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

Average Error: 0.3 → 0.3

Time: 6.5s

Precision: binary64

Cost: 576

Math

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

↓

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

FPCore

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

↓

(FPCore (x y z) :precision binary64 (+ x (* (* (- 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(Float64(y - 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 + (((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[(y - x), $MachinePrecision] * 6.0), $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. Final simplification 0.3

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

Alternatives

Alternative 1
Error	7.1
Cost	713

\[\begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{-78} \lor \neg \left(y \leq 5 \cdot 10^{-81}\right):\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + -6 \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 2
Error	7.0
Cost	712

\[\begin{array}{l} \mathbf{if}\;y \leq -7.4 \cdot 10^{-78}:\\ \;\;\;\;x + y \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{-82}:\\ \;\;\;\;x + -6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \end{array} \]

Alternative 3
Error	7.1
Cost	712

\[\begin{array}{l} \mathbf{if}\;y \leq -9.6 \cdot 10^{-78}:\\ \;\;\;\;x + z \cdot \frac{y}{0.16666666666666666}\\ \mathbf{elif}\;y \leq 2.45 \cdot 10^{-82}:\\ \;\;\;\;x + -6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \end{array} \]

Alternative 4
Error	7.2
Cost	712

\[\begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{-78}:\\ \;\;\;\;x + z \cdot \frac{y}{0.16666666666666666}\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-80}:\\ \;\;\;\;x + -6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(y \cdot 6\right)\\ \end{array} \]

Alternative 5
Error	24.6
Cost	585

\[\begin{array}{l} \mathbf{if}\;z \leq -1350000000000 \lor \neg \left(z \leq 72\right):\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6
Error	24.6
Cost	584

\[\begin{array}{l} \mathbf{if}\;z \leq -1350000000000:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 72:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \end{array} \]

Alternative 7
Error	23.5
Cost	448

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

Alternative 8
Error	23.5
Cost	448

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

Alternative 9
Error	35.1
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023027 
(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)))