Average Error: 0.0 → 0.0
Time: 9.3s
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 r84988 = 1.0;
        double r84989 = x;
        double r84990 = r84989 - r84988;
        double r84991 = r84988 / r84990;
        double r84992 = r84989 + r84988;
        double r84993 = r84989 / r84992;
        double r84994 = r84991 + r84993;
        return r84994;
}
↓
double f(double x) {
        double r84995 = 1.0;
        double r84996 = x;
        double r84997 = r84996 - r84995;
        double r84998 = r84995 / r84997;
        double r84999 = r84996 + r84995;
        double r85000 = r84996 / r84999;
        double r85001 = r84998 + r85000;
        double r85002 = 3.0;
        double r85003 = pow(r85001, r85002);
        double r85004 = cbrt(r85003);
        return r85004;
}

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 2019209 
(FPCore (x)
  :name "Asymptote B"
  :precision binary64
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))