Average Error: 0.0 → 0.1
Time: 15.0s
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 r34595 = x;
        double r34596 = 1.0;
        double r34597 = r34595 + r34596;
        double r34598 = r34596 - r34595;
        double r34599 = r34597 / r34598;
        return r34599;
}
↓
double f(double x) {
        double r34600 = x;
        double r34601 = 1.0;
        double r34602 = r34600 + r34601;
        double r34603 = r34601 - r34600;
        double r34604 = r34602 / r34603;
        double r34605 = cbrt(r34604);
        double r34606 = r34605 * r34605;
        double r34607 = r34606 * r34605;
        return r34607;
}

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)))