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

Average Error: 0.2 → 0.2

Time: 19.8s

Precision: binary64

Cost: 576

Math

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

↓

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

FPCore

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

↓

(FPCore (x y z) :precision binary64 (+ x (* (- 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 + ((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 + ((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 + ((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 + ((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(y - x) * Float64(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 + ((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[(y - x), $MachinePrecision] * N[(6.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Target

Original	0.2
Target	0.2
Herbie	0.2

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

Derivation

1. Initial program 0.2

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

2. Simplified 0.2

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

   [Start] 0.2	\[ x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   rational.json-simplify-2 [=>] 0.2	\[ x + \color{blue}{z \cdot \left(\left(y - x\right) \cdot 6\right)} \]
   rational.json-simplify-43 [=>] 0.2	\[ x + \color{blue}{\left(y - x\right) \cdot \left(6 \cdot z\right)} \]

3. Final simplification 0.2

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

Alternatives

Alternative 1
Error	24.0
Cost	712

\[\begin{array}{l} \mathbf{if}\;z \leq -0.165:\\ \;\;\;\;\left(x \cdot -6\right) \cdot z\\ \mathbf{elif}\;z \leq 0.165:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\left(-5 \cdot x - x\right) \cdot z\\ \end{array} \]

Alternative 2
Error	7.5
Cost	712

\[\begin{array}{l} t_0 := x + 6 \cdot \left(z \cdot y\right)\\ \mathbf{if}\;y \leq -1.4 \cdot 10^{-132}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-134}:\\ \;\;\;\;x + -6 \cdot \left(z \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Error	7.5
Cost	712

\[\begin{array}{l} t_0 := x + 6 \cdot \left(z \cdot y\right)\\ \mathbf{if}\;y \leq -9 \cdot 10^{-133}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-133}:\\ \;\;\;\;x + x \cdot \left(z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 4
Error	7.6
Cost	712

\[\begin{array}{l} t_0 := x + y \cdot \left(6 \cdot z\right)\\ \mathbf{if}\;y \leq -2.8 \cdot 10^{-137}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-132}:\\ \;\;\;\;x + x \cdot \left(z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 5
Error	7.5
Cost	712

\[\begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{-134}:\\ \;\;\;\;x + y \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-135}:\\ \;\;\;\;x + x \cdot \left(z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(6 \cdot y\right) \cdot z\\ \end{array} \]

Alternative 6
Error	24.0
Cost	584

\[\begin{array}{l} t_0 := -6 \cdot \left(z \cdot x\right)\\ \mathbf{if}\;z \leq -0.165:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 0.165:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 7
Error	24.0
Cost	584

\[\begin{array}{l} \mathbf{if}\;z \leq -0.165:\\ \;\;\;\;\left(x \cdot -6\right) \cdot z\\ \mathbf{elif}\;z \leq 0.165:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(z \cdot x\right)\\ \end{array} \]

Alternative 8
Error	0.2
Cost	576

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

Alternative 9
Error	23.2
Cost	448

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

Alternative 10
Error	35.0
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023068 
(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)))