
SciMLBenchmarks.jl
Scientific machine learning (SciML) benchmarks, AI for science, and (differential) equation solvers. Covers Julia, Python (PyTorch, Jax), MATLAB, R
Anything that continues to improve the SciMLBenchmarks of differential equation solvers, inverse problems, scientific machine learning, and equation discovery really. But there's a lot of other applications in mind, like generating compiler passes that improve floating point roundoff (like Herbie), a pureJulia simple implementation of XLAtransformations for BLAS fusion, and a few others that are a bit more out there and will require a paper to describe the connection.

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Metatheory.jl
Makes Julia reason with equations. General purpose metaprogramming, symbolic computation and algebraic equational reasoning library for the Julia programming language: EGraphs & equality saturation, term rewriting and more.
From that example you can see how this makes some rather difficult compiler questions all be subsumed in the egraph saturation solve. That solve itself isn't easy, it's an NPhard 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.

From that example you can see how this makes some rather difficult compiler questions all be subsumed in the egraph saturation solve. That solve itself isn't easy, it's an NPhard 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.