Average Error: 0.0 → 0.0
Time: 9.1s
Precision: 64
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
↓
\[\sqrt[3]{{\left(\left(\sqrt[3]{\frac{1}{x - 1}} \cdot \sqrt[3]{\frac{1}{x - 1}}\right) \cdot \sqrt[3]{\frac{1}{x - 1}} + \frac{x}{x + 1}\right)}^{3}}\]
\frac{1}{x - 1} + \frac{x}{x + 1}
↓
\sqrt[3]{{\left(\left(\sqrt[3]{\frac{1}{x - 1}} \cdot \sqrt[3]{\frac{1}{x - 1}}\right) \cdot \sqrt[3]{\frac{1}{x - 1}} + \frac{x}{x + 1}\right)}^{3}}
double f(double x) {
        double r91034 = 1.0;
        double r91035 = x;
        double r91036 = r91035 - r91034;
        double r91037 = r91034 / r91036;
        double r91038 = r91035 + r91034;
        double r91039 = r91035 / r91038;
        double r91040 = r91037 + r91039;
        return r91040;
}
↓
double f(double x) {
        double r91041 = 1.0;
        double r91042 = x;
        double r91043 = r91042 - r91041;
        double r91044 = r91041 / r91043;
        double r91045 = cbrt(r91044);
        double r91046 = r91045 * r91045;
        double r91047 = r91046 * r91045;
        double r91048 = r91042 + r91041;
        double r91049 = r91042 / r91048;
        double r91050 = r91047 + r91049;
        double r91051 = 3.0;
        double r91052 = pow(r91050, r91051);
        double r91053 = cbrt(r91052);
        return r91053;
}

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. Using strategy rm

  6. Applied add-cube-cbrt0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019326 
(FPCore (x)
  :name "Asymptote B"
  :precision binary64
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))