simplipy 0.4.1

Efficient Simplification of Mathematical Expressions

SimpliPy:
Efficient Simplification of Mathematical Expressions

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

As of 0.3.0 the inline phase (simplify, conversions, validation) is a compiled Rust extension (simplipy._core). 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 unavailable at runtime, the package transparently falls back to a slower pure-Python implementation.

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

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 = 2025,
    publisher = {GitHub},
    version = {0.3.1},
    url = {https://github.com/psaegert/simplipy}
}