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### 1.14 `erf`, `erff`, `erfc`, `erfcf`—error function

Synopsis

         #include <math.h>
         double erf(double x);
         float erff(float x);
         double erfc(double x);
         float erfcf(float x);

Description
`erf` calculates an approximation to the “error function”, which estimates the probability that an observation will fall within x standard deviations of the mean (assuming a normal distribution).

`erfc` calculates the complementary probability; that is, `erfc(`x`)` is `1 - erf(`x`)`. `erfc` is computed directly, so that you can use it to avoid the loss of precision that would result from subtracting large probabilities (on large x) from 1.

`erff` and `erfcf` differ from `erf` and `erfc` only in the argument and result types.

Returns
For positive arguments, `erf` and all its variants return a probability—a number between 0 and 1.

Portability
None of the variants of `erf` are ANSI C.