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cl-waffe
Discontinued [Still Experimental] Common Lisp Differentiable Matrix Operations for Mathematical Optimization.
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cl-waffe performs basic mathematical operations (e.g.: sin/cos, exp...) via mgl-mat, and I pay a lot of attention to the overhead between cl-waffe and mgl-mat in the benchmarks. codes are here
But the other part about SIMD: I'm unsure if mgl-mat uses SIMD for transcendental functions or even for something like element-wise multiplication and division*. SIMD easily provides a speed-boost of 4-8 times which numpy uses. Libraries like sleef have been put to use by many.