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

Average Error: 0.3 → 0.3

Time: 9.0s

Precision: binary64

Cost: 704

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

double code(double x, double y, double z) {
	return x + (((6.0 * y) + (x * -6.0)) * 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) * 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 = x + (((6.0d0 * y) + (x * (-6.0d0))) * z)
end function

Java

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

↓

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

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Target

Original	0.3
Target	0.2
Herbie	0.3

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

Derivation

1. Initial program 0.3

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

2. Taylor expanded in y around 0 0.3

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

3. Final simplification 0.3

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

Alternatives

Alternative 1
Error	12.1
Cost	712

\[\begin{array}{l} t_0 := \frac{y - x}{\frac{0.16666666666666666}{z}}\\ \mathbf{if}\;z \leq -7.444965926460898 \cdot 10^{-8}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 3.1713488635460527 \cdot 10^{-16}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	12.1
Cost	712

\[\begin{array}{l} t_0 := \left(y - x\right) \cdot \left(6 \cdot z\right)\\ \mathbf{if}\;z \leq -7.444965926460898 \cdot 10^{-8}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 3.1713488635460527 \cdot 10^{-16}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Error	17.7
Cost	712

\[\begin{array}{l} \mathbf{if}\;y \leq -1.9982044482918197 \cdot 10^{+63}:\\ \;\;\;\;\left(y - x\right) \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;y \leq 8.129433021767384 \cdot 10^{-70}:\\ \;\;\;\;x \cdot \left(1 + -6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y - x}{\frac{0.16666666666666666}{z}}\\ \end{array} \]

Alternative 4
Error	17.7
Cost	712

\[\begin{array}{l} \mathbf{if}\;y \leq -1.9982044482918197 \cdot 10^{+63}:\\ \;\;\;\;6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{elif}\;y \leq 8.129433021767384 \cdot 10^{-70}:\\ \;\;\;\;x \cdot \left(1 + -6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y - x}{\frac{0.16666666666666666}{z}}\\ \end{array} \]

Alternative 5
Error	1.2
Cost	712

\[\begin{array}{l} t_0 := \left(y - x\right) \cdot \left(6 \cdot z\right)\\ \mathbf{if}\;z \leq -0.006713650935853108:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 3.1713488635460527 \cdot 10^{-16}:\\ \;\;\;\;x + \left(6 \cdot y\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 6
Error	1.2
Cost	712

\[\begin{array}{l} t_0 := \left(y - x\right) \cdot \left(6 \cdot z\right)\\ \mathbf{if}\;z \leq -34.09398674516787:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 3.1713488635460527 \cdot 10^{-16}:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 7
Error	1.2
Cost	712

\[\begin{array}{l} \mathbf{if}\;z \leq -34.09398674516787:\\ \;\;\;\;\frac{6}{\frac{\frac{1}{y - x}}{z}}\\ \mathbf{elif}\;z \leq 3.1713488635460527 \cdot 10^{-16}:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \left(6 \cdot z\right)\\ \end{array} \]

Alternative 8
Error	24.2
Cost	584

\[\begin{array}{l} t_0 := x \cdot \left(-6 \cdot z\right)\\ \mathbf{if}\;z \leq -34.09398674516787:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 3.1713488635460527 \cdot 10^{-16}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 9
Error	23.8
Cost	584

\[\begin{array}{l} \mathbf{if}\;z \leq -34.09398674516787:\\ \;\;\;\;x \cdot \left(-6 \cdot z\right)\\ \mathbf{elif}\;z \leq 2.7413903904586815 \cdot 10^{-56}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(6 \cdot z\right)\\ \end{array} \]

Alternative 10
Error	23.8
Cost	584

\[\begin{array}{l} \mathbf{if}\;z \leq -34.09398674516787:\\ \;\;\;\;x \cdot \left(-6 \cdot z\right)\\ \mathbf{elif}\;z \leq 2.7413903904586815 \cdot 10^{-56}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\left(6 \cdot y\right) \cdot z\\ \end{array} \]

Alternative 11
Error	0.2
Cost	576

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

Alternative 12
Error	0.3
Cost	576

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

Alternative 13
Error	34.5
Cost	64

\[x \]

Reproduce

herbie shell --seed 2022318 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, E"
  :precision binary64

  :herbie-target
  (- x (* (* 6.0 z) (- x y)))

  (+ x (* (* (- y x) 6.0) z)))