I have found in https://github.com/timschmidt/hyperreal and the geometry layers built atop it, that exactness and speed are not fundamentally opposed. Hyperreal retains exact mathematical structure at the scalar level, and at each level higher up through vertices, vectors, matrices, triangles, curves, etc. And uses it to choose optimal datatypes, dispatch against the fastest algorithms, and eliminate large chunks of needless calculation where simpler proofs are sufficient.
The downside is a bit of additional code and API complexity. But the slightly more complex API accurately represents issues like uncertainty in decidable equality of arbitrary computables in bounded time, which is a limitation of math itself, so representing it accurately in the API permits the algorithms to be more robust.
> Floating Point is used on separate hardware with parallel operations, and there's race conditions that make most Machine Learning and AI computing irreproducible
Deterministic reproducibility is, I think, one of the most awesome superpowers of a system like hyperreal. It makes simulation much more interesting and useful. As well as cross-platform use.