Average Error: 0.0 → 0.0
Time: 5.6s
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 r116151 = 1.0;
        double r116152 = x;
        double r116153 = r116152 - r116151;
        double r116154 = r116151 / r116153;
        double r116155 = r116152 + r116151;
        double r116156 = r116152 / r116155;
        double r116157 = r116154 + r116156;
        return r116157;
}
↓
double f(double x) {
        double r116158 = 1.0;
        double r116159 = x;
        double r116160 = r116159 - r116158;
        double r116161 = r116158 / r116160;
        double r116162 = r116159 + r116158;
        double r116163 = r116159 / r116162;
        double r116164 = r116161 + r116163;
        double r116165 = 3.0;
        double r116166 = pow(r116164, r116165);
        double r116167 = cbrt(r116166);
        return r116167;
}

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 2019350 
(FPCore (x)
  :name "Asymptote B"
  :precision binary64
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))