Oxide-enzyme is the rust frontend of Enzyme, a tool which can differentiate your Rust functions f(x,y) in the calculus sense.
This autodiff crate will not differentiate your code directly, but rather create some function declarations d_f which will later be filled by oxide-enzyme.
When using the same settings for the differentiate_ext macro and the build.rs file from oxide-enzyme function signatures are guaranteed to match.
It is possible to use oxide-enzyme without this frontend by writing function declarations manually, although not recommended. Writing function declarations which do not match Enzymes expectation is not guaranteed to be catched as a compile time error and can just lead to incorrect gradients.
It is possible to differentiate the same function multiple times by adding multiple macros with different settings.