Average Error: 0.0 → 0.0
Time: 2.0s
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 r167766 = 1.0;
        double r167767 = x;
        double r167768 = r167767 - r167766;
        double r167769 = r167766 / r167768;
        double r167770 = r167767 + r167766;
        double r167771 = r167767 / r167770;
        double r167772 = r167769 + r167771;
        return r167772;
}
↓
double f(double x) {
        double r167773 = 1.0;
        double r167774 = x;
        double r167775 = r167774 - r167773;
        double r167776 = r167773 / r167775;
        double r167777 = r167774 + r167773;
        double r167778 = r167774 / r167777;
        double r167779 = r167776 + r167778;
        double r167780 = 3.0;
        double r167781 = pow(r167779, r167780);
        double r167782 = cbrt(r167781);
        return r167782;
}

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 2020064 
(FPCore (x)
  :name "Asymptote B"
  :precision binary64
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))