I agree, that it's the same algorithm as long as it x is real. My point was that with this optimisation we give more information to this function than the compa

I agree, that it's the same algorithm as long as it x is real. My point was that with this optimisation we give more information to this function than the comparable python function (or the other julia implementations), so it gains an advantage for optimising. Yes I was using complex inputs when switching to to cis/exp. LoopVectorization not supporting complex does explain this. As a side note, I generally dislike silent fall-backs, for optimisation libraries/modules. That's why I always do python=False when using numba (and I wish it was default). I'm using the library/module because I want speed up, the problem with the fall-backs is they are often slower than the default code (e.g. unwrapped loops in numba, and in this example), so I would like to know if it doesn't speed up the code, because rather not use it then. A failure would save me benchmarking the slow-down.