I think a great start is to make arrays of similar data. Instead of an array of (x,y,z) use an array for x, an array for y and another one for z. If you then square these and sum them for example, the compiler might figure out good optimizations for it if you write it as a simple loop.

Also read about SIMD instructions like AVX2. They are often used under the hood when possible, but just knowing what they require can help "triggering" them, depending on which language you use. In C++ for example, the compiler really looks for opportunities to use those instructions. You can tell the compiler did it, by looking in the assembly code if any XMM or YMM registers are being used (these are the names of the SIMD registers).

A more accruate keyword for googling is "SIMD". Single Instruction Multiple Data.

Numpy's tutorial for broadcasting is also a good starting point.

https://numpy.org/doc/stable/user/basics.broadcasting.html

The gist of it is that you give numpy two arrays, and what operation to apply. Then numpy will figure out what the for loop(s) should look like depending on the shape of the arrays.

You can look at various tutorials to see how it works. For example: https://jakevdp.github.io/PythonDataScienceHandbook/02.05-co...