Average Error: 0.0 → 0.0
Time: 12.9s
Precision: 64
\[\frac{x}{x - y} + \frac{y}{x - y}\]
\[\frac{\frac{x}{x - y} \cdot \frac{x}{x - y} - \frac{y}{x - y} \cdot \frac{y}{x - y}}{\frac{x}{x - y} - \frac{y}{x - y}}\]
\frac{x}{x - y} + \frac{y}{x - y}
\frac{\frac{x}{x - y} \cdot \frac{x}{x - y} - \frac{y}{x - y} \cdot \frac{y}{x - y}}{\frac{x}{x - y} - \frac{y}{x - y}}
double f(double x, double y) {
        double r7832416 = x;
        double r7832417 = y;
        double r7832418 = r7832416 - r7832417;
        double r7832419 = r7832416 / r7832418;
        double r7832420 = r7832417 / r7832418;
        double r7832421 = r7832419 + r7832420;
        return r7832421;
}

double f(double x, double y) {
        double r7832422 = x;
        double r7832423 = y;
        double r7832424 = r7832422 - r7832423;
        double r7832425 = r7832422 / r7832424;
        double r7832426 = r7832425 * r7832425;
        double r7832427 = r7832423 / r7832424;
        double r7832428 = r7832427 * r7832427;
        double r7832429 = r7832426 - r7832428;
        double r7832430 = r7832425 - r7832427;
        double r7832431 = r7832429 / r7832430;
        return r7832431;
}

Error

Bits error versus x

Bits error versus y

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Results

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Derivation

  1. Initial program 0.0

    \[\frac{x}{x - y} + \frac{y}{x - y}\]
  2. Using strategy rm
  3. Applied flip-+0.0

    \[\leadsto \color{blue}{\frac{\frac{x}{x - y} \cdot \frac{x}{x - y} - \frac{y}{x - y} \cdot \frac{y}{x - y}}{\frac{x}{x - y} - \frac{y}{x - y}}}\]
  4. Final simplification0.0

    \[\leadsto \frac{\frac{x}{x - y} \cdot \frac{x}{x - y} - \frac{y}{x - y} \cdot \frac{y}{x - y}}{\frac{x}{x - y} - \frac{y}{x - y}}\]

Reproduce

herbie shell --seed 1 
(FPCore (x y)
  :name "x/(x-y)+y/(x-y)"
  (+ (/ x (- x y)) (/ y (- x y))))