Average Error: 0.0 → 0.0
Time: 9.2s
Precision: 64
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
↓
\[\sqrt[3]{\left(\left(\frac{1}{x - 1} + \frac{x}{x + 1}\right) \cdot \left(\frac{1}{x - 1} + \frac{x}{x + 1}\right)\right) \cdot \left(\frac{1}{x - 1} + \frac{x}{x + 1}\right)}\]
\frac{1}{x - 1} + \frac{x}{x + 1}
↓
\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)}
double f(double x) {
        double r3497631 = 1.0;
        double r3497632 = x;
        double r3497633 = r3497632 - r3497631;
        double r3497634 = r3497631 / r3497633;
        double r3497635 = r3497632 + r3497631;
        double r3497636 = r3497632 / r3497635;
        double r3497637 = r3497634 + r3497636;
        return r3497637;
}
↓
double f(double x) {
        double r3497638 = 1.0;
        double r3497639 = x;
        double r3497640 = r3497639 - r3497638;
        double r3497641 = r3497638 / r3497640;
        double r3497642 = r3497639 + r3497638;
        double r3497643 = r3497639 / r3497642;
        double r3497644 = r3497641 + r3497643;
        double r3497645 = r3497644 * r3497644;
        double r3497646 = r3497645 * r3497644;
        double r3497647 = cbrt(r3497646);
        return r3497647;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2019129 
(FPCore (x)
  :name "Asymptote B"
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))