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I am looking for the numerical approximation of error function, which must be efficient and accurate. Thanks in advance $$\mathrm{erf}(z)=\frac2{\sqrt\pi}\int_0^z e^{-t^2} \,\mathrm dt$$

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Wiki suggests an approximation en.wikipedia.org/wiki/… – user17762 Jun 3 '11 at 2:37
possible duplicate of Definite integral of Normal Distribution – user17762 Jun 3 '11 at 2:43
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possible duplicate of How to accurately calculate erf(x) with a computer? – J. M. Jul 23 '11 at 15:26

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"Efficient and accurate" is probably contradictory... Have you tried the one listed in http://en.wikipedia.org/wiki/Error_function#Approximation_with_elementary_functions ?

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yes, I have tried this. Its accuracy is up to 2 decimal places. Do we have more than this? – shaikh Jun 3 '11 at 2:40
@shaikh, C99 has an erf function, which should be quite accurate. – lhf Jun 3 '11 at 2:42
where can I find the derivation of C99 erf...? – shaikh Jun 3 '11 at 2:45
@shaikh, oh, you have to read the code. See for instance the cephes library. – lhf Jun 3 '11 at 2:48
@shaikh: Or boost's implementation – ziyuang Jun 3 '11 at 2:51
up vote 1 down vote

How about this: Computation of the error function erf in arbitrary precision with correct rounding

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I will try this. thx – shaikh Jun 3 '11 at 2:42

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