Data.Colour.RGB:hslsv from colour-2.3.3, C

Average Error: 0.0 → 0.1

Time: 53.7s

Precision: 64

Math

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

↓

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

C

double f(double x, double y) {
        double r41031543 = x;
        double r41031544 = y;
        double r41031545 = r41031543 - r41031544;
        double r41031546 = 2.0;
        double r41031547 = r41031543 + r41031544;
        double r41031548 = r41031546 - r41031547;
        double r41031549 = r41031545 / r41031548;
        return r41031549;
}

↓

double f(double x, double y) {
        double r41031550 = 1.0;
        double r41031551 = 2.0;
        double r41031552 = y;
        double r41031553 = x;
        double r41031554 = r41031552 + r41031553;
        double r41031555 = r41031551 - r41031554;
        double r41031556 = r41031550 / r41031555;
        double r41031557 = r41031556 * r41031553;
        double r41031558 = r41031552 / r41031555;
        double r41031559 = r41031557 - r41031558;
        return r41031559;
}

Error

Bits error versus x

Bits error versus y

Target

Original	0.0
Target	0.0
Herbie	0.1

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

Derivation

1. Initial program 0.0

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

3. Applied div-sub 0.0

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

5. Applied div-inv 0.1

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

6. Final simplification 0.1

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

Reproduce

herbie shell --seed 2019200 
(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))))