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

Average Error: 2.7 → 0.1

Time: 5.2s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;y \cdot z = -\infty:\\ \;\;\;\;x \cdot 1 + \left(x \cdot z\right) \cdot \left(-y\right)\\ \mathbf{elif}\;y \cdot z \le 1.45551293622058124 \cdot 10^{302}:\\ \;\;\;\;x \cdot 1 + x \cdot \left(-y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 1 + \left(x \cdot \left(y \cdot 1\right)\right) \cdot \left(-1 \cdot z\right)\\ \end{array}\]

C

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

↓

double code(double x, double y, double z) {
	double temp;
	if (((y * z) <= -inf.0)) {
		temp = ((x * 1.0) + ((x * z) * -y));
	} else {
		double temp_1;
		if (((y * z) <= 1.4555129362205812e+302)) {
			temp_1 = ((x * 1.0) + (x * -(y * z)));
		} else {
			temp_1 = ((x * 1.0) + ((x * (y * 1.0)) * (-1.0 * z)));
		}
		temp = temp_1;
	}
	return temp;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

1. Split input into 3 regimes

2. if (* y z) < -inf.0

   1. Initial program 64.0

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

   3. Applied sub-neg 64.0

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

   4. Applied distribute-lft-in 64.0

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

   6. Applied *-commutative 64.0

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

   7. Applied distribute-rgt-neg-in 64.0

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

   8. Applied associate-*r* 0.3

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

   if -inf.0 < (* y z) < 1.4555129362205812e+302

   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

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

   if 1.4555129362205812e+302 < (* y z)

   1. Initial program 58.4

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

   3. Applied sub-neg 58.4

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

   4. Applied distribute-lft-in 58.4

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

   6. Applied add-cube-cbrt 58.5

      \[\leadsto x \cdot 1 + x \cdot \left(-y \cdot \color{blue}{\left(\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \sqrt[3]{z}\right)}\right)\]

   7. Applied associate-*r* 58.5

      \[\leadsto x \cdot 1 + x \cdot \left(-\color{blue}{\left(y \cdot \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)\right) \cdot \sqrt[3]{z}}\right)\]

   8. Applied distribute-rgt-neg-in 58.5

      \[\leadsto x \cdot 1 + x \cdot \color{blue}{\left(\left(y \cdot \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)\right) \cdot \left(-\sqrt[3]{z}\right)\right)}\]

   9. Applied associate-*r* 29.7

      \[\leadsto x \cdot 1 + \color{blue}{\left(x \cdot \left(y \cdot \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)\right)\right) \cdot \left(-\sqrt[3]{z}\right)}\]
   10. Using strategy rm

   11. Applied *-un-lft-identity 29.7

       \[\leadsto x \cdot 1 + \left(x \cdot \left(y \cdot \left(\sqrt[3]{z} \cdot \color{blue}{\left(1 \cdot \sqrt[3]{z}\right)}\right)\right)\right) \cdot \left(-\sqrt[3]{z}\right)\]

   12. Applied *-un-lft-identity 29.7

       \[\leadsto x \cdot 1 + \left(x \cdot \left(y \cdot \left(\color{blue}{\left(1 \cdot \sqrt[3]{z}\right)} \cdot \left(1 \cdot \sqrt[3]{z}\right)\right)\right)\right) \cdot \left(-\sqrt[3]{z}\right)\]

   13. Applied swap-sqr 29.7

       \[\leadsto x \cdot 1 + \left(x \cdot \left(y \cdot \color{blue}{\left(\left(1 \cdot 1\right) \cdot \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)\right)}\right)\right) \cdot \left(-\sqrt[3]{z}\right)\]

   14. Applied associate-*r* 29.7

       \[\leadsto x \cdot 1 + \left(x \cdot \color{blue}{\left(\left(y \cdot \left(1 \cdot 1\right)\right) \cdot \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)\right)}\right) \cdot \left(-\sqrt[3]{z}\right)\]

   15. Applied associate-*r* 1.3

       \[\leadsto x \cdot 1 + \color{blue}{\left(\left(x \cdot \left(y \cdot \left(1 \cdot 1\right)\right)\right) \cdot \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)\right)} \cdot \left(-\sqrt[3]{z}\right)\]

   16. Applied associate-*l* 1.3

       \[\leadsto x \cdot 1 + \color{blue}{\left(x \cdot \left(y \cdot \left(1 \cdot 1\right)\right)\right) \cdot \left(\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \left(-\sqrt[3]{z}\right)\right)}\]

   17. Simplified 0.2

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

4. Final simplification 0.1

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z = -\infty:\\ \;\;\;\;x \cdot 1 + \left(x \cdot z\right) \cdot \left(-y\right)\\ \mathbf{elif}\;y \cdot z \le 1.45551293622058124 \cdot 10^{302}:\\ \;\;\;\;x \cdot 1 + x \cdot \left(-y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 1 + \left(x \cdot \left(y \cdot 1\right)\right) \cdot \left(-1 \cdot z\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020066 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1 (* y z))))