How does NumPy optimize reduction chains like mean, var, and std?

NumPy optimizes reductions by fusing partial passes and minimizing intermediate arrays.

Functions like mean, variance, and standard deviation are computed using numerically stable one-pass or two-pass algorithms in C. NumPy avoids repeated full-array scans when possible and reuses intermediate buffers. For large arrays, reductions are vectorized and may use parallel execution depending on backend libraries.