Average Error: 0.0 → 0.0
Time: 3.0s
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 r142829 = 1.0;
        double r142830 = x;
        double r142831 = r142830 - r142829;
        double r142832 = r142829 / r142831;
        double r142833 = r142830 + r142829;
        double r142834 = r142830 / r142833;
        double r142835 = r142832 + r142834;
        return r142835;
}
↓
double f(double x) {
        double r142836 = 1.0;
        double r142837 = x;
        double r142838 = r142837 - r142836;
        double r142839 = r142836 / r142838;
        double r142840 = r142837 + r142836;
        double r142841 = r142837 / r142840;
        double r142842 = r142839 + r142841;
        double r142843 = 3.0;
        double r142844 = pow(r142842, r142843);
        double r142845 = cbrt(r142844);
        return r142845;
}

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 2020035 
(FPCore (x)
  :name "Asymptote B"
  :precision binary64
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))