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 r53152 = x;
        double r53153 = 1.0;
        double r53154 = r53152 + r53153;
        double r53155 = r53153 - r53152;
        double r53156 = r53154 / r53155;
        return r53156;
}
↓
double f(double x) {
        double r53157 = x;
        double r53158 = 1.0;
        double r53159 = r53157 + r53158;
        double r53160 = r53158 - r53157;
        double r53161 = r53159 / r53160;
        double r53162 = cbrt(r53161);
        double r53163 = r53162 * r53162;
        double r53164 = r53163 * r53162;
        return r53164;
}

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)))