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

Average Error: 0.33% → 0.26%

Time: 8.3s

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	0.33%
Target	0.26%
Herbie	0.26%

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

Derivation

1. Initial program 0.33

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

2. Simplified 0.26

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

   [Start] 0.33	\[ x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   associate-*l* [=>] 0.26	\[ x + \color{blue}{\left(y - x\right) \cdot \left(6 \cdot z\right)} \]

3. Final simplification 0.26

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

Alternatives

Alternative 1
Error	37.56%
Cost	848

\[\begin{array}{l} t_0 := 6 \cdot \left(y \cdot z\right)\\ t_1 := -6 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;z \leq -5.4 \cdot 10^{+70}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -0.00115:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 10^{-27}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9.1 \cdot 10^{+105}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	37.59%
Cost	848

\[\begin{array}{l} t_0 := y \cdot \left(6 \cdot z\right)\\ t_1 := -6 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;z \leq -1.85 \cdot 10^{+72}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -0.00115:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-26}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+105}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Error	19.62%
Cost	713

\[\begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{-8} \lor \neg \left(z \leq 9.8 \cdot 10^{-29}\right):\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4
Error	1.73%
Cost	713

\[\begin{array}{l} \mathbf{if}\;z \leq -0.165 \lor \neg \left(z \leq 0.17\right):\\ \;\;\;\;\left(y - x\right) \cdot \left(6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \end{array} \]

Alternative 5
Error	19.61%
Cost	712

\[\begin{array}{l} \mathbf{if}\;z \leq -1.12 \cdot 10^{-8}:\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{-29}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \left(6 \cdot z\right)\\ \end{array} \]

Alternative 6
Error	37.3%
Cost	585

\[\begin{array}{l} \mathbf{if}\;z \leq -0.00115 \lor \neg \left(z \leq 0.0125\right):\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7
Error	0.33%
Cost	576

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

Alternative 8
Error	53.75%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023102 
(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)))