Can the Eureqa symbolic regression program, computer algebra and numerical analysis help each other?

TL;DR

This paper explores how Eureqa symbolic regression, computer algebra, and numerical analysis can complement each other to improve mathematical modeling and discovery, especially in experimental mathematics.

Contribution

It demonstrates the mutual benefits and potential integrations of Eureqa with computer algebra and numerical methods for enhanced mathematical problem solving.

Findings

Eureqa can find concise expressions approximating or equivalent to known formulas.

Numerical data generation enables Eureqa to discover expressions without explicit formulas.

Combining Eureqa with algebraic and numerical tools enhances its effectiveness in experimental mathematics.

Abstract

The Eureqa symbolic regression program has recently received extensive press praise. A representative quote is "There are very clever 'thinking machines' in existence today, such as Watson, the IBM computer that conquered Jeopardy! last year. But next to Eureqa, Watson is merely a glorified search engine." The program was designed to work with noisy experimental data. However, if the data is generated from an expression for which there exists more concise equivalent expressions, sometimes some of the Eureqa results are one or more of those more concise equivalents. If not, perhaps one or more of the returned Eureqa results might be a sufficiently accurate approximation that is more concise than the given expression. Moreover, when there is no known closed form expression, the data points can be generated by numerical methods, enabling Eureqa to find expressions that concisely fit those data points with sufficient accuracy. In contrast to typical regression software, the user does not have to explicitly or implicitly provide a specific expression or class of expressions containiing unknown constants for the software to determine. Is Eureqa useful enough in these regards to provide an additional tool for experimental mathematics, computer algebra users and numerical analysis? Yes if used carefully. Can computer algebra and numerical methods help Eureqa? Definitely.