1.5445685386657715) + 0.5861128568649292)*exp(0.1231540888547897*x1)/((0.9377985596656799*x1 - exp(0.376332700252533*x1))*(exp(2.4178924560546875*x0) + 42.5792884826660156)),saturated,800.116333,45,13,43,12,311,327,100,2,111,(0.0003700088418555 + ((10.84005657269455 * ((x0 + 0.05402615519978466) + (-0.24622951978313723 * (((1.0232990980148315 * x0) - exp((-4.979659080505371 * x0))) * (x0 + 0.5782157005654891))))) * ((exp((0.1231540888547897 * x1)) / (exp((2.4178924560546875 * x0)) + 42.579288482666016)) / (exp((0.376332700252533 * x1)) + (-0.9377985596656799 * x1))))),saturated,753.567000,45,13,43,12,257,277,107,2,111,(0.0003700088418555 - (((10.84005657269455 * ((x0 - (0.24622951978313723 * (((1.0232990980148315 * x0) - exp((-4.979659080505371 * x0))) * (x0 + 0.5782157005654891)))) + 0.05402615519978466)) * exp((0.1231540888547897 * x1))) / (((0.9377985596656799 * x1) - exp((0.376332700252533 * x1))) * (exp((2.4178924560546875 * x0)) + 42.579288482666016)))) +kotanchek,135,Operon,Operon,16,1,kept,12.0,11.0,((-0.0158226937055588) + (1.0497971773147583 * (((exp(((-0.3585180342197418) * x1)) - ((((exp((1.7362647056579590 * x1)) - (-7144.3906250000000000)) + ((-3211.7934570312500000) * x1)) / (exp((3.3592488765716553 * x1)) - (-8749.7304687500000000))) - (-252.0166625976562500))) - (-251.8914642333984375)) / (exp((0.7833101749420166 * x0)) + log(exp(((-1.7847769260406494) * x0))))))),-0.0158226937055588 - 1.0497971773147583*(0.1251983642578125 - exp(-0.3585180342197418*x1) + (-3211.79345703125*x1 + exp(1.736264705657959*x1) + 7144.390625)/(exp(3.3592488765716553*x1) + 8749.73046875))/(exp(0.7833101749420166*x0) + log(exp(-1.7847769260406494*x0))),saturated,297.340959,41,12,37,11,125,140,70,2,98,(-0.0158226937055588 + ((-0.1251983642578125 + (exp((-0.3585180342197418 * x1)) - (((exp((1.736264705657959 * x1)) + 7144.390625) + (-3211.79345703125 * x1)) / (exp((3.3592488765716553 * x1)) + 8749.73046875)))) * (1.0497971773147583 / (exp((0.7833101749420166 * x0)) + (-1.7847769260406494 * x0))))),saturated,301.579584,39,11,37,11,150,168,83,2,98,(-0.0158226937055588 - ((1.0497971773147583 * ((0.1251983642578125 - exp((-0.3585180342197418 * x1))) + ((((-3211.79345703125 * x1) + exp((1.736264705657959 * x1))) + 7144.390625) / (exp((3.3592488765716553 * x1)) + 8749.73046875)))) / (exp((0.7833101749420166 * x0)) + (-1.7847769260406494 * x0)))) +kotanchek,99,GOMEA,GOMEA,10,1,kept,4.0,4.0,0.001573-0.008457*((exp(((x0+x0)-(x0*x0)))*(((x1-x0)-(2.400000+x1))+(exp(x1)+(-15.584000*x1))))),(0.008457*x0 + 0.131793888*x1 - 0.008457*exp(x1) + 0.001573*exp(x0*(x0 - 2)) + 0.0202968)*exp(x0*(2 - x0)),saturated,278.971209,27,4,27,4,170,182,67,1,56,(0.001573 - (0.008457 * (exp(((x0 + x0) - (x0 * x0))) * (((x1 - x0) - (2.4 + x1)) + (exp(x1) + (-15.584 * x1)))))),saturated,32502.601000,30,7,28,6,159,171,66,2,65,((((0.008457 * ((x0 + (15.584000000000001 * x1)) - exp(x1))) + (0.001573 * exp((x0 * (x0 + -2.0))))) + 0.0202968) * exp((x0 * (2.0 - x0)))) +kotanchek,136,Operon,Operon,17,1,kept,11.0,8.0,((-0.0000000143612136) + (1.0000000000000000 * (((0.0493797957897186 - (0.0001029339036904 * x0)) / (exp(((-0.0000001355219865) * x0)) + (((-0.0032123271375895) * x1) * (((-41.7853355407714844) * x1) + 208.9266815185546875)))) / exp((((-1.8152447938919067) * x0) * (1.1029279232025146 - (0.5508886575698853 * x0))))))),-1.0*(0.0001029339036904*x0 - 0.0493797957897186)*exp(-1.8152447938919067*x0*(0.5508886575698853*x0 - 1.1029279232025146))/(0.0032123271375895*x1*(41.7853355407714844*x1 - 208.9266815185546875) + exp(-1.355219865e-7*x0)) - 1.43612136e-8,saturated,385.695083,35,11,29,8,149,161,66,2,75,(-1.43612136e-08 + (((0.0493797957897186 + (-0.0001029339036904 * x0)) / (exp((-1.355219865e-07 * x0)) + ((0.13422816731090328 * x1) * (x1 + -5.000000091292728)))) / exp(((-0.9999977676678355 * x0) * (2.0020886399582447 - x0))))),saturated,377.447833,35,11,29,8,230,249,94,2,75,((((0.0493797957897186 - (0.0001029339036904 * x0)) * exp((-0.9999977676678355 * (x0 * (x0 - 2.0020886399582447))))) / ((0.13422816731090328 * (x1 * (x1 - 5.000000091292728))) + exp((-1.355219865e-07 * x0)))) - 1.43612136e-08) +kotanchek,137,Operon,Operon,18,1,kept,13.0,11.0,((-0.0000026597272154) + (1.0000067949295044 * ((exp(((1.3812974691390991 * x0) * (((-0.7240105271339417) * x0) + 1.4479488134384155))) * (((-0.0016091535799205) * x1) - (-0.0074326260946691))) * (exp((1.1061540842056274 * x1)) - ((((-4.3172826766967773) * x1) + (-5.3209042549133301)) - exp((((3.6427340507507324 * x1) - 0.0311711747199297) - exp((0.6457238197326660 * x1))))))))),(-1.0000067949295044*(0.0016091535799205*x1 - 0.0074326260946691)*(4.3172826766967773*x1 + exp(1.1061540842056274*x1) + 0.969309637568713*exp(3.6427340507507324*x1 - exp(0.645723819732666*x1)) + 5.3209042549133301) - 2.6597272154e-6*exp(1.3812974691390991*x0*(0.7240105271339417*x0 - 1.4479488134384155)))*exp(-1.3812974691390991*x0*(0.7240105271339417*x0 - 1.4479488134384155)),saturated,392.695916,43,13,39,11,234,250,89,2,101,(-2.6597272154e-06 + (((-0.0016091645140056373 * (x1 + -4.618966261154704)) * exp(((-1.0000739087601787 * x0) * (x0 + -1.9999002212996078)))) * (((exp((1.1061540842056274 * x1)) + (4.317282676696777 * x1)) + 5.32090425491333) + exp((((3.6427340507507324 * x1) + -0.0311711747199297) - exp((0.645723819732666 * x1))))))),saturated,540.190958,54,16,48,13,332,357,134,2,122,((((-0.0016091645140056373 * (x1 - 4.618966261154704)) * ((((4.317282676696777 * x1) + exp((1.1061540842056274 * x1))) + (0.969309637568713 * exp(((3.6427340507507324 * x1) - exp((0.645723819732666 * x1)))))) + 5.32090425491333)) - (2.6597272154e-06 * exp((1.0000739087601787 * (x0 * (x0 - 1.9999002212996078)))))) * exp((-1.0000739087601787 * (x0 * (x0 - 1.9999002212996078))))) +kotanchek,138,Operon,Operon,19,1,kept,12.0,12.0,(0.0034536698367447 + (0.9867714047431946 * ((((((-0.6941707730293274) * x1) + exp((0.2583339512348175 * x1))) * (((-0.6002479791641235) * x1) + exp((0.2208170741796494 * x1)))) * (exp(((-0.8911798000335693) * x0)) - (0.7564386129379272 + ((-1.2858601808547974) * x0)))) / exp(((((-2.1546506881713867) * x1) + exp((0.6885151863098145 * x0))) + exp(((-1.0648982524871826) * x0))))))),(0.9867714047431946*(0.6002479791641235*x1 - exp(0.2208170741796494*x1))*(0.6941707730293274*x1 - exp(0.2583339512348175*x1))*((1.2858601808547974*x0 - 0.7564386129379272)*exp(0.8911798000335693*x0) + 1)*exp(((2.1546506881713867*x1 - exp(0.6885151863098145*x0))*exp(1.0648982524871826*x0) - 1)*exp(-1.0648982524871826*x0)) + 0.0034536698367447*exp(0.8911798000335693*x0))*exp(-0.8911798000335693*x0),saturated,358.618458,47,12,47,12,328,344,101,2,116,(0.0034536698367447 + (0.9867714047431946 * (((((-0.6941707730293274 * x1) + exp((0.2583339512348175 * x1))) * ((-0.6002479791641235 * x1) + exp((0.2208170741796494 * x1)))) * (exp((-0.8911798000335693 * x0)) + ((1.2858601808547974 * x0) + -0.7564386129379272))) / exp((((-2.1546506881713867 * x1) + exp((0.6885151863098145 * x0))) + exp((-1.0648982524871826 * x0))))))),saturated,918.147000,66,17,64,16,519,538,134,2,156,((((((1.2688500569654266 * ((exp((0.8911798000335693 * x0)) * (x0 + -0.5882743895491591)) + 0.7776895302374424)) * ((0.6002479791641235 * x1) - exp((0.2208170741796494 * x1)))) * ((0.6941707730293274 * x1) - exp((0.2583339512348175 * x1)))) * exp((((((2.1546506881713867 * x1) - exp((0.6885151863098145 * x0))) * exp((1.0648982524871826 * x0))) + -1.0) * exp((-1.0648982524871826 * x0))))) + (0.0034536698367447 * exp((0.8911798000335693 * x0)))) * exp((-0.8911798000335693 * x0))) +kotanchek,124,Operon,Operon,5,1,kept,13.0,10.0,(0.0000468041762360 + (0.9997506737709045 * (exp(((-0.0447766110301018) * x0)) - (0.8708053827285767 + ((((4.6947760581970215 * x1) - exp((0.6812457442283630 * x1))) * ((-2.2019169330596924) * x1)) * (((exp(((-5.3575110435485840) * x0)) + (15.1773414611816406 * x0)) * exp(((-2.3313734531402588) * x0))) * ((((-0.0015166908269748) * x1) * (4.4051661491394043 * x0)) - ((-0.0298569388687611) * x0)))))))),(-2.2013679374139911*x0*x1*(0.0066812750896996385*x1 - 0.0298569388687611)*(4.6947760581970215*x1 - exp(0.681245744228363*x1))*(15.1773414611816406*x0*exp(5.357511043548584*x0) + 1)*exp(0.0447766110301018*x0) + 0.9997506737709045*exp(7.6888844966888428*x0) - 0.8705414639299889*exp(7.7336611077189446*x0))*exp(-7.7336611077189446*x0),saturated,8064.621709,49,13,41,10,852,865,175,2,100,(0.9997506737709045 * (-0.8707585668799217 + (exp((-0.0447766110301018 * x0)) + (-0.01471161275443955 * ((x0 * (x1 + -4.468748624763382)) * (((exp((-5.357511043548584 * x0)) + (15.17734146118164 * x0)) * exp((-2.331373453140259 * x0))) * (((4.6947760581970215 * x1) - exp((0.681245744228363 * x1))) * x1))))))),saturated,12237.541875,55,14,51,12,1414,1439,315,2,122,(((((((-0.22322749986795287 * (((x1 - 4.468748624763382) * x0) * ((exp((5.357511043548584 * x0)) * x0) + 0.06588769202812311))) * x1) * ((4.6947760581970215 * x1) - exp((0.681245744228363 * x1)))) * exp((0.0447766110301018 * x0))) + (0.9997506737709045 * exp((7.688884496688843 * x0)))) - (0.8705414639299889 * exp((7.7336611077189445 * x0)))) * exp((-7.7336611077189445 * x0))) +kotanchek,141,Operon,Operon,22,1,kept,13.0,10.0,(0.0000054139832173 + (0.9996626973152161 * (exp(((((-0.1160286292433739) * x0) * ((-17.2363529205322266) + (8.6183118820190430 * x0))) + exp((exp((((1.4520825147628784 * x1) + (-7.2530150413513184)) * ((-0.1153997406363487) * x1))) + (-2.4340145587921143))))) * (exp((((1.4263883829116821 * x1) + (-7.1799330711364746)) * ((-0.0031533578876406) * x1))) + (-0.9611204862594604))))),-0.9607962977390443*exp(-0.99997091406255149*x0**2 + 1.99991040252437864*x0 + 0.087684112024531059*exp(exp(-0.16756994558621315*x1**2 + 0.83699605460347808*x1))) + 0.9996626973152161*exp(-0.99997091406255149*x0**2 + 1.99991040252437864*x0 - 0.0044979130580934735*x1**2 + 0.022640898582599801*x1 + 0.087684112024531059*exp(exp(-0.16756994558621315*x1**2 + 0.83699605460347808*x1))) + 5.4139832173e-6,saturated,323.393750,41,13,35,10,136,149,66,2,91,(5.4139832173e-06 + (0.9996626973152161 * (exp((((-0.9999709140625515 * x0) * (x0 + -1.999968573485206)) + exp((exp(((-0.16756994558621316 * x1) * (x1 + -4.99490557018085))) + -2.4340145587921143)))) * (exp(((-0.004497913058093474 * x1) * (x1 + -5.033645223946721))) + -0.9611204862594604)))),saturated,1945.932417,65,15,65,15,2793,2833,711,2,175,(((-0.9607962977390443 * exp((((-0.9999709140625515 * (x0 ** 2.0)) + (1.9999104025243786 * x0)) + (0.08768411202453105 * exp(exp(((-0.16756994558621316 * (x1 ** 2.0)) + (0.836996054603478 * x1)))))))) + (0.9996626973152161 * exp((((((-0.9999709140625515 * (x0 ** 2.0)) + (1.9999104025243786 * x0)) + (-0.004497913058093474 * (x1 ** 2.0))) + (0.0226408985825998 * x1)) + (0.08768411202453105 * exp(exp(((-0.16756994558621316 * (x1 ** 2.0)) + (0.836996054603478 * x1))))))))) + 5.4139832173e-06) +kotanchek,129,Operon,Operon,10,1,kept,13.0,12.0,((-0.0019379730802029) + (1.0046592950820923 * ((((996.6720581054687500 + ((-386.7166748046875000) * x0)) + exp((1.7618920803070068 * x0))) - (((1074.8041992187500000 * x0) + 882.8044433593750000) * exp(((-1.9537824392318726) * x0)))) / (((((-15.7029571533203125) * x1) * ((-22.8576602935791016) * x1)) + 2638.8918457031250000) + (exp((2.8161077499389648 * x0)) - (1794.9840087890625000 * x1)))))),(-1079.8120291383820754*x0 + (-388.518501905768068*x0 + 1.0046592950820923*exp(1.7618920803070068*x0) + 1001.315847324258372)*exp(1.9537824392318726*x0) + (-0.695602220697333891*x1**2 + 3.4786306884278888622*x1 - 0.0019379730802029*exp(2.8161077499389648*x0) - 5.1141013585396011999)*exp(1.9537824392318726*x0) - 886.917689760768567)*exp(-1.9537824392318726*x0)/(358.932860215223628*x1**2 - 1794.9840087890625*x1 + exp(2.8161077499389648*x0) + 2638.891845703125),saturated,579.977750,44,13,40,12,287,308,113,2,107,(-0.0019379730802029 + (1.0046592950820923 * ((((996.6720581054688 + (-386.7166748046875 * x0)) + exp((1.7618920803070068 * x0))) + (-1074.80419921875 * (exp((-1.9537824392318726 * x0)) * (x0 + 0.8213630389619475)))) / (((x1 * ((358.9328602152236 * x1) + -1794.9840087890625)) + exp((2.816107749938965 * x0))) + 2638.891845703125)))),saturated,12637.621417,69,18,62,16,6391,6456,1880,2,163,((((exp((1.9537824392318726 * x0)) * (-0.6956022206973339 * (((((x1 ** 2.0) - (5.000890717313407 * x1)) - (-0.002786036361787492 * exp((2.816107749938965 * x0)))) + -1432.1428487779078) + (-1.44430144871437 * (exp((1.7618920803070068 * x0)) + (-386.7166748046875 * x0)))))) + (-1079.812029138382 * x0)) - 886.9176897607686) * (exp((-1.9537824392318726 * x0)) / (((358.9328602152236 * ((x1 ** 2.0) - (5.000890717313407 * x1))) + exp((2.816107749938965 * x0))) - -2638.891845703125))) +kotanchek,140,Operon,Operon,21,1,kept,14.0,8.0,(0.0000354178737325 + (0.9998701810836792 * (((21.8554801940917969 * x1) - ((21.8578433990478516 * x1) - 0.0542484000325203)) * exp(((((-1.2365419864654541) - ((-0.6182689070701599) * x0)) * ((-1.6172654628753662) * x0)) - (exp(((((-0.0128339584916830) * x1) - (0.0000608815898886 * x1)) - ((((-1.6681232452392578) * x1) - (-6.2428498268127441)) * ((-0.1763334870338440) * x1)))) * ((-0.3036648035049438) * x1))))))),(-0.00236289816734826241*x1 + 3.54178737325e-5*exp(1.6172654628753662*x0*(0.6182689070701599*x0 - 1.2365419864654541) - 0.3036648035049438*x1*exp(x1*(1.0879286389089487 - 0.29414598863525044*x1))) + 0.05424135756401594)*exp(-1.6172654628753662*x0*(0.6182689070701599*x0 - 1.2365419864654541) + 0.3036648035049438*x1*exp(x1*(1.0879286389089487 - 0.29414598863525044*x1))),saturated,2401.330041,47,14,29,8,161,174,70,2,75,(3.54178737325e-05 + ((-0.0023628981673482485 * (x1 + -22.955435961460857)) * exp((((0.999904950174269 * x0) * (2.0000067483987736 - x0)) + (0.3036648035049438 * (exp((-0.29414598863525043 * (x1 * (-3.6986009700714013 + x1)))) * x1)))))),saturated,446.057667,55,15,51,13,267,288,111,2,127,((3.54178737325e-05 * ((exp(((0.999904950174269 * (x0 * (x0 - 2.0000067483987736))) - ((0.3036648035049438 * x1) * exp((x1 * (-0.29414598863525043 * (x1 + -3.6986009700714013))))))) + (-66.71485095899558 * x1)) + 1531.4684888676197)) * exp((-0.999904950174269 * ((x0 * (x0 - 2.0000067483987736)) - (0.30369366953530874 * (exp((x1 * (-0.29414598863525043 * (x1 + -3.6986009700714013)))) * x1)))))) +kotanchek,142,Operon,Operon,23,1,kept,11.0,10.0,(0.0008338154293597 + (0.9979702830314636 * ((exp(exp(exp(((0.0654336437582970 + ((-0.0385530032217503) * x1)) * ((-17.4296455383300781) + (5.2765936851501465 * x1)))))) * (exp(((-0.6076733469963074) * x0)) + ((-0.9865196943283081) + (0.7046096920967102 * x0)))) * exp((exp(((-4.4563603401184082) * x0)) - exp((0.6908147931098938 * x0))))))),(((0.7031795338484663*x0 - 0.9845173385649346)*exp(0.6076733469963074*x0) + 0.9979702830314636)*exp((1 - exp(5.147175133228302*x0))*exp(-4.4563603401184082*x0) + exp(exp(-(0.0385530032217503*x1 - 0.065433643758297)*(5.2765936851501465*x1 - 17.4296455383300781)))) + 0.0008338154293597*exp(0.6076733469963074*x0))*exp(-0.6076733469963074*x0),saturated,331.694417,40,11,38,10,181,195,77,2,94,(0.0008338154293597 + (0.9979702830314636 * ((exp(exp(exp((-0.2034285333434609 * ((x1 + -1.697238562244654) * (x1 + -3.3032002421149307)))))) * (exp((-0.6076733469963074 * x0)) + (-0.9865196943283081 + (0.7046096920967102 * x0)))) * exp((exp((-4.456360340118408 * x0)) - exp((0.6908147931098938 * x0))))))),saturated,413.299667,53,15,49,13,201,218,93,2,122,((((((0.7031795338484663 * (x0 + -1.4000938468398256)) * exp((0.6076733469963074 * x0))) + 0.9979702830314636) * exp((((1.0 - exp((5.147175133228302 * x0))) * exp((-4.456360340118408 * x0))) + exp(exp((-0.2034285333434609 * ((x1 + -3.3032002421149307) * (x1 + -1.697238562244654)))))))) + (0.0008338154293597 * exp((0.6076733469963074 * x0)))) * exp((-0.6076733469963074 * x0))) +kotanchek,143,Operon,Operon,24,1,kept,11.0,10.0,(0.0000109874044938 + (0.9998849630355835 * (exp(((227.2529296875000000 * x0) * ((-0.0044004078954458) * x0))) * (((exp((0.0044344896450639 * x1)) - 0.9905131459236145) * exp(((1.9999943971633911 * x0) - (0.0865126922726631 * x1)))) * (exp(((-0.2363450229167938) * x1)) + exp(exp(exp(((1.1673830747604370 * x1) - exp((0.4206682443618774 * x1))))))))))),(0.9998849630355835*(exp(0.0044344896450639*x1) - 0.9905131459236145)*(exp(0.2363450229167938*x1 + exp(exp(1.167383074760437*x1 - exp(0.4206682443618774*x1)))) + 1)*exp(1.9999943971633911*x0 - 0.0865126922726631*x1) + 1.09874044938e-5*exp(1.000005586060064296*x0**2 + 0.2363450229167938*x1))*exp(-1.000005586060064296*x0**2 - 0.2363450229167938*x1),saturated,367.489584,45,11,43,10,329,344,97,2,101,(1.09874044938e-05 + (0.9998849630355835 * (exp((-1.0000055860600643 * (x0 * x0))) * (((exp((0.0044344896450639 * x1)) + -0.9905131459236145) * exp(((1.9999943971633911 * x0) + (-0.0865126922726631 * x1)))) * (exp((-0.2363450229167938 * x1)) + exp(exp(exp(((1.167383074760437 * x1) - exp((0.4206682443618774 * x1))))))))))),saturated,360.097791,59,14,59,14,301,322,121,2,149,(((((0.9998849630355835 * (exp((0.0044344896450639 * x1)) + -0.9905131459236145)) * (exp(((0.2363450229167938 * x1) + exp(exp(((1.167383074760437 * x1) - exp((0.4206682443618774 * x1))))))) + 1.0)) * exp(((1.9999943971633911 * x0) + (-0.0865126922726631 * x1)))) + (1.09874044938e-05 * exp(((1.0000055860600643 * (x0 ** 2.0)) + (0.2363450229167938 * x1))))) * exp((-1.0000055860600643 * ((x0 ** 2.0) + (0.23634370268667476 * x1))))) +kotanchek,144,Operon,Operon,25,1,kept,13.0,13.0,((-0.0021912427619100) + (1.0060203075408936 * ((((-1.9571648836135864) + ((-0.1280445605516434) * x1)) + (((-4.9479722976684570) * x0) + (((exp(((-25.1299152374267578) * x0)) - ((-1013.9223632812500000) + ((-2498.2419433593750000) * x0))) / ((-763.4477539062500000) - exp((2.6487932205200195 * x1)))) / exp(((-1.3105899095535278) * x1))))) / ((-64.6880645751953125) - exp((2.9050159454345703 * x0)))))),-0.00219124276191 + 1.0060203075408936*(4.947972297668457*x0 + 0.1280445605516434*x1 + 1.9571648836135864 + (2498.241943359375*x0 + 1013.92236328125 + exp(-25.1299152374267578*x0))*exp(1.3105899095535278*x1)/(exp(2.6487932205200195*x1) + 763.44775390625))/(exp(2.9050159454345703*x0) + 64.6880645751953125),saturated,339.952792,43,13,43,13,256,277,109,2,115,(-0.00219124276191 + (((-1.9571648836135864 + (-0.1280445605516434 * x1)) + ((-4.947972297668457 * x0) + ((((exp((-25.129915237426758 * x0)) + 1013.92236328125) + (2498.241943359375 * x0)) / (-763.44775390625 - exp((2.6487932205200195 * x1)))) / exp((-1.3105899095535278 * x1))))) * (1.0060203075408936 / (-64.68806457519531 - exp((2.9050159454345703 * x0)))))),saturated,288.221250,43,13,43,13,267,288,111,1,115,(-0.00219124276191 + ((1.0060203075408936 * ((((4.947972297668457 * x0) + (0.1280445605516434 * x1)) + 1.9571648836135864) + (((((2498.241943359375 * x0) + 1013.92236328125) + exp((-25.129915237426758 * x0))) * exp((1.3105899095535278 * x1))) / (exp((2.6487932205200195 * x1)) + 763.44775390625)))) / (exp((2.9050159454345703 * x0)) + 64.68806457519531))) +kotanchek,145,Operon,Operon,26,1,kept,14.0,9.0,((-0.0000017344426624) + (1.0000044107437134 * (exp((exp(((1.8745909929275513 - (0.6161273121833801 * x1)) * ((-0.4286146163940430) - (1.4141622781753540 - (0.9453756809234619 * x1))))) - (((0.6846604943275452 * x0) - 1.3692940473556519) * (1.4605207443237305 * x0)))) * ((1.0031132698059082 - ((-0.9088089466094971) * x1)) * (0.0477729775011539 - (0.0077679147943854 * x1)))))),(-1.0000044107437134*(0.0077679147943854*x1 - 0.0477729775011539)*(0.9088089466094971*x1 + 1.0031132698059082) - 1.7344426624e-6*exp(1.4605207443237305*x0*(0.6846604943275452*x0 - 1.3692940473556519) - exp((1.8745909929275513 - 0.6161273121833801*x1)*(0.9453756809234619*x1 - 1.842776894569397))))*exp(-1.4605207443237305*x0*(0.6846604943275452*x0 - 1.3692940473556519) + exp((1.8745909929275513 - 0.6161273121833801*x1)*(0.9453756809234619*x1 - 1.842776894569397))),saturated,1057.504583,41,14,31,9,155,167,64,2,82,(-1.7344426624e-06 + ((-0.007059581599505541 * ((-1.103766939738251 - x1) * (6.150038815524072 - x1))) * exp((exp((0.5824717772909054 * ((3.042538377798143 - x1) * (x1 + -1.9492535420091783)))) + (-0.9999608547843195 * (x0 * (x0 + -1.9999606501329321))))))),saturated,650.511458,63,20,51,14,212,232,99,2,131,((-1.7344426624e-06 * (exp(((0.9999608547843195 * (x0 * (x0 - 1.9999606501329321))) - exp(((-0.5824717772909054 * (x1 + -3.042538377798143)) * (x1 - 1.9492535420091783))))) + (4070.230600610912 * ((x1 + 1.103766939738251) * (x1 - 6.150038815524072))))) * exp(((-0.9999608547843195 * (x0 * (x0 - 1.9999606501329321))) + exp(((-0.5824717772909054 * (x1 + -3.042538377798143)) * (x1 - 1.9492535420091783)))))) +kotanchek,146,Operon,Operon,27,1,kept,13.0,11.0,((-0.0020811073482037) + (0.9979038834571838 * ((((((-0.0209705717861652) * x1) - ((0.0227618105709553 * x0) + 0.0106864003464580)) * exp((0.0658860057592392 * x0))) + (0.0203825030475855 * x1)) * ((40.4724655151367188 / ((-62.7512664794921875) - exp((2.9289722442626953 * x0)))) / (exp((0.1633399575948715 * x1)) + ((-0.8682605624198914) - (0.2447641491889954 * x1))))))),(0.823201001967915342*x1 - 0.0020811073482037*(exp(2.9289722442626953*x0) + 62.7512664794921875)*(0.2447641491889954*x1 - exp(0.1633399575948715*x1) + 0.8682605624198914) - (0.919295595092965231*x0 + 0.846951704896531438*x1 + 0.431598388681541098)*exp(0.0658860057592392*x0))/((exp(2.9289722442626953*x0) + 62.7512664794921875)*(0.2447641491889954*x1 - exp(0.1633399575948715*x1) + 0.8682605624198914)),saturated,1794.993834,42,13,38,11,190,206,86,2,100,(-0.0020811073482037 + (((0.8232010019679153 / (-62.75126647949219 - exp((2.9289722442626953 * x0)))) * (x1 + (-1.0288516448253082 * (exp((0.0658860057592392 * x0)) * ((x1 + (1.0854167832453585 * x0)) + 0.5095903180621942))))) / (exp((0.1633399575948715 * x1)) + (-0.8682605624198914 + (-0.2447641491889954 * x1))))),saturated,622.117500,56,16,56,16,345,366,129,2,146,((((0.8232010019679153 * x1) + (-0.0020811073482037 * ((exp((2.9289722442626953 * x0)) + 62.75126647949219) * (((0.2447641491889954 * x1) - exp((0.1633399575948715 * x1))) + 0.8682605624198914)))) + (-0.9192955950929652 * (exp((0.0658860057592392 * x0)) * ((x0 + (0.9213050833892902 * x1)) + 0.46948815047666476)))) / ((exp((2.9289722442626953 * x0)) + 62.75126647949219) * (((0.2447641491889954 * x1) - exp((0.1633399575948715 * x1))) + 0.8682605624198914))) +kotanchek,149,Operon,Operon,30,1,kept,11.0,11.0,(0.0002253897109767 + (0.9994593262672424 * (exp(exp((0.0994609072804451 * x1))) * (exp((((-0.5447754859924316) * x0) - exp((0.6602987051010132 * x0)))) * ((((-1.3688123226165771) + exp((0.1289836019277573 - exp((1.1763114929199219 * x0))))) + exp((0.6509695649147034 * x0))) / (((-0.9415363073348999) * x1) + exp((0.3773067891597748 * x1)))))))),((0.0002122125961842825*x1 - 0.0002253897109767*exp(0.3773067891597748*x1))*exp(0.5447754859924316*x0 + exp(0.6602987051010132*x0) + exp(1.1763114929199219*x0)) + ((1.3680722417486634 - 0.9994593262672424*exp(0.6509695649147034*x0))*exp(exp(1.1763114929199219*x0)) - 1.137056359314377)*exp(exp(0.0994609072804451*x1)))*exp(-0.5447754859924316*x0 - exp(0.6602987051010132*x0) - exp(1.1763114929199219*x0))/(0.9415363073348999*x1 - exp(0.3773067891597748*x1)),saturated,383.640417,43,11,43,11,300,314,91,2,105,(0.0002253897109767 + (0.9994593262672424 * (exp(exp((0.0994609072804451 * x1))) * (((-1.3688123226165771 + exp((0.1289836019277573 - exp((1.1763114929199219 * x0))))) + exp((0.6509695649147034 * x0))) * (exp(((-0.5447754859924316 * x0) - exp((0.6602987051010132 * x0)))) / ((-0.9415363073348999 * x1) + exp((0.3773067891597748 * x1)))))))),saturated,508.603333,72,17,72,17,454,477,157,2,170,(((((0.0002122125961842825 * x1) + (-0.0002253897109767 * exp((0.3773067891597748 * x1)))) * exp((((0.5447754859924316 * x0) + exp((0.6602987051010132 * x0))) + exp((1.1763114929199219 * x0))))) + ((((1.3680722417486635 + (-0.9994593262672424 * exp((0.6509695649147034 * x0)))) * exp(exp((1.1763114929199219 * x0)))) + -1.137056359314377) * exp(exp((0.0994609072804451 * x1))))) * (exp((((-0.5447754859924316 * x0) - exp((0.6602987051010132 * x0))) - exp((1.1763114929199219 * x0)))) / ((0.9415363073348999 * x1) - exp((0.3773067891597748 * x1))))) +kotanchek,139,Operon,Operon,20,1,kept,13.0,10.0,(0.0004888178664260 + (0.9988220334053040 * (exp((((((-5.1766362190246582) - (0.0070227989926934 * x0)) + (1.1790944337844849 * x1)) * ((-0.3277454376220703) * x1)) + (exp(((6.3319468498229980 * x1) * ((-0.0836486071348190) * x1))) * ((-1.0949771404266357) * x1)))) / (6.3024258613586426 / (0.0139735620468855 + exp(((2.2476174831390381 * x0) - exp((0.8711588978767395 * x0))))))))),(0.15848215518555634*exp(2.2476174831390381*x0 - exp(0.8711588978767395*x0)) + 0.0022145602288095083)*exp(-x1*(0.3277454376220703*(-0.0070227989926934*x0 + 1.1790944337844849*x1 - 5.1766362190246582)*exp(0.52965853443939874*x1**2) + 1.0949771404266357)*exp(-0.52965853443939874*x1**2)) + 0.000488817866426,saturated,2336.114625,45,13,39,11,187,205,92,2,101,(0.000488817866426 + (exp((x1 * ((-0.002301690329192133 * ((-737.1186651377163 - x0) + (167.89522738885566 * x1))) + (exp((-0.5296585344393987 * (x1 * x1))) * -1.0949771404266357)))) * (0.998822033405304 / (6.302425861358643 / (0.0139735620468855 + exp(((2.247617483139038 * x0) - exp((0.8711588978767395 * x0))))))))),saturated,4677.621875,48,13,44,11,217,235,94,2,116,((((0.15848215518555633 * exp(((2.247617483139038 * x0) - exp((0.8711588978767395 * x0))))) + 0.002214560228809508) * exp((((-1.0949771404266357 + (0.002301690329192133 * (exp((0.5296585344393987 * (x1 ** 2.0))) * ((x0 + (-167.89522738885566 * x1)) + 737.1186651377163)))) * x1) * exp((-0.5296585344393987 * (x1 ** 2.0)))))) + 0.000488817866426) +kotanchek,147,Operon,Operon,28,1,kept,12.0,11.0,(0.0014168095076457 + (0.9966097474098206 * (((4.5074963569641113 * x0) + exp(((-2.2596077919006348) * x0))) * ((((-0.0000623191444902) * x0) - exp(((0.5578119754791260 * x0) - exp((0.7266396284103394 * x0))))) * ((exp((1.8929998874664307 * x1)) * ((-0.0988849624991417) - ((-0.0229831431061029) * x1))) * (exp((0.2581167519092560 * x1)) + ((-0.6963179111480713) * x1))))))),(0.9966097474098206*(6.23191444902e-5*x0 + exp(0.557811975479126*x0 - exp(0.7266396284103394*x0)))*(0.0229831431061029*x1 - 0.0988849624991417)*(0.6963179111480713*x1 - exp(0.258116751909256*x1))*(4.5074963569641113*x0*exp(2.2596077919006348*x0) + 1)*exp(1.8929998874664307*x1) + 0.0014168095076457*exp(2.2596077919006348*x0))*exp(-2.2596077919006348*x0),saturated,1068.594959,46,12,44,11,736,750,136,2,108,(0.0014168095076457 + (((-0.022905224445656968 * (((4.507496356964111 * x0) + exp((-2.2596077919006348 * x0))) * (4.302499533794574 - x1))) * ((exp((0.258116751909256 * x1)) + (-0.6963179111480713 * x1)) * exp((1.8929998874664307 * x1)))) * ((-6.23191444902e-05 * x0) - exp(((0.557811975479126 * x0) - exp((0.7266396284103394 * x0))))))),saturated,2139.767875,58,15,54,13,811,827,149,2,130,((((((0.10324521574424408 * ((x1 + -4.302499533794574) * ((exp((2.2596077919006348 * x0)) * x0) + 0.22185264741367866))) * ((6.23191444902e-05 * x0) + exp(((0.557811975479126 * x0) - exp((0.7266396284103394 * x0)))))) * ((0.6963179111480713 * x1) - exp((0.258116751909256 * x1)))) * exp((1.8929998874664307 * x1))) + (0.0014168095076457 * exp((2.2596077919006348 * x0)))) * exp((-2.2596077919006348 * x0))) +kotanchek,151,SBP,SBP,2,1,kept,5.0,1.0,-0.000871-0.000000*((exp((((-13.691000*(-13.691000))-exp((1.294000-x1)))-(x0*x0)))*(((-5.521000+x1)*exp(x0))*exp(x0)))),-0.000871000000000000,saturated,329.043667,27,6,1,1,3,4,3,2,6,-0.000871,saturated,259.421917,1,1,1,1,3,4,3,1,6,-0.000871 +kotanchek,150,SBP,SBP,1,1,kept,5.0,4.0,0.053829-0.000194*(((((exp(((x0+19.367000)-(x0*x0)))*exp((-13.819000+x0)))-(x1*exp(x1)))*(-1.237000-x1))+exp(x0))),((0.053829 - 0.000194*exp(x0))*exp(x0*(x0 - 1)) - 0.000194*(x1 + 1.237)*(x1*exp(x0**2 - x0 + x1) - 256.723594926263*exp(x0)))*exp(x0*(1 - x0)),saturated,278.231625,29,5,29,5,101,112,55,1,62,(0.053829 - (0.000194 * ((((exp(((x0 + 19.367) - (x0 * x0))) * exp((-13.819 + x0))) - (x1 * exp(x1))) * (-1.237 - x1)) + exp(x0)))),saturated,796.648458,42,7,40,6,102,113,56,2,86,((-0.000194 * ((((x1 * exp((((x0 ** 2.0) - x0) + x1))) - (256.723594926263 * exp(x0))) * (x1 - -1.237)) - (exp((x0 * (x0 - 1.0))) * (277.46907216494844 - exp(x0))))) * exp((x0 * (1.0 - x0)))) +kotanchek,153,SBP,SBP,4,1,kept,7.0,5.0,1.105782+0.007318*((0.199000+((-7.153000+x0)*(((-7.153000+x0)*(x0-(x0*x0)))-(((x1-12.520000)+x0)+(-7.153000+x0)))))),-0.007318*(x0 - 7.153)*(x0*(x0 - 7.153)*(x0 - 1) + 2*x0 + x1 - 19.673) + 1.107238282,saturated,306.387833,29,7,25,5,146,154,49,2,58,(0.007318 * (151.3034001093195 + ((-7.153 + x0) * (((-7.153 + x0) * (x0 - (x0 * x0))) - ((x0 + x0) + (-19.673 + x1)))))),saturated,309.484125,25,7,23,7,93,105,50,2,63,(((-0.007318 * (x0 - 7.153)) * (((x0 * (((x0 - 1.0) * (x0 - 7.153)) + 2.0)) + x1) - 19.673)) + 1.107238282) +kotanchek,152,SBP,SBP,3,1,kept,7.0,6.0,0.164127-0.000918*((((((17.900000-(9.729000*x1))+7.431000)-x0)-((x1+x0)*((exp((7.431000-exp(x0)))-2.295000)*x0)))*x0)),(-0.000918*x0*(x0*(x0 + x1)*(2.295*exp(exp(x0)) - 1687.49422412485) + (-x0 - 9.729*x1 + 25.331)*exp(exp(x0))) + 0.164127*exp(exp(x0)))*exp(-exp(x0)),saturated,328.581916,29,7,27,6,127,141,65,2,64,(0.164127 - (0.000918 * ((((25.331 + (-9.729 * x1)) - x0) - ((x1 + x0) * ((exp((7.431 - exp(x0))) - 2.295) * x0))) * x0))),saturated,1158.411083,43,8,41,7,232,247,89,2,86,((((-0.000918 * x0) * (((x0 * (x0 + x1)) * ((2.295 * exp(exp(x0))) + -1687.49422412485)) + (((25.331 - x0) + (-9.729 * x1)) * exp(exp(x0))))) + (0.164127 * exp(exp(x0)))) * exp((-1.0 * exp(x0)))) +kotanchek,148,Operon,Operon,29,1,kept,12.0,9.0,((-0.0000438776442024) + (1.0001060962677002 * (exp((((((-0.3045227825641632) * x1) * exp((0.5642136931419373 * x1))) - (4.0260410308837891 + ((-1.9999954700469971) * x0))) - (((-0.6665219664573669) * x0) * ((-1.5003671646118164) * x0)))) * (exp(exp((0.6489872336387634 * x1))) - (exp((1.3141704797744751 * x1)) * ((-0.1860205531120300) * exp((1.5301641225814819 * x1)))))))),(0.0033198587205338268*exp(2.844334602355957*x1) - 4.38776442024e-5*exp(1.0000276729651318*x0**2 - 1.9999954700469971*x0 + 0.3045227825641632*x1*exp(0.5642136931419373*x1)) + 0.017846730724074654*exp(exp(0.6489872336387634*x1)))*exp(-1.0000276729651318*x0**2 + 1.9999954700469971*x0 - 0.3045227825641632*x1*exp(0.5642136931419373*x1)),saturated,3073.180542,45,12,41,11,278,299,116,2,103,(-4.38776442024e-05 + (1.0001060962677002 * (exp(((x0 * ((-1.0000276729651318 * x0) + 1.999995470046997)) + (((-0.3045227825641632 * x1) * exp((0.5642136931419373 * x1))) + -4.026041030883789))) * (exp(exp((0.6489872336387634 * x1))) + (0.18602055311203 * (exp((1.314170479774475 * x1)) * exp((1.530164122581482 * x1)))))))),saturated,407.028750,56,13,56,13,194,211,91,2,141,((-4.38776442024e-05 * (exp(((1.0000276729651318 * ((x0 ** 2.0) + (-1.9999401257736307 * x0))) + ((0.3045227825641632 * x1) * exp((0.5642136931419373 * x1))))) + (-406.73858062549493 * (exp(exp((0.6489872336387634 * x1))) + (0.18602055311203 * exp((2.844334602355957 * x1))))))) * exp((-1.0000276729651318 * (((x0 ** 2.0) + (-1.9999401257736307 * x0)) + (0.3045143557490144 * (exp((0.5642136931419373 * x1)) * x1)))))) +kotanchek,154,SBP,SBP,5,1,kept,5.0,4.0,0.009179-0.000004*((exp(((x0+x0)-(x0*x0)))*(-18.822000*((exp(x1)+(x1*(-19.513000)))*(exp(x1)+(5.700000*(-18.822000))))))),(-7.5288e-5*(19.513*x1 - exp(x1))*(exp(x1) - 107.2854) + 0.009179*exp(x0*(x0 - 2)))*exp(x0*(2 - x0)),saturated,465.676792,28,6,24,4,167,177,58,2,51,(0.009179 - (-7.528799999999999e-05 * (exp(((x0 + x0) - (x0 * x0))) * ((exp(x1) + (x1 * -19.513)) * (exp(x1) + -107.2854))))),saturated,325.270584,29,6,29,6,125,135,56,2,66,((((-7.5288e-05 * ((19.513 * x1) - exp(x1))) * (exp(x1) + -107.2854)) + (0.009179 * exp((x0 * (x0 + -2.0))))) * exp((x0 * (2.0 - x0)))) +kotanchek,156,SBP,SBP,7,1,kept,4.0,4.0,-14.026870+14.029048*(exp(exp((((x0+((x0+x0)-(exp(exp(exp((-0.884000-(x1*x1)))))+x0)))-1.493000)-(x0*x0))))),14.029048*exp(0.224697550736354*exp(-x0**2 + 2*x0 - exp(exp(0.413127093878218*exp(-x1**2))))) - 14.02687,saturated,311.512000,28,4,28,4,71,78,39,2,56,(-14.02687 + (14.029048 * exp(exp((((x0 + (((x0 + x0) - exp(exp(exp((-0.884 - (x1 * x1)))))) - x0)) + -1.493) - (x0 * x0)))))),saturated,309.394625,28,7,26,6,75,86,48,2,69,((14.029048 * exp((0.224697550736354 * exp((((2.0 * x0) - (x0 ** 2.0)) - exp(exp((0.413127093878218 * exp((-1.0 * (x1 ** 2.0))))))))))) - 14.02687) +kotanchek,158,SBP,SBP,9,1,kept,6.0,5.0,0.018312-0.003546*(((((x0-(x0+((x0-13.713000)*x0)))-((x0*x0)+1.354000))-(20.118000+1.354000))*(x1+(x0*7.506000)))),0.003546*(7.506*x0 + x1)*(x0**2 + x0*(x0 - 13.713) + 22.826) + 0.018312,saturated,312.118417,29,7,21,5,92,103,49,2,52,(0.018312 - (0.003546 * ((-22.825999999999997 + (((13.713 - x0) * x0) - (x0 * x0))) * (x1 + (x0 * 7.506))))),saturated,340.900208,21,5,21,5,80,89,41,2,56,(((0.003546 * ((7.506 * x0) + x1)) * (((x0 ** 2.0) + (x0 * (x0 + -13.713))) + 22.826)) + 0.018312) +kotanchek,159,SBP,SBP,10,1,kept,4.0,3.0,0.001314-0.043497*((exp(((x0+x0)-(x0*x0)))*(((x0-6.297000)-(x0-(x1+1.578000)))*x1))),(-0.043497*x1*(x1 - 4.719) + 0.001314*exp(x0*(x0 - 2)))*exp(x0*(2 - x0)),saturated,365.639958,24,4,22,3,164,173,55,2,45,(0.001314 - (0.043497 * (exp(((x0 + x0) - (x0 * x0))) * (((-4.718999999999999 + x0) - (x0 - x1)) * x1)))),saturated,324.819584,23,5,23,5,115,124,50,2,54,((((-0.043497 * x1) * (x1 + -4.719)) + (0.001314 * exp((x0 * (x0 + -2.0))))) * exp((x0 * (2.0 - x0)))) +kotanchek,160,SBP,SBP,11,1,kept,7.0,7.0,0.040413-0.000597*(((6.648000-x0)*((exp(x1)-(x1*15.197000))*(2.753000+((x0*9.675000)-((x0*(6.648000-x0))*x0)))))),-0.000597*(x0 - 6.648)*(15.197*x1 - exp(x1))*(x0**2*(x0 - 6.648) + 9.675*x0 + 2.753) + 0.040413,saturated,293.176167,28,7,28,7,189,202,70,1,70,(0.040413 - (0.000597 * ((6.648 - x0) * ((exp(x1) - (x1 * 15.197)) * (2.753 + ((x0 * 9.675) - ((x0 * (6.648 - x0)) * x0))))))),saturated,292.903833,28,7,28,7,147,160,63,1,74,((((-0.000597 * (x0 - 6.648)) * ((15.197 * x1) - exp(x1))) * ((((x0 ** 2.0) * (x0 - 6.648)) + (9.675 * x0)) + 2.753)) + 0.040413) +kotanchek,161,SBP,SBP,12,1,kept,6.0,5.0,0.149913+0.001414*((((-14.224000*x0)*x0)-((0.405000-(-6.959000*((x0*x1)-((x1-(-14.412000*x1))-exp(x1)))))-exp(x1)))),-0.020112736*x0**2 - 0.009840026*x0*x1 + 0.151654480712*x1 - 0.008426026*exp(x1) + 0.14934033,saturated,427.800083,29,6,25,5,247,259,78,2,57,(0.001414 * ((-6.959 * (((((x1 * (x0 + -14.412)) - x1) + exp(x1)) + -15.176822703517248) + (2.0439718350337692 * (x0 * x0)))) + exp(x1))),saturated,5090.799083,22,5,20,5,765,790,193,2,54,((((x1 * (0.151654480712 + (-0.009840026 * x0))) + (-0.020112736 * (x0 ** 2.0))) + (-0.008426026 * exp(x1))) + 0.14934033) +kotanchek,157,SBP,SBP,8,1,kept,5.0,4.0,0.144574+0.000155*(((((x1-(11.267000*7.230000))*3.308000)+(x1+(exp((7.230000-(x0*x0)))*((x0*x1)+exp(x0)))))*x0)),0.213934488133493*x0**2*x1*exp(-x0**2) + 0.00066774*x0*x1 + 0.213934488133493*x0*exp(-x0**2 + x0) - 0.0417680106234*x0 + 0.144574,saturated,301.383708,29,6,27,5,86,94,42,2,60,(0.144574 + (0.000155 * ((((x1 + -81.46041) * 3.308) + (x1 + (exp((7.23 - (x0 * x0))) * ((x0 * x1) + exp(x0))))) * x0))),saturated,6569.296958,39,7,31,5,99,108,47,2,78,(0.213934488133493 * (0.6757863178646879 + (((exp((-1.0 * (x0 ** 2.0))) * x1) * (x0 ** 2.0)) + (x0 * ((exp((x0 - (x0 ** 2.0))) + (0.00312123587844956 * x1)) + -0.19523738779947053))))) +kotanchek,164,SBP,SBP,15,1,kept,7.0,4.0,-0.000469-0.008133*((((((-12.866000+((-2.656000-exp(-2.656000))-exp(-2.656000)))*x1)+exp(x1))-4.334000)*exp((x0+(x0-(x0*x0)))))),(0.127382764000369*x1 - 0.008133*exp(x1) - 0.000469*exp(x0*(x0 - 2)) + 0.035248422)*exp(x0*(2 - x0)),saturated,302.219416,29,7,21,4,113,125,56,2,47,(-0.000469 - (0.008133 * ((((-15.662457149928537 * x1) + exp(x1)) - 4.334) * exp((x0 + (x0 - (x0 * x0))))))),saturated,454.965792,26,6,26,6,499,518,131,2,62,(((((0.127382764000369 * x1) + (-0.008133 * exp(x1))) + (-0.000469 * exp((x0 * (x0 + -2.0))))) + 0.035248422) * exp((x0 * (2.0 - x0)))) +kotanchek,165,SBP,SBP,16,1,kept,6.0,5.0,0.009361+0.001754*((((4.923000-x1)*((((x0*x0)-16.384000)*((((x0*x0)-(-1.015000+x0))-x0)-3.101000))+x0))*x1)),-0.001754*x1*(x0 - (x0**2 - 16.384)*(-x0**2 + 2*x0 + 2.086))*(x1 - 4.923) + 0.009361,saturated,284.766584,29,6,29,6,118,127,48,2,68,(0.009361 + (0.001754 * (((4.923 - x1) * ((((x0 * x0) + -16.384) * (((((x0 * x0) + 1.015) - x0) - x0) + -3.101)) + x0)) * x1))),saturated,834.382042,29,7,27,6,139,150,56,2,73,((((-0.001754 * x1) * (x0 + (((x0 ** 2.0) + -16.384) * (((x0 ** 2.0) + (-2.0 * x0)) + -2.086)))) * (x1 + -4.923)) + 0.009361) +kotanchek,162,SBP,SBP,13,1,kept,6.0,6.0,0.170654+0.002714*(((x0-6.237000)*((((-16.211000-x0)+x1)+(exp(x1)+(-16.310000*(x1-x0))))+exp((3.307000-(x0+x0)))))),(0.002714*(x0 - 6.237)*((15.31*x0 - 15.31*x1 + exp(x1) - 16.211)*exp(2*x0) + 27.3030932054114) + 0.170654*exp(2*x0))*exp(-2*x0),saturated,312.228833,29,6,29,6,277,286,67,2,67,(0.170654 + (0.002714 * ((x0 + -6.237) * ((((-16.211 - x0) + x1) + (exp(x1) + (-16.31 * (x1 - x0)))) + exp((3.307 - (x0 + x0))))))),saturated,8493.723584,37,10,35,9,156,169,70,2,87,((((0.002714 * (x0 + -6.237)) * (((((15.31 * (x0 - x1)) + exp(x1)) + -16.211) * exp((2.0 * x0))) + 27.3030932054114)) + (0.170654 * exp((2.0 * x0)))) * exp((-2.0 * x0))) +kotanchek,166,SBP,SBP,17,1,kept,5.0,3.0,-0.025349+0.010788*((((((((((x0+x0)-(x0*x0))*(-5.542000+x0))*(-5.542000+x0))+x1)+x1)+12.501000)+x0)+x1)),x0*(0.662680172064 - 0.331340086032*x0)*(0.180440274269217*x0 - 1)**2 + 0.010788*x0 + 0.032364*x1 + 0.109511788,saturated,308.312208,29,5,27,4,270,275,49,2,57,(0.010788 * ((10.151259547645532 + (x1 + x0)) + ((((((x0 + x0) - (x0 * x0)) * (-5.542 + x0)) * (-5.542 + x0)) + x1) + x1))),saturated,1063.106708,25,7,23,7,216,235,93,2,67,(((x0 * (((((0.180440274269217 * x0) + -1.0) ** 2.0) * (0.662680172064 + (-0.331340086032 * x0))) + 0.010788)) + (0.032364 * x1)) + 0.109511788) 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- x0))))))),saturated,330.517083,29,7,27,6,133,143,54,2,68,(((-0.0149 * ((x1 - x0) + 2.332)) * (((((x0 ** 2.0) - x0) + x1) + exp((1.71257827818735 * exp((-1.0 * x0))))) + -11.7)) + 0.000939) +kotanchek,168,SBP,SBP,19,1,kept,5.0,4.0,0.025140-0.013750*((exp(((x0-x1)-exp(x0)))*(exp(x0)*(((x1*(-17.939000))*(x1-((exp(x0)-0.338000)*(-3.388000))))*x1)))),(x1**2*(0.24666125*x1 + 0.835688315*exp(x0) - 0.28246265047)*exp(x0) + 0.02514*exp(-x0 + x1 + exp(x0)))*exp(x0 - x1 - exp(x0)),saturated,1575.581791,29,5,27,4,495,507,90,2,55,(0.02514 - (((-0.24666125 * (exp(((x0 - x1) - exp(x0))) * ((x1 - ((exp(x0) - 0.338) * -3.388)) * x1))) * exp(x0)) * x1)),saturated,484.355875,37,5,35,4,495,511,130,2,70,(((((x1 ** 2.0) * (((0.24666125 * x1) + (0.835688315 * exp(x0))) + -0.28246265047)) * exp(x0)) + (0.02514 * exp(((x1 - x0) + exp(x0))))) * exp(((x0 - x1) - exp(x0)))) 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+ (((x0 * ((-5.937 * x0) + 6.407)) + exp(x0)) + x0)) - exp((2.577 - x1))) - x1) - x1))),saturated,1751.482167,27,7,27,7,3339,3383,813,2,72,(((0.429537 + (((-0.166241937 * (x0 ** 2.0)) + (0.235404407 * x0)) - (0.056002 * x1))) + (0.028001 * exp(x0))) - (0.368426127648911 * exp((-1.0 * x1)))) +kotanchek,163,SBP,SBP,14,1,kept,5.0,5.0,0.208799-0.009239*(((((-9.621000+x0)*(x1+x1))+exp(x1))-(((exp(x0)*(-4.627000+x0))+x0)-exp((-17.386000*x0))))),((0.009239*x0 - 0.018478*x1*(x0 - 9.621) + (0.009239*x0 - 0.042748853)*exp(x0) - 0.009239*exp(x1) + 0.208799)*exp(17.386*x0) - 0.009239)*exp(-17.386*x0),saturated,288.639958,28,5,28,5,156,167,67,1,61,(0.208799 - (0.009239 * ((((-9.621 + x0) * (x1 + x1)) + exp(x1)) - (((exp(x0) * (-4.627 + x0)) + x0) - exp((-17.386 * x0)))))),saturated,7749.798583,39,10,35,8,180,197,85,2,83,((((0.009239 * ((22.5997402316268 - ((2.0 * ((x0 - 9.621) * x1)) - x0)) - (exp(x1) - (exp(x0) * (x0 - 4.627))))) * exp((17.386 * x0))) - 0.009239) * exp((-17.386 * x0))) 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x1))),saturated,2199.791750,21,5,19,4,1003,1028,215,2,53,(((0.117570555858 + (0.039334 * (x1 + (x0 ** 3.0)))) + (-0.274865992 * (x0 ** 2.0))) + (0.411866314 * x0)) +kotanchek,175,SBP,SBP,26,1,kept,5.0,1.0,0.029215-0.000000*(((((((x1*x1)-x1)-14.532000)*4.291000)*(x1*exp(x0)))*exp((((x0+exp(4.291000))+x0)-exp(x0))))),0.0292150000000000,saturated,469.261167,29,5,1,1,3,4,3,2,6,0.029215,saturated,274.516167,1,1,1,1,3,4,3,1,6,0.029215 +kotanchek,177,SBP,SBP,28,1,kept,5.0,4.0,0.001695-0.003018*((3.647000*((((((-9.189000+(x1+x1))*x1)+x1)*x1)-4.450000)*exp(((x0+x0)-(x0*x0)))))),(x1**2*(0.090133424094 - 0.022013292*x1) + 0.001695*exp(x0*(x0 - 2)) + 0.0489795747)*exp(x0*(2 - x0)),saturated,387.976792,28,5,26,4,105,116,53,2,55,(0.001695 - (0.011006645999999998 * ((((((-9.189 + (x1 + x1)) * x1) + x1) * x1) - 4.45) * exp(((x0 + x0) - (x0 * x0)))))),saturated,368.494250,27,6,27,6,218,232,83,2,68,(((((x1 ** 2.0) * (0.022013292 * (4.0945 - x1))) + (0.001695 * exp((x0 * (x0 + -2.0))))) + 0.0489795747) * exp((x0 * (2.0 - x0)))) +kotanchek,174,SBP,SBP,25,1,kept,6.0,6.0,0.101111-0.009711*(((((x1-(x0-4.696000))*(((x0+x1)+(-2.186000-x1))*(x0*(4.648000-x0))))-(x1*3.723000))+x0)),0.009711*x0*(x0 - 4.648)*(x0 - 2.186)*(-x0 + x1 + 4.696) - 0.009711*x0 + 0.036154053*x1 + 0.101111,saturated,457.814958,29,6,29,6,261,277,91,2,68,(0.101111 - (0.009711 * (((((x1 - x0) - -4.696) * (((x0 + x1) + (-2.186 - x1)) * (x0 * (4.648 - x0)))) - (x1 * 3.723)) + x0))),saturated,2785.157375,29,8,25,6,119,127,45,2,62,(-0.009711 * (x0 + (((4.648 - x0) * ((((x1 - x0) + 4.696) * (x0 + -2.186)) * x0)) + (-3.7230000000000003 * (x1 + 2.796671233512879))))) +kotanchek,179,SBP,SBP,30,1,kept,5.0,2.0,0.045524+0.000000*(exp(((x0+x1)-(((-1.333000*x1)+(x1*x1))-(((17.339000+x0)+(2.682000*x1))-(x0*x0)))))),0.0455240000000000,saturated,318.017917,28,5,1,1,3,4,3,2,6,0.045524,saturated,260.932958,1,1,1,1,3,4,3,1,6,0.045524 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0.2581807926919453)*((x0 + 2*x1 + 0.22830720104631077)*exp(2.33304710784059*x1) + (0.2581807926919453*x1 - 0.2581807926919453*exp(x0) - 0.054439872343823197*exp(x1) - 0.4815994347419402)*exp(2.33304710784059*x1) + 1)*exp(-2.33304710784059*x1)/((-x0 + exp(0.90803626203097926*x0) + 0.4782812307154963)*(-x1 + exp(x0) + 0.21085949801377927*exp(x1) + 1.86535733243554)),saturated,337.962875,45,10,39,8,232,246,80,2,89,((((((x1 - (-0.22830720104631075 - x0)) + exp((x1 * -2.33304710784059))) + x1) / (((exp(x0) - -1.86535733243554) - x1) + exp((x1 - 1.5565632534973677)))) - 0.2581807926919453) * ((x0 + 0.2581807926919453) / ((exp((x0 / 1.1012776051072322)) + 0.4782812307154963) - x0))),saturated,3980.356833,69,17,54,12,213,229,92,2,126,((((x0 + 0.2581807926919453) * ((exp((2.33304710784059 * x1)) * (((0.2581807926919453 * ((x1 * 8.746509642126433) + ((-0.21085949801377926 * exp(x1)) - exp(x0)))) + x0) + -0.2532922336956295)) + 1.0)) * exp((-2.33304710784059 * x1))) / (((0.4782812307154963 - x0) + exp((0.9080362620309793 * x0))) * (((exp(x0) - x1) + (0.21085949801377926 * exp(x1))) + 1.86535733243554))) +kotanchek,178,SBP,SBP,29,1,kept,6.0,5.0,0.106297-0.005360*(((exp(x1)+(-20.176000*x1))+(exp(1.704000)-(x0*((-9.587000-x1)+exp((((x0-exp(x0))+4.797000)+x0))))))),-0.00536*x0*(x1 - 121.14643251667*exp(2*x0 - exp(x0)) + 9.587) + 0.10814336*x1 - 0.00536*exp(x1) + 0.0768390455121224,saturated,320.829959,29,6,26,5,103,113,51,2,58,(0.00536 * ((14.335642819425818 + (x0 * ((-9.587 - x1) + exp((((x0 - exp(x0)) + 4.797) + x0))))) - (exp(x1) + (-20.176 * x1)))),saturated,7295.353917,28,7,26,6,197,210,73,2,62,(((-0.00536 * (exp(x1) + (((x1 + (-121.14643251667 * exp(((2.0 * x0) - exp(x0))))) + 9.587) * x0))) + (0.10814336 * x1)) + 0.0768390455121224) +kotanchek,182,SRjl,SRjl,3,1,kept,9.0,6.0,(((((((x0 / exp((x0 * x0) + -0.12087468709548371)) * (x1 / 0.5947634776272314)) / ((exp(x1 - x0) - x1) + 2.2629335889059945)) * (x1 + (((exp((0.27943051594577284 + 0.10597416087671603) + 1.2206854231318682) + exp(x1)) + 2.523828871594013) * -0.0454913207896129))) - (x0 * 0.05041963936946082)) - -0.18147813675635233) + -0.01334030820098058),(-1.8973651416268622*x0*x1*(-x1 + 0.0454913207896129*exp(x1) + 0.34150870393486484) + (0.16813782855537175 - 0.05041963936946082*x0)*(-x1 + exp(-x0 + x1) + 2.2629335889059945)*exp(x0**2))*exp(-x0**2)/(-x1 + exp(-x0 + x1) + 2.2629335889059945),saturated,771.593417,45,11,34,7,262,273,88,2,78,(0.16813782855537174 + ((((((x1 + ((7.507117797574302 + exp(x1)) * -0.0454913207896129)) / ((exp((x1 - x0)) - x1) + 2.2629335889059945)) / exp(((x0 * x0) + -0.12087468709548371))) * x1) + -0.029987760052091382) * (x0 / 0.5947634776272314))),saturated,1728.171792,60,13,50,8,407,421,113,2,113,(((((-0.0863136463127769 * x0) * x1) * ((exp(x1) + (-21.982215126810114 * x1)) + 7.507117797574302)) + (((0.16813782855537174 + (-0.05041963936946082 * x0)) * ((exp((x1 - x0)) - x1) + 2.2629335889059945)) * exp((x0 ** 2.0)))) * (exp((-1.0 * (x0 ** 2.0))) / ((exp((x1 - x0)) - x1) + 2.2629335889059945))) +kotanchek,184,SRjl,SRjl,5,1,kept,9.0,7.0,((exp(((-1.5650412257786985 - x1) - x1) / 2.725807745015068) * ((x0 + 0.2515421021268282) * x1)) * (exp((((x0 / -0.6595888099113719) * x0) - (x1 / 0.8882302129082629)) / 2.725807745015068) * ((((x0 * (x1 - -0.9190110064157119)) * 0.22136372638482898) + (x1 + 1.3549310295276753)) * x1))),0.56317950580238818*x1**2*(x0 + 0.2515421021268282)*(0.22136372638482898*x0*(x1 + 0.9190110064157119) + x1 + 1.3549310295276753)*exp(-0.5562006597670384*x0**2 - 1.14675521804359*x1),saturated,356.240541,41,9,41,9,525,538,102,1,97,((exp((((-1.5650412257786985 - x1) - x1) / 2.725807745015068)) * ((x0 + 0.2515421021268282) * x1)) * (exp(((((x0 / -0.6595888099113719) * x0) - (x1 / 0.8882302129082629)) / 2.725807745015068)) * ((((x0 * (x1 - -0.9190110064157119)) * 0.22136372638482898) + (x1 + 1.3549310295276753)) * x1))),saturated,336.175250,32,7,32,7,318,331,85,2,84,((((0.5631795058023882 * (x1 ** 2.0)) * (x0 + 0.2515421021268282)) * ((((0.22136372638482898 * x0) * (x1 + 0.9190110064157119)) + x1) + 1.3549310295276753)) * exp((-0.5562006597670384 * ((x0 ** 2.0) + (2.061765296222234 * x1))))) +kotanchek,185,SRjl,SRjl,6,1,kept,8.0,7.0,((((x1 + (exp((x1 + (1.309561009058676 * 0.2713771555143059)) * (-1.598800435582104 * x1)) - 0.2946268534853358)) / ((((exp(x0) - x0) + 1.0705549811404007) - x0) - x0)) / (((exp(x1) - 0.6303983601001658) + 3.1507918286409375) - (x1 * x1))) * ((x1 / (1.309561009058676 + 0.06685590531260745)) - -0.48872997975581867)),(0.7265240564533295*x1 + 0.48872997975581867)*((x1 - 0.2946268534853358)*exp(1.598800435582104*x1*(x1 + 0.3553849416107877)) + 1)*exp(-1.598800435582104*x1*(x1 + 0.3553849416107877))/((-3*x0 + exp(x0) + 1.0705549811404007)*(-x1**2 + exp(x1) + 2.5203934685407717)),saturated,385.027375,44,10,38,7,271,281,88,2,84,((x1 + (exp(((x1 + 0.3553849416107877) * (-1.598800435582104 * x1))) + -0.2946268534853358)) * ((((x1 / 1.3764169143712834) + 0.48872997975581867) / ((((exp(x0) - x0) + 1.0705549811404007) - x0) - x0)) / ((2.520393468540772 + exp(x1)) - (x1 * x1)))),saturated,347.594250,49,12,47,11,326,341,97,2,117,(((((0.7265240564533295 * x1) + 0.48872997975581867) * (((x1 + -0.2946268534853358) * exp(((1.598800435582104 * x1) * (x1 + 0.3553849416107877)))) + 1.0)) * exp(((-1.598800435582104 * x1) * (x1 + 0.3553849416107877)))) / ((((-3.0 * x0) + exp(x0)) + 1.0705549811404007) * ((exp(x1) - (x1 ** 2.0)) + 2.520393468540772))) +kotanchek,183,SRjl,SRjl,4,1,kept,9.0,7.0,(((((x0 * x1) / 0.3268050163951488) + (((x1 + -0.5544986714499122) * x1) + 0.30370477454811745)) - ((((0.12540124052297874 - (exp(x1 + x0) * 0.003973572440442301)) / -0.7122963745947987) * x1) * (x1 + -0.7286282015526498))) / (((exp(x1) + 2.758453524484197) - -1.4870260456714612) + exp(x0 * x0))),(3.059928550150751*x0*x1 - x1*(x1 - 0.7286282015526498)*(0.005578538066689911*exp(x0 + x1) - 0.17605205500914596) + x1*(x1 - 0.5544986714499122) + 0.30370477454811745)/(exp(x0**2) + exp(x1) + 4.2454795701556582),saturated,2721.585417,42,9,34,7,206,219,79,2,78,(((x1 * ((0.0055785380666899115 * ((x1 + -0.7286282015526498) * (31.55881575145519 - exp((x1 + x0))))) + ((x1 + -0.5544986714499122) + (x0 / 0.3268050163951488)))) + 0.30370477454811745) / ((4.245479570155658 + exp(x1)) + exp((x0 * x0)))),saturated,466.199042,38,7,34,7,226,240,83,2,82,(((x1 * ((-0.005578538066689911 * ((x1 + -0.7286282015526498) * (exp((x0 + x1)) + -31.558815751455192))) + ((x1 + -0.5544986714499122) + (3.059928550150751 * x0)))) + 0.30370477454811745) / ((exp((x0 ** 2.0)) + exp(x1)) + 4.245479570155658)) +kotanchek,187,SRjl,SRjl,8,1,kept,7.0,6.0,(((exp(((x0 + x0) - (x0 * (x0 + 0.040585192647742296))) + -1.0149512623308583) / ((x1 * (exp(x1) * 0.040585192647742296)) + (3.8606907267233312 - x1))) * ((log(exp(x1) - x1) + (log(0.8419832071038463) * x1)) - -1.122619161739475)) * 0.6992234510287301),(-0.043585757930282754*x1 + 0.25341262808852694*log(-x1 + exp(x1)) + 0.28448587211893945)*exp(x0*(1.9594148073522577 - x0))/(0.040585192647742296*x1*exp(x1) - x1 + 3.8606907267233312),saturated,313.530917,38,7,37,7,146,155,58,2,82,((exp((((x0 + x0) - (x0 * (x0 + 0.040585192647742296))) + -1.0149512623308583)) * (((log((exp(x1) - x1)) + (-0.1719952089958853 * x1)) + 1.122619161739475) / ((x1 * (exp(x1) * 0.040585192647742296)) + (3.8606907267233312 - x1)))) * 0.6992234510287301),saturated,345.048709,33,7,31,6,234,246,79,2,69,(((((-0.043585757930282756 * x1) + (0.25341262808852694 * log((exp(x1) - x1)))) + 0.28448587211893944) * exp((x0 * (1.9594148073522577 - x0)))) / ((((0.040585192647742296 * x1) * exp(x1)) - x1) + 3.8606907267233312)) +kotanchek,176,SBP,SBP,27,1,kept,5.0,5.0,3.531127+0.009016*(((((((x0*x0)+20.982000)*(x0-18.033000))+((15.309000*x1)-exp(x1)))+(exp(x0)+exp(x0)))+x0)),0.009016*x0 + 0.138025944*x1 + 0.009016*(x0 - 18.033)*(x0**2 + 20.982) + 0.018032*exp(x0) - 0.009016*exp(x1) + 3.531127,saturated,345.603458,28,5,28,5,526,534,81,2,61,(3.531127 + (0.009016 * ((((((x0 * x0) + 20.982) * (x0 + -18.033)) + ((15.309 * x1) - exp(x1))) + (exp(x0) + exp(x0))) + x0))),saturated,13144.638666,31,8,27,6,414,433,117,2,68,(((-0.009016 * (((exp(x1) - x0) + (-15.309000000000001 * x1)) + ((-20.982 - (x0 ** 2.0)) * (x0 + -18.033)))) + (0.018032 * exp(x0))) + 3.531127) +kotanchek,186,SRjl,SRjl,7,1,kept,8.0,6.0,((((x1 / (exp(((x0 - 0.7606913305573865) * x0) + 1.5634875728815227) + exp(x1))) / 1.5634875728815227) * (((((exp(x1) * (x0 - -0.19417161363442786)) - x0) * -0.013296556398828556) - -0.3269889622210912) + 1.4134785703367858)) * (x1 + (x0 + ((x0 + -0.3269889622210912) * x1)))),0.63959574565533024*x1*(0.013296556398828556*x0 - (0.013296556398828556*x0 + 0.0025818138117417178)*exp(x1) + 1.740467532557877)*(x0 + x1*(x0 - 0.3269889622210912) + x1)/(exp(x1) + 4.7754469558976339*exp(x0*(x0 - 0.7606913305573865))),saturated,484.986000,40,8,36,6,263,271,65,2,77,(((x1 / (exp((((x0 + -0.7606913305573865) * x0) + 1.5634875728815227)) + exp(x1))) * ((-130.89611177155723 + ((exp(x1) * (x0 + 0.19417161363442786)) - x0)) * -0.008504420904556904)) * (x1 + (x0 + ((x0 + -0.3269889622210912) * x1)))),saturated,2416.618500,40,8,34,6,260,268,64,2,74,(((x1 * (0.6730110377789088 + x0)) + x0) * (x1 * ((0.0017808638611416302 / (exp((x0 * (x0 + -0.7606913305573865))) + (0.20940448281286198 * exp(x1)))) * ((x0 + ((-0.19417161363442784 - x0) * exp(x1))) + 130.8961117715572)))) +kotanchek,188,SRjl,SRjl,9,1,kept,8.0,7.0,(((((exp(x1 - ((x1 * 2.5453490974043493) + ((x0 * 0.5411409793785076) * x0))) * x1) * (x0 + 0.4339810714841567)) * (((((x0 + x1) / 0.9520033739001882) + exp((0.8325766331394892 / 0.6756390603608541) - (((x1 * 2.5453490974043493) * x1) * x1))) * x1) - -0.40562409423561496)) * x1) / 1.5660393014789127),0.63855357848020481*x1**2*(x0 + 0.4339810714841567)*(x1*(1.050416445377896*(x0 + x1)*exp(2.5453490974043493*x1**3) + 3.429039507965635) + 0.40562409423561496*exp(2.5453490974043493*x1**3))*exp(-0.5411409793785076*x0**2 - 2.5453490974043493*x1**3 - 1.5453490974043493*x1),saturated,525.806042,45,9,43,8,547,562,113,2,96,((((exp(((x1 - (x1 * 2.5453490974043493)) - ((x0 * 0.5411409793785076) * x0))) * x1) * (x0 + 0.4339810714841567)) * (((((x0 + x1) / 0.9520033739001882) + exp((2.5453490974043493 * (0.4841301322429487 - ((x1 * x1) * x1))))) * x1) - -0.40562409423561496)) * (x1 / 1.5660393014789127)),saturated,687.668500,52,10,50,9,509,532,154,2,130,((((0.2590127168919437 * (exp((2.5453490974043493 * (x1 ** 3.0))) + (2.589630301319675 * (x1 * ((exp((2.5453490974043493 * (x1 ** 3.0))) * (x0 + x1)) + 3.264457180820327))))) * (x1 ** 2.0)) * (x0 + 0.4339810714841567)) * exp((((-0.5411409793785076 * (x0 ** 2.0)) + (-2.5453490974043493 * (x1 ** 3.0))) + (-1.5453490974043493 * x1)))) +kotanchek,191,SRjl,SRjl,12,1,kept,9.0,8.0,(((((x1 - -0.8573197210520271) - (((((((x0 + 0.243655222569968) * ((x1 + -2.4978659229280784) - 0.6006378442243304)) - x0) * (x1 - -0.011366947974237162)) * x1) * 0.8729303966766084) - x0)) + (x0 * 0.32999628448933405)) / ((((exp(x0) * x0) * x0) * x0) - -11.469419384037693)) / 1.3572025597522632),(0.97995415270370898*x0 + 0.64318357669171258*x1*(x0 - (x0 + 0.243655222569968)*(x1 - 3.0985037671524088))*(x1 + 0.011366947974237162) + 0.73680969197592353*x1 + 0.63168147959322877)/(x0**3*exp(x0) + 11.469419384037693),saturated,409.313916,42,9,40,8,450,464,109,2,92,(((((x0 * 0.32999628448933405) + ((x1 + 0.8573197210520271) + (-0.8729303966766084 * (((((x0 + 0.243655222569968) * (-3.0985037671524087 + x1)) - x0) * (x1 + 0.011366947974237162)) * x1)))) + x0) / ((((exp(x0) * x0) * x0) * x0) + 11.469419384037693)) / 1.3572025597522632),saturated,1129.097125,36,8,34,8,249,267,101,2,87,((((x1 * ((((x1 + 0.011366947974237162) * (x0 - ((x0 + 0.243655222569968) * (x1 + -3.0985037671524087)))) * 0.6431835766917126) + 0.7368096919759235)) + (0.979954152703709 * x0)) + 0.6316814795932287) / (((x0 ** 3.0) * exp(x0)) + 11.469419384037693)) +kotanchek,190,SRjl,SRjl,11,1,kept,5.0,3.0,(exp(((x0 + -0.21546645087388747) - (x0 * x0)) - (x1 - x0)) * (((x1 + (((exp(((x1 - (x1 * x1)) + (x1 + 0.7393127343318426)) * x1) + (x1 * x1)) - x1) * -0.07637600437144379)) * 0.7393127343318426) * (x1 + (x1 * 0.05221153846822916)))),-0.84825644735156917*x1*(0.05646575262919287*x1**2 - 0.7957784869610355*x1 + 0.05646575262919287*exp(x1*(-x1**2 + 2*x1 + 0.7393127343318426)))*exp(-x0**2 + 2*x0 - x1),saturated,288.462209,43,5,43,5,137,143,49,1,84,(exp((((x0 + -0.21546645087388747) - (x0 * x0)) - (x1 - x0))) * (((x1 + (((exp((((x1 - (x1 * x1)) + (x1 + 0.7393127343318426)) * x1)) + (x1 * x1)) - x1) * -0.07637600437144379)) * 0.7393127343318426) * (x1 + (x1 * 0.05221153846822916)))),saturated,1981.762250,43,9,35,5,123,129,44,2,84,(((-0.04789743872227167 * x1) * (exp((x1 * (((2.0 * x1) - (x1 ** 2.0)) + 0.7393127343318426))) + ((x1 ** 2.0) + (-14.093117507648643 * x1)))) * exp((((2.0 * x0) - (x0 ** 2.0)) - x1))) +kotanchek,193,SRjl,SRjl,14,1,kept,7.0,5.0,(exp((-0.7318040896636137 - (x0 * x0)) + ((x0 + x0) - x1)) * ((((x1 - -0.039858290344846364) / 0.9598793817164541) * x1) - (exp((0.13235515895495698 - x0) + (((x0 + 0.09098361423696229) - x1) * x1)) * ((x1 * (x1 / 0.9039712460608937)) - (0.16031841194029647 / 0.9446831697758643))))),0.4810403668350914*(x1*(1.041797562326844*x1 + 0.041524269719776521) + (0.1937217302155371 - 1.2627765219929556*x1**2)*exp(-x0 + x1*(x0 - x1 + 0.09098361423696229)))*exp(-x0**2 + 2*x0 - x1),saturated,312.350833,43,8,41,7,104,114,56,2,89,(exp(((-0.7318040896636137 - (x0 * x0)) + ((x0 + x0) - x1))) * ((((x1 + 0.039858290344846364) / 0.9598793817164541) * x1) - (exp(((0.13235515895495698 - x0) + (((x0 + 0.09098361423696229) - x1) * x1))) * ((x1 * (x1 / 0.9039712460608937)) + -0.1697060105117927)))),saturated,446.280791,43,9,37,6,91,99,46,2,87,((0.5011466815496091 * ((x1 * (x1 + 0.03985829034484636)) + (1.2121131471766524 * (exp(((x1 * ((x0 - x1) + 0.09098361423696229)) - x0)) * (0.15340935378636836 - (x1 ** 2.0)))))) * exp((((2.0 * x0) - (x0 ** 2.0)) - x1))) +kotanchek,194,SRjl,SRjl,15,1,kept,8.0,5.0,((((exp((((x1 * x1) + (x0 * x0)) + x0) * -0.17830776423842798) / 1.4092295785725586) * x1) / ((((exp(x0) - x0) - x0) / 0.34806215833743864) + 1.7208022848793882)) * ((((x0 - -0.17948040180341088) - -0.42075853691198073) + (((x0 + -0.1759177414425294) * x0) - -0.3726818556226753)) * x1)),x1**2*(0.70960758644657689*x0*(x0 - 0.1759177414425294) + 0.70960758644657689*x0 + 0.69039197667392207)*exp(-0.17830776423842798*x0**2 - 0.17830776423842798*x0 - 0.17830776423842798*x1**2)/(-5.7461000918722219*x0 + 2.8730500459361109*exp(x0) + 1.7208022848793882),saturated,496.140292,43,8,39,6,487,496,89,2,82,(((exp(((((x1 * x1) + (x0 * x0)) + x0) * -0.17830776423842798)) * (x1 / 1.4092295785725586)) / ((((exp(x0) - x0) - x0) / 0.34806215833743864) + 1.7208022848793882)) * (((0.9729207943380669 + x0) + ((x0 + -0.1759177414425294) * x0)) * x1)),saturated,1625.711083,45,10,35,6,280,290,73,2,88,((((-0.12349377405560806 * ((x0 * (0.8240822585574706 + x0)) + 0.972920794338067)) * (x1 ** 2.0)) * exp((-0.17830776423842798 * (((x0 ** 2.0) + x0) + (x1 ** 2.0))))) / ((x0 + (-0.5 * exp(x0))) + -0.2994730786735579)) +kotanchek,195,SRjl,SRjl,16,1,kept,5.0,4.0,(((x1 + (0.6193677368705359 * x0)) / ((exp(x0 * x0) - x1) + (exp(x1) + 2.853886507925958))) * ((x1 * (((x1 + ((0.05317370141890812 / 1.1778919118254807) - 0.2923135815181234)) / (((exp(x1) + 1.6282363698705866) - (x0 + x1)) + exp(0.5154765131661209))) * (x1 + x1))) + x0)),(0.6193677368705359*x0 + x1)*(x0*(x0 + x1 - exp(x1) - 3.3026725724919279) + x1**2*(0.4943409476627152 - 2*x1))/((x0 + x1 - exp(x1) - 3.3026725724919279)*(-x1 + exp(x0**2) + exp(x1) + 2.853886507925958)),saturated,297.148875,45,7,40,5,142,149,54,2,79,(((x1 + (0.6193677368705359 * x0)) / ((exp((x0 * x0)) - x1) + (exp(x1) + 2.853886507925958))) * ((x1 * (((x1 + -0.24717047383135762) / (((exp(x1) + 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* (((x1 + ((-0.05289584830175453 + (x0 * x1)) + (log((x0 - -0.7116175810554622)) * 0.40296766612240004))) + x0) + ((exp((x1 + x0)) + (x1 * x1)) * -0.029820142635731767))) - -0.011424247853121624),saturated,53229.378042,55,9,51,7,846,860,149,2,114,((((0.011424247853121624 * (exp((x0 ** 2.0)) + exp(x1))) + (x1 * (((((-0.029820142635731767 * (exp((x0 + x1)) + (x1 ** 2.0))) + ((x0 * x1) + x0)) + x1) + (0.40296766612240004 * log((x0 + 0.7116175810554622)))) + -0.05289584830175455))) + 0.04003901096107706) / ((exp((x0 ** 2.0)) + exp(x1)) + 3.5047393470316366)) diff --git a/python/egglog/exp/param_eq/artifacts/haskell_live_rows.csv b/python/egglog/exp/param_eq/artifacts/haskell_live_rows.csv new file mode 100644 index 00000000..0f015f3b --- /dev/null +++ b/python/egglog/exp/param_eq/artifacts/haskell_live_rows.csv @@ -0,0 +1,342 @@ 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25.21*exp(0.3431*plog(0.1054*x1)) + 1170.44*exp(0.9429*plog(0.1054*x1)) - 318.39*exp(0.7986*plog(0.3056*x1)) + 5.1*exp(0.9189*plog(0.1912*plog(0.354*plog(0.452*x0)))) - 5.01*exp(0.7665*exp(0.983*plog(0.4818*x0))) + 175.077,62,194.0,55.0,162.0,41.0,162.0,42.0,153.0,40.0,55.0,28.0 +pagie,63,FEAT,FEAT,4,0,drop_feat,-1220.65+1839.35*exp(0.9414*plog(0.0776*x1))-1445.64*plog(0.1027*plog(0.0459*x1))+1062.76*plog(0.1183*plog(0.1671*(0.1862*x1*x1)))+264.74*plog(0.6611*plog(0.1671*(0.3881*x0-0.6949*x0)))+181.90*exp(0.3441*plog(0.9860*x0))+136.25*(0.1917*plog(0.8057*x1)*(0.6542*x1*x1))+22.38*plog(0.4034*(0.4107*x1/0.3788*x0))+13.55*(0.1372*x0*x0)+9.99*exp(0.9617*plog(0.1006*plog(0.1671*plog(0.1121*(0.4346*x0*x0)))))+0.18*(0.3234*plog(0.8057*x1)*x1),1.85906*x0**2 + 17.087131575*x1**2*plog(0.8057*x1) + 0.058212*x1*plog(0.8057*x1) + 22.38*plog(0.437371647307286*x0*x1) + 264.74*plog(0.6611*plog(-0.05126628*x0)) - 1445.64*plog(0.1027*plog(0.0459*x1)) + 1062.76*plog(0.1183*plog(0.03111402*x1**2)) + 181.9*exp(0.3441*plog(0.986*x0)) + 1839.35*exp(0.9414*plog(0.0776*x1)) + 9.99*exp(0.9617*plog(0.1006*plog(0.1671*plog(0.04871866*x0**2)))) - 1220.65,63,142.0,38.0,112.0,27.0,122.0,29.0,110.0,27.0,38.0,21.0 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0.04*plog(0.05814242*x1 - 0.20140813*exp(0.0971*plog(0.34089419*x1 - 0.059344*plog(0.254*exp(0.03565512*x0**2))))) + 4.79*plog(0.6811*plog(0.4666*x1)) + 0.0507295936*plog(0.4443*plog(0.34089419*x1 - 0.059344*plog(0.254*x1))) + 0.157136*plog(0.4859*plog(0.344*plog(0.4666*plog(0.254*plog(0.34089419*x1 - 0.059344*plog(0.254*x1)))))) + 1.21*exp(0.11045081*plog(0.4666*x0) + 0.45619192*plog(0.0975*plog(0.9314*plog(0.4666*plog(0.254*x0))))) - 4.77*exp(0.8765*plog(0.0975*plog(0.3709*plog(0.1125*x0)))) + 0.94*exp(0.8767*plog(0.6486*plog(0.3955*plog(0.4666*x0)))) + 0.27*exp(0.7277*plog(0.344*plog(0.4666*plog(0.254*plog(0.4666*plog(0.254*x1)))))) - 24.8439,64,269.0,75.0,231.0,56.0,227.0,56.0,217.0,55.0,75.0,43.0 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391.41*exp(0.7611*plog(0.3476856*x1**2)) - 2.0*exp(0.0974*exp(0.0724582374677117*x0**2*plog(0.5886*x0))) + 12.18*exp(0.0974*exp(0.0724582374677117*x0**2*plog(0.5775*plog(0.226852100840336*x0**2)))) - 264.266,65,191.0,52.0,163.0,38.0,163.0,38.0,157.0,38.0,52.0,32.0 +pagie,66,FEAT,FEAT,7,0,drop_feat,4742.22-628.68*(0.1914*x0/0.0243*(0.9427*(0.2095*x1*(0.0571*x0*x1))-0.0667*x0))-80.65*exp(0.7243*exp(0.6896*plog(0.5464*x1)))-52.70*exp(0.9915*plog(0.9947*(0.0970*x0*plog(0.3820*plog(0.1819*x0)))))+37.38*exp(0.6167*plog(0.5464*x1))+32.88*exp(0.9167*plog(0.6156*x1))+12.12*(0.1917*x0*x0)+1.73*exp(0.6896*plog(0.4049*(0.9427*(0.2095*x1*(0.0571*x0*x1))-0.0667*x0)))-1.29*exp(0.9016*plog(0.3234*plog(0.3820*plog(0.3602*exp(0.9016*plog(0.3421*plog(0.3820*plog(0.3602*x1))))))))+0.05*plog(0.2122*plog(0.3820*plog(0.1819*x0)))+0.05*plog(0.0367*(0.5423*x1+0.1700*(0.0291*x1-0.0010*plog(0.1845*x1)))),2.323404*x0**2 - 4951.82518518518*x0*(0.011277001615*x0*x1**2 - 0.0667*x0) + 0.05*plog(0.0200839649*x1 - 6.239e-6*plog(0.1845*x1)) + 0.05*plog(0.2122*plog(0.382*plog(0.1819*x0))) + 37.38*exp(0.6167*plog(0.5464*x1)) + 32.88*exp(0.9167*plog(0.6156*x1)) - 52.7*exp(0.9915*plog(0.0964859*x0*plog(0.382*plog(0.1819*x0)))) + 1.73*exp(0.6896*plog(0.0045660579539135*x0*x1**2 - 0.02700683*x0)) - 1.29*exp(0.9016*plog(0.3234*plog(0.382*plog(0.3602*exp(0.9016*plog(0.3421*plog(0.382*plog(0.3602*x1)))))))) - 80.65*exp(0.7243*exp(0.6896*plog(0.5464*x1))) + 4742.22,66,191.0,53.0,157.0,39.0,165.0,41.0,154.0,39.0,53.0,29.0 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7.01608925869894*plog(0.1171*x1)*plog(0.2855*x1) + 0.02*plog(0.1306*plog(0.1306*plog(0.012686696455432*x0**2 + 7.904812e-5*x1*plog(0.6882*x1) + 4.0757210672e-5*x1*plog(0.6882*plog(0.4103*plog(0.4103*x1)))))) - 9.45*plog(0.6882*plog(0.4103*plog(0.3573*plog(0.2855*x1)))) + 9.41*plog(0.1306*plog(0.3205*plog(0.4103*plog(0.4103*x1)))) + 45.59*exp(0.6096*plog(0.2652396*x0**2)) + 1.1*exp(0.8248*plog(0.9288*plog(0.3203*plog(0.1858*x0)))) - 1052.19*exp(0.6096*exp(0.8056*plog(0.02766562*x0**2))) + 1057.91,67,241.0,65.0,203.0,47.0,205.0,47.0,191.0,46.0,65.0,38.0 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0.023235*plog(0.7374*plog(0.9899*x1)) - 0.21*plog(0.4541*plog(0.4727*plog(0.3112*plog(0.176*x0)))) + 0.59*exp(0.4658*plog(0.907017*x1 - 0.0206498*plog(0.4086*plog(0.3995*x1)))) - 1.46*exp(0.4754*plog(0.0591*plog(0.4086*plog(0.176*x0)))) - 51.3734,68,202.0,56.0,174.0,42.0,176.0,43.0,168.0,42.0,56.0,32.0 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0.23*plog(0.4921*plog(0.7543*plog(0.4908*x0))) + 0.04*plog(0.6516*plog(0.6808*plog(0.9998*x0))) - 1.8*plog(0.0101*plog(0.4908*exp(0.9368*plog(0.5124*plog(0.7543*plog(0.4908*x0)))))) - 26.34*exp(0.1466*plog(0.2826594*x0)) - 3.95*exp(0.7529*plog(0.4921*plog(0.7543*plog(0.4908*x0)))) + 0.88*exp(0.3047*plog(0.4921*plog(0.4921*plog(1.96631434440154*x1**2*plog(0.1023*x1))))) + 8.36124,69,223.0,61.0,183.0,45.0,187.0,47.0,181.0,45.0,61.0,33.0 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+ 1.495433004*x1**2*plog(0.4262*x1) + 0.005232924*plog(0.0218988126*x0*(13.0532155844156*x0 + 11.3002805194805*plog(0.8893*x0)) + 0.018939*x0 + 0.01844864575*plog(0.0527*plog(0.1544*x1))) + 0.044412*plog(0.0218988126*x0*(22.6460237174026*x0 + 8.30457615376623*plog(0.8893*x0)) + 0.018939*x0 + 0.01844864575*plog(0.0527*plog(0.1544*plog(0.4262*x1)))) - 2.5*plog(0.2372*plog(0.408*x0)) - 0.16*plog(0.1544*plog(-0.0280305538844444*x0**2 + 0.22415776*x1)) + 0.0011022276*plog(0.535*plog(0.6112*plog(0.8893*x0))) - 11.12*exp(0.0701*plog(0.0527*x0)) + 27.12*exp(0.555*plog(0.012552003584*x1**2*plog(0.4537*x1))) - 1.7*exp(0.555*plog(0.00150281812630282*x1**2*plog(0.4262*x1) + 0.015560158712*x1 + 0.00804424*plog(0.535*plog(0.6112*exp(0.555*plog(0.1544*x1)))))) - 0.22*exp(0.6215*plog(0.309560193316789*x0**2 + 0.017410875456*x0 + 0.016960086249808*x1 + 0.14375424*plog(0.8893*plog(0.021591452896*x0 + 0.017410875456*x1 + 0.14375424*plog(0.8893*x0))))) + 2.5*exp(0.7355*plog(0.2621*plog(0.4993*plog(0.0527*plog(0.3923*x1))))) + 1063.93,70,357.0,103.0,275.0,67.0,285.0,70.0,267.0,66.0,103.0,52.0 +pagie,71,FEAT,FEAT,12,0,drop_feat,-2.85886-7468.42*exp(0.7553*plog(0.3431*(0.0008*x0*x0)))+103.55*plog(0.3330*plog(0.3055*x1))-101.48*plog(0.3330*plog(0.3772*x1))+43.26*exp(0.9163*plog(0.3431*x0))+15.33*(0.3387*x0*x0)+11.88*(0.5357*exp(0.4973*plog(0.3474*x0))-0.8771*(0.3320*plog(0.3772*x1)/0.7932*(0.1596*x1/0.0400*x1)))-3.82*(0.7560*x1*x1)-0.28*plog(0.3223*plog(0.3223*plog(0.3862*plog(0.3474*x1))))+0.07*plog(0.3223*plog(0.3862*plog(0.3330*x0)))-0.05*plog(0.7633*(0.1692*x1-0.6511*plog(0.5213*x1))),5.192271*x0**2 - 17.4017860774584*x1**2*plog(0.3772*x1) - 2.88792*x1**2 - 0.05*plog(0.12915036*x1 - 0.49698463*plog(0.5213*x1)) + 103.55*plog(0.333*plog(0.3055*x1)) - 101.48*plog(0.333*plog(0.3772*x1)) + 0.07*plog(0.3223*plog(0.3862*plog(0.333*x0))) - 0.28*plog(0.3223*plog(0.3223*plog(0.3862*plog(0.3474*x1)))) + 43.26*exp(0.9163*plog(0.3431*x0)) + 6.364116*exp(0.4973*plog(0.3474*x0)) - 7468.42*exp(0.7553*plog(0.00027448*x0**2)) - 2.85886,71,154.0,42.0,136.0,33.0,136.0,33.0,132.0,33.0,42.0,24.0 +pagie,72,FEAT,FEAT,13,0,drop_feat,21233.7-23766.51*exp(0.0604*exp(0.0604*(0.3917*x1*x1)))+2094.16*exp(0.0947*plog(0.9472*x0))+1151.92*exp(0.5012*exp(0.9637*plog(0.4671*x1)))+1127.05*exp(0.5336*plog(0.6225*exp(0.7956*plog(0.0557*x0))))+993.75*plog(0.6533*plog(0.1215*x0))+856.32*exp(0.7220*plog(0.1215*x0))-778.14*exp(0.9637*plog(0.3413*x1))+153.91*(0.0985*x0*x0)+1.70*exp(0.4867*plog(0.0241*plog(0.4671*plog(0.5677*x1))))+0.04*plog(0.4833*plog(0.9108*exp(0.3821*x1))),15.160135*x0**2 + 993.75*plog(0.6533*plog(0.1215*x0)) + 0.04*plog(0.4833*plog(0.9108*exp(0.3821*x1))) + 856.32*exp(0.722*plog(0.1215*x0)) + 2094.16*exp(0.0947*plog(0.9472*x0)) - 778.14*exp(0.9637*plog(0.3413*x1)) + 1.7*exp(0.4867*plog(0.0241*plog(0.4671*plog(0.5677*x1)))) + 1127.05*exp(0.5336*plog(0.6225*exp(0.7956*plog(0.0557*x0)))) - 23766.51*exp(0.0604*exp(0.02365868*x1**2)) + 1151.92*exp(0.5012*exp(0.9637*plog(0.4671*x1))) + 21233.7,72,134.0,37.0,130.0,35.0,130.0,35.0,128.0,35.0,37.0,24.0 +pagie,73,FEAT,FEAT,14,0,drop_feat,68.3233-66.30*(0.0583*exp(0.8911*plog(0.6911*x0))*plog(0.5829*x0))+49.32*(0.3347*x1*(0.1994*x1*plog(0.7962*x1)))+31.42*exp(0.8849*plog(0.1209*x1))-28.94*exp(0.8849*exp(0.8849*(0.0574*x1*x1)))+20.46*(0.0583*exp(0.8911*plog(0.6911*x0))*plog(0.6911*x0))+2.91*exp(0.9651*plog(0.2782*plog(0.4340*plog(0.4521*x0))))+2.33*exp(0.8242*plog(0.2782*plog(0.4108*plog(0.4521*x1))))-0.09*plog(0.2078*plog(0.1484*plog(0.9824*x0)))+0.04*plog(0.7508*(0.9933*exp(0.9765*exp(0.2743*x1))-0.1006*x1))-0.02*plog(0.6911*(0.7367*plog(0.9824*plog(0.7595*x0))*(0.0736*x0+0.2684*plog(0.6911*x0)))),3.2915763576*x1**2*plog(0.7962*x1) - 3.86529*plog(0.5829*x0)*exp(0.8911*plog(0.6911*x0)) + 1.192818*plog(0.6911*x0)*exp(0.8911*plog(0.6911*x0)) - 0.02*plog(0.50913337*(0.0736*x0 + 0.2684*plog(0.6911*x0))*plog(0.9824*plog(0.7595*x0))) + 0.04*plog(-0.07553048*x1 + 0.74576964*exp(0.9765*exp(0.2743*x1))) - 0.09*plog(0.2078*plog(0.1484*plog(0.9824*x0))) + 31.42*exp(0.8849*plog(0.1209*x1)) + 2.91*exp(0.9651*plog(0.2782*plog(0.434*plog(0.4521*x0)))) + 2.33*exp(0.8242*plog(0.2782*plog(0.4108*plog(0.4521*x1)))) - 28.94*exp(0.8849*exp(0.05079326*x1**2)) + 68.3233,73,184.0,50.0,159.0,40.0,172.0,44.0,166.0,42.0,50.0,31.0 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+ 0.00466813256139638*x1*exp(0.0986219*x0*x1) - 1.55375949395341*x1 - 0.035423104*plog(0.2667*x0)*plog(0.3074*x0) + 0.1137513468*plog(0.2667*x0) - 1.944821529*plog(0.2887*x0) - 15.53*plog(0.4241*x0) + 0.00282158894437805*plog(0.4382*x0) - 0.1684367048*plog(0.7097*x0) - 0.07809097752576*plog(0.7628*x1) + 0.0432188676*plog(0.7716*x1) - 14.5*plog(0.328998461907582*x0*x1) - 14.43*plog(0.334502975653742*x1*plog(0.2578*x0)) - 5.94*plog(1.6368961935502*x0*plog(0.08628174*x1)*plog(0.3942*x1)) - 1.12885265785632*plog(0.17277756*x1 + 0.17576804*exp(0.7037*x1)) + 0.3221655471*plog(0.17277756*plog(0.7673*x0) + 0.17576804*exp(0.18417911819618*x0**2)) + 0.0210329144754562*plog(0.17277756*plog(0.7673*x1) + 0.17576804*exp(0.1418*x1)) + 0.2427914268*plog(0.17277756*plog(0.7673*x1) + 0.17576804*exp(0.0035712516767616*x1**2 + 0.100375410144*x1)) + 1.250742801*exp(0.2963*x1) - 0.54*exp(0.3174*plog(0.17277756*plog(0.6891*x0) + 0.17576804*exp(0.0119853*x1))) + 0.45*exp(0.3174*plog(0.512594884984*x1 + 0.267524484624*plog(0.7673*x1) + 0.272154869616*exp(0.7281*x1))) - 35.8536,74,416.0,124.0,281.0,69.0,273.0,67.0,266.0,66.0,124.0,42.0 +pagie,75,FEAT,FEAT,16,0,drop_feat,-3974.01+4116.06*exp(0.0327*plog(0.0142*exp(0.8261*plog(0.4494*x1))))+377.50*plog(0.8694*plog(0.0656*x0))+335.35*exp(0.3851*plog(0.4763*x0))+124.08*exp(0.9256*plog(0.4494*x1))+112.06*plog(0.5961*(0.1310*plog(0.2073*x1)-0.2361*(0.3511*x1*x1)))-66.11*plog(0.6807*x1)-43.93*(0.3511*x1*x1)-43.02*(0.4579*plog(0.6240*x0)-0.8180*(0.3511*x1*x1))+14.35*(0.2213*x0*x0)+0.20*(0.3217*plog(0.7458*x1)*x1),3.175655*x0**2 - 3.068487604*x1**2 + 0.06434*x1*plog(0.7458*x1) - 19.698858*plog(0.624*x0) - 66.11*plog(0.6807*x1) + 112.06*plog(-0.049413536631*x1**2 + 0.0780891*plog(0.2073*x1)) + 377.5*plog(0.8694*plog(0.0656*x0)) + 335.35*exp(0.3851*plog(0.4763*x0)) + 124.08*exp(0.9256*plog(0.4494*x1)) + 4116.06*exp(0.0327*plog(0.0142*exp(0.8261*plog(0.4494*x1)))) - 3974.01,75,129.0,35.0,113.0,28.0,111.0,28.0,106.0,27.0,35.0,18.0 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6983.73*exp(-0.043614601318*x1**2),76,174.0,50.0,114.0,28.0,118.0,30.0,101.0,26.0,50.0,22.0 +pagie,77,FEAT,FEAT,18,0,drop_feat,1615.33-9124.00*exp(0.8594*plog(0.1584*(0.0229*x0*x0)))-2443.32*exp(0.8594*(0.0229*x0*x0))+865.33*exp(0.8594*exp(0.4389*plog(0.1255*x0)))-343.74*exp(0.4389*plog(0.9786*x0))+133.05*(0.6983*x0*x0)+116.84*exp(0.4389*plog(0.1656*x1))+82.14*plog(0.2153*plog(0.1656*x1))+36.77*(0.0490*plog(0.4031*plog(0.3247*x1))-0.4792*plog(0.4947*x0))+6.64*plog(0.1883*x1)-0.23*(0.0146*(0.3111*exp(0.7003*x1)*plog(0.8099*plog(0.3911*plog(0.3247*x1))))-0.7943*(0.0532*plog(0.4068*plog(0.3911*plog(0.3911*x1)))-0.8992*x0)),92.908815*x0**2 - 0.1642739488*x0 - 17.620184*plog(0.4947*x0) + 6.64*plog(0.1883*x1) + 82.14*plog(0.2153*plog(0.1656*x1)) + 1.80173*plog(0.4031*plog(0.3247*x1)) - 0.0010446738*plog(0.8099*plog(0.3911*plog(0.3247*x1)))*exp(0.7003*x1) + 0.0097190548*plog(0.4068*plog(0.3911*plog(0.3911*x1))) - 2443.32*exp(0.01968026*x0**2) - 343.74*exp(0.4389*plog(0.9786*x0)) - 9124.0*exp(0.8594*plog(0.00362736*x0**2)) + 116.84*exp(0.4389*plog(0.1656*x1)) + 865.33*exp(0.8594*exp(0.4389*plog(0.1255*x0))) + 1615.33,77,160.0,44.0,146.0,37.0,146.0,37.0,143.0,37.0,44.0,27.0 +pagie,78,FEAT,FEAT,19,0,drop_feat,3.46966-47.82*exp(0.8998*plog(0.5877*(0.1773*(0.0255*x1/0.7944*x1)-0.2609*(0.1967*x1*x1))))+10.31*(0.1041*x1*x1)+0.69*plog(0.4807*(0.1773*(0.0255*x1/0.7944*(0.1448*x1-0.3499*x1))-0.2609*(0.1967*x1*x1)))-0.37*plog(0.4807*(0.2247*(0.1773*(0.0255*x1/0.7944*x1)-0.2609*(0.1967*x1*x1))-0.0950*(0.1967*x1*x1)))-0.07*(0.2055*x0*x0)-0.05*plog(0.9959*(0.5141*plog(0.5877*x1)-0.1025*x1))+0.03*plog(0.4807*(0.1773*(0.0255*x1/0.7944*x1)-0.2609*(0.1967*x1*x1)))-0.01*plog(0.2938*(0.0830*x0/0.1487*exp(0.9262*plog(0.2938*(0.0830*x0/0.1487*exp(0.9262*(0.7115*(0.2055*x0*x0)/0.6674*(0.3059*x1/0.2886*x1))))))))-0.00*exp(0.9262*(0.5502*(0.1430*x0*x0)/0.5718*(0.7457*x1/0.2853*x1)))-0.00*exp(0.4454*(0.7115*(0.2055*x0*x0)/0.6674*(0.3059*x1/0.2886*x1))),-0.014385*x0**2 + 1.073271*x1**2 + 0.69*plog(-0.0252301696000351*x1**2) + 0.03*plog(-0.0219332611386737*x1**2) - 0.37*plog(-0.01391100432786*x1**2) - 0.01*plog(0.163990585070612*x0*exp(0.9262*plog(0.163990585070612*x0*exp(0.215074268858751*x0**2*x1**2)))) - 0.05*plog(-0.10207975*x1 + 0.51199219*plog(0.5877*x1)) - 47.82*exp(0.8998*plog(-0.0268154307701239*x1**2)) + 3.46966,78,196.0,58.0,104.0,23.0,112.0,27.0,92.0,21.0,72.0,1.0 +pagie,79,FEAT,FEAT,20,0,drop_feat,6046.96-6026.31*exp(0.0911*(0.3811*x0*x0))-1989.80*exp(0.5219*plog(0.4331*x0))-1811.31*exp(0.9277*plog(0.5787*(0.2426*x0*x0)))+1715.78*(0.2426*x0*x0)+1543.95*exp(0.5990*plog(0.3652*x0))-442.16*plog(0.2571*plog(0.2891*x0))-175.23*(0.6701*plog(0.2683*(0.6701*plog(0.1056*x1)-0.2963*(0.1195*x1*x1)))-0.2963*(0.0958*x1*x1))+64.34*exp(0.5687*plog(0.3652*x1))+57.33*(0.7110*plog(0.5907*x0)-0.8188*exp(0.9277*(0.0958*x1*x1)))-20.53*(0.6701*plog(0.6701*x1)-0.2963*(0.0958*x1*x1)),416.248228*x0**2 + 5.5567533104*x1**2 + 40.76163*plog(0.5907*x0) - 13.757153*plog(0.6701*x1) - 117.421623*plog(-0.009499926155*x1**2 + 0.17978783*plog(0.1056*x1)) - 442.16*plog(0.2571*plog(0.2891*x0)) - 6026.31*exp(0.03471821*x0**2) - 46.941804*exp(0.08887366*x1**2) + 1543.95*exp(0.599*plog(0.3652*x0)) - 1989.8*exp(0.5219*plog(0.4331*x0)) - 1811.31*exp(0.9277*plog(0.14039262*x0**2)) + 64.34*exp(0.5687*plog(0.3652*x1)) + 6046.96,79,151.0,42.0,129.0,31.0,125.0,31.0,117.0,30.0,42.0,22.0 +pagie,80,FEAT,FEAT,21,0,drop_feat,180.72-30733.13*(0.0010*x1*x1)-568.59*exp(0.6467*exp(0.6467*plog(0.9309*x0)))+499.97*exp(0.8051*plog(0.7056*x0))+443.77*exp(0.7036*plog(0.0578*x1))+420.16*exp(0.3511*(0.2990*x1*x1))+160.67*(0.0514*plog(0.2732*x1)/0.3997*(0.5357*x0/0.0788*x0))+86.67*exp(0.3573*plog(0.4720*x0))+50.93*(0.9163*x0*x0)+3.38*plog(0.8627*exp(0.7036*plog(0.2913*x1)))+0.05*plog(0.9821*plog(0.9707*exp(0.1243*x1))),140.462111704337*x0**2*plog(0.2732*x1) + 46.667159*x0**2 - 30.73313*x1**2 + 0.05*plog(0.9821*plog(0.9707*exp(0.1243*x1))) + 3.38*plog(0.8627*exp(0.7036*plog(0.2913*x1))) + 420.16*exp(0.1049789*x1**2) + 86.67*exp(0.3573*plog(0.472*x0)) + 499.97*exp(0.8051*plog(0.7056*x0)) + 443.77*exp(0.7036*plog(0.0578*x1)) - 568.59*exp(0.6467*exp(0.6467*plog(0.9309*x0))) + 180.72,80,125.0,35.0,107.0,28.0,111.0,28.0,104.0,28.0,35.0,18.0 +pagie,81,FEAT,FEAT,22,0,drop_feat,105.342-531.05*exp(0.1489*plog(0.1059*x0))-308.80*exp(0.9980*plog(0.1059*x0))-197.29*plog(0.0947*plog(0.1095*x0))-79.08*exp(0.4794*plog(0.1023*x1))+48.59*exp(0.6828*plog(0.9104*x1))+44.13*(0.8226*exp(0.8717*plog(0.9104*x1))-0.5269*(0.0851*x0/0.9976*x0))-5.91*exp(0.9865*plog(0.1023*(0.2048*plog(0.9104*x1)-0.6681*plog(0.0941*exp(0.5523*x1)))))+0.75*exp(0.7792*plog(0.5661*plog(0.4135*plog(0.4173*x1))))-0.72*(0.1008*exp(0.6841*plog(0.9104*plog(0.5661*plog(0.4290*plog(0.4240*x0)))))+0.2293*x1)-0.29*plog(0.4135*plog(0.4272*x1)),-1.98351388803128*x0**2 - 0.165096*x1 - 197.29*plog(0.0947*plog(0.1095*x0)) - 0.29*plog(0.4135*plog(0.4272*x1)) - 531.05*exp(0.1489*plog(0.1059*x0)) - 308.8*exp(0.998*plog(0.1059*x0)) - 79.08*exp(0.4794*plog(0.1023*x1)) + 48.59*exp(0.6828*plog(0.9104*x1)) + 36.301338*exp(0.8717*plog(0.9104*x1)) - 5.91*exp(0.9865*plog(0.02095104*plog(0.9104*x1) - 0.06834663*plog(0.0941*exp(0.5523*x1)))) + 0.75*exp(0.7792*plog(0.5661*plog(0.4135*plog(0.4173*x1)))) - 0.072576*exp(0.6841*plog(0.9104*plog(0.5661*plog(0.429*plog(0.424*x0))))) + 105.342,81,168.0,47.0,158.0,42.0,160.0,43.0,157.0,42.0,47.0,30.0 +pagie,82,FEAT,FEAT,23,0,drop_feat,-20645.1+22593.06*exp(0.0342*plog(0.0288*x0))+1642.20*plog(0.3477*plog(0.1143*x0))+685.81*exp(0.5799*plog(0.9824*x0))-596.61*exp(0.8515*exp(0.8515*plog(0.1528*x1)))+527.77*exp(0.8814*plog(0.4350*(0.2907*x1-0.6680*x1)))-369.33*plog(0.0678*x0)+50.11*(0.4834*x0*x0)+10.67*(0.4853*x1*x1)-4.25*exp(0.8814*plog(0.4350*(0.6698*x1-0.4404*(0.6256*x1/0.9696*exp(0.8814*plog(0.4350*x1))))))+0.15*(0.9578*(0.6256*x1/0.9696*exp(0.8814*plog(0.4350*(0.0469*x1+0.7478*x1))))-0.8056*(0.3042*x1-0.1685*x1)),24.223174*x0**2 + 5.178151*x1**2 + 0.0926979702970297*x1*exp(0.8814*plog(0.3456945*x1)) - 0.016397988*x1 - 369.33*plog(0.0678*x0) + 1642.2*plog(0.3477*plog(0.1143*x0)) + 22593.06*exp(0.0342*plog(0.0288*x0)) + 685.81*exp(0.5799*plog(0.9824*x0)) + 527.77*exp(0.8814*plog(-0.1641255*x1)) - 4.25*exp(0.8814*plog(-0.123606326732673*x1*exp(0.8814*plog(0.435*x1)) + 0.291363*x1)) - 596.61*exp(0.8515*exp(0.8515*plog(0.1528*x1))) - 20645.1,82,155.0,45.0,117.0,31.0,125.0,33.0,115.0,31.0,45.0,21.0 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- 1916.12*exp(0.2818*exp(0.7934*plog(0.8877*x1))) + 1889.9,83,170.0,46.0,152.0,37.0,152.0,37.0,150.0,37.0,46.0,28.0 +pagie,84,FEAT,FEAT,25,0,drop_feat,10169.3-10169.80*exp(0.2343*exp(0.8759*plog(0.7054*x0)))+5326.11*exp(0.8984*plog(0.1634*x0))+1226.99*exp(0.8759*plog(0.5721*x0))+649.63*(0.1747*x0*x0)+44.54*exp(0.9998*plog(0.2254*x1))-9.54*exp(0.6872*plog(0.7054*x1))-2.02*plog(0.4792*(0.2734*plog(0.8311*x1)-0.0506*(0.3565*x1*x1)))+1.88*plog(0.3602*plog(0.4355*x1))+0.66*plog(0.6986*x0)+0.05*(0.9340*x1+0.1757*plog(0.0118*(0.2734*exp(0.8115*x1)-0.0506*(0.9766*x1-0.0849*x1)))),113.490361*x0**2 + 0.0467*x1 + 0.66*plog(0.6986*x0) + 0.008785*plog(-0.000532416236*x1 + 0.00322612*exp(0.8115*x1)) - 2.02*plog(-0.00864424088*x1**2 + 0.13101328*plog(0.8311*x1)) + 1.88*plog(0.3602*plog(0.4355*x1)) + 5326.11*exp(0.8984*plog(0.1634*x0)) + 1226.99*exp(0.8759*plog(0.5721*x0)) + 44.54*exp(0.9998*plog(0.2254*x1)) - 9.54*exp(0.6872*plog(0.7054*x1)) - 10169.8*exp(0.2343*exp(0.8759*plog(0.7054*x0))) + 10169.3,84,138.0,39.0,122.0,32.0,126.0,34.0,120.0,32.0,39.0,23.0 +pagie,85,FEAT,FEAT,26,0,drop_feat,637.433-788.81*(0.0049*x0*x0)-515.20*plog(0.1041*plog(0.3325*x0))+506.60*plog(0.0564*plog(0.3198*x0))-160.32*plog(0.9210*plog(0.3325*x1))+127.50*plog(0.1454*plog(0.2873*x1))-91.51*(0.0797*plog(0.0559*plog(0.3891*x1))-0.3873*(0.4035*x1*x1))+12.06*plog(0.1073*plog(0.4632*x0))-1.13*exp(0.5913*plog(0.1041*plog(0.2851*plog(0.0965*plog(0.2851*plog(0.1462*x0))))))-0.17*(0.0797*plog(0.6259*plog(0.3891*plog(0.3891*x1)))-0.3873*(0.3800*plog(0.3325*plog(0.9210*exp(0.0258*x1)))*plog(0.2851*(0.4035*plog(0.3325*plog(0.6259*plog(0.3891*plog(0.3891*x1))))*x1))))+0.00*exp(0.7213*(0.4813*x1/0.0102*plog(0.2873*x1))),-3.865169*x0**2 + 14.3007755805*x1**2 + 0.02501958*plog(0.11503785*x1*plog(0.3325*plog(0.6259*plog(0.3891*plog(0.3891*x1)))))*plog(0.3325*plog(0.921*exp(0.0258*x1))) + 506.6*plog(0.0564*plog(0.3198*x0)) - 515.2*plog(0.1041*plog(0.3325*x0)) + 12.06*plog(0.1073*plog(0.4632*x0)) + 127.5*plog(0.1454*plog(0.2873*x1)) - 160.32*plog(0.921*plog(0.3325*x1)) - 7.293347*plog(0.0559*plog(0.3891*x1)) - 0.013549*plog(0.6259*plog(0.3891*plog(0.3891*x1))) - 1.13*exp(0.5913*plog(0.1041*plog(0.2851*plog(0.0965*plog(0.2851*plog(0.1462*x0)))))) + 637.433,85,179.0,47.0,167.0,41.0,169.0,42.0,165.0,41.0,52.0,1.0 +pagie,86,FEAT,FEAT,27,0,drop_feat,5221.38-4310.27*exp(0.2280*plog(0.1229*x1))+3821.11*(0.7474*plog(0.9040*plog(0.0542*x1))-0.7662*(0.0545*x0*x0))-3047.80*(0.0545*x0*x0)-1863.38*(0.4025*plog(0.2795*x0)/0.9285*(0.0864*x0/0.7917*x0))-247.71*exp(0.8807*plog(0.9756*x1))-172.28*plog(0.0542*x1)+30.08*plog(0.2795*plog(0.4829*(0.3995*x0*x0)))-15.32*(0.3016*x1*x1)+3.05*plog(0.9655*x0)+0.04*plog(0.9743*(0.4304*(0.0864*x0/0.7917*x0)-0.8980*x1)),-88.1532856536812*x0**2*plog(0.2795*x0) - 325.666629269*x0**2 - 4.620512*x1**2 + 3.05*plog(0.9655*x0) - 172.28*plog(0.0542*x1) + 0.04*plog(0.0457633767942403*x0**2 - 0.8749214*x1) + 30.08*plog(0.2795*plog(0.19291855*x0**2)) + 2855.897614*plog(0.904*plog(0.0542*x1)) - 4310.27*exp(0.228*plog(0.1229*x1)) - 247.71*exp(0.8807*plog(0.9756*x1)) + 5221.38,86,133.0,37.0,105.0,25.0,105.0,25.0,95.0,24.0,37.0,16.0 +pagie,87,FEAT,FEAT,28,0,drop_feat,-123.354-597.80*(0.0104*(0.0104*x1*plog(0.7861*x1))*plog(0.7861*x1))+301.65*exp(0.3320*(0.4565*x1*x1))+194.93*exp(0.4474*plog(0.6568*x0))-143.36*(0.8414*(0.0489*x0-0.4023*(0.4984*x0+0.0035*x0))+0.9517*(0.1651*x1*x1))-131.21*exp(0.4666*(0.4565*x1*x1))+122.42*(0.1661*(0.6893*(0.7041*x0+0.2828*(0.0104*x1*plog(0.7861*x1)))-0.0115*x0)-0.6136*plog(0.6737*x0))+113.29*plog(0.4141*plog(0.1569*x0))+60.98*plog(0.0637*plog(0.4197*(0.4565*(0.4984*x0+0.0035*x0)*plog(0.1569*(0.1200*x0*x0)))))+4.51*exp(0.7100*plog(0.4920*x1))+0.77*exp(0.7300*plog(0.9098*plog(0.4141*plog(0.4141*x1)))),28.0920341276515*x0 - 22.5255360512*x1**2 - 0.064658048*x1*plog(0.7861*x1)**2 + 0.0412233261634114*x1*plog(0.7861*x1) - 75.116912*plog(0.6737*x0) + 113.29*plog(0.4141*plog(0.1569*x0)) + 60.98*plog(0.0637*plog(0.096160551795*x0*plog(0.018828*x0**2))) + 301.65*exp(0.151558*x1**2) - 131.21*exp(0.2130029*x1**2) + 194.93*exp(0.4474*plog(0.6568*x0)) + 4.51*exp(0.71*plog(0.492*x1)) + 0.77*exp(0.73*plog(0.9098*plog(0.4141*plog(0.4141*x1)))) - 123.354,87,186.0,52.0,142.0,34.0,132.0,31.0,127.0,31.0,52.0,24.0 +pagie,88,FEAT,FEAT,29,0,drop_feat,-20.2023+1889.79*exp(0.6835*plog(0.5511*x1))-1111.17*exp(0.6334*plog(0.7846*x1))-384.13*(0.0986*(0.9151*exp(0.2747*(0.1426*x1+0.1367*plog(0.5019*x1)))-0.3215*plog(0.1038*plog(0.4280*x0)))+0.4384*(0.4333*x1-0.6701*x1))-346.38*exp(0.8234*plog(0.9078*x1))-253.40*(0.0350*x0*x0)+251.95*(0.0986*(0.9151*(0.4734*x1-0.3270*exp(0.1872*x1))-0.3215*plog(0.1038*plog(0.4530*x0)))+0.4384*(0.4333*x1-0.6701*x1))+83.08*plog(0.1206*plog(0.1206*x0))+27.72*(0.3874*x1-0.4887*(0.2657*x1*x1))+2.85*plog(0.8063*x0)+0.02*exp(0.9128*x1),-8.869*x0**2 - 3.5993751948*x1**2 + 35.2226247501318*x1 + 2.85*plog(0.8063*x0) + 83.08*plog(0.1206*plog(0.1206*x0)) + 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+pagie,121,Operon,Operon,2,1,kept,((-0.0615618973970413) + (1.0497297048568726 * (((((3.4508244991302490 * x0) * (exp(((2.5524139404296875 * x0) * ((-1.6356614828109741) * x0))) * (((2.4663076400756836 * x0) * ((-0.0845688283443451) * x0)) * (3.5071039199829102 * x0)))) - exp(((3.0741317272186279 * x0) * ((-0.2599562704563141) * x0)))) - exp(((0.0030150315724313 * x1) * ((-247.1376800537109375) * x1)))) + 1.9547927379608154))),-2.6497601004867348*x0**4*exp(-4.174885170550624*x0**2) + 1.9904421064789234 - 1.0497297048568726*exp(-0.745127908099363587*x1**2) - 1.0497297048568726*exp(-0.79913981869918164*x0**2),121,48.0,13.0,34.0,6.0,40.0,11.0,26.0,6.0,13.0,6.0 +pagie,122,Operon,Operon,3,1,kept,(0.0000011243114386 + (0.9999998211860657 * (((((-1.5812002420425415) + exp((((-0.1428712755441666) * x1) * (6.4702811241149902 * x1)))) + exp(((0.0134312557056546 * x0) * ((-68.7404861450195312) * x0)))) * (-1.2517620325088501)) - ((exp((((-0.0396961532533169) * x1) * (152.2495422363281250 * x1))) + exp(((1.0955569744110107 * x0) * ((-5.6038808822631836) * x0)))) * (-0.2742688059806824))))),1.9792871991701026 + 0.2742687569375981*exp(-6.043721161360625488*x1**2) - 1.2517618086763563*exp(-0.9244173173316527744*x1**2) + 0.2742687569375981*exp(-6.1393707843319587*x0**2) - 1.2517618086763563*exp(-0.923271046744764579*x0**2),122,45.0,13.0,33.0,7.0,45.0,13.0,29.0,7.0,13.0,7.0 +pagie,123,Operon,Operon,4,1,kept,(0.0130726965144277 + (0.9919041991233826 * (exp(((((58.9215812683105469 * x0) * exp((((-5.0386314392089844) * x1) * (2.4705743789672852 * x1)))) + (log(((0.4419521391391754 * x0) * (0.1393797099590302 * x0))) / (0.0113436263054609 * x0))) / (381.6167297363281250 * x0))) - (exp(((((-0.8848519921302795) * x1) * (0.9313139915466309 * x1)) + 0.1248256787657738)) + (-0.9970148205757141))))),0.9919041991233826*exp(0.1543998904582130231*exp(-12.448313738768775*x1**2) + 0.2310046294243750492*log(x0**2)/x0**2 - 0.6438346264391826885/x0**2) + 1.002015883631724 - 1.123778793245288*exp(-0.8240750407188386*x1**2),123,47.0,13.0,37.0,8.0,43.0,10.0,34.0,8.0,13.0,8.0 +pagie,124,Operon,Operon,5,1,kept,((-0.0197761859744787) + (1.0117771625518799 * ((exp(((1.6896657943725586 * x1) * ((-1.6174912452697754) * x1))) * ((0.0575970448553562 * x1) * ((-14.7621564865112305) * x1))) - (exp(((0.4481753110885620 * x1) * ((-1.8585087060928345) * x1))) - (1.9719880819320679 - exp((((0.2870940864086151 * x0) * ((-1.9049599170684814) * x0)) / exp((((-0.2803071439266205) * x0) * (0.7164036631584167 * x0)))))))))),-0.860270199378549024*x1**2*exp(-2.7330196298294141*x1**2) + 1.975436320148873 - 1.0117771625518799*exp(-0.54690272703580685*x0**2*exp(0.2008130647185045*x0**2)) - 1.0117771625518799*exp(-0.83293771751395694*x1**2),124,49.0,13.0,37.0,7.0,47.0,12.0,32.0,7.0,13.0,7.0 +pagie,125,Operon,Operon,6,1,kept,(0.0004403672355693 + (0.9997187852859497 * (exp((((-13.4114389419555664) * x0) * (0.2287123352289200 * x0))) - ((-3.1294746398925781) + (exp((exp((((-3.3788871765136719) * x0) * (0.2795567214488983 * x0))) - (-0.1448028236627579))) + ((1.0040752887725830 + ((1.8763431310653687 * x1) * (0.6411635279655457 * x1))) / exp(((1.1580088138580322 * x1) * (1.2662296295166016 * x1))))))))),-1.2027044682559756*x1**2*exp(-1.4663050713484154*x1**2) - 1.155486617848524*exp(exp(-0.94459062121188704*x0**2)) + 3.1290349528121623 - 1.0037929280273658*exp(-1.4663050713484154*x1**2) + 0.9997187852859497*exp(-3.06736151919473366*x0**2),125,45.0,13.0,35.0,8.0,52.0,14.0,31.0,8.0,13.0,8.0 +pagie,126,Operon,Operon,7,1,kept,(0.0028247879818082 + (0.9984024167060852 * (0.7176343202590942 - ((exp(((4.5870537757873535 * x1) * ((-0.0708576515316963) * x1))) / ((((-2.5320065021514893) * x1) * ((-0.5026428699493408) * x1)) + exp((((-1.5353101491928101) * x1) * (1.0705516338348389 * x1))))) + ((-3.4508912563323975) / exp(exp(exp(((1.6964559555053711 * x0) * ((-0.5267499089241028) * x0)))))))))),0.7193126276397166 + 3.4453781701121642*exp(-exp(exp(-0.89360802005620601*x0**2))) - 0.9984024167060852*exp(-0.32502785800189209*x1**2)/(1.2726950149718163*x1**2 + exp(-1.6436287886615731*x1**2)),126,44.0,12.0,36.0,8.0,42.0,11.0,32.0,8.0,12.0,7.0 +pagie,127,Operon,Operon,8,1,kept,((-0.0218773111701012) + (1.0134590864181519 * ((((((-0.3641613721847534) * x0) * (2.2286646366119385 * x0)) * exp((((-2.4582626819610596) * x0) * (1.0862829685211182 * x0)))) + (1.9716572761535645 - exp(((((-2.4894037246704102) * x1) * (0.2193875461816788 * x1)) * exp((((-0.4357891678810120) * x1) * ((-0.4778871238231659) * x1))))))) - exp((((-1.3948150873184204) * x0) * (0.5922598838806152 * x0)))))),-0.8225168802330056*x0**2*exp(-2.6703688835653453*x0**2) + 1.9763166706501921 - 1.0134590864181519*exp(-0.54614417461097283*x1**2*exp(0.2082580320319476*x1**2)) - 1.0134590864181519*exp(-0.82609302165013783*x0**2),127,49.0,13.0,39.0,8.0,47.0,12.0,32.0,7.0,13.0,7.0 +pagie,128,Operon,Operon,9,1,kept,((-0.0000084446337496) + (1.0000045299530029 * ((((exp(((1.8677622079849243 * x1) * ((-3.2215218544006348) * x1))) + exp(((4.2088832855224609 * x0) * ((-1.4519027471542358) * x0)))) * 0.2748067975044250) - ((exp(((0.5492876768112183 * x1) * ((-1.6836870908737183) * x1))) + exp(((1.3932512998580933 * x0) * ((-0.6629599928855896) * x0)))) * 1.2524310350418091)) + 1.9792671203613281))),1.9792676417146139 + 0.27480804236630257*exp(-6.0170367718470175*x1**2) - 1.2524367084955372*exp(-0.92482857062306332*x1**2) + 0.27480804236630257*exp(-6.1108892047016068*x0**2) - 1.2524367084955372*exp(-0.92366987184176*x0**2),128,45.0,13.0,33.0,7.0,45.0,13.0,29.0,7.0,13.0,7.0 +pagie,129,Operon,Operon,10,1,kept,(0.0000002913372725 + (1.0000000000000000 * ((1.0092900991439819 / ((((-9.8911437988281250) * x0) * ((-0.0619828216731548) * x0)) - exp((((-5.2376017570495605) * x0) * ((-0.1814788132905960) * x0))))) + ((2.9227268695831299 / ((-1.9528466463088989) - exp((((-1044.4626464843750000) * x1) * ((-0.0013573808828369) * x1))))) + (((241.8676300048828125 * x1) * (0.0000091869978860 * x1)) - (-1.9428678750991821)))))),0.002222037405546688681*x1**2 + 1.9428681664364546 - 2.9227268695831299/(exp(1.4177336291751259086*x1**2) + 1.9528466463088989) + 1.0092900991439819/(0.61308100222629464*x0**2 - exp(0.95051375135809475*x0**2)),129,43.0,13.0,33.0,8.0,33.0,8.0,29.0,8.0,14.0,8.0 +pagie,130,Operon,Operon,11,1,kept,((-0.0000135196241899) + (1.0000069141387939 * ((1.2255471944808960 * exp(((-1.7740323543548584) * exp(((2.9035081863403320 * x1) * ((-0.4098204970359802) * x1)))))) - ((1.2498761415481567 * exp(((0.1515025645494461 * x0) * ((-6.0828857421875000) * x0)))) + ((-0.7505750060081482) - (0.2749604582786560 * exp(((1.1432402133941650 * x0) * ((-5.4770793914794922) * x0))))))))),0.75056667596372507 + 1.2255556680842971*exp(-1.7740323543548584*exp(-1.1899171680740323*x1**2)) + 0.27496235939342737*exp(-6.261617412291798*x0**2) - 1.2498847833652745*exp(-0.92157278980266706*x0**2),130,41.0,13.0,31.0,8.0,39.0,12.0,28.0,8.0,13.0,8.0 +pagie,131,Operon,Operon,12,1,kept,((-0.0001345924683847) + (1.0000907182693481 * (((0.0052004987373948 * x0) * ((-5.5132131576538086) * x0)) - (log((((-29.4069671630859375) * x1) * (((-0.0669591948390007) + (((7.1831178665161133 * x0) * ((-12.8945026397705078) * x0)) * (((-0.0048121302388608) * x0) * ((-3.7251195907592773) * x0)))) * (11.7470531463623047 * x1)))) * ((-0.1758960038423538) + ((5.9699630737304688 * x1) * (0.0000638487472315 * x1))))))),-0.028674059090422408*x0**2 - 1.0000907182693481*(0.0003811746632760055*x1**2 - 0.1758960038423538)*log(x1**2*(573.554050429521172*x0**4 + 23.1307328639999089)) - 0.0001345924683847,131,48.0,14.0,32.0,6.0,32.0,8.0,24.0,6.0,14.0,6.0 +pagie,132,Operon,Operon,13,1,kept,((-0.0000847672417876) + (1.0000656843185425 * ((exp((((-1.8279364109039307) * x1) * (2.2386462688446045 * x1))) - ((-1.5547065734863281) + ((-1.6497515439987183) / exp(exp(((0.0022635490167886 * x0) * ((-443.1721801757812500) * x0))))))) - exp(exp(((-1.6148645877838135) + exp((0.5693863630294800 + ((0.0016070556594059 * x1) * ((-348.2632751464843750) * x1)))))))))),-1.0000656843185425*exp(0.19891760449084139*exp(1.767182310249908*exp(-0.5596784672873918045*x1**2))) + 1.5547239260863535 + 1.6498599068046503*exp(-exp(-1.003141952704949999*x0**2)) + 1.0000656843185425*exp(-4.0921030259552823*x1**2),132,41.0,12.0,35.0,9.0,45.0,14.0,32.0,9.0,12.0,8.0 +pagie,133,Operon,Operon,14,1,kept,(0.0049303476698697 + (0.9968529939651489 * ((((exp((((-0.1228989660739899) * x1) * (28.5782623291015625 * x1))) - (0.0001418351894245 * x0)) - exp((((-0.9014899730682373) * x1) * (0.9040312170982361 * x1)))) - exp((((-0.1503573954105377) * x1) * (16.6330261230468750 * x1)))) + (((-1.0727374553680420) * exp((((-0.1865450739860535) * x0) * (4.1227397918701172 * x0)))) - (-1.9877362251281738))))),-0.0001413888332274268*x0 + 1.986411154901873 + 0.9968529939651489*exp(-3.51223889243783649*x1**2) - 0.9968529939651489*exp(-2.50089848565676186*x1**2) - 0.9968529939651489*exp(-0.814975077554734653*x1**2) - 1.069361544122188*exp(-0.76907679949965783*x0**2),133,47.0,13.0,37.0,8.0,51.0,15.0,33.0,8.0,13.0,8.0 +pagie,134,Operon,Operon,15,1,kept,((-0.0000022516087483) + (1.0000016689300537 * (((((51.6682472229003906 * x0) * ((-0.0001894439337775) * x0)) + 2.5324115753173828) + ((-46.3591499328613281) / (((13.0968494415283203 * x0) * (2.1884925365447998 * x0)) + 34.0089225769042969))) + (((-1351.7908935546875000) / (((17.2840843200683594 * x1) * (47.4518127441406250 * x1)) + 990.7814331054687500)) + ((0.0012052881065756 * x1) * ((-8.2380609512329102) * x1)))))),-0.00978825234117588218*x0**2 - 0.0099292534569677497*x1**2 + 2.5324135501264209 - 1351.7931495991360721/(820.161132609820926*x1**2 + 990.78143310546875) - 46.3592273030399151/(28.6623572550356584*x0**2 + 34.0089225769042969),134,45.0,15.0,29.0,7.0,35.0,10.0,25.0,7.0,15.0,7.0 +pagie,135,Operon,Operon,16,1,kept,(0.0071523520164192 + (0.9955711960792542 * (((exp(((0.0195227134972811 * x1) * ((-151.1385955810546875) * x1))) * ((396057.1250000000000000 * x1) * ((-0.0000024948039936) * x1))) + ((85.4024658203125000 * x1) / ((43.1343650817871094 * x1) - (((-47.3760452270507812) * x1) * exp(((0.9379857182502747 * x0) * ((-1.2238332033157349) * x0))))))) - exp(((185448.0000000000000000 * x1) * ((-0.0000044009234443) * x1)))))),-0.9837088628772344519805*x1**2*exp(-2.950635499910365785*x1**2) + 85.0242350448461413*x1/(43.1343650817871094*x1 + 47.3760452270507812*x1*exp(-1.1479380662306441*x0**2)) + 0.0071523520164192 - 0.9955711960792542*exp(-0.816142450898546401501*x1**2),135,50.0,13.0,38.0,8.0,50.0,13.0,34.0,8.0,13.0,8.0 +pagie,136,Operon,Operon,17,1,kept,(0.0005329695995897 + (0.9996598958969116 * (((2.9738872051239014 + exp(((100.4859924316406250 * x1) * ((-0.0308157186955214) * x1)))) - ((((0.7702111005783081 * x0) * (1.5427883863449097 * x0)) + 1.0054689645767212) * exp((((-1.7126119136810303) * x0) * (0.8499408960342407 * x0))))) - exp(exp((((100.9902267456054688 * x1) * ((-0.0091333612799644) * x1)) + 0.0902468413114548)))))),-1.1878686045713406*x0**2*exp(-1.4556189044729706*x0**2) - 0.9996598958969116*exp(1.09444440445747*exp(-0.9223802266131381654*x1**2)) + 2.9734087434829063 + 0.9996598958969116*exp(-3.096548075613729891*x1**2) - 1.0051270004563406*exp(-1.4556189044729706*x0**2),136,45.0,13.0,37.0,9.0,54.0,15.0,31.0,8.0,13.0,8.0 +pagie,137,Operon,Operon,18,1,kept,(0.0000816054744064 + (1.0001157522201538 * (((((-0.0021946807391942) * x0) * (13.7494821548461914 * x0)) + (-8.4071483612060547)) + ((log((((6955.1982421875000000 * x1) * (16.8089103698730469 * x1)) + 27880.0878906250000000)) + log((((85251.5703125000000000 * x0) * (3.5084772109985352 * x0)) + 63949.3125000000000000))) * (((1.2129596471786499 * x1) * ((-0.0008703975472599) * x1)) + 0.3835373818874359))))),-0.0301792165661435915*x0**2 - 1.0001157522201538*(0.0010557571018295306*x1**2 - 0.3835373818874359)*(log(299103.191643245522053*x0**2 + 63949.3125) + log(116909.30385762825625*x1**2 + 27880.087890625)) - 8.4080399018196203,137,45.0,14.0,31.0,7.0,37.0,10.0,27.0,7.0,14.0,7.0 +pagie,138,Operon,Operon,19,1,kept,((-0.0000098704376796) + (1.0000013113021851 * ((exp(exp(((-0.1284630000591278) - exp((((-1.7482314109802246) * x0) * (0.6576864719390869 * x0)))))) - exp((0.2162327617406845 + (((-0.0238646697252989) * x1) * (38.5694580078125000 * x1))))) - exp((((-0.9399499893188477) - exp(((1.4266452789306641 * x1) * ((-5.3529791831970215) * x1)))) * 0.8908159136772156))))),1.0000013113021851*exp(0.8794461012701917*exp(-exp(-1.1497881488206758*x0**2))) - 9.8704376796e-6 - 0.4328685844136254*exp(-0.8908159136772156*exp(-7.6368024799221532*x1**2)) - 1.24139292161274*exp(-0.92044737684023015*x1**2),138,41.0,12.0,35.0,9.0,45.0,14.0,34.0,10.0,12.0,9.0 +pagie,139,Operon,Operon,20,1,kept,((-0.0000002506655221) + (1.0000001192092896 * (((((-0.0002352308656555) * x0) + 1.9712915420532227) - (exp((((-0.0005102988216095) * x1) * (2861.8625488281250000 * x1))) * (1.0045522451400757 + ((0.0003667365817819 * x1) * (3236.1384277343750000 * x1))))) + (exp((((-0.0249317195266485) * x0) * (58.4497108459472656 * x0))) * ((-1.0050251483917236) + (((-0.0338098518550396) * x0) * (35.2732009887695312 * x0))))))),-1.1925818420501513*x0**2*exp(-1.45725179722486209*x0**2) - 0.0002352308936972044*x0 - 1.1868104866391750118*x1**2*exp(-1.4604050862753523738*x1**2) + 1.9712915263839649 - 1.0045523648920352*exp(-1.4604050862753523738*x1**2) - 1.0050252682000576*exp(-1.45725179722486209*x0**2),139,47.0,14.0,37.0,9.0,59.0,15.0,31.0,8.0,14.0,8.0 +pagie,140,Operon,Operon,21,1,kept,(0.0056000440381467 + (0.9965137243270874 * ((0.7391300201416016 + (exp((((-26.2499160766601562) * x1) * (0.1143757924437523 * x1))) * (((-49.5787200927734375) * x1) * (0.0202242378145456 * x1)))) - (exp(((2.2524499893188477 * x1) * ((-0.3599792122840881) * x1))) + (exp((exp((((-0.7799134254455566) * x0) * (1.5038967132568359 * x0))) * (-1.7264224290847778))) * (-1.2398984432220459)))))),-0.999196165577684391*x1**2*exp(-3.00235495284999869*x1**2) + 0.7421532531714092 + 1.2355758154425587*exp(-1.7264224290847778*exp(-1.1729092371524529*x0**2)) - 0.9965137243270874*exp(-0.810835172864301451*x1**2),140,45.0,13.0,37.0,9.0,45.0,13.0,31.0,8.0,13.0,8.0 +pagie,141,Operon,Operon,22,1,kept,(0.0059260418638587 + (0.9963514208793640 * (((1.9877398014068604 + ((((-0.0255243461579084) * x1) * (39.2693595886230469 * x1)) * exp((((-0.0006980864563957) * x1) * (4245.9946289062500000 * x1))))) - exp((((-0.0209862142801285) * x1) * (38.7934265136718750 * x1)))) - exp((exp((-2.6416935920715332)) + ((0.0101619474589825 * x0) * ((-75.6802444458007812) * x0))))))),-0.998667666466396711*x1**2*exp(-2.9640713443683392264*x1**2) + 1.9864134173340489 - 0.996351420879364*exp(-0.81412716147633626667*x1**2) - 1.0699214810013096*exp(-0.769058667741179754*x0**2),141,42.0,12.0,34.0,8.0,40.0,11.0,28.0,7.0,12.0,7.0 +pagie,142,Operon,Operon,23,1,kept,(0.0007810645620339 + (0.9995014071464539 * (((((-1.0057448148727417) + ((0.7655488848686218 * x0) * ((-1.5458080768585205) * x0))) * exp(((0.4586827158927917 * x0) * ((-3.1686115264892578) * x0)))) + (2.9749636650085449 + exp(((-0.3110347986221313) + ((3.0109248161315918 * x1) * ((-1.1550782918930054) * x1)))))) - exp(exp(((23.0867309570312500 * x1) * ((-0.0377156287431717) * x1))))))),-1.1828016188405823*x0**2*exp(-1.4533873405792973*x0**2) - 0.9995014071464539*exp(exp(-0.870730573668879675*x1**2)) + 2.9742614339476462 + 0.7323230656900827*exp(-3.4778538936355404*x1**2) - 1.0052433576955551*exp(-1.4533873405792973*x0**2),142,45.0,13.0,37.0,9.0,52.0,14.0,31.0,8.0,13.0,8.0 +pagie,143,Operon,Operon,24,1,kept,(0.0049892361275852 + (0.9968150258064270 * (exp(((-0.7375680804252625) / (exp((((-7.8003888130187988) * x1) * ((-0.0912654846906662) * x1))) - 0.9434194564819336))) - (exp(((((-11.2235412597656250) * x0) * (0.0819300860166550 * x0)) - (exp(((((-56.8530616760253906) * x0) * (0.1006406396627426 * x0)) - 1.4147840738296509)) - 0.2206120193004608))) - 0.9837305545806885)))),-1.242868435105807*exp(-0.919545700824074031*x0**2 - 0.24297807310963717*exp(-5.72172849386055215*x0**2)) + 0.985586634278505 + 0.996815025806427*exp(-0.7375680804252625/(exp(0.71190626579581106*x1**2) - 0.9434194564819336)),143,41.0,13.0,33.0,9.0,41.0,13.0,30.0,9.0,13.0,9.0 +pagie,144,Operon,Operon,25,1,kept,((-0.0000055456266637) + (1.0000027418136597 * ((((exp((((-4.2250251770019531) * x1) * (1.4258037805557251 * x1))) + exp((((-1.1716369390487671) * x0) * (5.2204809188842773 * x0)))) * 0.2746707499027252) - (-1.9792732000350952)) - ((exp((((-1.7990413904190063) * x1) * (0.5140095949172974 * x1))) + exp(((1.8088867664337158 * x0) * ((-0.5105684995651245) * x0)))) * 1.2522673606872559)))),1.9792730812067276 + 0.2746715029987392*exp(-6.0240568703125063*x1**2) - 1.252270794171011*exp(-0.92472453632872492*x1**2) + 0.2746715029987392*exp(-6.1165082841640697*x0**2) - 1.252270794171011*exp(-0.92356060222127209*x0**2),144,45.0,13.0,33.0,7.0,45.0,13.0,29.0,7.0,13.0,7.0 +pagie,145,Operon,Operon,26,1,kept,((-0.0001599656243343) + (1.0001020431518555 * ((exp(((25.9337768554687500 * x1) * ((-0.1575351804494858) * x1))) - (exp(exp(exp(((17.7164573669433594 * x1) * ((-0.0314616635441780) * x1))))) * 0.1594999134540558)) - ((-1.1739871501922607) - (exp((exp((((-0.3572374880313873) * x0) * (3.2828271389007568 * x0))) * (-1.7236351966857910))) * 1.2407730817794800))))),-0.15951618932794533*exp(exp(exp(-0.557389220873545688*x1**2))) + 1.1739469819169699 + 1.2408996941754822*exp(-1.723635196685791*exp(-1.1727489207421725*x0**2)) + 1.0001020431518555*exp(-4.08548221666296794*x1**2),145,41.0,12.0,33.0,8.0,43.0,13.0,30.0,8.0,12.0,8.0 +pagie,146,Operon,Operon,27,1,kept,((-0.0639297738671303) + (1.0392827987670898 * ((1.9780735969543457 + ((exp((((-2.4385366439819336) * x1) * (2.2576689720153809 * x1))) * ((((-10.0973072052001953) * x1) * (391.6708374023437500 * x1)) * (((-0.0011133030056953) * x1) * ((-1.3449389934539795) * x1)))) - exp((((-1.7093311548233032) * x1) * (0.4650919437408447 * x1))))) - exp((((-1.2320897579193115) * x0) * (0.5889392495155334 * x0)))))),-6.154269525587394387*x1**4*exp(-5.5054085182405289*x1**2) + 1.9918480901428665 - 1.0392827987670898*exp(-0.79499614929355283*x1**2) - 1.0392827987670898*exp(-0.72562601736477455*x0**2),146,48.0,13.0,36.0,7.0,40.0,11.0,26.0,6.0,13.0,6.0 +pagie,147,Operon,Operon,28,1,kept,((-0.0000072608104347) + (1.0000052452087402 * (((-1.2524669170379639) * (exp((((-0.8438813686370850) * x0) * (1.0945762395858765 * x0))) + (exp((((-0.6344506740570068) * x1) * (1.4577195644378662 * x1))) + (-1.5802922248840332)))) + (0.2748360037803650 * (exp(((19.0184898376464844 * x0) * ((-0.3212499320507050) * x0))) + exp((((-0.8187244534492493) * x1) * (7.3472332954406738 * x1)))))))),1.9792668517605557 + 0.27483744535257415*exp(-6.0153595641737924*x1**2) - 1.252473486488384*exp(-0.92485116024369056*x1**2) + 0.27483744535257415*exp(-6.10968856805095664*x0**2) - 1.252473486488384*exp(-0.92369249513936332*x0**2),147,45.0,13.0,33.0,7.0,45.0,13.0,29.0,7.0,13.0,7.0 +pagie,148,Operon,Operon,29,1,kept,((-0.0000072977472882) + (1.0000039339065552 * ((0.2748106420040131 * (exp(((0.8403434157371521 * x1) * ((-7.1597433090209961) * x1))) + exp(((2.1294348239898682 * x0) * ((-2.8703227043151855) * x0))))) - ((-1.9792662858963013) + (1.2524309158325195 * (exp(((1.7403106689453125 * x1) * ((-0.5314179658889771) * x1))) + exp(((0.6934723854064941 * x0) * ((-1.3319598436355591) * x0))))))))),1.9792667743976297 + 0.27481172308339912*exp(-6.016643148103924*x1**2) - 1.2524358427787092*exp(-0.92483235570580301*x1**2) + 0.27481172308339912*exp(-6.1121651226575295*x0**2) - 1.2524358427787092*exp(-0.92367737003161206*x0**2),148,45.0,13.0,33.0,7.0,45.0,13.0,29.0,7.0,13.0,7.0 +pagie,149,Operon,Operon,30,1,kept,((-0.0166908428072929) + (1.0103557109832764 * ((-1.0929064750671387) * ((((-1.8171284198760986) + exp(((0.4634887576103210 * x0) * ((-1.7064006328582764) * x0)))) + ((exp((((-0.0545985996723175) * x1) * (290.8274841308593750 * x1))) + exp((((-6.8895225524902344) * x0) * (4.0632553100585938 * x0)))) * (-0.0849393755197525))) + exp((((-0.0165483560413122) * x1) * (47.9090309143066406 * x1))))))),1.9898265121958887 + 0.093792122361465658*exp(-15.87877337976806101*x1**2) - 1.1042242986546854*exp(-0.7928157011641792664*x1**2) + 0.093792122361465658*exp(-27.993889095174382*x0**2) - 1.1042242986546854*exp(-0.79089750930894803*x0**2),149,45.0,13.0,33.0,7.0,45.0,13.0,33.0,7.0,13.0,7.0 +pagie,150,SBP,SBP,1,1,kept,0.004376-0.000000*((((exp(4.787000)+((exp(x1)-exp(((x0-(x0*x0))+(15.039000-x1))))*x1))*15.260000)*(exp(x0)*x1))),0.00437600000000000,150,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,5.0,2.0 +pagie,151,SBP,SBP,2,1,kept,0.166642-0.018385*(((((x0*x1)+((((-5.488000+x1)*(x1+0.546000))+x1)*x1))+(x0*x0))+exp((-13.828000*x0)))),-0.018385*x0**2 - 0.018385*x0*x1 - 0.018385*x1**3 + 0.07247367*x1**2 + 0.05508969648*x1 + 0.166642 - 0.018385*exp(-13.828*x0),151,30.0,6.0,26.0,5.0,40.0,10.0,27.0,5.0,5.0,2.0 +pagie,152,SBP,SBP,3,1,kept,0.084583-0.012464*((((exp(x1)-(x0*(x1-1.179000)))+x1)+(x1*((-17.342000-(x0*(x1-3.045000)))+(x0*x0))))),0.012464*x0*(x1 - 1.179) + 0.012464*x1*(-x0**2 + x0*(x1 - 3.045) + 17.342) - 0.012464*x1 - 0.012464*exp(x1) + 0.084583,152,28.0,5.0,26.0,5.0,36.0,9.0,25.0,5.0,5.0,5.0 +pagie,153,SBP,SBP,4,1,kept,-0.000465+0.164361*(exp((x0*(2.011000-x0)))),0.164361*exp(-x0**2 + 2.011*x0) - 0.000465,153,10.0,3.0,10.0,3.0,14.0,4.0,11.0,3.0,3.0,3.0 +pagie,154,SBP,SBP,5,1,kept,0.018176+0.001712*((((((-8.935000*x0)+18.954000)*((x0*(x0-5.120000))*(x0-4.881000)))+x1)-((x1*18.328000)*(x1-4.881000)))),-0.001712*x0*(x0 - 5.12)*(x0 - 4.881)*(8.935*x0 - 18.954) - 0.031377536*x1*(x1 - 4.881) + 0.001712*x1 + 0.018176,154,31.0,9.0,29.0,8.0,33.0,10.0,25.0,7.0,8.0,7.0 +pagie,155,SBP,SBP,6,1,kept,0.012711-0.000000*((x1-(((16.817000*((16.817000*x1)-exp(x1)))-exp(x1))*exp(((19.315000-x0)*(17.099000+x0)))))),0.0127110000000000,155,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,6.0,1.0 +pagie,156,SBP,SBP,7,1,kept,0.112902-0.007452*(((((x0*(x1*x0))+((((x0-x1)+x0)*x0)+(x1*(-20.819000))))-(x0-exp(x1)))+x1)),-0.007452*x0**2*x1 - 0.007452*x0*(2*x0 - x1) + 0.007452*x0 + 0.147691188*x1 - 0.007452*exp(x1) + 0.112902,156,28.0,3.0,24.0,3.0,34.0,8.0,25.0,4.0,3.0,3.0 +pagie,157,SBP,SBP,8,1,kept,0.230781+0.006661*((((x1*x1)*(x0-x1))-((((x0*x0)-(19.670000+x0))+4.294000)*((x1+x0)-(x0*x0))))),0.006661*x1**2*(x0 - x1) + 0.006661*(-x0**2 + x0 + 15.376)*(-x0**2 + x0 + x1) + 0.230781,157,29.0,4.0,27.0,3.0,33.0,6.0,24.0,3.0,4.0,3.0 +pagie,158,SBP,SBP,9,1,kept,-0.135470+0.008287*((((x1*15.772000)-exp(x1))+exp(((x0-(9.538000-(4.169000-((x0*x0)-((x0+8.367000)+x1)))))-x1)))),0.130702564*x1 - 0.008287*exp(x1) + 0.16611627946936*exp(-x0**2 + 2*x0) - 0.13547,158,29.0,6.0,25.0,4.0,23.0,6.0,20.0,5.0,6.0,4.0 +pagie,159,SBP,SBP,10,1,kept,0.154306-0.001732*((((-20.410000+(((exp(11.767000)*(x0+(x0+(x0+x1))))*(-1.883000+x0))*exp((-7.374000-x0))))*x0)-x1)),(-0.001732*x0*(0.000627353738614736*(x0 - 1.883)*(386780.368892305*x0 + 128926.789630768*x1) - 20.41*exp(x0)) + (0.001732*x1 + 0.154306)*exp(x0))*exp(-x0),159,28.0,6.0,28.0,6.0,38.0,10.0,32.0,7.0,6.0,5.0 +pagie,160,SBP,SBP,11,1,kept,-0.056784-0.009562*((((-18.680000-((x0+(((x0+x0)-(x0*x0))-16.065000))+x0))+x0)*((x1+8.713000)-(x0*x0)))),0.009562*(-x0**2 + 3*x0 + 2.615)*(-x0**2 + x1 + 8.713) - 0.056784,160,29.0,5.0,23.0,4.0,25.0,7.0,19.0,5.0,5.0,4.0 +pagie,161,SBP,SBP,12,1,kept,0.667683-0.006309*((((x0*x0)-(x0-exp(exp((exp(((exp(x1)+0.069000)-x1))*(-0.069000))))))*((-6.657000+x0)*(-6.908000+x0)))),-0.006309*(x0 - 6.908)*(x0 - 6.657)*(x0**2 - x0 + exp(exp(-0.0739290984312359*exp(-x1 + exp(x1))))) + 0.667683,161,29.0,6.0,29.0,6.0,33.0,8.0,26.0,5.0,6.0,5.0 +pagie,162,SBP,SBP,13,0,paper_manual_drop,0.103875+0.010630*((exp(x0)-((exp(x1)+(((x0+x1)-(x0*x0))*(-7.894000)))+(((x1*(-7.894000))-(2.824000*x0))+x1)))),-0.08391322*x0**2 + 0.11393234*x0 + 0.15719644*x1 + 0.01063*exp(x0) - 0.01063*exp(x1) + 0.103875,162,29.0,5.0,27.0,4.0,27.0,7.0,22.0,5.0,5.0,5.0 +pagie,163,SBP,SBP,14,1,kept,0.001352+0.001458*((exp(((x0+(x0+2.705000))-(x0*x0)))*((exp(-11.964000)-(((x1+x1)-10.429000)*x1))-x1))),(-0.021803393734787*x1*(2*x1 - 10.429) - 0.021803393734787*x1 + 0.001352*exp(x0*(x0 - 2)) + 1.38875269916455e-7)*exp(x0*(2 - x0)),163,26.0,5.0,26.0,5.0,33.0,9.0,25.0,6.0,5.0,4.0 +pagie,164,SBP,SBP,15,1,kept,1.139001+0.010850*(((((x0*x0)-(-6.659000+x0))*(-12.488000+x0))-((13.571000-(exp(x0)-x0))-((x1*14.814000)-exp(x1))))),0.01085*x0**3 - 0.1463448*x0**2 + 0.19689495*x0 + 0.1607319*x1 + 0.01085*exp(x0) - 0.01085*exp(x1) + 0.0894957768,164,29.0,6.0,27.0,5.0,31.0,7.0,25.0,5.0,6.0,5.0 +pagie,165,SBP,SBP,16,1,kept,0.040499-0.003093*((x0-exp((((((((exp(1.871000)-1.708000)+(x1*(-1.785000)))+x1)*x1)+(x0-x1))-(x0*x0))+x0)))),-0.003093*x0 + 0.003093*exp(-x0**2 + 2*x0 - 0.785*x1**2 + 3.78678794091585*x1) + 0.040499,165,26.0,4.0,26.0,4.0,30.0,8.0,22.0,5.0,5.0,4.0 +pagie,166,SBP,SBP,17,1,kept,-0.065845-0.048266*(((x0-(x1+x1))-(x1+((x1+(x1+((3.579000-x0)*((3.247000-x0)*x0))))-(x1*x1))))),0.048266*x0*(x0 - 3.579)*(x0 - 3.247) - 0.048266*x0 - 0.048266*x1**2 + 0.24133*x1 - 0.065845,166,29.0,4.0,29.0,4.0,27.0,7.0,22.0,5.0,4.0,4.0 +pagie,167,SBP,SBP,18,1,kept,-8343620.960004+0.024527*((x0-((x0*x0)+(((20.791000-(x0-(x1*x0)))+((x1*x1)*(x1-4.494000)))-exp(19.645000))))),-0.024527*x0**2 - 0.024527*x0*x1 + 0.049054*x0 + x1**2*(0.110224338 - 0.024527*x1) + 94.8131869230419,167,27.0,5.0,21.0,3.0,29.0,7.0,19.0,4.0,5.0,3.0 +pagie,168,SBP,SBP,19,1,kept,0.012782+0.160826*((exp(((x0*x0)-exp(x0)))*((x0-(((-13.585000-x0)+exp((2.825000-(x1*x1))))*x0))+2.825000))),((0.160826*x0*((x0 + 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2.216379564*x0*x1*(0.002577416956*x0**2*x1 - 0.7286*x1) + 0.05*x0*(8.52657505513197*x0**2 + 6.16952492668622*x0) + 4.61*x0*(0.380961181229167*x0*x1 + 0.824043041427083*x0) + 0.01490058519552*x1**4 - 0.31274*x1*(-0.2856*x0 + 0.25812216*x1**2) - 5.769885*x1 + 18.520268*(-0.1998*x0 + 0.04*x1)*(0.02911776*x0 + 0.00021168*x1) - 21.7795,61,239.0,69.0,125.0,24.0,165.0,37.0,112.0,24.0,69.0,15.0 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0.051056*x1**2 + 64.132562*x1*(0.11908184*x0 + 0.06604384*x1)*(0.0363178*x0 + 0.004637442791488*x1**2 + 0.00612940488*x1) + 0.065872*x1 + 0.68*(0.06537609*x0 - 0.06338241*x1)*(-0.04956112*x0**2 + 0.8282*x0)*(0.199297988048168*x0**2 + 0.096280154052356*x1**2) - 420.113,62,221.0,63.0,109.0,23.0,161.0,34.0,104.0,22.0,63.0,19.0 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0.3442*x1*(0.12634837472*x0*x1 - 0.1447599*x1)) + 0.3221137816*x0*x1**2 - 2.860315*x0 + 1.16145*x1*(0.1822155*x0 + 0.15907615*x1) + 0.18*x1 + 22.41*(0.7561*x0 + 0.6847*x1)*(0.1572291*x1 - 0.1257039*(0.878*x0 + 0.1994*x1)*(0.063137957064*x0*x1 + 0.42971838*x0))*(0.12211570416688*x1**2 - 0.1447599*x1) - 9.09*(0.7561*x0 + 0.6847*x1)*(0.27904905*x1 - 0.1989603*(0.42971838*x0 + 0.37096332*x1)*(0.878*x0 + 0.1994*x1))*(0.1725128*x1*(0.26132032*x0 - 0.21928056*x1) - 0.1447599*x1) + 0.321159,63,263.0,76.0,141.0,30.0,185.0,45.0,127.0,28.0,76.0,22.0 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0.05310385389288*x1**3*(0.4384*x0 + 0.5905*x1) - 0.0438371424*x1**3 - 0.154269306*x1**2 + 0.9485639424*x1 + 0.310671,64,213.0,60.0,107.0,21.0,121.0,25.0,85.0,19.0,60.0,16.0 +kotanchek,65,FEAT,FEAT,6,0,drop_feat,0.289841-407252.69*(0.0074*(0.1404*(0.1791*x0*(0.1901*x0*x0))*x0)*(0.0069*(0.4026*x0+0.0270*x1)*(0.3683*x0*x1)))+4301.88*(0.0069*(0.0640*x0*x1)*(0.0306*x1+0.1079*(0.3683*x0*x1)))-648.64*(0.0069*(0.7977*(0.4427*x1+0.3851*x0)-0.7927*x1)*(0.2139*x1*x1))-313.72*(0.1836*(0.2647*(0.2254*x1-0.2190*x0)*x1)*(0.0306*x1+0.1079*(0.3683*(0.5782*x1*x1)*x1)))-218.19*(0.0074*(0.1404*x0*x0)*(0.2439*(0.3330*x0-0.8432*x1)*(0.3330*x0-0.8432*x1)))+155.47*(0.0074*(0.1404*x0*x0)*x0)+41.86*(0.0069*(0.3665*(0.6915*x1+0.6368*x0)*x1)*(0.3683*x1*x1))-1.23*(0.3503*x0+0.4008*(0.5782*x1*x1))+0.52*(0.2723*(0.7396*x0-0.5930*x1)*(0.9178*x0-0.5519*x1))+0.16*x1,-5.30569414396523*x0**5*x1*(0.00277794*x0 + 0.0001863*x1) + 0.1615271112*x0**3 - 0.2266906824*x0**2*(0.0812187*x0 - 0.20565648*x1)*(0.333*x0 - 0.8432*x1) + 1.899710208*x0*x1*(0.03973957*x0*x1 + 0.0306*x1) - 0.430869*x0 + 0.1063775622*x1**3*(0.2333872*x0 + 0.25343475*x1) - 138.744096*x1**2*(0.002119640463*x0 - 0.003032951649*x1) - 0.2850433488*x1**2 - 57.598992*x1*(-0.0579693*x0 + 0.05966338*x1)*(0.022977419374*x1**3 + 0.0306*x1) + 0.16*x1 + 0.52*(0.20139308*x0 - 0.1614739*x1)*(0.9178*x0 - 0.5519*x1) + 0.289841,65,213.0,60.0,121.0,25.0,147.0,34.0,109.0,22.0,60.0,18.0 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0.74743,66,195.0,56.0,87.0,18.0,109.0,23.0,73.0,16.0,56.0,14.0 +kotanchek,67,FEAT,FEAT,8,0,drop_feat,0.291669-25313.94*(0.1133*(0.0004*(0.2681*x0*x0)*x0)*(0.1300*x0*x0))-13321.93*(0.1133*(0.0004*(0.5083*x1-0.2322*x0)*x0)*(0.1300*x0*x0))+198.05*(0.4790*(0.0883*x1*x1)*(0.3457*x0+0.0242*(0.1064*x1*(0.0934*(0.0883*x1*x1)+0.4695*x1))))+33.39*(0.0538*(0.6208*(0.0822*x0+0.8086*(0.1300*x0*x0))+0.3639*x1)*(0.5895*x0+0.0968*(0.4790*(0.0883*x1*x1)*x0)))-32.98*(0.2845*(0.6226*x0-0.0279*(0.3766*x1*x0))*(0.1276*(0.1768*x1*x0)*x0))+6.40*(0.1761*x0*(0.2681*x0*x0))+4.81*(0.5586*(0.1803*x1-0.2948*x0)-0.2993*(0.1618*x0-0.2753*x0))-2.57*(0.4790*(0.0883*(0.2638*x1+0.7304*x0)*x1)*(0.6208*x0+0.3639*(0.7328*x1+0.9303*x1)))-1.98*(0.3123*x1+0.1391*(0.3766*x1*x0))-1.83*(0.0883*x1*x1),-0.0399843291471624*x0**5 - 196.21870697*x0**3*(-9.288e-5*x0 + 0.00020332*x1) + 0.302159424*x0**3 - 0.7440182464*x0**2*x1*(-0.00298928133*x0*x1 + 0.1771297*x0) - 0.1037224188*x0*x1 - 0.6286897513*x0 + 8.376663385*x1**2*(0.3457*x0 + 0.00257488*x1*(0.00824722*x1**2 + 0.4695*x1)) - 0.161589*x1**2 - 1.23103*x1*(0.06449432*x0 + 0.02329354*x1)*(0.6208*x0 + 0.60520209*x1) - 0.1339120602*x1 + 33.39*(0.00409422376*x0*x1**2 + 0.5895*x0)*(0.00351084028672*x0**2 + 0.002745401088*x0 + 0.01957782*x1) + 0.291669,67,225.0,64.0,117.0,22.0,143.0,32.0,103.0,21.0,64.0,18.0 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* (((-0.4060201048851013) * x0) + 0.8120366930961609)) - ((((-0.8767948746681213) * x1) / (((-0.3692416250705719) * x1) + exp((0.4968747496604919 * x1)))) + (0.7100588083267212 * x1))) - exp(((1.4052648544311523 - exp((0.1799458712339401 * x1))) * exp(exp((0.2937204837799072 * x1))))))))),0.9999927282333374*exp(-2.4630110263824463*x0*(0.4060201048851013*x0 - 0.8120366930961609) - 0.7100588083267212*x1 - 0.8767948746681213*x1/(0.3692416250705719*x1 - exp(0.4968747496604919*x1)) - exp(-(exp(0.1799458712339401*x1) - 1.4052648544311523)*exp(exp(0.2937204837799072*x1)))) + 3.4507245346e-6,128,45.0,12.0,41.0,11.0,49.0,14.0,41.0,11.0,12.0,11.0 +kotanchek,129,Operon,Operon,10,1,kept,((-0.0019379730802029) + (1.0046592950820923 * ((((996.6720581054687500 + ((-386.7166748046875000) * x0)) + exp((1.7618920803070068 * x0))) - (((1074.8041992187500000 * x0) + 882.8044433593750000) * exp(((-1.9537824392318726) * x0)))) / (((((-15.7029571533203125) * x1) * ((-22.8576602935791016) * x1)) + 2638.8918457031250000) + (exp((2.8161077499389648 * x0)) - (1794.9840087890625000 * x1)))))),(-1079.8120291383820754*x0 + (-388.518501905768068*x0 + 1.0046592950820923*exp(1.7618920803070068*x0) + 1001.315847324258372)*exp(1.9537824392318726*x0) + (-0.695602220697333891*x1**2 + 3.4786306884278888622*x1 - 0.0019379730802029*exp(2.8161077499389648*x0) - 5.1141013585396011999)*exp(1.9537824392318726*x0) - 886.917689760768567)*exp(-1.9537824392318726*x0)/(358.932860215223628*x1**2 - 1794.9840087890625*x1 + exp(2.8161077499389648*x0) + 2638.891845703125),129,44.0,13.0,40.0,12.0,77.0,22.0,60.0,16.0,13.0,12.0 +kotanchek,130,Operon,Operon,11,1,kept,(0.0006644097738899 + (0.9983761310577393 * ((((exp((0.3564732372760773 * x1)) * ((2.8750302791595459 * x1) + (-16.9938793182373047))) + (8.4957685470581055 + 8.5495948791503906)) + (3.2266986370086670 * x1)) / exp((((((-0.4841774106025696) * x0) + 0.9682721495628357) * ((-2.0647206306457520) * x0)) + ((0.0918822064995766 * x1) * ((3.7386786937713623 * x1) + (-3.2311415672302246)))))))),(3.2214589013059937*x1 + (2.8703616067811596*x1 - 16.9662834854038927)*exp(0.3564732372760773*x1) + 0.0006644097738899*exp(2.064720630645752*x0*(0.4841774106025696*x0 - 0.9682721495628357) + 0.0918822064995766*x1*(3.7386786937713623*x1 - 3.2311415672302246)) + 17.01768398993113)*exp(-2.064720630645752*x0*(0.4841774106025696*x0 - 0.9682721495628357) - 0.0918822064995766*x1*(3.7386786937713623*x1 - 3.2311415672302246)),130,41.0,13.0,37.0,11.0,62.0,19.0,52.0,14.0,13.0,10.0 +kotanchek,131,Operon,Operon,12,1,kept,((-0.0007296766270883) + (1.0011714696884155 * (((((-796.1662597656250000) * x0) - (-3327.3220214843750000)) + ((((-416.2025756835937500) * x0) + 5066.6352539062500000) / ((1.3030259609222412 * x0) - exp((0.6703483462333679 * x0))))) / (((-34525.6953125000000000) - exp((2.9498600959777832 * x0))) - ((((-0.1925518661737442) * x0) + ((-19.2132587432861328) * x1)) * (((-239.9505157470703125) * x1) + 1202.1625976562500000)))))),1.0011714696884155*(796.166259765625*x0 - 3327.322021484375 + (416.20257568359375*x0 - 5066.63525390625)/(1.3030259609222412*x0 - exp(0.6703483462333679*x0)))/((0.1925518661737442*x0 + 19.2132587432861328*x1)*(239.9505157470703125*x1 - 1202.16259765625) + exp(2.9498600959777832*x0) + 34525.6953125) - 0.0007296766270883,131,45.0,14.0,41.0,12.0,45.0,14.0,41.0,12.0,14.0,12.0 +kotanchek,132,Operon,Operon,13,1,kept,(0.0036648171953857 + (0.9917431473731995 * (((0.7433260083198547 * x1) / ((exp(exp((0.5352578163146973 * x0))) * (exp((2.5961806774139404 * x1)) - (1.9263886213302612 - (297.5476074218750000 * x1)))) * exp(((-1.0667701959609985) * x1)))) / exp(((exp(((-0.1313982456922531) * x0)) * ((-6.9308919906616211) * x0)) - (((-4.3688435554504395) * x0) + 3.7469267845153809)))))),(31.249866299263655*x1*exp(x0*(6.9308919906616211 - 4.3688435554504395*exp(0.1313982456922531*x0))*exp(-0.1313982456922531*x0) + 1.0667701959609985*x1) + (1.090457588125561273*x1 + 0.0036648171953857*exp(2.5961806774139404*x1) - 0.0070598621444464934)*exp(exp(0.5352578163146973*x0)))*exp(-exp(0.5352578163146973*x0))/(297.547607421875*x1 + exp(2.5961806774139404*x1) - 1.9263886213302612),132,45.0,12.0,41.0,11.0,64.0,17.0,62.0,16.0,12.0,10.0 +kotanchek,133,Operon,Operon,14,1,kept,((-0.0022257824894041) + (1.0057435035705566 * (((exp(((((-0.7701046466827393) * x1) - (-3.8445262908935547)) * (1.3931946754455566 * x1))) + (((15.1122426986694336 * x1) - (-13.2947568893432617)) * (((-2.5437910556793213) * x1) - (-15.1461124420166016)))) / (exp((2.8625166416168213 * x0)) + (((-3.6063053607940674) * x0) + 62.3201675415039062))) * ((0.0344910286366940 * x0) + 0.0158514883369207)))),-1.0057435035705566*(0.034491028636694*x0 + 0.0158514883369207)*((2.5437910556793213*x1 - 15.1461124420166016)*(15.1122426986694336*x1 + 13.2947568893432617) - exp(-1.3931946754455566*x1*(0.7701046466827393*x1 - 3.8445262908935547)))/(-3.6063053607940674*x0 + exp(2.8625166416168213*x0) + 62.3201675415039062) - 0.0022257824894041,133,43.0,14.0,37.0,11.0,49.0,17.0,37.0,11.0,14.0,11.0 +kotanchek,134,Operon,Operon,15,1,kept,(0.0003700088418555 + (0.9992044568061829 * (((exp((0.1231540888547897 * x1)) * (((((-2.6712670326232910) * x0) - 1.5445685386657715) * ((1.0232990980148315 * x0) - exp(((-4.9796590805053711) * x0)))) - (((-10.8486871719360352) * x0) - 0.5861128568649292))) / (exp((2.4178924560546875 * x0)) - (-42.5792884826660156))) / (exp((0.3763327002525330 * x1)) - (0.9377985596656799 * x1))))),0.0003700088418555 - 0.9992044568061829*(10.8486871719360352*x0 - (1.0232990980148315*x0 - exp(-4.9796590805053711*x0))*(2.671267032623291*x0 + 1.5445685386657715) + 0.5861128568649292)*exp(0.1231540888547897*x1)/((0.9377985596656799*x1 - exp(0.376332700252533*x1))*(exp(2.4178924560546875*x0) + 42.5792884826660156)),134,45.0,13.0,43.0,12.0,47.0,14.0,43.0,12.0,13.0,12.0 +kotanchek,135,Operon,Operon,16,1,kept,((-0.0158226937055588) + (1.0497971773147583 * (((exp(((-0.3585180342197418) * x1)) - ((((exp((1.7362647056579590 * x1)) - (-7144.3906250000000000)) + ((-3211.7934570312500000) * x1)) / (exp((3.3592488765716553 * x1)) - (-8749.7304687500000000))) - (-252.0166625976562500))) - (-251.8914642333984375)) / (exp((0.7833101749420166 * x0)) + log(exp(((-1.7847769260406494) * x0))))))),-0.0158226937055588 - 1.0497971773147583*(0.1251983642578125 - exp(-0.3585180342197418*x1) + (-3211.79345703125*x1 + exp(1.736264705657959*x1) + 7144.390625)/(exp(3.3592488765716553*x1) + 8749.73046875))/(exp(0.7833101749420166*x0) + log(exp(-1.7847769260406494*x0))),135,41.0,12.0,37.0,11.0,45.0,14.0,37.0,11.0,12.0,11.0 +kotanchek,136,Operon,Operon,17,1,kept,((-0.0000000143612136) + (1.0000000000000000 * (((0.0493797957897186 - (0.0001029339036904 * x0)) / (exp(((-0.0000001355219865) * x0)) + (((-0.0032123271375895) * x1) * (((-41.7853355407714844) * x1) + 208.9266815185546875)))) / exp((((-1.8152447938919067) * x0) * (1.1029279232025146 - (0.5508886575698853 * x0))))))),-1.0*(0.0001029339036904*x0 - 0.0493797957897186)*exp(-1.8152447938919067*x0*(0.5508886575698853*x0 - 1.1029279232025146))/(0.0032123271375895*x1*(41.7853355407714844*x1 - 208.9266815185546875) + exp(-1.355219865e-7*x0)) - 1.43612136e-8,136,33.0,10.0,29.0,8.0,39.0,13.0,29.0,8.0,11.0,8.0 +kotanchek,137,Operon,Operon,18,1,kept,((-0.0000026597272154) + (1.0000067949295044 * ((exp(((1.3812974691390991 * x0) * (((-0.7240105271339417) * x0) + 1.4479488134384155))) * (((-0.0016091535799205) * x1) - (-0.0074326260946691))) * (exp((1.1061540842056274 * x1)) - ((((-4.3172826766967773) * x1) + (-5.3209042549133301)) - exp((((3.6427340507507324 * x1) - 0.0311711747199297) - exp((0.6457238197326660 * x1))))))))),(-1.0000067949295044*(0.0016091535799205*x1 - 0.0074326260946691)*(4.3172826766967773*x1 + exp(1.1061540842056274*x1) + 0.969309637568713*exp(3.6427340507507324*x1 - exp(0.645723819732666*x1)) + 5.3209042549133301) - 2.6597272154e-6*exp(1.3812974691390991*x0*(0.7240105271339417*x0 - 1.4479488134384155)))*exp(-1.3812974691390991*x0*(0.7240105271339417*x0 - 1.4479488134384155)),137,43.0,13.0,39.0,11.0,58.0,18.0,48.0,13.0,13.0,11.0 +kotanchek,138,Operon,Operon,19,1,kept,(0.0034536698367447 + (0.9867714047431946 * ((((((-0.6941707730293274) * x1) + exp((0.2583339512348175 * x1))) * (((-0.6002479791641235) * x1) + exp((0.2208170741796494 * x1)))) * (exp(((-0.8911798000335693) * x0)) - (0.7564386129379272 + ((-1.2858601808547974) * x0)))) / exp(((((-2.1546506881713867) * x1) + exp((0.6885151863098145 * x0))) + exp(((-1.0648982524871826) * x0))))))),(0.9867714047431946*(0.6002479791641235*x1 - exp(0.2208170741796494*x1))*(0.6941707730293274*x1 - exp(0.2583339512348175*x1))*((1.2858601808547974*x0 - 0.7564386129379272)*exp(0.8911798000335693*x0) + 1)*exp(((2.1546506881713867*x1 - exp(0.6885151863098145*x0))*exp(1.0648982524871826*x0) - 1)*exp(-1.0648982524871826*x0)) + 0.0034536698367447*exp(0.8911798000335693*x0))*exp(-0.8911798000335693*x0),138,47.0,12.0,47.0,12.0,70.0,19.0,64.0,16.0,12.0,12.0 +kotanchek,139,Operon,Operon,20,1,kept,(0.0004888178664260 + (0.9988220334053040 * (exp((((((-5.1766362190246582) - (0.0070227989926934 * x0)) + (1.1790944337844849 * x1)) * ((-0.3277454376220703) * x1)) + (exp(((6.3319468498229980 * x1) * ((-0.0836486071348190) * x1))) * ((-1.0949771404266357) * x1)))) / (6.3024258613586426 / (0.0139735620468855 + exp(((2.2476174831390381 * x0) - exp((0.8711588978767395 * x0))))))))),(0.15848215518555634*exp(2.2476174831390381*x0 - exp(0.8711588978767395*x0)) + 0.0022145602288095083)*exp(-x1*(0.3277454376220703*(-0.0070227989926934*x0 + 1.1790944337844849*x1 - 5.1766362190246582)*exp(0.52965853443939874*x1**2) + 1.0949771404266357)*exp(-0.52965853443939874*x1**2)) + 0.000488817866426,139,45.0,13.0,39.0,11.0,52.0,15.0,42.0,11.0,13.0,10.0 +kotanchek,140,Operon,Operon,21,1,kept,(0.0000354178737325 + (0.9998701810836792 * (((21.8554801940917969 * x1) - ((21.8578433990478516 * x1) - 0.0542484000325203)) * exp(((((-1.2365419864654541) - ((-0.6182689070701599) * x0)) * ((-1.6172654628753662) * x0)) - (exp(((((-0.0128339584916830) * x1) - (0.0000608815898886 * x1)) - ((((-1.6681232452392578) * x1) - (-6.2428498268127441)) * ((-0.1763334870338440) * x1)))) * ((-0.3036648035049438) * x1))))))),(-0.00236289816734826241*x1 + 3.54178737325e-5*exp(1.6172654628753662*x0*(0.6182689070701599*x0 - 1.2365419864654541) - 0.3036648035049438*x1*exp(x1*(1.0879286389089487 - 0.29414598863525044*x1))) + 0.05424135756401594)*exp(-1.6172654628753662*x0*(0.6182689070701599*x0 - 1.2365419864654541) + 0.3036648035049438*x1*exp(x1*(1.0879286389089487 - 0.29414598863525044*x1))),140,47.0,14.0,29.0,8.0,59.0,17.0,51.0,13.0,14.0,8.0 +kotanchek,141,Operon,Operon,22,1,kept,(0.0000054139832173 + (0.9996626973152161 * (exp(((((-0.1160286292433739) * x0) * ((-17.2363529205322266) + (8.6183118820190430 * x0))) + exp((exp((((1.4520825147628784 * x1) + (-7.2530150413513184)) * ((-0.1153997406363487) * x1))) + (-2.4340145587921143))))) * (exp((((1.4263883829116821 * x1) + (-7.1799330711364746)) * ((-0.0031533578876406) * x1))) + (-0.9611204862594604))))),-0.9607962977390443*exp(-0.99997091406255149*x0**2 + 1.99991040252437864*x0 + 0.087684112024531059*exp(exp(-0.16756994558621315*x1**2 + 0.83699605460347808*x1))) + 0.9996626973152161*exp(-0.99997091406255149*x0**2 + 1.99991040252437864*x0 - 0.0044979130580934735*x1**2 + 0.022640898582599801*x1 + 0.087684112024531059*exp(exp(-0.16756994558621315*x1**2 + 0.83699605460347808*x1))) + 5.4139832173e-6,141,41.0,13.0,35.0,10.0,75.0,20.0,60.0,15.0,13.0,10.0 +kotanchek,142,Operon,Operon,23,1,kept,(0.0008338154293597 + (0.9979702830314636 * ((exp(exp(exp(((0.0654336437582970 + ((-0.0385530032217503) * x1)) * ((-17.4296455383300781) + (5.2765936851501465 * x1)))))) * (exp(((-0.6076733469963074) * x0)) + ((-0.9865196943283081) + (0.7046096920967102 * x0)))) * 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exp(0.4206682443618774*x1)))) + 1)*exp(1.9999943971633911*x0 - 0.0865126922726631*x1) + 1.09874044938e-5*exp(1.000005586060064296*x0**2 + 0.2363450229167938*x1))*exp(-1.000005586060064296*x0**2 - 0.2363450229167938*x1),143,45.0,11.0,43.0,10.0,61.0,15.0,57.0,14.0,11.0,10.0 +kotanchek,144,Operon,Operon,25,1,kept,((-0.0021912427619100) + (1.0060203075408936 * ((((-1.9571648836135864) + ((-0.1280445605516434) * x1)) + (((-4.9479722976684570) * x0) + (((exp(((-25.1299152374267578) * x0)) - ((-1013.9223632812500000) + ((-2498.2419433593750000) * x0))) / ((-763.4477539062500000) - exp((2.6487932205200195 * x1)))) / exp(((-1.3105899095535278) * x1))))) / ((-64.6880645751953125) - exp((2.9050159454345703 * x0)))))),-0.00219124276191 + 1.0060203075408936*(4.947972297668457*x0 + 0.1280445605516434*x1 + 1.9571648836135864 + (2498.241943359375*x0 + 1013.92236328125 + exp(-25.1299152374267578*x0))*exp(1.3105899095535278*x1)/(exp(2.6487932205200195*x1) + 763.44775390625))/(exp(2.9050159454345703*x0) 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1.842776894569397))),145,41.0,14.0,31.0,9.0,67.0,22.0,51.0,14.0,14.0,9.0 +kotanchek,146,Operon,Operon,27,1,kept,((-0.0020811073482037) + (0.9979038834571838 * ((((((-0.0209705717861652) * x1) - ((0.0227618105709553 * x0) + 0.0106864003464580)) * exp((0.0658860057592392 * x0))) + (0.0203825030475855 * x1)) * ((40.4724655151367188 / ((-62.7512664794921875) - exp((2.9289722442626953 * x0)))) / (exp((0.1633399575948715 * x1)) + ((-0.8682605624198914) - (0.2447641491889954 * x1))))))),(0.823201001967915342*x1 - 0.0020811073482037*(exp(2.9289722442626953*x0) + 62.7512664794921875)*(0.2447641491889954*x1 - exp(0.1633399575948715*x1) + 0.8682605624198914) - (0.919295595092965231*x0 + 0.846951704896531438*x1 + 0.431598388681541098)*exp(0.0658860057592392*x0))/((exp(2.9289722442626953*x0) + 62.7512664794921875)*(0.2447641491889954*x1 - exp(0.1633399575948715*x1) + 0.8682605624198914)),146,42.0,13.0,38.0,11.0,56.0,16.0,56.0,16.0,13.0,11.0 +kotanchek,147,Operon,Operon,28,1,kept,(0.0014168095076457 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x1),0.51261115262063534*x1*(0.6214063774224301*x0*x1*(1.8394445968539718*x0 + 3*x1 - 0.16055540314602817*exp(x1) - 0.6904329788496647) + x1 - 0.2570477604364112)*exp(-0.6022120672089649*x0**2 - x1),208,45.0,8.0,41.0,6.0,39.0,9.0,34.0,7.0,8.0,6.0 +kotanchek,209,SRjl,SRjl,30,1,kept,(((((x1 + ((x0 + (0.22599078633925967 * -1.0472058462434648)) - ((-0.041129877765828333 - 0.6933744860762721) + (log(0.3913793270250966) * -0.04529560337326411)))) / (exp(x1) + (((7.787500628085413 - x1) - x1) - x1))) / ((exp(x0) - ((x0 - 0.5311915415003168) / 0.6723070296996237)) - x0)) - 0.01811268853996139) * x1),x1*(x0 + x1 - 0.01811268853996139*(-2.487415653599196*x0 + exp(x0) + 0.7901026138870583)*(-3*x1 + exp(x1) + 7.787500628085413) + 0.45535468020164982)/((-2.487415653599196*x0 + exp(x0) + 0.7901026138870583)*(-3*x1 + exp(x1) + 7.787500628085413)),209,33.0,6.0,31.0,5.0,33.0,6.0,31.0,5.0,8.0,5.0 diff --git a/python/egglog/exp/param_eq/artifacts/pagie_runtime_compare.csv b/python/egglog/exp/param_eq/artifacts/pagie_runtime_compare.csv new file mode 100644 index 00000000..1db1b2da --- /dev/null +++ b/python/egglog/exp/param_eq/artifacts/pagie_runtime_compare.csv @@ -0,0 +1,634 @@ +implementation,algorithm_raw,algorithm,algo_row,node_count,after_nodes,runtime_ms,status +Archived Haskell,,,,45,,212.200000000,archived_benchmark +Archived Haskell,,,,41,,16.150000000,archived_benchmark +Archived Haskell,,,,34,,193.600000000,archived_benchmark +Archived Haskell,,,,48,,717.900000000,archived_benchmark +Archived Haskell,,,,37,,26.040000000,archived_benchmark +Archived Haskell,,,,45,,199.100000000,archived_benchmark +Archived Haskell,,,,25,,117.200000000,archived_benchmark +Archived Haskell,,,,38,,186.800000000,archived_benchmark +Archived Haskell,,,,41,,23.130000000,archived_benchmark +Archived Haskell,,,,44,,51.680000000,archived_benchmark +Archived Haskell,,,,40,,160.200000000,archived_benchmark +Archived Haskell,,,,25,,5.692000000,archived_benchmark 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Haskell,,,,48,,29.450000000,archived_benchmark +Archived Haskell,,,,19,,442.100000000,archived_benchmark +Archived Haskell,,,,17,,52.570000000,archived_benchmark +Archived Haskell,,,,17,,70.240000000,archived_benchmark +Archived Haskell,,,,19,,243.000000000,archived_benchmark +Archived Haskell,,,,19,,340.200000000,archived_benchmark +Archived Haskell,,,,19,,128.100000000,archived_benchmark +Archived Haskell,,,,17,,53.480000000,archived_benchmark +Archived Haskell,,,,16,,115.200000000,archived_benchmark +Archived Haskell,,,,19,,237.200000000,archived_benchmark +Archived Haskell,,,,14,,47.630000000,archived_benchmark +Archived Haskell,,,,17,,53.940000000,archived_benchmark +Archived Haskell,,,,20,,93.280000000,archived_benchmark +Archived Haskell,,,,16,,129.500000000,archived_benchmark +Archived Haskell,,,,19,,107.900000000,archived_benchmark +Archived Haskell,,,,19,,327.000000000,archived_benchmark +Archived Haskell,,,,19,,317.200000000,archived_benchmark +Archived Haskell,,,,21,,320.700000000,archived_benchmark +Archived Haskell,,,,21,,313.500000000,archived_benchmark +Archived Haskell,,,,21,,123.100000000,archived_benchmark +Archived Haskell,,,,17,,57.440000000,archived_benchmark +Archived Haskell,,,,17,,55.740000000,archived_benchmark +Archived Haskell,,,,17,,54.740000000,archived_benchmark +Archived Haskell,,,,19,,336.200000000,archived_benchmark +Archived Haskell,,,,18,,134.900000000,archived_benchmark +Archived Haskell,,,,16,,53.960000000,archived_benchmark +Archived Haskell,,,,1,,0.146800000,archived_benchmark +Archived Haskell,,,,1,,0.147200000,archived_benchmark +Archived Haskell,,,,21,,270.100000000,archived_benchmark +Archived Haskell,,,,19,,56.220000000,archived_benchmark +Archived Haskell,,,,17,,53.840000000,archived_benchmark +Archived Haskell,,,,63,,6.460000000,archived_benchmark +Archived Haskell,,,,77,,3.451000000,archived_benchmark +Archived Haskell,,,,40,,105.000000000,archived_benchmark +Archived Haskell,,,,29,,86.170000000,archived_benchmark +Archived Haskell,,,,89,,1.360000000,archived_benchmark +Archived Haskell,,,,64,,52.330000000,archived_benchmark +Archived Haskell,,,,58,,1.405000000,archived_benchmark +Archived Haskell,,,,67,,4.851000000,archived_benchmark +Archived Haskell,,,,71,,46.370000000,archived_benchmark +Archived Haskell,,,,66,,4.088000000,archived_benchmark +Archived Haskell,,,,51,,3.149000000,archived_benchmark +Archived Haskell,,,,83,,37.770000000,archived_benchmark +Archived Haskell,,,,37,,2.279000000,archived_benchmark +Archived Haskell,,,,78,,226.800000000,archived_benchmark +Archived Haskell,,,,67,,24.290000000,archived_benchmark +Archived Haskell,,,,29,,0.540800000,archived_benchmark +Archived Haskell,,,,72,,2.782000000,archived_benchmark +Archived Haskell,,,,55,,14.230000000,archived_benchmark +Archived Haskell,,,,33,,0.783700000,archived_benchmark +Archived Haskell,,,,67,,219.500000000,archived_benchmark +Archived Haskell,,,,59,,6.614000000,archived_benchmark +Archived Haskell,,,,25,,4.901000000,archived_benchmark +Archived Haskell,,,,66,,27.150000000,archived_benchmark +Archived Haskell,,,,43,,160.500000000,archived_benchmark +Archived Haskell,,,,32,,2.992000000,archived_benchmark +Archived Haskell,,,,29,,2.482000000,archived_benchmark +Archived Haskell,,,,85,,7.570000000,archived_benchmark +Archived Haskell,,,,69,,13.310000000,archived_benchmark +Archived Haskell,,,,56,,1.331000000,archived_benchmark +Archived Haskell,,,,32,,7.101000000,archived_benchmark +Archived Haskell,,,,79,,13.280000000,archived_benchmark +Archived Haskell,,,,55,,4.221000000,archived_benchmark +Archived Haskell,,,,89,,109.200000000,archived_benchmark +Archived Haskell,,,,217,,410.000000000,archived_benchmark +Archived Haskell,,,,116,,1039.000000000,archived_benchmark +Archived Haskell,,,,194,,379.400000000,archived_benchmark +Archived Haskell,,,,142,,473.500000000,archived_benchmark +Archived Haskell,,,,269,,380.200000000,archived_benchmark +Archived Haskell,,,,191,,590.700000000,archived_benchmark +Archived Haskell,,,,191,,377.100000000,archived_benchmark +Archived Haskell,,,,241,,440.900000000,archived_benchmark +Archived Haskell,,,,202,,358.800000000,archived_benchmark +Archived Haskell,,,,223,,663.900000000,archived_benchmark +Archived Haskell,,,,357,,531.900000000,archived_benchmark +Archived Haskell,,,,154,,493.200000000,archived_benchmark +Archived Haskell,,,,134,,555.700000000,archived_benchmark +Archived Haskell,,,,184,,329.300000000,archived_benchmark +Archived Haskell,,,,416,,707.500000000,archived_benchmark +Archived Haskell,,,,129,,527.900000000,archived_benchmark +Archived Haskell,,,,174,,339.700000000,archived_benchmark +Archived Haskell,,,,160,,590.300000000,archived_benchmark +Archived Haskell,,,,196,,463.500000000,archived_benchmark +Archived Haskell,,,,151,,643.600000000,archived_benchmark +Archived Haskell,,,,125,,709.800000000,archived_benchmark +Archived Haskell,,,,168,,1315.000000000,archived_benchmark +Archived Haskell,,,,155,,305.200000000,archived_benchmark +Archived Haskell,,,,170,,373.500000000,archived_benchmark +Archived Haskell,,,,138,,309.200000000,archived_benchmark +Archived Haskell,,,,179,,663.600000000,archived_benchmark +Archived Haskell,,,,133,,594.100000000,archived_benchmark +Archived Haskell,,,,186,,423.500000000,archived_benchmark +Archived Haskell,,,,165,,453.100000000,archived_benchmark +Archived Haskell,,,,131,,1150.000000000,archived_benchmark +Archived Haskell,,,,1,,0.139700000,archived_benchmark +Archived Haskell,,,,30,,253.500000000,archived_benchmark +Archived Haskell,,,,28,,274.600000000,archived_benchmark +Archived Haskell,,,,10,,0.954400000,archived_benchmark +Archived Haskell,,,,31,,435.000000000,archived_benchmark +Archived Haskell,,,,1,,0.166900000,archived_benchmark +Archived Haskell,,,,28,,157.900000000,archived_benchmark +Archived Haskell,,,,29,,5.302000000,archived_benchmark +Archived Haskell,,,,29,,73.570000000,archived_benchmark +Archived Haskell,,,,28,,393.900000000,archived_benchmark +Archived Haskell,,,,29,,262.800000000,archived_benchmark +Archived Haskell,,,,29,,393.600000000,archived_benchmark +Archived Haskell,,,,29,,225.200000000,archived_benchmark +Archived Haskell,,,,26,,4.449000000,archived_benchmark +Archived Haskell,,,,29,,173.700000000,archived_benchmark +Archived Haskell,,,,26,,81.570000000,archived_benchmark +Archived Haskell,,,,29,,294.500000000,archived_benchmark +Archived Haskell,,,,27,,53.530000000,archived_benchmark +Archived Haskell,,,,28,,3.177000000,archived_benchmark +Archived Haskell,,,,28,,221.100000000,archived_benchmark +Archived Haskell,,,,28,,4.708000000,archived_benchmark +Archived Haskell,,,,31,,262.300000000,archived_benchmark +Archived Haskell,,,,29,,130.800000000,archived_benchmark +Archived Haskell,,,,27,,65.000000000,archived_benchmark +Archived Haskell,,,,29,,24.890000000,archived_benchmark +Archived Haskell,,,,28,,5.798000000,archived_benchmark +Archived Haskell,,,,27,,20.730000000,archived_benchmark +Archived Haskell,,,,28,,306.400000000,archived_benchmark +Archived Haskell,,,,28,,85.760000000,archived_benchmark +Archived Haskell,,,,28,,23.420000000,archived_benchmark +Archived Haskell,,,,43,,14.500000000,archived_benchmark +Archived Haskell,,,,23,,25.420000000,archived_benchmark +Archived Haskell,,,,27,,3.468000000,archived_benchmark +Archived Haskell,,,,49,,31.470000000,archived_benchmark +Archived Haskell,,,,23,,2.993000000,archived_benchmark +Archived Haskell,,,,53,,36.180000000,archived_benchmark +Archived Haskell,,,,21,,8.431000000,archived_benchmark +Archived Haskell,,,,20,,225.500000000,archived_benchmark +Archived Haskell,,,,31,,102.600000000,archived_benchmark +Archived Haskell,,,,25,,5.126000000,archived_benchmark +Archived Haskell,,,,24,,294.000000000,archived_benchmark +Archived Haskell,,,,15,,130.600000000,archived_benchmark +Archived Haskell,,,,33,,5.123000000,archived_benchmark +Archived Haskell,,,,29,,281.400000000,archived_benchmark +Archived Haskell,,,,45,,36.260000000,archived_benchmark +Archived Haskell,,,,47,,126.000000000,archived_benchmark +Archived Haskell,,,,49,,111.500000000,archived_benchmark +Archived Haskell,,,,23,,6.700000000,archived_benchmark +Archived Haskell,,,,25,,13.980000000,archived_benchmark +Archived Haskell,,,,39,,45.590000000,archived_benchmark +Archived Haskell,,,,43,,5.005000000,archived_benchmark +Archived Haskell,,,,27,,4.470000000,archived_benchmark +Archived Haskell,,,,27,,268.900000000,archived_benchmark +Archived Haskell,,,,29,,2.533000000,archived_benchmark +Archived Haskell,,,,20,,1.174000000,archived_benchmark +Archived Haskell,,,,16,,1.082000000,archived_benchmark +Archived Haskell,,,,53,,254.400000000,archived_benchmark +Archived Haskell,,,,41,,8.862000000,archived_benchmark +Archived Haskell,,,,17,,1.122000000,archived_benchmark +Archived Haskell,,,,27,,11.140000000,archived_benchmark +Archived Haskell,,,,44,,233.900000000,archived_benchmark +Archived Haskell,,,,39,,266.900000000,archived_benchmark +Archived Haskell,,,,35,,11.920000000,archived_benchmark +Archived Haskell,,,,41,,461.700000000,archived_benchmark +Archived Haskell,,,,44,,59.140000000,archived_benchmark +Archived Haskell,,,,31,,275.600000000,archived_benchmark +Archived Haskell,,,,28,,107.900000000,archived_benchmark +Archived Haskell,,,,37,,112.200000000,archived_benchmark +Archived Haskell,,,,35,,515.900000000,archived_benchmark +Archived Haskell,,,,36,,155.000000000,archived_benchmark +Archived Haskell,,,,33,,11.260000000,archived_benchmark +Archived Haskell,,,,41,,283.900000000,archived_benchmark +Archived Haskell,,,,42,,532.300000000,archived_benchmark +Archived Haskell,,,,43,,149.600000000,archived_benchmark +Archived Haskell,,,,41,,241.400000000,archived_benchmark +Archived Haskell,,,,34,,143.200000000,archived_benchmark +Archived Haskell,,,,42,,28.950000000,archived_benchmark +Archived Haskell,,,,43,,371.300000000,archived_benchmark +Archived Haskell,,,,42,,339.400000000,archived_benchmark +Archived Haskell,,,,35,,101.400000000,archived_benchmark +Archived Haskell,,,,31,,339.800000000,archived_benchmark +Archived Haskell,,,,31,,200.300000000,archived_benchmark +Archived Haskell,,,,37,,198.200000000,archived_benchmark +Archived Haskell,,,,26,,4.090000000,archived_benchmark +Archived Haskell,,,,41,,231.500000000,archived_benchmark +Archived Haskell,,,,43,,90.390000000,archived_benchmark +Archived Haskell,,,,42,,129.600000000,archived_benchmark +Archived Haskell,,,,44,,203.500000000,archived_benchmark +Archived Haskell,,,,35,,42.310000000,archived_benchmark +Archived Haskell,,,,28,,11.360000000,archived_benchmark +Live Haskell,Operon,Operon,1,39,31,65.329,saturated +Live Haskell,Operon,Operon,2,48,34,246.738,saturated +Live Haskell,Operon,Operon,3,45,33,1480.4409999999998,saturated +Live Haskell,Operon,Operon,4,47,37,393.28999999999996,saturated +Live Haskell,Operon,Operon,5,49,37,301.294,saturated +Live Haskell,Operon,Operon,6,45,35,1790.443,saturated +Live Haskell,Operon,Operon,7,44,36,46.411,saturated +Live Haskell,Operon,Operon,8,49,39,81.535,saturated +Live Haskell,Operon,Operon,9,45,33,1352.33,saturated +Live Haskell,Operon,Operon,10,43,33,380.983,saturated +Live Haskell,Operon,Operon,11,41,31,3594.2059999999997,saturated +Live Haskell,Operon,Operon,12,48,32,2125.07,saturated +Live Haskell,Operon,Operon,13,41,35,54.144,saturated +Live Haskell,Operon,Operon,14,47,37,151.29899999999998,saturated +Live Haskell,Operon,Operon,15,45,29,754.6500000000001,saturated +Live Haskell,Operon,Operon,16,50,38,387.974,saturated +Live Haskell,Operon,Operon,17,45,37,1182.942,saturated +Live Haskell,Operon,Operon,18,45,31,2054.6639999999998,saturated +Live Haskell,Operon,Operon,19,41,35,68.841,saturated +Live Haskell,Operon,Operon,20,47,37,1465.374,saturated +Live Haskell,Operon,Operon,21,45,37,3641.356,saturated +Live Haskell,Operon,Operon,22,42,34,110.607,saturated +Live Haskell,Operon,Operon,23,45,37,201.139,saturated +Live Haskell,Operon,Operon,24,41,33,366.697,saturated +Live Haskell,Operon,Operon,25,45,33,1218.068,saturated +Live Haskell,Operon,Operon,26,41,33,4412.607999999999,saturated +Live Haskell,Operon,Operon,27,48,36,244.91299999999998,saturated +Live Haskell,Operon,Operon,28,45,33,929.767,saturated +Live Haskell,Operon,Operon,29,45,33,1005.7560000000001,saturated +Live Haskell,Operon,Operon,30,45,33,197.646,saturated +Live Haskell,GOMEA,GP-GOMEA,1,19,19,1608.662,saturated +Live Haskell,GOMEA,GP-GOMEA,2,17,17,291.779,saturated +Live Haskell,GOMEA,GP-GOMEA,3,17,17,290.49199999999996,saturated +Live Haskell,GOMEA,GP-GOMEA,4,19,19,1317.443,saturated +Live Haskell,GOMEA,GP-GOMEA,5,19,19,1635.3819999999998,saturated +Live Haskell,GOMEA,GP-GOMEA,6,19,17,657.273,saturated +Live Haskell,GOMEA,GP-GOMEA,25,16,16,292.588,saturated +Live Haskell,GOMEA,GP-GOMEA,26,1,1,0.348,saturated +Live Haskell,GOMEA,GP-GOMEA,27,1,1,0.32,saturated +Live Haskell,GOMEA,GP-GOMEA,28,21,21,1594.139,saturated +Live Haskell,GOMEA,GP-GOMEA,29,19,19,306.329,saturated +Live Haskell,GOMEA,GP-GOMEA,30,17,17,307.37199999999996,saturated +Live Haskell,EPLEX,EPLEX,1,29,22,536.438,saturated +Live Haskell,EPLEX,EPLEX,2,89,73,7.266,saturated +Live Haskell,EPLEX,EPLEX,3,64,48,302.601,saturated +Live Haskell,EPLEX,EPLEX,4,58,46,6.409,saturated +Live Haskell,EPLEX,EPLEX,5,67,54,661.822,saturated +Live Haskell,EPLEX,EPLEX,6,71,44,1034.526,saturated +Live Haskell,EPLEX,EPLEX,7,66,58,23.314999999999998,saturated +Live Haskell,EPLEX,EPLEX,8,51,43,30.43,saturated +Live Haskell,EPLEX,EPLEX,9,83,50,850.705,saturated +Live Haskell,EPLEX,EPLEX,10,37,24,9.313,saturated +Live Haskell,EPLEX,EPLEX,11,78,50,1333.088,saturated +Live Haskell,EPLEX,EPLEX,12,67,43,168.049,saturated +Live Haskell,GOMEA,GP-GOMEA,7,17,17,293.575,saturated +Live Haskell,GOMEA,GP-GOMEA,8,16,14,653.524,saturated +Live Haskell,GOMEA,GP-GOMEA,9,19,19,1311.402,saturated +Live Haskell,GOMEA,GP-GOMEA,10,14,14,254.963,saturated +Live Haskell,GOMEA,GP-GOMEA,11,17,17,299.165,saturated +Live Haskell,GOMEA,GP-GOMEA,12,20,18,451.718,saturated +Live Haskell,GOMEA,GP-GOMEA,13,16,14,612.305,saturated +Live Haskell,GOMEA,GP-GOMEA,14,19,17,620.408,saturated +Live Haskell,GOMEA,GP-GOMEA,15,19,19,1711.722,saturated +Live Haskell,GOMEA,GP-GOMEA,16,19,19,1373.9470000000001,saturated +Live Haskell,GOMEA,GP-GOMEA,17,21,21,1563.397,saturated +Live Haskell,GOMEA,GP-GOMEA,18,21,21,1590.5819999999999,saturated +Live Haskell,GOMEA,GP-GOMEA,19,21,19,807.5649999999999,saturated +Live Haskell,GOMEA,GP-GOMEA,20,17,17,307.69,saturated +Live Haskell,GOMEA,GP-GOMEA,21,17,17,301.305,saturated +Live Haskell,GOMEA,GP-GOMEA,22,17,17,294.59499999999997,saturated +Live Haskell,GOMEA,GP-GOMEA,23,19,19,1644.719,saturated +Live Haskell,GOMEA,GP-GOMEA,24,18,14,743.892,saturated +Live Haskell,EPLEX,EPLEX,13,29,27,2.592,saturated +Live Haskell,EPLEX,EPLEX,14,72,46,15.588,saturated +Live Haskell,EPLEX,EPLEX,15,55,36,92.545,saturated +Live Haskell,EPLEX,EPLEX,16,33,28,3.233,saturated +Live Haskell,EPLEX,EPLEX,17,67,45,1569.7369999999999,saturated +Live Haskell,EPLEX,EPLEX,18,59,57,112.905,saturated +Live Haskell,EPLEX,EPLEX,19,25,20,30.688,saturated +Live Haskell,EPLEX,EPLEX,20,66,46,2819.846,saturated +Live Haskell,EPLEX,EPLEX,21,43,29,1804.38,saturated +Live Haskell,EPLEX,EPLEX,22,32,27,14.822000000000001,saturated +Live Haskell,EPLEX,EPLEX,23,29,16,17.589000000000002,saturated +Live Haskell,EPLEX,EPLEX,24,85,57,183.134,saturated +Live Haskell,EPLEX,EPLEX,25,69,40,1490.616,saturated +Live Haskell,EPLEX,EPLEX,26,56,32,6.193,saturated +Live Haskell,EPLEX,EPLEX,27,32,22,38.96,saturated +Live Haskell,EPLEX,EPLEX,28,79,45,660.704,saturated +Live Haskell,EPLEX,EPLEX,29,55,49,23.256,saturated +Live Haskell,EPLEX,EPLEX,30,89,67,936.4879999999999,saturated +Live Haskell,FEAT,FEAT,19,196,102,7033.058,saturated +Live Haskell,FEAT,FEAT,20,151,129,5693.588,saturated +Live Haskell,FEAT,FEAT,21,125,107,5429.928999999999,saturated +Live Haskell,FEAT,FEAT,22,168,158,8960.52,saturated +Live Haskell,FEAT,FEAT,23,155,117,2908.0879999999997,saturated +Live Haskell,FEAT,FEAT,24,170,152,3797.662,saturated +Live Haskell,FEAT,FEAT,25,138,122,4579.621999999999,saturated +Live Haskell,FEAT,FEAT,26,179,165,4903.648999999999,saturated +Live Haskell,FEAT,FEAT,27,133,105,5060.751,saturated +Live Haskell,FEAT,FEAT,28,186,142,3299.164,saturated +Live Haskell,FEAT,FEAT,29,165,135,3724.513,saturated +Live Haskell,FEAT,FEAT,30,131,113,8674.763,saturated +Live Haskell,SBP,SBP,1,1,1,0.357,saturated +Live Haskell,SBP,SBP,2,30,26,1623.767,saturated +Live Haskell,SBP,SBP,3,28,26,1827.426,saturated +Live Haskell,SBP,SBP,4,10,10,3.0149999999999997,saturated +Live Haskell,SBP,SBP,5,31,29,3025.396,saturated +Live Haskell,SBP,SBP,6,1,1,0.367,saturated +Live Haskell,SBP,SBP,7,28,24,1012.72,saturated +Live Haskell,SBP,SBP,8,29,27,21.676000000000002,saturated +Live Haskell,SBP,SBP,9,29,25,528.854,saturated +Live Haskell,SBP,SBP,10,28,28,2671.439,saturated +Live Haskell,SBP,SBP,11,29,23,1527.794,saturated +Live Haskell,SBP,SBP,12,29,29,2537.798,saturated +Live Haskell,SBP,SBP,13,29,27,1065.06,saturated +Live Haskell,SBP,SBP,14,26,26,20.739,saturated +Live Haskell,SBP,SBP,15,29,27,1154.155,saturated +Live Haskell,SBP,SBP,16,26,26,438.303,saturated +Live Haskell,SBP,SBP,17,29,29,1693.189,saturated +Live Haskell,SBP,SBP,18,27,21,288.389,saturated +Live Haskell,SBP,SBP,19,28,28,12.546,saturated +Live Haskell,SBP,SBP,20,28,22,1098.771,saturated +Live Haskell,SBP,SBP,21,28,28,23.990000000000002,saturated +Live Haskell,SBP,SBP,22,31,29,1598.17,saturated +Live Haskell,SBP,SBP,23,29,29,667.135,saturated +Live Haskell,SBP,SBP,24,27,25,310.47,saturated +Live Haskell,FEAT,FEAT,1,217,185,4700.094,saturated +Live Haskell,FEAT,FEAT,2,116,114,8964.145,saturated +Live Haskell,FEAT,FEAT,3,194,160,4662.339,saturated +Live Haskell,FEAT,FEAT,4,142,110,6398.497,saturated +Live Haskell,FEAT,FEAT,5,269,231,7446.367,saturated +Live Haskell,FEAT,FEAT,6,191,163,4022.83,saturated +Live Haskell,FEAT,FEAT,7,191,157,8780.519999999999,saturated +Live Haskell,FEAT,FEAT,8,241,203,4747.16,saturated +Live Haskell,FEAT,FEAT,9,202,170,3436.1000000000004,saturated +Live Haskell,FEAT,FEAT,10,223,181,3742.037,saturated +Live Haskell,FEAT,FEAT,11,357,275,4493.65,saturated +Live Haskell,FEAT,FEAT,12,154,136,7617.788,saturated +Live Haskell,FEAT,FEAT,13,134,130,4183.656,saturated +Live Haskell,FEAT,FEAT,14,184,159,3993.773,saturated +Live Haskell,FEAT,FEAT,15,416,279,5598.429,saturated +Live Haskell,FEAT,FEAT,16,129,113,5647.898999999999,saturated +Live Haskell,FEAT,FEAT,17,174,114,2735.3360000000002,saturated +Live Haskell,FEAT,FEAT,18,160,144,5508.09,saturated +Live Haskell,SBP,SBP,25,29,29,136.163,saturated +Live Haskell,SBP,SBP,26,28,28,25.141000000000002,saturated +Live Haskell,SBP,SBP,27,27,25,110.67699999999999,saturated +Live Haskell,SBP,SBP,28,28,28,1928.367,saturated +Live Haskell,SBP,SBP,29,28,28,491.417,saturated +Live Haskell,SBP,SBP,30,28,26,132.452,saturated +Live Haskell,Bingo,Bingo,1,43,34,161.226,saturated +Live Haskell,Bingo,Bingo,2,23,19,137.132,saturated +Live Haskell,Bingo,Bingo,3,27,23,14.467,saturated +Live Haskell,Bingo,Bingo,4,49,40,185.827,saturated +Live Haskell,Bingo,Bingo,5,23,22,12.401,saturated +Live Haskell,Bingo,Bingo,6,53,43,191.67999999999998,saturated +Live Haskell,Bingo,Bingo,7,21,19,38.735,saturated +Live Haskell,Bingo,Bingo,8,20,20,1575.9479999999999,saturated +Live Haskell,Bingo,Bingo,9,31,27,568.3009999999999,saturated +Live Haskell,Bingo,Bingo,10,25,23,23.323,saturated +Live Haskell,Bingo,Bingo,11,24,22,2470.504,saturated +Live Haskell,Bingo,Bingo,12,15,13,1212.757,saturated +Live Haskell,Bingo,Bingo,13,33,29,32.252,saturated +Live Haskell,Bingo,Bingo,14,29,25,3188.18,saturated +Live Haskell,Bingo,Bingo,15,45,39,213.452,saturated +Live Haskell,Bingo,Bingo,16,47,42,1060.12,saturated +Live Haskell,Bingo,Bingo,17,49,36,868.6930000000001,saturated +Live Haskell,Bingo,Bingo,18,23,21,26.939999999999998,saturated +Live Haskell,Bingo,Bingo,19,25,23,57.342999999999996,saturated +Live Haskell,Bingo,Bingo,20,39,32,340.452,saturated +Live Haskell,Bingo,Bingo,21,43,33,267.963,saturated +Live Haskell,Bingo,Bingo,22,27,27,28.387,saturated +Live Haskell,Bingo,Bingo,23,27,23,1995.568,saturated +Live Haskell,Bingo,Bingo,24,29,21,39.910000000000004,saturated +Live Haskell,Bingo,Bingo,25,20,17,27.237000000000002,saturated +Live Haskell,Bingo,Bingo,26,16,16,4.484,saturated +Live Haskell,Bingo,Bingo,27,53,45,827.724,saturated +Live Haskell,Bingo,Bingo,28,41,37,133.738,saturated +Live Haskell,Bingo,Bingo,29,17,16,4.229,saturated +Live Haskell,Bingo,Bingo,30,27,25,54.53,saturated +Live Haskell,SRjl,PySR,19,42,36,1611.8809999999999,saturated +Live Haskell,SRjl,PySR,20,39,23,1505.0300000000002,saturated +Live Haskell,SRjl,PySR,21,33,23,1038.8690000000001,saturated +Live Haskell,SRjl,PySR,22,31,21,1360.3590000000002,saturated +Live Haskell,SRjl,PySR,23,39,19,1208.911,saturated +Live Haskell,SRjl,PySR,24,28,26,281.008,saturated +Live Haskell,SRjl,PySR,25,41,27,1574.154,saturated +Live Haskell,SRjl,PySR,26,45,39,542.3280000000001,saturated +Live Haskell,SRjl,PySR,27,42,34,1072.959,saturated +Live Haskell,SRjl,PySR,28,44,36,1363.402,saturated +Live Haskell,SRjl,PySR,29,35,29,249.337,saturated +Live Haskell,SRjl,PySR,30,28,26,27.695999999999998,saturated +Live Haskell,SRjl,PySR,1,46,34,1538.615,saturated +Live Haskell,SRjl,PySR,2,39,37,1534.084,saturated +Live Haskell,SRjl,PySR,3,35,31,57.991,saturated +Live Haskell,SRjl,PySR,4,41,31,2544.34,saturated +Live Haskell,SRjl,PySR,5,42,36,300.829,saturated +Live Haskell,SRjl,PySR,6,33,29,4011.863,saturated +Live Haskell,SRjl,PySR,7,28,24,574.1899999999999,saturated +Live Haskell,SRjl,PySR,8,39,31,3375.787,saturated +Live Haskell,SRjl,PySR,9,37,27,1667.841,saturated +Live Haskell,SRjl,PySR,10,38,30,703.514,saturated +Live Haskell,SRjl,PySR,11,33,27,42.230999999999995,saturated +Live Haskell,SRjl,PySR,12,41,33,2879.2219999999998,saturated +Live Haskell,SRjl,PySR,13,44,34,2146.1960000000004,saturated +Live Haskell,SRjl,PySR,14,43,37,660.914,saturated +Live Haskell,SRjl,PySR,15,41,35,1172.102,saturated +Live Haskell,SRjl,PySR,16,34,30,827.414,saturated +Live Haskell,SRjl,PySR,17,42,42,107.308,saturated +Live Haskell,SRjl,PySR,18,47,34,2381.748,saturated +Egglog,Operon,Operon,1,39,31,105.838791,saturated +Egglog,Operon,Operon,3,45,33,156.246958,saturated +Egglog,Operon,Operon,4,47,37,153.747166,saturated +Egglog,Operon,Operon,5,49,37,117.175500,saturated +Egglog,Operon,Operon,7,44,36,63.928250,saturated +Egglog,Operon,Operon,8,49,39,91.700291,saturated +Egglog,Operon,Operon,9,45,33,130.759417,saturated +Egglog,Operon,Operon,6,45,35,450.486458,saturated +Egglog,Operon,Operon,2,48,34,906.358708,saturated +Egglog,Operon,Operon,13,41,35,60.785208,saturated +Egglog,Operon,Operon,14,47,37,71.381083,saturated +Egglog,Operon,Operon,12,48,32,567.433833,saturated +Egglog,Operon,Operon,10,45,33,1269.690666,saturated +Egglog,Operon,Operon,17,45,37,141.148583,saturated +Egglog,Operon,Operon,16,50,36,779.861833,saturated +Egglog,Operon,Operon,19,41,35,59.188458,saturated +Egglog,Operon,Operon,15,45,29,1878.312667,saturated +Egglog,Operon,Operon,21,45,37,534.792500,saturated +Egglog,Operon,Operon,22,43,34,94.886291,saturated +Egglog,Operon,Operon,11,41,31,3208.953875,saturated +Egglog,Operon,Operon,24,41,33,73.659583,saturated +Egglog,Operon,Operon,23,45,37,97.936416,saturated +Egglog,Operon,Operon,25,45,33,156.988084,saturated +Egglog,Operon,Operon,26,41,33,217.740792,saturated +Egglog,Operon,Operon,28,45,33,133.859958,saturated +Egglog,Operon,Operon,29,45,33,139.886583,saturated +Egglog,Operon,Operon,30,45,33,83.274250,saturated +Egglog,GOMEA,GP-GOMEA,1,20,17,50.160667,saturated +Egglog,GOMEA,GP-GOMEA,2,20,17,49.523917,saturated +Egglog,GOMEA,GP-GOMEA,3,21,17,43.315083,saturated +Egglog,GOMEA,GP-GOMEA,4,20,17,49.965542,saturated +Egglog,GOMEA,GP-GOMEA,5,21,17,50.728333,saturated +Egglog,GOMEA,GP-GOMEA,6,18,17,42.698833,saturated +Egglog,GOMEA,GP-GOMEA,7,19,17,44.818166,saturated +Egglog,GOMEA,GP-GOMEA,8,19,14,73.878208,saturated +Egglog,Operon,Operon,27,48,36,849.791875,saturated +Egglog,GOMEA,GP-GOMEA,9,21,17,51.635583,saturated +Egglog,GOMEA,GP-GOMEA,10,19,14,51.388209,saturated +Egglog,GOMEA,GP-GOMEA,12,20,20,24.024250,saturated +Egglog,GOMEA,GP-GOMEA,11,21,17,43.533375,saturated +Egglog,GOMEA,GP-GOMEA,13,14,14,24.365125,saturated +Egglog,GOMEA,GP-GOMEA,14,19,17,48.070166,saturated +Egglog,GOMEA,GP-GOMEA,15,20,17,48.982083,saturated +Egglog,GOMEA,GP-GOMEA,16,20,17,49.962750,saturated +Egglog,GOMEA,GP-GOMEA,17,21,17,48.439750,saturated +Egglog,GOMEA,GP-GOMEA,18,21,17,45.059292,saturated +Egglog,GOMEA,GP-GOMEA,19,20,19,48.743000,saturated +Egglog,GOMEA,GP-GOMEA,20,21,17,44.484958,saturated +Egglog,GOMEA,GP-GOMEA,21,19,17,41.699667,saturated +Egglog,GOMEA,GP-GOMEA,22,21,17,45.342875,saturated +Egglog,GOMEA,GP-GOMEA,23,21,17,47.197291,saturated +Egglog,GOMEA,GP-GOMEA,25,18,16,50.141083,saturated +Egglog,GOMEA,GP-GOMEA,24,17,14,77.089625,saturated +Egglog,GOMEA,GP-GOMEA,26,19,1,34.941791,saturated +Egglog,GOMEA,GP-GOMEA,27,20,1,33.243708,saturated +Egglog,GOMEA,GP-GOMEA,29,19,19,46.383458,saturated +Egglog,GOMEA,GP-GOMEA,28,21,17,51.072792,saturated +Egglog,GOMEA,GP-GOMEA,30,21,17,49.021959,saturated +Egglog,EPLEX,EPLEX,2,93,89,58.228791,saturated +Egglog,EPLEX,EPLEX,1,49,23,140.629875,saturated +Egglog,EPLEX,EPLEX,3,74,58,54.098417,saturated +Egglog,EPLEX,EPLEX,4,65,52,49.693375,saturated +Egglog,EPLEX,EPLEX,5,73,57,83.567208,saturated +Egglog,EPLEX,EPLEX,7,72,64,60.095792,saturated +Egglog,EPLEX,EPLEX,8,64,47,55.362375,saturated +Egglog,EPLEX,EPLEX,9,73,53,56.438666,saturated +Egglog,EPLEX,EPLEX,10,37,31,40.343917,saturated +Egglog,EPLEX,EPLEX,11,81,62,71.635458,saturated +Egglog,EPLEX,EPLEX,12,74,44,62.351167,saturated +Egglog,EPLEX,EPLEX,13,29,29,23.275666,saturated +Egglog,EPLEX,EPLEX,14,72,51,50.519708,saturated +Egglog,EPLEX,EPLEX,15,69,43,52.980083,saturated +Egglog,EPLEX,EPLEX,16,33,29,45.851167,saturated +Egglog,EPLEX,EPLEX,17,61,53,54.531833,saturated +Egglog,Operon,Operon,20,47,35,3974.796834,saturated +Egglog,EPLEX,EPLEX,19,30,23,53.429708,saturated +Egglog,EPLEX,EPLEX,18,71,59,90.905500,saturated +Egglog,EPLEX,EPLEX,21,61,37,62.319875,saturated +Egglog,EPLEX,EPLEX,22,48,28,47.834791,saturated +Egglog,EPLEX,EPLEX,23,49,17,51.562584,saturated +Egglog,EPLEX,EPLEX,24,83,62,76.622958,saturated +Egglog,EPLEX,EPLEX,20,66,46,477.779041,saturated +Egglog,EPLEX,EPLEX,26,64,38,49.352333,saturated +Egglog,EPLEX,EPLEX,27,31,24,47.622250,saturated +Egglog,EPLEX,EPLEX,28,73,48,59.021000,saturated +Egglog,EPLEX,EPLEX,29,67,53,61.951208,saturated +Egglog,EPLEX,EPLEX,30,83,67,51.955375,saturated +Egglog,EPLEX,EPLEX,6,73,45,1812.553209,saturated +Egglog,EPLEX,EPLEX,25,96,45,3099.679291,saturated +Egglog,FEAT,FEAT,2,116,114,2675.306709,saturated +Egglog,FEAT,FEAT,4,142,112,2369.962625,saturated +Egglog,Operon,Operon,18,45,31,12270.911958,saturated +Egglog,FEAT,FEAT,1,217,187,10940.644916,saturated +Egglog,FEAT,FEAT,6,191,163,4250.472250,saturated +Egglog,FEAT,FEAT,5,269,227,10069.516125,saturated +Egglog,FEAT,FEAT,7,191,157,4784.424750,saturated +Egglog,FEAT,FEAT,3,194,160,13164.997500,saturated +Egglog,FEAT,FEAT,11,357,271,18099.805791,saturated +Egglog,FEAT,FEAT,9,202,172,18838.350250,saturated +Egglog,FEAT,FEAT,13,134,130,5357.171500,saturated +Egglog,FEAT,FEAT,12,154,136,8365.361084,saturated +Egglog,FEAT,FEAT,10,223,183,27856.841625,saturated +Egglog,FEAT,FEAT,14,184,159,7148.111458,saturated +Egglog,FEAT,FEAT,16,129,113,5335.383000,saturated +Egglog,FEAT,FEAT,8,241,203,39041.561125,saturated +Egglog,FEAT,FEAT,18,160,146,1906.356958,saturated +Egglog,FEAT,FEAT,20,151,129,1866.408500,saturated +Egglog,FEAT,FEAT,19,242,104,4575.022417,saturated +Egglog,FEAT,FEAT,22,168,158,3761.840625,saturated +Egglog,FEAT,FEAT,21,125,107,6844.487500,saturated +Egglog,FEAT,FEAT,17,174,116,14500.616917,saturated +Egglog,FEAT,FEAT,23,155,115,2968.172833,saturated +Egglog,FEAT,FEAT,25,138,122,4822.483750,saturated +Egglog,FEAT,FEAT,27,133,103,5166.333334,saturated +Egglog,FEAT,FEAT,15,416,279,29904.225375,saturated +Egglog,FEAT,FEAT,26,196,167,11262.057416,saturated +Egglog,FEAT,FEAT,24,170,152,15092.015583,saturated +Egglog,SBP,SBP,1,29,1,143.359542,saturated +Egglog,SBP,SBP,2,28,26,63.196000,saturated +Egglog,SBP,SBP,3,28,28,30.644417,saturated +Egglog,SBP,SBP,4,10,10,20.247375,saturated +Egglog,SBP,SBP,5,29,29,295.455167,saturated +Egglog,SBP,SBP,6,26,1,37.939000,saturated +Egglog,SBP,SBP,7,28,26,62.636542,saturated +Egglog,SBP,SBP,8,29,27,48.170167,saturated +Egglog,SBP,SBP,9,29,25,76.428709,saturated +Egglog,SBP,SBP,10,29,28,91.023416,saturated +Egglog,SBP,SBP,11,29,27,56.085625,saturated +Egglog,SBP,SBP,12,29,29,60.574750,saturated +Egglog,FEAT,FEAT,29,165,135,5571.941250,saturated +Egglog,SBP,SBP,14,27,26,53.534417,saturated +Egglog,FEAT,FEAT,30,131,113,4763.681125,saturated +Egglog,SBP,SBP,15,29,27,85.899000,saturated +Egglog,SBP,SBP,16,29,26,63.513167,saturated +Egglog,SBP,SBP,17,29,29,99.489083,saturated +Egglog,SBP,SBP,18,28,21,81.509875,saturated +Egglog,SBP,SBP,19,28,28,20.980417,saturated +Egglog,SBP,SBP,21,28,28,41.260125,saturated +Egglog,SBP,SBP,22,29,29,54.594250,saturated +Egglog,SBP,SBP,20,29,24,137.537458,saturated +Egglog,SBP,SBP,23,29,29,54.618333,saturated +Egglog,SBP,SBP,25,29,29,226.535583,saturated +Egglog,SBP,SBP,26,29,28,67.517708,saturated +Egglog,SBP,SBP,27,29,25,73.296375,saturated +Egglog,SBP,SBP,28,28,28,70.379792,saturated +Egglog,SBP,SBP,29,28,28,30.618459,saturated +Egglog,SBP,SBP,24,29,25,552.809500,saturated +Egglog,SBP,SBP,30,28,26,89.657458,saturated +Egglog,Bingo,Bingo,1,40,36,62.702958,saturated +Egglog,Bingo,Bingo,3,34,24,43.909500,saturated +Egglog,Bingo,Bingo,2,22,18,73.117166,saturated +Egglog,Bingo,Bingo,5,21,21,25.035625,saturated +Egglog,Bingo,Bingo,4,50,40,72.459500,saturated +Egglog,Bingo,Bingo,7,27,19,51.864125,saturated +Egglog,Bingo,Bingo,6,52,44,83.785250,saturated +Egglog,Bingo,Bingo,8,19,19,57.882584,saturated +Egglog,Bingo,Bingo,9,29,25,60.111417,saturated +Egglog,Bingo,Bingo,10,23,21,54.424917,saturated +Egglog,Bingo,Bingo,11,22,20,58.281750,saturated +Egglog,Bingo,Bingo,13,32,32,49.131041,saturated +Egglog,Bingo,Bingo,12,15,12,58.248917,saturated +Egglog,Bingo,Bingo,14,28,28,31.387791,saturated +Egglog,Bingo,Bingo,16,48,44,242.608167,saturated +Egglog,Bingo,Bingo,15,44,38,419.521667,saturated +Egglog,Bingo,Bingo,18,21,19,59.497542,saturated +Egglog,Bingo,Bingo,19,23,21,62.785208,saturated +Egglog,Bingo,Bingo,20,46,32,424.360833,saturated +Egglog,FEAT,FEAT,28,186,146,8980.431833,saturated +Egglog,Bingo,Bingo,22,26,26,24.990458,saturated +Egglog,Bingo,Bingo,23,26,26,38.838208,saturated +Egglog,Bingo,Bingo,24,28,22,44.786584,saturated +Egglog,Bingo,Bingo,21,37,27,365.354833,saturated +Egglog,Bingo,Bingo,26,15,15,21.652583,saturated +Egglog,Bingo,Bingo,25,18,16,43.366667,saturated +Egglog,Bingo,Bingo,28,37,37,47.020583,saturated +Egglog,Bingo,Bingo,29,15,15,32.776375,saturated +Egglog,Bingo,Bingo,30,25,23,64.492542,saturated +Egglog,Bingo,Bingo,27,52,50,170.342292,saturated +Egglog,SRjl,PySR,2,41,37,100.255583,saturated +Egglog,SRjl,PySR,3,39,31,67.543333,saturated +Egglog,Bingo,Bingo,17,58,36,3333.434542,saturated +Egglog,SRjl,PySR,4,40,31,2459.031166,saturated +Egglog,SRjl,PySR,5,42,36,609.322666,saturated +Egglog,SRjl,PySR,6,32,29,100.721792,saturated +Egglog,SRjl,PySR,7,37,24,58.742167,saturated +Egglog,SRjl,PySR,8,40,31,146.059417,saturated +Egglog,SRjl,PySR,9,37,27,132.030833,saturated +Egglog,SRjl,PySR,11,35,27,56.076750,saturated +Egglog,SRjl,PySR,10,45,30,74.886125,saturated +Egglog,SRjl,PySR,13,44,36,460.011500,saturated +Egglog,SRjl,PySR,14,43,37,62.262708,saturated +Egglog,SRjl,PySR,15,43,33,2958.407042,saturated +Egglog,SRjl,PySR,12,41,33,4074.732625,saturated +Egglog,SRjl,PySR,17,44,42,102.848750,saturated +Egglog,SRjl,PySR,18,44,43,125.789666,saturated +Egglog,SRjl,PySR,19,44,36,147.283542,saturated +Egglog,SRjl,PySR,16,45,30,1341.010291,saturated +Egglog,SRjl,PySR,21,31,23,74.662458,saturated +Egglog,SRjl,PySR,1,44,34,8812.673666,saturated +Egglog,SRjl,PySR,20,42,23,1928.663083,saturated +Egglog,SRjl,PySR,24,29,26,50.395416,saturated +Egglog,SRjl,PySR,23,38,19,1121.870250,saturated +Egglog,SRjl,PySR,26,45,39,599.320542,saturated +Egglog,SRjl,PySR,22,41,21,2772.032042,saturated +Egglog,SRjl,PySR,27,45,34,165.503959,saturated +Egglog,SRjl,PySR,29,43,29,59.976375,saturated +Egglog,SRjl,PySR,30,28,26,47.211542,saturated +Egglog,SRjl,PySR,28,45,36,1329.933167,saturated +Egglog,SRjl,PySR,25,41,27,7912.424375,saturated +Egglog,SBP,SBP,13,29,27,41802.704584,saturated diff --git a/python/egglog/exp/param_eq/artifacts/pagie_runtime_scatter.csv b/python/egglog/exp/param_eq/artifacts/pagie_runtime_scatter.csv new file mode 100644 index 00000000..b1b49f1e --- /dev/null +++ b/python/egglog/exp/param_eq/artifacts/pagie_runtime_scatter.csv @@ -0,0 +1,214 @@ +benchmark_name,node_count,runtime_ms +Egg/45,45,212.200000000 +Egg/41,41,16.150000000 +Egg/34,34,193.600000000 +Egg/48,48,717.900000000 +Egg/37,37,26.040000000 +Egg/45,45,199.100000000 +Egg/25,25,117.200000000 +Egg/38,38,186.800000000 +Egg/41,41,23.130000000 +Egg/44,44,51.680000000 +Egg/40,40,160.200000000 +Egg/25,25,5.692000000 +Egg/43,43,92.390000000 +Egg/44,44,271.000000000 +Egg/32,32,89.710000000 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b/python/egglog/exp/param_eq/generate_haskell_golden.py new file mode 100644 index 00000000..0a4261bf --- /dev/null +++ b/python/egglog/exp/param_eq/generate_haskell_golden.py @@ -0,0 +1,457 @@ +"""Regenerate Haskell-backed golden cases for the retained param-eq baseline.""" + +from __future__ import annotations + +import ast +import csv +import json +import math +import os +import subprocess +import tempfile +from dataclasses import dataclass +from pathlib import Path +from typing import Any + +from egglog.exp.param_eq.paths import ARTIFACT_DIR, GOLDEN_PATH, REPO_ROOT, llvm_bin_dir, param_eq_data_dir +from egglog.exp.param_eq.pipeline import parse_expression, render_num + +HASKELL_ROOT = param_eq_data_dir() + + +@dataclass(frozen=True) +class GoldenCaseSpec: + case_id: str + category: str + source: str + notes: str + compare_root_analysis: bool = True + compare_rewrite_tree: bool = True + compare_simplify_e: bool = True + compare_simplify_e_render: bool = True + compare_param_count: bool = True + expected_mismatch: bool = False + + +def _corpus_case( + dataset: str, + algorithm: str, + algo_row: str, + *, + notes: str, + expected_mismatch: bool, + compare_simplify_e_render: bool = True, +) -> GoldenCaseSpec: + with (ARTIFACT_DIR / "haskell_paper_rows.csv").open() as handle: + rows = list(csv.DictReader(handle)) + for row in rows: + if row["dataset"] == dataset and row["algorithm"] == algorithm and row["algo_row"] == algo_row: + return GoldenCaseSpec( + case_id=f"{dataset}_{algorithm.lower()}_{algo_row}", + category="corpus", + source=row["original_expr"], + notes=notes, + compare_root_analysis=not expected_mismatch, + compare_rewrite_tree=not expected_mismatch, + compare_simplify_e=not expected_mismatch, + compare_simplify_e_render=compare_simplify_e_render and not expected_mismatch, + compare_param_count=not expected_mismatch, + expected_mismatch=expected_mismatch, + ) + msg = f"Missing corpus canary {dataset=} {algorithm=} {algo_row=}" + raise ValueError(msg) + + +CASE_SPECS: tuple[GoldenCaseSpec, ...] = ( + GoldenCaseSpec( + case_id="x_minus_x", + category="analysis", + source="x0 - x0", + notes="Mixed class stays non-constant even after 0 is introduced.", + ), + GoldenCaseSpec( + case_id="two_minus_two", + category="analysis", + source="2 - 2", + notes="Purely constant class prunes to the constant leaf.", + ), + GoldenCaseSpec( + case_id="x_div_x", + category="analysis", + source="x0 / x0", + notes="Mixed class stays non-constant even after 1 is introduced.", + ), + GoldenCaseSpec( + case_id="two_div_two", + category="analysis", + source="2 / 2", + notes="Purely constant division prunes to 1.", + ), + GoldenCaseSpec( + case_id="zero_div_x", + category="analysis", + source="0 / x0", + notes="Identity rewrite reaches 0 for any denominator shape.", + ), + GoldenCaseSpec( + case_id="zero_mul_x", + category="analysis", + source="0 * x0", + notes="Identity rewrite reaches 0 for any multiplicand shape.", + compare_root_analysis=False, + compare_rewrite_tree=False, + compare_simplify_e=False, + compare_param_count=False, + ), + GoldenCaseSpec( + case_id="log_mul_const_var", + category="guards", + source="log(2 * x0)", + notes="Covers the Haskell log-product guard bundle.", + ), + GoldenCaseSpec( + case_id="log_div_const_var", + category="guards", + source="log(2 / x0)", + notes="Covers the Haskell log-division guard bundle.", + ), + GoldenCaseSpec( + case_id="log_exp_var", + category="guards", + source="log(exp(x0))", + notes="Only fires for a non-constant argument.", + ), + GoldenCaseSpec( + case_id="exp_log_var", + category="guards", + source="exp(log(x0))", + notes="Only fires for a non-constant argument.", + ), + GoldenCaseSpec( + case_id="sqrt_negative_times_difference", + category="guards", + source="sqrt((-2.0) * (x0 - x1))", + notes="Covers the negative-a square-root rewrite shape.", + ), + GoldenCaseSpec( + case_id="x_mul_inverse_x", + category="guards", + source="x0 * (1 / x0)", + notes="Uses the same non-zero guard as x / x.", + compare_root_analysis=False, + compare_rewrite_tree=False, + compare_simplify_e=False, + compare_param_count=False, + ), + GoldenCaseSpec( + case_id="negative_const_div_self", + category="guards", + source="(-2) / (-2)", + notes="Negative constants still satisfy is_not_zero.", + ), + GoldenCaseSpec( + case_id="negative_const_pow_two", + category="analysis", + source="(-2) ** 2", + notes="Haskell folds negative-base powers with integer exponents.", + ), + GoldenCaseSpec( + case_id="negative_const_pow_three", + category="analysis", + source="(-2) ** 3", + notes="Haskell folds negative-base powers with integer exponents.", + ), + GoldenCaseSpec( + case_id="negative_const_pow_var", + category="analysis", + source="(-2) ** x0", + notes="Negative-base powers with non-constant exponents remain non-constant.", + compare_rewrite_tree=False, + ), + GoldenCaseSpec( + case_id="sbp_zero_times_quadratic", + category="schedule", + source="0.004376 - (0.0 * (x1 * x1))", + notes="Retired as a direct-Haskell parity canary: live Haskell extracts `x1`, while the explicit-analysis Egglog loop reaches the semantically constant form.", + compare_root_analysis=False, + compare_rewrite_tree=False, + compare_simplify_e=False, + compare_simplify_e_render=False, + compare_param_count=False, + ), + GoldenCaseSpec( + case_id="x0_sq_plus_x1_sq", + category="schedule", + source="(((51.6682472229003906 * x0) * ((-0.0001894439337775) * x0)) + ((0.0012052881065756 * x1) * ((-8.2380609512329102) * x1)))", + notes="Reduced Haskell-backed schedule canary for the direct Haskell-style inner loop.", + ), + GoldenCaseSpec( + case_id="sub_add_left_assoc", + category="extraction", + source="x0 - (x0 + x1)", + notes="Haskell and Python keep semantically equivalent but different extracted subtraction normal forms.", + compare_root_analysis=False, + compare_param_count=False, + expected_mismatch=True, + ), + GoldenCaseSpec( + case_id="nonconstant_power_exponent_count", + category="reporting", + source="(2.0 ** x0) + (x1 ** (x0 + 3.0))", + notes="Constants count as parameters, but non-constant exponents are still traversed.", + compare_root_analysis=False, + compare_rewrite_tree=False, + compare_simplify_e=False, + ), + _corpus_case( + "pagie", + "SBP", + "1", + notes="Current direct-Haskell baseline mismatch: explicit saturated analysis drives this row to a different endpoint than live Haskell.", + expected_mismatch=True, + compare_simplify_e_render=False, + ), + _corpus_case( + "pagie", + "Operon", + "15", + notes="Large corpus canary for the direct Haskell-style baseline; this should now match current FixTree.hs again.", + expected_mismatch=False, + ), +) + + +def _source_to_haskell_expr(source: str) -> str: + tree = ast.parse(source.replace("^", "**"), mode="eval") + + def const(value: float) -> str: + rendered = repr(float(value)) + if float(value) < 0.0 or math.copysign(1.0, float(value)) < 0.0: + return f"(Const ({rendered}))" + return f"(Const {rendered})" + + def emit(node: ast.AST) -> str: + if isinstance(node, ast.Expression): + return emit(node.body) + if isinstance(node, ast.Constant) and isinstance(node.value, int | float): + return const(float(node.value)) + if isinstance(node, ast.Name): + if node.id.startswith("x") and node.id[1:].isdigit(): + return f"(Var {int(node.id[1:])})" + msg = f"Unsupported variable name: {node.id!r}" + raise ValueError(msg) + if isinstance(node, ast.UnaryOp) and isinstance(node.op, ast.USub): + if isinstance(node.operand, ast.Constant) and isinstance(node.operand.value, int | float): + return const(float(-node.operand.value)) + return f"(Mul {const(-1.0)} {emit(node.operand)})" + if isinstance(node, ast.BinOp): + lhs = emit(node.left) + rhs = emit(node.right) + match node.op: + case ast.Add(): + return f"(Add {lhs} {rhs})" + case ast.Sub(): + return f"(Sub {lhs} {rhs})" + case ast.Mult(): + return f"(Mul {lhs} {rhs})" + case ast.Div(): + return f"(Div {lhs} {rhs})" + case ast.Pow(): + return f"(Power {lhs} {rhs})" + msg = f"Unsupported binary operator: {ast.dump(node.op)}" + raise TypeError(msg) + if isinstance(node, ast.Call) and isinstance(node.func, ast.Name): + args = [emit(arg) for arg in node.args] + match node.func.id: + case "exp": + return f"(Fun Exp {args[0]})" + case "log": + return f"(Fun Log {args[0]})" + case "sqrt": + return f"(Fun Sqrt {args[0]})" + case "abs": + return f"(Fun Abs {args[0]})" + case "plog": + return f"(Fun Log (Fun Abs {args[0]}))" + case "square": + return f"(Power {args[0]} (Const 2.0))" + case "cube": + return f"(Power {args[0]} (Const 3.0))" + msg = f"Unsupported function call: {node.func.id}" + raise ValueError(msg) + msg = f"Unsupported AST node: {ast.dump(node)}" + raise TypeError(msg) + + return emit(tree) + + +def _normalize_haskell_pretty(expr: str) -> str: + replacements = { + "Log(": "log(", + "Exp(": "exp(", + "Sqrt(": "sqrt(", + "Abs(": "abs(", + "^": "**", + } + normalized = expr + for old, new in replacements.items(): + normalized = normalized.replace(old, new) + return normalized + + +def _canonicalize(expr: str) -> str: + return render_num(parse_expression(_normalize_haskell_pretty(expr))) + + +def _parse_analysis(text: str) -> dict[str, Any]: + if text == "Nothing": + return {"kind": "none", "value": None} + if text.startswith("Just "): + value_text = text.removeprefix("Just ").strip() + if value_text.startswith("(") and value_text.endswith(")"): + value_text = value_text[1:-1] + return {"kind": "some", "value": float(value_text)} + msg = f"Unexpected Haskell analysis output: {text!r}" + raise ValueError(msg) + + +def _build_haskell_program(cases: list[GoldenCaseSpec]) -> str: + case_lines = [] + for index, case in enumerate(cases): + source_literal = json.dumps(case.source) + prefix = " " if index == 0 else " , " + case_lines.append(f'{prefix}("{case.case_id}", {source_literal}, {_source_to_haskell_expr(case.source)})') + joined_case_lines = "\n".join(case_lines) + return "\n".join([ + "import Data.List (intercalate, sort)", + "import qualified Data.Set as S", + "import Data.SRTree", + "import Data.SRTree.Print", + "import FixTree", + "import Reparam (replaceConstsWithParams)", + "import qualified Data.Equality.Graph.Lens as L", + "import Data.Equality.Graph.Lens hiding ((^.))", + "import Data.Equality.Graph.Monad", + "import Data.Equality.Saturation", + "import Data.Equality.Saturation.Scheduler", + "import Data.Equality.Extraction", + "", + "cases :: [(String, String, SRTree Int Double)]", + "cases =", + " [", + joined_case_lines, + " ]", + "", + "sanitize :: String -> String", + "sanitize = map (\\c -> if c == '\\t' || c == '\\n' then ' ' else c)", + "", + "emitCase :: (String, String, SRTree Int Double) -> IO ()", + "emitCase (caseId, source, expr) = do", + " let ((root, beforeData, afterData, afterNodes), egr) =", + " egraph $ do", + " root <- represent (toFixTree expr)", + " beforeData <- gets (L.^. _class root._data)", + " runEqualitySaturation (BackoffScheduler 2500 30) (rewritesBasic <> rewritesFun)", + " afterData <- gets (L.^. _class root._data)", + " afterNodes <- gets (L.^. _class root._nodes)", + " pure (root, beforeData, afterData, afterNodes)", + " rewriteTreeExpr = relabelParams . toSRTree $ extractBest egr cost2 root", + " simplifiedExpr = simplifyE expr", + " paramCount = recountParams . replaceConstsWithParams $ simplifiedExpr", + " fields =", + " [ caseId", + " , source", + " , show beforeData", + " , show afterData", + " , show (sort (map show (S.toList afterNodes)))", + " , showDefault rewriteTreeExpr", + " , showDefault simplifiedExpr", + " , show paramCount", + " ]", + ' putStrLn (intercalate "\\t" (map sanitize fields))', + "", + "main :: IO ()", + "main = mapM_ emitCase cases", + "", + ]) + + +def _run_haskell_cases(cases: list[GoldenCaseSpec]) -> list[dict[str, Any]]: + program = _build_haskell_program(cases) + with tempfile.NamedTemporaryFile("w", suffix=".hs", delete=False) as handle: + handle.write(program) + temp_path = Path(handle.name) + try: + env = dict(os.environ) + llvm_bin = llvm_bin_dir() + if llvm_bin is not None: + env["PATH"] = f"{llvm_bin}:{env['PATH']}" + output = subprocess.check_output( + ["stack", "exec", "--", "runghc", "-isrc", str(temp_path)], + cwd=HASKELL_ROOT, + env=env, + text=True, + timeout=180, + ) + finally: + temp_path.unlink(missing_ok=True) + + results = [] + for line in output.splitlines(): + ( + case_id, + source, + analysis_before, + analysis_after, + after_nodes, + rewrite_tree_expr, + simplify_e_expr, + param_count, + ) = line.split( + "\t", + maxsplit=7, + ) + results.append({ + "case_id": case_id, + "source": source, + "analysis_before": _parse_analysis(analysis_before), + "analysis_after": _parse_analysis(analysis_after), + "after_nodes_haskell": ast.literal_eval(after_nodes), + "rewrite_tree_expr_haskell": rewrite_tree_expr, + "rewrite_tree_expr_python": _canonicalize(rewrite_tree_expr), + "simplify_e_expr_haskell": simplify_e_expr, + "simplify_e_expr_python": _canonicalize(simplify_e_expr), + "simplify_e_param_count": int(param_count), + }) + return results + + +def main() -> None: + haskell_rows = {row["case_id"]: row for row in _run_haskell_cases(list(CASE_SPECS))} + portable_source = os.path.relpath(HASKELL_ROOT / "src" / "FixTree.hs", REPO_ROOT) + portable_generator = os.path.relpath(Path(__file__).resolve(), REPO_ROOT) + payload: dict[str, Any] = { + "source_of_truth": portable_source, + "generator": portable_generator, + "cases": [], + } + for case in CASE_SPECS: + payload["cases"].append({ + "case_id": case.case_id, + "category": case.category, + "source": case.source, + "notes": case.notes, + "compare_root_analysis": case.compare_root_analysis, + "compare_rewrite_tree": case.compare_rewrite_tree, + "compare_simplify_e": case.compare_simplify_e, + "compare_simplify_e_render": case.compare_simplify_e_render, + "compare_param_count": case.compare_param_count, + "expected_mismatch": case.expected_mismatch, + **haskell_rows[case.case_id], + }) + GOLDEN_PATH.write_text(json.dumps(payload, indent=2, sort_keys=False) + "\n") + print(GOLDEN_PATH) + + +if __name__ == "__main__": + main() diff --git a/python/egglog/exp/param_eq/haskell_golden.json b/python/egglog/exp/param_eq/haskell_golden.json new file mode 100644 index 00000000..f31fa1fe --- /dev/null +++ b/python/egglog/exp/param_eq/haskell_golden.json @@ -0,0 +1,1833 @@ +{ + "source_of_truth": "../param-eq-haskell/src/FixTree.hs", + "generator": "python/egglog/exp/param_eq/generate_haskell_golden.py", + "cases": [ + { + "case_id": "x_minus_x", + "category": "analysis", + "source": "x0 - x0", + "notes": "Mixed class stays non-constant even after 0 is introduced.", + "compare_root_analysis": true, + "compare_rewrite_tree": true, + "compare_simplify_e": true, + "compare_simplify_e_render": true, + "compare_param_count": true, + "expected_mismatch": false, + "analysis_before": { + "kind": "none", + "value": null + }, + "analysis_after": { + "kind": "none", + "value": null + }, + "after_nodes_haskell": [ + "ConstF 0.0", + "SubF 1 1" + ], + "rewrite_tree_expr_haskell": "(x0) - (x0)", + "rewrite_tree_expr_python": "(x0 - x0)", + "simplify_e_expr_haskell": "(x0) - (x0)", + "simplify_e_expr_python": "(x0 - x0)", + "simplify_e_param_count": 0 + }, + { + "case_id": "two_minus_two", + "category": "analysis", + "source": "2 - 2", + "notes": "Purely constant class prunes to the constant leaf.", + "compare_root_analysis": true, + "compare_rewrite_tree": true, + "compare_simplify_e": true, + "compare_simplify_e_render": true, + "compare_param_count": true, + "expected_mismatch": false, + "analysis_before": { + "kind": "some", + "value": 0.0 + }, + "analysis_after": { + "kind": "some", + "value": 0.0 + }, + "after_nodes_haskell": [ + "ConstF 0.0" + ], + "rewrite_tree_expr_haskell": "0.0", + "rewrite_tree_expr_python": "0.0", + "simplify_e_expr_haskell": "0.0", + "simplify_e_expr_python": "0.0", + "simplify_e_param_count": 1 + }, + { + "case_id": "x_div_x", + "category": "analysis", + "source": "x0 / x0", + "notes": "Mixed class stays non-constant even after 1 is introduced.", + "compare_root_analysis": true, + "compare_rewrite_tree": true, + "compare_simplify_e": true, + "compare_simplify_e_render": true, + "compare_param_count": true, + "expected_mismatch": false, + "analysis_before": { + "kind": "none", + "value": null + }, + "analysis_after": { + "kind": "none", + "value": null + }, + "after_nodes_haskell": [ + "ConstF 1.0", + "DivF 1 1" + ], + "rewrite_tree_expr_haskell": "(x0) / (x0)", + "rewrite_tree_expr_python": "(x0 / x0)", + "simplify_e_expr_haskell": "(x0) / (x0)", + "simplify_e_expr_python": "(x0 / x0)", + "simplify_e_param_count": 0 + }, + { + "case_id": "two_div_two", + "category": "analysis", + "source": "2 / 2", + "notes": "Purely constant division prunes to 1.", + "compare_root_analysis": true, + "compare_rewrite_tree": true, + "compare_simplify_e": true, + "compare_simplify_e_render": true, + "compare_param_count": true, + "expected_mismatch": false, + "analysis_before": { + "kind": "some", + "value": 1.0 + }, + "analysis_after": { + "kind": "some", + "value": 1.0 + }, + "after_nodes_haskell": [ + "ConstF 1.0" + ], + "rewrite_tree_expr_haskell": "1.0", + "rewrite_tree_expr_python": "1.0", + "simplify_e_expr_haskell": "1.0", + "simplify_e_expr_python": "1.0", + "simplify_e_param_count": 1 + }, + { + "case_id": "zero_div_x", + "category": "analysis", + "source": "0 / x0", + "notes": "Identity rewrite reaches 0 for any denominator shape.", + "compare_root_analysis": true, + "compare_rewrite_tree": true, + "compare_simplify_e": true, + "compare_simplify_e_render": true, + "compare_param_count": true, + "expected_mismatch": false, + "analysis_before": { + "kind": "none", + "value": null + }, + "analysis_after": { + "kind": "none", + "value": null + }, + "after_nodes_haskell": [ + "ConstF 0.0", + "DivF 1 2" + ], + "rewrite_tree_expr_haskell": "0.0", + "rewrite_tree_expr_python": "0.0", + "simplify_e_expr_haskell": "0.0", + "simplify_e_expr_python": "0.0", + "simplify_e_param_count": 1 + }, + { + "case_id": "zero_mul_x", + "category": "analysis", + "source": "0 * x0", + "notes": "Identity rewrite reaches 0 for any multiplicand shape.", + "compare_root_analysis": false, + "compare_rewrite_tree": false, + "compare_simplify_e": false, + "compare_simplify_e_render": true, + "compare_param_count": false, + "expected_mismatch": false, + "analysis_before": { + "kind": "none", + "value": null + }, + "analysis_after": { + "kind": "none", + "value": null + }, + "after_nodes_haskell": [ + "ConstF 0.0", + "MulF 1 10", + "MulF 1 12", + "MulF 1 120", + "MulF 1 122", + "MulF 1 124", + "MulF 1 126", + "MulF 1 130", + "MulF 1 132", + "MulF 1 136", + "MulF 1 138", + "MulF 1 140", + "MulF 1 142", + "MulF 1 144", + "MulF 1 146", + "MulF 1 150", + "MulF 1 152", + "MulF 1 156", + "MulF 1 158", + "MulF 1 180", + "MulF 1 182", + "MulF 1 184", + "MulF 1 186", + "MulF 1 19", + "MulF 1 190", + "MulF 1 192", + "MulF 1 196", + "MulF 1 198", + "MulF 1 2", + "MulF 1 200", + "MulF 1 202", + "MulF 1 204", + "MulF 1 206", + "MulF 1 21", + "MulF 1 210", + "MulF 1 212", + "MulF 1 216", + "MulF 1 218", + "MulF 1 23", + "MulF 1 25", + "MulF 1 27", + "MulF 1 29", + "MulF 1 31", + "MulF 1 33", + "MulF 1 35", + "MulF 1 37", + "MulF 1 39", + "MulF 1 5", + "MulF 1 62", + "MulF 1 72", + "MulF 1 74", + "MulF 1 78", + "MulF 1 8", + "MulF 1 80", + "MulF 1 84", + "MulF 1 86", + "MulF 1 90", + "MulF 1 92", + "MulF 1 96", + "MulF 1 98", + "MulF 10 1", + "MulF 100 1", + "MulF 102 1", + "MulF 104 1", + "MulF 106 1", + "MulF 108 1", + "MulF 110 1", + "MulF 112 1", + "MulF 114 1", + "MulF 116 1", + "MulF 118 1", + "MulF 12 1", + "MulF 120 1", + "MulF 122 1", + "MulF 124 1", + "MulF 126 1", + "MulF 128 1", + "MulF 130 1", + "MulF 132 1", + "MulF 134 1", + "MulF 136 1", + "MulF 138 1", + "MulF 140 1", + "MulF 142 1", + "MulF 144 1", + "MulF 146 1", + "MulF 148 1", + "MulF 150 1", + "MulF 152 1", + "MulF 154 1", + "MulF 156 1", + "MulF 158 1", + "MulF 160 1", + "MulF 162 1", + "MulF 164 1", + "MulF 166 1", + "MulF 168 1", + "MulF 17 1", + "MulF 170 1", + "MulF 172 1", + "MulF 174 1", + "MulF 176 1", + "MulF 178 1", + "MulF 180 1", + "MulF 182 1", + "MulF 184 1", + "MulF 186 1", + "MulF 188 1", + "MulF 19 1", + "MulF 190 1", + "MulF 192 1", + "MulF 194 1", + "MulF 196 1", + "MulF 198 1", + "MulF 2 1", + "MulF 200 1", + "MulF 202 1", + "MulF 204 1", + "MulF 206 1", + "MulF 208 1", + "MulF 21 1", + "MulF 210 1", + "MulF 212 1", + "MulF 214 1", + "MulF 216 1", + "MulF 218 1", + "MulF 23 1", + "MulF 25 1", + "MulF 27 1", + "MulF 29 1", + "MulF 31 1", + "MulF 33 1", + "MulF 35 1", + "MulF 37 1", + "MulF 39 1", + "MulF 5 1", + "MulF 52 1", + "MulF 54 1", + "MulF 56 1", + "MulF 58 1", + "MulF 60 1", + "MulF 62 1", + "MulF 64 1", + "MulF 66 1", + "MulF 68 1", + "MulF 70 1", + "MulF 72 1", + "MulF 74 1", + "MulF 76 1", + "MulF 78 1", + "MulF 8 1", + "MulF 80 1", + "MulF 82 1", + "MulF 84 1", + "MulF 86 1", + "MulF 88 1", + "MulF 90 1", + "MulF 92 1", + "MulF 94 1", + "MulF 96 1", + "MulF 98 1" + ], + "rewrite_tree_expr_haskell": "0.0", + "rewrite_tree_expr_python": "0.0", + "simplify_e_expr_haskell": "0.0", + "simplify_e_expr_python": "0.0", + "simplify_e_param_count": 1 + }, + { + "case_id": "log_mul_const_var", + "category": "guards", + "source": "log(2 * x0)", + "notes": "Covers the Haskell log-product guard bundle.", + "compare_root_analysis": true, + "compare_rewrite_tree": true, + "compare_simplify_e": true, + "compare_simplify_e_render": true, + "compare_param_count": true, + "expected_mismatch": false, + "analysis_before": { + "kind": "none", + "value": null + }, + "analysis_after": { + "kind": "none", + "value": null + }, + "after_nodes_haskell": [ + "AddF 6 8", + "AddF 8 6", + "FunF Log 3" + ], + "rewrite_tree_expr_haskell": "Log((2.0) * (x0))", + "rewrite_tree_expr_python": "log((2.0 * x0))", + "simplify_e_expr_haskell": "Log((2.0) * (x0))", + "simplify_e_expr_python": "log((2.0 * x0))", + "simplify_e_param_count": 1 + }, + { + "case_id": "log_div_const_var", + "category": "guards", + "source": "log(2 / x0)", + "notes": "Covers the Haskell log-division guard bundle.", + "compare_root_analysis": true, + "compare_rewrite_tree": true, + "compare_simplify_e": true, + "compare_simplify_e_render": true, + "compare_param_count": true, + "expected_mismatch": false, + "analysis_before": { + "kind": "none", + "value": null + }, + "analysis_after": { + "kind": "none", + "value": null + }, + "after_nodes_haskell": [ + "FunF Log 3", + "SubF 5 7" + ], + "rewrite_tree_expr_haskell": "Log((2.0) / (x0))", + "rewrite_tree_expr_python": "log((2.0 / x0))", + "simplify_e_expr_haskell": "Log((2.0) / (x0))", + "simplify_e_expr_python": "log((2.0 / x0))", + "simplify_e_param_count": 1 + }, + { + "case_id": "log_exp_var", + "category": "guards", + "source": "log(exp(x0))", + "notes": "Only fires for a non-constant argument.", + "compare_root_analysis": true, + "compare_rewrite_tree": true, + "compare_simplify_e": true, + "compare_simplify_e_render": true, + "compare_param_count": true, + "expected_mismatch": false, + "analysis_before": { + "kind": "none", + "value": null + }, + "analysis_after": { + "kind": "none", + "value": null + }, + "after_nodes_haskell": [ + "FunF Log 2", + "VarF 0" + ], + "rewrite_tree_expr_haskell": "x0", + "rewrite_tree_expr_python": "x0", + "simplify_e_expr_haskell": "x0", + "simplify_e_expr_python": "x0", + "simplify_e_param_count": 0 + }, + { + "case_id": "exp_log_var", + "category": "guards", + "source": "exp(log(x0))", + "notes": "Only fires for a non-constant argument.", + "compare_root_analysis": true, + "compare_rewrite_tree": true, + "compare_simplify_e": true, + "compare_simplify_e_render": true, + "compare_param_count": true, + "expected_mismatch": false, + "analysis_before": { + "kind": "none", + "value": null + }, + "analysis_after": { + "kind": "none", + "value": null + }, + "after_nodes_haskell": [ + "FunF Exp 2", + "VarF 0" + ], + "rewrite_tree_expr_haskell": "x0", + "rewrite_tree_expr_python": "x0", + "simplify_e_expr_haskell": "x0", + "simplify_e_expr_python": "x0", + "simplify_e_param_count": 0 + }, + { + "case_id": "sqrt_negative_times_difference", + "category": "guards", + "source": "sqrt((-2.0) * (x0 - x1))", + "notes": "Covers the negative-a square-root rewrite shape.", + "compare_root_analysis": true, + "compare_rewrite_tree": true, + "compare_simplify_e": true, + "compare_simplify_e_render": true, + "compare_param_count": true, + "expected_mismatch": false, + "analysis_before": { + "kind": "none", + "value": null + }, + "analysis_after": { + "kind": "none", + "value": null + }, + "after_nodes_haskell": [ + "FunF Sqrt 5", + "MulF 11 14", + "MulF 14 11" + ], + "rewrite_tree_expr_haskell": "Sqrt((-2.0) * ((x0) - (x1)))", + "rewrite_tree_expr_python": "sqrt((-2.0 * (x0 - x1)))", + "simplify_e_expr_haskell": "Sqrt((-2.0) * ((x0) - (x1)))", + "simplify_e_expr_python": "sqrt((-2.0 * (x0 - x1)))", + "simplify_e_param_count": 1 + }, + { + "case_id": "x_mul_inverse_x", + "category": "guards", + "source": "x0 * (1 / x0)", + "notes": "Uses the same non-zero guard as x / x.", + "compare_root_analysis": false, + "compare_rewrite_tree": false, + "compare_simplify_e": false, + "compare_simplify_e_render": true, + "compare_param_count": false, + "expected_mismatch": false, + "analysis_before": { + "kind": "none", + "value": null + }, + "analysis_after": { + "kind": "none", + "value": null + }, + "after_nodes_haskell": [ + "ConstF 1.0", + "DivF 1 1", + "DivF 6 1", + "DivF 9 9", + "MulF 1 3", + "MulF 118 155", + "MulF 126 54", + "MulF 130 290", + "MulF 130 301", + "MulF 15 9", + "MulF 152 309", + "MulF 155 118", + "MulF 2 13", + "MulF 27 33", + "MulF 290 130", + "MulF 3 1", + "MulF 309 152", + "MulF 33 27", + "MulF 54 69", + "MulF 69 54", + "MulF 9 15" + ], + "rewrite_tree_expr_haskell": "(x0) / (x0)", + "rewrite_tree_expr_python": "(x0 / x0)", + "simplify_e_expr_haskell": "(x0) / (x0)", + "simplify_e_expr_python": "(x0 / x0)", + "simplify_e_param_count": 0 + }, + { + "case_id": "negative_const_div_self", + "category": "guards", + "source": "(-2) / (-2)", + "notes": "Negative constants still satisfy is_not_zero.", + "compare_root_analysis": true, + "compare_rewrite_tree": true, + "compare_simplify_e": true, + "compare_simplify_e_render": true, + "compare_param_count": true, + "expected_mismatch": false, + "analysis_before": { + "kind": "some", + "value": 1.0 + }, + "analysis_after": { + "kind": "some", + "value": 1.0 + }, + "after_nodes_haskell": [ + "ConstF 1.0" + ], + "rewrite_tree_expr_haskell": "1.0", + "rewrite_tree_expr_python": "1.0", + "simplify_e_expr_haskell": "1.0", + "simplify_e_expr_python": "1.0", + "simplify_e_param_count": 1 + }, + { + "case_id": "negative_const_pow_two", + "category": "analysis", + "source": "(-2) ** 2", + "notes": "Haskell folds negative-base powers with integer exponents.", + "compare_root_analysis": true, + "compare_rewrite_tree": true, + "compare_simplify_e": true, + "compare_simplify_e_render": true, + "compare_param_count": true, + "expected_mismatch": false, + "analysis_before": { + "kind": "some", + "value": 4.0 + }, + "analysis_after": { + "kind": "some", + "value": 4.0 + }, + "after_nodes_haskell": [ + "ConstF 4.0" + ], + "rewrite_tree_expr_haskell": "4.0", + "rewrite_tree_expr_python": "4.0", + "simplify_e_expr_haskell": "4.0", + "simplify_e_expr_python": "4.0", + "simplify_e_param_count": 1 + }, + { + "case_id": "negative_const_pow_three", + "category": "analysis", + "source": "(-2) ** 3", + "notes": "Haskell folds negative-base powers with integer exponents.", + "compare_root_analysis": true, + "compare_rewrite_tree": true, + "compare_simplify_e": true, + "compare_simplify_e_render": true, + "compare_param_count": true, + "expected_mismatch": false, + "analysis_before": { + "kind": "some", + "value": -8.0 + }, + "analysis_after": { + "kind": "some", + "value": -8.0 + }, + "after_nodes_haskell": [ + "ConstF (-8.0)" + ], + "rewrite_tree_expr_haskell": "-8.0", + "rewrite_tree_expr_python": "-8.0", + "simplify_e_expr_haskell": "-8.0", + "simplify_e_expr_python": "-8.0", + "simplify_e_param_count": 1 + }, + { + "case_id": "negative_const_pow_var", + "category": "analysis", + "source": "(-2) ** x0", + "notes": "Negative-base powers with non-constant exponents remain non-constant.", + "compare_root_analysis": true, + "compare_rewrite_tree": false, + "compare_simplify_e": true, + "compare_simplify_e_render": true, + "compare_param_count": true, + "expected_mismatch": false, + "analysis_before": { + "kind": "none", + "value": null + }, + "analysis_after": { + "kind": "none", + "value": null + }, + "after_nodes_haskell": [ + "PowerF 1 2" + ], + "rewrite_tree_expr_haskell": "(-2.0)**(x0)", + "rewrite_tree_expr_python": "(-2.0 ** x0)", + "simplify_e_expr_haskell": "(-2.0)**(x0)", + "simplify_e_expr_python": "(-2.0 ** x0)", + "simplify_e_param_count": 1 + }, + { + "case_id": "sbp_zero_times_quadratic", + "category": "schedule", + "source": "0.004376 - (0.0 * (x1 * x1))", + "notes": "Retired as a direct-Haskell parity canary: live Haskell extracts `x1`, while the explicit-analysis Egglog loop reaches the semantically constant form.", + "compare_root_analysis": false, + "compare_rewrite_tree": false, + "compare_simplify_e": false, + "compare_simplify_e_render": false, + "compare_param_count": false, + "expected_mismatch": false, + "analysis_before": { + "kind": "none", + "value": null + }, + "analysis_after": { + "kind": "none", + "value": null + }, + "after_nodes_haskell": [ + "ConstF (-1.0)", + "ConstF 0.0", + "ConstF 1.0", + "ConstF 4.376e-3", + "ConstF Infinity", + "DivF 17 2", + "DivF 2 54", + "DivF 3 2", + "DivF 373 2", + "DivF 375 2", + "DivF 377 2", + "DivF 380 2", + "DivF 382 2", + "DivF 4 2", + "DivF 48 2", + "DivF 50 2", + "DivF 54 2", + "MulF 12 12", + "MulF 12 17", + "MulF 12 22", + "MulF 12 24", + "MulF 12 28", + "MulF 12 3", + "MulF 12 30", + "MulF 12 36", + "MulF 12 38", + "MulF 12 4", + "MulF 12 41", + "MulF 12 43", + "MulF 12 54", + "MulF 17 12", + "MulF 17 17", + "MulF 17 22", + "MulF 17 24", + "MulF 17 28", + "MulF 17 3", + "MulF 17 30", + "MulF 17 36", + "MulF 17 38", + "MulF 17 4", + "MulF 17 41", + "MulF 17 43", + "MulF 17 54", + "MulF 2 372", + "MulF 2 373", + "MulF 22 12", + "MulF 22 17", + "MulF 22 22", + "MulF 22 24", + "MulF 22 28", + "MulF 22 3", + "MulF 22 30", + "MulF 22 36", + "MulF 22 38", + "MulF 22 41", + "MulF 22 43", + "MulF 22 54", + "MulF 24 12", + "MulF 24 17", + "MulF 24 22", + "MulF 24 24", + "MulF 24 28", + "MulF 24 3", + "MulF 24 30", + "MulF 24 36", + "MulF 24 38", + "MulF 24 41", + "MulF 24 43", + "MulF 24 54", + "MulF 246 3", + "MulF 248 3", + "MulF 28 12", + "MulF 28 17", + "MulF 28 22", + "MulF 28 24", + "MulF 28 28", + "MulF 28 3", + "MulF 28 30", + "MulF 28 36", + "MulF 28 38", + "MulF 28 41", + "MulF 28 43", + "MulF 28 54", + "MulF 3 12", + "MulF 3 17", + "MulF 3 22", + "MulF 3 24", + "MulF 3 28", + "MulF 3 3", + "MulF 3 30", + "MulF 3 36", + "MulF 3 38", + "MulF 3 4", + "MulF 3 41", + "MulF 3 43", + "MulF 3 48", + "MulF 3 54", + "MulF 30 12", + "MulF 30 17", + "MulF 30 22", + "MulF 30 24", + "MulF 30 28", + "MulF 30 3", + "MulF 30 30", + "MulF 30 36", + "MulF 30 38", + "MulF 30 41", + "MulF 30 43", + "MulF 30 54", + "MulF 350 3", + "MulF 36 12", + "MulF 36 17", + "MulF 36 22", + "MulF 36 24", + "MulF 36 28", + "MulF 36 3", + "MulF 36 30", + "MulF 36 36", + "MulF 36 38", + "MulF 36 41", + "MulF 36 43", + "MulF 36 54", + "MulF 372 2", + "MulF 372 3", + "MulF 372 4", + "MulF 38 12", + "MulF 38 17", + "MulF 38 22", + "MulF 38 24", + "MulF 38 28", + "MulF 38 3", + "MulF 38 30", + "MulF 38 36", + "MulF 38 38", + "MulF 38 4", + "MulF 38 41", + "MulF 38 43", + "MulF 38 54", + "MulF 4 12", + "MulF 4 17", + "MulF 4 22", + "MulF 4 24", + "MulF 4 28", + "MulF 4 3", + "MulF 4 30", + "MulF 4 36", + "MulF 4 38", + "MulF 4 4", + "MulF 4 41", + "MulF 4 43", + "MulF 4 54", + "MulF 41 12", + "MulF 41 17", + "MulF 41 22", + "MulF 41 24", + "MulF 41 28", + "MulF 41 3", + "MulF 41 30", + "MulF 41 36", + "MulF 41 38", + "MulF 41 4", + "MulF 41 41", + "MulF 41 43", + "MulF 41 54", + "MulF 43 12", + "MulF 43 17", + "MulF 43 22", + "MulF 43 24", + "MulF 43 28", + "MulF 43 3", + "MulF 43 30", + "MulF 43 36", + "MulF 43 38", + "MulF 43 4", + "MulF 43 41", + "MulF 43 43", + "MulF 43 54", + "MulF 54 12", + "MulF 54 17", + "MulF 54 22", + "MulF 54 24", + "MulF 54 28", + "MulF 54 3", + "MulF 54 30", + "MulF 54 36", + "MulF 54 373", + "MulF 54 38", + "MulF 54 384", + "MulF 54 41", + "MulF 54 43", + "SubF 10 4", + "VarF 1" + ], + "rewrite_tree_expr_haskell": "x1", + "rewrite_tree_expr_python": "x1", + "simplify_e_expr_haskell": "x1", + "simplify_e_expr_python": "x1", + "simplify_e_param_count": 0 + }, + { + "case_id": "x0_sq_plus_x1_sq", + "category": "schedule", + "source": "(((51.6682472229003906 * x0) * ((-0.0001894439337775) * x0)) + ((0.0012052881065756 * x1) * ((-8.2380609512329102) * x1)))", + "notes": "Reduced Haskell-backed schedule canary for the direct Haskell-style inner loop.", + "compare_root_analysis": true, + "compare_rewrite_tree": true, + "compare_simplify_e": true, + "compare_simplify_e_render": true, + "compare_param_count": true, + "expected_mismatch": false, + "analysis_before": { + "kind": "none", + "value": null + }, + "analysis_after": { + "kind": "none", + "value": null + }, + "after_nodes_haskell": [ + "AddF 12 6", + "AddF 6 12", + "MulF 1 131", + "MulF 10 133", + "MulF 129 4", + "MulF 131 1", + "MulF 133 10", + "MulF 135 7", + "MulF 25 60", + "MulF 29 65", + "MulF 4 129", + "MulF 60 25", + "MulF 65 29", + "MulF 7 135" + ], + "rewrite_tree_expr_haskell": "((-9.78823600529464e-3) * ((x0) * (x0))) + ((-9.929236885765901e-3) * ((x1) * (x1)))", + "rewrite_tree_expr_python": "((-0.00978823600529464 * (x0 * x0)) + (-0.009929236885765901 * (x1 * x1)))", + "simplify_e_expr_haskell": "((-9.78823600529464e-3) * ((x0) * (x0))) + ((-9.929236885765901e-3) * ((x1) * (x1)))", + "simplify_e_expr_python": "((-0.00978823600529464 * (x0 * x0)) + (-0.009929236885765901 * (x1 * x1)))", + "simplify_e_param_count": 2 + }, + { + "case_id": "sub_add_left_assoc", + "category": "extraction", + "source": "x0 - (x0 + x1)", + "notes": "Haskell and Python keep semantically equivalent but different extracted subtraction normal forms.", + "compare_root_analysis": false, + "compare_rewrite_tree": true, + "compare_simplify_e": true, + "compare_simplify_e_render": true, + "compare_param_count": false, + "expected_mismatch": true, + "analysis_before": { + "kind": "none", + "value": null + }, + "analysis_after": { + "kind": "none", + "value": null + }, + "after_nodes_haskell": [ + "MulF 11 2", + "MulF 2 11", + "SubF 1 3", + "SubF 6 2", + "SubF 9 1" + ], + "rewrite_tree_expr_haskell": "(x0) - ((x0) + (x1))", + "rewrite_tree_expr_python": "(x0 - (x0 + x1))", + "simplify_e_expr_haskell": "(x0) - ((x0) + (x1))", + "simplify_e_expr_python": "(x0 - (x0 + x1))", + "simplify_e_param_count": 0 + }, + { + "case_id": "nonconstant_power_exponent_count", + "category": "reporting", + "source": "(2.0 ** x0) + (x1 ** (x0 + 3.0))", + "notes": "Constants count as parameters, but non-constant exponents are still traversed.", + "compare_root_analysis": false, + "compare_rewrite_tree": false, + "compare_simplify_e": false, + "compare_simplify_e_render": true, + "compare_param_count": true, + "expected_mismatch": false, + "analysis_before": { + "kind": "none", + "value": null + }, + "analysis_after": { + "kind": "none", + "value": null + }, + "after_nodes_haskell": [ + "AddF 3 7", + "AddF 7 3" + ], + "rewrite_tree_expr_haskell": "((2.0)**(x0)) + ((x1)**((x0) + (3.0)))", + "rewrite_tree_expr_python": "((2.0 ** x0) + (x1 ** (x0 + 3.0)))", + "simplify_e_expr_haskell": "((2.0)**(x0)) + ((x1)**((x0) + (3.0)))", + "simplify_e_expr_python": "((2.0 ** x0) + (x1 ** (x0 + 3.0)))", + 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"MulF 90 165", + "MulF 90 167", + "MulF 90 17", + "MulF 90 179", + "MulF 90 18", + "MulF 90 181", + "MulF 90 19", + "MulF 90 20", + "MulF 90 21", + "MulF 90 214", + "MulF 90 32", + "MulF 90 38", + "MulF 90 45", + "MulF 90 6", + "MulF 90 84", + "MulF 90 86", + "MulF 90 88", + "MulF 90 90", + "MulF 90 92", + "MulF 90 94", + "MulF 92 100", + "MulF 92 102", + "MulF 92 110", + "MulF 92 165", + "MulF 92 167", + "MulF 92 17", + "MulF 92 179", + "MulF 92 18", + "MulF 92 181", + "MulF 92 19", + "MulF 92 20", + "MulF 92 21", + "MulF 92 214", + "MulF 92 32", + "MulF 92 38", + "MulF 92 45", + "MulF 92 6", + "MulF 92 84", + "MulF 92 86", + "MulF 92 88", + "MulF 92 90", + "MulF 92 92", + "MulF 92 94", + "MulF 94 100", + "MulF 94 102", + "MulF 94 110", + "MulF 94 165", + "MulF 94 167", + "MulF 94 17", + "MulF 94 179", + "MulF 94 18", + "MulF 94 181", + "MulF 94 19", + "MulF 94 20", + "MulF 94 21", + "MulF 94 214", + "MulF 94 32", + "MulF 94 38", + "MulF 94 45", + "MulF 94 6", + "MulF 94 84", + "MulF 94 86", + "MulF 94 88", + "MulF 94 90", + "MulF 94 92", + "MulF 94 94", + "SubF 1504 2", + "SubF 2 4", + "SubF 36 22", + "SubF 7 14", + "VarF 1" + ], + "rewrite_tree_expr_haskell": "x1", + "rewrite_tree_expr_python": "x1", + "simplify_e_expr_haskell": "x1", + "simplify_e_expr_python": "x1", + "simplify_e_param_count": 0 + }, + { + "case_id": "pagie_operon_15", + "category": "corpus", + "source": "((-0.0000022516087483) + (1.0000016689300537 * (((((51.6682472229003906 * x0) * ((-0.0001894439337775) * x0)) + 2.5324115753173828) + ((-46.3591499328613281) / (((13.0968494415283203 * x0) * (2.1884925365447998 * x0)) + 34.0089225769042969))) + (((-1351.7908935546875000) / (((17.2840843200683594 * x1) * (47.4518127441406250 * x1)) + 990.7814331054687500)) + ((0.0012052881065756 * x1) * ((-8.2380609512329102) * x1))))))", + "notes": "Large corpus canary for the direct Haskell-style baseline; this should now match current FixTree.hs again.", + "compare_root_analysis": true, + "compare_rewrite_tree": true, + "compare_simplify_e": true, + "compare_simplify_e_render": true, + "compare_param_count": true, + "expected_mismatch": false, + "analysis_before": { + "kind": "none", + "value": null + }, + "analysis_after": { + "kind": "none", + "value": null + }, + "after_nodes_haskell": [ + "AddF 1 38", + "AddF 38 1", + "MulF 1017 939", + "MulF 1019 939", + "MulF 1023 943", + "MulF 1025 943", + "MulF 1027 943", + "MulF 158 2", + "MulF 2 158", + "MulF 939 1017", + "MulF 939 1019", + "MulF 943 1023", + "MulF 943 1025", + "MulF 943 1027" + ], + "rewrite_tree_expr_haskell": "(-2.2516087483e-6) + (((((x0) * (x0)) + (-258.7199137768597)) + (((((x1) * (x1)) + ((165.99479114520634) / (((x1) * (x1)) + (1.2080326581103884)))) + ((162.89497489770397) / (((x0) * (x0)) + (1.186536134285651)))) * (1.0144051369822908))) * (-9.788252341175882e-3))", + "rewrite_tree_expr_python": "(-2.2516087483e-06 + ((((x0 * x0) + -258.7199137768597) + ((((x1 * x1) + (165.99479114520634 / ((x1 * x1) + 1.2080326581103884))) + (162.89497489770397 / ((x0 * x0) + 1.186536134285651))) * 1.0144051369822908)) * -0.009788252341175882))", + "simplify_e_expr_haskell": "(-9.788252341175882e-3) * (((x0) * (x0)) + ((((((x1) * (x1)) + ((165.99479114520634) / (((x1) * (x1)) + (1.2080326581103884)))) + ((162.89497489770397) / (((x0) * (x0)) + (1.186536134285651)))) * (1.0144051369822908)) + (-258.7196837451166)))", + "simplify_e_expr_python": "(-0.009788252341175882 * ((x0 * x0) + (((((x1 * x1) + (165.99479114520634 / ((x1 * x1) + 1.2080326581103884))) + (162.89497489770397 / ((x0 * x0) + 1.186536134285651))) * 1.0144051369822908) + -258.7196837451166)))", + "simplify_e_param_count": 7 + } + ] +} diff --git a/python/egglog/exp/param_eq/normalize_archives.py b/python/egglog/exp/param_eq/normalize_archives.py new file mode 100644 index 00000000..717a6ed3 --- /dev/null +++ b/python/egglog/exp/param_eq/normalize_archives.py @@ -0,0 +1,158 @@ +"""Normalize extracted param-eq-haskell result files into checked-in CSV artifacts.""" + +from __future__ import annotations + +import argparse +import csv +from collections import defaultdict +from pathlib import Path + +from egglog.exp.param_eq.paths import ARTIFACT_DIR, param_eq_data_dir + +DATASETS = ("pagie", "kotanchek") +DROP_INDEXES: dict[str, set[int]] = {"pagie": {16, 162}, "kotanchek": {1}} +ALGORITHM_RENAMES = {"SRjl": "PySR", "GOMEA": "GP-GOMEA"} +RUNTIME_PATH = Path("runtimes") + + +def _parse_args() -> argparse.Namespace: + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument( + "--source-dir", + type=Path, + default=param_eq_data_dir(), + help="Path to the extracted param-eq-haskell checkout", + ) + parser.add_argument( + "--output-dir", + type=Path, + default=ARTIFACT_DIR, + help="Directory to write normalized artifacts into", + ) + args = parser.parse_args() + args.source_dir = args.source_dir.resolve() + return args + + +def _read_text(source_dir: Path, relative_path: Path) -> str: + path = source_dir / relative_path + return path.read_text(encoding="utf-8", errors="replace") + + +def _read_csv_text(text: str) -> list[dict[str, str]]: + return list(csv.DictReader(text.splitlines())) + + +def _clean_algorithm(name: str) -> str: + return ALGORITHM_RENAMES.get(name, name) + + +def _paper_row_status(dataset: str, raw_index: int, raw_algorithm: str, n_rank: str) -> tuple[bool, str]: + if raw_algorithm == "FEAT": + return False, "drop_feat" + if n_rank == "" or n_rank.lower() == "nan": + return False, "missing_rank" + if raw_index in DROP_INDEXES[dataset]: + return False, "paper_manual_drop" + return True, "kept" + + +def _load_expression_lines(source_dir: Path, relative_path: Path) -> list[str]: + return [line.strip() for line in _read_text(source_dir, relative_path).splitlines() if line.strip()] + + +def _load_results_rows_by_algorithm(source_dir: Path, dataset: str) -> dict[str, list[dict[str, str]]]: + rows = _read_csv_text(_read_text(source_dir, Path("results") / f"{dataset}_results")) + grouped: defaultdict[str, list[dict[str, str]]] = defaultdict(list) + for row in rows: + grouped[row["algorithm"]].append(row) + return dict(grouped) + + +def _normalize_haskell_rows(source_dir: Path) -> list[dict[str, str]]: + rows: list[dict[str, str]] = [] + for dataset in DATASETS: + table_path = Path("results") / f"{dataset}_table_counts.csv" + raw_rows = _read_csv_text(_read_text(source_dir, table_path)) + results_rows_by_algorithm = _load_results_rows_by_algorithm(source_dir, dataset) + exprs_by_algorithm = { + path_algorithm: _load_expression_lines( + source_dir, + Path("results") / "exprs" / f"{path_algorithm}_exprs_{dataset}", + ) + for path_algorithm in ("Bingo", "EPLEX", "FEAT", "GOMEA", "Operon", "SBP", "SRjl") + } + algo_counts: defaultdict[str, int] = defaultdict(int) + for raw_index, raw_row in enumerate(raw_rows): + raw_algorithm = raw_row["algorithm"] + algo_counts[raw_algorithm] += 1 + algo_row = algo_counts[raw_algorithm] + exprs = exprs_by_algorithm[raw_algorithm] + sympy_exprs = results_rows_by_algorithm[raw_algorithm] + is_paper_row, drop_reason = _paper_row_status(dataset, raw_index, raw_algorithm, raw_row["n_rank"]) + row = { + "dataset": dataset, + "raw_index": str(raw_index), + "algorithm_raw": raw_algorithm, + "algorithm": _clean_algorithm(raw_algorithm), + "algo_row": str(algo_row), + "is_paper_row": "1" if is_paper_row else "0", + "drop_reason": drop_reason, + "original_expr": exprs[algo_row - 1], + "sympy_expr": sympy_exprs[algo_row - 1]["expr_sympy"].strip(), + } + for key, value in raw_row.items(): + if key == "": + row["raw_csv_index"] = value + else: + row[key] = value + rows.append(row) + return rows + + +def _to_runtime_multiplier(unit: str) -> float: + return {"ms": 1.0, "μs": 0.001, "ns": 1e-6, "s": 1000.0}[unit] + + +def _normalize_runtime_rows(source_dir: Path) -> list[dict[str, str]]: + lines = _read_text(source_dir, RUNTIME_PATH).splitlines() + benchmark_lines = [line for line in lines if line.startswith("benchmarking ")] + time_lines = [line for line in lines if line.startswith("time")] + rows: list[dict[str, str]] = [] + for benchmark_line, time_line in zip(benchmark_lines, time_lines, strict=True): + benchmark_name = benchmark_line.removeprefix("benchmarking ").strip() + node_count = int(benchmark_name.split("/")[-1]) + _, numeric, unit, *_ = time_line.split() + runtime_ms = float(numeric) * _to_runtime_multiplier(unit) + rows.append({ + "benchmark_name": benchmark_name, + "node_count": str(node_count), + "runtime_ms": f"{runtime_ms:.9f}", + }) + return rows + + +def _write_csv(path: Path, rows: list[dict[str, str]]) -> None: + if not rows: + msg = f"No rows available for {path.name}" + raise ValueError(msg) + path.parent.mkdir(parents=True, exist_ok=True) + with path.open("w", newline="", encoding="utf-8") as handle: + writer = csv.DictWriter(handle, fieldnames=list(rows[0])) + writer.writeheader() + writer.writerows(rows) + + +def main() -> None: + args = _parse_args() + args.output_dir.mkdir(parents=True, exist_ok=True) + + haskell_rows = _normalize_haskell_rows(args.source_dir) + runtime_rows = _normalize_runtime_rows(args.source_dir) + + _write_csv(args.output_dir / "haskell_paper_rows.csv", haskell_rows) + _write_csv(args.output_dir / "pagie_runtime_scatter.csv", runtime_rows) + + +if __name__ == "__main__": + main() diff --git a/python/egglog/exp/param_eq/paths.py b/python/egglog/exp/param_eq/paths.py new file mode 100644 index 00000000..2448ff83 --- /dev/null +++ b/python/egglog/exp/param_eq/paths.py @@ -0,0 +1,30 @@ +"""Shared path helpers for the retained param-eq replication package.""" + +from __future__ import annotations + +import os +import shutil +from pathlib import Path + +PARAM_EQ_DATA_DIR_ENV = "EGGLOG_PARAM_EQ_DATA_DIR" +PARAM_EQ_DIR = Path(__file__).resolve().parent +REPO_ROOT = PARAM_EQ_DIR.parents[3] +ARTIFACT_DIR = PARAM_EQ_DIR / "artifacts" +GOLDEN_PATH = PARAM_EQ_DIR / "haskell_golden.json" + + +def default_data_dir() -> Path: + return (REPO_ROOT.parent / "param-eq-haskell").resolve() + + +def param_eq_data_dir() -> Path: + configured = os.environ.get(PARAM_EQ_DATA_DIR_ENV) + return Path(configured).expanduser().resolve() if configured else default_data_dir() + + +def llvm_bin_dir() -> Path | None: + for tool in ("opt", "llvm-config"): + resolved = shutil.which(tool) + if resolved is not None: + return Path(resolved).resolve().parent + return None diff --git a/python/egglog/exp/param_eq/pipeline.py b/python/egglog/exp/param_eq/pipeline.py new file mode 100644 index 00000000..932f3292 --- /dev/null +++ b/python/egglog/exp/param_eq/pipeline.py @@ -0,0 +1,1408 @@ +# mypy: disable-error-code="empty-body" + +""" +Helpers for reproducing the paper-era param-eq EqSat pipeline in egglog. + +The archived source of truth is `param-eq-haskell/src/FixTree.hs`, together +with the reporting code in `param-eq-haskell/src/Main.hs`. + +This module mirrors that paper experiment harness only. + +Design notes for future agents: + +- The paper-facing Haskell source is `param-eq-haskell/src/FixTree.hs`. +- That Haskell implementation keeps analysis inside hegg rebuild; this Python + file has to approximate that with explicit Egglog rulesets plus a schedule. +- Numeric literals stay as constants in the EqSat language, matching + `FixTree.toFixTree (Const x) = ConstF x`. The paper only turns constants into + fitted parameters later for reporting, via + `recountParams . replaceConstsWithParams` in `Main.hs`. +- Mixed classes are intentional and paper-faithful. A class may contain both a + constant representative and a non-constant representative while its analysis + still says "not constant". Only classes whose analysis is definitively + constant get pruned to leaf nodes. + +Quick symbol map back to the Haskell file: + +- `joinA` -> `join_const_value` +- `evalConstant` -> `const_seed_rules | const_propagation_rules` +- `modifyA` -> `const_prune_rules` +- `rewritesBasic` -> `_basic_rewrites` +- `rewritesFun` -> `_fun_rewrites` +- `rewriteTree` -> `_run_single_pass_*` +- `simplifyE` -> `run_paper_pipeline` +""" + +from __future__ import annotations + +import argparse +import ast +import json +import math +import time +from collections.abc import Iterable, Mapping +from dataclasses import dataclass +from itertools import count +from typing import ClassVar, Literal, TypeAlias + +import egglog +from egglog import * +from egglog.deconstruct import get_callable_args +from egglog.egraph import FactLike + +__all__ = [ + "Num", + "NumLike", + "PaperPipelineReport", + "count_nodes", + "count_params", + "parse_expression", + "render_num", + "run_paper_pipeline", +] + + +MAX_PASSES = 2 +HASKELL_INNER_ITERATION_LIMIT = 30 +BACKOFF_MATCH_LIMIT = 1000 +BACKOFF_BAN_LENGTH = 30 +CONST_MERGE_TOLERANCE = 1e-6 + + +# Language and ruleset declarations +language_rules = ruleset(name="param_eq_hegg_lang") +const_merge_rules = ruleset(name="param_eq_hegg_const_merge") +const_seed_rules = ruleset(name="param_eq_hegg_const_seed") +const_propagation_rules = ruleset(name="param_eq_hegg_const_propagation") +const_prune_rules = ruleset(name="param_eq_hegg_const_prune") +basic_add_comm_rules = ruleset(name="param_eq_hegg_basic_add_comm") +basic_mul_comm_rules = ruleset(name="param_eq_hegg_basic_mul_comm") +basic_add_assoc_rules = ruleset(name="param_eq_hegg_basic_add_assoc") +basic_mul_assoc_rules = ruleset(name="param_eq_hegg_basic_mul_assoc") +basic_mul_div_rules = ruleset(name="param_eq_hegg_basic_mul_div") +basic_product_regroup_rules = ruleset(name="param_eq_hegg_basic_product_regroup") +basic_other_rules = ruleset(name="param_eq_hegg_basic_other") +fun_rules = ruleset(name="param_eq_hegg_fun") + + +class OptionalF64(Expr, ruleset=language_rules): + """ + Explicit stand-in for Haskell's `Maybe Double` analysis domain. + + `none` corresponds to `Nothing`, `some(x)` corresponds to `Just x`. + """ + + none: ClassVar[OptionalF64] + + @classmethod + def some(cls, value: f64Like) -> OptionalF64: ... + + +class Num(Expr, ruleset=language_rules): + """ + Paper EqSat language subset. + + This is deliberately closer to `FixTree`'s `SRTreeF` than to the broader + experimental translations that were removed during cleanup. The paper + corpus only needs constants, + variables, arithmetic, and a small unary-function set. + """ + + @method(cost=5) + def __init__(self, value: f64Like) -> None: ... + + __match_args__ = ("value",) + + @method(preserve=True) # type: ignore[prop-decorator] + @property + def value(self) -> float: + match get_callable_args(self, Num): + case (f64(value),): + return value + raise ExprValueError(self, "Num") + + @method(cost=1) + @classmethod + def var(cls, name: StringLike) -> Num: ... + + @method(cost=1) + def __add__(self, other: NumLike) -> Num: ... + + @method(cost=1) + def __sub__(self, other: NumLike) -> Num: ... + + @method(cost=1) + def __mul__(self, other: NumLike) -> Num: ... + + @method(cost=1) + def __truediv__(self, other: NumLike) -> Num: ... + + @method(cost=1) + def __pow__(self, other: NumLike) -> Num: ... + + @method(cost=1) + def exp(self) -> Num: ... + + @method(cost=1) + def log(self) -> Num: ... + + @method(cost=1) + def sqrt(self) -> Num: ... + + @method(cost=1) + def __abs__(self) -> Num: ... + + def __radd__(self, other: NumLike) -> Num: ... + + def __rsub__(self, other: NumLike) -> Num: ... + + def __rmul__(self, other: NumLike) -> Num: ... + + def __rtruediv__(self, other: NumLike) -> Num: ... + + def __rpow__(self, other: NumLike) -> Num: ... + + +NumLike: TypeAlias = Num | StringLike | f64Like | i64Like + +converter(f64, Num, Num) +converter(i64, Num, lambda value: Num(f64.from_i64(value))) +converter(String, Num, Num.var) + + +# Analysis domain and merge +@function +def join_const_value(old: OptionalF64, new: OptionalF64) -> OptionalF64: ... + + +@function( + merge=lambda old, new: join_const_value(old, new), +) +def const_value(num: Num) -> OptionalF64: ... + + +# Surface syntax helpers +# Convenience wrappers keep the parser and rewrites close to the Haskell +# surface syntax while still using the operator-overloaded Python DSL. + + +def exp(x: NumLike) -> Num: + return convert(x, Num).exp() + + +def log(x: NumLike) -> Num: + return convert(x, Num).log() + + +def sqrt(x: NumLike) -> Num: + return convert(x, Num).sqrt() + + +def neg(x: NumLike) -> Num: + return Num(-1.0) * convert(x, Num) + + +def square(x: NumLike) -> Num: + value = convert(x, Num) + return value**2 + + +def cube(x: NumLike) -> Num: + value = convert(x, Num) + return value**3 + + +def plog(x: NumLike) -> Num: + return log(abs(convert(x, Num))) + + +def _render_float(value: float) -> str: + if value == 0.0: + return "0.0" + if value.is_integer(): + return f"{value:.1f}" + return repr(value) + + +def _safe_pow(base: float, exponent: float) -> float | None: + if base == 0.0 and exponent < 0.0: + return None + if base < 0.0 and not exponent.is_integer(): + return None + try: + value = base**exponent + except (OverflowError, ValueError): + return None + if isinstance(value, complex): + return None + value = float(value) + return value if math.isfinite(value) else None + + +def _combine_binary(lhs: float, rhs: float, op: Literal["add", "sub", "mul", "div", "pow"]) -> float | None: + if op == "add": + value = lhs + rhs + elif op == "sub": + value = lhs - rhs + elif op == "mul": + value = lhs * rhs + elif op == "div": + if rhs == 0.0: + return None + value = lhs / rhs + else: + return _safe_pow(lhs, rhs) + return value if math.isfinite(value) else None + + +# Analysis algebra +@const_merge_rules.register +def _const_merge( + merged: OptionalF64, + other: OptionalF64, + a: f64, + b: f64, +) -> Iterable[RewriteOrRule]: + """ + Mirror `FixTree.joinA` on `Maybe Double`. + + The Haskell behavior is: + - `Nothing` dominates any merge + - `Just a` with `Just b` is allowed only when the constants agree up to the + tolerance used in the paper code + - differing constants are an invariant violation + + This is the key reason mixed classes remain possible: if one representative + analyzes to `none` and another to `some(a)`, the class analysis stays + `none`. + """ + yield rewrite(join_const_value(OptionalF64.none, other)).to(OptionalF64.none) + yield rewrite(join_const_value(other, OptionalF64.none)).to(OptionalF64.none) + yield rewrite(join_const_value(OptionalF64.some(a), OptionalF64.some(a))).to(OptionalF64.some(a)) + yield rewrite(join_const_value(OptionalF64.some(a), OptionalF64.some(b))).to( + OptionalF64.some(a), + eq(a).to(b), + ) + yield rewrite(join_const_value(OptionalF64.some(a), OptionalF64.some(b))).to( + OptionalF64.some(a), + abs(a - b) <= CONST_MERGE_TOLERANCE, + ) + yield rule( + eq(merged).to(join_const_value(OptionalF64.some(a), OptionalF64.some(b))), + abs(a - b) > CONST_MERGE_TOLERANCE, + ).then(panic("Merged different constant values")) + + +@const_seed_rules.register +def _const_seed( + num: Num, + a: f64, + s: String, +) -> Iterable[RewriteOrRule]: + """ + Seed the explicit analysis with leaf facts. + + This corresponds to the leaf cases in `FixTree.evalConstant`: + - `ConstF x -> Just x` + - `VarF _ -> Nothing` + + The paper harness's benchmark expressions do not materialize `ParamF` + before EqSat, so there is no separate parameter leaf here. + """ + yield rule(eq(num).to(Num(a))).then(set_(const_value(num)).to(OptionalF64.some(a))) + yield rule(eq(num).to(Num.var(s))).then(set_(const_value(num)).to(OptionalF64.none)) + + +@const_propagation_rules.register +def _const_propagation( + num: Num, + x: Num, + y: Num, + a: f64, + b: f64, +) -> Iterable[RewriteOrRule]: + """ + Explicit approximation of `FixTree.makeA` + `evalConstant`. + + In Haskell this logic is one algebra over `SRTreeF (Maybe Double)` and runs + as part of rebuild. In Egglog we spell it as rules: + - if any required child is `none`, the parent becomes `none` + - if all required children are `some`, compute the folded constant + - when a folded constant exists, union the class with `Num(constant)` + """ + yield rule(eq(num).to(x + y), const_value(x) == OptionalF64.none).then(set_(const_value(num)).to(OptionalF64.none)) + yield rule(eq(num).to(x + y), const_value(y) == OptionalF64.none).then(set_(const_value(num)).to(OptionalF64.none)) + yield rule(eq(num).to(x + y), const_value(x) == OptionalF64.some(a), const_value(y) == OptionalF64.some(b)).then( + set_(const_value(num)).to(OptionalF64.some(a + b)), + union(num).with_(Num(a + b)), + ) + yield rule(eq(num).to(x - y), const_value(x) == OptionalF64.none).then(set_(const_value(num)).to(OptionalF64.none)) + yield rule(eq(num).to(x - y), const_value(y) == OptionalF64.none).then(set_(const_value(num)).to(OptionalF64.none)) + yield rule(eq(num).to(x - y), const_value(x) == OptionalF64.some(a), const_value(y) == OptionalF64.some(b)).then( + set_(const_value(num)).to(OptionalF64.some(a - b)), + union(num).with_(Num(a - b)), + ) + yield rule(eq(num).to(x * y), const_value(x) == OptionalF64.none).then(set_(const_value(num)).to(OptionalF64.none)) + yield rule(eq(num).to(x * y), const_value(y) == OptionalF64.none).then(set_(const_value(num)).to(OptionalF64.none)) + yield rule(eq(num).to(x * y), const_value(x) == OptionalF64.some(a), const_value(y) == OptionalF64.some(b)).then( + set_(const_value(num)).to(OptionalF64.some(a * b)), + union(num).with_(Num(a * b)), + ) + yield rule(eq(num).to(x / y), const_value(x) == OptionalF64.none).then(set_(const_value(num)).to(OptionalF64.none)) + yield rule(eq(num).to(x / y), const_value(y) == OptionalF64.none).then(set_(const_value(num)).to(OptionalF64.none)) + yield rule( + eq(num).to(x / y), + const_value(x) == OptionalF64.some(a), + const_value(y) == OptionalF64.some(b), + eq(b).to(f64(0.0)), + ).then( + set_(const_value(num)).to(OptionalF64.none), + ) + yield rule( + eq(num).to(x / y), + const_value(x) == OptionalF64.some(a), + const_value(y) == OptionalF64.some(b), + b > 0.0, + ).then( + set_(const_value(num)).to(OptionalF64.some(a / b)), + union(num).with_(Num(a / b)), + ) + yield rule( + eq(num).to(x / y), + const_value(x) == OptionalF64.some(a), + const_value(y) == OptionalF64.some(b), + b < 0.0, + ).then( + set_(const_value(num)).to(OptionalF64.some(a / b)), + union(num).with_(Num(a / b)), + ) + yield rule(eq(num).to(x**y), const_value(x) == OptionalF64.none).then(set_(const_value(num)).to(OptionalF64.none)) + yield rule(eq(num).to(x**y), const_value(y) == OptionalF64.none).then(set_(const_value(num)).to(OptionalF64.none)) + yield rule( + eq(num).to(x**y), + const_value(x) == OptionalF64.some(a), + const_value(y) == OptionalF64.some(b), + a < 0.0, + eq(f64.from_i64(b.to_i64())).to(b), + ).then( + set_(const_value(num)).to(OptionalF64.some(a**b)), + union(num).with_(Num(a**b)), + ) + yield rule( + eq(num).to(x**y), + const_value(x) == OptionalF64.some(a), + const_value(y) == OptionalF64.some(b), + a < 0.0, + ne(f64.from_i64(b.to_i64())).to(b), + ).then( + set_(const_value(num)).to(OptionalF64.none), + ) + yield rule( + eq(num).to(x**y), + const_value(x) == OptionalF64.some(a), + const_value(y) == OptionalF64.some(b), + eq(a).to(f64(0.0)), + b < 0.0, + ).then( + set_(const_value(num)).to(OptionalF64.none), + ) + yield rule( + eq(num).to(x**y), + const_value(x) == OptionalF64.some(a), + const_value(y) == OptionalF64.some(b), + eq(a).to(f64(0.0)), + b >= 0.0, + ).then( + set_(const_value(num)).to(OptionalF64.some(a**b)), + union(num).with_(Num(a**b)), + ) + yield rule( + eq(num).to(x**y), const_value(x) == OptionalF64.some(a), const_value(y) == OptionalF64.some(b), a > 0.0 + ).then( + set_(const_value(num)).to(OptionalF64.some(a**b)), + union(num).with_(Num(a**b)), + ) + yield rule(eq(num).to(exp(x)), const_value(x) == OptionalF64.none).then(set_(const_value(num)).to(OptionalF64.none)) + yield rule(eq(num).to(exp(x)), const_value(x) == OptionalF64.some(a)).then( + set_(const_value(num)).to(OptionalF64.some(a.exp())), + union(num).with_(Num(a.exp())), + ) + yield rule(eq(num).to(log(x)), const_value(x) == OptionalF64.none).then(set_(const_value(num)).to(OptionalF64.none)) + yield rule(eq(num).to(log(x)), const_value(x) == OptionalF64.some(a), a <= 0.0).then( + set_(const_value(num)).to(OptionalF64.none), + ) + yield rule(eq(num).to(log(x)), const_value(x) == OptionalF64.some(a), a > 0.0).then( + set_(const_value(num)).to(OptionalF64.some(a.log())), + union(num).with_(Num(a.log())), + ) + yield rule(eq(num).to(sqrt(x)), const_value(x) == OptionalF64.none).then( + set_(const_value(num)).to(OptionalF64.none) + ) + yield rule(eq(num).to(sqrt(x)), const_value(x) == OptionalF64.some(a), a < 0.0).then( + set_(const_value(num)).to(OptionalF64.none), + ) + yield rule(eq(num).to(sqrt(x)), const_value(x) == OptionalF64.some(a), a >= 0.0).then( + set_(const_value(num)).to(OptionalF64.some(a.sqrt())), + union(num).with_(Num(a.sqrt())), + ) + yield rule(eq(num).to(abs(x)), const_value(x) == OptionalF64.none).then(set_(const_value(num)).to(OptionalF64.none)) + yield rule(eq(num).to(abs(x)), const_value(x) == OptionalF64.some(a)).then( + set_(const_value(num)).to(OptionalF64.some(abs(a))), + union(num).with_(Num(abs(a))), + ) + + +# Guard helpers +GuardConditions: TypeAlias = tuple[FactLike, ...] +GuardCases: TypeAlias = tuple[GuardConditions, ...] +_CONST_GUARD_COUNTER = count() + + +def _fresh_const_guard_value(prefix: str = "_const_value") -> f64: + return var(f"{prefix}_{next(_CONST_GUARD_COUNTER)}", f64) + + +def is_const(num: Num, value: f64 | None = None) -> GuardConditions: + if value is None: + value = _fresh_const_guard_value() + return (const_value(num) == OptionalF64.some(value),) + + +def is_not_const(num: Num) -> GuardConditions: + return (const_value(num) == OptionalF64.none,) + + +def _is_nonnegative_const(num: Num, value: f64 | None = None) -> GuardConditions: + if value is None: + value = _fresh_const_guard_value("_nonnegative_const_value") + return (*is_const(num, value), value >= 0.0) + + +def _is_positive_const(num: Num, value: f64 | None = None) -> GuardConditions: + if value is None: + value = _fresh_const_guard_value("_positive_const_value") + return (*is_const(num, value), value > 0.0) + + +def is_negative(num: Num, value: f64 | None = None) -> GuardConditions: + if value is None: + value = _fresh_const_guard_value("_negative_const_value") + return (*is_const(num, value), value < 0.0) + + +def is_not_zero(num: Num, value: f64 | None = None) -> GuardCases: + if value is None: + value = _fresh_const_guard_value("_nonzero_const_value") + return ( + is_not_const(num), + _is_positive_const(num, value), + is_negative(num, value), + ) + + +def is_not_neg_consts( + left: Num, + right: Num, + left_value: f64 | None = None, + right_value: f64 | None = None, +) -> GuardCases: + if left_value is None: + left_value = _fresh_const_guard_value("_left_nonnegative_const_value") + if right_value is None: + right_value = _fresh_const_guard_value("_right_nonnegative_const_value") + return ( + _is_nonnegative_const(left, left_value), + _is_nonnegative_const(right, right_value), + ) + + +# `rewritesBasic` +@const_prune_rules.register +def _const_prune( + num: Num, + x: Num, + y: Num, + a: f64, +) -> Iterable[RewriteOrRule]: + """ + Approximate `FixTree.modifyA`. + + Haskell does two things once an e-class analysis becomes `Just d`: + - inserts the constant representative `ConstF d` + - prunes the class down to leaf e-nodes + + Egglog cannot filter a class's node set directly, so we approximate that by + deleting composite representatives that are already known constant. This is + intentionally weaker than the hegg implementation, but it serves the same + purpose: keep truly constant classes from carrying around redundant call + nodes. + """ + yield rule(eq(num).to(x + y), const_value(num) == OptionalF64.some(a)).then( + union(num).with_(Num(a)), + delete(x + y), + ) + yield rule(eq(num).to(x - y), const_value(num) == OptionalF64.some(a)).then( + union(num).with_(Num(a)), + delete(x - y), + ) + yield rule(eq(num).to(x * y), const_value(num) == OptionalF64.some(a)).then( + union(num).with_(Num(a)), + delete(x * y), + ) + yield rule(eq(num).to(x / y), const_value(num) == OptionalF64.some(a)).then( + union(num).with_(Num(a)), + delete(x / y), + ) + yield rule(eq(num).to(x**y), const_value(num) == OptionalF64.some(a)).then( + union(num).with_(Num(a)), + delete(x**y), + ) + yield rule(eq(num).to(exp(x)), const_value(num) == OptionalF64.some(a)).then( + union(num).with_(Num(a)), + delete(exp(x)), + ) + yield rule(eq(num).to(log(x)), const_value(num) == OptionalF64.some(a)).then( + union(num).with_(Num(a)), + delete(log(x)), + ) + yield rule(eq(num).to(sqrt(x)), const_value(num) == OptionalF64.some(a)).then( + union(num).with_(Num(a)), + delete(sqrt(x)), + ) + yield rule(eq(num).to(abs(x)), const_value(num) == OptionalF64.some(a)).then( + union(num).with_(Num(a)), + delete(abs(x)), + ) + + +@basic_add_comm_rules.register +def _basic_add_comm(x: Num, y: Num) -> Iterable[RewriteOrRule]: + yield rewrite(x + y).to(y + x) + + +@basic_mul_comm_rules.register +def _basic_mul_comm(x: Num, y: Num) -> Iterable[RewriteOrRule]: + yield rewrite(x * y).to(y * x) + + +@basic_add_assoc_rules.register +def _basic_add_assoc(x: Num, y: Num, z: Num) -> Iterable[RewriteOrRule]: + yield rewrite(x + (y + z)).to((x + y) + z) + + +@basic_mul_assoc_rules.register +def _basic_mul_assoc(x: Num, y: Num, z: Num) -> Iterable[RewriteOrRule]: + yield rewrite(x * (y * z)).to((x * y) * z) + + +@basic_mul_div_rules.register +def _basic_mul_div(x: Num, y: Num, z: Num) -> Iterable[RewriteOrRule]: + yield rewrite(x * (y / z)).to((x * y) / z) + yield rewrite((x * y) / z).to(x * (y / z)) + + +@basic_product_regroup_rules.register +def _basic_product_regroup(a: Num, b: Num, x: Num, y: Num) -> Iterable[RewriteOrRule]: + yield rewrite((a * x) * (b * y)).to( + (a * b) * (x * y), + *is_const(a), + *is_const(b), + *is_not_const(x), + *is_not_const(y), + ) + + +@basic_other_rules.register +def _basic_rewrites( + x: Num, + y: Num, + z: Num, + a: Num, + b: Num, + c: Num, + d: Num, +) -> Iterable[RewriteOrRule]: + """ + Translation of `FixTree.rewritesBasic`. + + Guard style differs from Haskell only where Egglog soundness requires it: + we avoid `!= none`-style class tests and instead match explicit + `const_value(...) == some(...)` or `== none` cases. + """ + yield rewrite(a * x + b).to( + a * (x + (b / a)), + *is_const(a), + *is_const(b), + *is_not_const(x), + ) + yield rewrite(a * x - b).to( + a * (x - (b / a)), + *is_const(a), + *is_const(b), + *is_not_const(x), + ) + yield rewrite(b - (a * x)).to( + a * ((b / a) - x), + *is_const(a), + *is_const(b), + *is_not_const(x), + ) + yield rewrite(a * x + (b * y)).to( + a * (x + ((b / a) * y)), + *is_const(a), + *is_const(b), + *is_not_const(x), + *is_not_const(y), + ) + yield rewrite(a * x - (b * y)).to( + a * (x - ((b / a) * y)), + *is_const(a), + *is_const(b), + *is_not_const(x), + *is_not_const(y), + ) + yield rewrite(a * x + (b / y)).to( + a * (x + ((b / a) / y)), + *is_const(a), + *is_const(b), + *is_not_const(x), + *is_not_const(y), + ) + yield rewrite(a * x - (b / y)).to( + a * (x - ((b / a) / y)), + *is_const(a), + *is_const(b), + *is_not_const(x), + *is_not_const(y), + ) + yield rewrite(a / (b * x)).to( + (a / b) / x, + *is_const(a), + *is_const(b), + *is_not_const(x), + ) + yield rewrite(x / (b * y)).to( + (Num(1.0) / b) * x / y, + *is_const(b), + *is_not_const(x), + *is_not_const(y), + ) + yield rewrite((x / a) + b).to( + (x + (b * a)) / a, + *is_const(a), + *is_const(b), + *is_not_const(x), + ) + yield rewrite((x / a) - b).to( + (x - (b * a)) / a, + *is_const(a), + *is_const(b), + *is_not_const(x), + ) + yield rewrite(b - (x / a)).to( + ((b * a) - x) / a, + *is_const(a), + *is_const(b), + *is_not_const(x), + ) + yield rewrite((x / a) + (b * y)).to( + (x + ((b * a) * y)) / a, + *is_const(a), + *is_const(b), + *is_not_const(x), + *is_not_const(y), + ) + yield rewrite((x / a) + (y / b)).to( + (x + (y / (b * a))) / a, + *is_const(a), + *is_const(b), + *is_not_const(x), + *is_not_const(y), + ) + yield rewrite((x / a) - (b * y)).to( + (x - ((b * a) * y)) / a, + *is_const(a), + *is_const(b), + *is_not_const(x), + *is_not_const(y), + ) + yield rewrite((x / a) - (b / y)).to( + (x - (y / (b * a))) / a, + *is_const(a), + *is_const(b), + *is_not_const(x), + *is_not_const(y), + ) + yield rewrite((b + (a * x)) / (c + (d * y))).to( + (a / d) * (((b / a) + x) / ((c / d) + y)), + *is_const(a), + *is_const(b), + *is_const(c), + *is_const(d), + ) + yield rewrite((b + x) / (c + (d * y))).to( + (Num(1.0) / d) * ((b + x) / ((c / d) + y)), + *is_const(b), + *is_const(c), + *is_const(d), + ) + + yield rewrite(Num(0.0) + x).to(x) + yield rewrite(x - Num(0.0)).to(x) + yield rewrite(Num(1.0) * x).to(x) + yield rewrite(Num(0.0) * x).to(Num(0.0)) + yield rewrite(Num(0.0) / x).to(Num(0.0)) + yield rewrite(x - x).to(Num(0.0)) + for guard in is_not_zero(x): + yield rewrite(x / x).to(Num(1.0), *guard) + yield rewrite((x * y) + (x * z)).to(x * (y + z)) + yield rewrite(x - (y + z)).to((x - y) - z) + yield rewrite(x - (y - z)).to((x - y) + z) + yield rewrite(Num(-1.0) * (x + y)).to((Num(-1.0) * x) - y) + yield rewrite(x - a).to( + x + (Num(-1.0) * a), + *is_const(a), + *is_not_const(x), + ) + yield rewrite(x - (a * y)).to( + x + ((Num(-1.0) * a) * y), + *is_const(a), + *is_not_const(y), + ) + yield rewrite((Num(1.0) / x) * (Num(1.0) / y)).to(Num(1.0) / (x * y)) + for guard in is_not_zero(x): + yield rewrite(x * (Num(1.0) / x)).to(Num(1.0), *guard) + yield rewrite(x - (Num(-1.0) * y)).to(x + y, *is_not_const(y)) + yield rewrite(x + (Num(-1.0) * y)).to(x - y, *is_not_const(y)) + yield rewrite(Num(0.0) - x).to(Num(-1.0) * x, *is_not_const(x)) + + +# `rewritesFun` +@fun_rules.register +def _fun_rewrites(x: Num, y: Num, a: Num, b: Num, c: f64, d: f64) -> Iterable[RewriteOrRule]: + """ + Translation of `FixTree.rewritesFun`. + + The unary function subset here is the subset exercised by the archived + paper corpora. + """ + yield rewrite(log(x * y)).to( + log(x) + log(y), + const_value(x) == OptionalF64.some(c), + c > 0.0, + const_value(y) == OptionalF64.none, + ) + yield rewrite(log(x * y)).to( + log(x) + log(y), + const_value(x) == OptionalF64.some(c), + c > 0.0, + const_value(y) == OptionalF64.some(d), + d > 0.0, + ) + yield rewrite(log(x * y)).to( + log(x) + log(y), + const_value(y) == OptionalF64.some(c), + c > 0.0, + const_value(x) == OptionalF64.none, + ) + yield rewrite(log(x * y)).to( + log(x) + log(y), + const_value(y) == OptionalF64.some(c), + c > 0.0, + const_value(x) == OptionalF64.some(d), + d > 0.0, + ) + yield rewrite(log(x * y)).to( + log(x) + log(y), + const_value(x) == OptionalF64.some(c), + c > 0.0, + const_value(y) == OptionalF64.some(d), + d < 0.0, + ) + yield rewrite(log(x * y)).to( + log(x) + log(y), + const_value(y) == OptionalF64.some(c), + c > 0.0, + const_value(x) == OptionalF64.some(d), + d < 0.0, + ) + yield rewrite(log(x / y)).to( + log(x) - log(y), + const_value(x) == OptionalF64.some(c), + c > 0.0, + const_value(y) == OptionalF64.none, + ) + yield rewrite(log(x / y)).to( + log(x) - log(y), + const_value(x) == OptionalF64.some(c), + c > 0.0, + const_value(y) == OptionalF64.some(d), + d > 0.0, + ) + yield rewrite(log(x / y)).to( + log(x) - log(y), + const_value(y) == OptionalF64.some(c), + c > 0.0, + const_value(x) == OptionalF64.none, + ) + yield rewrite(log(x / y)).to( + log(x) - log(y), + const_value(y) == OptionalF64.some(c), + c > 0.0, + const_value(x) == OptionalF64.some(d), + d > 0.0, + ) + yield rewrite(log(x / y)).to( + log(x) - log(y), + const_value(x) == OptionalF64.some(c), + c > 0.0, + const_value(y) == OptionalF64.some(d), + d < 0.0, + ) + yield rewrite(log(x / y)).to( + log(x) - log(y), + const_value(y) == OptionalF64.some(c), + c > 0.0, + const_value(x) == OptionalF64.some(d), + d < 0.0, + ) + yield rewrite(log(x**y)).to(y * log(x), const_value(x) == OptionalF64.some(c), c > 0.0) + yield rewrite(log(Num(1.0))).to(Num(0.0)) + yield rewrite(log(sqrt(x))).to(Num(0.5) * log(x), *is_not_const(x)) + yield rewrite(log(exp(x))).to(x, *is_not_const(x)) + yield rewrite(exp(log(x))).to(x, *is_not_const(x)) + yield rewrite(x ** Num(0.5)).to(sqrt(x)) + for guard in is_not_neg_consts(a, x, c, d): + yield rewrite(sqrt(a * x)).to(sqrt(a) * sqrt(x), *guard) + yield rewrite(sqrt(a * (x - y))).to(sqrt(Num(-1.0) * a) * sqrt(y - x), *is_negative(a, c)) + yield rewrite(sqrt(a * (b + y))).to(sqrt(Num(-1.0) * a) * sqrt(b - y), *is_negative(a, c), *is_negative(b, d)) + for guard in is_not_neg_consts(a, x, c, d): + yield rewrite(sqrt(a / x)).to(sqrt(a) / sqrt(x), *guard) + yield rewrite(abs(x * y)).to(abs(x) * abs(y)) + + +@dataclass(frozen=True) +class PaperPipelineReport: + status: str + passes: int + total_sec: float + total_size: int + node_count: int + eclass_count: int + before_nodes: int + before_params: int + after_nodes: int + after_params: int + rendered: str + extracted: Num + extracted_cost: int + + +def _normalize_expression(source: str) -> str: + return source.strip().replace("^", "**") + + +def _from_ast(node: ast.AST) -> Num: # noqa: C901, PLR0911, PLR0912 + if isinstance(node, ast.Expression): + return _from_ast(node.body) + if isinstance(node, ast.Constant): + if isinstance(node.value, int | float): + return Num(float(node.value)) + msg = f"Unsupported constant: {node.value!r}" + raise ValueError(msg) + if isinstance(node, ast.Name): + return Num.var(node.id) + if isinstance(node, ast.UnaryOp) and isinstance(node.op, ast.USub): + if isinstance(node.operand, ast.Constant) and isinstance(node.operand.value, int | float): + return Num(float(-node.operand.value)) + return neg(_from_ast(node.operand)) + if isinstance(node, ast.BinOp): + lhs = _from_ast(node.left) + rhs = _from_ast(node.right) + if isinstance(node.op, ast.Add): + return lhs + rhs + if isinstance(node.op, ast.Sub): + return lhs - rhs + if isinstance(node.op, ast.Mult): + return lhs * rhs + if isinstance(node.op, ast.Div): + return lhs / rhs + if isinstance(node.op, ast.Pow): + return lhs**rhs + msg = f"Unsupported binary operator: {ast.dump(node.op)}" + raise TypeError(msg) + if isinstance(node, ast.Call): + if not isinstance(node.func, ast.Name): + msg = f"Unsupported call target: {ast.dump(node.func)}" + raise TypeError(msg) + name = node.func.id + args = [_from_ast(arg) for arg in node.args] + if name == "exp": + return exp(args[0]) + if name == "log": + return log(args[0]) + if name == "sqrt": + return sqrt(args[0]) + if name == "abs": + return abs(args[0]) + if name == "plog": + return plog(args[0]) + if name == "square": + return square(args[0]) + if name == "cube": + return cube(args[0]) + msg = f"Unsupported function call: {name}" + raise ValueError(msg) + msg = f"Unsupported AST node: {ast.dump(node)}" + raise TypeError(msg) + + +def parse_expression(source: str) -> Num: + """ + Parse the archived paper expression syntax into the Egglog DSL. + + The input strings come from the normalized copies of the Haskell benchmark + corpora. Numeric literals are kept as constants here; the paper's + parameter-count reporting projects them to fitted parameters later. + """ + return _from_ast(ast.parse(_normalize_expression(source), mode="eval")) + + +def render_num(num: Num) -> str: # noqa: C901, PLR0911, PLR0912 + """Render a `Num` back into a Python-like surface syntax for reports.""" + match get_callable_args(num, Num): + case (value_expr,) if isinstance(value_expr, f64): + return _render_float(float(value_expr.value)) + case _: + pass + match get_callable_args(num, Num.var): + case (name_expr,) if isinstance(name_expr, String): + return name_expr.value + case _: + pass + match get_callable_args(num, Num.__add__): + case (lhs, rhs) if isinstance(lhs, Num) and isinstance(rhs, Num): + return f"({render_num(lhs)} + {render_num(rhs)})" + case _: + pass + match get_callable_args(num, Num.__sub__): + case (lhs, rhs) if isinstance(lhs, Num) and isinstance(rhs, Num): + return f"({render_num(lhs)} - {render_num(rhs)})" + case _: + pass + match get_callable_args(num, Num.__mul__): + case (lhs, rhs) if isinstance(lhs, Num) and isinstance(rhs, Num): + return f"({render_num(lhs)} * {render_num(rhs)})" + case _: + pass + match get_callable_args(num, Num.__truediv__): + case (lhs, rhs) if isinstance(lhs, Num) and isinstance(rhs, Num): + return f"({render_num(lhs)} / {render_num(rhs)})" + case _: + pass + match get_callable_args(num, Num.__pow__): + case (lhs, rhs) if isinstance(lhs, Num) and isinstance(rhs, Num): + return f"({render_num(lhs)} ** {render_num(rhs)})" + case _: + pass + match get_callable_args(num, Num.exp): + case (inner,) if isinstance(inner, Num): + return f"exp({render_num(inner)})" + case _: + pass + match get_callable_args(num, Num.log): + case (inner,) if isinstance(inner, Num): + return f"log({render_num(inner)})" + case _: + pass + match get_callable_args(num, Num.sqrt): + case (inner,) if isinstance(inner, Num): + return f"sqrt({render_num(inner)})" + case _: + pass + match get_callable_args(num, Num.__abs__): + case (inner,) if isinstance(inner, Num): + return f"abs({render_num(inner)})" + case _: + pass + msg = f"Unsupported Num node for rendering: {num!r}" + raise TypeError(msg) + + +def _eval_num(num: Num, env: Mapping[str, float]) -> float | None: # noqa: C901, PLR0911, PLR0912 + """ + Structural evaluator for notebook/debugging use. + + This is not part of the EqSat algorithm. It is only used for artifact + checks and mirrors the real-domain restrictions used elsewhere in the + replication notebooks. + """ + match get_callable_args(num, Num): + case (value_expr,) if isinstance(value_expr, f64): + value = float(value_expr.value) + return value if math.isfinite(value) else None + case _: + pass + match get_callable_args(num, Num.var): + case (name_expr,) if isinstance(name_expr, String): + env_value = env.get(name_expr.value) + if env_value is None or not math.isfinite(env_value): + return None + return float(env_value) + case _: + pass + match get_callable_args(num, Num.__add__): + case (lhs, rhs) if isinstance(lhs, Num) and isinstance(rhs, Num): + left = _eval_num(lhs, env) + right = _eval_num(rhs, env) + return None if left is None or right is None else _combine_binary(left, right, "add") + case _: + pass + match get_callable_args(num, Num.__sub__): + case (lhs, rhs) if isinstance(lhs, Num) and isinstance(rhs, Num): + left = _eval_num(lhs, env) + right = _eval_num(rhs, env) + return None if left is None or right is None else _combine_binary(left, right, "sub") + case _: + pass + match get_callable_args(num, Num.__mul__): + case (lhs, rhs) if isinstance(lhs, Num) and isinstance(rhs, Num): + left = _eval_num(lhs, env) + right = _eval_num(rhs, env) + return None if left is None or right is None else _combine_binary(left, right, "mul") + case _: + pass + match get_callable_args(num, Num.__truediv__): + case (lhs, rhs) if isinstance(lhs, Num) and isinstance(rhs, Num): + left = _eval_num(lhs, env) + right = _eval_num(rhs, env) + return None if left is None or right is None else _combine_binary(left, right, "div") + case _: + pass + match get_callable_args(num, Num.__pow__): + case (lhs, rhs) if isinstance(lhs, Num) and isinstance(rhs, Num): + left = _eval_num(lhs, env) + right = _eval_num(rhs, env) + return None if left is None or right is None else _combine_binary(left, right, "pow") + case _: + pass + match get_callable_args(num, Num.exp): + case (inner,) if isinstance(inner, Num): + inner_value = _eval_num(inner, env) + if inner_value is None: + return None + try: + result = math.exp(inner_value) + except OverflowError: + return None + return result if math.isfinite(result) else None + case _: + pass + match get_callable_args(num, Num.log): + case (inner,) if isinstance(inner, Num): + inner_value = _eval_num(inner, env) + if inner_value is None or inner_value <= 0.0: + return None + result = math.log(inner_value) + return result if math.isfinite(result) else None + case _: + pass + match get_callable_args(num, Num.sqrt): + case (inner,) if isinstance(inner, Num): + inner_value = _eval_num(inner, env) + if inner_value is None or inner_value < 0.0: + return None + result = math.sqrt(inner_value) + return result if math.isfinite(result) else None + case _: + pass + match get_callable_args(num, Num.__abs__): + case (inner,) if isinstance(inner, Num): + inner_value = _eval_num(inner, env) + if inner_value is None: + return None + result = abs(inner_value) + return result if math.isfinite(result) else None + case _: + pass + msg = f"Unsupported Num node for evaluation: {num!r}" + raise TypeError(msg) + + +def count_params(num: Num) -> int: # noqa: C901, PLR0911, PLR0912 + """ + Mirror the paper harness's parameter counting: + + recountParams . replaceConstsWithParams + + from ``param-eq-haskell/src/Main.hs``. + + That means numeric leaves are counted as parameters for reporting, but the + EqSat language itself still sees them as constants. Power exponents follow + the Haskell projection too: constant exponents are not counted as + parameters, but non-constant exponent subexpressions are still traversed. + """ + match get_callable_args(num, Num): + case (_value_expr,): + return 1 + case _: + pass + match get_callable_args(num, Num.var): + case (_name_expr,): + return 0 + case _: + pass + match get_callable_args(num, Num.__add__): + case (lhs, rhs) if isinstance(lhs, Num) and isinstance(rhs, Num): + return count_params(lhs) + count_params(rhs) + case _: + pass + match get_callable_args(num, Num.__sub__): + case (lhs, rhs) if isinstance(lhs, Num) and isinstance(rhs, Num): + return count_params(lhs) + count_params(rhs) + case _: + pass + match get_callable_args(num, Num.__mul__): + case (lhs, rhs) if isinstance(lhs, Num) and isinstance(rhs, Num): + return count_params(lhs) + count_params(rhs) + case _: + pass + match get_callable_args(num, Num.__truediv__): + case (lhs, rhs) if isinstance(lhs, Num) and isinstance(rhs, Num): + return count_params(lhs) + count_params(rhs) + case _: + pass + match get_callable_args(num, Num.__pow__): + case (lhs, rhs) if isinstance(lhs, Num) and isinstance(rhs, Num): + match get_callable_args(rhs, Num): + case (_value_expr,): + return count_params(lhs) + case _: + return count_params(lhs) + count_params(rhs) + case _: + pass + match get_callable_args(num, Num.exp): + case (inner,) if isinstance(inner, Num): + return count_params(inner) + case _: + pass + match get_callable_args(num, Num.log): + case (inner,) if isinstance(inner, Num): + return count_params(inner) + case _: + pass + match get_callable_args(num, Num.sqrt): + case (inner,) if isinstance(inner, Num): + return count_params(inner) + case _: + pass + match get_callable_args(num, Num.__abs__): + case (inner,) if isinstance(inner, Num): + return count_params(inner) + case _: + pass + msg = f"Unsupported Num node while counting parameters: {num!r}" + raise TypeError(msg) + + +def count_nodes(num: Num) -> int: # noqa: C901, PLR0911, PLR0912 + """Count AST nodes in the rendered tree, matching the paper tables' style.""" + match get_callable_args(num, Num): + case (_value_expr,): + return 1 + case _: + pass + match get_callable_args(num, Num.var): + case (_name_expr,): + return 1 + case _: + pass + match get_callable_args(num, Num.__add__): + case (lhs, rhs) if isinstance(lhs, Num) and isinstance(rhs, Num): + return 1 + count_nodes(lhs) + count_nodes(rhs) + case _: + pass + match get_callable_args(num, Num.__sub__): + case (lhs, rhs) if isinstance(lhs, Num) and isinstance(rhs, Num): + return 1 + count_nodes(lhs) + count_nodes(rhs) + case _: + pass + match get_callable_args(num, Num.__mul__): + case (lhs, rhs) if isinstance(lhs, Num) and isinstance(rhs, Num): + return 1 + count_nodes(lhs) + count_nodes(rhs) + case _: + pass + match get_callable_args(num, Num.__truediv__): + case (lhs, rhs) if isinstance(lhs, Num) and isinstance(rhs, Num): + return 1 + count_nodes(lhs) + count_nodes(rhs) + case _: + pass + match get_callable_args(num, Num.__pow__): + case (lhs, rhs) if isinstance(lhs, Num) and isinstance(rhs, Num): + return 1 + count_nodes(lhs) + count_nodes(rhs) + case _: + pass + match get_callable_args(num, Num.exp): + case (inner,) if isinstance(inner, Num): + return 1 + count_nodes(inner) + case _: + pass + match get_callable_args(num, Num.log): + case (inner,) if isinstance(inner, Num): + return 1 + count_nodes(inner) + case _: + pass + match get_callable_args(num, Num.sqrt): + case (inner,) if isinstance(inner, Num): + return 1 + count_nodes(inner) + case _: + pass + match get_callable_args(num, Num.__abs__): + case (inner,) if isinstance(inner, Num): + return 1 + count_nodes(inner) + case _: + pass + msg = f"Unsupported Num node while counting nodes: {num!r}" + raise TypeError(msg) + + +def _serialized_counts(egraph: egglog.EGraph) -> tuple[int, int]: + payload = json.loads(egraph._serialize().to_json()) + return len(payload.get("nodes", {})), len(payload.get("class_data", {})) + + +analysis_schedule = const_merge_rules | const_seed_rules | const_propagation_rules | const_prune_rules +basic_rules = ( + basic_add_comm_rules + | basic_mul_comm_rules + | basic_add_assoc_rules + | basic_mul_assoc_rules + | basic_mul_div_rules + | basic_product_regroup_rules + | basic_other_rules +) +rewrite_ruleset = basic_rules | fun_rules + + +def _make_rewrite_scheduler() -> BackOff: + """Build the retained per-pass scheduler configuration.""" + return back_off( + match_limit=BACKOFF_MATCH_LIMIT, + ban_length=BACKOFF_BAN_LENGTH, + fresh_rematch=True, + ).persistent() + + +def _graph_size(egraph: egglog.EGraph) -> int: + return sum(size for _, size in egraph.all_function_sizes()) + + +def _run_single_pass_egraph(num: Num) -> tuple[egglog.EGraph, float]: + """ + Run one `rewriteTree`-like pass and return the populated e-graph. + + This mirrors Haskell at the control-flow level: + - one fresh-rematch backoff scheduler per outer pass + - up to 30 inner rewrite rounds + - one saturated analysis round after each rewrite round + - stop when total egraph size stops changing + """ + egraph = egglog.EGraph() + egraph.register(num) + rewrite_scheduler = _make_rewrite_scheduler() + + start = time.perf_counter() + previous_size = _graph_size(egraph) + for _ in range(HASKELL_INNER_ITERATION_LIMIT): + egraph.run(run(rewrite_ruleset, scheduler=rewrite_scheduler)) + egraph.run(analysis_schedule.saturate()) + current_size = _graph_size(egraph) + if current_size == previous_size: + break + previous_size = current_size + elapsed = time.perf_counter() - start + return egraph, elapsed + + +def _run_single_pass(num: Num) -> tuple[Num, int, int, int, int, float]: + egraph, elapsed = _run_single_pass_egraph(num) + extracted, cost = egraph.extract(num, include_cost=True) + total_size = _graph_size(egraph) + node_count, eclass_count = _serialized_counts(egraph) + return extracted, int(cost), total_size, node_count, eclass_count, elapsed + + +def run_paper_pipeline(num: Num) -> PaperPipelineReport: + """ + Approximate `simplifyE` from `FixTree.hs`. + + Haskell does: + relabelParams . toSRTree . rewriteUntilNoChange [rewriteTree] 2 . toFixTree + + Here we mirror that as: + - run `_run_single_pass` on the current extracted term + - extract + - stop early if the rendered term is unchanged + - otherwise rebuild from the extracted term and try again + """ + before_nodes = count_nodes(num) + before_params = count_params(num) + current = num + last_cost = 0 + total_size = 0 + node_count = 0 + eclass_count = 0 + total_sec = 0.0 + passes = 0 + status = "saturated" + for pass_index in range(1, MAX_PASSES + 1): + extracted, last_cost, total_size, node_count, eclass_count, elapsed = _run_single_pass(current) + total_sec += elapsed + passes = pass_index + if render_num(extracted) == render_num(current): + current = extracted + break + current = extracted + after_nodes = count_nodes(current) + after_params = count_params(current) + return PaperPipelineReport( + status=status, + passes=passes, + total_sec=total_sec, + total_size=total_size, + node_count=node_count, + eclass_count=eclass_count, + before_nodes=before_nodes, + before_params=before_params, + after_nodes=after_nodes, + after_params=after_params, + rendered=render_num(current), + extracted=current, + extracted_cost=last_cost, + ) + + +def _cli() -> None: + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument("--expr", required=True) + args = parser.parse_args() + report = run_paper_pipeline(parse_expression(args.expr)) + payload = { + "status": report.status, + "passes": report.passes, + "total_sec": report.total_sec, + "total_size": report.total_size, + "node_count": report.node_count, + "eclass_count": report.eclass_count, + "before_nodes": report.before_nodes, + "before_params": report.before_params, + "after_nodes": report.after_nodes, + "after_params": report.after_params, + "rendered": report.rendered, + "extracted_cost": report.extracted_cost, + } + print(json.dumps(payload, sort_keys=True)) + + +if __name__ == "__main__": + _cli() diff --git a/python/egglog/exp/param_eq/replication.ipynb b/python/egglog/exp/param_eq/replication.ipynb new file mode 100644 index 00000000..d8cb98e4 --- /dev/null +++ b/python/egglog/exp/param_eq/replication.ipynb @@ -0,0 +1,1539 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "d2afd959", + "metadata": {}, + "source": [ + "# 2026-03 - Param-Eq Baseline Thesis Check\n", + "\n", + "This notebook is intentionally comparison-first.\n", + "\n", + "Its main claim is:\n", + "- the archived Haskell artifact,\n", + "- a fresh live Haskell rerun, and\n", + "- the retained Egglog baseline\n", + "\n", + "all support the same qualitative paper conclusions on the retained param-eq\n", + "metrics.\n", + "\n", + "The notebook reads only checked-in artifacts:\n", + "- archived Haskell rows\n", + "- live Haskell rows\n", + "- Egglog rows\n", + "- Pagie runtime comparison rows for all three implementations\n", + "\n", + "Offline regeneration commands from the repository root:\n", + "- `uv run python -m egglog.exp.param_eq.normalize_archives`\n", + "- `uv run python -m egglog.exp.param_eq.run_haskell_corpus`\n", + "- `uv run python -m egglog.exp.param_eq.run_egglog_corpus`\n", + "- `uv run python python/egglog/exp/param_eq/replication.py`" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "11145b5d", + "metadata": { + "execution": { + "iopub.execute_input": "2026-04-06T10:07:47.059888Z", + "iopub.status.busy": "2026-04-06T10:07:47.059812Z", + "iopub.status.idle": "2026-04-06T10:07:48.083204Z", + "shell.execute_reply": "2026-04-06T10:07:48.082591Z" + } + }, + "outputs": [], + "source": [ + "from __future__ import annotations\n", + "\n", + "import os\n", + "from io import StringIO\n", + "from typing import Any\n", + "\n", + "import altair as alt\n", + "import jupytext\n", + "import nbformat\n", + "import pandas as pd\n", + "from IPython.display import SVG, display\n", + "from nbclient import NotebookClient\n", + "\n", + "from egglog.exp.param_eq.paths import ARTIFACT_DIR, PARAM_EQ_DIR\n", + "\n", + "alt.data_transformers.disable_max_rows()\n", + "alt.renderers.enable(\"default\")\n", + "\n", + "ALGORITHM_ORDER = [\"Bingo\", \"EPLEX\", \"GP-GOMEA\", \"Operon\", \"PySR\", \"SBP\"]\n", + "DATASET_ORDER = [\"pagie\", \"kotanchek\"]\n", + "DATASET_LABELS = {\"pagie\": \"Pagie-1\", \"kotanchek\": \"Kotanchek\"}\n", + "IMPLEMENTATION_ORDER = [\"Archived Haskell\", \"Live Haskell\", \"Egglog\"]\n", + "METHOD_ORDER = [\"EqSat\", \"Sympy\", \"Sympy + EqSat\"]\n", + "COMPARISON_ORDER = [\"Sympy x EqSat\", \"Sympy + EqSat x EqSat\"]\n", + "DELTA_ORDER = [\"Δ == 0\", \"Δ <= 1\"]\n", + "\n", + "BOX_COLOR = \"#4C78A8\"\n", + "POINT_COLOR = \"#F58518\"\n", + "TABLE_FILL = \"#F7F7F7\"\n", + "\n", + "ARCHIVED_HASKELL_PATH = ARTIFACT_DIR / \"haskell_paper_rows.csv\"\n", + "LIVE_HASKELL_PATH = ARTIFACT_DIR / \"haskell_live_rows.csv\"\n", + "EGGLOG_PATH = ARTIFACT_DIR / \"egglog_paper_rows.csv\"\n", + "RUNTIME_PATH = ARTIFACT_DIR / \"pagie_runtime_compare.csv\"\n", + "\n", + "for required_path in [ARCHIVED_HASKELL_PATH, LIVE_HASKELL_PATH, EGGLOG_PATH, RUNTIME_PATH]:\n", + " if not required_path.exists():\n", + " msg = f\"Missing required artifact: {required_path}\"\n", + " raise FileNotFoundError(msg)\n", + "\n", + "\n", + "def _coerce_numeric(frame: pd.DataFrame, columns: list[str]) -> pd.DataFrame:\n", + " for column in columns:\n", + " if column in frame.columns:\n", + " frame[column] = pd.to_numeric(frame[column], errors=\"coerce\")\n", + " return frame\n", + "\n", + "\n", + "def _paper_haskell_frame(path: os.PathLike[str] | str) -> pd.DataFrame:\n", + " frame = pd.read_csv(path)\n", + " frame = frame[frame[\"is_paper_row\"] == 1].copy()\n", + " return _coerce_numeric(\n", + " frame,\n", + " [\n", + " \"raw_index\",\n", + " \"algo_row\",\n", + " \"orig_nodes\",\n", + " \"orig_params\",\n", + " \"simpl_nodes\",\n", + " \"simpl_params\",\n", + " \"orig_runtime_ms\",\n", + " \"orig_nodes_sympy\",\n", + " \"orig_params_sympy\",\n", + " \"simpl_nodes_sympy\",\n", + " \"simpl_params_sympy\",\n", + " \"sympy_runtime_ms\",\n", + " \"n_params\",\n", + " \"n_rank\",\n", + " ],\n", + " )\n", + "\n", + "\n", + "def _paper_egglog_frame(path: os.PathLike[str] | str) -> pd.DataFrame:\n", + " frame = pd.read_csv(path)\n", + " frame = frame[frame[\"is_paper_row\"] == 1].copy()\n", + " return _coerce_numeric(\n", + " frame,\n", + " [\n", + " \"raw_index\",\n", + " \"algo_row\",\n", + " \"orig_runtime_ms\",\n", + " \"orig_nodes\",\n", + " \"orig_params\",\n", + " \"simpl_nodes\",\n", + " \"simpl_params\",\n", + " \"orig_total_size\",\n", + " \"orig_egraph_nodes\",\n", + " \"orig_eclass_count\",\n", + " \"orig_passes\",\n", + " \"orig_extracted_cost\",\n", + " \"sympy_runtime_ms\",\n", + " \"orig_nodes_sympy\",\n", + " \"orig_params_sympy\",\n", + " \"simpl_nodes_sympy\",\n", + " \"simpl_params_sympy\",\n", + " \"sympy_total_size\",\n", + " \"sympy_egraph_nodes\",\n", + " \"sympy_eclass_count\",\n", + " \"sympy_passes\",\n", + " \"sympy_extracted_cost\",\n", + " \"n_params\",\n", + " \"n_rank\",\n", + " ],\n", + " )\n", + "\n", + "\n", + "def _paper_runtime_frame() -> pd.DataFrame:\n", + " frame = pd.read_csv(RUNTIME_PATH)\n", + " return _coerce_numeric(frame, [\"node_count\", \"runtime_ms\"])\n", + "\n", + "\n", + "def add_paper_metrics(frame: pd.DataFrame) -> pd.DataFrame:\n", + " result = frame.copy()\n", + " result[\"orig_x_egg\"] = (result[\"orig_params\"] - result[\"simpl_params\"]) / result[\"orig_params\"]\n", + " result[\"orig_x_sympy\"] = (result[\"orig_params\"] - result[\"orig_params_sympy\"]) / result[\"orig_params\"]\n", + " result[\"orig_x_sympyegg\"] = (result[\"orig_params\"] - result[\"simpl_params_sympy\"]) / result[\"orig_params\"]\n", + " result[\"sympy_x_egg\"] = (result[\"orig_params_sympy\"] - result[\"simpl_params\"]) / result[\"orig_params_sympy\"]\n", + " result[\"sympyegg_x_egg\"] = (result[\"simpl_params_sympy\"] - result[\"simpl_params\"]) / result[\"simpl_params_sympy\"]\n", + " result[\"orig_rank\"] = result[\"n_params\"] - result[\"n_rank\"]\n", + " result[\"simpl_rank\"] = result[\"simpl_params\"] - result[\"n_rank\"]\n", + " result[\"sympy_rank\"] = result[\"orig_params_sympy\"] - result[\"n_rank\"]\n", + " return result\n", + "\n", + "\n", + "def with_implementation(frame: pd.DataFrame, implementation: str) -> pd.DataFrame:\n", + " result = frame.copy()\n", + " result[\"implementation\"] = implementation\n", + " result[\"dataset_label\"] = result[\"dataset\"].map(DATASET_LABELS)\n", + " return result\n", + "\n", + "\n", + "def melt_methods(frame: pd.DataFrame, *, columns: dict[str, str], value_name: str) -> pd.DataFrame:\n", + " melted = frame.melt(\n", + " id_vars=[\"implementation\", \"dataset\", \"dataset_label\", \"algorithm\", \"raw_index\"],\n", + " value_vars=list(columns.values()),\n", + " var_name=\"method_key\",\n", + " value_name=value_name,\n", + " )\n", + " inverse = {value: key for key, value in columns.items()}\n", + " melted[\"method\"] = melted[\"method_key\"].map(inverse)\n", + " return melted.drop(columns=[\"method_key\"])\n", + "\n", + "\n", + "def _point_layer(frame: pd.DataFrame, *, y: str, tooltip: list[str]) -> alt.Chart:\n", + " return (\n", + " alt.Chart(frame)\n", + " .transform_calculate(jitter=\"(random() - 0.5) * 18\")\n", + " .mark_circle(size=38, color=POINT_COLOR, opacity=0.68, stroke=\"white\", strokeWidth=0.7)\n", + " .encode(\n", + " xOffset=alt.XOffset(\"jitter:Q\"),\n", + " y=alt.Y(f\"{y}:Q\"),\n", + " tooltip=tooltip,\n", + " )\n", + " )\n", + "\n", + "\n", + "def faceted_boxplot(frame: pd.DataFrame, *, y: str, title: str, method_sort: list[str]) -> Any:\n", + " base = (\n", + " alt.Chart(frame)\n", + " .encode(\n", + " x=alt.X(\"algorithm:N\", sort=ALGORITHM_ORDER, title=\"Algorithm\"),\n", + " y=alt.Y(f\"{y}:Q\", title=y.replace(\"_\", \" \")),\n", + " )\n", + " .properties(width=115, height=170)\n", + " )\n", + " layered = alt.layer(\n", + " _point_layer(\n", + " frame,\n", + " y=y,\n", + " tooltip=[\"implementation\", \"dataset\", \"algorithm\", \"method\", \"raw_index\", y],\n", + " ).encode(x=alt.X(\"algorithm:N\", sort=ALGORITHM_ORDER, title=\"Algorithm\")),\n", + " base.mark_boxplot(size=16, opacity=0.58, color=BOX_COLOR, outliers=False),\n", + " )\n", + " return layered.facet(\n", + " row=alt.Row(\"implementation:N\", sort=IMPLEMENTATION_ORDER, title=None),\n", + " column=alt.Column(\"method:N\", sort=method_sort, title=None),\n", + " ).properties(title=title)\n", + "\n", + "\n", + "def rank_boxplot(frame: pd.DataFrame, *, title: str) -> Any:\n", + " base = (\n", + " alt.Chart(frame)\n", + " .encode(\n", + " x=alt.X(\"algorithm:N\", sort=ALGORITHM_ORDER, title=\"Algorithm\"),\n", + " y=alt.Y(\"simpl_rank:Q\", title=\"simplified params - rank\"),\n", + " )\n", + " .properties(width=115, height=170)\n", + " )\n", + " layered = alt.layer(\n", + " _point_layer(\n", + " frame,\n", + " y=\"simpl_rank\",\n", + " tooltip=[\"implementation\", \"dataset\", \"algorithm\", \"raw_index\", \"simpl_rank\", \"n_rank\", \"simpl_params\"],\n", + " ).encode(x=alt.X(\"algorithm:N\", sort=ALGORITHM_ORDER, title=\"Algorithm\")),\n", + " base.mark_boxplot(size=16, opacity=0.58, color=BOX_COLOR, outliers=False),\n", + " )\n", + " return layered.facet(\n", + " row=alt.Row(\"implementation:N\", sort=IMPLEMENTATION_ORDER, title=None),\n", + " column=alt.Column(\"dataset_label:N\", sort=[DATASET_LABELS[d] for d in DATASET_ORDER], title=None),\n", + " ).properties(title=title)\n", + "\n", + "\n", + "def runtime_chart(frame: pd.DataFrame, *, title: str) -> Any:\n", + " return (\n", + " alt.Chart(frame)\n", + " .mark_circle(size=70, opacity=0.78, stroke=\"white\", strokeWidth=0.8, color=BOX_COLOR)\n", + " .encode(\n", + " x=alt.X(\"node_count:Q\", title=\"number of nodes\"),\n", + " y=alt.Y(\"runtime_ms:Q\", title=\"runtime (ms)\"),\n", + " tooltip=[\"implementation\", \"node_count\", \"runtime_ms\"],\n", + " )\n", + " .properties(width=220, height=220)\n", + " .facet(column=alt.Column(\"implementation:N\", sort=IMPLEMENTATION_ORDER, title=None))\n", + " .properties(title=title)\n", + " )\n", + "\n", + "\n", + "def comparison_table(frame: pd.DataFrame, *, implementation: str) -> pd.DataFrame:\n", + " rows: list[dict[str, object]] = []\n", + " for dataset in DATASET_ORDER:\n", + " dataset_frame = frame[frame[\"dataset\"] == dataset]\n", + " for algorithm in ALGORITHM_ORDER:\n", + " algo_frame = dataset_frame[dataset_frame[\"algorithm\"] == algorithm]\n", + " for delta in [0, 1]:\n", + " eligible = algo_frame[algo_frame[\"orig_rank\"] > delta]\n", + " percent = float(\"nan\")\n", + " if not eligible.empty:\n", + " percent = 100.0 * (eligible[\"simpl_rank\"] <= delta).sum() / len(eligible)\n", + " rows.append({\n", + " \"implementation\": implementation,\n", + " \"dataset\": dataset,\n", + " \"dataset_label\": DATASET_LABELS[dataset],\n", + " \"algorithm\": algorithm,\n", + " \"delta\": f\"Δ {'==' if delta == 0 else '<='} {delta}\",\n", + " \"percent\": percent,\n", + " })\n", + " result = pd.DataFrame(rows)\n", + " result[\"percent_label\"] = result[\"percent\"].map(lambda value: \"n/a\" if pd.isna(value) else f\"{value:.2f}%\")\n", + " return result\n", + "\n", + "\n", + "def faceted_table4_chart(frame: pd.DataFrame) -> Any:\n", + " base = alt.Chart(frame).encode(\n", + " x=alt.X(\"dataset_label:N\", sort=[DATASET_LABELS[d] for d in DATASET_ORDER], title=None),\n", + " y=alt.Y(\"algorithm:N\", sort=ALGORITHM_ORDER, title=None),\n", + " )\n", + " layered = alt.layer(\n", + " base.mark_rect(fill=TABLE_FILL, stroke=\"#DDDDDD\"),\n", + " base.mark_text(fontSize=11).encode(text=\"percent_label:N\"),\n", + " ).properties(width=120, height=18 * len(ALGORITHM_ORDER))\n", + " return layered.facet(\n", + " row=alt.Row(\"delta:N\", sort=DELTA_ORDER, title=None),\n", + " column=alt.Column(\"implementation:N\", sort=IMPLEMENTATION_ORDER, title=None),\n", + " ).properties(title=\"Faceted Table 4 analog\")\n", + "\n", + "\n", + "def show_chart(chart: Any) -> None:\n", + " buffer = StringIO()\n", + " chart.save(buffer, format=\"svg\")\n", + " display(SVG(buffer.getvalue()))\n", + "\n", + "\n", + "archived_haskell = with_implementation(\n", + " add_paper_metrics(_paper_haskell_frame(ARCHIVED_HASKELL_PATH)), \"Archived Haskell\"\n", + ")\n", + "live_haskell = with_implementation(add_paper_metrics(_paper_haskell_frame(LIVE_HASKELL_PATH)), \"Live Haskell\")\n", + "egglog = with_implementation(add_paper_metrics(_paper_egglog_frame(EGGLOG_PATH)), \"Egglog\")\n", + "runtime_rows = _paper_runtime_frame()\n", + "\n", + "combined = pd.concat([archived_haskell, live_haskell, egglog], ignore_index=True)\n", + "\n", + "haskell_columns = {\n", + " \"EqSat\": \"orig_x_egg\",\n", + " \"Sympy\": \"orig_x_sympy\",\n", + " \"Sympy + EqSat\": \"orig_x_sympyegg\",\n", + "}\n", + "comparison_columns = {\n", + " \"Sympy x EqSat\": \"sympy_x_egg\",\n", + " \"Sympy + EqSat x EqSat\": \"sympyegg_x_egg\",\n", + "}\n", + "\n", + "egglog_vs_live = egglog.merge(\n", + " live_haskell[\n", + " [\n", + " \"dataset\",\n", + " \"algorithm\",\n", + " \"raw_index\",\n", + " \"simpl_params\",\n", + " \"simpl_params_sympy\",\n", + " ]\n", + " ],\n", + " on=[\"dataset\", \"algorithm\", \"raw_index\"],\n", + " suffixes=(\"_egglog\", \"_live\"),\n", + ")\n", + "egglog_vs_live[\"orig_exact\"] = egglog_vs_live[\"simpl_params_egglog\"] == egglog_vs_live[\"simpl_params_live\"]\n", + "egglog_vs_live[\"sympy_exact\"] = egglog_vs_live[\"simpl_params_sympy_egglog\"] == egglog_vs_live[\"simpl_params_sympy_live\"]\n", + "egglog_vs_live[\"orig_gap\"] = (egglog_vs_live[\"simpl_params_egglog\"] - egglog_vs_live[\"simpl_params_live\"]).abs()\n", + "egglog_vs_live[\"sympy_gap\"] = (\n", + " egglog_vs_live[\"simpl_params_sympy_egglog\"] - egglog_vs_live[\"simpl_params_sympy_live\"]\n", + ").abs()\n", + "\n", + "archive_drift = live_haskell.merge(\n", + " archived_haskell[\n", + " [\n", + " \"dataset\",\n", + " \"algorithm\",\n", + " \"raw_index\",\n", + " \"simpl_params\",\n", + " \"simpl_params_sympy\",\n", + " ]\n", + " ],\n", + " on=[\"dataset\", \"algorithm\", \"raw_index\"],\n", + " suffixes=(\"_live\", \"_archived\"),\n", + ")\n", + "archive_drift[\"orig_drift\"] = archive_drift[\"simpl_params_live\"] - archive_drift[\"simpl_params_archived\"]\n", + "archive_drift[\"sympy_drift\"] = archive_drift[\"simpl_params_sympy_live\"] - archive_drift[\"simpl_params_sympy_archived\"]\n", + "\n", + "live_fallback_rows = live_haskell[live_haskell[\"baseline_source\"] != \"live_haskell\"][\n", + " [\"dataset\", \"algorithm\", \"algo_row\", \"baseline_source\", \"orig_live_status\", \"sympy_live_status\"]\n", + "].drop_duplicates()\n", + "\n", + "runtime_compare = runtime_rows[[\"implementation\", \"node_count\", \"runtime_ms\"]].copy()\n", + "\n", + "table4_source = pd.concat(\n", + " [\n", + " comparison_table(archived_haskell, implementation=\"Archived Haskell\"),\n", + " comparison_table(live_haskell, implementation=\"Live Haskell\"),\n", + " comparison_table(egglog, implementation=\"Egglog\"),\n", + " ],\n", + " ignore_index=True,\n", + ")" + ] + }, + { + "cell_type": "markdown", + "id": "4198df15", + "metadata": {}, + "source": [ + "## 1. Artifact Overview" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "c19fdf9c", + "metadata": { + "execution": { + "iopub.execute_input": "2026-04-06T10:07:48.084510Z", + "iopub.status.busy": "2026-04-06T10:07:48.084425Z", + "iopub.status.idle": "2026-04-06T10:07:48.092266Z", + "shell.execute_reply": "2026-04-06T10:07:48.091937Z" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + " comparison exact_matches total_rows max_gap\n", + "0 Egglog vs live Haskell (original) 317 341 3\n", + "1 Egglog vs live Haskell (sympy) 325 341 6\n", + "2 Live vs archived Haskell (original) 333 341 3\n", + "3 Live vs archived Haskell (sympy) 328 341 2" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "artifact_summary = pd.DataFrame([\n", + " {\n", + " \"implementation\": \"Archived Haskell\",\n", + " \"rows\": len(archived_haskell),\n", + " \"original_median_simpl_rank\": float(archived_haskell[\"simpl_rank\"].median()),\n", + " \"sympy_median_simpl_rank\": float(archived_haskell[\"sympy_rank\"].median()),\n", + " },\n", + " {\n", + " \"implementation\": \"Live Haskell\",\n", + " \"rows\": len(live_haskell),\n", + " \"original_median_simpl_rank\": float(live_haskell[\"simpl_rank\"].median()),\n", + " \"sympy_median_simpl_rank\": float(live_haskell[\"sympy_rank\"].median()),\n", + " },\n", + " {\n", + " \"implementation\": \"Egglog\",\n", + " \"rows\": len(egglog),\n", + " \"original_median_simpl_rank\": float(egglog[\"simpl_rank\"].median()),\n", + " \"sympy_median_simpl_rank\": float(egglog[\"sympy_rank\"].median()),\n", + " },\n", + "])\n", + "display(artifact_summary)\n", + "display(\n", + " pd.DataFrame([\n", + " {\n", + " \"comparison\": \"Egglog vs live Haskell (original)\",\n", + " \"exact_matches\": int(egglog_vs_live[\"orig_exact\"].sum()),\n", + " \"total_rows\": len(egglog_vs_live),\n", + " \"max_gap\": int(egglog_vs_live[\"orig_gap\"].max()),\n", + " },\n", + " {\n", + " \"comparison\": \"Egglog vs live Haskell (sympy)\",\n", + " \"exact_matches\": int(egglog_vs_live[\"sympy_exact\"].sum()),\n", + " \"total_rows\": len(egglog_vs_live),\n", + " \"max_gap\": int(egglog_vs_live[\"sympy_gap\"].max()),\n", + " },\n", + " {\n", + " \"comparison\": \"Live vs archived Haskell (original)\",\n", + " \"exact_matches\": int((archive_drift[\"orig_drift\"] == 0).sum()),\n", + " \"total_rows\": len(archive_drift),\n", + " \"max_gap\": int(archive_drift[\"orig_drift\"].abs().max()),\n", + " },\n", + " {\n", + " \"comparison\": \"Live vs archived Haskell (sympy)\",\n", + " \"exact_matches\": int((archive_drift[\"sympy_drift\"] == 0).sum()),\n", + " \"total_rows\": len(archive_drift),\n", + " \"max_gap\": int(archive_drift[\"sympy_drift\"].abs().max()),\n", + " },\n", + " ])\n", + ")\n", + "# -" + ] + }, + { + "cell_type": "markdown", + "id": "dbafaba9", + "metadata": {}, + "source": [ + "The retained question is no longer whether Egglog finishes the corpus; it does.\n", + "\n", + "The useful question is whether the three result sets support the same practical\n", + "thesis. After correcting the live Haskell rerun to follow the checked-in\n", + "Haskell Sympy modules directly, archived and live Haskell are much closer than\n", + "they first appeared. The rest of this notebook therefore compares archived\n", + "Haskell, live Haskell, and Egglog with the same plots and the same table\n", + "layouts." + ] + }, + { + "cell_type": "markdown", + "id": "142e49e5", + "metadata": {}, + "source": [ + "## 2. Reduction Ratios" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "3af4351d", + "metadata": { + "execution": { + "iopub.execute_input": "2026-04-06T10:07:48.093258Z", + "iopub.status.busy": "2026-04-06T10:07:48.093176Z", + "iopub.status.idle": "2026-04-06T10:07:48.521433Z", + "shell.execute_reply": "2026-04-06T10:07:48.520962Z" + } + }, + "outputs": [ + { + "data": { + "image/svg+xml": [ + "−1.5−1.0−0.50.00.51.0ratioArchived Haskell−1.5−1.0−0.50.00.51.0ratioLive Haskell−1.5−1.0−0.50.00.51.0ratioEgglogEqSatSympySympy + EqSatBingoEPLEXOperonSBPGOMEASRjlAlgorithmBingoEPLEXOperonSBPGOMEASRjlAlgorithmBingoEPLEXOperonSBPGOMEASRjlAlgorithmPagie reduction ratios across archived Haskell, live Haskell, and Egglog" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "show_chart(\n", + " faceted_boxplot(\n", + " melt_methods(combined[combined[\"dataset\"] == \"pagie\"], columns=haskell_columns, value_name=\"ratio\"),\n", + " y=\"ratio\",\n", + " method_sort=METHOD_ORDER,\n", + " title=\"Pagie reduction ratios across archived Haskell, live Haskell, and Egglog\",\n", + " )\n", + ")" + ] + }, + { + "cell_type": "markdown", + "id": "40c59d4a", + "metadata": {}, + "source": [ + "Across the Pagie rows, all three implementations preserve the same qualitative\n", + "story: EqSat helps on its own, Sympy alone is not the main source of the gain,\n", + "and the combined pipeline remains the strongest or near-strongest path. The\n", + "archived and live Haskell views are now close enough that the archive reads as\n", + "a slightly stale version of the same picture rather than a conflicting one,\n", + "and Egglog tracks that shared picture closely enough to support the same\n", + "conclusion." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "c20880f7", + "metadata": { + "execution": { + "iopub.execute_input": "2026-04-06T10:07:48.526297Z", + "iopub.status.busy": "2026-04-06T10:07:48.526202Z", + "iopub.status.idle": "2026-04-06T10:07:48.745553Z", + "shell.execute_reply": "2026-04-06T10:07:48.745160Z" + } + }, + "outputs": [ + { + "data": { + "image/svg+xml": [ + "−1.5−1.0−0.50.00.51.0ratioArchived Haskell−1.5−1.0−0.50.00.51.0ratioLive Haskell−1.5−1.0−0.50.00.51.0ratioEgglogEqSatSympySympy + EqSatBingoEPLEXOperonSBPGOMEASRjlAlgorithmBingoEPLEXOperonSBPGOMEASRjlAlgorithmBingoEPLEXOperonSBPGOMEASRjlAlgorithmKotanchek reduction ratios across archived Haskell, live Haskell, and Egglog" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "show_chart(\n", + " faceted_boxplot(\n", + " melt_methods(combined[combined[\"dataset\"] == \"kotanchek\"], columns=haskell_columns, value_name=\"ratio\"),\n", + " y=\"ratio\",\n", + " method_sort=METHOD_ORDER,\n", + " title=\"Kotanchek reduction ratios across archived Haskell, live Haskell, and Egglog\",\n", + " )\n", + ")" + ] + }, + { + "cell_type": "markdown", + "id": "b34fda2b", + "metadata": {}, + "source": [ + "Kotanchek tells the same story. The per-algorithm spread changes a little\n", + "between the archived artifact and the live rerun, but the headline result does\n", + "not: EqSat is still the meaningful simplification step, and Egglog lands in\n", + "the same visual regime as both Haskell baselines." + ] + }, + { + "cell_type": "markdown", + "id": "0a772725", + "metadata": {}, + "source": [ + "## 3. EqSat Versus Sympy Comparisons" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "d698765b", + "metadata": { + "execution": { + "iopub.execute_input": "2026-04-06T10:07:48.751779Z", + "iopub.status.busy": "2026-04-06T10:07:48.751668Z", + "iopub.status.idle": "2026-04-06T10:07:48.931049Z", + "shell.execute_reply": "2026-04-06T10:07:48.930695Z" + } + }, + "outputs": [ + { + "data": { + "image/svg+xml": [ + "−1.0−0.50.00.5ratioArchived Haskell−1.0−0.50.00.5ratioLive Haskell−1.0−0.50.00.5ratioEgglogSympy x EqSatSympy + EqSat x EqSatBingoEPLEXOperonSBPGOMEASRjlAlgorithmBingoEPLEXOperonSBPGOMEASRjlAlgorithmPagie EqSat-vs-Sympy comparison ratios across all three implementations" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "show_chart(\n", + " faceted_boxplot(\n", + " melt_methods(combined[combined[\"dataset\"] == \"pagie\"], columns=comparison_columns, value_name=\"ratio\"),\n", + " y=\"ratio\",\n", + " method_sort=COMPARISON_ORDER,\n", + " title=\"Pagie EqSat-vs-Sympy comparison ratios across all three implementations\",\n", + " )\n", + ")" + ] + }, + { + "cell_type": "markdown", + "id": "7c323104", + "metadata": {}, + "source": [ + "These comparison ratios make the thesis more explicit: rerunning EqSat after\n", + "the Sympy-derived starting point still matters in all three result sets. The\n", + "archive, the live rerun, and Egglog all agree that the simplification is not\n", + "coming only from the symbolic preprocessing step." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "17af7a9e", + "metadata": { + "execution": { + "iopub.execute_input": "2026-04-06T10:07:48.934329Z", + "iopub.status.busy": "2026-04-06T10:07:48.934252Z", + "iopub.status.idle": "2026-04-06T10:07:49.026740Z", + "shell.execute_reply": "2026-04-06T10:07:49.026311Z" + } + }, + "outputs": [ + { + "data": { + "image/svg+xml": [ + "−0.4−0.20.00.20.40.6ratioArchived Haskell−0.4−0.20.00.20.40.6ratioLive Haskell−0.4−0.20.00.20.40.6ratioEgglogSympy x EqSatSympy + EqSat x EqSatBingoEPLEXOperonSBPGOMEASRjlAlgorithmBingoEPLEXOperonSBPGOMEASRjlAlgorithmKotanchek EqSat-vs-Sympy comparison ratios across all three implementations" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "show_chart(\n", + " faceted_boxplot(\n", + " melt_methods(combined[combined[\"dataset\"] == \"kotanchek\"], columns=comparison_columns, value_name=\"ratio\"),\n", + " y=\"ratio\",\n", + " method_sort=COMPARISON_ORDER,\n", + " title=\"Kotanchek EqSat-vs-Sympy comparison ratios across all three implementations\",\n", + " )\n", + ")" + ] + }, + { + "cell_type": "markdown", + "id": "49c29f8e", + "metadata": {}, + "source": [ + "The Kotanchek comparison view reaches the same conclusion. Even where archive\n", + "drift is visible, it is now a narrow tail instead of a broad Sympy split, and\n", + "the three implementations still agree on the sign and rough scale of the\n", + "EqSat contribution. That is the notebook's central evidence that the retained\n", + "Egglog baseline is good enough to count as hitting the paper baseline in\n", + "practice." + ] + }, + { + "cell_type": "markdown", + "id": "cb018172", + "metadata": {}, + "source": [ + "## 4. Rank Target And Runtime Shape" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "f4f6827b", + "metadata": { + "execution": { + "iopub.execute_input": "2026-04-06T10:07:49.030378Z", + "iopub.status.busy": "2026-04-06T10:07:49.030238Z", + "iopub.status.idle": "2026-04-06T10:07:49.207341Z", + "shell.execute_reply": "2026-04-06T10:07:49.206869Z" + } + }, + "outputs": [ + { + "data": { + "image/svg+xml": [ + "0246simplified params - rankArchived Haskell0246simplified params - rankLive Haskell0246simplified params - rankEgglogPagie-1KotanchekBingoEPLEXOperonSBPGOMEASRjlAlgorithmBingoEPLEXOperonSBPGOMEASRjlAlgorithmSimplified parameters minus rank across all three implementations" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "show_chart(rank_boxplot(combined, title=\"Simplified parameters minus rank across all three implementations\"))" + ] + }, + { + "cell_type": "markdown", + "id": "b48b5475", + "metadata": {}, + "source": [ + "All three implementations keep the simplified expressions clustered near the\n", + "paper rank target. This is the most direct coarse-grained thesis check: the\n", + "live rerun and the Egglog replication lead to the same qualitative conclusion\n", + "as the archived paper outputs about how often the target rank is met or nearly\n", + "met." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "cdb51896", + "metadata": { + "execution": { + "iopub.execute_input": "2026-04-06T10:07:49.210197Z", + "iopub.status.busy": "2026-04-06T10:07:49.210123Z", + "iopub.status.idle": "2026-04-06T10:07:49.265318Z", + "shell.execute_reply": "2026-04-06T10:07:49.264843Z" + } + }, + "outputs": [ + { + "data": { + "image/svg+xml": [ + "010,00020,00030,00040,000runtime (ms)Archived HaskellLive HaskellEgglog0100200300400number of nodes0100200300400number of nodes0100200300400number of nodesPagie runtime versus expression size (Figure 9 analog) across archived Haskell, live Haskell, and Egglog" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "show_chart(\n", + " runtime_chart(\n", + " runtime_compare,\n", + " title=\"Pagie runtime versus expression size (Figure 9 analog) across archived Haskell, live Haskell, and Egglog\",\n", + " )\n", + ")" + ] + }, + { + "cell_type": "markdown", + "id": "88834f6d", + "metadata": {}, + "source": [ + "This faceted Figure 9 analog is now closer to the archived benchmark setup:\n", + "all three facets are built from the broader Pagie original-expression sweep,\n", + "and the x-axis is the input expression node count rather than e-graph size.\n", + "\n", + "With that apples-to-apples population, live Haskell and Egglog now occupy a\n", + "much more similar node-count range to the archived Haskell plot. The main\n", + "remaining difference is the runtime tail: Egglog still has noticeably slower\n", + "cases at comparable input sizes, which points more toward rewrite-search and\n", + "implementation overhead than toward a simple “Egglog starts from larger input\n", + "trees” explanation." + ] + }, + { + "cell_type": "markdown", + "id": "e14a84c3", + "metadata": {}, + "source": [ + "## 5. Faceted Table 4 Analog" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "90862b4d", + "metadata": { + "execution": { + "iopub.execute_input": "2026-04-06T10:07:49.267065Z", + "iopub.status.busy": "2026-04-06T10:07:49.266961Z", + "iopub.status.idle": "2026-04-06T10:07:49.333160Z", + "shell.execute_reply": "2026-04-06T10:07:49.332727Z" + } + }, + "outputs": [ + { + "data": { + "image/svg+xml": [ + "Δ == 0BingoEPLEXGP-GOMEAOperonPySRSBPΔ <= 1BingoEPLEXGP-GOMEAOperonPySRSBPArchived HaskellLive HaskellEgglogPagie-1KotanchekPagie-1KotanchekPagie-1Kotanchek27.78%28.00%n/a66.67%n/a47.62%22.22%18.75%n/a74.07%n/a65.22%44.44%32.00%n/a66.67%n/a47.62%22.22%18.75%n/a74.07%n/a65.22%55.56%40.00%n/a70.00%n/a42.86%22.22%18.75%n/a85.19%n/a65.22%33.33%45.45%n/a100.00%n/a60.00%66.67%37.50%n/a94.44%n/a100.00%55.56%54.55%n/a100.00%n/a60.00%66.67%43.75%n/a94.44%n/a100.00%66.67%63.64%n/a100.00%n/a60.00%66.67%50.00%n/a94.44%n/a100.00%Faceted Table 4 analog" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "show_chart(faceted_table4_chart(table4_source))" + ] + }, + { + "cell_type": "markdown", + "id": "7231f15e", + "metadata": {}, + "source": [ + "The faceted Table 4 analog says the same thing as the boxplots in a paper-style\n", + "summary format. Archived Haskell, live Haskell, and Egglog differ row by row,\n", + "but they preserve the same practical ordering of algorithms and the same\n", + "overall conclusion about how often EqSat reaches the target rank or stays\n", + "within one extra parameter. The biggest archived-versus-live shifts are now\n", + "concentrated in a small Pagie Bingo and Pagie EPLEX tail rather than spread\n", + "across the whole table." + ] + }, + { + "cell_type": "markdown", + "id": "f8d97be7", + "metadata": {}, + "source": [ + "## 6. Archive Drift" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "5d8fa700", + "metadata": { + "execution": { + "iopub.execute_input": "2026-04-06T10:07:49.334108Z", + "iopub.status.busy": "2026-04-06T10:07:49.334033Z", + "iopub.status.idle": "2026-04-06T10:07:49.340311Z", + "shell.execute_reply": "2026-04-06T10:07:49.339872Z" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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datasetalgorithmalgo_roworig_driftsympy_driftsimpl_params_livesimpl_params_archivedsimpl_params_sympy_livesimpl_params_sympy_archived
19pagieBingo21-3.00.04.07.04.04.0
30pagieEPLEX5-2.0-2.011.013.011.013.0
203kotanchekEPLEX4-2.0-2.08.010.08.010.0
3pagieBingo4-2.00.06.08.06.06.0
0pagieBingo1-1.0-2.07.08.06.08.0
6pagieBingo7-1.0-1.04.05.04.05.0
47pagieEPLEX23-1.0-1.04.05.03.04.0
23pagieBingo25-1.00.03.04.03.03.0
8pagieBingo90.0-1.05.05.06.07.0
9pagieBingo100.0-1.04.04.05.06.0
31pagieEPLEX60.0-1.07.07.07.08.0
34pagieEPLEX90.0-1.014.014.010.011.0
\n", + "
" + ], + "text/plain": [ + " dataset algorithm algo_row orig_drift sympy_drift \\\n", + "19 pagie Bingo 21 -3.0 0.0 \n", + "30 pagie EPLEX 5 -2.0 -2.0 \n", + "203 kotanchek EPLEX 4 -2.0 -2.0 \n", + "3 pagie Bingo 4 -2.0 0.0 \n", + "0 pagie Bingo 1 -1.0 -2.0 \n", + "6 pagie Bingo 7 -1.0 -1.0 \n", + "47 pagie EPLEX 23 -1.0 -1.0 \n", + "23 pagie Bingo 25 -1.0 0.0 \n", + "8 pagie Bingo 9 0.0 -1.0 \n", + "9 pagie Bingo 10 0.0 -1.0 \n", + "31 pagie EPLEX 6 0.0 -1.0 \n", + "34 pagie EPLEX 9 0.0 -1.0 \n", + "\n", + " simpl_params_live simpl_params_archived simpl_params_sympy_live \\\n", + "19 4.0 7.0 4.0 \n", + "30 11.0 13.0 11.0 \n", + "203 8.0 10.0 8.0 \n", + "3 6.0 8.0 6.0 \n", + "0 7.0 8.0 6.0 \n", + "6 4.0 5.0 4.0 \n", + "47 4.0 5.0 3.0 \n", + "23 3.0 4.0 3.0 \n", + "8 5.0 5.0 6.0 \n", + "9 4.0 4.0 5.0 \n", + "31 7.0 7.0 7.0 \n", + "34 14.0 14.0 10.0 \n", + "\n", + " simpl_params_sympy_archived \n", + "19 4.0 \n", + "30 13.0 \n", + "203 10.0 \n", + "3 6.0 \n", + "0 8.0 \n", + "6 5.0 \n", + "47 4.0 \n", + "23 3.0 \n", + "8 7.0 \n", + "9 6.0 \n", + "31 8.0 \n", + "34 11.0 " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "display(\n", + " archive_drift[\n", + " [\n", + " \"dataset\",\n", + " \"algorithm\",\n", + " \"algo_row\",\n", + " \"orig_drift\",\n", + " \"sympy_drift\",\n", + " \"simpl_params_live\",\n", + " \"simpl_params_archived\",\n", + " \"simpl_params_sympy_live\",\n", + " \"simpl_params_sympy_archived\",\n", + " ]\n", + " ]\n", + " .sort_values([\"orig_drift\", \"sympy_drift\"], key=lambda column: column.abs(), ascending=False)\n", + " .head(12)\n", + ")" + ] + }, + { + "cell_type": "markdown", + "id": "6f91e246", + "metadata": {}, + "source": [ + "Archive drift is real, but after correcting the live rerun to use the actual\n", + "checked-in Haskell Sympy modules it is much smaller than the earlier draft of\n", + "this notebook suggested. The remaining drift is a short tail, mostly in Pagie\n", + "Bingo and Pagie EPLEX Sympy rows plus a few EPLEX rows on Kotanchek. That is\n", + "enough to justify reporting the live rerun separately, but not enough to\n", + "overturn the main thesis of the paper figures: the archived artifact and the\n", + "live rerun still support the same qualitative story, and Egglog remains close\n", + "enough to the live rerun to support that same story too." + ] + }, + { + "cell_type": "markdown", + "id": "95833960", + "metadata": {}, + "source": [ + "### Live-Haskell fallback rows" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "f468f42c", + "metadata": { + "execution": { + "iopub.execute_input": "2026-04-06T10:07:49.341282Z", + "iopub.status.busy": "2026-04-06T10:07:49.341201Z", + "iopub.status.idle": "2026-04-06T10:07:49.344568Z", + "shell.execute_reply": "2026-04-06T10:07:49.343985Z" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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datasetalgorithmalgo_rowbaseline_sourceorig_live_statussympy_live_status
14pagieBingo15archived_fallbackarchived_fallback_stack_overflowarchived_fallback_stack_overflow
15pagieBingo16archived_fallbackarchived_fallback_stack_overflowarchived_fallback_stack_overflow
22pagieBingo24archived_fallbackarchived_fallback_stack_overflowarchived_fallback_stack_overflow
25pagieBingo27archived_fallbackarchived_fallback_stack_overflowarchived_fallback_stack_overflow
40pagieEPLEX16archived_fallbackarchived_fallback_stack_overflowarchived_fallback_stack_overflow
42pagieEPLEX18archived_fallbackarchived_fallback_stack_overflowarchived_fallback_stack_overflow
44pagieEPLEX20archived_fallbackarchived_fallback_stack_overflowarchived_fallback_stack_overflow
49pagieEPLEX25archived_fallbackarchived_fallback_stack_overflowarchived_fallback_stack_overflow
205kotanchekEPLEX8archived_fallbackarchived_fallback_stack_overflowarchived_fallback_stack_overflow
212kotanchekEPLEX19archived_fallbackarchived_fallback_stack_overflowarchived_fallback_stack_overflow
\n", + "
" + ], + "text/plain": [ + " dataset algorithm algo_row baseline_source \\\n", + "14 pagie Bingo 15 archived_fallback \n", + "15 pagie Bingo 16 archived_fallback \n", + "22 pagie Bingo 24 archived_fallback \n", + "25 pagie Bingo 27 archived_fallback \n", + "40 pagie EPLEX 16 archived_fallback \n", + "42 pagie EPLEX 18 archived_fallback \n", + "44 pagie EPLEX 20 archived_fallback \n", + "49 pagie EPLEX 25 archived_fallback \n", + "205 kotanchek EPLEX 8 archived_fallback \n", + "212 kotanchek EPLEX 19 archived_fallback \n", + "\n", + " orig_live_status sympy_live_status \n", + "14 archived_fallback_stack_overflow archived_fallback_stack_overflow \n", + "15 archived_fallback_stack_overflow archived_fallback_stack_overflow \n", + "22 archived_fallback_stack_overflow archived_fallback_stack_overflow \n", + "25 archived_fallback_stack_overflow archived_fallback_stack_overflow \n", + "40 archived_fallback_stack_overflow archived_fallback_stack_overflow \n", + "42 archived_fallback_stack_overflow archived_fallback_stack_overflow \n", + "44 archived_fallback_stack_overflow archived_fallback_stack_overflow \n", + "49 archived_fallback_stack_overflow archived_fallback_stack_overflow \n", + "205 archived_fallback_stack_overflow archived_fallback_stack_overflow \n", + "212 archived_fallback_stack_overflow archived_fallback_stack_overflow " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "display(live_fallback_rows if not live_fallback_rows.empty else pd.DataFrame([{\"status\": \"none\"}]))" + ] + }, + { + "cell_type": "markdown", + "id": "81a5fea5", + "metadata": {}, + "source": [ + "## 7. Conclusion" + ] + }, + { + "cell_type": "markdown", + "id": "5914ae9d", + "metadata": { + "lines_to_next_cell": 2 + }, + "source": [ + "Archived Haskell, live Haskell, and Egglog all support the same qualitative\n", + "paper conclusion on the retained param-eq metrics.\n", + "\n", + "The remaining Egglog-versus-live differences are a small row-level tail rather\n", + "than a broad failure mode, and the archived-versus-live Haskell differences\n", + "are now modest enough to read as archive drift rather than a contradictory\n", + "result set.\n", + "\n", + "Taken together, these plots support the retained thesis: the Egglog baseline\n", + "behaves close enough to both Haskell baselines that it reproduces the paper's\n", + "practical conclusions, while the remaining archive drift is a caveat that\n", + "sharpens interpretation rather than evidence of a replication failure." + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "aa997f40", + "metadata": { + "execution": { + "iopub.execute_input": "2026-04-06T10:07:49.345606Z", + "iopub.status.busy": "2026-04-06T10:07:49.345540Z", + "iopub.status.idle": "2026-04-06T10:07:49.347652Z", + "shell.execute_reply": "2026-04-06T10:07:49.347287Z" + } + }, + "outputs": [], + "source": [ + "def _write_executed_notebook() -> None:\n", + " source_path = PARAM_EQ_DIR / \"replication.py\"\n", + " output_path = source_path.with_suffix(\".ipynb\")\n", + " notebook = jupytext.read(source_path, fmt=\"py:light\")\n", + " previous = os.environ.get(\"EGGLOG_PARAM_EQ_SYNC_IPYNB\")\n", + " os.environ[\"EGGLOG_PARAM_EQ_SYNC_IPYNB\"] = \"0\"\n", + " try:\n", + " executed = NotebookClient(notebook, timeout=600, kernel_name=\"python3\").execute()\n", + " finally:\n", + " if previous is None:\n", + " os.environ.pop(\"EGGLOG_PARAM_EQ_SYNC_IPYNB\", None)\n", + " else:\n", + " os.environ[\"EGGLOG_PARAM_EQ_SYNC_IPYNB\"] = previous\n", + " with output_path.open(\"w\", encoding=\"utf-8\") as handle:\n", + " nbformat.write(executed, handle)" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "9e8bd803", + "metadata": { + "execution": { + "iopub.execute_input": "2026-04-06T10:07:49.348568Z", + "iopub.status.busy": "2026-04-06T10:07:49.348507Z", + "iopub.status.idle": "2026-04-06T10:07:49.350032Z", + "shell.execute_reply": "2026-04-06T10:07:49.349715Z" + } + }, + "outputs": [], + "source": [ + "if __name__ == \"__main__\" and os.environ.get(\"EGGLOG_PARAM_EQ_SYNC_IPYNB\", \"1\") != \"0\":\n", + " _write_executed_notebook()" + ] + } + ], + "metadata": { + "jupytext": { + "cell_metadata_filter": "-all", + "main_language": "python", + "notebook_metadata_filter": "-all", + "text_representation": { + "extension": ".py", + "format_name": "light" + } + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.13.11" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/python/egglog/exp/param_eq/replication.py b/python/egglog/exp/param_eq/replication.py new file mode 100644 index 00000000..63bf5d74 --- /dev/null +++ b/python/egglog/exp/param_eq/replication.py @@ -0,0 +1,612 @@ +# # 2026-03 - Param-Eq Baseline Thesis Check +# +# This notebook is intentionally comparison-first. +# +# Its main claim is: +# - the archived Haskell artifact, +# - a fresh live Haskell rerun, and +# - the retained Egglog baseline +# +# all support the same qualitative paper conclusions on the retained param-eq +# metrics. +# +# The notebook reads only checked-in artifacts: +# - archived Haskell rows +# - live Haskell rows +# - Egglog rows +# - Pagie runtime comparison rows for all three implementations +# +# Offline regeneration commands from the repository root: +# - `uv run python -m egglog.exp.param_eq.normalize_archives` +# - `uv run python -m egglog.exp.param_eq.run_haskell_corpus` +# - `uv run python -m egglog.exp.param_eq.run_egglog_corpus` +# - `uv run python python/egglog/exp/param_eq/replication.py` + +# + +from __future__ import annotations + +import os +from io import StringIO +from typing import Any + +import altair as alt +import jupytext +import nbformat +import pandas as pd +from IPython.display import SVG, display +from nbclient import NotebookClient + +from egglog.exp.param_eq.paths import ARTIFACT_DIR, PARAM_EQ_DIR + +alt.data_transformers.disable_max_rows() +alt.renderers.enable("default") + +ALGORITHM_ORDER = ["Bingo", "EPLEX", "GP-GOMEA", "Operon", "PySR", "SBP"] +DATASET_ORDER = ["pagie", "kotanchek"] +DATASET_LABELS = {"pagie": "Pagie-1", "kotanchek": "Kotanchek"} +IMPLEMENTATION_ORDER = ["Archived Haskell", "Live Haskell", "Egglog"] +METHOD_ORDER = ["EqSat", "Sympy", "Sympy + EqSat"] +COMPARISON_ORDER = ["Sympy x EqSat", "Sympy + EqSat x EqSat"] +DELTA_ORDER = ["Δ == 0", "Δ <= 1"] + +BOX_COLOR = "#4C78A8" +POINT_COLOR = "#F58518" +TABLE_FILL = "#F7F7F7" + +ARCHIVED_HASKELL_PATH = ARTIFACT_DIR / "haskell_paper_rows.csv" +LIVE_HASKELL_PATH = ARTIFACT_DIR / "haskell_live_rows.csv" +EGGLOG_PATH = ARTIFACT_DIR / "egglog_paper_rows.csv" +RUNTIME_PATH = ARTIFACT_DIR / "pagie_runtime_compare.csv" + +for required_path in [ARCHIVED_HASKELL_PATH, LIVE_HASKELL_PATH, EGGLOG_PATH, RUNTIME_PATH]: + if not required_path.exists(): + msg = f"Missing required artifact: {required_path}" + raise FileNotFoundError(msg) + + +def _coerce_numeric(frame: pd.DataFrame, columns: list[str]) -> pd.DataFrame: + for column in columns: + if column in frame.columns: + frame[column] = pd.to_numeric(frame[column], errors="coerce") + return frame + + +def _paper_haskell_frame(path: os.PathLike[str] | str) -> pd.DataFrame: + frame = pd.read_csv(path) + frame = frame[frame["is_paper_row"] == 1].copy() + return _coerce_numeric( + frame, + [ + "raw_index", + "algo_row", + "orig_nodes", + "orig_params", + "simpl_nodes", + "simpl_params", + "orig_runtime_ms", + "orig_nodes_sympy", + "orig_params_sympy", + "simpl_nodes_sympy", + "simpl_params_sympy", + "sympy_runtime_ms", + "n_params", + "n_rank", + ], + ) + + +def _paper_egglog_frame(path: os.PathLike[str] | str) -> pd.DataFrame: + frame = pd.read_csv(path) + frame = frame[frame["is_paper_row"] == 1].copy() + return _coerce_numeric( + frame, + [ + "raw_index", + "algo_row", + "orig_runtime_ms", + "orig_nodes", + "orig_params", + "simpl_nodes", + "simpl_params", + "orig_total_size", + "orig_egraph_nodes", + "orig_eclass_count", + "orig_passes", + "orig_extracted_cost", + "sympy_runtime_ms", + "orig_nodes_sympy", + "orig_params_sympy", + "simpl_nodes_sympy", + "simpl_params_sympy", + "sympy_total_size", + "sympy_egraph_nodes", + "sympy_eclass_count", + "sympy_passes", + "sympy_extracted_cost", + "n_params", + "n_rank", + ], + ) + + +def _paper_runtime_frame() -> pd.DataFrame: + frame = pd.read_csv(RUNTIME_PATH) + return _coerce_numeric(frame, ["node_count", "runtime_ms"]) + + +def add_paper_metrics(frame: pd.DataFrame) -> pd.DataFrame: + result = frame.copy() + result["orig_x_egg"] = (result["orig_params"] - result["simpl_params"]) / result["orig_params"] + result["orig_x_sympy"] = (result["orig_params"] - result["orig_params_sympy"]) / result["orig_params"] + result["orig_x_sympyegg"] = (result["orig_params"] - result["simpl_params_sympy"]) / result["orig_params"] + result["sympy_x_egg"] = (result["orig_params_sympy"] - result["simpl_params"]) / result["orig_params_sympy"] + result["sympyegg_x_egg"] = (result["simpl_params_sympy"] - result["simpl_params"]) / result["simpl_params_sympy"] + result["orig_rank"] = result["n_params"] - result["n_rank"] + result["simpl_rank"] = result["simpl_params"] - result["n_rank"] + result["sympy_rank"] = result["orig_params_sympy"] - result["n_rank"] + return result + + +def with_implementation(frame: pd.DataFrame, implementation: str) -> pd.DataFrame: + result = frame.copy() + result["implementation"] = implementation + result["dataset_label"] = result["dataset"].map(DATASET_LABELS) + return result + + +def melt_methods(frame: pd.DataFrame, *, columns: dict[str, str], value_name: str) -> pd.DataFrame: + melted = frame.melt( + id_vars=["implementation", "dataset", "dataset_label", "algorithm", "raw_index"], + value_vars=list(columns.values()), + var_name="method_key", + value_name=value_name, + ) + inverse = {value: key for key, value in columns.items()} + melted["method"] = melted["method_key"].map(inverse) + return melted.drop(columns=["method_key"]) + + +def _point_layer(frame: pd.DataFrame, *, y: str, tooltip: list[str]) -> alt.Chart: + return ( + alt.Chart(frame) + .transform_calculate(jitter="(random() - 0.5) * 18") + .mark_circle(size=38, color=POINT_COLOR, opacity=0.68, stroke="white", strokeWidth=0.7) + .encode( + xOffset=alt.XOffset("jitter:Q"), + y=alt.Y(f"{y}:Q"), + tooltip=tooltip, + ) + ) + + +def faceted_boxplot(frame: pd.DataFrame, *, y: str, title: str, method_sort: list[str]) -> Any: + base = ( + alt.Chart(frame) + .encode( + x=alt.X("algorithm:N", sort=ALGORITHM_ORDER, title="Algorithm"), + y=alt.Y(f"{y}:Q", title=y.replace("_", " ")), + ) + .properties(width=115, height=170) + ) + layered = alt.layer( + _point_layer( + frame, + y=y, + tooltip=["implementation", "dataset", "algorithm", "method", "raw_index", y], + ).encode(x=alt.X("algorithm:N", sort=ALGORITHM_ORDER, title="Algorithm")), + base.mark_boxplot(size=16, opacity=0.58, color=BOX_COLOR, outliers=False), + ) + return layered.facet( + row=alt.Row("implementation:N", sort=IMPLEMENTATION_ORDER, title=None), + column=alt.Column("method:N", sort=method_sort, title=None), + ).properties(title=title) + + +def rank_boxplot(frame: pd.DataFrame, *, title: str) -> Any: + base = ( + alt.Chart(frame) + .encode( + x=alt.X("algorithm:N", sort=ALGORITHM_ORDER, title="Algorithm"), + y=alt.Y("simpl_rank:Q", title="simplified params - rank"), + ) + .properties(width=115, height=170) + ) + layered = alt.layer( + _point_layer( + frame, + y="simpl_rank", + tooltip=["implementation", "dataset", "algorithm", "raw_index", "simpl_rank", "n_rank", "simpl_params"], + ).encode(x=alt.X("algorithm:N", sort=ALGORITHM_ORDER, title="Algorithm")), + base.mark_boxplot(size=16, opacity=0.58, color=BOX_COLOR, outliers=False), + ) + return layered.facet( + row=alt.Row("implementation:N", sort=IMPLEMENTATION_ORDER, title=None), + column=alt.Column("dataset_label:N", sort=[DATASET_LABELS[d] for d in DATASET_ORDER], title=None), + ).properties(title=title) + + +def runtime_chart(frame: pd.DataFrame, *, title: str) -> Any: + return ( + alt.Chart(frame) + .mark_circle(size=70, opacity=0.78, stroke="white", strokeWidth=0.8, color=BOX_COLOR) + .encode( + x=alt.X("node_count:Q", title="number of nodes"), + y=alt.Y("runtime_ms:Q", title="runtime (ms)"), + tooltip=["implementation", "node_count", "runtime_ms"], + ) + .properties(width=220, height=220) + .facet(column=alt.Column("implementation:N", sort=IMPLEMENTATION_ORDER, title=None)) + .properties(title=title) + ) + + +def comparison_table(frame: pd.DataFrame, *, implementation: str) -> pd.DataFrame: + rows: list[dict[str, object]] = [] + for dataset in DATASET_ORDER: + dataset_frame = frame[frame["dataset"] == dataset] + for algorithm in ALGORITHM_ORDER: + algo_frame = dataset_frame[dataset_frame["algorithm"] == algorithm] + for delta in [0, 1]: + eligible = algo_frame[algo_frame["orig_rank"] > delta] + percent = float("nan") + if not eligible.empty: + percent = 100.0 * (eligible["simpl_rank"] <= delta).sum() / len(eligible) + rows.append({ + "implementation": implementation, + "dataset": dataset, + "dataset_label": DATASET_LABELS[dataset], + "algorithm": algorithm, + "delta": f"Δ {'==' if delta == 0 else '<='} {delta}", + "percent": percent, + }) + result = pd.DataFrame(rows) + result["percent_label"] = result["percent"].map(lambda value: "n/a" if pd.isna(value) else f"{value:.2f}%") + return result + + +def faceted_table4_chart(frame: pd.DataFrame) -> Any: + base = alt.Chart(frame).encode( + x=alt.X("dataset_label:N", sort=[DATASET_LABELS[d] for d in DATASET_ORDER], title=None), + y=alt.Y("algorithm:N", sort=ALGORITHM_ORDER, title=None), + ) + layered = alt.layer( + base.mark_rect(fill=TABLE_FILL, stroke="#DDDDDD"), + base.mark_text(fontSize=11).encode(text="percent_label:N"), + ).properties(width=120, height=18 * len(ALGORITHM_ORDER)) + return layered.facet( + row=alt.Row("delta:N", sort=DELTA_ORDER, title=None), + column=alt.Column("implementation:N", sort=IMPLEMENTATION_ORDER, title=None), + ).properties(title="Faceted Table 4 analog") + + +def show_chart(chart: Any) -> None: + buffer = StringIO() + chart.save(buffer, format="svg") + display(SVG(buffer.getvalue())) + + +archived_haskell = with_implementation( + add_paper_metrics(_paper_haskell_frame(ARCHIVED_HASKELL_PATH)), "Archived Haskell" +) +live_haskell = with_implementation(add_paper_metrics(_paper_haskell_frame(LIVE_HASKELL_PATH)), "Live Haskell") +egglog = with_implementation(add_paper_metrics(_paper_egglog_frame(EGGLOG_PATH)), "Egglog") +runtime_rows = _paper_runtime_frame() + +combined = pd.concat([archived_haskell, live_haskell, egglog], ignore_index=True) + +haskell_columns = { + "EqSat": "orig_x_egg", + "Sympy": "orig_x_sympy", + "Sympy + EqSat": "orig_x_sympyegg", +} +comparison_columns = { + "Sympy x EqSat": "sympy_x_egg", + "Sympy + EqSat x EqSat": "sympyegg_x_egg", +} + +egglog_vs_live = egglog.merge( + live_haskell[ + [ + "dataset", + "algorithm", + "raw_index", + "simpl_params", + "simpl_params_sympy", + ] + ], + on=["dataset", "algorithm", "raw_index"], + suffixes=("_egglog", "_live"), +) +egglog_vs_live["orig_exact"] = egglog_vs_live["simpl_params_egglog"] == egglog_vs_live["simpl_params_live"] +egglog_vs_live["sympy_exact"] = egglog_vs_live["simpl_params_sympy_egglog"] == egglog_vs_live["simpl_params_sympy_live"] +egglog_vs_live["orig_gap"] = (egglog_vs_live["simpl_params_egglog"] - egglog_vs_live["simpl_params_live"]).abs() +egglog_vs_live["sympy_gap"] = ( + egglog_vs_live["simpl_params_sympy_egglog"] - egglog_vs_live["simpl_params_sympy_live"] +).abs() + +archive_drift = live_haskell.merge( + archived_haskell[ + [ + "dataset", + "algorithm", + "raw_index", + "simpl_params", + "simpl_params_sympy", + ] + ], + on=["dataset", "algorithm", "raw_index"], + suffixes=("_live", "_archived"), +) +archive_drift["orig_drift"] = archive_drift["simpl_params_live"] - archive_drift["simpl_params_archived"] +archive_drift["sympy_drift"] = archive_drift["simpl_params_sympy_live"] - archive_drift["simpl_params_sympy_archived"] + +live_fallback_rows = live_haskell[live_haskell["baseline_source"] != "live_haskell"][ + ["dataset", "algorithm", "algo_row", "baseline_source", "orig_live_status", "sympy_live_status"] +].drop_duplicates() + +runtime_compare = runtime_rows[["implementation", "node_count", "runtime_ms"]].copy() + +table4_source = pd.concat( + [ + comparison_table(archived_haskell, implementation="Archived Haskell"), + comparison_table(live_haskell, implementation="Live Haskell"), + comparison_table(egglog, implementation="Egglog"), + ], + ignore_index=True, +) + +# - + +# ## 1. Artifact Overview + +artifact_summary = pd.DataFrame([ + { + "implementation": "Archived Haskell", + "rows": len(archived_haskell), + "original_median_simpl_rank": float(archived_haskell["simpl_rank"].median()), + "sympy_median_simpl_rank": float(archived_haskell["sympy_rank"].median()), + }, + { + "implementation": "Live Haskell", + "rows": len(live_haskell), + "original_median_simpl_rank": float(live_haskell["simpl_rank"].median()), + "sympy_median_simpl_rank": float(live_haskell["sympy_rank"].median()), + }, + { + "implementation": "Egglog", + "rows": len(egglog), + "original_median_simpl_rank": float(egglog["simpl_rank"].median()), + "sympy_median_simpl_rank": float(egglog["sympy_rank"].median()), + }, +]) +display(artifact_summary) +display( + pd.DataFrame([ + { + "comparison": "Egglog vs live Haskell (original)", + "exact_matches": int(egglog_vs_live["orig_exact"].sum()), + "total_rows": len(egglog_vs_live), + "max_gap": int(egglog_vs_live["orig_gap"].max()), + }, + { + "comparison": "Egglog vs live Haskell (sympy)", + "exact_matches": int(egglog_vs_live["sympy_exact"].sum()), + "total_rows": len(egglog_vs_live), + "max_gap": int(egglog_vs_live["sympy_gap"].max()), + }, + { + "comparison": "Live vs archived Haskell (original)", + "exact_matches": int((archive_drift["orig_drift"] == 0).sum()), + "total_rows": len(archive_drift), + "max_gap": int(archive_drift["orig_drift"].abs().max()), + }, + { + "comparison": "Live vs archived Haskell (sympy)", + "exact_matches": int((archive_drift["sympy_drift"] == 0).sum()), + "total_rows": len(archive_drift), + "max_gap": int(archive_drift["sympy_drift"].abs().max()), + }, + ]) +) +# - + +# The retained question is no longer whether Egglog finishes the corpus; it does. +# +# The useful question is whether the three result sets support the same practical +# thesis. After correcting the live Haskell rerun to follow the checked-in +# Haskell Sympy modules directly, archived and live Haskell are much closer than +# they first appeared. The rest of this notebook therefore compares archived +# Haskell, live Haskell, and Egglog with the same plots and the same table +# layouts. + +# ## 2. Reduction Ratios + +# + +show_chart( + faceted_boxplot( + melt_methods(combined[combined["dataset"] == "pagie"], columns=haskell_columns, value_name="ratio"), + y="ratio", + method_sort=METHOD_ORDER, + title="Pagie reduction ratios across archived Haskell, live Haskell, and Egglog", + ) +) +# - + +# Across the Pagie rows, all three implementations preserve the same qualitative +# story: EqSat helps on its own, Sympy alone is not the main source of the gain, +# and the combined pipeline remains the strongest or near-strongest path. The +# archived and live Haskell views are now close enough that the archive reads as +# a slightly stale version of the same picture rather than a conflicting one, +# and Egglog tracks that shared picture closely enough to support the same +# conclusion. + +# + +show_chart( + faceted_boxplot( + melt_methods(combined[combined["dataset"] == "kotanchek"], columns=haskell_columns, value_name="ratio"), + y="ratio", + method_sort=METHOD_ORDER, + title="Kotanchek reduction ratios across archived Haskell, live Haskell, and Egglog", + ) +) +# - + +# Kotanchek tells the same story. The per-algorithm spread changes a little +# between the archived artifact and the live rerun, but the headline result does +# not: EqSat is still the meaningful simplification step, and Egglog lands in +# the same visual regime as both Haskell baselines. + +# ## 3. EqSat Versus Sympy Comparisons + +# + +show_chart( + faceted_boxplot( + melt_methods(combined[combined["dataset"] == "pagie"], columns=comparison_columns, value_name="ratio"), + y="ratio", + method_sort=COMPARISON_ORDER, + title="Pagie EqSat-vs-Sympy comparison ratios across all three implementations", + ) +) +# - + +# These comparison ratios make the thesis more explicit: rerunning EqSat after +# the Sympy-derived starting point still matters in all three result sets. The +# archive, the live rerun, and Egglog all agree that the simplification is not +# coming only from the symbolic preprocessing step. + +# + +show_chart( + faceted_boxplot( + melt_methods(combined[combined["dataset"] == "kotanchek"], columns=comparison_columns, value_name="ratio"), + y="ratio", + method_sort=COMPARISON_ORDER, + title="Kotanchek EqSat-vs-Sympy comparison ratios across all three implementations", + ) +) +# - + +# The Kotanchek comparison view reaches the same conclusion. Even where archive +# drift is visible, it is now a narrow tail instead of a broad Sympy split, and +# the three implementations still agree on the sign and rough scale of the +# EqSat contribution. That is the notebook's central evidence that the retained +# Egglog baseline is good enough to count as hitting the paper baseline in +# practice. + +# ## 4. Rank Target And Runtime Shape + +# + +show_chart(rank_boxplot(combined, title="Simplified parameters minus rank across all three implementations")) +# - + +# All three implementations keep the simplified expressions clustered near the +# paper rank target. This is the most direct coarse-grained thesis check: the +# live rerun and the Egglog replication lead to the same qualitative conclusion +# as the archived paper outputs about how often the target rank is met or nearly +# met. + +# + +show_chart( + runtime_chart( + runtime_compare, + title="Pagie runtime versus expression size (Figure 9 analog) across archived Haskell, live Haskell, and Egglog", + ) +) +# - + +# This faceted Figure 9 analog is now closer to the archived benchmark setup: +# all three facets are built from the broader Pagie original-expression sweep, +# and the x-axis is the input expression node count rather than e-graph size. +# +# With that apples-to-apples population, live Haskell and Egglog now occupy a +# much more similar node-count range to the archived Haskell plot. The main +# remaining difference is the runtime tail: Egglog still has noticeably slower +# cases at comparable input sizes, which points more toward rewrite-search and +# implementation overhead than toward a simple “Egglog starts from larger input +# trees” explanation. + +# ## 5. Faceted Table 4 Analog + +# + +show_chart(faceted_table4_chart(table4_source)) +# - + +# The faceted Table 4 analog says the same thing as the boxplots in a paper-style +# summary format. Archived Haskell, live Haskell, and Egglog differ row by row, +# but they preserve the same practical ordering of algorithms and the same +# overall conclusion about how often EqSat reaches the target rank or stays +# within one extra parameter. The biggest archived-versus-live shifts are now +# concentrated in a small Pagie Bingo and Pagie EPLEX tail rather than spread +# across the whole table. + +# ## 6. Archive Drift + +# + +display( + archive_drift[ + [ + "dataset", + "algorithm", + "algo_row", + "orig_drift", + "sympy_drift", + "simpl_params_live", + "simpl_params_archived", + "simpl_params_sympy_live", + "simpl_params_sympy_archived", + ] + ] + .sort_values(["orig_drift", "sympy_drift"], key=lambda column: column.abs(), ascending=False) + .head(12) +) +# - + +# Archive drift is real, but after correcting the live rerun to use the actual +# checked-in Haskell Sympy modules it is much smaller than the earlier draft of +# this notebook suggested. The remaining drift is a short tail, mostly in Pagie +# Bingo and Pagie EPLEX Sympy rows plus a few EPLEX rows on Kotanchek. That is +# enough to justify reporting the live rerun separately, but not enough to +# overturn the main thesis of the paper figures: the archived artifact and the +# live rerun still support the same qualitative story, and Egglog remains close +# enough to the live rerun to support that same story too. + +# ### Live-Haskell fallback rows + +# + +display(live_fallback_rows if not live_fallback_rows.empty else pd.DataFrame([{"status": "none"}])) +# - + +# ## 7. Conclusion + +# Archived Haskell, live Haskell, and Egglog all support the same qualitative +# paper conclusion on the retained param-eq metrics. +# +# The remaining Egglog-versus-live differences are a small row-level tail rather +# than a broad failure mode, and the archived-versus-live Haskell differences +# are now modest enough to read as archive drift rather than a contradictory +# result set. +# +# Taken together, these plots support the retained thesis: the Egglog baseline +# behaves close enough to both Haskell baselines that it reproduces the paper's +# practical conclusions, while the remaining archive drift is a caveat that +# sharpens interpretation rather than evidence of a replication failure. + + +def _write_executed_notebook() -> None: + source_path = PARAM_EQ_DIR / "replication.py" + output_path = source_path.with_suffix(".ipynb") + notebook = jupytext.read(source_path, fmt="py:light") + previous = os.environ.get("EGGLOG_PARAM_EQ_SYNC_IPYNB") + os.environ["EGGLOG_PARAM_EQ_SYNC_IPYNB"] = "0" + try: + executed = NotebookClient(notebook, timeout=600, kernel_name="python3").execute() + finally: + if previous is None: + os.environ.pop("EGGLOG_PARAM_EQ_SYNC_IPYNB", None) + else: + os.environ["EGGLOG_PARAM_EQ_SYNC_IPYNB"] = previous + with output_path.open("w", encoding="utf-8") as handle: + nbformat.write(executed, handle) + + +if __name__ == "__main__" and os.environ.get("EGGLOG_PARAM_EQ_SYNC_IPYNB", "1") != "0": + _write_executed_notebook() diff --git a/python/egglog/exp/param_eq/run_egglog_corpus.py b/python/egglog/exp/param_eq/run_egglog_corpus.py new file mode 100644 index 00000000..c25cf154 --- /dev/null +++ b/python/egglog/exp/param_eq/run_egglog_corpus.py @@ -0,0 +1,224 @@ +"""Run the retained Egglog param-eq baseline across the paper rows.""" + +from __future__ import annotations + +import argparse +import contextlib +import csv +import json +import os +import pathlib +import signal +import subprocess +import sys +import time +from concurrent.futures import Future, ThreadPoolExecutor, as_completed + +from rich.progress import BarColumn, MofNCompleteColumn, Progress, SpinnerColumn, TextColumn, TimeElapsedColumn + +from egglog.exp.param_eq.paths import ARTIFACT_DIR + +TIMEOUT_SEC = 180.0 + +OUTPUT_DIR = ARTIFACT_DIR +HASKELL_ROWS_PATH = OUTPUT_DIR / "haskell_paper_rows.csv" +EGGLOG_ROWS_PATH = OUTPUT_DIR / "egglog_paper_rows.csv" +DEFAULT_WORKERS = max(1, min(os.cpu_count() or 1, 4)) + + +def _load_rows() -> list[dict[str, str]]: + with HASKELL_ROWS_PATH.open(newline="", encoding="utf-8") as handle: + return [row for row in csv.DictReader(handle) if row["is_paper_row"] == "1"] + + +def _run_one(source: str) -> dict[str, str]: + start = time.perf_counter() + proc: subprocess.Popen[str] | None = None + try: + proc = subprocess.Popen( + [ + sys.executable, + "-m", + "egglog.exp.param_eq", + f"--expr={source}", + ], + text=True, + stdout=subprocess.PIPE, + stderr=subprocess.PIPE, + start_new_session=True, + ) + stdout, stderr = proc.communicate(timeout=TIMEOUT_SEC) + except subprocess.TimeoutExpired: + if proc is not None: + with contextlib.suppress(ProcessLookupError): + os.killpg(proc.pid, signal.SIGKILL) + with contextlib.suppress(subprocess.TimeoutExpired): + proc.communicate(timeout=1.0) + return { + "status": "timeout", + "runtime_ms": f"{TIMEOUT_SEC * 1000.0:.6f}", + "before_nodes": "na", + "before_params": "na", + "after_nodes": "na", + "after_params": "na", + "total_size": "na", + "egraph_nodes": "na", + "eclass_count": "na", + "passes": "na", + "extracted_cost": "na", + "rendered": "timeout", + } + elapsed_ms = (time.perf_counter() - start) * 1000.0 + if proc.returncode != 0: + message = stderr.strip() or stdout.strip() or "subprocess failure" + return { + "status": "failed", + "runtime_ms": f"{elapsed_ms:.6f}", + "before_nodes": "na", + "before_params": "na", + "after_nodes": "na", + "after_params": "na", + "total_size": "na", + "egraph_nodes": "na", + "eclass_count": "na", + "passes": "na", + "extracted_cost": "na", + "rendered": message.splitlines()[0], + } + payload = json.loads(stdout) + return { + "status": str(payload["status"]), + "runtime_ms": f"{elapsed_ms:.6f}", + "before_nodes": str(payload["before_nodes"]), + "before_params": str(payload["before_params"]), + "after_nodes": str(payload["after_nodes"]), + "after_params": str(payload["after_params"]), + "total_size": str(payload["total_size"]), + "egraph_nodes": str(payload["node_count"]), + "eclass_count": str(payload["eclass_count"]), + "passes": str(payload["passes"]), + "extracted_cost": str(payload["extracted_cost"]), + "rendered": str(payload["rendered"]), + } + + +def _run_row(source_row: dict[str, str]) -> dict[str, str]: + original = _run_one(source_row["original_expr"]) + sympy = _run_one(source_row["sympy_expr"]) + return { + "dataset": source_row["dataset"], + "raw_index": source_row["raw_index"], + "algorithm_raw": source_row["algorithm_raw"], + "algorithm": source_row["algorithm"], + "algo_row": source_row["algo_row"], + "is_paper_row": source_row["is_paper_row"], + "drop_reason": source_row["drop_reason"], + "n_params": source_row["n_params"], + "n_rank": source_row["n_rank"], + "original_expr": source_row["original_expr"], + "sympy_expr": source_row["sympy_expr"], + "orig_status": original["status"], + "orig_runtime_ms": original["runtime_ms"], + "orig_nodes": original["before_nodes"], + "orig_params": original["before_params"], + "simpl_nodes": original["after_nodes"], + "simpl_params": original["after_params"], + "orig_total_size": original["total_size"], + "orig_egraph_nodes": original["egraph_nodes"], + "orig_eclass_count": original["eclass_count"], + "orig_passes": original["passes"], + "orig_extracted_cost": original["extracted_cost"], + "orig_rendered": original["rendered"], + "sympy_status": sympy["status"], + "sympy_runtime_ms": sympy["runtime_ms"], + "orig_nodes_sympy": sympy["before_nodes"], + "orig_params_sympy": sympy["before_params"], + "simpl_nodes_sympy": sympy["after_nodes"], + "simpl_params_sympy": sympy["after_params"], + "sympy_total_size": sympy["total_size"], + "sympy_egraph_nodes": sympy["egraph_nodes"], + "sympy_eclass_count": sympy["eclass_count"], + "sympy_passes": sympy["passes"], + "sympy_extracted_cost": sympy["extracted_cost"], + "sympy_rendered": sympy["rendered"], + } + + +def main() -> None: + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument( + "--output", + default=str(EGGLOG_ROWS_PATH), + help="Where to write the resulting CSV artifact.", + ) + parser.add_argument( + "--workers", + type=int, + default=DEFAULT_WORKERS, + help="Number of Egglog rows to evaluate in parallel.", + ) + args = parser.parse_args() + output_path = pathlib.Path(args.output) + + rows = _load_rows() + total = len(rows) + OUTPUT_DIR.mkdir(parents=True, exist_ok=True) + temp_path = output_path.with_suffix(".csv.partial") + completed_keys: set[tuple[str, str, str, str]] = set() + fieldnames: list[str] | None = None + if temp_path.exists(): + with temp_path.open(newline="", encoding="utf-8") as handle: + reader = csv.DictReader(handle) + fieldnames = list(reader.fieldnames) if reader.fieldnames is not None else None + for row in reader: + completed_keys.add((row["dataset"], row["raw_index"], row["algorithm"], row["algo_row"])) + + pending_rows = [ + row + for row in rows + if ( + row["dataset"], + row["raw_index"], + row["algorithm"], + row["algo_row"], + ) + not in completed_keys + ] + with temp_path.open("a" if completed_keys else "w", newline="", encoding="utf-8") as handle: + writer: csv.DictWriter[str] | None = None + if fieldnames is not None: + writer = csv.DictWriter(handle, fieldnames=fieldnames) + with Progress( + SpinnerColumn(), + TextColumn("[progress.description]{task.description}"), + BarColumn(), + MofNCompleteColumn(), + TimeElapsedColumn(), + ) as progress: + task = progress.add_task("egglog rows", total=total, completed=len(completed_keys)) + with ThreadPoolExecutor(max_workers=args.workers) as executor: + futures: dict[Future[dict[str, str]], tuple[str, str, str, str]] = { + executor.submit(_run_row, row): ( + row["dataset"], + row["raw_index"], + row["algorithm"], + row["algo_row"], + ) + for row in pending_rows + } + for future in as_completed(futures): + output_row = future.result() + if fieldnames is None: + fieldnames = list(output_row) + writer = csv.DictWriter(handle, fieldnames=fieldnames) + writer.writeheader() + assert writer is not None + writer.writerow(output_row) + handle.flush() + completed_keys.add(futures[future]) + progress.advance(task) + temp_path.replace(output_path) + + +if __name__ == "__main__": + main() diff --git a/python/egglog/exp/param_eq/run_haskell_corpus.py b/python/egglog/exp/param_eq/run_haskell_corpus.py new file mode 100644 index 00000000..7aaca3af --- /dev/null +++ b/python/egglog/exp/param_eq/run_haskell_corpus.py @@ -0,0 +1,333 @@ +"""Run the current local param-eq Haskell pipeline across the retained corpus.""" + +from __future__ import annotations + +import argparse +import csv +import json +import os +import subprocess +import tempfile +from concurrent.futures import ThreadPoolExecutor, as_completed +from pathlib import Path + +from rich.progress import BarColumn, MofNCompleteColumn, Progress, SpinnerColumn, TextColumn, TimeElapsedColumn + +from egglog.exp.param_eq.generate_haskell_golden import _canonicalize +from egglog.exp.param_eq.paths import ARTIFACT_DIR, llvm_bin_dir, param_eq_data_dir + +ARCHIVED_ROWS_PATH = ARTIFACT_DIR / "haskell_paper_rows.csv" +LIVE_ROWS_PATH = ARTIFACT_DIR / "haskell_live_rows.csv" +HASKELL_ROOT = param_eq_data_dir() +DEFAULT_BATCH_SIZE = 24 +DEFAULT_WORKERS = 2 + + +def _load_rows() -> list[dict[str, str]]: + with ARCHIVED_ROWS_PATH.open(newline="", encoding="utf-8") as handle: + return [row for row in csv.DictReader(handle) if row["is_paper_row"] == "1"] + + +def _build_haskell_program(rows: list[dict[str, str]]) -> str: + case_lines: list[str] = [] + for index, row in enumerate(rows): + dataset = json.dumps(row["dataset"]) + raw_index = json.dumps(row["raw_index"]) + algorithm = json.dumps(row["algorithm"]) + raw_algorithm = json.dumps(row["algorithm_raw"]) + algo_row = json.dumps(row["algo_row"]) + zero_index = int(row["algo_row"]) - 1 + prefix = " " if index == 0 else " , " + case_lines.append(f"{prefix}(({dataset}, {raw_index}, {algorithm}, {algo_row}), {raw_algorithm}, {zero_index})") + joined_case_lines = "\n".join(case_lines) + return "\n".join([ + "import Data.List (intercalate)", + "import qualified Data.Map as M", + "import Data.SRTree", + "import Data.SRTree.Print", + "import Data.Time.Clock.POSIX (getPOSIXTime)", + "import FixTree", + "import KotanchekSR (kotanchekSR)", + "import KotanchekSympy (kotanchekSympy)", + "import PagieSR (pagieSR)", + "import PagieSympy (pagieSympy)", + "import Reparam (replaceConstsWithParams)", + "", + "type RowId = (String, String, String, String)", + "type RowCase = (RowId, String, Int)", + "", + "cases :: [RowCase]", + "cases =", + " [", + joined_case_lines, + " ]", + "", + "sanitize :: String -> String", + "sanitize = map (\\c -> if c == '\\t' || c == '\\n' then ' ' else c)", + "", + "lookupOriginal :: String -> String -> Int -> SRTree Int Double", + "lookupOriginal dataset algorithm rowIndex = case dataset of", + ' "pagie" -> (pagieSR M.! algorithm) !! rowIndex', + ' "kotanchek" -> (kotanchekSR M.! algorithm) !! rowIndex', + ' _ -> error "unknown dataset"', + "", + "lookupSympy :: String -> String -> Int -> SRTree Int Double", + "lookupSympy dataset algorithm rowIndex = case dataset of", + ' "pagie" -> (pagieSympy M.! algorithm) !! rowIndex', + ' "kotanchek" -> (kotanchekSympy M.! algorithm) !! rowIndex', + ' _ -> error "unknown dataset"', + "", + "emitExpr :: RowId -> String -> SRTree Int Double -> IO ()", + "emitExpr (dataset, rawIndex, algorithm, algoRow) label expr = do", + " start <- getPOSIXTime", + " let simplified = simplifyE expr", + " end <- getPOSIXTime", + " let beforeNodes = countNodes expr", + " beforeParams = recountParams (replaceConstsWithParams expr)", + " afterNodes = countNodes simplified", + " afterParams = recountParams (replaceConstsWithParams simplified)", + " runtimeMs = (realToFrac (end - start) :: Double) * 1000.0", + " rendered = showDefault simplified", + " fields =", + " [ dataset", + " , rawIndex", + " , algorithm", + " , algoRow", + " , label", + " , show beforeNodes", + " , show beforeParams", + " , show afterNodes", + " , show afterParams", + " , show runtimeMs", + " , rendered", + " ]", + ' putStrLn (intercalate "\\t" (map sanitize fields))', + "", + "emitCase :: RowCase -> IO ()", + "emitCase (rowId@(dataset, _, _, _), rawAlgorithm, rowIndex) = do", + " let originalExpr = lookupOriginal dataset rawAlgorithm rowIndex", + " sympyExpr = lookupSympy dataset rawAlgorithm rowIndex", + ' emitExpr rowId "original" originalExpr', + ' emitExpr rowId "sympy" sympyExpr', + "", + "main :: IO ()", + "main = mapM_ emitCase cases", + "", + ]) + + +def _run_haskell_chunk(rows: list[dict[str, str]]) -> list[dict[str, str]]: + program = _build_haskell_program(rows) + with tempfile.NamedTemporaryFile("w", suffix=".hs", delete=False) as handle: + handle.write(program) + temp_path = Path(handle.name) + try: + env = dict(os.environ) + llvm_bin = llvm_bin_dir() + if llvm_bin is not None: + env["PATH"] = f"{llvm_bin}:{env['PATH']}" + output = subprocess.check_output( + ["stack", "exec", "--", "runghc", "-isrc", str(temp_path), "+RTS", "-K3G", "-RTS"], + cwd=HASKELL_ROOT, + env=env, + text=True, + timeout=3600, + ) + finally: + temp_path.unlink(missing_ok=True) + + results: list[dict[str, str]] = [] + for line in output.splitlines(): + ( + dataset, + raw_index, + algorithm, + algo_row, + label, + before_nodes, + before_params, + after_nodes, + after_params, + runtime_ms, + rendered, + ) = line.split("\t", maxsplit=10) + results.append({ + "dataset": dataset, + "raw_index": raw_index, + "algorithm": algorithm, + "algo_row": algo_row, + "label": label, + "status": "saturated", + "before_nodes": before_nodes, + "before_params": before_params, + "after_nodes": after_nodes, + "after_params": after_params, + "runtime_ms": runtime_ms, + "rendered_haskell": rendered, + "rendered_python": _canonicalize(rendered), + }) + return results + + +def _archived_fallback_results(row: dict[str, str], *, reason: str) -> list[dict[str, str]]: + return [ + { + "dataset": row["dataset"], + "raw_index": row["raw_index"], + "algorithm": row["algorithm"], + "algo_row": row["algo_row"], + "label": "original", + "status": reason, + "before_nodes": row["orig_nodes"], + "before_params": row["orig_params"], + "after_nodes": row["simpl_nodes"], + "after_params": row["simpl_params"], + "runtime_ms": "na", + "rendered_haskell": "", + "rendered_python": "", + }, + { + "dataset": row["dataset"], + "raw_index": row["raw_index"], + "algorithm": row["algorithm"], + "algo_row": row["algo_row"], + "label": "sympy", + "status": reason, + "before_nodes": row["orig_nodes_sympy"], + "before_params": row["orig_params_sympy"], + "after_nodes": row["simpl_nodes_sympy"], + "after_params": row["simpl_params_sympy"], + "runtime_ms": "na", + "rendered_haskell": "", + "rendered_python": "", + }, + ] + + +def _run_haskell_rows_serial(rows: list[dict[str, str]], *, batch_size: int) -> list[dict[str, str]]: + results: list[dict[str, str]] = [] + total = len(rows) + for start in range(0, total, batch_size): + batch = rows[start : start + batch_size] + try: + batch_results = _run_haskell_chunk(batch) + except subprocess.CalledProcessError: + if len(batch) == 1: + row = batch[0] + print( + f"live Haskell failed on {row['dataset']} {row['algorithm']}#{row['algo_row']}", + flush=True, + ) + batch_results = _archived_fallback_results(row, reason="archived_fallback_stack_overflow") + results.extend(batch_results) + end = start + len(batch) + print(f"[{end}/{total}] live Haskell rows complete", flush=True) + continue + print( + f"live Haskell batch overflow; splitting {batch[0]['dataset']} {batch[0]['algorithm']}#{batch[0]['algo_row']} .. {batch[-1]['dataset']} {batch[-1]['algorithm']}#{batch[-1]['algo_row']}", + flush=True, + ) + mid = len(batch) // 2 + batch_results = _run_haskell_rows_serial(batch[:mid], batch_size=max(1, mid)) + batch_results.extend(_run_haskell_rows_serial(batch[mid:], batch_size=max(1, len(batch) - mid))) + results.extend(batch_results) + end = start + len(batch) + print(f"[{end}/{total}] live Haskell rows complete", flush=True) + return results + + +def _run_haskell_rows(rows: list[dict[str, str]], *, batch_size: int, workers: int) -> list[dict[str, str]]: + if workers <= 1: + return _run_haskell_rows_serial(rows, batch_size=batch_size) + + batches = [rows[start : start + batch_size] for start in range(0, len(rows), batch_size)] + results: list[dict[str, str]] = [] + with Progress( + SpinnerColumn(), + TextColumn("[progress.description]{task.description}"), + BarColumn(), + MofNCompleteColumn(), + TimeElapsedColumn(), + ) as progress: + task = progress.add_task("live Haskell rows", total=len(rows)) + with ThreadPoolExecutor(max_workers=workers) as executor: + futures = { + executor.submit(_run_haskell_rows_serial, batch, batch_size=batch_size): len(batch) for batch in batches + } + for future in as_completed(futures): + results.extend(future.result()) + progress.advance(task, futures[future]) + return results + + +def _write_live_rows(rows: list[dict[str, str]], live_results: list[dict[str, str]], output_path: Path) -> None: + indexed = { + (row["dataset"], row["raw_index"], row["algorithm"], row["algo_row"], row["label"]): row for row in live_results + } + output_rows: list[dict[str, str]] = [] + for row in rows: + original = indexed[(row["dataset"], row["raw_index"], row["algorithm"], row["algo_row"], "original")] + sympy = indexed[(row["dataset"], row["raw_index"], row["algorithm"], row["algo_row"], "sympy")] + output_row = dict(row) + output_row.update({ + "orig_nodes": original["before_nodes"], + "orig_params": original["before_params"], + "simpl_nodes": original["after_nodes"], + "simpl_params": original["after_params"], + "orig_live_status": original["status"], + "orig_nodes_sympy": sympy["before_nodes"], + "orig_params_sympy": sympy["before_params"], + "simpl_nodes_sympy": sympy["after_nodes"], + "simpl_params_sympy": sympy["after_params"], + "sympy_live_status": sympy["status"], + "orig_runtime_ms": original["runtime_ms"], + "sympy_runtime_ms": sympy["runtime_ms"], + "orig_rendered_haskell": original["rendered_haskell"], + "orig_rendered_python": original["rendered_python"], + "sympy_rendered_haskell": sympy["rendered_haskell"], + "sympy_rendered_python": sympy["rendered_python"], + "baseline_source": ( + "live_haskell" + if original["status"] == "saturated" and sympy["status"] == "saturated" + else "archived_fallback" + ), + }) + output_rows.append(output_row) + + output_path.parent.mkdir(parents=True, exist_ok=True) + with output_path.open("w", newline="", encoding="utf-8") as handle: + writer = csv.DictWriter(handle, fieldnames=list(output_rows[0])) + writer.writeheader() + writer.writerows(output_rows) + + +def main() -> None: + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument( + "--output", + type=Path, + default=LIVE_ROWS_PATH, + help="Path to write the live Haskell corpus artifact.", + ) + parser.add_argument( + "--batch-size", + type=int, + default=DEFAULT_BATCH_SIZE, + help="Number of rows to evaluate per temporary Haskell runner invocation.", + ) + parser.add_argument( + "--workers", + type=int, + default=DEFAULT_WORKERS, + help="Number of Haskell batches to evaluate in parallel.", + ) + args = parser.parse_args() + + rows = _load_rows() + live_results = _run_haskell_rows(rows, batch_size=args.batch_size, workers=args.workers) + _write_live_rows(rows, live_results, args.output) + print(args.output) + + +if __name__ == "__main__": + main() diff --git a/python/egglog/exp/param_eq/run_runtime_compare.py b/python/egglog/exp/param_eq/run_runtime_compare.py new file mode 100644 index 00000000..0fbaa51a --- /dev/null +++ b/python/egglog/exp/param_eq/run_runtime_compare.py @@ -0,0 +1,268 @@ +"""Build an apples-to-apples Pagie runtime sweep for archived Haskell, live Haskell, and Egglog.""" + +from __future__ import annotations + +import argparse +import csv +import json +import os +import subprocess +import tempfile +import time +from collections import defaultdict +from concurrent.futures import ProcessPoolExecutor, ThreadPoolExecutor, as_completed +from pathlib import Path + +from rich.progress import BarColumn, MofNCompleteColumn, Progress, SpinnerColumn, TextColumn, TimeElapsedColumn + +from egglog.exp.param_eq.paths import ARTIFACT_DIR, llvm_bin_dir, param_eq_data_dir +from egglog.exp.param_eq.pipeline import parse_expression, run_paper_pipeline + +ARCHIVED_RUNTIME_PATH = ARTIFACT_DIR / "pagie_runtime_scatter.csv" +RUNTIME_COMPARE_PATH = ARTIFACT_DIR / "pagie_runtime_compare.csv" +HASKELL_ROOT = param_eq_data_dir() +DEFAULT_BATCH_SIZE = 18 +DEFAULT_HASKELL_WORKERS = 2 +DEFAULT_EGGLOG_WORKERS = max(1, min(os.cpu_count() or 1, 4)) +ALGORITHM_RENAMES = {"SRjl": "PySR", "GOMEA": "GP-GOMEA"} + + +def _clean_algorithm(name: str) -> str: + return ALGORITHM_RENAMES.get(name, name) + + +def _load_pagie_rows() -> list[dict[str, str]]: + results_path = HASKELL_ROOT / "results" / "pagie_results" + with results_path.open(newline="", encoding="utf-8") as handle: + raw_rows = list(csv.DictReader(handle)) + counts: defaultdict[str, int] = defaultdict(int) + rows: list[dict[str, str]] = [] + for raw_index, row in enumerate(raw_rows): + raw_algorithm = row["algorithm"] + counts[raw_algorithm] += 1 + rows.append({ + "raw_index": str(raw_index), + "algorithm_raw": raw_algorithm, + "algorithm": _clean_algorithm(raw_algorithm), + "algo_row": str(counts[raw_algorithm]), + "expr": row["expr"].strip(), + }) + return rows + + +def _build_haskell_program(rows: list[dict[str, str]]) -> str: + case_lines: list[str] = [] + for index, row in enumerate(rows): + algorithm = json.dumps(row["algorithm_raw"]) + algo_row = json.dumps(row["algo_row"]) + zero_index = int(row["algo_row"]) - 1 + prefix = " " if index == 0 else " , " + case_lines.append(f"{prefix}({algorithm}, {algo_row}, {zero_index})") + joined_case_lines = "\n".join(case_lines) + return "\n".join([ + "import Control.Exception (evaluate)", + "import Data.List (intercalate)", + "import qualified Data.Map as M", + "import Data.SRTree", + "import Data.Time.Clock.POSIX (getPOSIXTime)", + "import FixTree (simplifyE)", + "import PagieSR (pagieSR)", + "", + "type RowCase = (String, String, Int)", + "", + "cases :: [RowCase]", + "cases =", + " [", + joined_case_lines, + " ]", + "", + "sanitize :: String -> String", + "sanitize = map (\\c -> if c == '\\t' || c == '\\n' then ' ' else c)", + "", + "emitCase :: RowCase -> IO ()", + "emitCase (algorithm, algoRow, rowIndex) = do", + " let expr = (pagieSR M.! algorithm) !! rowIndex", + " beforeNodes = countNodes expr", + " start <- getPOSIXTime", + " afterNodes <- evaluate (countNodes (simplifyE expr))", + " end <- getPOSIXTime", + " let runtimeMs = (realToFrac (end - start) :: Double) * 1000.0", + " fields = [algorithm, algoRow, show beforeNodes, show afterNodes, show runtimeMs]", + ' putStrLn (intercalate "\\t" (map sanitize fields))', + "", + "main :: IO ()", + "main = mapM_ emitCase cases", + "", + ]) + + +def _run_haskell_chunk(rows: list[dict[str, str]]) -> list[dict[str, str]]: + program = _build_haskell_program(rows) + with tempfile.NamedTemporaryFile("w", suffix=".hs", delete=False) as handle: + handle.write(program) + temp_path = Path(handle.name) + try: + env = dict(os.environ) + llvm_bin = llvm_bin_dir() + if llvm_bin is not None: + env["PATH"] = f"{llvm_bin}:{env['PATH']}" + output = subprocess.check_output( + ["stack", "exec", "--", "runghc", "-isrc", str(temp_path), "+RTS", "-K3G", "-RTS"], + cwd=HASKELL_ROOT, + env=env, + text=True, + timeout=3600, + ) + finally: + temp_path.unlink(missing_ok=True) + + results: list[dict[str, str]] = [] + for line in output.splitlines(): + algorithm_raw, algo_row, before_nodes, after_nodes, runtime_ms = line.split("\t", maxsplit=4) + results.append({ + "implementation": "Live Haskell", + "algorithm_raw": algorithm_raw, + "algorithm": _clean_algorithm(algorithm_raw), + "algo_row": algo_row, + "node_count": before_nodes, + "after_nodes": after_nodes, + "runtime_ms": runtime_ms, + "status": "saturated", + }) + return results + + +def _run_haskell_rows_serial(rows: list[dict[str, str]], *, batch_size: int) -> list[dict[str, str]]: + results: list[dict[str, str]] = [] + for start in range(0, len(rows), batch_size): + batch = rows[start : start + batch_size] + try: + results.extend(_run_haskell_chunk(batch)) + except subprocess.CalledProcessError: + if len(batch) == 1: + row = batch[0] + print( + f"live Haskell runtime sweep failed on {row['algorithm_raw']}#{row['algo_row']}", + flush=True, + ) + results.append({ + "implementation": "Live Haskell", + "algorithm_raw": row["algorithm_raw"], + "algorithm": row["algorithm"], + "algo_row": row["algo_row"], + "node_count": "na", + "after_nodes": "na", + "runtime_ms": "na", + "status": "stack_overflow", + }) + continue + mid = len(batch) // 2 + results.extend(_run_haskell_rows_serial(batch[:mid], batch_size=max(1, mid))) + results.extend(_run_haskell_rows_serial(batch[mid:], batch_size=max(1, len(batch) - mid))) + return results + + +def _run_haskell_rows(rows: list[dict[str, str]], *, batch_size: int, workers: int) -> list[dict[str, str]]: + if workers <= 1: + return _run_haskell_rows_serial(rows, batch_size=batch_size) + + batches = [rows[start : start + batch_size] for start in range(0, len(rows), batch_size)] + results: list[dict[str, str]] = [] + with Progress( + SpinnerColumn(), + TextColumn("[progress.description]{task.description}"), + BarColumn(), + MofNCompleteColumn(), + TimeElapsedColumn(), + ) as progress: + task = progress.add_task("live Haskell runtime rows", total=len(rows)) + with ThreadPoolExecutor(max_workers=workers) as executor: + futures = { + executor.submit(_run_haskell_rows_serial, batch, batch_size=batch_size): len(batch) for batch in batches + } + for future in as_completed(futures): + batch_results = future.result() + results.extend(batch_results) + progress.advance(task, futures[future]) + return results + + +def _run_egglog_row(row: dict[str, str]) -> dict[str, str]: + num = parse_expression(row["expr"]) + start = time.perf_counter() + report = run_paper_pipeline(num) + elapsed_ms = (time.perf_counter() - start) * 1000.0 + return { + "implementation": "Egglog", + "algorithm_raw": row["algorithm_raw"], + "algorithm": row["algorithm"], + "algo_row": row["algo_row"], + "node_count": str(report.before_nodes), + "after_nodes": str(report.after_nodes), + "runtime_ms": f"{elapsed_ms:.6f}", + "status": report.status, + } + + +def _run_egglog_rows(rows: list[dict[str, str]], *, workers: int) -> list[dict[str, str]]: + results: list[dict[str, str]] = [] + with Progress( + SpinnerColumn(), + TextColumn("[progress.description]{task.description}"), + BarColumn(), + MofNCompleteColumn(), + TimeElapsedColumn(), + ) as progress: + task = progress.add_task("egglog runtime rows", total=len(rows)) + with ProcessPoolExecutor(max_workers=workers) as executor: + futures = [executor.submit(_run_egglog_row, row) for row in rows] + for future in as_completed(futures): + results.append(future.result()) + progress.advance(task) + return results + + +def _load_archived_runtime_rows() -> list[dict[str, str]]: + with ARCHIVED_RUNTIME_PATH.open(newline="", encoding="utf-8") as handle: + rows = list(csv.DictReader(handle)) + return [ + { + "implementation": "Archived Haskell", + "algorithm_raw": "", + "algorithm": "", + "algo_row": "", + "node_count": row["node_count"], + "after_nodes": "", + "runtime_ms": row["runtime_ms"], + "status": "archived_benchmark", + } + for row in rows + ] + + +def _write_rows(path: Path, rows: list[dict[str, str]]) -> None: + path.parent.mkdir(parents=True, exist_ok=True) + with path.open("w", newline="", encoding="utf-8") as handle: + writer = csv.DictWriter(handle, fieldnames=list(rows[0])) + writer.writeheader() + writer.writerows(rows) + + +def main() -> None: + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument("--output", type=Path, default=RUNTIME_COMPARE_PATH) + parser.add_argument("--haskell-workers", type=int, default=DEFAULT_HASKELL_WORKERS) + parser.add_argument("--egglog-workers", type=int, default=DEFAULT_EGGLOG_WORKERS) + parser.add_argument("--batch-size", type=int, default=DEFAULT_BATCH_SIZE) + args = parser.parse_args() + + rows = _load_pagie_rows() + archived_rows = _load_archived_runtime_rows() + live_rows = _run_haskell_rows(rows, batch_size=args.batch_size, workers=args.haskell_workers) + egglog_rows = _run_egglog_rows(rows, workers=args.egglog_workers) + _write_rows(args.output, archived_rows + live_rows + egglog_rows) + print(args.output) + + +if __name__ == "__main__": + main() diff --git a/python/egglog/exp/param_eq/test_pipeline.py b/python/egglog/exp/param_eq/test_pipeline.py new file mode 100644 index 00000000..5bb2d68c --- /dev/null +++ b/python/egglog/exp/param_eq/test_pipeline.py @@ -0,0 +1,271 @@ +"""Regression tests for the retained param-eq replication pipeline.""" + +from __future__ import annotations + +import json + +import pytest + +from egglog import EGraph, back_off, eq +from egglog.exp.param_eq import pipeline as param_eq_hegg +from egglog.exp.param_eq.paths import GOLDEN_PATH +from egglog.exp.param_eq.pipeline import count_nodes, count_params, parse_expression, render_num, run_paper_pipeline + +GOLDEN_FIXTURE = json.loads(GOLDEN_PATH.read_text()) +GOLDEN_CASES = GOLDEN_FIXTURE["cases"] +COMPARABLE_GOLDEN_CASES = [case for case in GOLDEN_CASES if not case["expected_mismatch"]] +GOLDEN_ANALYSIS_CASES = [case for case in COMPARABLE_GOLDEN_CASES if case["compare_root_analysis"]] +GOLDEN_REWRITE_CASES = [ + case for case in COMPARABLE_GOLDEN_CASES if case["compare_rewrite_tree"] and case["category"] != "corpus" +] +GOLDEN_SIMPLIFY_CASES = [case for case in COMPARABLE_GOLDEN_CASES if case["compare_simplify_e"]] +KNOWN_MISMATCH_CASE_IDS = {case["case_id"] for case in GOLDEN_CASES if case["expected_mismatch"]} + + +def _expected_analysis(case: dict[str, object]) -> param_eq_hegg.OptionalF64: + analysis = case["analysis_after"] + assert isinstance(analysis, dict) + match analysis["kind"]: + case "none": + return param_eq_hegg.OptionalF64.none + case "some": + value = analysis["value"] + assert isinstance(value, int | float) + return param_eq_hegg.OptionalF64.some(float(value)) + msg = f"Unexpected analysis fixture entry: {analysis!r}" + raise ValueError(msg) + + +def test_parse_expression_handles_leading_negative_literal() -> None: + expr = parse_expression("-0.000465+0.164361*(exp((x0*(2.011000-x0))))") + + assert render_num(expr) == "(-0.000465 + (0.164361 * exp((x0 * (2.011 - x0)))))" + assert count_params(expr) == 3 + assert count_nodes(expr) == 10 + + +def test_integer_power_exponents_do_not_count_as_parameters() -> None: + expr = parse_expression("plog(x0) + ((x0)^(-1))") + + assert count_params(expr) == 0 + + +def test_nonconstant_power_exponents_still_count_parameters() -> None: + expr = parse_expression("(2.0 ** x0) + (x1 ** (x0 + 3.0))") + + assert count_params(expr) == 2 + + +def test_run_paper_pipeline_saturates_simple_expression() -> None: + expr = parse_expression("exp(log(abs(x0)))") + report = run_paper_pipeline(expr) + + assert report.status == "saturated" + assert report.after_nodes <= report.before_nodes + assert report.after_params == 0 + + +@pytest.mark.parametrize( + ("source", "expected"), + [ + ("x0 - x0", param_eq_hegg.OptionalF64.none), + ("2 - 2", param_eq_hegg.OptionalF64.some(0.0)), + ("x0 / x0", param_eq_hegg.OptionalF64.none), + ("2 / 2", param_eq_hegg.OptionalF64.some(1.0)), + ], +) +def test_analysis_matches_haskell_canaries(source: str, expected: param_eq_hegg.OptionalF64) -> None: + expr = parse_expression(source) + egraph = EGraph(expr) + + egraph.run(param_eq_hegg.analysis_schedule.saturate()) + egraph.check(eq(param_eq_hegg.const_value(expr)).to(expected)) + + +@pytest.mark.parametrize( + ("source", "expected_analysis", "expected_render"), + [ + ("(-2) ** 2", param_eq_hegg.OptionalF64.some(4.0), "4.0"), + ("(-2) ** 3", param_eq_hegg.OptionalF64.some(-8.0), "-8.0"), + ("(-2) ** x0", param_eq_hegg.OptionalF64.none, "(-2.0 ** x0)"), + ], +) +def test_negative_power_cases_match_haskell_expectations( + source: str, + expected_analysis: param_eq_hegg.OptionalF64, + expected_render: str, +) -> None: + expr = parse_expression(source) + egraph, _ = param_eq_hegg._run_single_pass_egraph(expr) + egraph.check(eq(param_eq_hegg.const_value(expr)).to(expected_analysis)) + assert run_paper_pipeline(expr).rendered == expected_render + + +def test_merge_panics_on_different_constant_values() -> None: + egraph = EGraph( + param_eq_hegg.join_const_value(param_eq_hegg.OptionalF64.some(1.0), param_eq_hegg.OptionalF64.some(2.0)) + ) + + with pytest.raises(Exception, match="Merged different constant values"): + egraph.run(param_eq_hegg.analysis_schedule.saturate()) + + +def test_merge_accepts_close_constant_values() -> None: + expr = param_eq_hegg.join_const_value( + param_eq_hegg.OptionalF64.some(1.0), + param_eq_hegg.OptionalF64.some(1.0 + (param_eq_hegg.CONST_MERGE_TOLERANCE / 2.0)), + ) + egraph = EGraph(expr) + + egraph.run(param_eq_hegg.analysis_schedule.saturate()) + egraph.check(eq(expr).to(param_eq_hegg.OptionalF64.some(1.0))) + + +def test_merge_accepts_positive_and_negative_zero() -> None: + expr = param_eq_hegg.join_const_value(param_eq_hegg.OptionalF64.some(0.0), param_eq_hegg.OptionalF64.some(-0.0)) + egraph = EGraph(expr) + + egraph.run(param_eq_hegg.analysis_schedule.saturate()) + egraph.check(eq(expr).to(param_eq_hegg.OptionalF64.some(0.0))) + + +def test_constant_prune_deletes_composite_representatives() -> None: + expr = parse_expression("2 - 2") + egraph = EGraph(expr) + + egraph.run(param_eq_hegg.analysis_schedule.saturate()) + + payload = json.loads(egraph._serialize().to_json()) + ops = {node["op"] for node in payload["nodes"].values()} + assert "· - ·" not in ops + + +def test_zero_division_can_extract_zero_even_when_analysis_is_none() -> None: + expr = parse_expression("0 / x0") + egraph, _ = param_eq_hegg._run_single_pass_egraph(expr) + egraph.check(eq(param_eq_hegg.const_value(expr)).to(param_eq_hegg.OptionalF64.none)) + assert render_num(egraph.extract(expr)) == "0.0" + + +@pytest.mark.parametrize( + "source", + [ + "((-0.00978823600529464 * (x0 * x0)) + ((0.0012052881065756 * x1) * ((-8.2380609512329102) * x1)))", + "(((51.6682472229003906 * x0) * ((-0.0001894439337775) * x0)) + (-0.009929236885765901 * (x1 * x1)))", + ], +) +def test_reduced_schedule_case_normalizes_if_one_side_is_already_quadratic(source: str) -> None: + report = run_paper_pipeline(parse_expression(source)) + + assert report.rendered == "((-0.00978823600529464 * (x0 * x0)) + (-0.009929236885765901 * (x1 * x1)))" + + +def test_reduced_schedule_case_matches_haskell_canary() -> None: + case = next(case for case in GOLDEN_CASES if case["case_id"] == "x0_sq_plus_x1_sq") + report = run_paper_pipeline(parse_expression(case["source"])) + + assert report.rendered == case["simplify_e_expr_python"] + + +def test_add_comm_is_required_for_left_biased_factorization_path() -> None: + source = parse_expression("(1 / ((x0 * x0) + 1)) + (4 * (x1 * x1))") + expected = parse_expression("4 * ((x1 * x1) + (0.25 / ((x0 * x0) + 1)))") + + def bounded_schedule(basic_rules): + scheduler = back_off( + match_limit=param_eq_hegg.BACKOFF_MATCH_LIMIT, + ban_length=param_eq_hegg.BACKOFF_BAN_LENGTH, + fresh_rematch=True, + ).persistent() + round_sat = param_eq_hegg.run(basic_rules | param_eq_hegg.fun_rules, scheduler=scheduler) + ( + param_eq_hegg.analysis_schedule.saturate() + ) + return scheduler.scope( + round_sat + round_sat + round_sat + round_sat + param_eq_hegg.analysis_schedule.saturate() + ) + + no_add_comm_basic_rules = ( + param_eq_hegg.basic_mul_comm_rules + | param_eq_hegg.basic_add_assoc_rules + | param_eq_hegg.basic_mul_assoc_rules + | param_eq_hegg.basic_mul_div_rules + | param_eq_hegg.basic_product_regroup_rules + | param_eq_hegg.basic_other_rules + ) + + no_add_comm = EGraph(source) + no_add_comm.run(bounded_schedule(no_add_comm_basic_rules)) + with pytest.raises(Exception): + no_add_comm.check(eq(source).to(expected)) + + with_add_comm = EGraph(source) + with_add_comm.run(bounded_schedule(param_eq_hegg.basic_rules)) + with_add_comm.check(eq(source).to(expected)) + + +def test_reduced_pagie_second_pass_toy_reaches_haskell_form() -> None: + source = parse_expression("(-2.2516087483e-06) + (-0.009788252341175882 * ((x0 * x0) + 1))") + haskell_expected = "(-0.009788252341175882 * (1.0002300317431365 + (x0 * x0)))" + + baseline = run_paper_pipeline(source) + + assert baseline.rendered == haskell_expected + + egraph, _ = param_eq_hegg._run_single_pass_egraph(source) + assert render_num(egraph.extract(source)) == haskell_expected + + +def test_pagie_operon_15_matches_haskell_semantics_on_samples() -> None: + case = next(case for case in GOLDEN_CASES if case["case_id"] == "pagie_operon_15") + observed = run_paper_pipeline(parse_expression(case["source"])).extracted + expected = parse_expression(case["simplify_e_expr_python"]) + samples = ( + {"x0": -1.75, "x1": -1.25}, + {"x0": -0.5, "x1": 0.75}, + {"x0": 0.25, "x1": -1.5}, + {"x0": 0.5, "x1": 1.25}, + {"x0": 1.5, "x1": -0.25}, + {"x0": 1.75, "x1": 1.5}, + ) + + for env in samples: + observed_value = param_eq_hegg._eval_num(observed, env) + expected_value = param_eq_hegg._eval_num(expected, env) + assert observed_value is not None + assert expected_value is not None + assert abs(observed_value - expected_value) < 1e-9 + + +@pytest.mark.parametrize("case", GOLDEN_ANALYSIS_CASES, ids=lambda case: case["case_id"]) +def test_golden_root_analysis_matches_haskell(case: dict[str, object]) -> None: + expr = parse_expression(str(case["source"])) + egraph, _ = param_eq_hegg._run_single_pass_egraph(expr) + egraph.check(eq(param_eq_hegg.const_value(expr)).to(_expected_analysis(case))) + + +@pytest.mark.parametrize("case", GOLDEN_REWRITE_CASES, ids=lambda case: case["case_id"]) +def test_golden_rewrite_tree_reaches_haskell_form(case: dict[str, object]) -> None: + expr = parse_expression(str(case["source"])) + expected = parse_expression(str(case["rewrite_tree_expr_python"])) + egraph, _ = param_eq_hegg._run_single_pass_egraph(expr) + + egraph.check(eq(expr).to(expected)) + + +@pytest.mark.parametrize("case", GOLDEN_SIMPLIFY_CASES, ids=lambda case: case["case_id"]) +def test_golden_simplify_e_matches_haskell(case: dict[str, object]) -> None: + expr = parse_expression(str(case["source"])) + report = run_paper_pipeline(expr) + exact_form_case = case["category"] not in {"analysis", "guards", "corpus"} + + if case["compare_simplify_e_render"] and exact_form_case: + assert report.rendered == case["simplify_e_expr_python"] + if case["compare_param_count"] and case["category"] != "analysis": + assert report.after_params == case["simplify_e_param_count"] + + +def test_fixture_tracks_known_mismatches() -> None: + assert { + "sub_add_left_assoc", + }.issubset(KNOWN_MISMATCH_CASE_IDS) + assert "pagie_operon_15" not in KNOWN_MISMATCH_CASE_IDS diff --git a/python/egglog/exp/param_eq/test_replication_notebook.py b/python/egglog/exp/param_eq/test_replication_notebook.py new file mode 100644 index 00000000..2a46f4ff --- /dev/null +++ b/python/egglog/exp/param_eq/test_replication_notebook.py @@ -0,0 +1,18 @@ +"""Smoke test for running the retained param-eq notebook source in-process.""" + +from __future__ import annotations + +import json +import runpy +from pathlib import Path + + +def test_replication_notebook_runs_in_process() -> None: + notebook_source = Path(__file__).with_name("replication.py") + notebook_output = notebook_source.with_suffix(".ipynb") + + runpy.run_path(str(notebook_source), run_name="__main__") + + payload = json.loads(notebook_output.read_text()) + assert payload["cells"] + assert any(cell.get("outputs") for cell in payload["cells"] if cell.get("cell_type") == "code") diff --git a/python/egglog/pretty.py b/python/egglog/pretty.py index 008fb1bd..6dc41971 100644 --- a/python/egglog/pretty.py +++ b/python/egglog/pretty.py @@ -383,13 +383,18 @@ def uncached( # noqa: C901, PLR0911, PLR0912 case DefaultRewriteDecl(): msg = "default rewrites should not be pretty printed" raise TypeError(msg) - case BackOffDecl(_, match_limit, ban_length): + case BackOffDecl(_, match_limit, ban_length, fresh_rematch, persistent): list_args = [] if match_limit is not None: list_args.append(f"match_limit={match_limit}") if ban_length is not None: list_args.append(f"ban_length={ban_length}") - return f"back_off({', '.join(list_args)})", "scheduler" + if fresh_rematch: + list_args.append("fresh_rematch=True") + rendered = f"back_off({', '.join(list_args)})" + if persistent: + rendered += ".persistent()" + return rendered, "scheduler" case ValueDecl(value): return str(value), "value" case DummyDecl(): diff --git a/python/tests/test_high_level.py b/python/tests/test_high_level.py index 0efd66f8..e5f65b05 100644 --- a/python/tests/test_high_level.py +++ b/python/tests/test_high_level.py @@ -1200,7 +1200,8 @@ def test_sequence_repeat_saturate(self): def test_backoff_scheduler(self): """ Passing `scheduler=...` to run(...) hoists the scheduler to the - outer scope. This is equivalent to an explicit outer `bo.scope(...)`. + outer scope. This is equivalent to an explicit outer `bo.scope(...)` + around the whole repeated schedule. https://egraphs.zulipchat.com/#narrow/channel/375765-egg.2Fegglog/topic/.E2.9C.94.20Backoff.20Scheduler.20Example/with/538745863 """ @@ -1209,23 +1210,84 @@ def test_backoff_scheduler(self): grow = ruleset(rule(includes(x)).then(includes(x + 1))) shrink = ruleset(rule(includes(x)).then(includes(x - 1))) - e1 = EGraph() - e1.register(includes(i64(0))) - # default scheduler - with e1: - e1.run((grow + shrink) * 3) - e1.check(includes(i64(3)), includes(i64(-3))) - # back-off implicit outer hoisting bo = back_off(match_limit=1) - with e1: - e1.run((run(grow, scheduler=bo) + shrink) * 3) - e1.check(includes(i64(2)), includes(i64(-3))) - e1.check_fail(includes(i64(3))) - # back off inner hoisting - with e1: - e1.run(bo.scope(run(grow, scheduler=bo) + shrink) * 3) - e1.check(includes(i64(1)), includes(i64(-3))) - e1.check_fail(includes(i64(2))) + + def _run_and_collect(schedule: Schedule) -> set[int]: + egraph = EGraph() + egraph.register(includes(i64(0))) + with egraph: + egraph.run(schedule) + values = set() + for i in range(-3, 4): + try: + egraph.check(includes(i64(i))) + values.add(i) + except EggSmolError: + pass + return values + + default_values = _run_and_collect((grow + shrink) * 3) + assert default_values == {-3, -2, -1, 0, 1, 2, 3} + + implicit_values = _run_and_collect((run(grow, scheduler=bo) + shrink) * 3) + explicit_values = _run_and_collect(bo.scope((run(grow, scheduler=bo) + shrink) * 3)) + + assert implicit_values == explicit_values == {-3, -2, -1, 0, 1, 2} + + def test_backoff_scheduler_fresh_rematch_flag_changes_match_frontier(self): + r = relation("R", i64) + s = relation("S", i64) + seed = relation("Seed") + x = var("x", i64) + + copy = ruleset(rule(r(x)).then(s(x)), name="copy") + grow = ruleset(rule(seed()).then(r(i64(3))), name="grow") + + def _run_and_collect(*, fresh_rematch: bool) -> set[int]: + egraph = EGraph() + egraph.register(r(i64(0)), r(i64(1)), r(i64(2)), seed()) + bo = back_off(match_limit=2, ban_length=2, fresh_rematch=fresh_rematch) + schedule = bo.scope(seq(run(copy, scheduler=bo), run(grow), run(copy, scheduler=bo))) + egraph.run(schedule) + values = set() + for i in range(4): + try: + egraph.check(s(i64(i))) + values.add(i) + except EggSmolError: + pass + return values + + assert _run_and_collect(fresh_rematch=False) == {0, 1, 2} + assert _run_and_collect(fresh_rematch=True) == {0, 1, 2, 3} + + def test_persistent_scheduler_reuses_state_across_runs(self): + r = relation("R", i64) + s = relation("S", i64) + seed = relation("Seed") + x = var("x", i64) + + copy = ruleset(rule(r(x)).then(s(x)), name="copy") + grow = ruleset(rule(seed()).then(r(i64(3))), name="grow") + + def _run_and_collect(*, fresh_rematch: bool) -> set[int]: + egraph = EGraph() + egraph.register(r(i64(0)), r(i64(1)), r(i64(2)), seed()) + scheduler = back_off(match_limit=2, ban_length=2, fresh_rematch=fresh_rematch).persistent() + egraph.run(run(copy, scheduler=scheduler)) + egraph.run(run(grow)) + egraph.run(run(copy, scheduler=scheduler)) + values = set() + for i in range(4): + try: + egraph.check(s(i64(i))) + values.add(i) + except EggSmolError: + pass + return values + + assert _run_and_collect(fresh_rematch=False) == {0, 1, 2} + assert _run_and_collect(fresh_rematch=True) == {0, 1, 2, 3} def test_custom_scheduler_invalid_until(self): """ diff --git a/python/tests/test_pretty.py b/python/tests/test_pretty.py index d2a4dfc7..ebae004c 100644 --- a/python/tests/test_pretty.py +++ b/python/tests/test_pretty.py @@ -127,6 +127,8 @@ def my_very_long_function_name() -> A: ... r = ruleset(name="r") bo = back_off(ban_length=5) +bo_fresh = back_off(ban_length=5, fresh_rematch=True) +bo_persistent = back_off(ban_length=5).persistent() class BadRepr: @@ -236,6 +238,13 @@ def __repr__(self) -> str: '_scheduler_1 = back_off(ban_length=5)\n_scheduler_1.scope(run(ruleset(name="r"), scheduler=_scheduler_1))', id="scoped scheduler", ), + pytest.param(bo_fresh, "back_off(ban_length=5, fresh_rematch=True)", id="fresh-rematch scheduler"), + pytest.param( + run(r, h(), scheduler=bo_fresh), + 'run(ruleset(name="r"), h(), scheduler=back_off(ban_length=5, fresh_rematch=True))', + id="run with fresh-rematch scheduler", + ), + pytest.param(bo_persistent, "back_off(ban_length=5).persistent()", id="persistent scheduler"), # Functions pytest.param(f, "f", id="function"), pytest.param(A().method, "A().method", id="method"), diff --git a/src/conversions.rs b/src/conversions.rs index 00d46f87..6a88b6b6 100644 --- a/src/conversions.rs +++ b/src/conversions.rs @@ -641,6 +641,7 @@ convert_struct!( egglog_reports::RunReport: "{:?}" => RunReport( iterations: Vec, updated: bool, + can_stop: bool, search_and_apply_time_per_rule: HashMap, num_matches_per_rule: HashMap, search_and_apply_time_per_ruleset: HashMap, @@ -654,6 +655,7 @@ convert_struct!( .map(|i| Arc::new(i.clone().into())) .collect(), updated: r.updated, + can_stop: r.can_stop, search_and_apply_time_per_rule: r .search_and_apply_time_per_rule .iter() @@ -683,6 +685,7 @@ convert_struct!( r -> RunReport { iterations: r.iterations.iter().map(|i| i.as_ref().into()).collect(), updated: r.updated, + can_stop: r.can_stop, search_and_apply_time_per_rule: r .search_and_apply_time_per_rule .iter() diff --git a/src/egraph.rs b/src/egraph.rs index 4cad3d30..6c8a8715 100644 --- a/src/egraph.rs +++ b/src/egraph.rs @@ -22,7 +22,7 @@ use std::path::PathBuf; /// Create an empty EGraph. #[pyclass(unsendable)] pub struct EGraph { - pub(crate) egraph: egglog::EGraph, + pub(crate) egraph: egglog_experimental::ExperimentalEGraph, cmds: Option, } diff --git a/uv.lock b/uv.lock index d97e6708..d44dba96 100644 --- a/uv.lock +++ b/uv.lock @@ -46,6 +46,22 @@ wheels = [ { url = "https://files.pythonhosted.org/packages/7e/b3/6b4067be973ae96ba0d615946e314c5ae35f9f993eca561b356540bb0c2b/alabaster-1.0.0-py3-none-any.whl", hash = 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