Average Error: 0.0 → 0.0
Time: 1.8s
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 r127525 = 1.0;
        double r127526 = x;
        double r127527 = r127526 - r127525;
        double r127528 = r127525 / r127527;
        double r127529 = r127526 + r127525;
        double r127530 = r127526 / r127529;
        double r127531 = r127528 + r127530;
        return r127531;
}
↓
double f(double x) {
        double r127532 = 1.0;
        double r127533 = x;
        double r127534 = r127533 - r127532;
        double r127535 = r127532 / r127534;
        double r127536 = r127535 * r127535;
        double r127537 = r127533 + r127532;
        double r127538 = r127533 / r127537;
        double r127539 = r127538 * r127538;
        double r127540 = r127536 - r127539;
        double r127541 = r127535 - r127538;
        double r127542 = r127540 / r127541;
        return r127542;
}

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 2020033 
(FPCore (x)
  :name "Asymptote B"
  :precision binary64
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))