SimpliPy:
Efficient Simplification of Mathematical Expressions

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Publications

  • Saegert & Köthe 2026, Breaking the Simplification Bottleneck in Amortized Neural Symbolic Regression (preprint, under review) https://arxiv.org/abs/2602.08885

Usage

pip install simplipy

The compiled Rust extension (simplipy._core) is required: the inline phase (simplify, conversions, validation) runs on it exclusively, and there is no pure-Python fallback. Prebuilt wheels are published for Linux (x86_64/aarch64), macOS (x86_64/arm64) and Windows (x64) on CPython ≥ 3.11, so pip install simplipy does not compile anything for most users. Installing from the source distribution (an unsupported platform, or --no-binary) requires a Rust toolchain (rustup, MSRV 1.83). If the extension is missing at runtime, constructing an engine raises ImportError.

import simplipy as sp

engine = sp.SimpliPyEngine.load("dev_7-3", install=True)

# Simplify prefix expressions
engine.simplify(('/', '<constant>', '*', '/', '*', 'x3', '<constant>', 'x3', 'log', 'x3'))
# > ('/', '<constant>', 'log', 'x3')

# Simplify infix expressions
engine.simplify('x3 * sin(<constant> + 1) / (x3 * x3)')
# > '<constant> / x3'

Normalization

The root-exported normalize_skeleton, normalize_expression, and normalize_variable_token helpers (also available as simplipy.normalization) canonicalize a prefix token sequence so that two expressions that are "the same" up to variable renaming / constant values compare equal. They are pure-string helpers with no engine state, so consumers such as holdout matching and symbolic-recovery scoring share identical behavior by construction.

import simplipy as sp

# Skeleton form: variables -> x{n}, numeric literals -> <constant>
sp.normalize_skeleton(['+', 'v1', '2.5'])
# > ['+', 'x1', '<constant>']

# Expression form: variables canonicalized, numeric literals kept intact
sp.normalize_expression(['+', 'V1', '2.5'])
# > ['+', 'x1', '2.5']

# Classify / canonicalize a single token -> (normalized_token, is_variable)
sp.normalize_variable_token('X3')
# > ('x3', True)
sp.normalize_variable_token('sin')
# > ('sin', False)

More examples can be found in the documentation.

Performance

As of 0.6.0 the simplify hot path defers match-time certificates to completed matches (memoized generationally, never stopping memoization), memoizes whole fixpoint passes and rule-normal subtrees, and runs on interned token ids (~20× fewer allocations per call) — all at byte-identical outputs. On a 65,536-expression training-prior benchmark, large certificate-bearing rulesets simplify ~59× faster than 0.5.0 and certificate-free rulesets ~2.3× faster; see the CHANGELOG for details. As of 0.7.0 there is a single engine line; to reproduce the historical dev_7-3 / v23.0-era behavior byte-for-byte, install simplipy<=0.6.0. The comparison below dates from the 0.3.0 Rust cutover:

Simplification time and ratio ECDFs: SymPy vs SimpliPy (Python 0.2.15) vs SimpliPy (Rust 0.3.0)

Top row: SimpliPy 0.3.0 (Rust inline engine, green). Bottom row: SimpliPy 0.2.15 (pure Python, blue). Left: Empirical Cumulative Distribution Functions (ECDFs) of simplification wall-clock time across maximum pattern lengths Lmax = 0–7, with the SymPy [Meurer et al. 2017] baseline (orange, red). The Rust inline engine is roughly 5× to 100× faster than the pure-Python engine at the same Lmax (≈ 15× at Lmax = 4), and both are orders of magnitude faster than SymPy. Right: ECDF of the simplification ratio |τ ∗|/|τ | (inset: zoom on the low-ratio region where the Lmax curves separate); the Rust and Python engines produce near-identical simplification-ratio distributions, so the Rust rewrite buys the speed-up without sacrificing simplification quality. (0.3.0 does deliberately change behaviour on a small fraction of inputs via the conversion-quirk fixes and numeric folding; see the CHANGELOG.)
Source expressions are sampled with 0 to 17 unique variables and 1 to 35 symbols [Saegert & Köthe 2026]

Development

Setup

To set up the development environment, run the following commands:

pip install -e .[dev]
pre-commit install

Tests

Test the package with pytest:

pytest tests --cov src --cov-report html

or to skip integration tests,

pytest tests --cov src --cov-report html -m "not integration"

Citation

@misc{saegert2026breakingsimplificationbottleneckamortized,
  title   = {Breaking the Simplification Bottleneck in Amortized Neural Symbolic Regression},
  author  = {Paul Saegert and Ullrich Köthe},
  year    = {2026},
  eprint  = {2602.08885},
  archivePrefix =  {arXiv},
  primaryClass  = {cs.LG},
  url     = {https://arxiv.org/abs/2602.08885},
}

% Optionally
@software{simplipy-2025,
    author = {Paul Saegert},
    title = {Efficient Simplification of Mathematical Expressions},
    year = 2026,
    publisher = {GitHub},
    version = {0.7.0},
    url = {https://github.com/psaegert/simplipy}
}

Project links

Data verified by PyPI on Jul 24, 2026
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  • Released:
Newer release available (0.14.6)

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Avatar for psaegert from gravatar.com psaegert

Credits

Author: Paul Saegert

GitHub Statistics

Data verified by PyPI on Jul 24, 2026
The GitHub source repository was provided by the project maintainers and verified by PyPI at the time of upload. Stars, forks, and open issues/PRs are derived from that repository and have not been independently verified.

License expression

MIT
View SPDX License List

Requires

Python >=3.11

Provides Extra

dev torch

Tags

symbolic-regression simplification expression prefix rewriting rust

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