Average Error: 0.0 → 0.0
Time: 3.8s
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 r82400 = 1.0;
        double r82401 = x;
        double r82402 = r82401 - r82400;
        double r82403 = r82400 / r82402;
        double r82404 = r82401 + r82400;
        double r82405 = r82401 / r82404;
        double r82406 = r82403 + r82405;
        return r82406;
}
↓
double f(double x) {
        double r82407 = 1.0;
        double r82408 = x;
        double r82409 = r82408 - r82407;
        double r82410 = r82407 / r82409;
        double r82411 = r82410 * r82410;
        double r82412 = r82408 + r82407;
        double r82413 = r82408 / r82412;
        double r82414 = r82413 * r82413;
        double r82415 = r82411 - r82414;
        double r82416 = r82410 - r82413;
        double r82417 = r82415 / r82416;
        return r82417;
}

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))))