Learning to Prove Trigonometric Identities

TL;DR

This paper introduces AutoTrig, an AI system that efficiently proves trigonometric identities by learning from generated proof data, outperforming existing methods and human performance in speed and accuracy.

Contribution

The paper presents a novel automated proof system for trigonometric identities that learns to minimize proof steps and outperforms traditional symbolic and human methods.

Findings

AutoTrig can generate proofs in near-optimal steps.

AutoTrig outperforms Sympy, Matlab, and humans on synthetic datasets.

The system generalizes well to various identities.

Abstract

Automatic theorem proving with deep learning methods has attracted attentions recently. In this paper, we construct an automatic proof system for trigonometric identities. We define the normalized form of trigonometric identities, design a set of rules for the proof and put forward a method which can generate theoretically infinite trigonometric identities. Our goal is not only to complete the proof, but to complete the proof in as few steps as possible. For this reason, we design a model to learn proof data generated by random BFS (rBFS), and it is proved theoretically and experimentally that the model can outperform rBFS after a simple imitation learning. After further improvement through reinforcement learning, we get AutoTrig, which can give proof steps for identities in almost as short steps as BFS (theoretically shortest method), with a time cost of only one-thousandth. In addition, AutoTrig also beats Sympy, Matlab and human in the synthetic dataset, and performs well in many generalization tasks.