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Finally, there are certain types of algorithms/operations that can be very sensitive to implementation. For example, a "good" Fast Fourier Transform implementation may be 3-4 orders of magnitude faster than a naive recursive one (with the same complexity!). Another fun case is something like (a*b)%c when the numbers are 64 bit. Using a fast implementation like this one (https://github.com/kth-competitive-programming/kactl/blob/master/content/number-theory/ModMulLL.h#L20) can speed up your code by 3-4x compared to using a naive implementation.
Look at Cliff Click's AA language: https://github.com/cliffclick/aa