Average Error: 0.0 → 0.0
Time: 6.5s
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 r111774 = 1.0;
        double r111775 = x;
        double r111776 = r111775 - r111774;
        double r111777 = r111774 / r111776;
        double r111778 = r111775 + r111774;
        double r111779 = r111775 / r111778;
        double r111780 = r111777 + r111779;
        return r111780;
}
↓
double f(double x) {
        double r111781 = 1.0;
        double r111782 = x;
        double r111783 = r111782 - r111781;
        double r111784 = r111781 / r111783;
        double r111785 = r111782 + r111781;
        double r111786 = r111782 / r111785;
        double r111787 = r111784 + r111786;
        double r111788 = 3.0;
        double r111789 = pow(r111787, r111788);
        double r111790 = cbrt(r111789);
        return r111790;
}

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 2019323 
(FPCore (x)
  :name "Asymptote B"
  :precision binary64
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))