Complementary error function¶

erfc(x)¶

Computes 1 - erf(x) in a numerically stable way.

Parameters:	x (float) – a real scalar.

Description¶

\[1 - \mathrm{erf}(x) = \mathrm{erfc}(x) = \frac{2}{\sqrt{\pi}} \int_x^{\infty} \exp{(-t^2)}dt\]

For small \(x\), erfc(x) = 1 - erf(x); otherwise rational approximations are computed.

A special function expx2() is used to suppress error amplification in computing \(\exp{(-x^2)}\).

			Relative error
arithmetic	domain	# trials	peak	rms
IEEE	0, 26.6417	30000	1.3e-15	2.2e-16

message	condition	value returned
erfc underflow	x > 9.231948545 (DEC)	0.0