Average Error: 0.0 → 0.0
Time: 9.6s
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 r636296 = x;
        double r636297 = y;
        double r636298 = r636296 - r636297;
        double r636299 = 2.0;
        double r636300 = r636296 + r636297;
        double r636301 = r636299 - r636300;
        double r636302 = r636298 / r636301;
        return r636302;
}
↓
double f(double x, double y) {
        double r636303 = x;
        double r636304 = 2.0;
        double r636305 = y;
        double r636306 = r636303 + r636305;
        double r636307 = r636304 - r636306;
        double r636308 = r636303 / r636307;
        double r636309 = r636305 / r636307;
        double r636310 = r636308 - r636309;
        return r636310;
}

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

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

  5. Simplified0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019194 +o rules:numerics
(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))))