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 r94129 = x;
        double r94130 = 1.0;
        double r94131 = r94130 - r94129;
        double r94132 = r94129 / r94131;
        return r94132;
}
↓
double f(double x) {
        double r94133 = x;
        double r94134 = 1.0;
        double r94135 = r94134 - r94133;
        double r94136 = r94133 / r94135;
        double r94137 = cbrt(r94136);
        double r94138 = r94137 * r94137;
        double r94139 = r94138 * r94137;
        return r94139;
}

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 +o rules:numerics
(FPCore (x)
  :name "Numeric.Integration.TanhSinh:nonNegative from integration-0.2.1"
  :precision binary64
  (/ x (- 1 x)))