erf function

double erf(double x)

Approximate solution for the error function of x.

• Fractional error is less than 1.2e7.
• There is no standard erf() available in dart:math.
• The approximation is based on Chebyshev fitting.

Implementation

double erf(double x) {
  final z = x.abs();
  final t = 1.0 / (1.0 + 0.5 * z);

  // Approximate the complementary error function
  var erfc = t *
      exp(-z * z -
          1.26551223 +
          t *
              (1.00002368 +
                  t *
                      (0.37409196 +
                          t *
                              (0.09678418 +
                                  t *
                                      (-0.18628806 +
                                          t *
                                              (0.27886807 +
                                                  t *
                                                      (-1.13520398 +
                                                          t * (1.48851587 + t * (-0.82215223 + t * 0.17087277)))))))));

  if (x < 0.0) erfc = 2.0 - erfc;
  return 1.0 - erfc;
}