Average Error: 0.0 → 0.0
Time: 10.4s
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 r5308423 = 1.0;
        double r5308424 = x;
        double r5308425 = r5308424 - r5308423;
        double r5308426 = r5308423 / r5308425;
        double r5308427 = r5308424 + r5308423;
        double r5308428 = r5308424 / r5308427;
        double r5308429 = r5308426 + r5308428;
        return r5308429;
}
↓
double f(double x) {
        double r5308430 = 1.0;
        double r5308431 = x;
        double r5308432 = r5308431 - r5308430;
        double r5308433 = r5308430 / r5308432;
        double r5308434 = r5308433 * r5308433;
        double r5308435 = r5308431 + r5308430;
        double r5308436 = r5308431 / r5308435;
        double r5308437 = r5308436 * r5308436;
        double r5308438 = r5308434 - r5308437;
        double r5308439 = r5308433 - r5308436;
        double r5308440 = r5308438 / r5308439;
        return r5308440;
}

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 2019192 
(FPCore (x)
  :name "Asymptote B"
  (+ (/ 1.0 (- x 1.0)) (/ x (+ x 1.0))))