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

Average Error: 3.6 → 0.1

Time: 3.2s

Precision: binary64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\left(1 - y\right) \cdot z \le -5.90107994796645571 \cdot 10^{211} \lor \neg \left(\left(1 - y\right) \cdot z \le 3.6352226292813861 \cdot 10^{260}\right):\\ \;\;\;\;x \cdot 1 + \left(x \cdot z\right) \cdot \left(y - 1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 1 + x \cdot \left(z \cdot \left(y - 1\right)\right)\\ \end{array}\]

C

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

↓

double code(double x, double y, double z) {
	double VAR;
	if (((((double) (((double) (1.0 - y)) * z)) <= -5.901079947966456e+211) || !(((double) (((double) (1.0 - y)) * z)) <= 3.635222629281386e+260))) {
		VAR = ((double) (((double) (x * 1.0)) + ((double) (((double) (x * z)) * ((double) (y - 1.0))))));
	} else {
		VAR = ((double) (((double) (x * 1.0)) + ((double) (x * ((double) (z * ((double) (y - 1.0))))))));
	}
	return VAR;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original	3.6
Target	0.2
Herbie	0.1

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

Derivation

1. Split input into 2 regimes

2. if (* (- 1.0 y) z) < -5.90107994796645571e211 or 3.6352226292813861e260 < (* (- 1.0 y) z)

   1. Initial program 25.6

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

   3. Applied sub-neg 25.6

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

   4. Applied distribute-lft-in 25.6

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

   5. Simplified 0.3

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

   if -5.90107994796645571e211 < (* (- 1.0 y) z) < 3.6352226292813861e260

   1. Initial program 0.1

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

   3. Applied sub-neg 0.1

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

   4. Applied distribute-lft-in 0.1

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

   5. Simplified 2.0

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

   7. Applied associate-*l* 0.1

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

4. Final simplification 0.1

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(1 - y\right) \cdot z \le -5.90107994796645571 \cdot 10^{211} \lor \neg \left(\left(1 - y\right) \cdot z \le 3.6352226292813861 \cdot 10^{260}\right):\\ \;\;\;\;x \cdot 1 + \left(x \cdot z\right) \cdot \left(y - 1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 1 + x \cdot \left(z \cdot \left(y - 1\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020147 
(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) (* (neg z) x))) (if (< (* x (- 1.0 (* (- 1.0 y) z))) 3.892237649663903e+134) (- (* (* x y) z) (- (* x z) x)) (+ x (* (- 1.0 y) (* (neg z) x)))))

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