Average Error: 0.0 → 0.0
Time: 3.3s
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 r88567 = 1.0;
        double r88568 = x;
        double r88569 = r88568 - r88567;
        double r88570 = r88567 / r88569;
        double r88571 = r88568 + r88567;
        double r88572 = r88568 / r88571;
        double r88573 = r88570 + r88572;
        return r88573;
}
↓
double f(double x) {
        double r88574 = 1.0;
        double r88575 = x;
        double r88576 = r88575 - r88574;
        double r88577 = r88574 / r88576;
        double r88578 = r88575 + r88574;
        double r88579 = r88575 / r88578;
        double r88580 = r88577 + r88579;
        double r88581 = 3.0;
        double r88582 = pow(r88580, r88581);
        double r88583 = cbrt(r88582);
        return r88583;
}

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 2020034 
(FPCore (x)
  :name "Asymptote B"
  :precision binary64
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))