Returns an approximation of the error function:

For abs(x) < 1, DPlot uses the approximation:

and iterates until any additional term is less than 1.E-10 times the current solution. In general the series converges within several steps for small x and takes up to 15 terms before converging to the solution for x close to 1.0.

For abs(x) > 1 DPlot uses an approximating 9th order polynomial that is accurate to +/- 1.E-7 for all values of x:

z = abs(x)

t = 1./(1.+0.5*z)

erf = 1.-t*exp(-z*z -1.26551223 +

t*( 1.00002368 +

t*( 3.7409196E-1 +

t*( 9.678418E-2 +

t*(-1.8628806E-1 +

t*( 2.7886807E-1 +

t*(-1.13520398 +

t*( 1.48851587 +

t*(-8.2215223E-1 +

t* 1.7087277E-1 )))))))))

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See also: