For every imperative function, is there a functional counterpart with identical performance or even instructions?


Currently, I haven’t learned about a functional language that can achieve the same performance as C/C++. And I have learned that some languages that favor functional programming to imperative programming, such as Scala and Rust, use imperative ways to implement their library functions for better efficiency.

So here comes my question, on today’s comptuters that execute imperative instructions, is this a limitation of the compiler or functional programming itself? For every imperative function with no side effects, either in a language without GC such as C/C++/Rust/assembly or one with GC such as Java, is there a pure functional counterpart in Haskell, Scala, etc. that can be compiled to run with identical performance in time and space (not just asymptotic but exactly the same) or even to the same instructions, with an optimal functional compiler that utilizes all modern and even undiscovered optimization techniques such as tail recursion, laziness, static analysis, formal verification, and so on which I don’t know about?

I am aware of the equivalence between λ-computable and Turing computable, but but I couldn’t find an answer to this question online. If there is, please share a compiler example or a proof. If not, please explain why and show a counter-example. Or is this a non-trivial open question?