You are calling the correlation sub 50_000 times 50_000 divided by 2 (I think): 11_250_000_000 calls in total. That is quiet a lot so any change to your correlation sub will go a long way.

I see you start with some array-references which you de-reference (turn back into an array), which you then reference again in the call to correlation and passing these references in the calls to mean and ss. And in those subs, you de-reference these references again and put everyting in an array again. I suggest that you keep working with references all the way through and never copy them into an array. This is less readable and you have to take care that you do not change any of the values of those arrays. I think you are OK on this point.

Another speed-up is looking for faster calculation of the correlation. Perhaps there is an XS module somewhere on CPAN that does this faster. Did you check?