Average Error: 0.0 → 0.0
Time: 20.4s
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 r1610899 = x;
        double r1610900 = 1.0;
        double r1610901 = r1610899 + r1610900;
        double r1610902 = r1610900 - r1610899;
        double r1610903 = r1610901 / r1610902;
        return r1610903;
}
↓
double f(double x) {
        double r1610904 = 1.0;
        double r1610905 = x;
        double r1610906 = r1610904 + r1610905;
        double r1610907 = r1610904 - r1610905;
        double r1610908 = r1610906 / r1610907;
        return r1610908;
}

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 2019168 +o rules:numerics
(FPCore (x)
  :name "Prelude:atanh from fay-base-0.20.0.1"
  (/ (+ x 1.0) (- 1.0 x)))