Function normal_cdf 

pub fn normal_cdf(x: f64) -> f64

Standard normal CDF Phi(x) evaluated via the exact special-function identity

Phi(x) = 0.5 * erfc(-x / sqrt(2)).

This is the exact Gaussian CDF semantics used throughout the codebase. The numerical erfc implementation may use internal approximations, but the returned function is the standard normal CDF itself rather than a separate polynomial surrogate surface.