What I suggested is very similar to memoization.

Only you don't cache the result of a function based on passed values.

You cache the optimized code based on passed types *

see https://en.m.wikipedia.org/wiki/Just-in-time_compilation

Hence the "slow" checking only happens at call time.

(of course you'll need kind of type of inference deduce implied types inside a sub)

*) and global states like bigint