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

Average Error: 0.4 → 0.2

Time: 21.2s

Precision: binary64

Cost: 960

Math

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

↓

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

FPCore

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

↓

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

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 ((y - x) * 4.0) - (((z * 6.0) * (y - x)) - x);
}

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 = ((y - x) * 4.0d0) - (((z * 6.0d0) * (y - x)) - x)
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 ((y - x) * 4.0) - (((z * 6.0) * (y - x)) - x);
}

Python

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

↓

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

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(Float64(y - x) * 4.0) - Float64(Float64(Float64(z * 6.0) * Float64(y - x)) - x))
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 = ((y - x) * 4.0) - (((z * 6.0) * (y - x)) - x);
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[(N[(y - x), $MachinePrecision] * 4.0), $MachinePrecision] - N[(N[(N[(z * 6.0), $MachinePrecision] * N[(y - x), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 0.4

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

2. Applied egg-rr 0.2

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

3. Applied egg-rr 0.2

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

Alternatives

Alternative 1
Error	21.2
Cost	1636

\[\begin{array}{l} t_0 := -6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{if}\;z \leq -650:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-39}:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-55}:\\ \;\;\;\;-3 \cdot x\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-101}:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-127}:\\ \;\;\;\;-3 \cdot x\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-180}:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-61}:\\ \;\;\;\;-3 \cdot x\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-24}:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;-3 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	21.2
Cost	1636

\[\begin{array}{l} \mathbf{if}\;z \leq -1200:\\ \;\;\;\;\left(-6 \cdot \left(y - x\right)\right) \cdot z\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-39}:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-57}:\\ \;\;\;\;-3 \cdot x\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-102}:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-127}:\\ \;\;\;\;-3 \cdot x\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-182}:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-60}:\\ \;\;\;\;-3 \cdot x\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-24}:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;-3 \cdot x\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \end{array} \]

Alternative 3
Error	21.1
Cost	1636

\[\begin{array}{l} \mathbf{if}\;z \leq -310000:\\ \;\;\;\;\left(-6 \cdot \left(y - x\right)\right) \cdot z\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-39}:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-53}:\\ \;\;\;\;-3 \cdot x\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-103}:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-127}:\\ \;\;\;\;-3 \cdot x\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-175}:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-61}:\\ \;\;\;\;-3 \cdot x\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-24}:\\ \;\;\;\;\left(4 + -6 \cdot z\right) \cdot y\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;-3 \cdot x\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \end{array} \]

Alternative 4
Error	21.4
Cost	1372

\[\begin{array}{l} t_0 := -6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{if}\;z \leq -0.024:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -3.25 \cdot 10^{-102}:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-127}:\\ \;\;\;\;-3 \cdot x\\ \mathbf{elif}\;z \leq -5.4 \cdot 10^{-183}:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-60}:\\ \;\;\;\;-3 \cdot x\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-24}:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;-3 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 5
Error	32.3
Cost	1244

\[\begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -0.15:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-104}:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-127}:\\ \;\;\;\;-3 \cdot x\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-183}:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-60}:\\ \;\;\;\;-3 \cdot x\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-24}:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;z \leq 0.58:\\ \;\;\;\;-3 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 6
Error	32.3
Cost	1244

\[\begin{array}{l} \mathbf{if}\;z \leq -0.15:\\ \;\;\;\;\left(-6 \cdot y\right) \cdot z\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-101}:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-127}:\\ \;\;\;\;-3 \cdot x\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-183}:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-60}:\\ \;\;\;\;-3 \cdot x\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-24}:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;z \leq 0.52:\\ \;\;\;\;-3 \cdot x\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \]

Alternative 7
Error	33.9
Cost	720

\[\begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+35}:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-20}:\\ \;\;\;\;-3 \cdot x\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+39}:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{+88}:\\ \;\;\;\;-3 \cdot x\\ \mathbf{else}:\\ \;\;\;\;4 \cdot y\\ \end{array} \]

Alternative 8
Error	1.8
Cost	712

\[\begin{array}{l} \mathbf{if}\;z \leq -0.57:\\ \;\;\;\;\left(-6 \cdot \left(y - x\right)\right) \cdot z\\ \mathbf{elif}\;z \leq 0.58:\\ \;\;\;\;-3 \cdot x + 4 \cdot y\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \end{array} \]

Alternative 9
Error	0.2
Cost	704

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

Alternative 10
Error	43.3
Cost	192

\[-3 \cdot x \]

Reproduce

herbie shell --seed 2023010 
(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))))