Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I

Average Error: 3.4 → 0.2

Time: 3.3s

Precision: binary64

Math

\[x \cdot \left(1 - y \cdot z\right)\]

↓

\[\begin{array}{l} \mathbf{if}\;y \cdot z \leq -6.519036621544818 \cdot 10^{+266} \lor \neg \left(y \cdot z \leq 3.807495575138799 \cdot 10^{+241}\right):\\ \;\;\;\;x \cdot 1 - z \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 1 - \left(y \cdot z\right) \cdot x\\ \end{array}\]

C

double code(double x, double y, double z) {
	return ((double) (x * ((double) (1.0 - ((double) (y * z))))));
}

↓

double code(double x, double y, double z) {
	double VAR;
	if (((((double) (y * z)) <= -6.519036621544818e+266) || !(((double) (y * z)) <= 3.807495575138799e+241))) {
		VAR = ((double) (((double) (x * 1.0)) - ((double) (z * ((double) (y * x))))));
	} else {
		VAR = ((double) (((double) (x * 1.0)) - ((double) (((double) (y * z)) * x))));
	}
	return VAR;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

1. Split input into 2 regimes

2. if (* y z) < -6.5190366215448184e266 or 3.8074955751387988e241 < (* y z)

   1. Initial program 40.4

      \[x \cdot \left(1 - y \cdot z\right)\]
   2. Using strategy rm

   3. Applied sub-neg 40.4

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

   4. Applied distribute-lft-in 40.4

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

   5. Simplified 40.4

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

   7. Applied associate-*r* 0.8

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

   if -6.5190366215448184e266 < (* y z) < 3.8074955751387988e241

   1. Initial program 0.1

      \[x \cdot \left(1 - y \cdot z\right)\]
   2. Using strategy rm

   3. Applied sub-neg 0.1

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

   4. Applied distribute-lft-in 0.1

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

   5. Simplified 0.1

      \[\leadsto x \cdot 1 + \color{blue}{x \cdot \left(y \cdot \left(-z\right)\right)}\]
3. Recombined 2 regimes into one program.

4. Final simplification 0.2

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -6.519036621544818 \cdot 10^{+266} \lor \neg \left(y \cdot z \leq 3.807495575138799 \cdot 10^{+241}\right):\\ \;\;\;\;x \cdot 1 - z \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 1 - \left(y \cdot z\right) \cdot x\\ \end{array}\]

Reproduce

herbie shell --seed 2020196 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1.0 (* y z))))