Awesome to see this here! A lot of this work was done by an undergrad as part of his thesis, and I summarized the work in this Twitter thread along with our planned directions for 2022 (https://twitter.com/ChrisRackauckas/status/14772748124604497...). Though the abstract also captures the idea quite well too:
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?
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?