diff --git a/.gitignore b/.gitignore index ed8cbe33..02661d9f 100644 --- a/.gitignore +++ b/.gitignore @@ -61,6 +61,7 @@ coverage.xml # Sphinx documentation docs/_build/ +docs/sg_execution_times.rst # PyCharm .idea/ diff --git a/docs/changelog.md b/docs/changelog.md index 261bc750..cf43ce81 100644 --- a/docs/changelog.md +++ b/docs/changelog.md @@ -4,6 +4,7 @@ _This project uses semantic versioning_ ## UNRELEASED +- Make docs builds fail on notebook execution errors and fix all doc issues [#369](https://github.com/egraphs-good/egglog-python/pull/369) - Add WIP `egglog.exp.any_expr` code for tracing arbitrary expressions with Python fallback [#366](https://github.com/egraphs-good/egglog-python/pull/366) - BREAKING: Remove support for Python 3.11 now that pyo3 has dropped support. - Allow mutating methods to update their underlying expression via `Expr.__replace_expr__`, and ensure default rewrites return the mutated receiver when using `mutates_self` or `mutates_first_arg`. diff --git a/docs/conf.py b/docs/conf.py index e0c8aed2..49142405 100644 --- a/docs/conf.py +++ b/docs/conf.py @@ -115,6 +115,7 @@ "**.ipynb_checkpoints", "auto_examples/*.ipynb", # "auto_examples/*.md5", + "conf.py", # Sphinx config file, not a notebook ] nitpicky = True @@ -164,8 +165,7 @@ # nb_execution_cache_path = '' # Exclude (POSIX) glob patterns for notebooks -# nb_execution_excludepatterns = () - +# Temporarily exclude notebooks with unrelated errors (not @egraph.class_ issues) # Execution timeout (seconds) nb_execution_timeout = 60 * 10 @@ -176,7 +176,7 @@ # nb_execution_allow_errors = False # Raise an exception on failed execution, rather than emitting a warning -nb_execution_raise_on_error = False +nb_execution_raise_on_error = True # Print traceback to stderr on execution error nb_execution_show_tb = True diff --git a/docs/explanation/2023_07_presentation.ipynb b/docs/explanation/2023_07_presentation.ipynb index 8c506beb..3ec9d80e 100644 --- a/docs/explanation/2023_07_presentation.ipynb +++ b/docs/explanation/2023_07_presentation.ipynb @@ -465,7 +465,7 @@ "source": [ "## Open Source Data Science Ecosystem in Python\n", "\n", - "> The term “ecosystem” is often used to describe the modern open-source scientific software. In biology, the term “ecosystem” is defined as a biological community of interacting organisms and their physical environment. Modern open-source scientific software development occurs in a similarly interconnected and interoperable fashion.\n", + "> The term \u201cecosystem\u201d is often used to describe the modern open-source scientific software. In biology, the term \u201cecosystem\u201d is defined as a biological community of interacting organisms and their physical environment. Modern open-source scientific software development occurs in a similarly interconnected and interoperable fashion.\n", "\n", "from [Jupyter Meets the Earth: Ecosystem](https://jupytearth.org/jupyter-resources/introduction/ecosystem.html)\n", "\n", @@ -984,7 +984,6 @@ "egraph = EGraph()\n", "\n", "\n", - "@egraph.class_\n", "class Structure(Expr): ...\n", "\n", "\n", @@ -993,7 +992,7 @@ "c = egraph.constant(\"c\", Structure)\n", "\n", "\n", - "@egraph.function\n", + "@function\n", "def operation(l: Structure, r: Structure) -> Structure: ...\n", "\n", "\n", @@ -3057,7 +3056,6 @@ "egraph = EGraph()\n", "\n", "\n", - "@egraph.class_\n", "class Num(Expr):\n", " @classmethod\n", " def var(cls, name: StringLike) -> Num: ...\n", @@ -5332,7 +5330,6 @@ "egraph = EGraph()\n", "\n", "\n", - "@egraph.class_\n", "class Bool(Expr):\n", " def to_py(self) -> PyObject: ...\n", "\n", @@ -5888,14 +5885,13 @@ "egraph = EGraph()\n", "\n", "\n", - "@egraph.class_\n", "class Num(Expr):\n", " def __init__(self, i: i64Like) -> None: ...\n", "\n", " def __add__(self, other: Num) -> Num: ...\n", "\n", "\n", - "@egraph.function\n", + "@function\n", "def fib(x: i64Like) -> Num: ...\n", "\n", "\n", @@ -12099,4 +12095,4 @@ }, "nbformat": 4, "nbformat_minor": 5 -} +} \ No newline at end of file diff --git a/docs/explanation/2023_11_09_portland_state.ipynb b/docs/explanation/2023_11_09_portland_state.ipynb index 84593c0f..2c01e403 100644 --- a/docs/explanation/2023_11_09_portland_state.ipynb +++ b/docs/explanation/2023_11_09_portland_state.ipynb @@ -170,7 +170,7 @@ "source": [ "_What is built on top of this?_\n", "\n", - "> The term “ecosystem” is often used to describe the modern open-source scientific software. In biology, the term “ecosystem” is defined as a biological community of interacting organisms and their physical environment. Modern open-source scientific software development occurs in a similarly interconnected and interoperable fashion.\n", + "> The term \u201cecosystem\u201d is often used to describe the modern open-source scientific software. In biology, the term \u201cecosystem\u201d is defined as a biological community of interacting organisms and their physical environment. Modern open-source scientific software development occurs in a similarly interconnected and interoperable fashion.\n", "\n", "[Jupyter Meets the Earth: Ecosystem](https://jupytearth.org/jupyter-resources/introduction/ecosystem.html)\n" ] @@ -313,7 +313,7 @@ "source": [ "## How do we manage the new complexity?\n", "\n", - "Integrated frameworks funded by companies with 💸?\n", + "Integrated frameworks funded by companies with \ud83d\udcb8?\n", "\n", " \n" ] @@ -465,14 +465,13 @@ "\n", "\n", "# 1. Describe domain with types & functions\n", - "@egraph.class_\n", "class Num(Expr):\n", " def __init__(self, i: i64Like) -> None: ...\n", "\n", " def __add__(self, other: Num) -> Num: ...\n", "\n", "\n", - "@egraph.function(cost=20)\n", + "@function(cost=20)\n", "def fib(x: i64Like) -> Num: ..." ] }, @@ -545,7 +544,7 @@ "version_minor": 0 }, "text/plain": [ - "VBox(children=(IntSlider(value=0, max=6), GraphvizWidget(dots=['digraph {stylesheet=\"/var/folders/xn/05ktz305…" + "VBox(children=(IntSlider(value=0, max=6), GraphvizWidget(dots=['digraph {stylesheet=\"/var/folders/xn/05ktz305\u2026" ] }, "execution_count": 3, @@ -1474,7 +1473,7 @@ "version_minor": 0 }, "text/plain": [ - "VBox(children=(IntSlider(value=0, max=3), GraphvizWidget(dots=['digraph {stylesheet=\"/var/folders/xn/05ktz305…" + "VBox(children=(IntSlider(value=0, max=3), GraphvizWidget(dots=['digraph {stylesheet=\"/var/folders/xn/05ktz305\u2026" ] }, "execution_count": 14, @@ -1509,7 +1508,7 @@ "version_minor": 0 }, "text/plain": [ - "VBox(children=(IntSlider(value=0, max=6), GraphvizWidget(dots=['digraph {stylesheet=\"/var/folders/xn/05ktz305…" + "VBox(children=(IntSlider(value=0, max=6), GraphvizWidget(dots=['digraph {stylesheet=\"/var/folders/xn/05ktz305\u2026" ] }, "execution_count": 15, @@ -1542,7 +1541,7 @@ "version_minor": 0 }, "text/plain": [ - "VBox(children=(IntSlider(value=0, max=9), GraphvizWidget(dots=['digraph {stylesheet=\"/var/folders/xn/05ktz305…" + "VBox(children=(IntSlider(value=0, max=9), GraphvizWidget(dots=['digraph {stylesheet=\"/var/folders/xn/05ktz305\u2026" ] }, "execution_count": 16, @@ -1731,4 +1730,4 @@ }, "nbformat": 4, "nbformat_minor": 5 -} +} \ No newline at end of file diff --git a/docs/explanation/2023_11_17_pytensor.ipynb b/docs/explanation/2023_11_17_pytensor.ipynb index 776d0c0a..22f5d6f0 100644 --- a/docs/explanation/2023_11_17_pytensor.ipynb +++ b/docs/explanation/2023_11_17_pytensor.ipynb @@ -133,7 +133,6 @@ "egraph = EGraph()\n", "\n", "\n", - "@egraph.class_\n", "class Int(Expr):\n", " def __init__(self, value: i64Like) -> None: ...\n", "\n", @@ -144,7 +143,6 @@ "converter(i64, Int, Int)\n", "\n", "\n", - "@egraph.class_\n", "class IntTuple(Expr):\n", " def __init__(self, first: Int) -> None: ...\n", "\n", @@ -183,7 +181,6 @@ "Shape = IntTuple\n", "\n", "\n", - "@egraph.class_\n", "class Tensor(Expr):\n", " def __init__(self, name: StringLike, shape: Shape) -> None: ...\n", "\n", @@ -199,17 +196,15 @@ " yield rewrite(Tensor(name, shape).shape).to(shape)\n", "\n", "\n", - "@egraph.class_\n", "class UnaryOp(Expr):\n", " def __call__(self, x: Tensor) -> Tensor: ...\n", "\n", "\n", - "@egraph.class_\n", "class BinaryOp(Expr):\n", " def __call__(self, x: Tensor, y: Tensor) -> Tensor: ...\n", "\n", "\n", - "@egraph.function(cost=1)\n", + "@function(cost=1)\n", "def Squeeze(axis: IntTuple) -> UnaryOp: ...\n", "\n", "\n", @@ -258,7 +253,6 @@ " yield (rewrite(Squeeze(axis=(i,))(x).shape[j]).to(x.shape[j], i > j))\n", "\n", "\n", - "@egraph.class_\n", "class OpType(Expr): ...\n", "\n", "\n", @@ -267,11 +261,11 @@ "ScalarDiv = egraph.constant(\"ScalarDiv\", OpType)\n", "\n", "\n", - "@egraph.function(cost=10)\n", + "@function(cost=10)\n", "def Reduce(scalar_op: OpType, axis: IntTuple) -> UnaryOp: ...\n", "\n", "\n", - "@egraph.function(cost=5)\n", + "@function(cost=5)\n", "def Elemwise(scalar_op: OpType) -> BinaryOp: ...\n", "\n", "\n", @@ -2527,4 +2521,4 @@ }, "nbformat": 4, "nbformat_minor": 0 -} +} \ No newline at end of file diff --git a/docs/explanation/2023_11_pydata_lightning_talk.ipynb b/docs/explanation/2023_11_pydata_lightning_talk.ipynb index 5ee372a7..f1038e0f 100644 --- a/docs/explanation/2023_11_pydata_lightning_talk.ipynb +++ b/docs/explanation/2023_11_pydata_lightning_talk.ipynb @@ -130,7 +130,6 @@ "egraph = EGraph()\n", "\n", "\n", - "@egraph.class_\n", "class NDArray(Expr):\n", " def __init__(self, i: i64Like) -> None: ...\n", "\n", @@ -139,7 +138,7 @@ " def __mul__(self, other: NDArray) -> NDArray: ...\n", "\n", "\n", - "@egraph.function(cost=2)\n", + "@function(cost=2)\n", "def arange(i: i64Like) -> NDArray: ...\n", "\n", "\n", @@ -167,7 +166,7 @@ "version_minor": 0 }, "text/plain": [ - "VBox(children=(IntSlider(value=0, max=1), GraphvizWidget(dots=['digraph {stylesheet=\"/var/folders/xn/05ktz305…" + "VBox(children=(IntSlider(value=0, max=1), GraphvizWidget(dots=['digraph {stylesheet=\"/var/folders/xn/05ktz305\u2026" ] }, "execution_count": 2, @@ -4067,7 +4066,7 @@ "assume_dtype-3429551472952562336\n", "\n", "\n", - "assume_dtype(NDArray_var("X"), ·)\n", + "assume_dtype(NDArray_var("X"), \u00b7)\n", "\n", "\n", "\n", @@ -4307,7 +4306,7 @@ "Slice___init__-15501507093852132239\n", "\n", "\n", - "Slice___init__(OptionalInt_none, ·, OptionalInt_none)\n", + "Slice___init__(OptionalInt_none, \u00b7, OptionalInt_none)\n", "\n", "\n", "\n", @@ -4487,7 +4486,7 @@ "TupleInt___getitem__-12686509587440430679\n", "\n", "\n", - "TupleInt___getitem__(·, Int___init__(0))\n", + "TupleInt___getitem__(\u00b7, Int___init__(0))\n", "\n", "\n", "\n", @@ -4547,7 +4546,7 @@ "NDArray_index-6690955771313385503\n", "\n", "\n", - "NDArray_index(·, TupleInt_EMPTY)\n", + "NDArray_index(\u00b7, TupleInt_EMPTY)\n", "\n", "\n", "\n", @@ -4567,7 +4566,7 @@ "NDArray_index-3712217405396014230\n", "\n", "\n", - "NDArray_index(·, TupleInt_EMPTY)\n", + "NDArray_index(\u00b7, TupleInt_EMPTY)\n", "\n", "\n", "\n", @@ -4617,7 +4616,7 @@ "TupleInt___getitem__-14078601210367663714\n", "\n", "\n", - "TupleInt___getitem__(·, Int___init__(0))\n", + "TupleInt___getitem__(\u00b7, Int___init__(0))\n", "\n", "\n", "\n", @@ -4647,7 +4646,7 @@ "TupleInt___getitem__-11929974989452939301\n", "\n", "\n", - "TupleInt___getitem__(·, Int___init__(0))\n", + "TupleInt___getitem__(\u00b7, Int___init__(0))\n", "\n", "\n", "\n", @@ -4667,7 +4666,7 @@ "TupleInt___getitem__-4501008190156617443\n", "\n", "\n", - "TupleInt___getitem__(·, Int___init__(0))\n", + "TupleInt___getitem__(\u00b7, Int___init__(0))\n", "\n", "\n", "\n", @@ -4707,7 +4706,7 @@ "TupleInt___getitem__-11605336705429392564\n", "\n", "\n", - "TupleInt___getitem__(·, Int___init__(0))\n", + "TupleInt___getitem__(\u00b7, Int___init__(0))\n", "\n", "\n", "\n", @@ -4727,7 +4726,7 @@ "TupleInt___getitem__-11375119588183991329\n", "\n", "\n", - "TupleInt___getitem__(·, Int___init__(0))\n", + "TupleInt___getitem__(\u00b7, Int___init__(0))\n", "\n", "\n", "\n", @@ -4747,7 +4746,7 @@ "TupleInt___getitem__-4381957443800611320\n", "\n", "\n", - "TupleInt___getitem__(·, Int___init__(0))\n", + "TupleInt___getitem__(\u00b7, Int___init__(0))\n", "\n", "\n", "\n", @@ -4867,7 +4866,7 @@ "Slice___init__-1162291712589082458\n", "\n", "\n", - "Slice___init__(OptionalInt_none, ·, OptionalInt_none)\n", + "Slice___init__(OptionalInt_none, \u00b7, OptionalInt_none)\n", "\n", "\n", "\n", @@ -4877,7 +4876,7 @@ "Slice___init__-14445438978175812750\n", "\n", "\n", - "Slice___init__(OptionalInt_none, ·, OptionalInt_none)\n", + "Slice___init__(OptionalInt_none, \u00b7, OptionalInt_none)\n", "\n", "\n", "\n", @@ -5087,7 +5086,7 @@ "assume_shape-3276222675780329179\n", "\n", "\n", - "assume_shape(assume_dtype(NDArray_var("y"), DType_int64), ·)\n", + "assume_shape(assume_dtype(NDArray_var("y"), DType_int64), \u00b7)\n", "\n", "\n", "\n", @@ -5117,7 +5116,7 @@ "svd-2189404700831293460\n", "\n", "\n", - "svd(·, FALSE)\n", + "svd(\u00b7, FALSE)\n", "\n", "\n", "\n", @@ -5227,7 +5226,7 @@ "reshape-4112525690760736104\n", "\n", "\n", - "reshape(·, TupleInt___init__(Int___init__(-1)), OptionalBool_none)\n", + "reshape(\u00b7, TupleInt___init__(Int___init__(-1)), OptionalBool_none)\n", "\n", "\n", "\n", @@ -5237,7 +5236,7 @@ "NDArray___getitem__-6343722845416298339\n", "\n", "\n", - "NDArray___getitem__(·, IndexKey_int(Int___init__(0)))\n", + "NDArray___getitem__(\u00b7, IndexKey_int(Int___init__(0)))\n", "\n", "\n", "\n", @@ -5257,7 +5256,7 @@ "sum-4880387995353894830\n", "\n", "\n", - "sum(·, OptionalIntOrTuple_none)\n", + "sum(\u00b7, OptionalIntOrTuple_none)\n", "\n", "\n", "\n", @@ -5307,7 +5306,7 @@ "mean-8154083004666556102\n", "\n", "\n", - "mean(·, ·, FALSE)\n", + "mean(\u00b7, \u00b7, FALSE)\n", "\n", "\n", "\n", @@ -5367,7 +5366,7 @@ "concat-9071020324919791953\n", "\n", "\n", - "concat(·, OptionalInt_some(Int___init__(0)))\n", + "concat(\u00b7, OptionalInt_some(Int___init__(0)))\n", "\n", "\n", "\n", @@ -5437,7 +5436,7 @@ "expand_dims-6453790381993539256\n", "\n", "\n", - "expand_dims(·, Int___init__(0))\n", + "expand_dims(\u00b7, Int___init__(0))\n", "\n", "\n", "\n", @@ -5447,7 +5446,7 @@ "mean-393645649769772465\n", "\n", "\n", - "mean(·, ·, TRUE)\n", + "mean(\u00b7, \u00b7, TRUE)\n", "\n", "\n", "\n", @@ -5587,7 +5586,7 @@ "asarray-9510298863856844727\n", "\n", "\n", - "asarray(·, OptionalDType_none, OptionalBool_none)\n", + "asarray(\u00b7, OptionalDType_none, OptionalBool_none)\n", "\n", "\n", "\n", @@ -5597,7 +5596,7 @@ "astype-12468708834165933853\n", "\n", "\n", - "astype(·, DType_int32)\n", + "astype(\u00b7, DType_int32)\n", "\n", "\n", "\n", @@ -5617,7 +5616,7 @@ "sum-1681433789052220133\n", "\n", "\n", - "sum(·, OptionalIntOrTuple_none)\n", + "sum(\u00b7, OptionalIntOrTuple_none)\n", "\n", "\n", "\n", @@ -5627,7 +5626,7 @@ "astype-14592420363448682842\n", "\n", "\n", - "astype(·, DType_int32)\n", + "astype(\u00b7, DType_int32)\n", "\n", "\n", "\n", @@ -5637,7 +5636,7 @@ "concat-430064524623572644\n", "\n", "\n", - "concat(·, OptionalInt_none)\n", + "concat(\u00b7, OptionalInt_none)\n", "\n", "\n", "\n", @@ -5667,7 +5666,7 @@ "TupleNDArray___getitem__-13683004811263061306\n", "\n", "\n", - "TupleNDArray___getitem__(·, Int___init__(0))\n", + "TupleNDArray___getitem__(\u00b7, Int___init__(0))\n", "\n", "\n", "\n", @@ -5687,7 +5686,7 @@ "asarray-17776165865978447989\n", "\n", "\n", - "asarray(·, OptionalDType_none, OptionalBool_none)\n", + "asarray(\u00b7, OptionalDType_none, OptionalBool_none)\n", "\n", "\n", "\n", @@ -5757,7 +5756,7 @@ "mean-15379324652549391956\n", "\n", "\n", - "mean(·, ·, FALSE)\n", + "mean(\u00b7, \u00b7, FALSE)\n", "\n", "\n", "\n", @@ -5797,7 +5796,7 @@ "sum-8113810327174539763\n", "\n", "\n", - "sum(·, OptionalIntOrTuple_none)\n", + "sum(\u00b7, OptionalIntOrTuple_none)\n", "\n", "\n", "\n", @@ -5857,7 +5856,7 @@ "svd-7253966389981509278\n", "\n", "\n", - "svd(·, FALSE)\n", + "svd(\u00b7, FALSE)\n", "\n", "\n", "\n", @@ -5927,7 +5926,7 @@ "TupleValue___getitem__-1353837537593392198\n", "\n", "\n", - "TupleValue___getitem__(·, Int___init__(0))\n", + "TupleValue___getitem__(\u00b7, Int___init__(0))\n", "\n", "\n", "\n", @@ -5937,7 +5936,7 @@ "sum-1955564354691009820\n", "\n", "\n", - "sum(·, OptionalIntOrTuple_none)\n", + "sum(\u00b7, OptionalIntOrTuple_none)\n", "\n", "\n", "\n", @@ -5977,7 +5976,7 @@ "mean-14339184933604096132\n", "\n", "\n", - "mean(·, ·, FALSE)\n", + "mean(\u00b7, \u00b7, FALSE)\n", "\n", "\n", "\n", @@ -6037,7 +6036,7 @@ "TupleValue___getitem__-9658389681233211557\n", "\n", "\n", - "TupleValue___getitem__(·, Int___init__(0))\n", + "TupleValue___getitem__(\u00b7, Int___init__(0))\n", "\n", "\n", "\n", @@ -6097,7 +6096,7 @@ "asarray-7902703286805427734\n", "\n", "\n", - "asarray(·, OptionalDType_none, OptionalBool_none)\n", + "asarray(\u00b7, OptionalDType_none, OptionalBool_none)\n", "\n", "\n", "\n", @@ -6107,7 +6106,7 @@ "NDArray_index-1182067134106770624\n", "\n", "\n", - "NDArray_index(·, TupleInt___init__(Int___init__(0)))\n", + "NDArray_index(\u00b7, TupleInt___init__(Int___init__(0)))\n", "\n", "\n", "\n", @@ -6117,7 +6116,7 @@ "NDArray___getitem__-17758114586016463110\n", "\n", "\n", - "NDArray___getitem__(·, IndexKey_int(Int___init__(0)))\n", + "NDArray___getitem__(\u00b7, IndexKey_int(Int___init__(0)))\n", "\n", "\n", "\n", @@ -6447,7 +6446,7 @@ "NDArray_index-12579319251068649370\n", "\n", "\n", - "NDArray_index(·, ALL_INDICES)\n", + "NDArray_index(\u00b7, ALL_INDICES)\n", "\n", "\n", "\n", @@ -6457,7 +6456,7 @@ "NDArray_index-16788298149597563309\n", "\n", "\n", - "NDArray_index(·, TupleInt___init__(Int___init__(0)))\n", + "NDArray_index(\u00b7, TupleInt___init__(Int___init__(0)))\n", "\n", "\n", "\n", @@ -6477,7 +6476,7 @@ "NDArray_index-17067340853146132798\n", "\n", "\n", - "NDArray_index(·, ALL_INDICES)\n", + "NDArray_index(\u00b7, ALL_INDICES)\n", "\n", "\n", "\n", @@ -6597,7 +6596,7 @@ "NDArray_index-15769018209198649053\n", "\n", "\n", - "NDArray_index(·, ALL_INDICES)\n", + "NDArray_index(\u00b7, ALL_INDICES)\n", "\n", "\n", "\n", @@ -6627,7 +6626,7 @@ "NDArray_index-5805179075406046989\n", "\n", "\n", - "NDArray_index(·, TupleInt_EMPTY)\n", + "NDArray_index(\u00b7, TupleInt_EMPTY)\n", "\n", "\n", "\n", @@ -6667,7 +6666,7 @@ "TupleValue___getitem__-7786309113067083429\n", "\n", "\n", - "TupleValue___getitem__(·, Int___init__(0))\n", + "TupleValue___getitem__(\u00b7, Int___init__(0))\n", "\n", "\n", "\n", @@ -6687,7 +6686,7 @@ "NDArray_index-9066298261712755353\n", "\n", "\n", - "NDArray_index(·, TupleInt_EMPTY)\n", + "NDArray_index(\u00b7, TupleInt_EMPTY)\n", "\n", "\n", "\n", @@ -6855,4 +6854,4 @@ }, "nbformat": 4, "nbformat_minor": 5 -} +} \ No newline at end of file diff --git a/docs/explanation/2023_12_02_congruence_closure.md b/docs/explanation/2023_12_02_congruence_closure.md index 0f14a2a0..1cd7d71c 100644 --- a/docs/explanation/2023_12_02_congruence_closure.md +++ b/docs/explanation/2023_12_02_congruence_closure.md @@ -120,7 +120,7 @@ def car(x: T) -> T: pass @function def cdr(x: T) -> T: pass -@function(default=Unit()) +@function def not_atom(x: T) -> Unit: pass ``` diff --git a/docs/explanation/2024_03_17_community_talk.ipynb b/docs/explanation/2024_03_17_community_talk.ipynb index 0e922d2b..dd0d2a86 100644 --- a/docs/explanation/2024_03_17_community_talk.ipynb +++ b/docs/explanation/2024_03_17_community_talk.ipynb @@ -24,6 +24,7 @@ "outputs": [ { "data": { + "image/jpeg": 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"text/html": [ "\n", " " + "" ] }, "execution_count": 1, @@ -90,25 +91,31 @@ }, { "cell_type": "code", - "execution_count": 1, + "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "from __future__ import annotations\n", "\n", + "import os\n", + "import numpy as np\n", + "\n", + "# Ensure SciPy array API support is enabled before importing sklearn/scipy\n", + "os.environ.setdefault(\"SCIPY_ARRAY_API\", \"1\")\n", + "\n", "import sklearn\n", - "from sklearn.datasets import make_classification\n", + "from sklearn import datasets\n", "from sklearn.discriminant_analysis import LinearDiscriminantAnalysis\n", "\n", "# Tell sklearn to treat arrays as following array API\n", "sklearn.set_config(array_api_dispatch=True)\n", "\n", - "X_np, y_np = make_classification(random_state=0, n_samples=1000000)\n", + "X_np, y_np = datasets.load_iris().data, datasets.load_iris().target\n", "\n", "\n", "# Assumption: I want to optimize calling this many times on data similar to that above\n", "def run_lda(x, y):\n", - " lda = LinearDiscriminantAnalysis()\n", + " lda = LinearDiscriminantAnalysis(n_components=2)\n", " return lda.fit(x, y).transform(x)" ] }, @@ -127,7 +134,7 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 3, "metadata": {}, "outputs": [], "source": [ @@ -145,13 +152,14 @@ "assume_shape(y_arr, y_np.shape)\n", "assume_value_one_of(y_arr, tuple(map(int, np.unique(y_np)))) # type: ignore[arg-type]\n", "\n", - "with EGraph():\n", + "egraph = EGraph()\n", + "with set_array_api_egraph(egraph):\n", " res = run_lda(X_arr, y_arr)" ] }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 4, "metadata": {}, "outputs": [ { @@ -165,9 +173,9 @@ ".output_html .hll { background-color: #ffffcc }\n", ".output_html { background: #f8f8f8; }\n", ".output_html .c { color: #3D7B7B; font-style: italic } /* Comment */\n", - ".output_html .err { border: 1px solid #FF0000 } /* Error */\n", + ".output_html .err { border: 1px solid #F00 } /* Error */\n", ".output_html .k { color: #008000; font-weight: bold } /* Keyword */\n", - ".output_html .o { color: #666666 } /* Operator */\n", + ".output_html .o { color: #666 } /* Operator */\n", ".output_html .ch { color: #3D7B7B; font-style: italic } /* Comment.Hashbang */\n", ".output_html .cm { color: #3D7B7B; font-style: italic } /* Comment.Multiline */\n", ".output_html .cp { color: #9C6500 } /* Comment.Preproc */\n", @@ -184,34 +192,34 @@ ".output_html .gp { color: #000080; font-weight: bold } /* Generic.Prompt */\n", ".output_html .gs { font-weight: bold } /* Generic.Strong */\n", ".output_html .gu { color: #800080; font-weight: bold } /* Generic.Subheading */\n", - ".output_html .gt { color: #0044DD } /* Generic.Traceback */\n", + ".output_html .gt { color: #04D } /* Generic.Traceback */\n", ".output_html .kc { color: #008000; font-weight: bold } /* Keyword.Constant */\n", ".output_html .kd { color: #008000; font-weight: bold } /* Keyword.Declaration */\n", ".output_html .kn { color: #008000; font-weight: bold } /* Keyword.Namespace */\n", ".output_html .kp { color: #008000 } /* Keyword.Pseudo */\n", ".output_html .kr { color: #008000; font-weight: bold } /* Keyword.Reserved */\n", ".output_html .kt { color: #B00040 } /* Keyword.Type */\n", - ".output_html .m { color: #666666 } /* Literal.Number */\n", + ".output_html .m { color: #666 } /* Literal.Number */\n", ".output_html .s { color: #BA2121 } /* Literal.String */\n", ".output_html .na { color: #687822 } /* Name.Attribute */\n", ".output_html .nb { color: #008000 } /* Name.Builtin */\n", - ".output_html .nc { color: #0000FF; font-weight: bold } /* Name.Class */\n", - ".output_html .no { color: #880000 } /* Name.Constant */\n", - ".output_html .nd { color: #AA22FF } /* Name.Decorator */\n", + ".output_html .nc { color: #00F; font-weight: bold } /* Name.Class */\n", + ".output_html .no { color: #800 } /* Name.Constant */\n", + ".output_html .nd { color: #A2F } /* Name.Decorator */\n", ".output_html .ni { color: #717171; font-weight: bold } /* Name.Entity */\n", ".output_html .ne { color: #CB3F38; font-weight: bold } /* Name.Exception */\n", - ".output_html .nf { color: #0000FF } /* Name.Function */\n", + ".output_html .nf { color: #00F } /* Name.Function */\n", ".output_html .nl { color: #767600 } /* Name.Label */\n", - ".output_html .nn { color: #0000FF; font-weight: bold } /* Name.Namespace */\n", + ".output_html .nn { color: #00F; font-weight: bold } /* Name.Namespace */\n", ".output_html .nt { color: #008000; font-weight: bold } /* Name.Tag */\n", ".output_html .nv { color: #19177C } /* Name.Variable */\n", - ".output_html .ow { color: #AA22FF; font-weight: bold } /* Operator.Word */\n", - ".output_html .w { color: #bbbbbb } /* Text.Whitespace */\n", - ".output_html .mb { color: #666666 } /* Literal.Number.Bin */\n", - ".output_html .mf { color: #666666 } /* Literal.Number.Float */\n", - ".output_html .mh { color: #666666 } /* Literal.Number.Hex */\n", - ".output_html .mi { color: #666666 } /* Literal.Number.Integer */\n", - ".output_html .mo { color: #666666 } /* Literal.Number.Oct */\n", + ".output_html .ow { color: #A2F; font-weight: bold } /* Operator.Word */\n", + ".output_html .w { color: #BBB } /* Text.Whitespace */\n", + ".output_html .mb { color: #666 } /* Literal.Number.Bin */\n", + ".output_html .mf { color: #666 } /* Literal.Number.Float */\n", + ".output_html .mh { color: #666 } /* Literal.Number.Hex */\n", + ".output_html .mi { color: #666 } /* Literal.Number.Integer */\n", + ".output_html .mo { color: #666 } /* Literal.Number.Oct */\n", ".output_html .sa { color: #BA2121 } /* Literal.String.Affix */\n", ".output_html .sb { color: #BA2121 } /* Literal.String.Backtick */\n", ".output_html .sc { color: #BA2121 } /* Literal.String.Char */\n", @@ -226,228 +234,375 @@ ".output_html .s1 { color: #BA2121 } /* Literal.String.Single */\n", ".output_html .ss { color: #19177C } /* Literal.String.Symbol */\n", ".output_html .bp { color: #008000 } /* Name.Builtin.Pseudo */\n", - ".output_html .fm { color: #0000FF } /* Name.Function.Magic */\n", + ".output_html .fm { color: #00F } /* Name.Function.Magic */\n", ".output_html .vc { color: #19177C } /* Name.Variable.Class */\n", ".output_html .vg { color: #19177C } /* Name.Variable.Global */\n", ".output_html .vi { color: #19177C } /* Name.Variable.Instance */\n", ".output_html .vm { color: #19177C } /* Name.Variable.Magic */\n", - ".output_html .il { color: #666666 } /* Literal.Number.Integer.Long */
_NDArray_1 = NDArray.var("X")\n",
+       ".output_html .il { color: #666 } /* Literal.Number.Integer.Long */
_NDArray_1 = NDArray.var("X")\n",
        "assume_dtype(_NDArray_1, DType.float64)\n",
-       "assume_shape(_NDArray_1, TupleInt(Int(1000000)) + TupleInt(Int(20)))\n",
+       "assume_shape(_NDArray_1, TupleInt.from_vec(Vec[Int](Int(150), Int(4))))\n",
        "assume_isfinite(_NDArray_1)\n",
        "_NDArray_2 = NDArray.var("y")\n",
        "assume_dtype(_NDArray_2, DType.int64)\n",
-       "assume_shape(_NDArray_2, TupleInt(Int(1000000)))\n",
-       "assume_value_one_of(_NDArray_2, TupleValue(Value.int(Int(0))) + TupleValue(Value.int(Int(1))))\n",
-       "_NDArray_3 = asarray(reshape(asarray(_NDArray_2), TupleInt(Int(-1))))\n",
-       "_NDArray_4 = astype(unique_counts(_NDArray_3)[Int(1)], asarray(_NDArray_1).dtype) / NDArray.scalar(Value.float(Float(1000000.0)))\n",
-       "_NDArray_5 = zeros(\n",
-       "    TupleInt(unique_inverse(_NDArray_3)[Int(0)].shape[Int(0)]) + TupleInt(asarray(_NDArray_1).shape[Int(1)]),\n",
+       "assume_shape(_NDArray_2, TupleInt.from_vec(Vec[Int](Int(150))))\n",
+       "_TupleValue_1 = TupleValue.from_vec(Vec[Value](Value.int(Int(0)), Value.int(Int(1)), Value.int(Int(2))))\n",
+       "assume_value_one_of(_NDArray_2, _TupleValue_1)\n",
+       "_NDArray_3 = zeros(\n",
+       "    TupleInt.from_vec(Vec[Int](NDArray.vector(_TupleValue_1).shape[Int(0)], asarray(_NDArray_1).shape[Int(1)])),\n",
        "    OptionalDType.some(asarray(_NDArray_1).dtype),\n",
        "    OptionalDevice.some(asarray(_NDArray_1).device),\n",
        ")\n",
-       "_MultiAxisIndexKey_1 = MultiAxisIndexKey(MultiAxisIndexKeyItem.slice(Slice()))\n",
-       "_IndexKey_1 = IndexKey.multi_axis(MultiAxisIndexKey(MultiAxisIndexKeyItem.int(Int(0))) + _MultiAxisIndexKey_1)\n",
+       "_MultiAxisIndexKeyItem_1 = MultiAxisIndexKeyItem.slice(Slice())\n",
+       "_IndexKey_1 = IndexKey.multi_axis(MultiAxisIndexKey.from_vec(Vec(MultiAxisIndexKeyItem.int(Int(0)), _MultiAxisIndexKeyItem_1)))\n",
+       "_IndexKey_2 = IndexKey.ndarray(unique_inverse(_NDArray_2)[Int(1)] == NDArray.scalar(Value.int(Int(0))))\n",
        "_OptionalIntOrTuple_1 = OptionalIntOrTuple.some(IntOrTuple.int(Int(0)))\n",
-       "_NDArray_5[_IndexKey_1] = mean(asarray(_NDArray_1)[ndarray_index(unique_inverse(_NDArray_3)[Int(1)] == NDArray.scalar(Value.int(Int(0))))], _OptionalIntOrTuple_1)\n",
-       "_IndexKey_2 = IndexKey.multi_axis(MultiAxisIndexKey(MultiAxisIndexKeyItem.int(Int(1))) + _MultiAxisIndexKey_1)\n",
-       "_NDArray_5[_IndexKey_2] = mean(asarray(_NDArray_1)[ndarray_index(unique_inverse(_NDArray_3)[Int(1)] == NDArray.scalar(Value.int(Int(1))))], _OptionalIntOrTuple_1)\n",
-       "_NDArray_6 = unique_values(concat(TupleNDArray(unique_values(asarray(_NDArray_3)))))\n",
-       "_NDArray_7 = concat(\n",
-       "    TupleNDArray(asarray(_NDArray_1)[ndarray_index(_NDArray_3 == _NDArray_6[IndexKey.int(Int(0))])] - _NDArray_5[_IndexKey_1])\n",
-       "    + TupleNDArray(asarray(_NDArray_1)[ndarray_index(_NDArray_3 == _NDArray_6[IndexKey.int(Int(1))])] - _NDArray_5[_IndexKey_2]),\n",
+       "_NDArray_3[_IndexKey_1] = mean(asarray(_NDArray_1)[_IndexKey_2], _OptionalIntOrTuple_1)\n",
+       "_IndexKey_3 = IndexKey.multi_axis(MultiAxisIndexKey.from_vec(Vec(MultiAxisIndexKeyItem.int(Int(1)), _MultiAxisIndexKeyItem_1)))\n",
+       "_IndexKey_4 = IndexKey.ndarray(unique_inverse(_NDArray_2)[Int(1)] == NDArray.scalar(Value.int(Int(1))))\n",
+       "_NDArray_3[_IndexKey_3] = mean(asarray(_NDArray_1)[_IndexKey_4], _OptionalIntOrTuple_1)\n",
+       "_IndexKey_5 = IndexKey.multi_axis(MultiAxisIndexKey.from_vec(Vec(MultiAxisIndexKeyItem.int(Int(2)), _MultiAxisIndexKeyItem_1)))\n",
+       "_IndexKey_6 = IndexKey.ndarray(unique_inverse(_NDArray_2)[Int(1)] == NDArray.scalar(Value.int(Int(2))))\n",
+       "_NDArray_3[_IndexKey_5] = mean(asarray(_NDArray_1)[_IndexKey_6], _OptionalIntOrTuple_1)\n",
+       "_NDArray_4 = zeros(TupleInt.from_vec(Vec[Int](Int(3), Int(4))), OptionalDType.some(DType.float64), OptionalDevice.some(_NDArray_1.device))\n",
+       "_IndexKey_7 = IndexKey.multi_axis(MultiAxisIndexKey.from_vec(Vec[MultiAxisIndexKeyItem](MultiAxisIndexKeyItem.int(Int(0)), _MultiAxisIndexKeyItem_1)))\n",
+       "_NDArray_4[_IndexKey_7] = mean(_NDArray_1[_IndexKey_2], _OptionalIntOrTuple_1)\n",
+       "_IndexKey_8 = IndexKey.multi_axis(MultiAxisIndexKey.from_vec(Vec[MultiAxisIndexKeyItem](MultiAxisIndexKeyItem.int(Int(1)), _MultiAxisIndexKeyItem_1)))\n",
+       "_NDArray_4[_IndexKey_8] = mean(_NDArray_1[_IndexKey_4], _OptionalIntOrTuple_1)\n",
+       "_IndexKey_9 = IndexKey.multi_axis(MultiAxisIndexKey.from_vec(Vec[MultiAxisIndexKeyItem](MultiAxisIndexKeyItem.int(Int(2)), _MultiAxisIndexKeyItem_1)))\n",
+       "_NDArray_4[_IndexKey_9] = mean(_NDArray_1[_IndexKey_6], _OptionalIntOrTuple_1)\n",
+       "_NDArray_5 = concat(\n",
+       "    TupleNDArray.from_vec(\n",
+       "        Vec[NDArray](\n",
+       "            _NDArray_1[IndexKey.ndarray(_NDArray_2 == NDArray.scalar(Value.int(Int(0))))] - _NDArray_4[_IndexKey_7],\n",
+       "            _NDArray_1[IndexKey.ndarray(_NDArray_2 == NDArray.scalar(Value.int(Int(1))))] - _NDArray_4[_IndexKey_8],\n",
+       "            _NDArray_1[IndexKey.ndarray(_NDArray_2 == NDArray.scalar(Value.int(Int(2))))] - _NDArray_4[_IndexKey_9],\n",
+       "        )\n",
+       "    ),\n",
        "    OptionalInt.some(Int(0)),\n",
        ")\n",
-       "_NDArray_8 = std(_NDArray_7, _OptionalIntOrTuple_1)\n",
-       "_NDArray_8[ndarray_index(std(_NDArray_7, _OptionalIntOrTuple_1) == NDArray.scalar(Value.int(Int(0))))] = NDArray.scalar(Value.float(Float(1.0)))\n",
+       "_NDArray_6 = std(_NDArray_5, _OptionalIntOrTuple_1)\n",
+       "_NDArray_6[IndexKey.ndarray(std(_NDArray_5, _OptionalIntOrTuple_1) == NDArray.scalar(Value.int(Int(0))))] = NDArray.scalar(\n",
+       "    Value.float(Float.rational(BigRat(BigInt.from_string("1"), BigInt.from_string("1"))))\n",
+       ")\n",
        "_TupleNDArray_1 = svd(\n",
-       "    sqrt(asarray(NDArray.scalar(Value.float(Float(1.0) / Float.from_int(asarray(_NDArray_1).shape[Int(0)] - _NDArray_6.shape[Int(0)]))))) * (_NDArray_7 / _NDArray_8), FALSE\n",
+       "    sqrt(\n",
+       "        asarray(\n",
+       "            NDArray.scalar(Value.float(Float.rational(BigRat(BigInt.from_string("1"), BigInt.from_string("147"))))),\n",
+       "            OptionalDType.some(DType.float64),\n",
+       "            OptionalBool.none,\n",
+       "            OptionalDevice.some(_NDArray_1.device),\n",
+       "        )\n",
+       "    )\n",
+       "    * (_NDArray_5 / _NDArray_6),\n",
+       "    Boolean(False),\n",
        ")\n",
        "_Slice_1 = Slice(OptionalInt.none, OptionalInt.some(sum(astype(_TupleNDArray_1[Int(1)] > NDArray.scalar(Value.float(Float(0.0001))), DType.int32)).to_value().to_int))\n",
-       "_NDArray_9 = (_TupleNDArray_1[Int(2)][IndexKey.multi_axis(MultiAxisIndexKey(MultiAxisIndexKeyItem.slice(_Slice_1)) + _MultiAxisIndexKey_1)] / _NDArray_8).T / _TupleNDArray_1[\n",
-       "    Int(1)\n",
-       "][IndexKey.slice(_Slice_1)]\n",
+       "_NDArray_7 = asarray(reshape(asarray(_NDArray_2), TupleInt.from_vec(Vec[Int](Int(-1)))))\n",
+       "_NDArray_8 = unique_values(concat(TupleNDArray.from_vec(Vec[NDArray](unique_values(asarray(_NDArray_7))))))\n",
+       "_NDArray_9 = std(\n",
+       "    concat(\n",
+       "        TupleNDArray.from_vec(\n",
+       "            Vec[NDArray](\n",
+       "                asarray(_NDArray_1)[IndexKey.ndarray(_NDArray_7 == _NDArray_8[IndexKey.int(Int(0))])] - _NDArray_3[_IndexKey_1],\n",
+       "                asarray(_NDArray_1)[IndexKey.ndarray(_NDArray_7 == _NDArray_8[IndexKey.int(Int(1))])] - _NDArray_3[_IndexKey_3],\n",
+       "                asarray(_NDArray_1)[IndexKey.ndarray(_NDArray_7 == _NDArray_8[IndexKey.int(Int(2))])] - _NDArray_3[_IndexKey_5],\n",
+       "            )\n",
+       "        ),\n",
+       "        OptionalInt.some(Int(0)),\n",
+       "    ),\n",
+       "    _OptionalIntOrTuple_1,\n",
+       ")\n",
+       "_NDArray_10 = copy(_NDArray_9)\n",
+       "_NDArray_10[IndexKey.ndarray(_NDArray_9 == NDArray.scalar(Value.int(Int(0))))] = NDArray.scalar(Value.float(Float(1.0)))\n",
+       "_NDArray_11 = astype(unique_counts(_NDArray_2)[Int(1)], DType.float64) / NDArray.scalar(Value.float(Float.rational(BigRat(BigInt.from_string("150"), BigInt.from_string("1")))))\n",
        "_TupleNDArray_2 = svd(\n",
        "    (\n",
-       "        sqrt(\n",
-       "            (NDArray.scalar(Value.int(asarray(_NDArray_1).shape[Int(0)])) * _NDArray_4)\n",
-       "            * NDArray.scalar(Value.float(Float(1.0) / Float.from_int(_NDArray_6.shape[Int(0)] - Int(1))))\n",
-       "        )\n",
-       "        * (_NDArray_5 - (_NDArray_4 @ _NDArray_5)).T\n",
+       "        sqrt((NDArray.scalar(Value.int(Int(150))) * _NDArray_11) * NDArray.scalar(Value.float(Float.rational(BigRat(BigInt.from_string("1"), BigInt.from_string("2"))))))\n",
+       "        * (_NDArray_4 - (_NDArray_11 @ _NDArray_4)).T\n",
        "    ).T\n",
-       "    @ _NDArray_9,\n",
-       "    FALSE,\n",
+       "    @ (\n",
+       "        (\n",
+       "            _TupleNDArray_1[Int(2)][IndexKey.multi_axis(MultiAxisIndexKey.from_vec(Vec[MultiAxisIndexKeyItem](MultiAxisIndexKeyItem.slice(_Slice_1), _MultiAxisIndexKeyItem_1)))]\n",
+       "            / _NDArray_6\n",
+       "        ).T\n",
+       "        / _TupleNDArray_1[Int(1)][IndexKey.slice(_Slice_1)]\n",
+       "    ),\n",
+       "    Boolean(False),\n",
        ")\n",
        "(\n",
-       "    (asarray(_NDArray_1) - (_NDArray_4 @ _NDArray_5))\n",
+       "    (asarray(_NDArray_1) - ((astype(unique_counts(_NDArray_2)[Int(1)], asarray(_NDArray_1).dtype) / NDArray.scalar(Value.float(Float(150.0)))) @ _NDArray_3))\n",
        "    @ (\n",
-       "        _NDArray_9\n",
+       "        (\n",
+       "            (_TupleNDArray_1[Int(2)][IndexKey.multi_axis(MultiAxisIndexKey.from_vec(Vec(MultiAxisIndexKeyItem.slice(_Slice_1), _MultiAxisIndexKeyItem_1)))] / _NDArray_10).T\n",
+       "            / _TupleNDArray_1[Int(1)][IndexKey.slice(_Slice_1)]\n",
+       "        )\n",
        "        @ _TupleNDArray_2[Int(2)].T[\n",
        "            IndexKey.multi_axis(\n",
-       "                _MultiAxisIndexKey_1\n",
-       "                + MultiAxisIndexKey(\n",
-       "                    MultiAxisIndexKeyItem.slice(\n",
-       "                        Slice(\n",
-       "                            OptionalInt.none,\n",
-       "                            OptionalInt.some(\n",
-       "                                sum(astype(_TupleNDArray_2[Int(1)] > (NDArray.scalar(Value.float(Float(0.0001))) * _TupleNDArray_2[Int(1)][IndexKey.int(Int(0))]), DType.int32))\n",
-       "                                .to_value()\n",
-       "                                .to_int\n",
-       "                            ),\n",
-       "                        )\n",
+       "                MultiAxisIndexKey.from_vec(\n",
+       "                    Vec(\n",
+       "                        _MultiAxisIndexKeyItem_1,\n",
+       "                        MultiAxisIndexKeyItem.slice(\n",
+       "                            Slice(\n",
+       "                                OptionalInt.none,\n",
+       "                                OptionalInt.some(\n",
+       "                                    sum(astype(_TupleNDArray_2[Int(1)] > (NDArray.scalar(Value.float(Float(0.0001))) * _TupleNDArray_2[Int(1)][IndexKey.int(Int(0))]), DType.int32))\n",
+       "                                    .to_value()\n",
+       "                                    .to_int\n",
+       "                                ),\n",
+       "                            )\n",
+       "                        ),\n",
        "                    )\n",
        "                )\n",
        "            )\n",
        "        ]\n",
        "    )\n",
-       ")[IndexKey.multi_axis(_MultiAxisIndexKey_1 + MultiAxisIndexKey(MultiAxisIndexKeyItem.slice(Slice(OptionalInt.none, OptionalInt.some(_NDArray_6.shape[Int(0)] - Int(1))))))]\n",
+       ")[IndexKey.multi_axis(MultiAxisIndexKey.from_vec(Vec(_MultiAxisIndexKeyItem_1, MultiAxisIndexKeyItem.slice(Slice(OptionalInt.none, OptionalInt.some(Int(2)))))))]\n",
        "
\n"
       ],
       "text/latex": [
        "\\begin{Verbatim}[commandchars=\\\\\\{\\}]\n",
        "\\PY{n}{\\PYZus{}NDArray\\PYZus{}1} \\PY{o}{=} \\PY{n}{NDArray}\\PY{o}{.}\\PY{n}{var}\\PY{p}{(}\\PY{l+s+s2}{\\PYZdq{}}\\PY{l+s+s2}{X}\\PY{l+s+s2}{\\PYZdq{}}\\PY{p}{)}\n",
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+       "\\PY{n}{assume\\PYZus{}shape}\\PY{p}{(}\\PY{n}{\\PYZus{}NDArray\\PYZus{}1}\\PY{p}{,} \\PY{n}{TupleInt}\\PY{o}{.}\\PY{n}{from\\PYZus{}vec}\\PY{p}{(}\\PY{n}{Vec}\\PY{p}{[}\\PY{n}{Int}\\PY{p}{]}\\PY{p}{(}\\PY{n}{Int}\\PY{p}{(}\\PY{l+m+mi}{150}\\PY{p}{)}\\PY{p}{,} \\PY{n}{Int}\\PY{p}{(}\\PY{l+m+mi}{4}\\PY{p}{)}\\PY{p}{)}\\PY{p}{)}\\PY{p}{)}\n",
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-       "\\PY{n}{\\PYZus{}NDArray\\PYZus{}3} \\PY{o}{=} \\PY{n}{asarray}\\PY{p}{(}\\PY{n}{reshape}\\PY{p}{(}\\PY{n}{asarray}\\PY{p}{(}\\PY{n}{\\PYZus{}NDArray\\PYZus{}2}\\PY{p}{)}\\PY{p}{,} \\PY{n}{TupleInt}\\PY{p}{(}\\PY{n}{Int}\\PY{p}{(}\\PY{o}{\\PYZhy{}}\\PY{l+m+mi}{1}\\PY{p}{)}\\PY{p}{)}\\PY{p}{)}\\PY{p}{)}\n",
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-       "\\PY{n}{\\PYZus{}NDArray\\PYZus{}5} \\PY{o}{=} \\PY{n}{zeros}\\PY{p}{(}\n",
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+       "\\PY{n}{assume\\PYZus{}shape}\\PY{p}{(}\\PY{n}{\\PYZus{}NDArray\\PYZus{}2}\\PY{p}{,} \\PY{n}{TupleInt}\\PY{o}{.}\\PY{n}{from\\PYZus{}vec}\\PY{p}{(}\\PY{n}{Vec}\\PY{p}{[}\\PY{n}{Int}\\PY{p}{]}\\PY{p}{(}\\PY{n}{Int}\\PY{p}{(}\\PY{l+m+mi}{150}\\PY{p}{)}\\PY{p}{)}\\PY{p}{)}\\PY{p}{)}\n",
+       "\\PY{n}{\\PYZus{}TupleValue\\PYZus{}1} \\PY{o}{=} \\PY{n}{TupleValue}\\PY{o}{.}\\PY{n}{from\\PYZus{}vec}\\PY{p}{(}\\PY{n}{Vec}\\PY{p}{[}\\PY{n}{Value}\\PY{p}{]}\\PY{p}{(}\\PY{n}{Value}\\PY{o}{.}\\PY{n}{int}\\PY{p}{(}\\PY{n}{Int}\\PY{p}{(}\\PY{l+m+mi}{0}\\PY{p}{)}\\PY{p}{)}\\PY{p}{,} \\PY{n}{Value}\\PY{o}{.}\\PY{n}{int}\\PY{p}{(}\\PY{n}{Int}\\PY{p}{(}\\PY{l+m+mi}{1}\\PY{p}{)}\\PY{p}{)}\\PY{p}{,} \\PY{n}{Value}\\PY{o}{.}\\PY{n}{int}\\PY{p}{(}\\PY{n}{Int}\\PY{p}{(}\\PY{l+m+mi}{2}\\PY{p}{)}\\PY{p}{)}\\PY{p}{)}\\PY{p}{)}\n",
+       "\\PY{n}{assume\\PYZus{}value\\PYZus{}one\\PYZus{}of}\\PY{p}{(}\\PY{n}{\\PYZus{}NDArray\\PYZus{}2}\\PY{p}{,} \\PY{n}{\\PYZus{}TupleValue\\PYZus{}1}\\PY{p}{)}\n",
+       "\\PY{n}{\\PYZus{}NDArray\\PYZus{}3} \\PY{o}{=} \\PY{n}{zeros}\\PY{p}{(}\n",
+       "    \\PY{n}{TupleInt}\\PY{o}{.}\\PY{n}{from\\PYZus{}vec}\\PY{p}{(}\\PY{n}{Vec}\\PY{p}{[}\\PY{n}{Int}\\PY{p}{]}\\PY{p}{(}\\PY{n}{NDArray}\\PY{o}{.}\\PY{n}{vector}\\PY{p}{(}\\PY{n}{\\PYZus{}TupleValue\\PYZus{}1}\\PY{p}{)}\\PY{o}{.}\\PY{n}{shape}\\PY{p}{[}\\PY{n}{Int}\\PY{p}{(}\\PY{l+m+mi}{0}\\PY{p}{)}\\PY{p}{]}\\PY{p}{,} \\PY{n}{asarray}\\PY{p}{(}\\PY{n}{\\PYZus{}NDArray\\PYZus{}1}\\PY{p}{)}\\PY{o}{.}\\PY{n}{shape}\\PY{p}{[}\\PY{n}{Int}\\PY{p}{(}\\PY{l+m+mi}{1}\\PY{p}{)}\\PY{p}{]}\\PY{p}{)}\\PY{p}{)}\\PY{p}{,}\n",
        "    \\PY{n}{OptionalDType}\\PY{o}{.}\\PY{n}{some}\\PY{p}{(}\\PY{n}{asarray}\\PY{p}{(}\\PY{n}{\\PYZus{}NDArray\\PYZus{}1}\\PY{p}{)}\\PY{o}{.}\\PY{n}{dtype}\\PY{p}{)}\\PY{p}{,}\n",
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        "\\PY{p}{)}\n",
-       "\\PY{n}{\\PYZus{}MultiAxisIndexKey\\PYZus{}1} \\PY{o}{=} \\PY{n}{MultiAxisIndexKey}\\PY{p}{(}\\PY{n}{MultiAxisIndexKeyItem}\\PY{o}{.}\\PY{n}{slice}\\PY{p}{(}\\PY{n}{Slice}\\PY{p}{(}\\PY{p}{)}\\PY{p}{)}\\PY{p}{)}\n",
-       "\\PY{n}{\\PYZus{}IndexKey\\PYZus{}1} \\PY{o}{=} \\PY{n}{IndexKey}\\PY{o}{.}\\PY{n}{multi\\PYZus{}axis}\\PY{p}{(}\\PY{n}{MultiAxisIndexKey}\\PY{p}{(}\\PY{n}{MultiAxisIndexKeyItem}\\PY{o}{.}\\PY{n}{int}\\PY{p}{(}\\PY{n}{Int}\\PY{p}{(}\\PY{l+m+mi}{0}\\PY{p}{)}\\PY{p}{)}\\PY{p}{)} \\PY{o}{+} \\PY{n}{\\PYZus{}MultiAxisIndexKey\\PYZus{}1}\\PY{p}{)}\n",
+       "\\PY{n}{\\PYZus{}MultiAxisIndexKeyItem\\PYZus{}1} \\PY{o}{=} \\PY{n}{MultiAxisIndexKeyItem}\\PY{o}{.}\\PY{n}{slice}\\PY{p}{(}\\PY{n}{Slice}\\PY{p}{(}\\PY{p}{)}\\PY{p}{)}\n",
+       "\\PY{n}{\\PYZus{}IndexKey\\PYZus{}1} \\PY{o}{=} \\PY{n}{IndexKey}\\PY{o}{.}\\PY{n}{multi\\PYZus{}axis}\\PY{p}{(}\\PY{n}{MultiAxisIndexKey}\\PY{o}{.}\\PY{n}{from\\PYZus{}vec}\\PY{p}{(}\\PY{n}{Vec}\\PY{p}{(}\\PY{n}{MultiAxisIndexKeyItem}\\PY{o}{.}\\PY{n}{int}\\PY{p}{(}\\PY{n}{Int}\\PY{p}{(}\\PY{l+m+mi}{0}\\PY{p}{)}\\PY{p}{)}\\PY{p}{,} \\PY{n}{\\PYZus{}MultiAxisIndexKeyItem\\PYZus{}1}\\PY{p}{)}\\PY{p}{)}\\PY{p}{)}\n",
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-       "\\PY{p}{)}\\PY{p}{[}\\PY{n}{IndexKey}\\PY{o}{.}\\PY{n}{multi\\PYZus{}axis}\\PY{p}{(}\\PY{n}{\\PYZus{}MultiAxisIndexKey\\PYZus{}1} \\PY{o}{+} \\PY{n}{MultiAxisIndexKey}\\PY{p}{(}\\PY{n}{MultiAxisIndexKeyItem}\\PY{o}{.}\\PY{n}{slice}\\PY{p}{(}\\PY{n}{Slice}\\PY{p}{(}\\PY{n}{OptionalInt}\\PY{o}{.}\\PY{n}{none}\\PY{p}{,} \\PY{n}{OptionalInt}\\PY{o}{.}\\PY{n}{some}\\PY{p}{(}\\PY{n}{\\PYZus{}NDArray\\PYZus{}6}\\PY{o}{.}\\PY{n}{shape}\\PY{p}{[}\\PY{n}{Int}\\PY{p}{(}\\PY{l+m+mi}{0}\\PY{p}{)}\\PY{p}{]} \\PY{o}{\\PYZhy{}} \\PY{n}{Int}\\PY{p}{(}\\PY{l+m+mi}{1}\\PY{p}{)}\\PY{p}{)}\\PY{p}{)}\\PY{p}{)}\\PY{p}{)}\\PY{p}{)}\\PY{p}{]}\n",
+       "\\PY{p}{)}\\PY{p}{[}\\PY{n}{IndexKey}\\PY{o}{.}\\PY{n}{multi\\PYZus{}axis}\\PY{p}{(}\\PY{n}{MultiAxisIndexKey}\\PY{o}{.}\\PY{n}{from\\PYZus{}vec}\\PY{p}{(}\\PY{n}{Vec}\\PY{p}{(}\\PY{n}{\\PYZus{}MultiAxisIndexKeyItem\\PYZus{}1}\\PY{p}{,} \\PY{n}{MultiAxisIndexKeyItem}\\PY{o}{.}\\PY{n}{slice}\\PY{p}{(}\\PY{n}{Slice}\\PY{p}{(}\\PY{n}{OptionalInt}\\PY{o}{.}\\PY{n}{none}\\PY{p}{,} \\PY{n}{OptionalInt}\\PY{o}{.}\\PY{n}{some}\\PY{p}{(}\\PY{n}{Int}\\PY{p}{(}\\PY{l+m+mi}{2}\\PY{p}{)}\\PY{p}{)}\\PY{p}{)}\\PY{p}{)}\\PY{p}{)}\\PY{p}{)}\\PY{p}{)}\\PY{p}{]}\n",
        "\\end{Verbatim}\n"
       ],
       "text/plain": [
        "_NDArray_1 = NDArray.var(\"X\")\n",
        "assume_dtype(_NDArray_1, DType.float64)\n",
-       "assume_shape(_NDArray_1, TupleInt(Int(1000000)) + TupleInt(Int(20)))\n",
+       "assume_shape(_NDArray_1, TupleInt.from_vec(Vec[Int](Int(150), Int(4))))\n",
        "assume_isfinite(_NDArray_1)\n",
        "_NDArray_2 = NDArray.var(\"y\")\n",
        "assume_dtype(_NDArray_2, DType.int64)\n",
-       "assume_shape(_NDArray_2, TupleInt(Int(1000000)))\n",
-       "assume_value_one_of(_NDArray_2, TupleValue(Value.int(Int(0))) + TupleValue(Value.int(Int(1))))\n",
-       "_NDArray_3 = asarray(reshape(asarray(_NDArray_2), TupleInt(Int(-1))))\n",
-       "_NDArray_4 = astype(unique_counts(_NDArray_3)[Int(1)], asarray(_NDArray_1).dtype) / NDArray.scalar(Value.float(Float(1000000.0)))\n",
-       "_NDArray_5 = zeros(\n",
-       "    TupleInt(unique_inverse(_NDArray_3)[Int(0)].shape[Int(0)]) + TupleInt(asarray(_NDArray_1).shape[Int(1)]),\n",
+       "assume_shape(_NDArray_2, TupleInt.from_vec(Vec[Int](Int(150))))\n",
+       "_TupleValue_1 = TupleValue.from_vec(Vec[Value](Value.int(Int(0)), Value.int(Int(1)), Value.int(Int(2))))\n",
+       "assume_value_one_of(_NDArray_2, _TupleValue_1)\n",
+       "_NDArray_3 = zeros(\n",
+       "    TupleInt.from_vec(Vec[Int](NDArray.vector(_TupleValue_1).shape[Int(0)], asarray(_NDArray_1).shape[Int(1)])),\n",
        "    OptionalDType.some(asarray(_NDArray_1).dtype),\n",
        "    OptionalDevice.some(asarray(_NDArray_1).device),\n",
        ")\n",
-       "_MultiAxisIndexKey_1 = MultiAxisIndexKey(MultiAxisIndexKeyItem.slice(Slice()))\n",
-       "_IndexKey_1 = IndexKey.multi_axis(MultiAxisIndexKey(MultiAxisIndexKeyItem.int(Int(0))) + _MultiAxisIndexKey_1)\n",
+       "_MultiAxisIndexKeyItem_1 = MultiAxisIndexKeyItem.slice(Slice())\n",
+       "_IndexKey_1 = IndexKey.multi_axis(MultiAxisIndexKey.from_vec(Vec(MultiAxisIndexKeyItem.int(Int(0)), _MultiAxisIndexKeyItem_1)))\n",
+       "_IndexKey_2 = IndexKey.ndarray(unique_inverse(_NDArray_2)[Int(1)] == NDArray.scalar(Value.int(Int(0))))\n",
        "_OptionalIntOrTuple_1 = OptionalIntOrTuple.some(IntOrTuple.int(Int(0)))\n",
-       "_NDArray_5[_IndexKey_1] = mean(asarray(_NDArray_1)[ndarray_index(unique_inverse(_NDArray_3)[Int(1)] == NDArray.scalar(Value.int(Int(0))))], _OptionalIntOrTuple_1)\n",
-       "_IndexKey_2 = IndexKey.multi_axis(MultiAxisIndexKey(MultiAxisIndexKeyItem.int(Int(1))) + _MultiAxisIndexKey_1)\n",
-       "_NDArray_5[_IndexKey_2] = mean(asarray(_NDArray_1)[ndarray_index(unique_inverse(_NDArray_3)[Int(1)] == NDArray.scalar(Value.int(Int(1))))], _OptionalIntOrTuple_1)\n",
-       "_NDArray_6 = unique_values(concat(TupleNDArray(unique_values(asarray(_NDArray_3)))))\n",
-       "_NDArray_7 = concat(\n",
-       "    TupleNDArray(asarray(_NDArray_1)[ndarray_index(_NDArray_3 == _NDArray_6[IndexKey.int(Int(0))])] - _NDArray_5[_IndexKey_1])\n",
-       "    + TupleNDArray(asarray(_NDArray_1)[ndarray_index(_NDArray_3 == _NDArray_6[IndexKey.int(Int(1))])] - _NDArray_5[_IndexKey_2]),\n",
+       "_NDArray_3[_IndexKey_1] = mean(asarray(_NDArray_1)[_IndexKey_2], _OptionalIntOrTuple_1)\n",
+       "_IndexKey_3 = IndexKey.multi_axis(MultiAxisIndexKey.from_vec(Vec(MultiAxisIndexKeyItem.int(Int(1)), _MultiAxisIndexKeyItem_1)))\n",
+       "_IndexKey_4 = IndexKey.ndarray(unique_inverse(_NDArray_2)[Int(1)] == NDArray.scalar(Value.int(Int(1))))\n",
+       "_NDArray_3[_IndexKey_3] = mean(asarray(_NDArray_1)[_IndexKey_4], _OptionalIntOrTuple_1)\n",
+       "_IndexKey_5 = IndexKey.multi_axis(MultiAxisIndexKey.from_vec(Vec(MultiAxisIndexKeyItem.int(Int(2)), _MultiAxisIndexKeyItem_1)))\n",
+       "_IndexKey_6 = IndexKey.ndarray(unique_inverse(_NDArray_2)[Int(1)] == NDArray.scalar(Value.int(Int(2))))\n",
+       "_NDArray_3[_IndexKey_5] = mean(asarray(_NDArray_1)[_IndexKey_6], _OptionalIntOrTuple_1)\n",
+       "_NDArray_4 = zeros(TupleInt.from_vec(Vec[Int](Int(3), Int(4))), OptionalDType.some(DType.float64), OptionalDevice.some(_NDArray_1.device))\n",
+       "_IndexKey_7 = IndexKey.multi_axis(MultiAxisIndexKey.from_vec(Vec[MultiAxisIndexKeyItem](MultiAxisIndexKeyItem.int(Int(0)), _MultiAxisIndexKeyItem_1)))\n",
+       "_NDArray_4[_IndexKey_7] = mean(_NDArray_1[_IndexKey_2], _OptionalIntOrTuple_1)\n",
+       "_IndexKey_8 = IndexKey.multi_axis(MultiAxisIndexKey.from_vec(Vec[MultiAxisIndexKeyItem](MultiAxisIndexKeyItem.int(Int(1)), _MultiAxisIndexKeyItem_1)))\n",
+       "_NDArray_4[_IndexKey_8] = mean(_NDArray_1[_IndexKey_4], _OptionalIntOrTuple_1)\n",
+       "_IndexKey_9 = IndexKey.multi_axis(MultiAxisIndexKey.from_vec(Vec[MultiAxisIndexKeyItem](MultiAxisIndexKeyItem.int(Int(2)), _MultiAxisIndexKeyItem_1)))\n",
+       "_NDArray_4[_IndexKey_9] = mean(_NDArray_1[_IndexKey_6], _OptionalIntOrTuple_1)\n",
+       "_NDArray_5 = concat(\n",
+       "    TupleNDArray.from_vec(\n",
+       "        Vec[NDArray](\n",
+       "            _NDArray_1[IndexKey.ndarray(_NDArray_2 == NDArray.scalar(Value.int(Int(0))))] - _NDArray_4[_IndexKey_7],\n",
+       "            _NDArray_1[IndexKey.ndarray(_NDArray_2 == NDArray.scalar(Value.int(Int(1))))] - _NDArray_4[_IndexKey_8],\n",
+       "            _NDArray_1[IndexKey.ndarray(_NDArray_2 == NDArray.scalar(Value.int(Int(2))))] - _NDArray_4[_IndexKey_9],\n",
+       "        )\n",
+       "    ),\n",
        "    OptionalInt.some(Int(0)),\n",
        ")\n",
-       "_NDArray_8 = std(_NDArray_7, _OptionalIntOrTuple_1)\n",
-       "_NDArray_8[ndarray_index(std(_NDArray_7, _OptionalIntOrTuple_1) == NDArray.scalar(Value.int(Int(0))))] = NDArray.scalar(Value.float(Float(1.0)))\n",
+       "_NDArray_6 = std(_NDArray_5, _OptionalIntOrTuple_1)\n",
+       "_NDArray_6[IndexKey.ndarray(std(_NDArray_5, _OptionalIntOrTuple_1) == NDArray.scalar(Value.int(Int(0))))] = NDArray.scalar(\n",
+       "    Value.float(Float.rational(BigRat(BigInt.from_string(\"1\"), BigInt.from_string(\"1\"))))\n",
+       ")\n",
        "_TupleNDArray_1 = svd(\n",
-       "    sqrt(asarray(NDArray.scalar(Value.float(Float(1.0) / Float.from_int(asarray(_NDArray_1).shape[Int(0)] - _NDArray_6.shape[Int(0)]))))) * (_NDArray_7 / _NDArray_8), FALSE\n",
+       "    sqrt(\n",
+       "        asarray(\n",
+       "            NDArray.scalar(Value.float(Float.rational(BigRat(BigInt.from_string(\"1\"), BigInt.from_string(\"147\"))))),\n",
+       "            OptionalDType.some(DType.float64),\n",
+       "            OptionalBool.none,\n",
+       "            OptionalDevice.some(_NDArray_1.device),\n",
+       "        )\n",
+       "    )\n",
+       "    * (_NDArray_5 / _NDArray_6),\n",
+       "    Boolean(False),\n",
        ")\n",
        "_Slice_1 = Slice(OptionalInt.none, OptionalInt.some(sum(astype(_TupleNDArray_1[Int(1)] > NDArray.scalar(Value.float(Float(0.0001))), DType.int32)).to_value().to_int))\n",
-       "_NDArray_9 = (_TupleNDArray_1[Int(2)][IndexKey.multi_axis(MultiAxisIndexKey(MultiAxisIndexKeyItem.slice(_Slice_1)) + _MultiAxisIndexKey_1)] / _NDArray_8).T / _TupleNDArray_1[\n",
-       "    Int(1)\n",
-       "][IndexKey.slice(_Slice_1)]\n",
+       "_NDArray_7 = asarray(reshape(asarray(_NDArray_2), TupleInt.from_vec(Vec[Int](Int(-1)))))\n",
+       "_NDArray_8 = unique_values(concat(TupleNDArray.from_vec(Vec[NDArray](unique_values(asarray(_NDArray_7))))))\n",
+       "_NDArray_9 = std(\n",
+       "    concat(\n",
+       "        TupleNDArray.from_vec(\n",
+       "            Vec[NDArray](\n",
+       "                asarray(_NDArray_1)[IndexKey.ndarray(_NDArray_7 == _NDArray_8[IndexKey.int(Int(0))])] - _NDArray_3[_IndexKey_1],\n",
+       "                asarray(_NDArray_1)[IndexKey.ndarray(_NDArray_7 == _NDArray_8[IndexKey.int(Int(1))])] - _NDArray_3[_IndexKey_3],\n",
+       "                asarray(_NDArray_1)[IndexKey.ndarray(_NDArray_7 == _NDArray_8[IndexKey.int(Int(2))])] - _NDArray_3[_IndexKey_5],\n",
+       "            )\n",
+       "        ),\n",
+       "        OptionalInt.some(Int(0)),\n",
+       "    ),\n",
+       "    _OptionalIntOrTuple_1,\n",
+       ")\n",
+       "_NDArray_10 = copy(_NDArray_9)\n",
+       "_NDArray_10[IndexKey.ndarray(_NDArray_9 == NDArray.scalar(Value.int(Int(0))))] = NDArray.scalar(Value.float(Float(1.0)))\n",
+       "_NDArray_11 = astype(unique_counts(_NDArray_2)[Int(1)], DType.float64) / NDArray.scalar(Value.float(Float.rational(BigRat(BigInt.from_string(\"150\"), BigInt.from_string(\"1\")))))\n",
        "_TupleNDArray_2 = svd(\n",
        "    (\n",
-       "        sqrt(\n",
-       "            (NDArray.scalar(Value.int(asarray(_NDArray_1).shape[Int(0)])) * _NDArray_4)\n",
-       "            * NDArray.scalar(Value.float(Float(1.0) / Float.from_int(_NDArray_6.shape[Int(0)] - Int(1))))\n",
-       "        )\n",
-       "        * (_NDArray_5 - (_NDArray_4 @ _NDArray_5)).T\n",
+       "        sqrt((NDArray.scalar(Value.int(Int(150))) * _NDArray_11) * NDArray.scalar(Value.float(Float.rational(BigRat(BigInt.from_string(\"1\"), BigInt.from_string(\"2\"))))))\n",
+       "        * (_NDArray_4 - (_NDArray_11 @ _NDArray_4)).T\n",
        "    ).T\n",
-       "    @ _NDArray_9,\n",
-       "    FALSE,\n",
+       "    @ (\n",
+       "        (\n",
+       "            _TupleNDArray_1[Int(2)][IndexKey.multi_axis(MultiAxisIndexKey.from_vec(Vec[MultiAxisIndexKeyItem](MultiAxisIndexKeyItem.slice(_Slice_1), _MultiAxisIndexKeyItem_1)))]\n",
+       "            / _NDArray_6\n",
+       "        ).T\n",
+       "        / _TupleNDArray_1[Int(1)][IndexKey.slice(_Slice_1)]\n",
+       "    ),\n",
+       "    Boolean(False),\n",
        ")\n",
        "(\n",
-       "    (asarray(_NDArray_1) - (_NDArray_4 @ _NDArray_5))\n",
+       "    (asarray(_NDArray_1) - ((astype(unique_counts(_NDArray_2)[Int(1)], asarray(_NDArray_1).dtype) / NDArray.scalar(Value.float(Float(150.0)))) @ _NDArray_3))\n",
        "    @ (\n",
-       "        _NDArray_9\n",
+       "        (\n",
+       "            (_TupleNDArray_1[Int(2)][IndexKey.multi_axis(MultiAxisIndexKey.from_vec(Vec(MultiAxisIndexKeyItem.slice(_Slice_1), _MultiAxisIndexKeyItem_1)))] / _NDArray_10).T\n",
+       "            / _TupleNDArray_1[Int(1)][IndexKey.slice(_Slice_1)]\n",
+       "        )\n",
        "        @ _TupleNDArray_2[Int(2)].T[\n",
        "            IndexKey.multi_axis(\n",
-       "                _MultiAxisIndexKey_1\n",
-       "                + MultiAxisIndexKey(\n",
-       "                    MultiAxisIndexKeyItem.slice(\n",
-       "                        Slice(\n",
-       "                            OptionalInt.none,\n",
-       "                            OptionalInt.some(\n",
-       "                                sum(astype(_TupleNDArray_2[Int(1)] > (NDArray.scalar(Value.float(Float(0.0001))) * _TupleNDArray_2[Int(1)][IndexKey.int(Int(0))]), DType.int32))\n",
-       "                                .to_value()\n",
-       "                                .to_int\n",
-       "                            ),\n",
-       "                        )\n",
+       "                MultiAxisIndexKey.from_vec(\n",
+       "                    Vec(\n",
+       "                        _MultiAxisIndexKeyItem_1,\n",
+       "                        MultiAxisIndexKeyItem.slice(\n",
+       "                            Slice(\n",
+       "                                OptionalInt.none,\n",
+       "                                OptionalInt.some(\n",
+       "                                    sum(astype(_TupleNDArray_2[Int(1)] > (NDArray.scalar(Value.float(Float(0.0001))) * _TupleNDArray_2[Int(1)][IndexKey.int(Int(0))]), DType.int32))\n",
+       "                                    .to_value()\n",
+       "                                    .to_int\n",
+       "                                ),\n",
+       "                            )\n",
+       "                        ),\n",
        "                    )\n",
        "                )\n",
        "            )\n",
        "        ]\n",
        "    )\n",
-       ")[IndexKey.multi_axis(_MultiAxisIndexKey_1 + MultiAxisIndexKey(MultiAxisIndexKeyItem.slice(Slice(OptionalInt.none, OptionalInt.some(_NDArray_6.shape[Int(0)] - Int(1))))))]"
+       ")[IndexKey.multi_axis(MultiAxisIndexKey.from_vec(Vec(_MultiAxisIndexKeyItem_1, MultiAxisIndexKeyItem.slice(Slice(OptionalInt.none, OptionalInt.some(Int(2)))))))]"
       ]
      },
      "metadata": {},
@@ -518,7 +673,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 4,
+   "execution_count": 5,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -544,7 +699,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 5,
+   "execution_count": 6,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -555,7 +710,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 6,
+   "execution_count": 7,
    "metadata": {},
    "outputs": [
     {
@@ -569,9 +724,9 @@
        ".output_html .hll { background-color: #ffffcc }\n",
        ".output_html { background: #f8f8f8; }\n",
        ".output_html .c { color: #3D7B7B; font-style: italic } /* Comment */\n",
-       ".output_html .err { border: 1px solid #FF0000 } /* Error */\n",
+       ".output_html .err { border: 1px solid #F00 } /* Error */\n",
        ".output_html .k { color: #008000; font-weight: bold } /* Keyword */\n",
-       ".output_html .o { color: #666666 } /* Operator */\n",
+       ".output_html .o { color: #666 } /* Operator */\n",
        ".output_html .ch { color: #3D7B7B; font-style: italic } /* Comment.Hashbang */\n",
        ".output_html .cm { color: #3D7B7B; font-style: italic } /* Comment.Multiline */\n",
        ".output_html .cp { color: #9C6500 } /* Comment.Preproc */\n",
@@ -588,34 +743,34 @@
        ".output_html .gp { color: #000080; font-weight: bold } /* Generic.Prompt */\n",
        ".output_html .gs { font-weight: bold } /* Generic.Strong */\n",
        ".output_html .gu { color: #800080; font-weight: bold } /* Generic.Subheading */\n",
-       ".output_html .gt { color: #0044DD } /* Generic.Traceback */\n",
+       ".output_html .gt { color: #04D } /* Generic.Traceback */\n",
        ".output_html .kc { color: #008000; font-weight: bold } /* Keyword.Constant */\n",
        ".output_html .kd { color: #008000; font-weight: bold } /* Keyword.Declaration */\n",
        ".output_html .kn { color: #008000; font-weight: bold } /* Keyword.Namespace */\n",
        ".output_html .kp { color: #008000 } /* Keyword.Pseudo */\n",
        ".output_html .kr { color: #008000; font-weight: bold } /* Keyword.Reserved */\n",
        ".output_html .kt { color: #B00040 } /* Keyword.Type */\n",
-       ".output_html .m { color: #666666 } /* Literal.Number */\n",
+       ".output_html .m { color: #666 } /* Literal.Number */\n",
        ".output_html .s { color: #BA2121 } /* Literal.String */\n",
        ".output_html .na { color: #687822 } /* Name.Attribute */\n",
        ".output_html .nb { color: #008000 } /* Name.Builtin */\n",
-       ".output_html .nc { color: #0000FF; font-weight: bold } /* Name.Class */\n",
-       ".output_html .no { color: #880000 } /* Name.Constant */\n",
-       ".output_html .nd { color: #AA22FF } /* Name.Decorator */\n",
+       ".output_html .nc { color: #00F; font-weight: bold } /* Name.Class */\n",
+       ".output_html .no { color: #800 } /* Name.Constant */\n",
+       ".output_html .nd { color: #A2F } /* Name.Decorator */\n",
        ".output_html .ni { color: #717171; font-weight: bold } /* Name.Entity */\n",
        ".output_html .ne { color: #CB3F38; font-weight: bold } /* Name.Exception */\n",
-       ".output_html .nf { color: #0000FF } /* Name.Function */\n",
+       ".output_html .nf { color: #00F } /* Name.Function */\n",
        ".output_html .nl { color: #767600 } /* Name.Label */\n",
-       ".output_html .nn { color: #0000FF; font-weight: bold } /* Name.Namespace */\n",
+       ".output_html .nn { color: #00F; font-weight: bold } /* Name.Namespace */\n",
        ".output_html .nt { color: #008000; font-weight: bold } /* Name.Tag */\n",
        ".output_html .nv { color: #19177C } /* Name.Variable */\n",
-       ".output_html .ow { color: #AA22FF; font-weight: bold } /* Operator.Word */\n",
-       ".output_html .w { color: #bbbbbb } /* Text.Whitespace */\n",
-       ".output_html .mb { color: #666666 } /* Literal.Number.Bin */\n",
-       ".output_html .mf { color: #666666 } /* Literal.Number.Float */\n",
-       ".output_html .mh { color: #666666 } /* Literal.Number.Hex */\n",
-       ".output_html .mi { color: #666666 } /* Literal.Number.Integer */\n",
-       ".output_html .mo { color: #666666 } /* Literal.Number.Oct */\n",
+       ".output_html .ow { color: #A2F; font-weight: bold } /* Operator.Word */\n",
+       ".output_html .w { color: #BBB } /* Text.Whitespace */\n",
+       ".output_html .mb { color: #666 } /* Literal.Number.Bin */\n",
+       ".output_html .mf { color: #666 } /* Literal.Number.Float */\n",
+       ".output_html .mh { color: #666 } /* Literal.Number.Hex */\n",
+       ".output_html .mi { color: #666 } /* Literal.Number.Integer */\n",
+       ".output_html .mo { color: #666 } /* Literal.Number.Oct */\n",
        ".output_html .sa { color: #BA2121 } /* Literal.String.Affix */\n",
        ".output_html .sb { color: #BA2121 } /* Literal.String.Backtick */\n",
        ".output_html .sc { color: #BA2121 } /* Literal.String.Char */\n",
@@ -630,12 +785,12 @@
        ".output_html .s1 { color: #BA2121 } /* Literal.String.Single */\n",
        ".output_html .ss { color: #19177C } /* Literal.String.Symbol */\n",
        ".output_html .bp { color: #008000 } /* Name.Builtin.Pseudo */\n",
-       ".output_html .fm { color: #0000FF } /* Name.Function.Magic */\n",
+       ".output_html .fm { color: #00F } /* Name.Function.Magic */\n",
        ".output_html .vc { color: #19177C } /* Name.Variable.Class */\n",
        ".output_html .vg { color: #19177C } /* Name.Variable.Global */\n",
        ".output_html .vi { color: #19177C } /* Name.Variable.Instance */\n",
        ".output_html .vm { color: #19177C } /* Name.Variable.Magic */\n",
-       ".output_html .il { color: #666666 } /* Literal.Number.Integer.Long */
A()[Slice(OptionalInt.none, OptionalInt.some(Int(1)), OptionalInt.some(Int(2)))]\n",
+       ".output_html .il { color: #666 } /* Literal.Number.Integer.Long */
A()[Slice(OptionalInt.none, OptionalInt.some(Int(1)), OptionalInt.some(Int(2)))]\n",
        "
\n"
       ],
       "text/latex": [
@@ -719,7 +874,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 7,
+   "execution_count": 8,
    "metadata": {},
    "outputs": [
     {
@@ -733,9 +888,9 @@
        ".output_html .hll { background-color: #ffffcc }\n",
        ".output_html { background: #f8f8f8; }\n",
        ".output_html .c { color: #3D7B7B; font-style: italic } /* Comment */\n",
-       ".output_html .err { border: 1px solid #FF0000 } /* Error */\n",
+       ".output_html .err { border: 1px solid #F00 } /* Error */\n",
        ".output_html .k { color: #008000; font-weight: bold } /* Keyword */\n",
-       ".output_html .o { color: #666666 } /* Operator */\n",
+       ".output_html .o { color: #666 } /* Operator */\n",
        ".output_html .ch { color: #3D7B7B; font-style: italic } /* Comment.Hashbang */\n",
        ".output_html .cm { color: #3D7B7B; font-style: italic } /* Comment.Multiline */\n",
        ".output_html .cp { color: #9C6500 } /* Comment.Preproc */\n",
@@ -752,34 +907,34 @@
        ".output_html .gp { color: #000080; font-weight: bold } /* Generic.Prompt */\n",
        ".output_html .gs { font-weight: bold } /* Generic.Strong */\n",
        ".output_html .gu { color: #800080; font-weight: bold } /* Generic.Subheading */\n",
-       ".output_html .gt { color: #0044DD } /* Generic.Traceback */\n",
+       ".output_html .gt { color: #04D } /* Generic.Traceback */\n",
        ".output_html .kc { color: #008000; font-weight: bold } /* Keyword.Constant */\n",
        ".output_html .kd { color: #008000; font-weight: bold } /* Keyword.Declaration */\n",
        ".output_html .kn { color: #008000; font-weight: bold } /* Keyword.Namespace */\n",
        ".output_html .kp { color: #008000 } /* Keyword.Pseudo */\n",
        ".output_html .kr { color: #008000; font-weight: bold } /* Keyword.Reserved */\n",
        ".output_html .kt { color: #B00040 } /* Keyword.Type */\n",
-       ".output_html .m { color: #666666 } /* Literal.Number */\n",
+       ".output_html .m { color: #666 } /* Literal.Number */\n",
        ".output_html .s { color: #BA2121 } /* Literal.String */\n",
        ".output_html .na { color: #687822 } /* Name.Attribute */\n",
        ".output_html .nb { color: #008000 } /* Name.Builtin */\n",
-       ".output_html .nc { color: #0000FF; font-weight: bold } /* Name.Class */\n",
-       ".output_html .no { color: #880000 } /* Name.Constant */\n",
-       ".output_html .nd { color: #AA22FF } /* Name.Decorator */\n",
+       ".output_html .nc { color: #00F; font-weight: bold } /* Name.Class */\n",
+       ".output_html .no { color: #800 } /* Name.Constant */\n",
+       ".output_html .nd { color: #A2F } /* Name.Decorator */\n",
        ".output_html .ni { color: #717171; font-weight: bold } /* Name.Entity */\n",
        ".output_html .ne { color: #CB3F38; font-weight: bold } /* Name.Exception */\n",
-       ".output_html .nf { color: #0000FF } /* Name.Function */\n",
+       ".output_html .nf { color: #00F } /* Name.Function */\n",
        ".output_html .nl { color: #767600 } /* Name.Label */\n",
-       ".output_html .nn { color: #0000FF; font-weight: bold } /* Name.Namespace */\n",
+       ".output_html .nn { color: #00F; font-weight: bold } /* Name.Namespace */\n",
        ".output_html .nt { color: #008000; font-weight: bold } /* Name.Tag */\n",
        ".output_html .nv { color: #19177C } /* Name.Variable */\n",
-       ".output_html .ow { color: #AA22FF; font-weight: bold } /* Operator.Word */\n",
-       ".output_html .w { color: #bbbbbb } /* Text.Whitespace */\n",
-       ".output_html .mb { color: #666666 } /* Literal.Number.Bin */\n",
-       ".output_html .mf { color: #666666 } /* Literal.Number.Float */\n",
-       ".output_html .mh { color: #666666 } /* Literal.Number.Hex */\n",
-       ".output_html .mi { color: #666666 } /* Literal.Number.Integer */\n",
-       ".output_html .mo { color: #666666 } /* Literal.Number.Oct */\n",
+       ".output_html .ow { color: #A2F; font-weight: bold } /* Operator.Word */\n",
+       ".output_html .w { color: #BBB } /* Text.Whitespace */\n",
+       ".output_html .mb { color: #666 } /* Literal.Number.Bin */\n",
+       ".output_html .mf { color: #666 } /* Literal.Number.Float */\n",
+       ".output_html .mh { color: #666 } /* Literal.Number.Hex */\n",
+       ".output_html .mi { color: #666 } /* Literal.Number.Integer */\n",
+       ".output_html .mo { color: #666 } /* Literal.Number.Oct */\n",
        ".output_html .sa { color: #BA2121 } /* Literal.String.Affix */\n",
        ".output_html .sb { color: #BA2121 } /* Literal.String.Backtick */\n",
        ".output_html .sc { color: #BA2121 } /* Literal.String.Char */\n",
@@ -794,12 +949,12 @@
        ".output_html .s1 { color: #BA2121 } /* Literal.String.Single */\n",
        ".output_html .ss { color: #19177C } /* Literal.String.Symbol */\n",
        ".output_html .bp { color: #008000 } /* Name.Builtin.Pseudo */\n",
-       ".output_html .fm { color: #0000FF } /* Name.Function.Magic */\n",
+       ".output_html .fm { color: #00F } /* Name.Function.Magic */\n",
        ".output_html .vc { color: #19177C } /* Name.Variable.Class */\n",
        ".output_html .vg { color: #19177C } /* Name.Variable.Global */\n",
        ".output_html .vi { color: #19177C } /* Name.Variable.Instance */\n",
        ".output_html .vm { color: #19177C } /* Name.Variable.Magic */\n",
-       ".output_html .il { color: #666666 } /* Literal.Number.Integer.Long */
Boolean(True) & Boolean(True)\n",
+       ".output_html .il { color: #666 } /* Literal.Number.Integer.Long */
Boolean(True) & Boolean(True)\n",
        "
\n"
       ],
       "text/latex": [
@@ -831,7 +986,7 @@
     "        egraph = EGraph()\n",
     "        egraph.register(self)\n",
     "        egraph.run(bool_rewrites.saturate())\n",
-    "        return egraph.eval(self.bool)\n",
+    "        return egraph.extract(self.bool).value\n",
     "\n",
     "\n",
     "x = var(\"x\", Boolean)\n",
@@ -847,7 +1002,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 8,
+   "execution_count": 9,
    "metadata": {},
    "outputs": [
     {
@@ -913,158 +1068,18 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 9,
+   "execution_count": 10,
    "metadata": {},
    "outputs": [
     {
      "data": {
-      "image/svg+xml": [
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "outer_cluster_i64-5871781006564002453\n",
-       "\n",
-       "\n",
-       "cluster_i64-5871781006564002453\n",
-       "\n",
-       "\n",
-       "\n",
-       "outer_cluster_3\n",
-       "\n",
-       "\n",
-       "cluster_3\n",
-       "\n",
-       "\n",
-       "\n",
-       "outer_cluster_1\n",
-       "\n",
-       "\n",
-       "cluster_1\n",
-       "\n",
-       "\n",
-       "\n",
-       "outer_cluster_2\n",
-       "\n",
-       "\n",
-       "cluster_2\n",
-       "\n",
-       "\n",
-       "\n",
-       "outer_cluster_0\n",
-       "\n",
-       "\n",
-       "cluster_0\n",
-       "\n",
-       "\n",
-       "\n",
-       "outer_cluster_i64-0\n",
-       "\n",
-       "\n",
-       "cluster_i64-0\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "ListOfInts___getitem__-1912573936028582372:s->ListOfInts___setitem__-5871781006564002453\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "ListOfInts___getitem__-1912573936028582372:s->i64-0\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "ListOfInts___setitem__-5871781006564002453:s->i64-0\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "ListOfInts___setitem__-5871781006564002453:s->Int___init__-5871781006564002453\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "ListOfInts___setitem__-5871781006564002453:s->ListOfInts___init__-0\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "Int___init__-5871781006564002453:s->i64-5871781006564002453\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "ListOfInts___getitem__-1912573936028582372\n",
-       "\n",
-       "\n",
-       "·[·]\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "ListOfInts___setitem__-5871781006564002453\n",
-       "\n",
-       "\n",
-       "·[·] = ·\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "i64-0\n",
-       "\n",
-       "\n",
-       "0\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "Int___init__-5871781006564002453\n",
-       "\n",
-       "\n",
-       "Int\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "i64-5871781006564002453\n",
-       "\n",
-       "\n",
-       "1\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "ListOfInts___init__-0\n",
-       "\n",
-       "\n",
-       "ListOfInts\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       ""
-      ],
+      "application/vnd.jupyter.widget-view+json": {
+       "model_id": "b3a8e2d4b3224529aa8edbc731df10e4",
+       "version_major": 2,
+       "version_minor": 1
+      },
       "text/plain": [
-       ""
+       "VisualizerWidget(egraphs=['{\"nodes\":{\"primitive-i64-0\":{\"op\":\"0\",\"children\":[],\"eclass\":\"i64-0\",\"cost\":1.0,\"su…"
       ]
      },
      "metadata": {},
@@ -1082,9 +1097,9 @@
     "xs = ListOfInts()\n",
     "xs[0] = Int(1)\n",
     "\n",
-    "egraph = EGraph()\n",
-    "egraph.register(xs[0])\n",
-    "egraph.display()"
+    "new_egraph = EGraph()\n",
+    "new_egraph.register(xs[0])\n",
+    "new_egraph.display()"
    ]
   },
   {
@@ -1125,7 +1140,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 10,
+   "execution_count": 11,
    "metadata": {},
    "outputs": [
     {
@@ -1139,9 +1154,9 @@
        ".output_html .hll { background-color: #ffffcc }\n",
        ".output_html { background: #f8f8f8; }\n",
        ".output_html .c { color: #3D7B7B; font-style: italic } /* Comment */\n",
-       ".output_html .err { border: 1px solid #FF0000 } /* Error */\n",
+       ".output_html .err { border: 1px solid #F00 } /* Error */\n",
        ".output_html .k { color: #008000; font-weight: bold } /* Keyword */\n",
-       ".output_html .o { color: #666666 } /* Operator */\n",
+       ".output_html .o { color: #666 } /* Operator */\n",
        ".output_html .ch { color: #3D7B7B; font-style: italic } /* Comment.Hashbang */\n",
        ".output_html .cm { color: #3D7B7B; font-style: italic } /* Comment.Multiline */\n",
        ".output_html .cp { color: #9C6500 } /* Comment.Preproc */\n",
@@ -1158,34 +1173,34 @@
        ".output_html .gp { color: #000080; font-weight: bold } /* Generic.Prompt */\n",
        ".output_html .gs { font-weight: bold } /* Generic.Strong */\n",
        ".output_html .gu { color: #800080; font-weight: bold } /* Generic.Subheading */\n",
-       ".output_html .gt { color: #0044DD } /* Generic.Traceback */\n",
+       ".output_html .gt { color: #04D } /* Generic.Traceback */\n",
        ".output_html .kc { color: #008000; font-weight: bold } /* Keyword.Constant */\n",
        ".output_html .kd { color: #008000; font-weight: bold } /* Keyword.Declaration */\n",
        ".output_html .kn { color: #008000; font-weight: bold } /* Keyword.Namespace */\n",
        ".output_html .kp { color: #008000 } /* Keyword.Pseudo */\n",
        ".output_html .kr { color: #008000; font-weight: bold } /* Keyword.Reserved */\n",
        ".output_html .kt { color: #B00040 } /* Keyword.Type */\n",
-       ".output_html .m { color: #666666 } /* Literal.Number */\n",
+       ".output_html .m { color: #666 } /* Literal.Number */\n",
        ".output_html .s { color: #BA2121 } /* Literal.String */\n",
        ".output_html .na { color: #687822 } /* Name.Attribute */\n",
        ".output_html .nb { color: #008000 } /* Name.Builtin */\n",
-       ".output_html .nc { color: #0000FF; font-weight: bold } /* Name.Class */\n",
-       ".output_html .no { color: #880000 } /* Name.Constant */\n",
-       ".output_html .nd { color: #AA22FF } /* Name.Decorator */\n",
+       ".output_html .nc { color: #00F; font-weight: bold } /* Name.Class */\n",
+       ".output_html .no { color: #800 } /* Name.Constant */\n",
+       ".output_html .nd { color: #A2F } /* Name.Decorator */\n",
        ".output_html .ni { color: #717171; font-weight: bold } /* Name.Entity */\n",
        ".output_html .ne { color: #CB3F38; font-weight: bold } /* Name.Exception */\n",
-       ".output_html .nf { color: #0000FF } /* Name.Function */\n",
+       ".output_html .nf { color: #00F } /* Name.Function */\n",
        ".output_html .nl { color: #767600 } /* Name.Label */\n",
-       ".output_html .nn { color: #0000FF; font-weight: bold } /* Name.Namespace */\n",
+       ".output_html .nn { color: #00F; font-weight: bold } /* Name.Namespace */\n",
        ".output_html .nt { color: #008000; font-weight: bold } /* Name.Tag */\n",
        ".output_html .nv { color: #19177C } /* Name.Variable */\n",
-       ".output_html .ow { color: #AA22FF; font-weight: bold } /* Operator.Word */\n",
-       ".output_html .w { color: #bbbbbb } /* Text.Whitespace */\n",
-       ".output_html .mb { color: #666666 } /* Literal.Number.Bin */\n",
-       ".output_html .mf { color: #666666 } /* Literal.Number.Float */\n",
-       ".output_html .mh { color: #666666 } /* Literal.Number.Hex */\n",
-       ".output_html .mi { color: #666666 } /* Literal.Number.Integer */\n",
-       ".output_html .mo { color: #666666 } /* Literal.Number.Oct */\n",
+       ".output_html .ow { color: #A2F; font-weight: bold } /* Operator.Word */\n",
+       ".output_html .w { color: #BBB } /* Text.Whitespace */\n",
+       ".output_html .mb { color: #666 } /* Literal.Number.Bin */\n",
+       ".output_html .mf { color: #666 } /* Literal.Number.Float */\n",
+       ".output_html .mh { color: #666 } /* Literal.Number.Hex */\n",
+       ".output_html .mi { color: #666 } /* Literal.Number.Integer */\n",
+       ".output_html .mo { color: #666 } /* Literal.Number.Oct */\n",
        ".output_html .sa { color: #BA2121 } /* Literal.String.Affix */\n",
        ".output_html .sb { color: #BA2121 } /* Literal.String.Backtick */\n",
        ".output_html .sc { color: #BA2121 } /* Literal.String.Char */\n",
@@ -1200,189 +1215,303 @@
        ".output_html .s1 { color: #BA2121 } /* Literal.String.Single */\n",
        ".output_html .ss { color: #19177C } /* Literal.String.Symbol */\n",
        ".output_html .bp { color: #008000 } /* Name.Builtin.Pseudo */\n",
-       ".output_html .fm { color: #0000FF } /* Name.Function.Magic */\n",
+       ".output_html .fm { color: #00F } /* Name.Function.Magic */\n",
        ".output_html .vc { color: #19177C } /* Name.Variable.Class */\n",
        ".output_html .vg { color: #19177C } /* Name.Variable.Global */\n",
        ".output_html .vi { color: #19177C } /* Name.Variable.Instance */\n",
        ".output_html .vm { color: #19177C } /* Name.Variable.Magic */\n",
-       ".output_html .il { color: #666666 } /* Literal.Number.Integer.Long */
_NDArray_1 = NDArray.var("X")\n",
+       ".output_html .il { color: #666 } /* Literal.Number.Integer.Long */
_NDArray_1 = NDArray.var("X")\n",
        "assume_dtype(_NDArray_1, DType.float64)\n",
-       "assume_shape(_NDArray_1, TupleInt(Int(1000000)) + TupleInt(Int(20)))\n",
+       "assume_shape(_NDArray_1, TupleInt.from_vec(Vec[Int](Int(150), Int(4))))\n",
        "assume_isfinite(_NDArray_1)\n",
        "_NDArray_2 = NDArray.var("y")\n",
        "assume_dtype(_NDArray_2, DType.int64)\n",
-       "assume_shape(_NDArray_2, TupleInt(Int(1000000)))\n",
-       "assume_value_one_of(_NDArray_2, TupleValue(Value.int(Int(0))) + TupleValue(Value.int(Int(1))))\n",
+       "assume_shape(_NDArray_2, TupleInt.from_vec(Vec[Int](Int(150))))\n",
+       "assume_value_one_of(_NDArray_2, TupleValue.from_vec(Vec[Value](Value.int(Int(0)), Value.int(Int(1)), Value.int(Int(2)))))\n",
        "_NDArray_3 = astype(\n",
-       "    NDArray.vector(TupleValue(sum(_NDArray_2 == NDArray.scalar(Value.int(Int(0)))).to_value()) + TupleValue(sum(_NDArray_2 == NDArray.scalar(Value.int(Int(1)))).to_value())),\n",
+       "    NDArray.vector(\n",
+       "        TupleValue.from_vec(\n",
+       "            Vec[Value](\n",
+       "                sum(_NDArray_2 == NDArray.scalar(Value.int(Int(0)))).to_value(),\n",
+       "                sum(_NDArray_2 == NDArray.scalar(Value.int(Int(1)))).to_value(),\n",
+       "                sum(_NDArray_2 == NDArray.scalar(Value.int(Int(2)))).to_value(),\n",
+       "            )\n",
+       "        )\n",
+       "    ),\n",
        "    DType.float64,\n",
-       ") / NDArray.scalar(Value.float(Float(1000000.0)))\n",
-       "_NDArray_4 = zeros(TupleInt(Int(2)) + TupleInt(Int(20)), OptionalDType.some(DType.float64), OptionalDevice.some(_NDArray_1.device))\n",
-       "_MultiAxisIndexKey_1 = MultiAxisIndexKey(MultiAxisIndexKeyItem.slice(Slice()))\n",
-       "_IndexKey_1 = IndexKey.multi_axis(MultiAxisIndexKey(MultiAxisIndexKeyItem.int(Int(0))) + _MultiAxisIndexKey_1)\n",
-       "_NDArray_5 = _NDArray_1[ndarray_index(_NDArray_2 == NDArray.scalar(Value.int(Int(0))))]\n",
+       ") / NDArray.scalar(Value.float(Float.rational(BigRat(BigInt.from_string("150"), BigInt.from_string("1")))))\n",
+       "_NDArray_4 = zeros(TupleInt.from_vec(Vec[Int](Int(3), Int(4))), OptionalDType.some(DType.float64), OptionalDevice.some(_NDArray_1.device))\n",
+       "_MultiAxisIndexKeyItem_1 = MultiAxisIndexKeyItem.slice(Slice())\n",
+       "_IndexKey_1 = IndexKey.multi_axis(MultiAxisIndexKey.from_vec(Vec[MultiAxisIndexKeyItem](MultiAxisIndexKeyItem.int(Int(0)), _MultiAxisIndexKeyItem_1)))\n",
+       "_NDArray_5 = _NDArray_1[IndexKey.ndarray(_NDArray_2 == NDArray.scalar(Value.int(Int(0))))]\n",
        "_OptionalIntOrTuple_1 = OptionalIntOrTuple.some(IntOrTuple.int(Int(0)))\n",
        "_NDArray_4[_IndexKey_1] = sum(_NDArray_5, _OptionalIntOrTuple_1) / NDArray.scalar(Value.int(_NDArray_5.shape[Int(0)]))\n",
-       "_IndexKey_2 = IndexKey.multi_axis(MultiAxisIndexKey(MultiAxisIndexKeyItem.int(Int(1))) + _MultiAxisIndexKey_1)\n",
-       "_NDArray_6 = _NDArray_1[ndarray_index(_NDArray_2 == NDArray.scalar(Value.int(Int(1))))]\n",
+       "_IndexKey_2 = IndexKey.multi_axis(MultiAxisIndexKey.from_vec(Vec[MultiAxisIndexKeyItem](MultiAxisIndexKeyItem.int(Int(1)), _MultiAxisIndexKeyItem_1)))\n",
+       "_NDArray_6 = _NDArray_1[IndexKey.ndarray(_NDArray_2 == NDArray.scalar(Value.int(Int(1))))]\n",
        "_NDArray_4[_IndexKey_2] = sum(_NDArray_6, _OptionalIntOrTuple_1) / NDArray.scalar(Value.int(_NDArray_6.shape[Int(0)]))\n",
-       "_NDArray_7 = concat(TupleNDArray(_NDArray_5 - _NDArray_4[_IndexKey_1]) + TupleNDArray(_NDArray_6 - _NDArray_4[_IndexKey_2]), OptionalInt.some(Int(0)))\n",
-       "_NDArray_8 = square(_NDArray_7 - expand_dims(sum(_NDArray_7, _OptionalIntOrTuple_1) / NDArray.scalar(Value.int(_NDArray_7.shape[Int(0)]))))\n",
-       "_NDArray_9 = sqrt(sum(_NDArray_8, _OptionalIntOrTuple_1) / NDArray.scalar(Value.int(_NDArray_8.shape[Int(0)])))\n",
-       "_NDArray_10 = copy(_NDArray_9)\n",
-       "_NDArray_10[ndarray_index(_NDArray_9 == NDArray.scalar(Value.int(Int(0))))] = NDArray.scalar(Value.float(Float(1.0)))\n",
-       "_TupleNDArray_1 = svd(sqrt(NDArray.scalar(Value.float(Float.rational(Rational(1, 999998))))) * (_NDArray_7 / _NDArray_10), FALSE)\n",
+       "_IndexKey_3 = IndexKey.multi_axis(MultiAxisIndexKey.from_vec(Vec[MultiAxisIndexKeyItem](MultiAxisIndexKeyItem.int(Int(2)), _MultiAxisIndexKeyItem_1)))\n",
+       "_NDArray_7 = _NDArray_1[IndexKey.ndarray(_NDArray_2 == NDArray.scalar(Value.int(Int(2))))]\n",
+       "_NDArray_4[_IndexKey_3] = sum(_NDArray_7, _OptionalIntOrTuple_1) / NDArray.scalar(Value.int(_NDArray_7.shape[Int(0)]))\n",
+       "_NDArray_8 = concat(\n",
+       "    TupleNDArray.from_vec(Vec[NDArray](_NDArray_5 - _NDArray_4[_IndexKey_1], _NDArray_6 - _NDArray_4[_IndexKey_2], _NDArray_7 - _NDArray_4[_IndexKey_3])), OptionalInt.some(Int(0))\n",
+       ")\n",
+       "_NDArray_9 = square(_NDArray_8 - expand_dims(sum(_NDArray_8, _OptionalIntOrTuple_1) / NDArray.scalar(Value.int(_NDArray_8.shape[Int(0)]))))\n",
+       "_NDArray_10 = sqrt(sum(_NDArray_9, _OptionalIntOrTuple_1) / NDArray.scalar(Value.int(_NDArray_9.shape[Int(0)])))\n",
+       "_NDArray_11 = copy(_NDArray_10)\n",
+       "_NDArray_11[IndexKey.ndarray(_NDArray_10 == NDArray.scalar(Value.int(Int(0))))] = NDArray.scalar(\n",
+       "    Value.float(Float.rational(BigRat(BigInt.from_string("1"), BigInt.from_string("1"))))\n",
+       ")\n",
+       "_TupleNDArray_1 = svd(\n",
+       "    sqrt(\n",
+       "        asarray(\n",
+       "            NDArray.scalar(Value.float(Float.rational(BigRat(BigInt.from_string("1"), BigInt.from_string("147"))))),\n",
+       "            OptionalDType.some(DType.float64),\n",
+       "            OptionalBool.none,\n",
+       "            OptionalDevice.some(_NDArray_1.device),\n",
+       "        )\n",
+       "    )\n",
+       "    * (_NDArray_8 / _NDArray_11),\n",
+       "    Boolean(False),\n",
+       ")\n",
        "_Slice_1 = Slice(OptionalInt.none, OptionalInt.some(sum(astype(_TupleNDArray_1[Int(1)] > NDArray.scalar(Value.float(Float(0.0001))), DType.int32)).to_value().to_int))\n",
-       "_NDArray_11 = (_TupleNDArray_1[Int(2)][IndexKey.multi_axis(MultiAxisIndexKey(MultiAxisIndexKeyItem.slice(_Slice_1)) + _MultiAxisIndexKey_1)] / _NDArray_10).T / _TupleNDArray_1[\n",
-       "    Int(1)\n",
-       "][IndexKey.slice(_Slice_1)]\n",
+       "_NDArray_12 = (\n",
+       "    _TupleNDArray_1[Int(2)][IndexKey.multi_axis(MultiAxisIndexKey.from_vec(Vec[MultiAxisIndexKeyItem](MultiAxisIndexKeyItem.slice(_Slice_1), _MultiAxisIndexKeyItem_1)))]\n",
+       "    / _NDArray_11\n",
+       ").T / _TupleNDArray_1[Int(1)][IndexKey.slice(_Slice_1)]\n",
        "_TupleNDArray_2 = svd(\n",
-       "    (sqrt((NDArray.scalar(Value.int(Int(1000000))) * _NDArray_3) * NDArray.scalar(Value.float(Float(1.0)))) * (_NDArray_4 - (_NDArray_3 @ _NDArray_4)).T).T @ _NDArray_11, FALSE\n",
+       "    (\n",
+       "        sqrt((NDArray.scalar(Value.int(Int(150))) * _NDArray_3) * NDArray.scalar(Value.float(Float.rational(BigRat(BigInt.from_string("1"), BigInt.from_string("2"))))))\n",
+       "        * (_NDArray_4 - (_NDArray_3 @ _NDArray_4)).T\n",
+       "    ).T\n",
+       "    @ _NDArray_12,\n",
+       "    Boolean(False),\n",
        ")\n",
        "(\n",
        "    (_NDArray_1 - (_NDArray_3 @ _NDArray_4))\n",
        "    @ (\n",
-       "        _NDArray_11\n",
+       "        _NDArray_12\n",
        "        @ _TupleNDArray_2[Int(2)].T[\n",
        "            IndexKey.multi_axis(\n",
-       "                _MultiAxisIndexKey_1\n",
-       "                + MultiAxisIndexKey(\n",
-       "                    MultiAxisIndexKeyItem.slice(\n",
-       "                        Slice(\n",
-       "                            OptionalInt.none,\n",
-       "                            OptionalInt.some(\n",
-       "                                sum(astype(_TupleNDArray_2[Int(1)] > (NDArray.scalar(Value.float(Float(0.0001))) * _TupleNDArray_2[Int(1)][IndexKey.int(Int(0))]), DType.int32))\n",
-       "                                .to_value()\n",
-       "                                .to_int\n",
-       "                            ),\n",
-       "                        )\n",
+       "                MultiAxisIndexKey.from_vec(\n",
+       "                    Vec[MultiAxisIndexKeyItem](\n",
+       "                        _MultiAxisIndexKeyItem_1,\n",
+       "                        MultiAxisIndexKeyItem.slice(\n",
+       "                            Slice(\n",
+       "                                OptionalInt.none,\n",
+       "                                OptionalInt.some(\n",
+       "                                    sum(astype(_TupleNDArray_2[Int(1)] > (NDArray.scalar(Value.float(Float(0.0001))) * _TupleNDArray_2[Int(1)][IndexKey.int(Int(0))]), DType.int32))\n",
+       "                                    .to_value()\n",
+       "                                    .to_int\n",
+       "                                ),\n",
+       "                            )\n",
+       "                        ),\n",
        "                    )\n",
        "                )\n",
        "            )\n",
        "        ]\n",
        "    )\n",
-       ")[IndexKey.multi_axis(_MultiAxisIndexKey_1 + MultiAxisIndexKey(MultiAxisIndexKeyItem.slice(Slice(OptionalInt.none, OptionalInt.some(Int(1))))))]\n",
+       ")[\n",
+       "    IndexKey.multi_axis(\n",
+       "        MultiAxisIndexKey.from_vec(Vec[MultiAxisIndexKeyItem](_MultiAxisIndexKeyItem_1, MultiAxisIndexKeyItem.slice(Slice(OptionalInt.none, OptionalInt.some(Int(2))))))\n",
+       "    )\n",
+       "]\n",
        "
\n"
       ],
       "text/latex": [
        "\\begin{Verbatim}[commandchars=\\\\\\{\\}]\n",
        "\\PY{n}{\\PYZus{}NDArray\\PYZus{}1} \\PY{o}{=} \\PY{n}{NDArray}\\PY{o}{.}\\PY{n}{var}\\PY{p}{(}\\PY{l+s+s2}{\\PYZdq{}}\\PY{l+s+s2}{X}\\PY{l+s+s2}{\\PYZdq{}}\\PY{p}{)}\n",
        "\\PY{n}{assume\\PYZus{}dtype}\\PY{p}{(}\\PY{n}{\\PYZus{}NDArray\\PYZus{}1}\\PY{p}{,} \\PY{n}{DType}\\PY{o}{.}\\PY{n}{float64}\\PY{p}{)}\n",
-       "\\PY{n}{assume\\PYZus{}shape}\\PY{p}{(}\\PY{n}{\\PYZus{}NDArray\\PYZus{}1}\\PY{p}{,} \\PY{n}{TupleInt}\\PY{p}{(}\\PY{n}{Int}\\PY{p}{(}\\PY{l+m+mi}{1000000}\\PY{p}{)}\\PY{p}{)} \\PY{o}{+} \\PY{n}{TupleInt}\\PY{p}{(}\\PY{n}{Int}\\PY{p}{(}\\PY{l+m+mi}{20}\\PY{p}{)}\\PY{p}{)}\\PY{p}{)}\n",
+       "\\PY{n}{assume\\PYZus{}shape}\\PY{p}{(}\\PY{n}{\\PYZus{}NDArray\\PYZus{}1}\\PY{p}{,} \\PY{n}{TupleInt}\\PY{o}{.}\\PY{n}{from\\PYZus{}vec}\\PY{p}{(}\\PY{n}{Vec}\\PY{p}{[}\\PY{n}{Int}\\PY{p}{]}\\PY{p}{(}\\PY{n}{Int}\\PY{p}{(}\\PY{l+m+mi}{150}\\PY{p}{)}\\PY{p}{,} \\PY{n}{Int}\\PY{p}{(}\\PY{l+m+mi}{4}\\PY{p}{)}\\PY{p}{)}\\PY{p}{)}\\PY{p}{)}\n",
        "\\PY{n}{assume\\PYZus{}isfinite}\\PY{p}{(}\\PY{n}{\\PYZus{}NDArray\\PYZus{}1}\\PY{p}{)}\n",
        "\\PY{n}{\\PYZus{}NDArray\\PYZus{}2} \\PY{o}{=} \\PY{n}{NDArray}\\PY{o}{.}\\PY{n}{var}\\PY{p}{(}\\PY{l+s+s2}{\\PYZdq{}}\\PY{l+s+s2}{y}\\PY{l+s+s2}{\\PYZdq{}}\\PY{p}{)}\n",
        "\\PY{n}{assume\\PYZus{}dtype}\\PY{p}{(}\\PY{n}{\\PYZus{}NDArray\\PYZus{}2}\\PY{p}{,} \\PY{n}{DType}\\PY{o}{.}\\PY{n}{int64}\\PY{p}{)}\n",
-       "\\PY{n}{assume\\PYZus{}shape}\\PY{p}{(}\\PY{n}{\\PYZus{}NDArray\\PYZus{}2}\\PY{p}{,} \\PY{n}{TupleInt}\\PY{p}{(}\\PY{n}{Int}\\PY{p}{(}\\PY{l+m+mi}{1000000}\\PY{p}{)}\\PY{p}{)}\\PY{p}{)}\n",
-       "\\PY{n}{assume\\PYZus{}value\\PYZus{}one\\PYZus{}of}\\PY{p}{(}\\PY{n}{\\PYZus{}NDArray\\PYZus{}2}\\PY{p}{,} \\PY{n}{TupleValue}\\PY{p}{(}\\PY{n}{Value}\\PY{o}{.}\\PY{n}{int}\\PY{p}{(}\\PY{n}{Int}\\PY{p}{(}\\PY{l+m+mi}{0}\\PY{p}{)}\\PY{p}{)}\\PY{p}{)} \\PY{o}{+} \\PY{n}{TupleValue}\\PY{p}{(}\\PY{n}{Value}\\PY{o}{.}\\PY{n}{int}\\PY{p}{(}\\PY{n}{Int}\\PY{p}{(}\\PY{l+m+mi}{1}\\PY{p}{)}\\PY{p}{)}\\PY{p}{)}\\PY{p}{)}\n",
+       "\\PY{n}{assume\\PYZus{}shape}\\PY{p}{(}\\PY{n}{\\PYZus{}NDArray\\PYZus{}2}\\PY{p}{,} \\PY{n}{TupleInt}\\PY{o}{.}\\PY{n}{from\\PYZus{}vec}\\PY{p}{(}\\PY{n}{Vec}\\PY{p}{[}\\PY{n}{Int}\\PY{p}{]}\\PY{p}{(}\\PY{n}{Int}\\PY{p}{(}\\PY{l+m+mi}{150}\\PY{p}{)}\\PY{p}{)}\\PY{p}{)}\\PY{p}{)}\n",
+       "\\PY{n}{assume\\PYZus{}value\\PYZus{}one\\PYZus{}of}\\PY{p}{(}\\PY{n}{\\PYZus{}NDArray\\PYZus{}2}\\PY{p}{,} \\PY{n}{TupleValue}\\PY{o}{.}\\PY{n}{from\\PYZus{}vec}\\PY{p}{(}\\PY{n}{Vec}\\PY{p}{[}\\PY{n}{Value}\\PY{p}{]}\\PY{p}{(}\\PY{n}{Value}\\PY{o}{.}\\PY{n}{int}\\PY{p}{(}\\PY{n}{Int}\\PY{p}{(}\\PY{l+m+mi}{0}\\PY{p}{)}\\PY{p}{)}\\PY{p}{,} \\PY{n}{Value}\\PY{o}{.}\\PY{n}{int}\\PY{p}{(}\\PY{n}{Int}\\PY{p}{(}\\PY{l+m+mi}{1}\\PY{p}{)}\\PY{p}{)}\\PY{p}{,} \\PY{n}{Value}\\PY{o}{.}\\PY{n}{int}\\PY{p}{(}\\PY{n}{Int}\\PY{p}{(}\\PY{l+m+mi}{2}\\PY{p}{)}\\PY{p}{)}\\PY{p}{)}\\PY{p}{)}\\PY{p}{)}\n",
        "\\PY{n}{\\PYZus{}NDArray\\PYZus{}3} \\PY{o}{=} \\PY{n}{astype}\\PY{p}{(}\n",
-       "    \\PY{n}{NDArray}\\PY{o}{.}\\PY{n}{vector}\\PY{p}{(}\\PY{n}{TupleValue}\\PY{p}{(}\\PY{n+nb}{sum}\\PY{p}{(}\\PY{n}{\\PYZus{}NDArray\\PYZus{}2} \\PY{o}{==} \\PY{n}{NDArray}\\PY{o}{.}\\PY{n}{scalar}\\PY{p}{(}\\PY{n}{Value}\\PY{o}{.}\\PY{n}{int}\\PY{p}{(}\\PY{n}{Int}\\PY{p}{(}\\PY{l+m+mi}{0}\\PY{p}{)}\\PY{p}{)}\\PY{p}{)}\\PY{p}{)}\\PY{o}{.}\\PY{n}{to\\PYZus{}value}\\PY{p}{(}\\PY{p}{)}\\PY{p}{)} \\PY{o}{+} \\PY{n}{TupleValue}\\PY{p}{(}\\PY{n+nb}{sum}\\PY{p}{(}\\PY{n}{\\PYZus{}NDArray\\PYZus{}2} \\PY{o}{==} \\PY{n}{NDArray}\\PY{o}{.}\\PY{n}{scalar}\\PY{p}{(}\\PY{n}{Value}\\PY{o}{.}\\PY{n}{int}\\PY{p}{(}\\PY{n}{Int}\\PY{p}{(}\\PY{l+m+mi}{1}\\PY{p}{)}\\PY{p}{)}\\PY{p}{)}\\PY{p}{)}\\PY{o}{.}\\PY{n}{to\\PYZus{}value}\\PY{p}{(}\\PY{p}{)}\\PY{p}{)}\\PY{p}{)}\\PY{p}{,}\n",
+       "    \\PY{n}{NDArray}\\PY{o}{.}\\PY{n}{vector}\\PY{p}{(}\n",
+       "        \\PY{n}{TupleValue}\\PY{o}{.}\\PY{n}{from\\PYZus{}vec}\\PY{p}{(}\n",
+       "            \\PY{n}{Vec}\\PY{p}{[}\\PY{n}{Value}\\PY{p}{]}\\PY{p}{(}\n",
+       "                \\PY{n+nb}{sum}\\PY{p}{(}\\PY{n}{\\PYZus{}NDArray\\PYZus{}2} \\PY{o}{==} \\PY{n}{NDArray}\\PY{o}{.}\\PY{n}{scalar}\\PY{p}{(}\\PY{n}{Value}\\PY{o}{.}\\PY{n}{int}\\PY{p}{(}\\PY{n}{Int}\\PY{p}{(}\\PY{l+m+mi}{0}\\PY{p}{)}\\PY{p}{)}\\PY{p}{)}\\PY{p}{)}\\PY{o}{.}\\PY{n}{to\\PYZus{}value}\\PY{p}{(}\\PY{p}{)}\\PY{p}{,}\n",
+       "                \\PY{n+nb}{sum}\\PY{p}{(}\\PY{n}{\\PYZus{}NDArray\\PYZus{}2} \\PY{o}{==} \\PY{n}{NDArray}\\PY{o}{.}\\PY{n}{scalar}\\PY{p}{(}\\PY{n}{Value}\\PY{o}{.}\\PY{n}{int}\\PY{p}{(}\\PY{n}{Int}\\PY{p}{(}\\PY{l+m+mi}{1}\\PY{p}{)}\\PY{p}{)}\\PY{p}{)}\\PY{p}{)}\\PY{o}{.}\\PY{n}{to\\PYZus{}value}\\PY{p}{(}\\PY{p}{)}\\PY{p}{,}\n",
+       "                \\PY{n+nb}{sum}\\PY{p}{(}\\PY{n}{\\PYZus{}NDArray\\PYZus{}2} \\PY{o}{==} \\PY{n}{NDArray}\\PY{o}{.}\\PY{n}{scalar}\\PY{p}{(}\\PY{n}{Value}\\PY{o}{.}\\PY{n}{int}\\PY{p}{(}\\PY{n}{Int}\\PY{p}{(}\\PY{l+m+mi}{2}\\PY{p}{)}\\PY{p}{)}\\PY{p}{)}\\PY{p}{)}\\PY{o}{.}\\PY{n}{to\\PYZus{}value}\\PY{p}{(}\\PY{p}{)}\\PY{p}{,}\n",
+       "            \\PY{p}{)}\n",
+       "        \\PY{p}{)}\n",
+       "    \\PY{p}{)}\\PY{p}{,}\n",
        "    \\PY{n}{DType}\\PY{o}{.}\\PY{n}{float64}\\PY{p}{,}\n",
-       "\\PY{p}{)} \\PY{o}{/} \\PY{n}{NDArray}\\PY{o}{.}\\PY{n}{scalar}\\PY{p}{(}\\PY{n}{Value}\\PY{o}{.}\\PY{n}{float}\\PY{p}{(}\\PY{n}{Float}\\PY{p}{(}\\PY{l+m+mf}{1000000.0}\\PY{p}{)}\\PY{p}{)}\\PY{p}{)}\n",
-       "\\PY{n}{\\PYZus{}NDArray\\PYZus{}4} \\PY{o}{=} \\PY{n}{zeros}\\PY{p}{(}\\PY{n}{TupleInt}\\PY{p}{(}\\PY{n}{Int}\\PY{p}{(}\\PY{l+m+mi}{2}\\PY{p}{)}\\PY{p}{)} \\PY{o}{+} \\PY{n}{TupleInt}\\PY{p}{(}\\PY{n}{Int}\\PY{p}{(}\\PY{l+m+mi}{20}\\PY{p}{)}\\PY{p}{)}\\PY{p}{,} \\PY{n}{OptionalDType}\\PY{o}{.}\\PY{n}{some}\\PY{p}{(}\\PY{n}{DType}\\PY{o}{.}\\PY{n}{float64}\\PY{p}{)}\\PY{p}{,} \\PY{n}{OptionalDevice}\\PY{o}{.}\\PY{n}{some}\\PY{p}{(}\\PY{n}{\\PYZus{}NDArray\\PYZus{}1}\\PY{o}{.}\\PY{n}{device}\\PY{p}{)}\\PY{p}{)}\n",
-       "\\PY{n}{\\PYZus{}MultiAxisIndexKey\\PYZus{}1} \\PY{o}{=} \\PY{n}{MultiAxisIndexKey}\\PY{p}{(}\\PY{n}{MultiAxisIndexKeyItem}\\PY{o}{.}\\PY{n}{slice}\\PY{p}{(}\\PY{n}{Slice}\\PY{p}{(}\\PY{p}{)}\\PY{p}{)}\\PY{p}{)}\n",
-       "\\PY{n}{\\PYZus{}IndexKey\\PYZus{}1} \\PY{o}{=} \\PY{n}{IndexKey}\\PY{o}{.}\\PY{n}{multi\\PYZus{}axis}\\PY{p}{(}\\PY{n}{MultiAxisIndexKey}\\PY{p}{(}\\PY{n}{MultiAxisIndexKeyItem}\\PY{o}{.}\\PY{n}{int}\\PY{p}{(}\\PY{n}{Int}\\PY{p}{(}\\PY{l+m+mi}{0}\\PY{p}{)}\\PY{p}{)}\\PY{p}{)} \\PY{o}{+} \\PY{n}{\\PYZus{}MultiAxisIndexKey\\PYZus{}1}\\PY{p}{)}\n",
-       "\\PY{n}{\\PYZus{}NDArray\\PYZus{}5} \\PY{o}{=} \\PY{n}{\\PYZus{}NDArray\\PYZus{}1}\\PY{p}{[}\\PY{n}{ndarray\\PYZus{}index}\\PY{p}{(}\\PY{n}{\\PYZus{}NDArray\\PYZus{}2} \\PY{o}{==} \\PY{n}{NDArray}\\PY{o}{.}\\PY{n}{scalar}\\PY{p}{(}\\PY{n}{Value}\\PY{o}{.}\\PY{n}{int}\\PY{p}{(}\\PY{n}{Int}\\PY{p}{(}\\PY{l+m+mi}{0}\\PY{p}{)}\\PY{p}{)}\\PY{p}{)}\\PY{p}{)}\\PY{p}{]}\n",
+       "\\PY{p}{)} \\PY{o}{/} \\PY{n}{NDArray}\\PY{o}{.}\\PY{n}{scalar}\\PY{p}{(}\\PY{n}{Value}\\PY{o}{.}\\PY{n}{float}\\PY{p}{(}\\PY{n}{Float}\\PY{o}{.}\\PY{n}{rational}\\PY{p}{(}\\PY{n}{BigRat}\\PY{p}{(}\\PY{n}{BigInt}\\PY{o}{.}\\PY{n}{from\\PYZus{}string}\\PY{p}{(}\\PY{l+s+s2}{\\PYZdq{}}\\PY{l+s+s2}{150}\\PY{l+s+s2}{\\PYZdq{}}\\PY{p}{)}\\PY{p}{,} \\PY{n}{BigInt}\\PY{o}{.}\\PY{n}{from\\PYZus{}string}\\PY{p}{(}\\PY{l+s+s2}{\\PYZdq{}}\\PY{l+s+s2}{1}\\PY{l+s+s2}{\\PYZdq{}}\\PY{p}{)}\\PY{p}{)}\\PY{p}{)}\\PY{p}{)}\\PY{p}{)}\n",
+       "\\PY{n}{\\PYZus{}NDArray\\PYZus{}4} \\PY{o}{=} \\PY{n}{zeros}\\PY{p}{(}\\PY{n}{TupleInt}\\PY{o}{.}\\PY{n}{from\\PYZus{}vec}\\PY{p}{(}\\PY{n}{Vec}\\PY{p}{[}\\PY{n}{Int}\\PY{p}{]}\\PY{p}{(}\\PY{n}{Int}\\PY{p}{(}\\PY{l+m+mi}{3}\\PY{p}{)}\\PY{p}{,} \\PY{n}{Int}\\PY{p}{(}\\PY{l+m+mi}{4}\\PY{p}{)}\\PY{p}{)}\\PY{p}{)}\\PY{p}{,} \\PY{n}{OptionalDType}\\PY{o}{.}\\PY{n}{some}\\PY{p}{(}\\PY{n}{DType}\\PY{o}{.}\\PY{n}{float64}\\PY{p}{)}\\PY{p}{,} \\PY{n}{OptionalDevice}\\PY{o}{.}\\PY{n}{some}\\PY{p}{(}\\PY{n}{\\PYZus{}NDArray\\PYZus{}1}\\PY{o}{.}\\PY{n}{device}\\PY{p}{)}\\PY{p}{)}\n",
+       "\\PY{n}{\\PYZus{}MultiAxisIndexKeyItem\\PYZus{}1} \\PY{o}{=} \\PY{n}{MultiAxisIndexKeyItem}\\PY{o}{.}\\PY{n}{slice}\\PY{p}{(}\\PY{n}{Slice}\\PY{p}{(}\\PY{p}{)}\\PY{p}{)}\n",
+       "\\PY{n}{\\PYZus{}IndexKey\\PYZus{}1} \\PY{o}{=} \\PY{n}{IndexKey}\\PY{o}{.}\\PY{n}{multi\\PYZus{}axis}\\PY{p}{(}\\PY{n}{MultiAxisIndexKey}\\PY{o}{.}\\PY{n}{from\\PYZus{}vec}\\PY{p}{(}\\PY{n}{Vec}\\PY{p}{[}\\PY{n}{MultiAxisIndexKeyItem}\\PY{p}{]}\\PY{p}{(}\\PY{n}{MultiAxisIndexKeyItem}\\PY{o}{.}\\PY{n}{int}\\PY{p}{(}\\PY{n}{Int}\\PY{p}{(}\\PY{l+m+mi}{0}\\PY{p}{)}\\PY{p}{)}\\PY{p}{,} \\PY{n}{\\PYZus{}MultiAxisIndexKeyItem\\PYZus{}1}\\PY{p}{)}\\PY{p}{)}\\PY{p}{)}\n",
+       "\\PY{n}{\\PYZus{}NDArray\\PYZus{}5} \\PY{o}{=} \\PY{n}{\\PYZus{}NDArray\\PYZus{}1}\\PY{p}{[}\\PY{n}{IndexKey}\\PY{o}{.}\\PY{n}{ndarray}\\PY{p}{(}\\PY{n}{\\PYZus{}NDArray\\PYZus{}2} \\PY{o}{==} \\PY{n}{NDArray}\\PY{o}{.}\\PY{n}{scalar}\\PY{p}{(}\\PY{n}{Value}\\PY{o}{.}\\PY{n}{int}\\PY{p}{(}\\PY{n}{Int}\\PY{p}{(}\\PY{l+m+mi}{0}\\PY{p}{)}\\PY{p}{)}\\PY{p}{)}\\PY{p}{)}\\PY{p}{]}\n",
        "\\PY{n}{\\PYZus{}OptionalIntOrTuple\\PYZus{}1} \\PY{o}{=} \\PY{n}{OptionalIntOrTuple}\\PY{o}{.}\\PY{n}{some}\\PY{p}{(}\\PY{n}{IntOrTuple}\\PY{o}{.}\\PY{n}{int}\\PY{p}{(}\\PY{n}{Int}\\PY{p}{(}\\PY{l+m+mi}{0}\\PY{p}{)}\\PY{p}{)}\\PY{p}{)}\n",
        "\\PY{n}{\\PYZus{}NDArray\\PYZus{}4}\\PY{p}{[}\\PY{n}{\\PYZus{}IndexKey\\PYZus{}1}\\PY{p}{]} \\PY{o}{=} \\PY{n+nb}{sum}\\PY{p}{(}\\PY{n}{\\PYZus{}NDArray\\PYZus{}5}\\PY{p}{,} \\PY{n}{\\PYZus{}OptionalIntOrTuple\\PYZus{}1}\\PY{p}{)} \\PY{o}{/} \\PY{n}{NDArray}\\PY{o}{.}\\PY{n}{scalar}\\PY{p}{(}\\PY{n}{Value}\\PY{o}{.}\\PY{n}{int}\\PY{p}{(}\\PY{n}{\\PYZus{}NDArray\\PYZus{}5}\\PY{o}{.}\\PY{n}{shape}\\PY{p}{[}\\PY{n}{Int}\\PY{p}{(}\\PY{l+m+mi}{0}\\PY{p}{)}\\PY{p}{]}\\PY{p}{)}\\PY{p}{)}\n",
-       "\\PY{n}{\\PYZus{}IndexKey\\PYZus{}2} \\PY{o}{=} \\PY{n}{IndexKey}\\PY{o}{.}\\PY{n}{multi\\PYZus{}axis}\\PY{p}{(}\\PY{n}{MultiAxisIndexKey}\\PY{p}{(}\\PY{n}{MultiAxisIndexKeyItem}\\PY{o}{.}\\PY{n}{int}\\PY{p}{(}\\PY{n}{Int}\\PY{p}{(}\\PY{l+m+mi}{1}\\PY{p}{)}\\PY{p}{)}\\PY{p}{)} \\PY{o}{+} \\PY{n}{\\PYZus{}MultiAxisIndexKey\\PYZus{}1}\\PY{p}{)}\n",
-       "\\PY{n}{\\PYZus{}NDArray\\PYZus{}6} \\PY{o}{=} \\PY{n}{\\PYZus{}NDArray\\PYZus{}1}\\PY{p}{[}\\PY{n}{ndarray\\PYZus{}index}\\PY{p}{(}\\PY{n}{\\PYZus{}NDArray\\PYZus{}2} \\PY{o}{==} \\PY{n}{NDArray}\\PY{o}{.}\\PY{n}{scalar}\\PY{p}{(}\\PY{n}{Value}\\PY{o}{.}\\PY{n}{int}\\PY{p}{(}\\PY{n}{Int}\\PY{p}{(}\\PY{l+m+mi}{1}\\PY{p}{)}\\PY{p}{)}\\PY{p}{)}\\PY{p}{)}\\PY{p}{]}\n",
+       "\\PY{n}{\\PYZus{}IndexKey\\PYZus{}2} \\PY{o}{=} \\PY{n}{IndexKey}\\PY{o}{.}\\PY{n}{multi\\PYZus{}axis}\\PY{p}{(}\\PY{n}{MultiAxisIndexKey}\\PY{o}{.}\\PY{n}{from\\PYZus{}vec}\\PY{p}{(}\\PY{n}{Vec}\\PY{p}{[}\\PY{n}{MultiAxisIndexKeyItem}\\PY{p}{]}\\PY{p}{(}\\PY{n}{MultiAxisIndexKeyItem}\\PY{o}{.}\\PY{n}{int}\\PY{p}{(}\\PY{n}{Int}\\PY{p}{(}\\PY{l+m+mi}{1}\\PY{p}{)}\\PY{p}{)}\\PY{p}{,} \\PY{n}{\\PYZus{}MultiAxisIndexKeyItem\\PYZus{}1}\\PY{p}{)}\\PY{p}{)}\\PY{p}{)}\n",
+       "\\PY{n}{\\PYZus{}NDArray\\PYZus{}6} \\PY{o}{=} \\PY{n}{\\PYZus{}NDArray\\PYZus{}1}\\PY{p}{[}\\PY{n}{IndexKey}\\PY{o}{.}\\PY{n}{ndarray}\\PY{p}{(}\\PY{n}{\\PYZus{}NDArray\\PYZus{}2} \\PY{o}{==} \\PY{n}{NDArray}\\PY{o}{.}\\PY{n}{scalar}\\PY{p}{(}\\PY{n}{Value}\\PY{o}{.}\\PY{n}{int}\\PY{p}{(}\\PY{n}{Int}\\PY{p}{(}\\PY{l+m+mi}{1}\\PY{p}{)}\\PY{p}{)}\\PY{p}{)}\\PY{p}{)}\\PY{p}{]}\n",
        "\\PY{n}{\\PYZus{}NDArray\\PYZus{}4}\\PY{p}{[}\\PY{n}{\\PYZus{}IndexKey\\PYZus{}2}\\PY{p}{]} \\PY{o}{=} \\PY{n+nb}{sum}\\PY{p}{(}\\PY{n}{\\PYZus{}NDArray\\PYZus{}6}\\PY{p}{,} \\PY{n}{\\PYZus{}OptionalIntOrTuple\\PYZus{}1}\\PY{p}{)} \\PY{o}{/} \\PY{n}{NDArray}\\PY{o}{.}\\PY{n}{scalar}\\PY{p}{(}\\PY{n}{Value}\\PY{o}{.}\\PY{n}{int}\\PY{p}{(}\\PY{n}{\\PYZus{}NDArray\\PYZus{}6}\\PY{o}{.}\\PY{n}{shape}\\PY{p}{[}\\PY{n}{Int}\\PY{p}{(}\\PY{l+m+mi}{0}\\PY{p}{)}\\PY{p}{]}\\PY{p}{)}\\PY{p}{)}\n",
-       "\\PY{n}{\\PYZus{}NDArray\\PYZus{}7} \\PY{o}{=} \\PY{n}{concat}\\PY{p}{(}\\PY{n}{TupleNDArray}\\PY{p}{(}\\PY{n}{\\PYZus{}NDArray\\PYZus{}5} \\PY{o}{\\PYZhy{}} \\PY{n}{\\PYZus{}NDArray\\PYZus{}4}\\PY{p}{[}\\PY{n}{\\PYZus{}IndexKey\\PYZus{}1}\\PY{p}{]}\\PY{p}{)} \\PY{o}{+} \\PY{n}{TupleNDArray}\\PY{p}{(}\\PY{n}{\\PYZus{}NDArray\\PYZus{}6} \\PY{o}{\\PYZhy{}} \\PY{n}{\\PYZus{}NDArray\\PYZus{}4}\\PY{p}{[}\\PY{n}{\\PYZus{}IndexKey\\PYZus{}2}\\PY{p}{]}\\PY{p}{)}\\PY{p}{,} \\PY{n}{OptionalInt}\\PY{o}{.}\\PY{n}{some}\\PY{p}{(}\\PY{n}{Int}\\PY{p}{(}\\PY{l+m+mi}{0}\\PY{p}{)}\\PY{p}{)}\\PY{p}{)}\n",
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+       "                                    \\PY{o}{.}\\PY{n}{to\\PYZus{}value}\\PY{p}{(}\\PY{p}{)}\n",
+       "                                    \\PY{o}{.}\\PY{n}{to\\PYZus{}int}\n",
+       "                                \\PY{p}{)}\\PY{p}{,}\n",
+       "                            \\PY{p}{)}\n",
+       "                        \\PY{p}{)}\\PY{p}{,}\n",
        "                    \\PY{p}{)}\n",
        "                \\PY{p}{)}\n",
        "            \\PY{p}{)}\n",
        "        \\PY{p}{]}\n",
        "    \\PY{p}{)}\n",
-       "\\PY{p}{)}\\PY{p}{[}\\PY{n}{IndexKey}\\PY{o}{.}\\PY{n}{multi\\PYZus{}axis}\\PY{p}{(}\\PY{n}{\\PYZus{}MultiAxisIndexKey\\PYZus{}1} \\PY{o}{+} \\PY{n}{MultiAxisIndexKey}\\PY{p}{(}\\PY{n}{MultiAxisIndexKeyItem}\\PY{o}{.}\\PY{n}{slice}\\PY{p}{(}\\PY{n}{Slice}\\PY{p}{(}\\PY{n}{OptionalInt}\\PY{o}{.}\\PY{n}{none}\\PY{p}{,} \\PY{n}{OptionalInt}\\PY{o}{.}\\PY{n}{some}\\PY{p}{(}\\PY{n}{Int}\\PY{p}{(}\\PY{l+m+mi}{1}\\PY{p}{)}\\PY{p}{)}\\PY{p}{)}\\PY{p}{)}\\PY{p}{)}\\PY{p}{)}\\PY{p}{]}\n",
+       "\\PY{p}{)}\\PY{p}{[}\n",
+       "    \\PY{n}{IndexKey}\\PY{o}{.}\\PY{n}{multi\\PYZus{}axis}\\PY{p}{(}\n",
+       "        \\PY{n}{MultiAxisIndexKey}\\PY{o}{.}\\PY{n}{from\\PYZus{}vec}\\PY{p}{(}\\PY{n}{Vec}\\PY{p}{[}\\PY{n}{MultiAxisIndexKeyItem}\\PY{p}{]}\\PY{p}{(}\\PY{n}{\\PYZus{}MultiAxisIndexKeyItem\\PYZus{}1}\\PY{p}{,} \\PY{n}{MultiAxisIndexKeyItem}\\PY{o}{.}\\PY{n}{slice}\\PY{p}{(}\\PY{n}{Slice}\\PY{p}{(}\\PY{n}{OptionalInt}\\PY{o}{.}\\PY{n}{none}\\PY{p}{,} \\PY{n}{OptionalInt}\\PY{o}{.}\\PY{n}{some}\\PY{p}{(}\\PY{n}{Int}\\PY{p}{(}\\PY{l+m+mi}{2}\\PY{p}{)}\\PY{p}{)}\\PY{p}{)}\\PY{p}{)}\\PY{p}{)}\\PY{p}{)}\n",
+       "    \\PY{p}{)}\n",
+       "\\PY{p}{]}\n",
        "\\end{Verbatim}\n"
       ],
       "text/plain": [
        "_NDArray_1 = NDArray.var(\"X\")\n",
        "assume_dtype(_NDArray_1, DType.float64)\n",
-       "assume_shape(_NDArray_1, TupleInt(Int(1000000)) + TupleInt(Int(20)))\n",
+       "assume_shape(_NDArray_1, TupleInt.from_vec(Vec[Int](Int(150), Int(4))))\n",
        "assume_isfinite(_NDArray_1)\n",
        "_NDArray_2 = NDArray.var(\"y\")\n",
        "assume_dtype(_NDArray_2, DType.int64)\n",
-       "assume_shape(_NDArray_2, TupleInt(Int(1000000)))\n",
-       "assume_value_one_of(_NDArray_2, TupleValue(Value.int(Int(0))) + TupleValue(Value.int(Int(1))))\n",
+       "assume_shape(_NDArray_2, TupleInt.from_vec(Vec[Int](Int(150))))\n",
+       "assume_value_one_of(_NDArray_2, TupleValue.from_vec(Vec[Value](Value.int(Int(0)), Value.int(Int(1)), Value.int(Int(2)))))\n",
        "_NDArray_3 = astype(\n",
-       "    NDArray.vector(TupleValue(sum(_NDArray_2 == NDArray.scalar(Value.int(Int(0)))).to_value()) + TupleValue(sum(_NDArray_2 == NDArray.scalar(Value.int(Int(1)))).to_value())),\n",
+       "    NDArray.vector(\n",
+       "        TupleValue.from_vec(\n",
+       "            Vec[Value](\n",
+       "                sum(_NDArray_2 == NDArray.scalar(Value.int(Int(0)))).to_value(),\n",
+       "                sum(_NDArray_2 == NDArray.scalar(Value.int(Int(1)))).to_value(),\n",
+       "                sum(_NDArray_2 == NDArray.scalar(Value.int(Int(2)))).to_value(),\n",
+       "            )\n",
+       "        )\n",
+       "    ),\n",
        "    DType.float64,\n",
-       ") / NDArray.scalar(Value.float(Float(1000000.0)))\n",
-       "_NDArray_4 = zeros(TupleInt(Int(2)) + TupleInt(Int(20)), OptionalDType.some(DType.float64), OptionalDevice.some(_NDArray_1.device))\n",
-       "_MultiAxisIndexKey_1 = MultiAxisIndexKey(MultiAxisIndexKeyItem.slice(Slice()))\n",
-       "_IndexKey_1 = IndexKey.multi_axis(MultiAxisIndexKey(MultiAxisIndexKeyItem.int(Int(0))) + _MultiAxisIndexKey_1)\n",
-       "_NDArray_5 = _NDArray_1[ndarray_index(_NDArray_2 == NDArray.scalar(Value.int(Int(0))))]\n",
+       ") / NDArray.scalar(Value.float(Float.rational(BigRat(BigInt.from_string(\"150\"), BigInt.from_string(\"1\")))))\n",
+       "_NDArray_4 = zeros(TupleInt.from_vec(Vec[Int](Int(3), Int(4))), OptionalDType.some(DType.float64), OptionalDevice.some(_NDArray_1.device))\n",
+       "_MultiAxisIndexKeyItem_1 = MultiAxisIndexKeyItem.slice(Slice())\n",
+       "_IndexKey_1 = IndexKey.multi_axis(MultiAxisIndexKey.from_vec(Vec[MultiAxisIndexKeyItem](MultiAxisIndexKeyItem.int(Int(0)), _MultiAxisIndexKeyItem_1)))\n",
+       "_NDArray_5 = _NDArray_1[IndexKey.ndarray(_NDArray_2 == NDArray.scalar(Value.int(Int(0))))]\n",
        "_OptionalIntOrTuple_1 = OptionalIntOrTuple.some(IntOrTuple.int(Int(0)))\n",
        "_NDArray_4[_IndexKey_1] = sum(_NDArray_5, _OptionalIntOrTuple_1) / NDArray.scalar(Value.int(_NDArray_5.shape[Int(0)]))\n",
-       "_IndexKey_2 = IndexKey.multi_axis(MultiAxisIndexKey(MultiAxisIndexKeyItem.int(Int(1))) + _MultiAxisIndexKey_1)\n",
-       "_NDArray_6 = _NDArray_1[ndarray_index(_NDArray_2 == NDArray.scalar(Value.int(Int(1))))]\n",
+       "_IndexKey_2 = IndexKey.multi_axis(MultiAxisIndexKey.from_vec(Vec[MultiAxisIndexKeyItem](MultiAxisIndexKeyItem.int(Int(1)), _MultiAxisIndexKeyItem_1)))\n",
+       "_NDArray_6 = _NDArray_1[IndexKey.ndarray(_NDArray_2 == NDArray.scalar(Value.int(Int(1))))]\n",
        "_NDArray_4[_IndexKey_2] = sum(_NDArray_6, _OptionalIntOrTuple_1) / NDArray.scalar(Value.int(_NDArray_6.shape[Int(0)]))\n",
-       "_NDArray_7 = concat(TupleNDArray(_NDArray_5 - _NDArray_4[_IndexKey_1]) + TupleNDArray(_NDArray_6 - _NDArray_4[_IndexKey_2]), OptionalInt.some(Int(0)))\n",
-       "_NDArray_8 = square(_NDArray_7 - expand_dims(sum(_NDArray_7, _OptionalIntOrTuple_1) / NDArray.scalar(Value.int(_NDArray_7.shape[Int(0)]))))\n",
-       "_NDArray_9 = sqrt(sum(_NDArray_8, _OptionalIntOrTuple_1) / NDArray.scalar(Value.int(_NDArray_8.shape[Int(0)])))\n",
-       "_NDArray_10 = copy(_NDArray_9)\n",
-       "_NDArray_10[ndarray_index(_NDArray_9 == NDArray.scalar(Value.int(Int(0))))] = NDArray.scalar(Value.float(Float(1.0)))\n",
-       "_TupleNDArray_1 = svd(sqrt(NDArray.scalar(Value.float(Float.rational(Rational(1, 999998))))) * (_NDArray_7 / _NDArray_10), FALSE)\n",
+       "_IndexKey_3 = IndexKey.multi_axis(MultiAxisIndexKey.from_vec(Vec[MultiAxisIndexKeyItem](MultiAxisIndexKeyItem.int(Int(2)), _MultiAxisIndexKeyItem_1)))\n",
+       "_NDArray_7 = _NDArray_1[IndexKey.ndarray(_NDArray_2 == NDArray.scalar(Value.int(Int(2))))]\n",
+       "_NDArray_4[_IndexKey_3] = sum(_NDArray_7, _OptionalIntOrTuple_1) / NDArray.scalar(Value.int(_NDArray_7.shape[Int(0)]))\n",
+       "_NDArray_8 = concat(\n",
+       "    TupleNDArray.from_vec(Vec[NDArray](_NDArray_5 - _NDArray_4[_IndexKey_1], _NDArray_6 - _NDArray_4[_IndexKey_2], _NDArray_7 - _NDArray_4[_IndexKey_3])), OptionalInt.some(Int(0))\n",
+       ")\n",
+       "_NDArray_9 = square(_NDArray_8 - expand_dims(sum(_NDArray_8, _OptionalIntOrTuple_1) / NDArray.scalar(Value.int(_NDArray_8.shape[Int(0)]))))\n",
+       "_NDArray_10 = sqrt(sum(_NDArray_9, _OptionalIntOrTuple_1) / NDArray.scalar(Value.int(_NDArray_9.shape[Int(0)])))\n",
+       "_NDArray_11 = copy(_NDArray_10)\n",
+       "_NDArray_11[IndexKey.ndarray(_NDArray_10 == NDArray.scalar(Value.int(Int(0))))] = NDArray.scalar(\n",
+       "    Value.float(Float.rational(BigRat(BigInt.from_string(\"1\"), BigInt.from_string(\"1\"))))\n",
+       ")\n",
+       "_TupleNDArray_1 = svd(\n",
+       "    sqrt(\n",
+       "        asarray(\n",
+       "            NDArray.scalar(Value.float(Float.rational(BigRat(BigInt.from_string(\"1\"), BigInt.from_string(\"147\"))))),\n",
+       "            OptionalDType.some(DType.float64),\n",
+       "            OptionalBool.none,\n",
+       "            OptionalDevice.some(_NDArray_1.device),\n",
+       "        )\n",
+       "    )\n",
+       "    * (_NDArray_8 / _NDArray_11),\n",
+       "    Boolean(False),\n",
+       ")\n",
        "_Slice_1 = Slice(OptionalInt.none, OptionalInt.some(sum(astype(_TupleNDArray_1[Int(1)] > NDArray.scalar(Value.float(Float(0.0001))), DType.int32)).to_value().to_int))\n",
-       "_NDArray_11 = (_TupleNDArray_1[Int(2)][IndexKey.multi_axis(MultiAxisIndexKey(MultiAxisIndexKeyItem.slice(_Slice_1)) + _MultiAxisIndexKey_1)] / _NDArray_10).T / _TupleNDArray_1[\n",
-       "    Int(1)\n",
-       "][IndexKey.slice(_Slice_1)]\n",
+       "_NDArray_12 = (\n",
+       "    _TupleNDArray_1[Int(2)][IndexKey.multi_axis(MultiAxisIndexKey.from_vec(Vec[MultiAxisIndexKeyItem](MultiAxisIndexKeyItem.slice(_Slice_1), _MultiAxisIndexKeyItem_1)))]\n",
+       "    / _NDArray_11\n",
+       ").T / _TupleNDArray_1[Int(1)][IndexKey.slice(_Slice_1)]\n",
        "_TupleNDArray_2 = svd(\n",
-       "    (sqrt((NDArray.scalar(Value.int(Int(1000000))) * _NDArray_3) * NDArray.scalar(Value.float(Float(1.0)))) * (_NDArray_4 - (_NDArray_3 @ _NDArray_4)).T).T @ _NDArray_11, FALSE\n",
+       "    (\n",
+       "        sqrt((NDArray.scalar(Value.int(Int(150))) * _NDArray_3) * NDArray.scalar(Value.float(Float.rational(BigRat(BigInt.from_string(\"1\"), BigInt.from_string(\"2\"))))))\n",
+       "        * (_NDArray_4 - (_NDArray_3 @ _NDArray_4)).T\n",
+       "    ).T\n",
+       "    @ _NDArray_12,\n",
+       "    Boolean(False),\n",
        ")\n",
        "(\n",
        "    (_NDArray_1 - (_NDArray_3 @ _NDArray_4))\n",
        "    @ (\n",
-       "        _NDArray_11\n",
+       "        _NDArray_12\n",
        "        @ _TupleNDArray_2[Int(2)].T[\n",
        "            IndexKey.multi_axis(\n",
-       "                _MultiAxisIndexKey_1\n",
-       "                + MultiAxisIndexKey(\n",
-       "                    MultiAxisIndexKeyItem.slice(\n",
-       "                        Slice(\n",
-       "                            OptionalInt.none,\n",
-       "                            OptionalInt.some(\n",
-       "                                sum(astype(_TupleNDArray_2[Int(1)] > (NDArray.scalar(Value.float(Float(0.0001))) * _TupleNDArray_2[Int(1)][IndexKey.int(Int(0))]), DType.int32))\n",
-       "                                .to_value()\n",
-       "                                .to_int\n",
-       "                            ),\n",
-       "                        )\n",
+       "                MultiAxisIndexKey.from_vec(\n",
+       "                    Vec[MultiAxisIndexKeyItem](\n",
+       "                        _MultiAxisIndexKeyItem_1,\n",
+       "                        MultiAxisIndexKeyItem.slice(\n",
+       "                            Slice(\n",
+       "                                OptionalInt.none,\n",
+       "                                OptionalInt.some(\n",
+       "                                    sum(astype(_TupleNDArray_2[Int(1)] > (NDArray.scalar(Value.float(Float(0.0001))) * _TupleNDArray_2[Int(1)][IndexKey.int(Int(0))]), DType.int32))\n",
+       "                                    .to_value()\n",
+       "                                    .to_int\n",
+       "                                ),\n",
+       "                            )\n",
+       "                        ),\n",
        "                    )\n",
        "                )\n",
        "            )\n",
        "        ]\n",
        "    )\n",
-       ")[IndexKey.multi_axis(_MultiAxisIndexKey_1 + MultiAxisIndexKey(MultiAxisIndexKeyItem.slice(Slice(OptionalInt.none, OptionalInt.some(Int(1))))))]"
+       ")[\n",
+       "    IndexKey.multi_axis(\n",
+       "        MultiAxisIndexKey.from_vec(Vec[MultiAxisIndexKeyItem](_MultiAxisIndexKeyItem_1, MultiAxisIndexKeyItem.slice(Slice(OptionalInt.none, OptionalInt.some(Int(2))))))\n",
+       "    )\n",
+       "]"
       ]
      },
      "metadata": {},
@@ -1392,7 +1521,10 @@
    "source": [
     "from egglog.exp.array_api_numba import array_api_numba_schedule\n",
     "\n",
-    "simplified_res = EGraph().simplify(res, array_api_numba_schedule)\n",
+    "egraph.register(res)\n",
+    "egraph.run(array_api_numba_schedule)\n",
+    "simplified_res = egraph.extract(res)\n",
+    "\n",
     "simplified_res"
    ]
   },
@@ -1413,37 +1545,7 @@
     "\n",
     "Well we showed how we can use eager evaluation to get a result, but what if we don't want to do the computation in egglog, but instead export a program so we can execute that back in Python or in this case feed it to Python?\n",
     "\n",
-    "Well in this case we have designed a `Program` object which we can use to convert a funtional egglog expression back to imperative Python code:\n"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 11,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       ""
-      ]
-     },
-     "execution_count": 11,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "from egglog.exp.array_api_program_gen import *\n",
-    "\n",
-    "egraph = EGraph()\n",
-    "fn_program = egraph.let(\n",
-    "    \"fn_program\",\n",
-    "    ndarray_function_two(simplified_res, NDArray.var(\"X\"), NDArray.var(\"y\")),\n",
-    ")\n",
-    "egraph.run(array_api_program_gen_schedule)\n",
-    "fn = egraph.eval(fn_program.py_object)\n",
-    "\n",
-    "fn"
+    "Well in this case we have designed a `Program` object which we can use to convert a funtional egglog expression back to imperative Python code:"
    ]
   },
   {
@@ -1457,69 +1559,86 @@
      "text": [
       "def __fn(X, y):\n",
       "    assert X.dtype == np.dtype(np.float64)\n",
-      "    assert X.shape == (1000000, 20,)\n",
+      "    assert X.shape == (150, 4, )\n",
       "    assert np.all(np.isfinite(X))\n",
       "    assert y.dtype == np.dtype(np.int64)\n",
-      "    assert y.shape == (1000000,)\n",
-      "    assert set(np.unique(y)) == set((0, 1,))\n",
+      "    assert y.shape == (150, )\n",
+      "    assert set(np.unique(y)) == set((0, 1, 2, ))\n",
       "    _0 = y == np.array(0)\n",
       "    _1 = np.sum(_0)\n",
       "    _2 = y == np.array(1)\n",
       "    _3 = np.sum(_2)\n",
-      "    _4 = np.array((_1, _3,)).astype(np.dtype(np.float64))\n",
-      "    _5 = _4 / np.array(1000000.0)\n",
-      "    _6 = np.zeros((2, 20,), dtype=np.dtype(np.float64))\n",
-      "    _7 = np.sum(X[_0], axis=0)\n",
-      "    _8 = _7 / np.array(X[_0].shape[0])\n",
-      "    _6[0, :] = _8\n",
-      "    _9 = np.sum(X[_2], axis=0)\n",
-      "    _10 = _9 / np.array(X[_2].shape[0])\n",
-      "    _6[1, :] = _10\n",
-      "    _11 = _5 @ _6\n",
-      "    _12 = X - _11\n",
-      "    _13 = np.sqrt(np.array(float(1 / 999998)))\n",
-      "    _14 = X[_0] - _6[0, :]\n",
-      "    _15 = X[_2] - _6[1, :]\n",
-      "    _16 = np.concatenate((_14, _15,), axis=0)\n",
-      "    _17 = np.sum(_16, axis=0)\n",
-      "    _18 = _17 / np.array(_16.shape[0])\n",
-      "    _19 = np.expand_dims(_18, 0)\n",
-      "    _20 = _16 - _19\n",
-      "    _21 = np.square(_20)\n",
+      "    _4 = y == np.array(2)\n",
+      "    _5 = np.sum(_4)\n",
+      "    _6 = np.array((_1, _3, _5, )).astype(np.dtype(np.float64))\n",
+      "    _7 = _6 / np.array(float(150))\n",
+      "    _8 = np.zeros((3, 4, ), dtype=np.dtype(np.float64))\n",
+      "    _9 = np.sum(X[_0], axis=0)\n",
+      "    _10 = _9 / np.array(X[_0].shape[0])\n",
+      "    _8[0, :,] = _10\n",
+      "    _11 = np.sum(X[_2], axis=0)\n",
+      "    _12 = _11 / np.array(X[_2].shape[0])\n",
+      "    _8[1, :,] = _12\n",
+      "    _13 = np.sum(X[_4], axis=0)\n",
+      "    _14 = _13 / np.array(X[_4].shape[0])\n",
+      "    _8[2, :,] = _14\n",
+      "    _15 = _7 @ _8\n",
+      "    _16 = X - _15\n",
+      "    _17 = np.sqrt(np.asarray(np.array(float(1 / 147)), np.dtype(np.float64)))\n",
+      "    _18 = X[_0] - _8[0, :,]\n",
+      "    _19 = X[_2] - _8[1, :,]\n",
+      "    _20 = X[_4] - _8[2, :,]\n",
+      "    _21 = np.concatenate((_18, _19, _20, ), axis=0)\n",
       "    _22 = np.sum(_21, axis=0)\n",
       "    _23 = _22 / np.array(_21.shape[0])\n",
-      "    _24 = np.sqrt(_23)\n",
-      "    _25 = _24 == np.array(0)\n",
-      "    _24[_25] = np.array(1.0)\n",
-      "    _26 = _16 / _24\n",
-      "    _27 = _13 * _26\n",
-      "    _28 = np.linalg.svd(_27, full_matrices=False)\n",
-      "    _29 = _28[1] > np.array(0.0001)\n",
-      "    _30 = _29.astype(np.dtype(np.int32))\n",
-      "    _31 = np.sum(_30)\n",
-      "    _32 = _28[2][:_31, :] / _24\n",
-      "    _33 = _32.T / _28[1][:_31]\n",
-      "    _34 = np.array(1000000) * _5\n",
-      "    _35 = _34 * np.array(1.0)\n",
-      "    _36 = np.sqrt(_35)\n",
-      "    _37 = _6 - _11\n",
-      "    _38 = _36 * _37.T\n",
-      "    _39 = _38.T @ _33\n",
-      "    _40 = np.linalg.svd(_39, full_matrices=False)\n",
-      "    _41 = np.array(0.0001) * _40[1][0]\n",
-      "    _42 = _40[1] > _41\n",
-      "    _43 = _42.astype(np.dtype(np.int32))\n",
-      "    _44 = np.sum(_43)\n",
-      "    _45 = _33 @ _40[2].T[:, :_44]\n",
-      "    _46 = _12 @ _45\n",
-      "    return _46[:, :1]\n",
+      "    _24 = np.expand_dims(_23, 0)\n",
+      "    _25 = _21 - _24\n",
+      "    _26 = np.square(_25)\n",
+      "    _27 = np.sum(_26, axis=0)\n",
+      "    _28 = _27 / np.array(_26.shape[0])\n",
+      "    _29 = np.sqrt(_28)\n",
+      "    _30 = _29 == np.array(0)\n",
+      "    _29[_30] = np.array(float(1))\n",
+      "    _31 = _21 / _29\n",
+      "    _32 = _17 * _31\n",
+      "    _33 = np.linalg.svd(_32, full_matrices=False)\n",
+      "    _34 = _33[1] > np.array(0.0001)\n",
+      "    _35 = _34.astype(np.dtype(np.int32))\n",
+      "    _36 = np.sum(_35)\n",
+      "    _37 = _33[2][:_36, :,] / _29\n",
+      "    _38 = _37.T / _33[1][:_36]\n",
+      "    _39 = np.array(150) * _7\n",
+      "    _40 = _39 * np.array(float(1 / 2))\n",
+      "    _41 = np.sqrt(_40)\n",
+      "    _42 = _8 - _15\n",
+      "    _43 = _41 * _42.T\n",
+      "    _44 = _43.T @ _38\n",
+      "    _45 = np.linalg.svd(_44, full_matrices=False)\n",
+      "    _46 = np.array(0.0001) * _45[1][0]\n",
+      "    _47 = _45[1] > _46\n",
+      "    _48 = _47.astype(np.dtype(np.int32))\n",
+      "    _49 = np.sum(_48)\n",
+      "    _50 = _38 @ _45[2].T[:, :_49,]\n",
+      "    _51 = _16 @ _50\n",
+      "    return _51[:, :2,]\n",
       "\n"
      ]
     }
    ],
    "source": [
+    "from egglog.exp.array_api_program_gen import *\n",
+    "import numpy as np\n",
     "import inspect\n",
     "\n",
+    "\n",
+    "egraph = EGraph()\n",
+    "fn_program = egraph.let(\n",
+    "    \"fn_program\",\n",
+    "    EvalProgram(ndarray_function_two_program(simplified_res, NDArray.var(\"X\"), NDArray.var(\"y\")), {\"np\": np}),\n",
+    ")\n",
+    "egraph.run(array_api_program_gen_schedule)\n",
+    "fn = egraph.extract(fn_program.as_py_object).value\n",
+    "\n",
     "print(inspect.getsource(fn))"
    ]
   },
@@ -1527,7 +1646,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "From there we can complete our work, by optimizing with numba and we can call with our original values:\n"
+    "From there we can complete our work, by optimizing with numba and we can call with our original values:"
    ]
   },
   {
@@ -1539,20 +1658,163 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/var/folders/xn/05ktz3056kqd9n8frgd6236h0000gn/T/egglog-9b40af4a-3b8a-4996-a78a-fd6284dbf541.py:56: NumbaPerformanceWarning: '@' is faster on contiguous arrays, called on (Array(float64, 2, 'C', False, aligned=True), Array(float64, 2, 'A', False, aligned=True))\n",
-      "  _45 = _33 @ _40[2].T[:, :_44]\n"
+      "/var/folders/xn/05ktz3056kqd9n8frgd6236h0000gn/T/egglog-39d7fedf-0738-45c9-8c02-1e5921b60da3.py:62: NumbaPerformanceWarning: '@' is faster on contiguous arrays, called on (Array(float64, 2, 'C', False, aligned=True), Array(float64, 2, 'A', False, aligned=True))\n",
+      "  _50 = _38 @ _45[2].T[:, :_49,]\n"
      ]
     },
     {
      "data": {
       "text/plain": [
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-       "       [ 0.63661245],\n",
-       "       [-1.603293  ],\n",
-       "       ...,\n",
-       "       [-1.1506433 ],\n",
-       "       [ 0.71687176],\n",
-       "       [-1.51119579]])"
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+       "       [ 8.08189937e+00,  7.63392750e-01],\n",
+       "       [ 7.18676904e+00, -3.60986823e-01],\n",
+       "       [ 8.31444876e+00,  6.44953177e-01],\n",
+       "       [ 7.67196741e+00, -1.34893840e-01],\n",
+       "       [-1.45927545e+00,  2.85437643e-02],\n",
+       "       [-1.79770574e+00,  4.84385502e-01],\n",
+       "       [-2.41694888e+00, -9.27840307e-02],\n",
+       "       [-2.26247349e+00, -1.58725251e+00],\n",
+       "       [-2.54867836e+00, -4.72204898e-01],\n",
+       "       [-2.42996725e+00, -9.66132066e-01],\n",
+       "       [-2.44848456e+00,  7.95961954e-01],\n",
+       "       [-2.22666513e-01, -1.58467318e+00],\n",
+       "       [-1.75020123e+00, -8.21180130e-01],\n",
+       "       [-1.95842242e+00, -3.51563753e-01],\n",
+       "       [-1.19376031e+00, -2.63445570e+00],\n",
+       "       [-1.85892567e+00,  3.19006544e-01],\n",
+       "       [-1.15809388e+00, -2.64340991e+00],\n",
+       "       [-2.66605725e+00, -6.42504540e-01],\n",
+       "       [-3.78367218e-01,  8.66389312e-02],\n",
+       "       [-1.20117255e+00,  8.44373592e-02],\n",
+       "       [-2.76810246e+00,  3.21995363e-02],\n",
+       "       [-7.76854039e-01, -1.65916185e+00],\n",
+       "       [-3.49805433e+00, -1.68495616e+00],\n",
+       "       [-1.09042788e+00, -1.62658350e+00],\n",
+       "       [-3.71589615e+00,  1.04451442e+00],\n",
+       "       [-9.97610366e-01, -4.90530602e-01],\n",
+       "       [-3.83525931e+00, -1.40595806e+00],\n",
+       "       [-2.25741249e+00, -1.42679423e+00],\n",
+       "       [-1.25571326e+00, -5.46424197e-01],\n",
+       "       [-1.43755762e+00, -1.34424979e-01],\n",
+       "       [-2.45906137e+00, -9.35277280e-01],\n",
+       "       [-3.51848495e+00,  1.60588866e-01],\n",
+       "       [-2.58979871e+00, -1.74611728e-01],\n",
+       "       [ 3.07487884e-01, -1.31887146e+00],\n",
+       "       [-1.10669179e+00, -1.75225371e+00],\n",
+       "       [-6.05524589e-01, -1.94298038e+00],\n",
+       "       [-8.98703769e-01, -9.04940034e-01],\n",
+       "       [-4.49846635e+00, -8.82749915e-01],\n",
+       "       [-2.93397799e+00,  2.73791065e-02],\n",
+       "       [-2.10360821e+00,  1.19156767e+00],\n",
+       "       [-2.14258208e+00,  8.87797815e-02],\n",
+       "       [-2.47945603e+00, -1.94073927e+00],\n",
+       "       [-1.32552574e+00, -1.62869550e-01],\n",
+       "       [-1.95557887e+00, -1.15434826e+00],\n",
+       "       [-2.40157020e+00, -1.59458341e+00],\n",
+       "       [-2.29248878e+00, -3.32860296e-01],\n",
+       "       [-1.27227224e+00, -1.21458428e+00],\n",
+       "       [-2.93176055e-01, -1.79871509e+00],\n",
+       "       [-2.00598883e+00, -9.05418042e-01],\n",
+       "       [-1.18166311e+00, -5.37570242e-01],\n",
+       "       [-1.61615645e+00, -4.70103580e-01],\n",
+       "       [-1.42158879e+00, -5.51244626e-01],\n",
+       "       [ 4.75973788e-01, -7.99905482e-01],\n",
+       "       [-1.54948259e+00, -5.93363582e-01],\n",
+       "       [-7.83947399e+00,  2.13973345e+00],\n",
+       "       [-5.50747997e+00, -3.58139892e-02],\n",
+       "       [-6.29200850e+00,  4.67175777e-01],\n",
+       "       [-5.60545633e+00, -3.40738058e-01],\n",
+       "       [-6.85055995e+00,  8.29825394e-01],\n",
+       "       [-7.41816784e+00, -1.73117995e-01],\n",
+       "       [-4.67799541e+00, -4.99095015e-01],\n",
+       "       [-6.31692685e+00, -9.68980756e-01],\n",
+       "       [-6.32773684e+00, -1.38328993e+00],\n",
+       "       [-6.85281335e+00,  2.71758963e+00],\n",
+       "       [-4.44072512e+00,  1.34723692e+00],\n",
+       "       [-5.45009572e+00, -2.07736942e-01],\n",
+       "       [-5.66033713e+00,  8.32713617e-01],\n",
+       "       [-5.95823722e+00, -9.40175447e-02],\n",
+       "       [-6.75926282e+00,  1.60023206e+00],\n",
+       "       [-5.80704331e+00,  2.01019882e+00],\n",
+       "       [-5.06601233e+00, -2.62733839e-02],\n",
+       "       [-6.60881882e+00,  1.75163587e+00],\n",
+       "       [-9.17147486e+00, -7.48255067e-01],\n",
+       "       [-4.76453569e+00, -2.15573720e+00],\n",
+       "       [-6.27283915e+00,  1.64948141e+00],\n",
+       "       [-5.36071189e+00,  6.46120732e-01],\n",
+       "       [-7.58119982e+00, -9.80722934e-01],\n",
+       "       [-4.37150279e+00, -1.21297458e-01],\n",
+       "       [-5.72317531e+00,  1.29327553e+00],\n",
+       "       [-5.27915920e+00, -4.24582377e-02],\n",
+       "       [-4.08087208e+00,  1.85936572e-01],\n",
+       "       [-4.07703640e+00,  5.23238483e-01],\n",
+       "       [-6.51910397e+00,  2.96976389e-01],\n",
+       "       [-4.58371942e+00, -8.56815813e-01],\n",
+       "       [-6.22824009e+00, -7.12719638e-01],\n",
+       "       [-5.22048773e+00,  1.46819509e+00],\n",
+       "       [-6.80015000e+00,  5.80895175e-01],\n",
+       "       [-3.81515972e+00, -9.42985932e-01],\n",
+       "       [-5.10748966e+00, -2.13059000e+00],\n",
+       "       [-6.79671631e+00,  8.63090395e-01],\n",
+       "       [-6.52449599e+00,  2.44503527e+00],\n",
+       "       [-4.99550279e+00,  1.87768525e-01],\n",
+       "       [-3.93985300e+00,  6.14020389e-01],\n",
+       "       [-5.20383090e+00,  1.14476808e+00],\n",
+       "       [-6.65308685e+00,  1.80531976e+00],\n",
+       "       [-5.10555946e+00,  1.99218201e+00],\n",
+       "       [-5.50747997e+00, -3.58139892e-02],\n",
+       "       [-6.79601924e+00,  1.46068695e+00],\n",
+       "       [-6.84735943e+00,  2.42895067e+00],\n",
+       "       [-5.64500346e+00,  1.67771734e+00],\n",
+       "       [-5.17956460e+00, -3.63475041e-01],\n",
+       "       [-4.96774090e+00,  8.21140550e-01],\n",
+       "       [-5.88614539e+00,  2.34509051e+00],\n",
+       "       [-4.68315426e+00,  3.32033811e-01]])"
       ]
      },
      "execution_count": 13,
@@ -1623,7 +1885,7 @@
     "egraph = EGraph()\n",
     "egraph.register(fn.compile())\n",
     "egraph.run(program_gen_ruleset.saturate())\n",
-    "print(egraph.eval(fn.statements))"
+    "print(egraph.extract(fn.statements).value)"
    ]
   },
   {
@@ -1642,7805 +1904,17 @@
    "outputs": [
     {
      "data": {
-      "image/svg+xml": [
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "outer_cluster_9\n",
-       "\n",
-       "\n",
-       "cluster_9\n",
-       "\n",
-       "\n",
-       "\n",
-       "outer_cluster_6\n",
-       "\n",
-       "\n",
-       "cluster_6\n",
-       "\n",
-       "\n",
-       "\n",
-       "outer_cluster_13\n",
-       "\n",
-       "\n",
-       "cluster_13\n",
-       "\n",
-       "\n",
-       "\n",
-       "outer_cluster_2\n",
-       "\n",
-       "\n",
-       "cluster_2\n",
-       "\n",
-       "\n",
-       "\n",
-       "outer_cluster_12\n",
-       "\n",
-       "\n",
-       "cluster_12\n",
-       "\n",
-       "\n",
-       "\n",
-       "outer_cluster_10\n",
-       "\n",
-       "\n",
-       "cluster_10\n",
-       "\n",
-       "\n",
-       "\n",
-       "outer_cluster_5\n",
-       "\n",
-       "\n",
-       "cluster_5\n",
-       "\n",
-       "\n",
-       "\n",
-       "outer_cluster_11\n",
-       "\n",
-       "\n",
-       "cluster_11\n",
-       "\n",
-       "\n",
-       "\n",
-       "outer_cluster_0\n",
-       "\n",
-       "\n",
-       "cluster_0\n",
-       "\n",
-       "\n",
-       "\n",
-       "outer_cluster_4\n",
-       "\n",
-       "\n",
-       "cluster_4\n",
-       "\n",
-       "\n",
-       "\n",
-       "outer_cluster_15\n",
-       "\n",
-       "\n",
-       "cluster_15\n",
-       "\n",
-       "\n",
-       "\n",
-       "outer_cluster_3\n",
-       "\n",
-       "\n",
-       "cluster_3\n",
-       "\n",
-       "\n",
-       "\n",
-       "outer_cluster_16\n",
-       "\n",
-       "\n",
-       "cluster_16\n",
-       "\n",
-       "\n",
-       "\n",
-       "outer_cluster_8\n",
-       "\n",
-       "\n",
-       "cluster_8\n",
-       "\n",
-       "\n",
-       "\n",
-       "outer_cluster_1\n",
-       "\n",
-       "\n",
-       "cluster_1\n",
-       "\n",
-       "\n",
-       "\n",
-       "outer_cluster_7\n",
-       "\n",
-       "\n",
-       "cluster_7\n",
-       "\n",
-       "\n",
-       "\n",
-       "outer_cluster_14\n",
-       "\n",
-       "\n",
-       "cluster_14\n",
-       "\n",
-       "\n",
-       "\n",
-       "outer_cluster_bool-0\n",
-       "\n",
-       "\n",
-       "cluster_bool-0\n",
-       "\n",
-       "\n",
-       "\n",
-       "outer_cluster_i64-0\n",
-       "\n",
-       "\n",
-       "cluster_i64-0\n",
-       "\n",
-       "\n",
-       "\n",
-       "outer_cluster_Program_next_sym-9249358851075372135-value\n",
-       "\n",
-       "\n",
-       "cluster_Program_next_sym-9249358851075372135-value\n",
-       "\n",
-       "\n",
-       "\n",
-       "outer_cluster_Program_next_sym-5040379952546458196-value\n",
-       "\n",
-       "\n",
-       "cluster_Program_next_sym-5040379952546458196-value\n",
-       "\n",
-       "\n",
-       "\n",
-       "outer_cluster_Program_next_sym-2546176790493825425-value\n",
-       "\n",
-       "\n",
-       "cluster_Program_next_sym-2546176790493825425-value\n",
-       "\n",
-       "\n",
-       "\n",
-       "outer_cluster_Program_next_sym-8417957797057827878-value\n",
-       "\n",
-       "\n",
-       "cluster_Program_next_sym-8417957797057827878-value\n",
-       "\n",
-       "\n",
-       "\n",
-       "outer_cluster_Program_next_sym-3377577844511369682-value\n",
-       "\n",
-       "\n",
-       "cluster_Program_next_sym-3377577844511369682-value\n",
-       "\n",
-       "\n",
-       "\n",
-       "outer_cluster_Program_next_sym-5871781006564002453-value\n",
-       "\n",
-       "\n",
-       "cluster_Program_next_sym-5871781006564002453-value\n",
-       "\n",
-       "\n",
-       "\n",
-       "outer_cluster_Program_next_sym-4208978898528913939-value\n",
-       "\n",
-       "\n",
-       "cluster_Program_next_sym-4208978898528913939-value\n",
-       "\n",
-       "\n",
-       "\n",
-       "outer_cluster_Program_next_sym-1714775736476281168-value\n",
-       "\n",
-       "\n",
-       "cluster_Program_next_sym-1714775736476281168-value\n",
-       "\n",
-       "\n",
-       "\n",
-       "outer_cluster_Program_expr-11743562013128004906-value\n",
-       "\n",
-       "\n",
-       "cluster_Program_expr-11743562013128004906-value\n",
-       "\n",
-       "\n",
-       "\n",
-       "outer_cluster_Program_expr-9249358851075372135-value\n",
-       "\n",
-       "\n",
-       "cluster_Program_expr-9249358851075372135-value\n",
-       "\n",
-       "\n",
-       "\n",
-       "outer_cluster_Program_expr-17615343019692007359-value\n",
-       "\n",
-       "\n",
-       "cluster_Program_expr-17615343019692007359-value\n",
-       "\n",
-       "\n",
-       "\n",
-       "outer_cluster_String-12969792886956269196\n",
-       "\n",
-       "\n",
-       "cluster_String-12969792886956269196\n",
-       "\n",
-       "\n",
-       "\n",
-       "outer_cluster_String-11226098287981005201\n",
-       "\n",
-       "\n",
-       "cluster_String-11226098287981005201\n",
-       "\n",
-       "\n",
-       "\n",
-       "outer_cluster_Program_expr-10080759905092916392-value\n",
-       "\n",
-       "\n",
-       "cluster_Program_expr-10080759905092916392-value\n",
-       "\n",
-       "\n",
-       "\n",
-       "outer_cluster_Program_expr-5871781006564002453-value\n",
-       "\n",
-       "\n",
-       "cluster_Program_expr-5871781006564002453-value\n",
-       "\n",
-       "\n",
-       "\n",
-       "outer_cluster_Program_expr-2546176790493825425-value\n",
-       "\n",
-       "\n",
-       "cluster_Program_expr-2546176790493825425-value\n",
-       "\n",
-       "\n",
-       "\n",
-       "outer_cluster_Program_expr-14289738803621830331-value\n",
-       "\n",
-       "\n",
-       "cluster_Program_expr-14289738803621830331-value\n",
-       "\n",
-       "\n",
-       "\n",
-       "outer_cluster_Program_expr-4208978898528913939-value\n",
-       "\n",
-       "\n",
-       "cluster_Program_expr-4208978898528913939-value\n",
-       "\n",
-       "\n",
-       "\n",
-       "outer_cluster_Program_expr-5040379952546458196-value\n",
-       "\n",
-       "\n",
-       "cluster_Program_expr-5040379952546458196-value\n",
-       "\n",
-       "\n",
-       "\n",
-       "outer_cluster_Program_expr-1714775736476281168-value\n",
-       "\n",
-       "\n",
-       "cluster_Program_expr-1714775736476281168-value\n",
-       "\n",
-       "\n",
-       "\n",
-       "outer_cluster_Program_expr-10912160959110460649-value\n",
-       "\n",
-       "\n",
-       "cluster_Program_expr-10912160959110460649-value\n",
-       "\n",
-       "\n",
-       "\n",
-       "outer_cluster_Program_expr-8417957797057827878-value\n",
-       "\n",
-       "\n",
-       "cluster_Program_expr-8417957797057827878-value\n",
-       "\n",
-       "\n",
-       "\n",
-       "outer_cluster_Program_expr-16783941965674463102-value\n",
-       "\n",
-       "\n",
-       "cluster_Program_expr-16783941965674463102-value\n",
-       "\n",
-       "\n",
-       "\n",
-       "outer_cluster_String-11355304735691241393\n",
-       "\n",
-       "\n",
-       "cluster_String-11355304735691241393\n",
-       "\n",
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-       "\n",
-       "\n",
-       "Program_next_sym-9249358851075372135-value\n",
-       "\n",
-       "\n",
-       "1\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "Program_next_sym-4208978898528913939\n",
-       "\n",
-       "\n",
-       "·.next_sym\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "Program_next_sym-4208978898528913939-value\n",
-       "\n",
-       "\n",
-       "0\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "Program_next_sym-5040379952546458196\n",
-       "\n",
-       "\n",
-       "·.next_sym\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "Program_next_sym-5040379952546458196-value\n",
-       "\n",
-       "\n",
-       "0\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "Program_next_sym-16783941965674463102\n",
-       "\n",
-       "\n",
-       "·.next_sym\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "Program_next_sym-16783941965674463102-value\n",
-       "\n",
-       "\n",
-       "0\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "Program_next_sym-17615343019692007359\n",
-       "\n",
-       "\n",
-       "·.next_sym\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "Program_next_sym-17615343019692007359-value\n",
-       "\n",
-       "\n",
-       "0\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "Program_next_sym-15952540911656918845\n",
-       "\n",
-       "\n",
-       "·.next_sym\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "Program_next_sym-15952540911656918845-value\n",
-       "\n",
-       "\n",
-       "1\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "Program_next_sym-8417957797057827878\n",
-       "\n",
-       "\n",
-       "·.next_sym\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "Program_next_sym-8417957797057827878-value\n",
-       "\n",
-       "\n",
-       "1\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "Program_next_sym-3377577844511369682\n",
-       "\n",
-       "\n",
-       "·.next_sym\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "Program_next_sym-3377577844511369682-value\n",
-       "\n",
-       "\n",
-       "1\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "Program_next_sym-5871781006564002453\n",
-       "\n",
-       "\n",
-       "·.next_sym\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "Program_next_sym-5871781006564002453-value\n",
-       "\n",
-       "\n",
-       "0\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n",
-       "\n"
-      ],
+      "application/vnd.jupyter.widget-view+json": {
+       "model_id": "2a45463df1ca40a2ac30f6f50da2b7b4",
+       "version_major": 2,
+       "version_minor": 1
+      },
       "text/plain": [
-       "EGraph(_flatted_deps=[], default_ruleset=None)"
+       "VisualizerWidget(egraphs=['{\"nodes\":{\"function-0-Program_statement\":{\"op\":\"·.statement\",\"children\":[\"function-…"
       ]
      },
-     "execution_count": 15,
      "metadata": {},
-     "output_type": "execute_result"
+     "output_type": "display_data"
     }
    ],
    "source": [
@@ -9582,7 +2056,7 @@
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": "Python 3 (ipykernel)",
+   "display_name": "egglog",
    "language": "python",
    "name": "python3"
   },
@@ -9596,7 +2070,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.12.1"
+   "version": "3.13.3"
   }
  },
  "nbformat": 4,
diff --git a/docs/explanation/indexing_pushdown.ipynb b/docs/explanation/indexing_pushdown.ipynb
index bea42460..508e7a8c 100644
--- a/docs/explanation/indexing_pushdown.ipynb
+++ b/docs/explanation/indexing_pushdown.ipynb
@@ -257,7 +257,7 @@
     "\n",
     "from egglog.exp.array_api import *\n",
     "\n",
-    "egraph = EGraph([array_api_module])\n",
+    "egraph = EGraph()\n",
     "\n",
     "\n",
     "@egraph.register\n",
@@ -267,6 +267,7 @@
     "\n",
     "res = abs(NDArray.var(\"x\"))[NDArray.var(\"idx\")]\n",
     "egraph.register(res)\n",
+    "egraph.run(array_api_schedule)\n",
     "egraph.run(100)\n",
     "egraph.display()\n",
     "\n",
@@ -720,10 +721,10 @@
     }
    ],
    "source": [
-    "egraph = EGraph([array_api_module])\n",
+    "egraph = EGraph()\n",
     "\n",
     "\n",
-    "@egraph.function(cost=0)\n",
+    "@function(cost=0)\n",
     "def value_abs(v: Value) -> Value:\n",
     "    \"\"\"Absolute value of a scalar value\"\"\"\n",
     "\n",
@@ -738,7 +739,7 @@
     "    yield rewrite(abs(x).index(ti)).to(value_abs(x.index(ti)))\n",
     "\n",
     "\n",
-    "@egraph.function(cost=0)\n",
+    "@function(cost=0)\n",
     "def translate_index(x: NDArray, y: IndexKey, z: TupleInt) -> TupleInt:\n",
     "    \"\"\"Translates indexing `z` into `x[y]` into an indexing directly into `x`\"\"\"\n",
     "\n",
@@ -752,12 +753,13 @@
     "    # Shape is more complicated and we will omit for now\n",
     "\n",
     "\n",
-    "@egraph.function\n",
+    "@function\n",
     "def an_index() -> TupleInt:\n",
     "    \"\"\"Some index into an array\"\"\"\n",
     "\n",
     "\n",
     "egraph.register(res.shape, res.dtype, res.index(an_index()))\n",
+    "egraph.run(array_api_schedule)\n",
     "egraph.run(100)\n",
     "egraph.display()\n",
     "\n",
diff --git a/docs/explanation/pldi_2023_presentation.ipynb b/docs/explanation/pldi_2023_presentation.ipynb
index 94acf518..508131db 100644
--- a/docs/explanation/pldi_2023_presentation.ipynb
+++ b/docs/explanation/pldi_2023_presentation.ipynb
@@ -429,7 +429,7 @@
    "source": [
     "## Open Source Data Science Ecosystem in Python\n",
     "\n",
-    "> The term “ecosystem” is often used to describe the modern open-source scientific software. In biology, the term “ecosystem” is defined as a biological community of interacting organisms and their physical environment. Modern open-source scientific software development occurs in a similarly interconnected and interoperable fashion.\n",
+    "> The term \u201cecosystem\u201d is often used to describe the modern open-source scientific software. In biology, the term \u201cecosystem\u201d is defined as a biological community of interacting organisms and their physical environment. Modern open-source scientific software development occurs in a similarly interconnected and interoperable fashion.\n",
     "\n",
     "from [Jupyter Meets the Earth: Ecosystem](https://jupytearth.org/jupyter-resources/introduction/ecosystem.html)\n",
     "\n",
@@ -2996,7 +2996,6 @@
     "egraph = EGraph()\n",
     "\n",
     "\n",
-    "@egraph.class_\n",
     "class Num(Expr):\n",
     "    @classmethod\n",
     "    def var(cls, name: StringLike) -> Num: ...\n",
@@ -4927,4 +4926,4 @@
  },
  "nbformat": 4,
  "nbformat_minor": 5
-}
+}
\ No newline at end of file
diff --git a/docs/reference/high-level.md b/docs/reference/high-level.md
index 5872ec77..8677b9bd 100644
--- a/docs/reference/high-level.md
+++ b/docs/reference/high-level.md
@@ -23,7 +23,6 @@ from egglog import *
 
 egraph = EGraph()
 
-@egraph.class_
 class Math(Expr):
     def __init__(self, value: i64Like) -> None:
         ...
diff --git a/docs/reference/python-integration.md b/docs/reference/python-integration.md
index 466ebc0a..2789a51d 100644
--- a/docs/reference/python-integration.md
+++ b/docs/reference/python-integration.md
@@ -204,8 +204,8 @@ Alongside this, we support a function `dict_update` method, which can allow you
 def my_add(a, b):
     return a + b
 
-amended_globals = PyObject(globals()).dict_update("one", 1)
-evalled = py_eval("my_add(one,  2)", locals(), amended_globals)
+amended_globals = PyObject({"my_add": my_add}).dict_update("one", 1)
+evalled = py_eval("my_add(one,  2)", {}, amended_globals)
 assert EGraph().extract(evalled).value == 3
 ```
 
diff --git a/docs/tutorials/getting-started.ipynb b/docs/tutorials/getting-started.ipynb
index 0644eae4..489c3dbe 100644
--- a/docs/tutorials/getting-started.ipynb
+++ b/docs/tutorials/getting-started.ipynb
@@ -83,7 +83,6 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "@egraph.class_\n",
     "class Dim(Expr):\n",
     "    \"\"\"\n",
     "    A dimension of a matix.\n",
@@ -108,8 +107,8 @@
     "tags": []
    },
    "source": [
-    "As you can see, you must wrap any class with the `egraph.class_` to register\n",
-    "it with the egraph and be able to use it like a Python class.\n",
+    "As you can see, you can define a class that inherits from `Expr` to create\n",
+    "a new type in the e-graph. The class will be automatically registered when you use it.\n",
     "\n",
     "### Testing in a notebook\n",
     "\n",
@@ -117,7 +116,8 @@
     "\n",
     "```python\n",
     "from matrix import *\n",
-    "```\n"
+    "```\n",
+    ""
    ]
   },
   {
@@ -408,7 +408,8 @@
     }
    ],
    "source": [
-    "egraph.simplify(res, 10)"
+    "egraph.run(10)\n",
+    "egraph.extract(res)"
    ]
   },
   {
@@ -429,7 +430,6 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "@egraph.class_\n",
     "class Matrix(Expr):\n",
     "    @classmethod\n",
     "    def identity(cls, dim: Dim) -> Matrix:\n",
@@ -459,7 +459,7 @@
     "        \"\"\"\n",
     "\n",
     "\n",
-    "@egraph.function\n",
+    "@function\n",
     "def kron(a: Matrix, b: Matrix) -> Matrix:\n",
     "    \"\"\"\n",
     "    Kronecker product of two matrices.\n",
@@ -530,8 +530,9 @@
     "x = Matrix.identity(Dim.named(\"x\"))\n",
     "y = Matrix.identity(Dim.named(\"y\"))\n",
     "x_mult_y = x @ y\n",
-    "print(egraph.simplify(x_mult_y.ncols(), 10))\n",
-    "print(egraph.simplify(x_mult_y.nrows(), 10))"
+    "egraph.run(10)\n",
+    "print(egraph.extract(x_mult_y.ncols()))\n",
+    "print(egraph.extract(x_mult_y.nrows()))"
    ]
   },
   {
@@ -1096,7 +1097,8 @@
     ")\n",
     "# Create an example which should equal the kronecker product of A and B\n",
     "ex1 = kron(Matrix.identity(n), B) @ kron(A, Matrix.identity(m))\n",
-    "egraph.simplify(ex1, 20)"
+    "egraph.run(20)\n",
+    "egraph.extract(ex1)"
    ]
   },
   {
@@ -1209,7 +1211,8 @@
    ],
    "source": [
     "ex2 = kron(Matrix.identity(p), C) @ kron(A, Matrix.identity(m))\n",
-    "egraph.simplify(ex2, 20)"
+    "egraph.run(20)\n",
+    "egraph.extract(ex2)"
    ]
   },
   {
@@ -1243,4 +1246,4 @@
  },
  "nbformat": 4,
  "nbformat_minor": 5
-}
+}
\ No newline at end of file
diff --git a/docs/tutorials/tut_2_datalog.py b/docs/tutorials/tut_2_datalog.py
index f1c479dd..66b2c942 100644
--- a/docs/tutorials/tut_2_datalog.py
+++ b/docs/tutorials/tut_2_datalog.py
@@ -150,7 +150,7 @@ def _(a: i64, b: i64, c: i64, ab: i64, bc: i64) -> Iterable[RewriteOrRule]:
 # Let's run our rules and check we get the desired shortest path
 
 egraph.run(run().saturate())
-egraph.check(path_len(1, 3) == 20)
+egraph.check(eq(path_len(1, 3)).to(20))
 egraph
 
 
diff --git a/python/egglog/egraph.py b/python/egglog/egraph.py
index 819248d0..a0b1cbd5 100644
--- a/python/egglog/egraph.py
+++ b/python/egglog/egraph.py
@@ -1042,9 +1042,9 @@ def extract_multiple(self, expr: BASE_EXPR, n: int) -> list[BASE_EXPR]:
         return [cast("BASE_EXPR", RuntimeExpr.__from_values__(self.__egg_decls__, expr)) for expr in new_exprs]
 
     def _run_extract(self, expr: RuntimeExpr, n: int) -> bindings._CommandOutput:
-        expr = self._state.typed_expr_to_egg(expr.__egg_typed_expr__)
+        egg_expr = self._state.typed_expr_to_egg(expr.__egg_typed_expr__)
         # If we have defined any cost tables use the custom extraction
-        args = (expr, bindings.Lit(span(2), bindings.Int(n)))
+        args = (egg_expr, bindings.Lit(span(2), bindings.Int(n)))
         if self._state.cost_callables:
             cmd: bindings._Command = bindings.UserDefined(span(2), "extract", list(args))
         else:
@@ -1052,7 +1052,7 @@ def _run_extract(self, expr: RuntimeExpr, n: int) -> bindings._CommandOutput:
         try:
             return self._egraph.run_program(cmd)[0]
         except BaseException as e:
-            e.add_note("Extracting: " + str(expr))
+            e.add_note("while extracting expr:\n" + str(expr))
             raise
 
     def push(self) -> None:
diff --git a/src/egraph.rs b/src/egraph.rs
index 76949074..a8b253e2 100644
--- a/src/egraph.rs
+++ b/src/egraph.rs
@@ -64,20 +64,19 @@ impl EGraph {
             cmds_str = cmds_str + &cmd.to_string() + "\n";
         }
         info!("Running commands:\n{}", cmds_str);
-        let res = py.detach(|| {
-            self.egraph.run_program(commands).map_err(|e| {
-                WrappedError::Egglog(e, "\nWhen running commands:\n".to_string() + &cmds_str)
-            })
-        });
-        if res.is_ok()
-            && let Some(cmds) = &mut self.cmds
-        {
-            cmds.push_str(&cmds_str);
-        }
+        let res = py.detach(|| self.egraph.run_program(commands));
         if let Some(err) = PyErr::take(py) {
             return Err(WrappedError::Py(err));
         }
-        res.map(|xs| xs.iter().map(|o| o.into()).collect())
+        match res {
+            Err(e) => Err(WrappedError::Egglog(e)),
+            Ok(outputs) => {
+                if let Some(cmds) = &mut self.cmds {
+                    cmds.push_str(&cmds_str);
+                }
+                Ok(outputs.into_iter().map(|o| o.into()).collect())
+            }
+        }
     }
 
     /// Returns the text of the commands that have been run so far, if `record` was passed.
@@ -133,7 +132,7 @@ impl EGraph {
             self.egraph
                 .eval_expr(&expr)
                 .map(|(s, v)| (s.name().to_string(), Value(v)))
-                .map_err(|e| WrappedError::Egglog(e, format!("\nWhen evaluating expr: {expr}")))
+                .map_err(|e| WrappedError::Egglog(e))
         });
         if let Some(err) = PyErr::take(py) {
             return Err(WrappedError::Py(err));
diff --git a/src/error.rs b/src/error.rs
index 8b468e11..5e225975 100644
--- a/src/error.rs
+++ b/src/error.rs
@@ -21,8 +21,7 @@ impl EggSmolError {
 // https://pyo3.rs/latest/function/error_handling.html#foreign-rust-error-types
 // TODO: Create classes for each of these errors
 pub enum WrappedError {
-    // Add additional context for egglog error
-    Egglog(egglog::Error, String),
+    Egglog(egglog::Error),
     ParseError(egglog::ast::ParseError),
     Py(PyErr),
 }
@@ -31,9 +30,7 @@ pub enum WrappedError {
 impl From for PyErr {
     fn from(error: WrappedError) -> Self {
         match error {
-            WrappedError::Egglog(error, str) => {
-                PyErr::new::(error.to_string() + &str)
-            }
+            WrappedError::Egglog(error) => PyErr::new::(error.to_string()),
             WrappedError::Py(error) => error,
             WrappedError::ParseError(error) => PyErr::new::(error.to_string()),
         }
@@ -43,7 +40,7 @@ impl From for PyErr {
 // Convert from an egglog::Error to a WrappedError
 impl From for WrappedError {
     fn from(other: egglog::Error) -> Self {
-        Self::Egglog(other, String::new())
+        Self::Egglog(other)
     }
 }