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

Average Error: 0.3 → 0.2

Time: 18.5s

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	0.3
Target	0.2
Herbie	0.2

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

Derivation

1. Initial program 0.3

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

2. Simplified 0.2

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

   [Start] 0.3	\[ x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   rational.json-simplify-2 [=>] 0.3	\[ x + \color{blue}{z \cdot \left(\left(y - x\right) \cdot 6\right)} \]
   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	23.7
Cost	848

\[\begin{array}{l} t_0 := y \cdot \left(z \cdot 6\right)\\ \mathbf{if}\;z \leq -1.85 \cdot 10^{+136}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{+74}:\\ \;\;\;\;-6 \cdot \left(z \cdot x\right)\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-88}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-60}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	23.7
Cost	848

\[\begin{array}{l} t_0 := y \cdot \left(z \cdot 6\right)\\ \mathbf{if}\;z \leq -1.05 \cdot 10^{+136}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{+74}:\\ \;\;\;\;z \cdot \left(x \cdot -6\right)\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{-89}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-60}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Error	23.8
Cost	848

\[\begin{array}{l} t_0 := y \cdot \left(z \cdot 6\right)\\ \mathbf{if}\;z \leq -7 \cdot 10^{+136}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{+74}:\\ \;\;\;\;\left(-6 \cdot z\right) \cdot x\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-88}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-59}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 4
Error	15.3
Cost	712

\[\begin{array}{l} t_0 := \left(1 + -6 \cdot z\right) \cdot x\\ \mathbf{if}\;x \leq -9.6 \cdot 10^{-113}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-99}:\\ \;\;\;\;y \cdot \left(z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 5
Error	8.0
Cost	712

\[\begin{array}{l} t_0 := x + 6 \cdot \left(z \cdot y\right)\\ \mathbf{if}\;y \leq -2 \cdot 10^{-229}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.26 \cdot 10^{-161}:\\ \;\;\;\;\left(1 + -6 \cdot z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 6
Error	8.0
Cost	712

\[\begin{array}{l} t_0 := x + 6 \cdot \left(z \cdot y\right)\\ \mathbf{if}\;y \leq -1.65 \cdot 10^{-229}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-159}:\\ \;\;\;\;x + \left(-6 \cdot x\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 7
Error	8.1
Cost	712

\[\begin{array}{l} t_0 := x + \left(6 \cdot y\right) \cdot z\\ \mathbf{if}\;y \leq -2 \cdot 10^{-229}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-160}:\\ \;\;\;\;x + \left(-6 \cdot x\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 8
Error	8.0
Cost	712

\[\begin{array}{l} t_0 := x + \left(z \cdot 6\right) \cdot y\\ \mathbf{if}\;y \leq -2 \cdot 10^{-229}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-160}:\\ \;\;\;\;x + \left(-6 \cdot x\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 9
Error	8.0
Cost	712

\[\begin{array}{l} t_0 := x + \left(z \cdot 6\right) \cdot y\\ \mathbf{if}\;y \leq -1.45 \cdot 10^{-229}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.08 \cdot 10^{-159}:\\ \;\;\;\;-6 \cdot \left(z \cdot x\right) + x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 10
Error	24.3
Cost	584

\[\begin{array}{l} t_0 := -6 \cdot \left(z \cdot x\right)\\ \mathbf{if}\;z \leq -1200000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.48 \cdot 10^{-5}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 11
Error	0.3
Cost	576

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

Alternative 12
Error	34.6
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023075 
(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)))