Average Error: 0.0 → 0.0
Time: 13.7s
Precision: 64
\[\frac{x - y}{2 - \left(x + y\right)}\]
↓
\[\frac{x}{2 - \left(x + y\right)} - \frac{1}{\frac{2 - x}{y} + -1}\]
\frac{x - y}{2 - \left(x + y\right)}
↓
\frac{x}{2 - \left(x + y\right)} - \frac{1}{\frac{2 - x}{y} + -1}
double f(double x, double y) {
        double r635273 = x;
        double r635274 = y;
        double r635275 = r635273 - r635274;
        double r635276 = 2.0;
        double r635277 = r635273 + r635274;
        double r635278 = r635276 - r635277;
        double r635279 = r635275 / r635278;
        return r635279;
}
↓
double f(double x, double y) {
        double r635280 = x;
        double r635281 = 2.0;
        double r635282 = y;
        double r635283 = r635280 + r635282;
        double r635284 = r635281 - r635283;
        double r635285 = r635280 / r635284;
        double r635286 = 1.0;
        double r635287 = r635281 - r635280;
        double r635288 = r635287 / r635282;
        double r635289 = -1.0;
        double r635290 = r635288 + r635289;
        double r635291 = r635286 / r635290;
        double r635292 = r635285 - r635291;
        return r635292;
}

Error

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Bits error versus y

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Results

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Target

Original0.0
Target0.0
Herbie0.0
\[\frac{x}{2 - \left(x + y\right)} - \frac{y}{2 - \left(x + y\right)}\]

Derivation

  1. Initial program 0.0

    \[\frac{x - y}{2 - \left(x + y\right)}\]
  2. Using strategy rm

  3. Applied div-sub0.0

    \[\leadsto \color{blue}{\frac{x}{2 - \left(x + y\right)} - \frac{y}{2 - \left(x + y\right)}}\]
  4. Using strategy rm

  5. Applied clear-num0.0

    \[\leadsto \frac{x}{2 - \left(x + y\right)} - \color{blue}{\frac{1}{\frac{2 - \left(x + y\right)}{y}}}\]
  6. Using strategy rm

  7. Applied add-sqr-sqrt0.0

    \[\leadsto \frac{x}{2 - \left(x + y\right)} - \frac{\color{blue}{\sqrt{1} \cdot \sqrt{1}}}{\frac{2 - \left(x + y\right)}{y}}\]

  8. Applied associate-/l*0.0

    \[\leadsto \frac{x}{2 - \left(x + y\right)} - \color{blue}{\frac{\sqrt{1}}{\frac{\frac{2 - \left(x + y\right)}{y}}{\sqrt{1}}}}\]

  9. Simplified0.0

    \[\leadsto \frac{x}{2 - \left(x + y\right)} - \frac{\sqrt{1}}{\color{blue}{\frac{2 - x}{y} + -1}}\]

  10. Final simplification0.0

    \[\leadsto \frac{x}{2 - \left(x + y\right)} - \frac{1}{\frac{2 - x}{y} + -1}\]

Reproduce

herbie shell --seed 2019306 
(FPCore (x y)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, C"
  :precision binary64

  :herbie-target
  (- (/ x (- 2 (+ x y))) (/ y (- 2 (+ x y))))

  (/ (- x y) (- 2 (+ x y))))