Average Error: 0.0 → 0.0
Time: 5.8s
Precision: 64
\[\frac{x + 1}{1 - x}\]
↓
\[\frac{1 + x}{1 - x}\]
\frac{x + 1}{1 - x}
↓
\frac{1 + x}{1 - x}
double f(double x) {
        double r1590111 = x;
        double r1590112 = 1.0;
        double r1590113 = r1590111 + r1590112;
        double r1590114 = r1590112 - r1590111;
        double r1590115 = r1590113 / r1590114;
        return r1590115;
}
↓
double f(double x) {
        double r1590116 = 1.0;
        double r1590117 = x;
        double r1590118 = r1590116 + r1590117;
        double r1590119 = r1590116 - r1590117;
        double r1590120 = r1590118 / r1590119;
        return r1590120;
}

Error

Bits error versus x

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Results

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Derivation

  1. Initial program 0.0

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

  2. Final simplification0.0

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

Reproduce

herbie shell --seed 2019171 
(FPCore (x)
  :name "Prelude:atanh from fay-base-0.20.0.1"
  (/ (+ x 1.0) (- 1.0 x)))