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

Average Error: 3.2 → 0.2

Time: 4.0s

Precision: binary64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\left(1 - y\right) \cdot z \leq -\infty \lor \neg \left(\left(1 - y\right) \cdot z \leq 1.2341549239216485 \cdot 10^{+305}\right):\\ \;\;\;\;\left(\sqrt[3]{-1} \cdot \sqrt[3]{-x}\right) \cdot \left(1 \cdot \left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right)\right) + z \cdot \left(\left(\sqrt[3]{-1} \cdot \sqrt[3]{-x}\right) \cdot \left(\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \left(y - 1\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(y - 1\right)\right)\\ \end{array}\]

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)) <= ((double) -(((double) INFINITY)))) || !(((double) (((double) (1.0 - y)) * z)) <= 1.2341549239216485e+305))) {
		VAR = ((double) (((double) (((double) (((double) cbrt(-1.0)) * ((double) cbrt(((double) -(x)))))) * ((double) (1.0 * ((double) (((double) cbrt(x)) * ((double) cbrt(x)))))))) + ((double) (z * ((double) (((double) (((double) cbrt(-1.0)) * ((double) cbrt(((double) -(x)))))) * ((double) (((double) (((double) cbrt(x)) * ((double) cbrt(x)))) * ((double) (y - 1.0))))))))));
	} else {
		VAR = ((double) (x * ((double) (1.0 + ((double) (z * ((double) (y - 1.0))))))));
	}
	return VAR;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original	3.2
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 (* (- 1.0 y) z) < -inf.0 or 1.23415492392164849e305 < (* (- 1.0 y) z)

   1. Initial program 61.5

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

   3. Applied add-cube-cbrt 61.5

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

   4. Applied associate-*l* 61.5

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

   5. Simplified 61.5

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

   7. Applied add-cube-cbrt 61.6

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

   8. Applied cbrt-prod 61.6

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

   9. Applied associate-*r* 61.6

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

   10. Taylor expanded around -inf 50.2

       \[\leadsto \left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \color{blue}{\left(\left(1 \cdot \left(\sqrt[3]{-1} \cdot e^{0.3333333333333333 \cdot \left(\log 1 - \log \left(\frac{-1}{x}\right)\right)}\right) + \sqrt[3]{-1} \cdot \left(z \cdot \left(y \cdot e^{0.3333333333333333 \cdot \left(\log 1 - \log \left(\frac{-1}{x}\right)\right)}\right)\right)\right) - 1 \cdot \left(\sqrt[3]{-1} \cdot \left(z \cdot e^{0.3333333333333333 \cdot \left(\log 1 - \log \left(\frac{-1}{x}\right)\right)}\right)\right)\right)}\]

   11. Simplified 33.9

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

   13. Applied distribute-lft-in 33.9

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

   14. Simplified 33.9

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

   15. Simplified 1.5

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

   if -inf.0 < (* (- 1.0 y) z) < 1.23415492392164849e305

   1. Initial program 0.1

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right)\]
3. Recombined 2 regimes into one program.

4. Final simplification 0.2

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(1 - y\right) \cdot z \leq -\infty \lor \neg \left(\left(1 - y\right) \cdot z \leq 1.2341549239216485 \cdot 10^{+305}\right):\\ \;\;\;\;\left(\sqrt[3]{-1} \cdot \sqrt[3]{-x}\right) \cdot \left(1 \cdot \left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right)\right) + z \cdot \left(\left(\sqrt[3]{-1} \cdot \sqrt[3]{-x}\right) \cdot \left(\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \left(y - 1\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(y - 1\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020196 
(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))))