# Generating Elementary Integrable Expressions

arXiv: https://arxiv.org/abs/2306.15572 · HTML: https://mlsanity.com/paper/2306.15572/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 12 references that are in the map.
- First posted on arXiv 27 Jun 2023.

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

- [Deep Learning for Symbolic Mathematics](https://mlsanity.com/paper/1912.01412/) (2019)
- [Can Neural Networks Learn Symbolic Rewriting?](https://mlsanity.com/paper/1911.04873/) (2019)
- [Applying machine learning to the problem of choosing a heuristic to select the variable ordering for cylindrical algebraic decomposition](https://mlsanity.com/paper/1404.6369/) (2014)

## Built on by (most cited first, 4 of 4)

- [Symbolic Integration Algorithm Selection with Machine Learning: LSTMs vs Tree LSTMs](https://mlsanity.com/paper/2404.14973/) (2024)
- [The Liouville Generator for Producing Integrable Expressions](https://mlsanity.com/paper/2406.11631/) (2024)
- [Transformers to Predict the Applicability of Symbolic Integration Routines](https://mlsanity.com/paper/2410.23948/) (2024)
- [Tree-Based Deep Learning for Ranking Symbolic Integration Algorithms](https://mlsanity.com/paper/2508.06383/) (2025)

## Abstract (arXiv)

There has been an increasing number of applications of machine learning to the field of Computer Algebra in recent years, including to the prominent sub-field of Symbolic Integration. However, machine learning models require an abundance of data for them to be successful and there exist few benchmarks on the scale required. While methods to generate new data already exist, they are flawed in several ways which may lead to bias in machine learning models trained upon them. In this paper, we describe how to use the Risch Algorithm for symbolic integration to create a dataset of elementary integrable expressions. Further, we show that data generated this way alleviates some of the flaws found in earlier methods.