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

Average Error: 3.5 → 0.2

Time: 2.1s

Precision: binary64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\left(1 - y\right) \cdot z \leq -\infty \lor \neg \left(\left(1 - y\right) \cdot z \leq 1.586906663317492 \cdot 10^{+145}\right):\\ \;\;\;\;x + \left(z \cdot x\right) \cdot \left(y - 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(y \cdot z - z\right)\\ \end{array}\]

FPCore

(FPCore (x y z) :precision binary64 (* x (- 1.0 (* (- 1.0 y) z))))

↓

(FPCore (x y z)
 :precision binary64
 (if (or (<= (* (- 1.0 y) z) (- INFINITY))
         (not (<= (* (- 1.0 y) z) 1.586906663317492e+145)))
   (+ x (* (* z x) (- y 1.0)))
   (+ x (* x (- (* y z) z)))))

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 tmp;
	if ((((1.0 - y) * z) <= -((double) INFINITY)) || !(((1.0 - y) * z) <= 1.586906663317492e+145)) {
		tmp = x + ((z * x) * (y - 1.0));
	} else {
		tmp = x + (x * ((y * z) - z));
	}
	return tmp;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original	3.5
Target	0.2
Herbie	0.2

\[\begin{array}{l} \mathbf{if}\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right) < -1.618195973607049 \cdot 10^{+50}:\\ \;\;\;\;x + \left(1 - y\right) \cdot \left(\left(-z\right) \cdot x\right)\\ \mathbf{elif}\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right) < 3.892237649663903 \cdot 10^{+134}:\\ \;\;\;\;\left(x \cdot y\right) \cdot z - \left(x \cdot z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(1 - y\right) \cdot \left(\left(-z\right) \cdot x\right)\\ \end{array}\]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 1 y) z) < -inf.0 or 1.58690666331749187e145 < (*.f64 (-.f64 1 y) z)

   1. Initial program 21.6

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

   3. Applied sub-neg_binary64 21.6

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

   4. Applied distribute-lft-in_binary64 21.6

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

   5. Simplified 21.6

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

   6. Simplified 21.6

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

   8. Applied *-un-lft-identity_binary64 21.6

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

   9. Applied distribute-rgt-out--_binary64 21.6

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

   10. Applied associate-*r*_binary64 1.1

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

   if -inf.0 < (*.f64 (-.f64 1 y) z) < 1.58690666331749187e145

   1. Initial program 0.1

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

   3. Applied sub-neg_binary64 0.1

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

   4. Applied distribute-lft-in_binary64 0.1

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

   5. Simplified 0.1

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

   6. Simplified 0.1

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

4. Final simplification 0.2

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(1 - y\right) \cdot z \leq -\infty \lor \neg \left(\left(1 - y\right) \cdot z \leq 1.586906663317492 \cdot 10^{+145}\right):\\ \;\;\;\;x + \left(z \cdot x\right) \cdot \left(y - 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(y \cdot z - z\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020224 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, J"
  :precision binary64

  :herbie-target
  (if (< (* x (- 1.0 (* (- 1.0 y) z))) -1.618195973607049e+50) (+ x (* (- 1.0 y) (* (- z) x))) (if (< (* x (- 1.0 (* (- 1.0 y) z))) 3.892237649663903e+134) (- (* (* x y) z) (- (* x z) x)) (+ x (* (- 1.0 y) (* (- z) x)))))

  (* x (- 1.0 (* (- 1.0 y) z))))