Average Error: 0.0 → 0.0
Time: 4.4m
Precision: 64
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
↓
\[\sqrt[3]{\left(\left(\sqrt[3]{\left(\frac{1}{x - 1} + \frac{x}{x + 1}\right) \cdot \left(\frac{1}{x - 1} + \frac{x}{x + 1}\right)} \cdot \sqrt[3]{\left(\frac{1}{x - 1} + \frac{x}{x + 1}\right) \cdot \left(\frac{1}{x - 1} + \frac{x}{x + 1}\right)}\right) \cdot \sqrt[3]{\left(\frac{1}{x - 1} + \frac{x}{x + 1}\right) \cdot \left(\frac{1}{x - 1} + \frac{x}{x + 1}\right)}\right) \cdot \left(\frac{1}{x - 1} + \frac{x}{x + 1}\right)}\]
\frac{1}{x - 1} + \frac{x}{x + 1}
↓
\sqrt[3]{\left(\left(\sqrt[3]{\left(\frac{1}{x - 1} + \frac{x}{x + 1}\right) \cdot \left(\frac{1}{x - 1} + \frac{x}{x + 1}\right)} \cdot \sqrt[3]{\left(\frac{1}{x - 1} + \frac{x}{x + 1}\right) \cdot \left(\frac{1}{x - 1} + \frac{x}{x + 1}\right)}\right) \cdot \sqrt[3]{\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 r42118275 = 1.0;
        double r42118276 = x;
        double r42118277 = r42118276 - r42118275;
        double r42118278 = r42118275 / r42118277;
        double r42118279 = r42118276 + r42118275;
        double r42118280 = r42118276 / r42118279;
        double r42118281 = r42118278 + r42118280;
        return r42118281;
}
↓
double f(double x) {
        double r42118282 = 1.0;
        double r42118283 = x;
        double r42118284 = r42118283 - r42118282;
        double r42118285 = r42118282 / r42118284;
        double r42118286 = r42118283 + r42118282;
        double r42118287 = r42118283 / r42118286;
        double r42118288 = r42118285 + r42118287;
        double r42118289 = r42118288 * r42118288;
        double r42118290 = cbrt(r42118289);
        double r42118291 = r42118290 * r42118290;
        double r42118292 = r42118291 * r42118290;
        double r42118293 = r42118292 * r42118288;
        double r42118294 = cbrt(r42118293);
        return r42118294;
}

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. Using strategy rm

  5. Applied add-cube-cbrt0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019125 
(FPCore (x)
  :name "Asymptote B"
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))