Average Error: 0.0 → 0.0
Time: 3.9s
Precision: 64
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
↓
\[\sqrt[3]{{\left(\frac{1}{x - 1} + \frac{x}{x + 1}\right)}^{3}}\]
\frac{1}{x - 1} + \frac{x}{x + 1}
↓
\sqrt[3]{{\left(\frac{1}{x - 1} + \frac{x}{x + 1}\right)}^{3}}
double f(double x) {
        double r135785 = 1.0;
        double r135786 = x;
        double r135787 = r135786 - r135785;
        double r135788 = r135785 / r135787;
        double r135789 = r135786 + r135785;
        double r135790 = r135786 / r135789;
        double r135791 = r135788 + r135790;
        return r135791;
}
↓
double f(double x) {
        double r135792 = 1.0;
        double r135793 = x;
        double r135794 = r135793 - r135792;
        double r135795 = r135792 / r135794;
        double r135796 = r135793 + r135792;
        double r135797 = r135793 / r135796;
        double r135798 = r135795 + r135797;
        double r135799 = 3.0;
        double r135800 = pow(r135798, r135799);
        double r135801 = cbrt(r135800);
        return r135801;
}

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

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

  3. Applied add-cbrt-cube0.0

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

  4. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019356 +o rules:numerics
(FPCore (x)
  :name "Asymptote B"
  :precision binary64
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))