Benchmarks are often not very interesting for people doing numerics. I have (actually with the help of two colleagues) tried to make simple but (we hope) interesting numerical benchmarks. We focused on coding and testing numerical algorithms; as an example, consider Gaussian elimination: this is something you will not use in practice, as you will use, say, lapack routines; but Gaussian elimination is a prototype of array manipulation.
We have compared C++, Python, Python+Pythran, Python+Numba (with some variations) on a small set of problems)., ranging from very simple ones (linear combination) to Weno solution of (simple) hyperbolic PDE problems.
But we are not sure that our Julia coding cannot be improved. If someone wants to have a look, to, propose improvements, you are welcome.
Everything is on Github: here
Thierry Dumont, Lyon -France-