[williamstein]

Sometimes it does. For example if you write a simple O(n) for loop in Python, then convert it to Cython, then compile it, the compiler may replace the for loop by an equivalent O(1) algorithm. I use this to surprise students when benchmarking Cython code for teaching purposes in my SageMath course.

[Fede_V]

If it's just a matter of speeding up a tight loop, I find numba performs admirably and it's a lot more convenient than Cython.

When you need to wrap some c code, or use high-level data structures (that cython handles beautifully with STL integration) that's when it makes sense to drop to Cython.