Automated Code Optimization with E-Graphs

TL;DR

This thesis introduces a high-level, generic code rewriting system in Julia using equality saturation with E-Graphs, enabling domain-specific optimizations by non-expert programmers within their programs.

Contribution

It presents a novel system that allows users to implement high-level compiler optimizations directly in Julia, simplifying the process and integrating symbolic mathematics with compiler techniques.

Findings

Successfully applied to scientific programs for domain-specific optimizations

Enables users to write optimizations as equations without complex rewriting strategies

Demonstrates practical solutions to two-language and high-level optimization challenges

Abstract

This thesis proposes an advanced, generic and high-level code rewriting and analysis system in the Julia programming language, providing applied equality saturation in the presence of multiple dispatch and metaprogramming. We show how our system can practically solve some challenging problems: Can programmers implement their own high-level compiler optimizations for their domain-specific scientific programs, without the requirement of them being compiler experts at all? Can these optimizers be implemented by users in the same language and inside the same programs they want to optimize, solving the two-language problem? Can these compiler optimizers be written in a high-level fashion, as equations, without the need to worry about the rewriting ordering? Thus, can symbolic mathematics do high-level compiler optimizations or vice-versa?