Average Error: 0.0 → 0.1
Time: 12.7s
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 r33411 = x;
        double r33412 = 1.0;
        double r33413 = r33411 + r33412;
        double r33414 = r33412 - r33411;
        double r33415 = r33413 / r33414;
        return r33415;
}
↓
double f(double x) {
        double r33416 = x;
        double r33417 = 1.0;
        double r33418 = r33416 + r33417;
        double r33419 = r33417 - r33416;
        double r33420 = r33418 / r33419;
        double r33421 = cbrt(r33420);
        double r33422 = r33421 * r33421;
        double r33423 = r33422 * r33421;
        return r33423;
}

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 
(FPCore (x)
  :name "Prelude:atanh from fay-base-0.20.0.1"
  :precision binary64
  (/ (+ x 1) (- 1 x)))