Average Error: 0.0 → 0.0
Time: 3.6s
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 r120149 = 1.0;
        double r120150 = x;
        double r120151 = r120150 - r120149;
        double r120152 = r120149 / r120151;
        double r120153 = r120150 + r120149;
        double r120154 = r120150 / r120153;
        double r120155 = r120152 + r120154;
        return r120155;
}
↓
double f(double x) {
        double r120156 = 1.0;
        double r120157 = x;
        double r120158 = r120157 - r120156;
        double r120159 = r120156 / r120158;
        double r120160 = r120157 + r120156;
        double r120161 = r120157 / r120160;
        double r120162 = r120159 + r120161;
        double r120163 = 3.0;
        double r120164 = pow(r120162, r120163);
        double r120165 = cbrt(r120164);
        return r120165;
}

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 2019354 
(FPCore (x)
  :name "Asymptote B"
  :precision binary64
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))