Average Error: 0.0 → 0.0
Time: 6.4s
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 r101907 = 1.0;
        double r101908 = x;
        double r101909 = r101908 - r101907;
        double r101910 = r101907 / r101909;
        double r101911 = r101908 + r101907;
        double r101912 = r101908 / r101911;
        double r101913 = r101910 + r101912;
        return r101913;
}
↓
double f(double x) {
        double r101914 = 1.0;
        double r101915 = x;
        double r101916 = r101915 - r101914;
        double r101917 = r101914 / r101916;
        double r101918 = r101915 + r101914;
        double r101919 = r101915 / r101918;
        double r101920 = r101917 + r101919;
        double r101921 = 3.0;
        double r101922 = pow(r101920, r101921);
        double r101923 = cbrt(r101922);
        return r101923;
}

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

    \[\leadsto \sqrt[3]{\color{blue}{{\left(\frac{1}{x - 1} + \frac{x}{1 + x}\right)}^{3}}}\]

  5. Final simplification0.0

    \[\leadsto \sqrt[3]{{\left(\frac{1}{x - 1} + \frac{x}{x + 1}\right)}^{3}}\]

Reproduce

herbie shell --seed 2019179 
(FPCore (x)
  :name "Asymptote B"
  (+ (/ 1.0 (- x 1.0)) (/ x (+ x 1.0))))