thank you for sharing the link to Herbie, that looks like a useful tool.

If I follow at high level, it looks like Herbie is trying to rewrite expressions to minimise error without runtime performance constraints.

Are there alternative tools that focus on rewriting code to maximise performance while keeping error below some configurable bound?

i guess compilers are generally focused on the latter problem, perhaps without giving the user much control over the degree of error they are willing to tolerate.