MatrixEquations.jl VS Metatheory.jl

I'd love to see something in the lines of Julia's https://juliasymbolics.github.io/Metatheory.jl/dev/

From that example you can see how this makes some rather difficult compiler questions all be subsumed in the e-graph saturation solve. That solve itself isn't easy, it's an NP-hard problem that requires good heuristics and such, and that's what Metatheory.jl, and that's what chunks of the thesis are about. But given a good enough solver, the ability to write such transformation passes becomes rather trivial and you get an optimal solution in the sense of the chosen cost function. So problems like enabling automatic FMA on specific codes is rather simple with this tool: just declare a*b + c = fma(a,b,c), the former is a cost of 2 the latter is a cost of one, and let it rip.

Well IMO it can definitely be rewritten in Julia, and to an easier degree than python since Julia allows hooking into the compiler pipeline at many areas of the stack. It's lispy an built from the ground up for codegen, with libraries like (https://github.com/JuliaSymbolics/Metatheory.jl) that provide high level pattern matching with e-graphs. The question is whether it's worth your time to learn Julia to do so.

You could also do it at the LLVM level: https://github.com/JuliaComputingOSS/llvm-cbe

For interesting takes on that, you can see https://github.com/JuliaLinearAlgebra/Octavian.jl which relies on loopvectorization.jl to do transforms on Julia AST beyond what LLVM does. Because of that, Octavian.jl beats openblas on many linalg benchmarks