Average Error: 0.0 → 0.8
Time: 2.8s
Precision: 64
\[\frac{x}{1 - x}\]
↓
\[\left(\sqrt[3]{\frac{x}{1 - x}} \cdot \sqrt[3]{\frac{x}{1 - x}}\right) \cdot \sqrt[3]{\frac{x}{1 - x}}\]
\frac{x}{1 - x}
↓
\left(\sqrt[3]{\frac{x}{1 - x}} \cdot \sqrt[3]{\frac{x}{1 - x}}\right) \cdot \sqrt[3]{\frac{x}{1 - x}}
double f(double x) {
        double r118101 = x;
        double r118102 = 1.0;
        double r118103 = r118102 - r118101;
        double r118104 = r118101 / r118103;
        return r118104;
}
↓
double f(double x) {
        double r118105 = x;
        double r118106 = 1.0;
        double r118107 = r118106 - r118105;
        double r118108 = r118105 / r118107;
        double r118109 = cbrt(r118108);
        double r118110 = r118109 * r118109;
        double r118111 = r118110 * r118109;
        return r118111;
}

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

    \[\frac{x}{1 - x}\]
  2. Using strategy rm

  3. Applied add-cube-cbrt0.8

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

  4. Final simplification0.8

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

Reproduce

herbie shell --seed 2020020 
(FPCore (x)
  :name "Numeric.Integration.TanhSinh:nonNegative from integration-0.2.1"
  :precision binary64
  (/ x (- 1 x)))