# Where are we now? A large benchmark study of recent symbolic regression methods

arXiv: https://arxiv.org/abs/1804.09331 · HTML: https://mlsanity.com/paper/1804.09331/

## Key facts

- Cited by 44 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Apr 2018.

## Built on by (most cited first, 30 of 44)

- [Rethinking Symbolic Regression Datasets and Benchmarks for Scientific Discovery](https://mlsanity.com/paper/2206.10540/) (2022)
- [A computational framework for physics-informed symbolic regression with straightforward integration of domain knowledge](https://mlsanity.com/paper/2209.06257/) (2022)
- [Shape-constrained Symbolic Regression -- Improving Extrapolation with Prior Knowledge](https://mlsanity.com/paper/2103.15624/) (2021)
- [AlphaForge: A Framework to Mine and Dynamically Combine Formulaic Alpha Factors](https://mlsanity.com/paper/2406.18394/) (2024)
- [Benchmarking sparse system identification with low-dimensional chaos](https://mlsanity.com/paper/2302.10787/) (2023)
- [Call for Action: towards the next generation of symbolic regression benchmark](https://mlsanity.com/paper/2505.03977/) (2025)
- [GSR: A Generalized Symbolic Regression Approach](https://mlsanity.com/paper/2205.15569/) (2022)
- [Problem-solving benefits of down-sampled lexicase selection](https://mlsanity.com/paper/2106.06085/) (2021)
- [Automated Learning of Interpretable Models with Quantified Uncertainty](https://mlsanity.com/paper/2205.01626/) (2022)
- [CoNSoLe: Convex Neural Symbolic Learning](https://mlsanity.com/paper/2206.00257/) (2022)
- [Knowledge Integration for Physics-informed Symbolic Regression Using Pre-trained Large Language Models](https://mlsanity.com/paper/2509.03036/) (2025)
- [Interpretable Symbolic Regression for Data Science: Analysis of the 2022 Competition](https://mlsanity.com/paper/2304.01117/) (2023)
- [MESSY Estimation: Maximum-Entropy based Stochastic and Symbolic densitY Estimation](https://mlsanity.com/paper/2306.04120/) (2023)
- [A-SR: Self-Evolving Agentic LLMs for Symbolic Regression via Hierarchical Coordination](https://mlsanity.com/paper/2608.04872/) (2026)
- [Symbolic Regression as Feature Engineering Method for Machine and Deep Learning Regression Tasks](https://mlsanity.com/paper/2311.06028/) (2023)
- [Generative and reproducible benchmarks for comprehensive evaluation of machine learning classifiers](https://mlsanity.com/paper/2107.06475/) (2021)
- [Symbolic-Regression Boosting](https://mlsanity.com/paper/2206.12082/) (2022)
- [Differentiable Genetic Programming for High-dimensional Symbolic Regression](https://mlsanity.com/paper/2304.08915/) (2023)
- [Particularity](https://mlsanity.com/paper/2306.06812/) (2023)
- [AutoNumerics-Zero: Automated Discovery of State-of-the-Art Mathematical Functions](https://mlsanity.com/paper/2312.08472/) (2023)
- [Interpretability in Symbolic Regression: a benchmark of Explanatory Methods using the Feynman data set](https://mlsanity.com/paper/2404.05908/) (2024)
- [Iterated Agent for Symbolic Regression](https://mlsanity.com/paper/2510.08317/) (2025)
- [Symbolic Regression with Fast Function Extraction and Nonlinear Least Squares Optimization](https://mlsanity.com/paper/2209.09675/) (2022)
- [Symbolic Metamodels for Interpreting Black-boxes Using Primitive Functions](https://mlsanity.com/paper/2302.04791/) (2023)
- [ISR: Invertible Symbolic Regression](https://mlsanity.com/paper/2405.06848/) (2024)
- [Univariate Skeleton Prediction in Multivariate Systems Using Transformers](https://mlsanity.com/paper/2406.17834/) (2024)
- [TinyverseGP: Towards a Modular Cross-domain Benchmarking Framework for Genetic Programming](https://mlsanity.com/paper/2504.10253/) (2025)
- [Data-driven Discovery of Digital Twins in Biomedical Research](https://mlsanity.com/paper/2508.21484/) (2025)
- [Exploring Hidden Semantics in Neural Networks with Symbolic Regression](https://mlsanity.com/paper/2204.10529/) (2022)
- [Information Fusion via Symbolic Regression: A Tutorial in the Context of Human Health](https://mlsanity.com/paper/2306.00153/) (2023)

## Abstract (arXiv)

In this paper we provide a broad benchmarking of recent genetic programming approaches to symbolic regression in the context of state of the art machine learning approaches. We use a set of nearly 100 regression benchmark problems culled from open source repositories across the web. We conduct a rigorous benchmarking of four recent symbolic regression approaches as well as nine machine learning approaches from scikit-learn. The results suggest that symbolic regression performs strongly compared to state-of-the-art gradient boosting algorithms, although in terms of running times is among the slowest of the available methodologies. We discuss the results in detail and point to future research directions that may allow symbolic regression to gain wider adoption in the machine learning community.