Average Error: 0.0 → 0.0
Time: 9.5s
Precision: 64
\[\frac{x - y}{2 - \left(x + y\right)}\]
↓
\[\frac{x}{\left(2 - x\right) - y} - \frac{y}{\left(2 - x\right) - y}\]
\frac{x - y}{2 - \left(x + y\right)}
↓
\frac{x}{\left(2 - x\right) - y} - \frac{y}{\left(2 - x\right) - y}
double f(double x, double y) {
        double r637252 = x;
        double r637253 = y;
        double r637254 = r637252 - r637253;
        double r637255 = 2.0;
        double r637256 = r637252 + r637253;
        double r637257 = r637255 - r637256;
        double r637258 = r637254 / r637257;
        return r637258;
}
↓
double f(double x, double y) {
        double r637259 = x;
        double r637260 = 2.0;
        double r637261 = r637260 - r637259;
        double r637262 = y;
        double r637263 = r637261 - r637262;
        double r637264 = r637259 / r637263;
        double r637265 = r637262 / r637263;
        double r637266 = r637264 - r637265;
        return r637266;
}

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. 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. Simplified0.0

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

  5. Simplified0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019194 
(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))))