Average Error: 0.0 → 0.0
Time: 6.8s
Precision: 64
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
↓
\[\left(\sqrt[3]{\frac{1}{x - 1} + \frac{x}{x + 1}} \cdot \sqrt[3]{\frac{1}{x - 1} + \frac{x}{x + 1}}\right) \cdot \sqrt[3]{\frac{1}{x - 1} + \frac{x}{x + 1}}\]
\frac{1}{x - 1} + \frac{x}{x + 1}
↓
\left(\sqrt[3]{\frac{1}{x - 1} + \frac{x}{x + 1}} \cdot \sqrt[3]{\frac{1}{x - 1} + \frac{x}{x + 1}}\right) \cdot \sqrt[3]{\frac{1}{x - 1} + \frac{x}{x + 1}}
double f(double x) {
        double r102350 = 1.0;
        double r102351 = x;
        double r102352 = r102351 - r102350;
        double r102353 = r102350 / r102352;
        double r102354 = r102351 + r102350;
        double r102355 = r102351 / r102354;
        double r102356 = r102353 + r102355;
        return r102356;
}
↓
double f(double x) {
        double r102357 = 1.0;
        double r102358 = x;
        double r102359 = r102358 - r102357;
        double r102360 = r102357 / r102359;
        double r102361 = r102358 + r102357;
        double r102362 = r102358 / r102361;
        double r102363 = r102360 + r102362;
        double r102364 = cbrt(r102363);
        double r102365 = r102364 * r102364;
        double r102366 = r102365 * r102364;
        return r102366;
}

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-cube-cbrt0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019351 
(FPCore (x)
  :name "Asymptote B"
  :precision binary64
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))