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Afterwards, you can have a look at https://github.com/rust-ml/oxide-enzyme, where I published some toy examples. The current approach has a lot of limitations, mostly due to using the ffi / c-abi to link the generated functions. @bytesnake and I are already looking at an alternative implementation which should solve most, if not all issues. For the meantime, we hope that this already helps those who want to do some early testing. This link might also help you to understand the Rust frontend a bit better. I will add a larger blog post once oxide-enzyme is ready to be published on crates.io.
Enzyme is an LLVM (incubator) project, which performs automatic differentiation of LLVM-IR code. Here is an introduction to AutoDiff, which was recommended by @DoogoMiercoles in an earlier post. You can also try it online, if you know some C/C++: https://enzyme.mit.edu/explorer.