Average Error: 0.0 → 0.0
Time: 7.1s
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 r114808 = 1.0;
        double r114809 = x;
        double r114810 = r114809 - r114808;
        double r114811 = r114808 / r114810;
        double r114812 = r114809 + r114808;
        double r114813 = r114809 / r114812;
        double r114814 = r114811 + r114813;
        return r114814;
}
↓
double f(double x) {
        double r114815 = 1.0;
        double r114816 = x;
        double r114817 = r114816 - r114815;
        double r114818 = r114815 / r114817;
        double r114819 = r114816 + r114815;
        double r114820 = r114816 / r114819;
        double r114821 = r114818 + r114820;
        double r114822 = 3.0;
        double r114823 = pow(r114821, r114822);
        double r114824 = cbrt(r114823);
        return r114824;
}

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 2019350 +o rules:numerics
(FPCore (x)
  :name "Asymptote B"
  :precision binary64
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))