Average Error: 0.0 → 0.1
Time: 13.4s
Precision: 64
\[\frac{x + 1}{1 - x}\]
↓
\[\left(\sqrt[3]{\frac{x + 1}{1 - x}} \cdot \sqrt[3]{\frac{x + 1}{1 - x}}\right) \cdot \sqrt[3]{\frac{x + 1}{1 - x}}\]
\frac{x + 1}{1 - x}
↓
\left(\sqrt[3]{\frac{x + 1}{1 - x}} \cdot \sqrt[3]{\frac{x + 1}{1 - x}}\right) \cdot \sqrt[3]{\frac{x + 1}{1 - x}}
double f(double x) {
        double r34982 = x;
        double r34983 = 1.0;
        double r34984 = r34982 + r34983;
        double r34985 = r34983 - r34982;
        double r34986 = r34984 / r34985;
        return r34986;
}
↓
double f(double x) {
        double r34987 = x;
        double r34988 = 1.0;
        double r34989 = r34987 + r34988;
        double r34990 = r34988 - r34987;
        double r34991 = r34989 / r34990;
        double r34992 = cbrt(r34991);
        double r34993 = r34992 * r34992;
        double r34994 = r34993 * r34992;
        return r34994;
}

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 add-cube-cbrt0.1

    \[\leadsto \color{blue}{\left(\sqrt[3]{\frac{x + 1}{1 - x}} \cdot \sqrt[3]{\frac{x + 1}{1 - x}}\right) \cdot \sqrt[3]{\frac{x + 1}{1 - x}}}\]

  4. Final simplification0.1

    \[\leadsto \left(\sqrt[3]{\frac{x + 1}{1 - x}} \cdot \sqrt[3]{\frac{x + 1}{1 - x}}\right) \cdot \sqrt[3]{\frac{x + 1}{1 - x}}\]

Reproduce

herbie shell --seed 2019303 +o rules:numerics
(FPCore (x)
  :name "Prelude:atanh from fay-base-0.20.0.1"
  :precision binary64
  (/ (+ x 1) (- 1 x)))