The current “top answer” sounds a bit too much like FUD in my ears. For one, it is not immediately obvious that the Average Developer would write faster code in C than what NumPy+Cython gives you anyway. Quite the contrary, the time it takes to even get the necessary C code to work correctly in a Python environment is usually much better invested in writing a quick prototype in Cython, benchmarking it, optimising it, rewriting it in a faster way, benchmarking it again, and then deciding if there is anything in it that truly requires the 5-10% more performance that you may or may not get from rewriting 2% of the code in hand-tuned C and calling it from your Cython code.
I’m writing a library in Cython that currently has about 18K lines of Cython code, which translate to almost 200K lines of C code. I once managed to get a speed-up of almost 25% for a couple of very important internal base level functions, by injecting some 20 lines of hand-tuned C code in the right places. It took me a couple of hours to rewrite and optimise this tiny part. That’s truly nothing compared to the huge amount of time I saved by not writing (and having to maintain) the library in plain C in the first place.
Even if you know C a lot better than Cython, if you know Python and C, you will learn Cython so quickly that it’s worth the investment in any case, especially when you are into numerics. 80-95% of the code you write will benefit so much from being written in a high-level language, that you can safely lay back and invest half of the time you saved into making your code just as fast as if you had written it in a low-level language right away.
That being said, your comment that you want “to be able to distribute the code as standalone C/C++ libraries” is a valid reason to stick to plain C/C++. Cython always depends on CPython, which is quite a dependency. However, using plain C/C++ (except for the Python interface) will not allow you to take advantage of NumPy either, as that also depends on CPython. So, as usual when writing something in C, you will have to do a lot of ground work before you get to the actual functionality. You should seriously think about this twice before you start this work.