Average Error: 0.0 → 0.0
Time: 2.0s
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 r119599 = 1.0;
        double r119600 = x;
        double r119601 = r119600 - r119599;
        double r119602 = r119599 / r119601;
        double r119603 = r119600 + r119599;
        double r119604 = r119600 / r119603;
        double r119605 = r119602 + r119604;
        return r119605;
}
↓
double f(double x) {
        double r119606 = 1.0;
        double r119607 = x;
        double r119608 = r119607 - r119606;
        double r119609 = r119606 / r119608;
        double r119610 = r119607 + r119606;
        double r119611 = r119607 / r119610;
        double r119612 = r119609 + r119611;
        double r119613 = 3.0;
        double r119614 = pow(r119612, r119613);
        double r119615 = cbrt(r119614);
        return r119615;
}

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 2020018 +o rules:numerics
(FPCore (x)
  :name "Asymptote B"
  :precision binary64
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))