SymbolicUtils.jl
Metatheory.jl
SymbolicUtils.jl | Metatheory.jl | |
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2 | 5 | |
507 | 337 | |
2.0% | 2.1% | |
8.3 | 8.1 | |
5 days ago | 6 days ago | |
Julia | Julia | |
GNU General Public License v3.0 or later | MIT License |
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SymbolicUtils.jl
- Open Source Math Engine for step-by-step solution?
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In 2022, the difference between symbolic computing and compiler optimizations will be erased in #julialang. Anyone who can come up with a set of symbolic mathematical rules will automatically receive an optimized compiler pass to build better code
The example is applied to the right-hand side of a generated mass-matrix ODE (DAE) which is then solved using the adaptive time stepping methods of DifferentialEquations.jl. It's a test example that comes from the robotics / rigid body dynamics simulation groups (specifically interested in control) where they before were generating the governing equations with SymPy, and recently switched to try Symbolics.jl (and we got the example because of some performance issues that needed fixing). The comparison is with and without applying the code simplifier before solving. The table shows an average global induced error of 1e-12 when chopping off the 1e-11 * sin(x) terms and smaller. Thus there's nothing "competitive" against standard adaptive time stepping here: it's used to enhance the simulation of generated models that are simulated with the adaptive time steppers.
Metatheory.jl
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[ANN] E-graphs and equality saturation: hegg 0.1
I'd love to see something in the lines of Julia's https://juliasymbolics.github.io/Metatheory.jl/dev/
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Twitter Thread: Symbolic Computing for Compiler Optimizations in Julia
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.
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Show HN: prometeo – a Python-to-C transpiler for high-performance computing
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
- From Julia to Rust
- Algebraic Metaprogramming in Julia with Metatheory.jl
What are some alternatives?
Symbolics.jl - Symbolic programming for the next generation of numerical software
JET.jl - An experimental code analyzer for Julia. No need for additional type annotations.
MLStyle.jl - Julia functional programming infrastructures and metaprogramming facilities
Dagger.jl - A framework for out-of-core and parallel execution
Pluto.jl - 🎈 Simple reactive notebooks for Julia
MacroTools.jl - MacroTools provides a library of tools for working with Julia code and expressions.
julia - The Julia Programming Language
acados - Fast and embedded solvers for nonlinear optimal control
SciMLBenchmarks.jl - Scientific machine learning (SciML) benchmarks, AI for science, and (differential) equation solvers. Covers Julia, Python (PyTorch, Jax), MATLAB, R
Octavian.jl - Multi-threaded BLAS-like library that provides pure Julia matrix multiplication