Average Error: 0.0 → 0.0
Time: 2.8s
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 r124787 = 1.0;
        double r124788 = x;
        double r124789 = r124788 - r124787;
        double r124790 = r124787 / r124789;
        double r124791 = r124788 + r124787;
        double r124792 = r124788 / r124791;
        double r124793 = r124790 + r124792;
        return r124793;
}
↓
double f(double x) {
        double r124794 = 1.0;
        double r124795 = x;
        double r124796 = r124795 - r124794;
        double r124797 = r124794 / r124796;
        double r124798 = r124795 + r124794;
        double r124799 = r124795 / r124798;
        double r124800 = r124797 + r124799;
        double r124801 = 3.0;
        double r124802 = pow(r124800, r124801);
        double r124803 = cbrt(r124802);
        return r124803;
}

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 
(FPCore (x)
  :name "Asymptote B"
  :precision binary64
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))