Average Error: 0.0 → 0.0
Time: 6.0s
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 r1738385 = 1.0;
        double r1738386 = x;
        double r1738387 = r1738386 - r1738385;
        double r1738388 = r1738385 / r1738387;
        double r1738389 = r1738386 + r1738385;
        double r1738390 = r1738386 / r1738389;
        double r1738391 = r1738388 + r1738390;
        return r1738391;
}
↓
double f(double x) {
        double r1738392 = 1.0;
        double r1738393 = x;
        double r1738394 = r1738393 - r1738392;
        double r1738395 = r1738392 / r1738394;
        double r1738396 = r1738393 + r1738392;
        double r1738397 = r1738393 / r1738396;
        double r1738398 = r1738395 + r1738397;
        double r1738399 = r1738398 * r1738398;
        double r1738400 = r1738399 * r1738398;
        double r1738401 = cbrt(r1738400);
        return r1738401;
}

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 2019154 +o rules:numerics
(FPCore (x)
  :name "Asymptote B"
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))