Average Error: 0.0 → 0.0
Time: 1.9s
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 r128830 = 1.0;
        double r128831 = x;
        double r128832 = r128831 - r128830;
        double r128833 = r128830 / r128832;
        double r128834 = r128831 + r128830;
        double r128835 = r128831 / r128834;
        double r128836 = r128833 + r128835;
        return r128836;
}
↓
double f(double x) {
        double r128837 = 1.0;
        double r128838 = x;
        double r128839 = r128838 - r128837;
        double r128840 = r128837 / r128839;
        double r128841 = r128838 + r128837;
        double r128842 = r128838 / r128841;
        double r128843 = r128840 + r128842;
        double r128844 = 3.0;
        double r128845 = pow(r128843, r128844);
        double r128846 = cbrt(r128845);
        return r128846;
}

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 2020003 
(FPCore (x)
  :name "Asymptote B"
  :precision binary64
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))