# Symbolic Regression with Fast Function Extraction and Nonlinear Least Squares Optimization

arXiv: https://arxiv.org/abs/2209.09675 · HTML: https://mlsanity.com/paper/2209.09675/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 11 references that are in the map.
- First posted on arXiv 20 Sep 2022.

## Builds on (most cited first, 3 of 3)

- [Where are we now? A large benchmark study of recent symbolic regression methods](https://mlsanity.com/paper/1804.09331/) (2018)
- [A Greedy Search Tree Heuristic for Symbolic Regression](https://mlsanity.com/paper/1801.01807/) (2018)
- [Symbolic Regression by Exhaustive Search: Reducing the Search Space Using Syntactical Constraints and Efficient Semantic Structure Deduplication](https://mlsanity.com/paper/2109.13895/) (2021)

## Built on by (most cited first, 2 of 2)

- [SymbolNet: Neural Symbolic Regression with Adaptive Dynamic Pruning for Compression](https://mlsanity.com/paper/2401.09949/) (2024)
- [When Good Equations Get Bad Scores: Improving Symbolic Regression Through Better Parameter Optimization](https://mlsanity.com/paper/2605.23272/) (2026)

## Abstract (arXiv)

Fast Function Extraction (FFX) is a deterministic algorithm for solving symbolic regression problems. We improve the accuracy of FFX by adding parameters to the arguments of nonlinear functions. Instead of only optimizing linear parameters, we optimize these additional nonlinear parameters with separable nonlinear least squared optimization using a variable projection algorithm. Both FFX and our new algorithm is applied on the PennML benchmark suite. We show that the proposed extensions of FFX leads to higher accuracy while providing models of similar length and with only a small increase in runtime on the given data. Our results are compared to a large set of regression methods that were already published for the given benchmark suite.