Average Error: 0.0 → 0.0
Time: 23.4s
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 r3926704 = 1.0;
        double r3926705 = x;
        double r3926706 = r3926705 - r3926704;
        double r3926707 = r3926704 / r3926706;
        double r3926708 = r3926705 + r3926704;
        double r3926709 = r3926705 / r3926708;
        double r3926710 = r3926707 + r3926709;
        return r3926710;
}
↓
double f(double x) {
        double r3926711 = 1.0;
        double r3926712 = x;
        double r3926713 = r3926712 - r3926711;
        double r3926714 = r3926711 / r3926713;
        double r3926715 = r3926712 + r3926711;
        double r3926716 = r3926712 / r3926715;
        double r3926717 = r3926714 + r3926716;
        double r3926718 = r3926717 * r3926717;
        double r3926719 = r3926718 * r3926717;
        double r3926720 = cbrt(r3926719);
        return r3926720;
}

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 2019142 
(FPCore (x)
  :name "Asymptote B"
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))