sreval

An evaluator for symbolic regression: triple-equivalence testing that reports its own failure rate.

Why this exists

Symbolic regression is supposed to find the equation, not merely a function that fits. The published benchmark results show those are very different achievements: a method can score above 0.999 on a coefficient of determination while recovering the correct expression structure zero percent of the time. An evaluation that reports only accuracy cannot tell a discovery from a good curve fit.

Testing structure directly is the fix, but no single structural test is reliable:

So sreval runs all three, reports them separately, reports whether they agreed, and publishes the symbolic-test failure rate as a first-class number. That last one is the contribution: it is a property of the measurement apparatus that the field currently absorbs silently into the scores of the methods being measured.

Install

pip install sreval               # numpy only
pip install "sreval[symbolic]"   # adds sympy, needed for the symbolic test

Use

import numpy as np
from sreval import check, summarise

verdict = check(
    candidate_infix="x*(a + b)",
    truth_infix="x*a + x*b",
    variables=["x", "a", "b"],
    candidate_fn=lambda X: X[:, 0] * (X[:, 1] + X[:, 2]),
    truth_fn=lambda X: X[:, 0] * X[:, 1] + X[:, 0] * X[:, 2],
    box=[(-3.0, 3.0), (-3.0, 3.0), (-3.0, 3.0)],
    candidate_tokens=["mul", "v0", "add", "v1", "v2"],
    truth_tokens=["add", "mul", "v0", "v1", "mul", "v0", "v2"],
)

verdict.recovered              # True: an algebraic rewrite of the same expression
verdict.agreed                 # True: the symbolic and numerical tests concur
verdict.structural.distance    # graded and non-zero: written differently

report = summarise([verdict])
report.symbolic_failure_rate   # the number nobody else publishes
report.notes                   # plain-language statements of what the rates mean

Accuracy and recovery are reported separately, always

from sreval import accuracy_solution, description_length

accuracy_solution is named at length on purpose. An accuracy solution is not a recovery, and the gap between those two rates is the measurement this package was built to expose. Nothing in the API merges them for you.

description_length is the recommended rule for picking one point off a Pareto front. Selecting the most accurate member reproduces the field's headline failure, because the most accurate member of a front is routinely the most over-parameterised one.

Scope

• It does not perform symbolic regression. It evaluates results from any engine.
• It does not decide whether a discovered equation is true. Fitting is not discovering, and no equivalence test changes that.
• The structural distance is a sequence edit distance over the pre-order traversal, not a full tree edit distance. The former is O(n*m), the latter O(n^2 m^2), and at the expression sizes symbolic regression actually produces the two agree closely enough that the extra cost buys nothing. This is stated because the number is reported, and a reported metric with an implicit definition is not reproducible.

Provenance

Written from published specifications. The widely used reference implementation of this evaluation protocol is GPL-3.0 licensed and no part of it is reproduced here, which is what allows this package to be MIT.

Built for SymLab, a public research lab on symbolic regression, and extracted as a standalone package because the evaluation problem is not specific to that lab.

Developed by Felipe Santibanez-Leal.