# Improving Genetic Programming for Symbolic Regression with Equality Graphs

arXiv: https://arxiv.org/abs/2501.17848 · HTML: https://mlsanity.com/paper/2501.17848/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 41 references that are in the map.
- First posted on arXiv 29 Jan 2025.

## Builds on (most cited first, 10 of 10)

- [AI Feynman: a Physics-Inspired Method for Symbolic Regression](https://mlsanity.com/paper/1905.11481/) (2019)
- [Contemporary Symbolic Regression Methods and their Relative Performance](https://mlsanity.com/paper/2107.14351/) (2021)
- [Symbolic Regression is NP-hard](https://mlsanity.com/paper/2207.01018/) (2022)
- [Shape-constrained Symbolic Regression -- Improving Extrapolation with Prior Knowledge](https://mlsanity.com/paper/2103.15624/) (2021)
- [The Inefficiency of Genetic Programming for Symbolic Regression](https://mlsanity.com/paper/2404.17292/) (2024)
- [Hash-Based Tree Similarity and Simplification in Genetic Programming for Symbolic Regression](https://mlsanity.com/paper/2107.10640/) (2021)
- [Phenotype Search Trajectory Networks for Linear Genetic Programming](https://mlsanity.com/paper/2211.08516/) (2022)
- [Unit-Aware Genetic Programming for the Development of Empirical Equations](https://mlsanity.com/paper/2405.18896/) (2024)
- [Inexact Simplification of Symbolic Regression Expressions with Locality-sensitive Hashing](https://mlsanity.com/paper/2404.05898/) (2024)
- [Online Diversity Control in Symbolic Regression via a Fast Hash-based Tree Similarity Measure](https://mlsanity.com/paper/1902.00882/) (2019)

## Built on by (most cited first, 5 of 5)

- [Bayesian Symbolic Regression via Posterior Sampling](https://mlsanity.com/paper/2512.10849/) (2025)
- [EGG-SR: Embedding Symbolic Equivalence into Symbolic Regression via Equality Graph](https://mlsanity.com/paper/2511.05849/) (2025)
- [Equality Graph Assisted Symbolic Regression](https://mlsanity.com/paper/2511.01009/) (2025)
- [Exploring Multi-view Symbolic Regression methods in physical sciences](https://mlsanity.com/paper/2509.10500/) (2025)
- [Symbolic Regression for Shared Expressions: Introducing Partial Parameter Sharing](https://mlsanity.com/paper/2601.04051/) (2026)

## Abstract (arXiv)

The search for symbolic regression models with genetic programming (GP) has a tendency of revisiting expressions in their original or equivalent forms. Repeatedly evaluating equivalent expressions is inefficient, as it does not immediately lead to better solutions. However, evolutionary algorithms require diversity and should allow the accumulation of inactive building blocks that can play an important role at a later point. The equality graph is a data structure capable of compactly storing expressions and their equivalent forms allowing an efficient verification of whether an expression has been visited in any of their stored equivalent forms. We exploit the e-graph to adapt the subtree operators to reduce the chances of revisiting expressions. Our adaptation, called eggp, stores every visited expression in the e-graph, allowing us to filter out from the available selection of subtrees all the combinations that would create already visited expressions. Results show that, for small expressions, this approach improves the performance of a simple GP algorithm to compete with PySR and Operon without increasing computational cost. As a highlight, eggp was capable of reliably delivering short and at the same time accurate models for a selected set of benchmarks from SRBench and a set of real-world datasets.