Average Error: 0.0 → 0.0
Time: 14.1s
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 r87739 = 1.0;
        double r87740 = x;
        double r87741 = r87740 - r87739;
        double r87742 = r87739 / r87741;
        double r87743 = r87740 + r87739;
        double r87744 = r87740 / r87743;
        double r87745 = r87742 + r87744;
        return r87745;
}
↓
double f(double x) {
        double r87746 = 1.0;
        double r87747 = x;
        double r87748 = r87747 - r87746;
        double r87749 = r87746 / r87748;
        double r87750 = r87747 + r87746;
        double r87751 = r87747 / r87750;
        double r87752 = r87749 + r87751;
        double r87753 = 3.0;
        double r87754 = pow(r87752, r87753);
        double r87755 = cbrt(r87754);
        return r87755;
}

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 2019323 +o rules:numerics
(FPCore (x)
  :name "Asymptote B"
  :precision binary64
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))