Hi,

> Well, I compared the results before and after the simplifications with a 
> 512-bit
> precise mpfr value. Unfortunately, I found that sometimes the error is very
> noticeable :-( .

Did you enable FMA? I'd expect 1 - x*x to be accurate with FMA, so the relative 
error
should be much better. If there is no FMA, 2*(1-fabs(x)) - (1-fabs(x))^2 should 
be
more accurate when abs(x)>0.5 and still much faster.

Wilco

    

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