Average Error: 0.0 → 0.0
Time: 2.8s
Precision: 64
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
↓
\[\sqrt[3]{{\left(\frac{\frac{1}{x - 1} \cdot \frac{1}{x - 1} - \frac{x}{x + 1} \cdot \frac{x}{x + 1}}{\frac{1}{x - 1} - \frac{x}{x + 1}}\right)}^{3}}\]
\frac{1}{x - 1} + \frac{x}{x + 1}
↓
\sqrt[3]{{\left(\frac{\frac{1}{x - 1} \cdot \frac{1}{x - 1} - \frac{x}{x + 1} \cdot \frac{x}{x + 1}}{\frac{1}{x - 1} - \frac{x}{x + 1}}\right)}^{3}}
double f(double x) {
        double r171202 = 1.0;
        double r171203 = x;
        double r171204 = r171203 - r171202;
        double r171205 = r171202 / r171204;
        double r171206 = r171203 + r171202;
        double r171207 = r171203 / r171206;
        double r171208 = r171205 + r171207;
        return r171208;
}
↓
double f(double x) {
        double r171209 = 1.0;
        double r171210 = x;
        double r171211 = r171210 - r171209;
        double r171212 = r171209 / r171211;
        double r171213 = r171212 * r171212;
        double r171214 = r171210 + r171209;
        double r171215 = r171210 / r171214;
        double r171216 = r171215 * r171215;
        double r171217 = r171213 - r171216;
        double r171218 = r171212 - r171215;
        double r171219 = r171217 / r171218;
        double r171220 = 3.0;
        double r171221 = pow(r171219, r171220);
        double r171222 = cbrt(r171221);
        return r171222;
}

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 flip-+0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2020036 
(FPCore (x)
  :name "Asymptote B"
  :precision binary64
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))