Complementary error function erfc(x) = 1 - erf(x).

The complementary error function is defined as the integral

\[\operatorname{erfc}(x) = \frac{2}{\sqrt{\tau}} \int^{\infty}_{x/\sqrt{2}} e^{-\frac12 t^2}dt\]

Although mathematically erfc(x) = 1-erf(x), in practice the RHS suffers catastrophic loss of precision at large values of x. This function, however, does not have such a drawback.

See also

  • erf(x) – the error function.