[asQuirreL]

You joke but in Rust all of versions 1 to 4 would probably have compiled to the same machine code because LLVM would use Loop Invariant Code Motion and Induction Variable Analysis to perform the same optimisations that are being done by hand here. (Same would be true of most modern C/C++ compilers)

[lifthrasiir]

While modern compilers do such analyses, the loop in question is too complex to be fully analyzed---it has two independent induction variables in a single loop after all.

[asQuirreL]

You're right -- I got nerd-sniped by this, and ended up rewriting the benchmarks in Rust. The compiler successfully inlines the square root operation, simplifies the exponentiation into multiplication and then does common-subexpression elimination over it, but no induction variable analysis, and therefore also no loop-invariant code motion. Here's it is in Godbolt:

https://godbolt.org/z/Pa6cqd1fb

But the funny thing is, I tried it on my machine, and guess what, the "unoptimised" version is consistently between 4 and 5 times faster than the hand-optimised variants:

https://gist.github.com/amnn/4be5c05975c250d0ea88b62c03f1719...

So that's fun.