So if the following function is evaluated with the floating-point arithmetic, we get poor results for certain range of values of $x$. Therefore, I need to provide an alternate function that can be used for those values of $x$. The function is:
$ f(x)= \sqrt{1+x}-\sqrt{1-x} $
I have found the range for this and it is: $-\sqrt{2} \le y \le \sqrt{2}$
So how would I make an alternate expression or function for this.
Do I just multiply by its conjugate.