Average Error: 0.0 → 0.0
Time: 10.7s
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 r78991 = 1.0;
        double r78992 = x;
        double r78993 = r78992 - r78991;
        double r78994 = r78991 / r78993;
        double r78995 = r78992 + r78991;
        double r78996 = r78992 / r78995;
        double r78997 = r78994 + r78996;
        return r78997;
}
↓
double f(double x) {
        double r78998 = 1.0;
        double r78999 = x;
        double r79000 = r78999 - r78998;
        double r79001 = r78998 / r79000;
        double r79002 = r78999 + r78998;
        double r79003 = r78999 / r79002;
        double r79004 = r79001 + r79003;
        double r79005 = 3.0;
        double r79006 = pow(r79004, r79005);
        double r79007 = cbrt(r79006);
        return r79007;
}

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 2019306 
(FPCore (x)
  :name "Asymptote B"
  :precision binary64
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))