Sorry for the delay, but here is an example code:

https://gist.github.com/Alexander-Barth/c8eb764f400cdb7a1eb5...

Do not hesitate to tell me if I missed something to optimize the python code. If somebody has numba, pythan,... installed, I would be interested to see the speed-up compared to the vanilla python version on your machine.

So in short, for my cases: the fastest Julia test case (with loops and avoiding unnecessary allocation) was about 10x faster than fastest python 3 test case (with vectorization).

The runtime with vectorization are relatively similar (julia is only about 25% faster than python). Explicit loop and careful memory management are clearly beneficial in Julia.

The speed difference compounds as code grows in complexity. Julia compiles things together, using interprocedural optimizations and automatic type specialization. Lots of allocation saving utilities, fancy performance macros, etc. let you get very fast code. Recent testing in large applications showed that using a Numba function in a Julia code or a Python code was about 10x slower than a Julia code (here's a quick writeup: http://juliadiffeq.org/2018/04/30/Jupyter.html). We had a crew that was more experienced in Python keep trying to make it better (and lots of Julia programmers come from Python and have more experience (many more years!) with Python). 10x seemed to be the amount that Pythran, Cython, Numba was behind defining a Julia-function using pyjulia (Numba was great and easiest in comparison, so our docs kept that and dumped the others).

Moral of the story is, these Python tools are built for microbenchmarks and can do okay there, but without the full stack optimized together and without a type system that's exploitable for all of the performance tricks, it falls apart in real-world code.