Average Error: 0.0 → 0.0
Time: 8.5s
Precision: 64
\[\frac{x + 1}{1 - x}\]
↓
\[\frac{1}{\frac{1 - x}{x + 1}}\]
\frac{x + 1}{1 - x}
↓
\frac{1}{\frac{1 - x}{x + 1}}
double f(double x) {
        double r50797 = x;
        double r50798 = 1.0;
        double r50799 = r50797 + r50798;
        double r50800 = r50798 - r50797;
        double r50801 = r50799 / r50800;
        return r50801;
}
↓
double f(double x) {
        double r50802 = 1.0;
        double r50803 = 1.0;
        double r50804 = x;
        double r50805 = r50803 - r50804;
        double r50806 = r50804 + r50803;
        double r50807 = r50805 / r50806;
        double r50808 = r50802 / r50807;
        return r50808;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\frac{x + 1}{1 - x}\]
  2. Using strategy rm

  3. Applied clear-num0.0

    \[\leadsto \color{blue}{\frac{1}{\frac{1 - x}{x + 1}}}\]

  4. Final simplification0.0

    \[\leadsto \frac{1}{\frac{1 - x}{x + 1}}\]

Reproduce

herbie shell --seed 2019208 +o rules:numerics
(FPCore (x)
  :name "Prelude:atanh from fay-base-0.20.0.1"
  :precision binary64
  (/ (+ x 1) (- 1 x)))