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

Average Error: 0.3 → 0.3

Time: 8.1s

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	9.8
Cost	978

\[\begin{array}{l} \mathbf{if}\;x \leq -95000000000 \lor \neg \left(x \leq -1.6 \cdot 10^{-69} \lor \neg \left(x \leq -1.15 \cdot 10^{-116}\right) \land x \leq 2.45 \cdot 10^{-62}\right):\\ \;\;\;\;x \cdot \left(1 + -6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \end{array} \]

Alternative 2
Error	9.8
Cost	976

\[\begin{array}{l} t_0 := x + \left(x \cdot -6\right) \cdot z\\ t_1 := x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;x \leq -55000000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{-69}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -3.8 \cdot 10^{-116}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-62}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + -6 \cdot z\right)\\ \end{array} \]

Alternative 3
Error	9.8
Cost	976

\[\begin{array}{l} t_0 := x + \left(x \cdot -6\right) \cdot z\\ t_1 := x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;x \leq -15000000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -5 \cdot 10^{-69}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -4 \cdot 10^{-116}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{-62}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{-0.16666666666666666}{x}}\\ \end{array} \]

Alternative 4
Error	24.3
Cost	585

\[\begin{array}{l} \mathbf{if}\;z \leq -0.44 \lor \neg \left(z \leq 0.016\right):\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5
Error	24.3
Cost	584

\[\begin{array}{l} \mathbf{if}\;z \leq -0.44:\\ \;\;\;\;\left(x \cdot -6\right) \cdot z\\ \mathbf{elif}\;z \leq 0.016:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 6
Error	0.3
Cost	576

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

Alternative 7
Error	23.4
Cost	448

\[x \cdot \left(1 + -6 \cdot z\right) \]

Alternative 8
Error	34.9
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023060 
(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)))