Average Error: 0.0 → 0.0
Time: 2.1s
Precision: 64
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
↓
\[\frac{\frac{1}{x - 1} \cdot \frac{1}{x - 1} - \frac{x}{x + 1} \cdot \frac{x}{x + 1}}{\frac{1}{x - 1} - \frac{x}{x + 1}}\]
\frac{1}{x - 1} + \frac{x}{x + 1}
↓
\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}}
double f(double x) {
        double r170291 = 1.0;
        double r170292 = x;
        double r170293 = r170292 - r170291;
        double r170294 = r170291 / r170293;
        double r170295 = r170292 + r170291;
        double r170296 = r170292 / r170295;
        double r170297 = r170294 + r170296;
        return r170297;
}
↓
double f(double x) {
        double r170298 = 1.0;
        double r170299 = x;
        double r170300 = r170299 - r170298;
        double r170301 = r170298 / r170300;
        double r170302 = r170301 * r170301;
        double r170303 = r170299 + r170298;
        double r170304 = r170299 / r170303;
        double r170305 = r170304 * r170304;
        double r170306 = r170302 - r170305;
        double r170307 = r170301 - r170304;
        double r170308 = r170306 / r170307;
        return r170308;
}

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 flip-+0.0

    \[\leadsto \color{blue}{\frac{\frac{1}{x - 1} \cdot \frac{1}{x - 1} - \frac{x}{x + 1} \cdot \frac{x}{x + 1}}{\frac{1}{x - 1} - \frac{x}{x + 1}}}\]

  4. Final simplification0.0

    \[\leadsto \frac{\frac{1}{x - 1} \cdot \frac{1}{x - 1} - \frac{x}{x + 1} \cdot \frac{x}{x + 1}}{\frac{1}{x - 1} - \frac{x}{x + 1}}\]

Reproduce

herbie shell --seed 2020046 
(FPCore (x)
  :name "Asymptote B"
  :precision binary64
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))