Average Error: 0.0 → 0.0
Time: 6.0s
Precision: 64
\[\frac{x - y}{2 - \left(x + y\right)}\]
↓
\[\frac{x}{2 - \left(x + y\right)} - \frac{y}{2 - \left(x + y\right)}\]
\frac{x - y}{2 - \left(x + y\right)}
↓
\frac{x}{2 - \left(x + y\right)} - \frac{y}{2 - \left(x + y\right)}
double f(double x, double y) {
        double r636496 = x;
        double r636497 = y;
        double r636498 = r636496 - r636497;
        double r636499 = 2.0;
        double r636500 = r636496 + r636497;
        double r636501 = r636499 - r636500;
        double r636502 = r636498 / r636501;
        return r636502;
}
↓
double f(double x, double y) {
        double r636503 = x;
        double r636504 = 2.0;
        double r636505 = y;
        double r636506 = r636503 + r636505;
        double r636507 = r636504 - r636506;
        double r636508 = r636503 / r636507;
        double r636509 = r636505 / r636507;
        double r636510 = r636508 - r636509;
        return r636510;
}

Error

Bits error versus x

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. Simplified0.0

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

  4. Applied div-sub0.0

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

  5. Simplified0.0

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

  6. Simplified0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019179 
(FPCore (x y)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, C"

  :herbie-target
  (- (/ x (- 2.0 (+ x y))) (/ y (- 2.0 (+ x y))))

  (/ (- x y) (- 2.0 (+ x y))))