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("acj-4-3", install=True)   # a published ruleset artifact

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

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

Token input returns the engine's native tagged form by default (n-ary +/* bags are delimited: <add> ... </add>, <mul> ... </mul>; tagged output is accepted back as input). The form parameter selects a different projection of the same canonical answer:

expr = ('/', '<constant>', '*', '/', '*', 'x3', '<constant>', 'x3', 'log', 'x3')

engine.simplify(expr, form='infix')      # the pretty rendering (a str)
# > '<constant>/log(x3)'

engine.simplify(expr, form='explicit')   # binary prefix -- what is_valid / prefix_to_infix read
# > ('/', '<constant>', 'log', '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 (measured at 0.11.0), large certificate-bearing rulesets simplify ~59× faster than 0.5.0 and certificate-free rulesets ~2.3× faster; see the CHANGELOG for details. Since 0.7.0 there is a single compiled engine line; the published ruleset artifacts (acj-2-1, acj-3-2, acj-4-3, …) are the distinguishing factor between engines. Rule application always considers every pattern in the loaded artifact (the former max_pattern_length knob was removed in 0.10.0). (To reproduce the historical dev_7-3 / v23.0-era behavior byte-for-byte, install simplipy<=0.6.0.)

Simplification time and ratio ECDFs: SimpliPy 0.11.0 vs SymPy across three axes (mined rulesets, safe vs aggressive, search budget) on 64k Lample-Charton expressions from the Flash-ANSR v23.0 prior

Empirical Cumulative Distribution Functions (ECDFs) of simplification wall-clock time (top row) and simplification ratio |simp| / |orig| in prefix tokens (bottom row, inset: zoom on the low-ratio tail), over 65,536 randomly generated Lample-Charton expressions sampled from the Flash-ANSR v23.0 training prior (0 to 17 unique variables, 1 to 35 symbols [Saegert & Köthe 2026]). Three axes vary SimpliPy (green) while SymPy [Meurer et al. 2017] (orange ratio=None / red ratio=1) is the fixed reference: Mined Rulesets — the 2-1/3-2/4-3 ruleset artifacts, every pattern active (darker = larger); Safe vs Aggressive — 4-3 in the deployed SOUND mode vs the training-only LOSSY mode; Search Budget — 4-3 SOUND at node budgets 1 to 48. SimpliPy is timed per call (perf_counter, gc off); SymPy is given each <constant> as a free symbol and simplified symbolically inside a per-expression worker with a 1 s timeout, then scored by its native prefix length; SymPy's workers run 24-wide while SimpliPy is timed single-threaded. Expressions SymPy does not finish inside its budget are scored as what they are — infinite time, ratio 1 (not simplified) — and stay in the denominator, so its time curve plateaus at the fraction it completed and its ratio curve carries a step at exactly 1; renormalising over only its successes would inflate its low-ratio tail. The measured quantities are the two ECDFs; the plot, not this caption, reports what they show.

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 = {0.12.0},
    url = {https://github.com/psaegert/simplipy}
}

Project links

Data verified by PyPI on Aug 8, 2026
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  • Released:
Newer release available (0.14.6)

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Credits

Author: Paul Saegert

GitHub Statistics

Data verified by PyPI on Aug 8, 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
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Requires

Python >=3.11

Provides Extra

dev torch

Tags

symbolic-regression simplification expression prefix rewriting rust

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