I find this benchmark a bit disorganized, but it seems that the "hand-written" Julia function is as slow as the "hand-written" C function.

The C function is of course naive. I'm pretty sure that a hand-unrolled loop would be faster.

Yes to this. When you're calling some big fast package (be it some field-specific thing, or just matrix algebra) the language you're in doesn't matter that much. In terms of speed, but also in terms of effort -- you spend most of your time reading this field-specific package's manual.

What's liberating is that for the things which aren't covered by such packages, there's no huge penalty for just writing it yourself. In speed but in effort too -- it's quicker to write the loop than to figure out how to make np.einsum do what you have in mind.