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

Average Error: 3.5 → 0.3

Time: 1.9s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;x \le -8.15902585295616486 \cdot 10^{63} \lor \neg \left(x \le 1.70388318803188497 \cdot 10^{-58}\right):\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(y - 1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 1 + z \cdot \left(x \cdot \left(y - 1\right)\right)\\ \end{array}\]

C

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

↓

double code(double x, double y, double z) {
	double VAR;
	if (((x <= -8.159025852956165e+63) || !(x <= 1.703883188031885e-58))) {
		VAR = (x * (1.0 + (z * (y - 1.0))));
	} else {
		VAR = ((x * 1.0) + (z * (x * (y - 1.0))));
	}
	return VAR;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original	3.5
Target	0.2
Herbie	0.3

\[\begin{array}{l} \mathbf{if}\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \lt -1.618195973607049 \cdot 10^{50}:\\ \;\;\;\;x + \left(1 - y\right) \cdot \left(\left(-z\right) \cdot x\right)\\ \mathbf{elif}\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \lt 3.8922376496639029 \cdot 10^{134}:\\ \;\;\;\;\left(x \cdot y\right) \cdot z - \left(x \cdot z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(1 - y\right) \cdot \left(\left(-z\right) \cdot x\right)\\ \end{array}\]

Derivation

1. Split input into 2 regimes

2. if x < -8.159025852956165e+63 or 1.703883188031885e-58 < x

   1. Initial program 0.4

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

   3. Applied sub-neg 0.4

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

   4. Applied distribute-lft-in 0.4

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

   5. Simplified 0.1

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

   7. Applied associate-*l* 0.4

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

   8. Applied distribute-lft-out 0.4

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

   if -8.159025852956165e+63 < x < 1.703883188031885e-58

   1. Initial program 5.5

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

   3. Applied sub-neg 5.5

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

   4. Applied distribute-lft-in 5.5

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

   5. Simplified 2.7

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

   7. Applied *-commutative 2.7

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

   8. Applied associate-*l* 0.3

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

4. Final simplification 0.3

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -8.15902585295616486 \cdot 10^{63} \lor \neg \left(x \le 1.70388318803188497 \cdot 10^{-58}\right):\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(y - 1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 1 + z \cdot \left(x \cdot \left(y - 1\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020078 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, J"
  :precision binary64

  :herbie-target
  (if (< (* x (- 1 (* (- 1 y) z))) -1.618195973607049e+50) (+ x (* (- 1 y) (* (- z) x))) (if (< (* x (- 1 (* (- 1 y) z))) 3.892237649663903e+134) (- (* (* x y) z) (- (* x z) x)) (+ x (* (- 1 y) (* (- z) x)))))

  (* x (- 1 (* (- 1 y) z))))