Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, D

Average Accuracy: 99.4% → 99.7%

Time: 13.8s

Precision: binary64

Cost: 960

Math

\[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

↓

\[4 \cdot \left(y - x\right) + \left(x + -6 \cdot \left(\left(y - x\right) \cdot z\right)\right) \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ x (* (* (- y x) 6.0) (- (/ 2.0 3.0) z))))

↓

(FPCore (x y z)
 :precision binary64
 (+ (* 4.0 (- y x)) (+ x (* -6.0 (* (- y x) z)))))

C

double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * ((2.0 / 3.0) - z));
}

↓

double code(double x, double y, double z) {
	return (4.0 * (y - x)) + (x + (-6.0 * ((y - x) * z)));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + (((y - x) * 6.0d0) * ((2.0d0 / 3.0d0) - z))
end function

↓

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (4.0d0 * (y - x)) + (x + ((-6.0d0) * ((y - x) * z)))
end function

Java

public static double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * ((2.0 / 3.0) - z));
}

↓

public static double code(double x, double y, double z) {
	return (4.0 * (y - x)) + (x + (-6.0 * ((y - x) * z)));
}

Python

def code(x, y, z):
	return x + (((y - x) * 6.0) * ((2.0 / 3.0) - z))

↓

def code(x, y, z):
	return (4.0 * (y - x)) + (x + (-6.0 * ((y - x) * z)))

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(Float64(y - x) * 6.0) * Float64(Float64(2.0 / 3.0) - z)))
end

↓

function code(x, y, z)
	return Float64(Float64(4.0 * Float64(y - x)) + Float64(x + Float64(-6.0 * Float64(Float64(y - x) * z))))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + (((y - x) * 6.0) * ((2.0 / 3.0) - z));
end

↓

function tmp = code(x, y, z)
	tmp = (4.0 * (y - x)) + (x + (-6.0 * ((y - x) * z)));
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(N[(y - x), $MachinePrecision] * 6.0), $MachinePrecision] * N[(N[(2.0 / 3.0), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_, z_] := N[(N[(4.0 * N[(y - x), $MachinePrecision]), $MachinePrecision] + N[(x + N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.4%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

2. Taylor expanded in z around 0 99.7%

   \[\leadsto \color{blue}{4 \cdot \left(y - x\right) + \left(-6 \cdot \left(z \cdot \left(y - x\right)\right) + x\right)} \]

3. Final simplification 99.7%

   \[\leadsto 4 \cdot \left(y - x\right) + \left(x + -6 \cdot \left(\left(y - x\right) \cdot z\right)\right) \]

Alternatives

Alternative 1
Accuracy	48.9%
Cost	1773

\[\begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ t_1 := 6 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;z \leq -8.8 \cdot 10^{+170}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -2.05 \cdot 10^{+91}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.1:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-58}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -3.15 \cdot 10^{-176}:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-190}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-246}:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-68}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 6200000000000:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+31} \lor \neg \left(z \leq 7.5 \cdot 10^{+134}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Accuracy	49.0%
Cost	1772

\[\begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ t_1 := 6 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;z \leq -1.32 \cdot 10^{+175}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -5.7 \cdot 10^{+91}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-58}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{-176}:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-190}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-245}:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-67}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 6200000000000:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;z \leq 1.52 \cdot 10^{+30}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+135}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot -6\right)\\ \end{array} \]

Alternative 3
Accuracy	48.9%
Cost	1772

\[\begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ t_1 := z \cdot \left(x \cdot 6\right)\\ \mathbf{if}\;z \leq -7.2 \cdot 10^{+170}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{+90}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.85:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-58}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-176}:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-190}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-245}:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-68}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 6200000000000:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+31}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+128}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot -6\right)\\ \end{array} \]

Alternative 4
Accuracy	67.1%
Cost	1372

\[\begin{array}{l} t_0 := -6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{if}\;z \leq -0.027:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-58}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -2.05 \cdot 10^{-176}:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-190}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-246}:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-67}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.64:\\ \;\;\;\;4 \cdot y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 5
Accuracy	67.5%
Cost	1372

\[\begin{array}{l} t_0 := x \cdot \left(-3 + z \cdot 6\right)\\ t_1 := -6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{if}\;z \leq -56000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-57}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -5.1 \cdot 10^{-176}:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-190}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{-246}:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-68}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 0.58:\\ \;\;\;\;4 \cdot y\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Accuracy	67.5%
Cost	1372

\[\begin{array}{l} t_0 := x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{if}\;z \leq -1200000000:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-57}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-176}:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-190}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-246}:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-68}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 0.56:\\ \;\;\;\;4 \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \end{array} \]

Alternative 7
Accuracy	67.9%
Cost	1372

\[\begin{array}{l} t_0 := x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{if}\;z \leq -250000000:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-57}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -5.4 \cdot 10^{-176}:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-190}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-246}:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-68}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 130000:\\ \;\;\;\;y \cdot \left(4 + -6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \end{array} \]

Alternative 8
Accuracy	48.5%
Cost	1244

\[\begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -1.85:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-57}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-176}:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-190}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-246}:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-67}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 6200000000000:\\ \;\;\;\;4 \cdot y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 9
Accuracy	97.1%
Cost	712

\[\begin{array}{l} \mathbf{if}\;z \leq -0.55:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq 0.55:\\ \;\;\;\;4 \cdot y + x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \end{array} \]

Alternative 10
Accuracy	99.4%
Cost	704

\[x + \left(0.6666666666666666 - z\right) \cdot \left(\left(y - x\right) \cdot 6\right) \]

Alternative 11
Accuracy	99.6%
Cost	704

\[x + \left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right) \]

Alternative 12
Accuracy	46.3%
Cost	456

\[\begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{-67}:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+42}:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;4 \cdot y\\ \end{array} \]

Alternative 13
Accuracy	32.1%
Cost	192

\[4 \cdot y \]

Reproduce

herbie shell --seed 2023151 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, D"
  :precision binary64
  (+ x (* (* (- y x) 6.0) (- (/ 2.0 3.0) z))))