Cdf.java

private static final double INV_SQRT_TWO = 1 / Math.sqrt(2.0);

public static double cdf(double mu, double sigma, double z) {
    return cdf((z - mu) / sigma);
}

public static double cdf(double z) {
    if (z < -6 || z > 6) return 0;
    return 0.5 * (1 + erf(Math.abs(z) * INV_SQRT_TWO) * (z > 0 ? 1 : -1));
}

private static double erf(double x) {
    // https://math.stackexchange.com/questions/2185974/integration-of-unintegrable-function/2186054#2186054
    return Math.sqrt(1 - Math.exp(-4 * x * x / Math.PI));
}