 
 
 
erf takes as argument a number a.
erf returns the floating point value of the error function at x=a, 
where the error function is defined by :
| erf(x)= | 
 | ∫ | 
 | e−t2dt | 
The normalization is chosen so that:
| erf(+∞)=1, erf(−∞)=−1 | 
since :
| ∫ | 
 | e−t2dt= | 
 | 
Input :
Output :
Input :
Output :
Remark
The relation between erf and normal_cdf is :
| normal_cdf(x)= | 
 | + | 
 | erf( | 
 | ) | 
Indeed, making the change of variable t=u*√2 in
| normal_cdf(x)= | 
 | + | 
 | ∫ | 
 | e−t2/2dt | 
gives :
| normal_cdf(x)= | 
 | + | 
 | ∫ | 
 | e−u2du= | 
 | + | 
 | erf( | 
 | ) | 
Check :
normal_cdf(1)=0.841344746069
 
 
