Average Error: 0.0 → 0.0
Time: 1.9s
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 r119658 = 1.0;
        double r119659 = x;
        double r119660 = r119659 - r119658;
        double r119661 = r119658 / r119660;
        double r119662 = r119659 + r119658;
        double r119663 = r119659 / r119662;
        double r119664 = r119661 + r119663;
        return r119664;
}
↓
double f(double x) {
        double r119665 = 1.0;
        double r119666 = x;
        double r119667 = r119666 - r119665;
        double r119668 = r119665 / r119667;
        double r119669 = r119666 + r119665;
        double r119670 = r119666 / r119669;
        double r119671 = r119668 + r119670;
        double r119672 = 3.0;
        double r119673 = pow(r119671, r119672);
        double r119674 = cbrt(r119673);
        return r119674;
}

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 
(FPCore (x)
  :name "Asymptote B"
  :precision binary64
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))