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

Average Accuracy: 99.6% → 99.7%

Time: 7.7s

Precision: binary64

Cost: 832

Math

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

↓

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

FPCore

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

↓

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

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 * (x * z)) + (6.0 * (z * y)));
}

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) * (x * z)) + (6.0d0 * (z * y)))
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 * (x * z)) + (6.0 * (z * y)));
}

Python

def code(x, y, z):
	return x + (((y - x) * 6.0) * z)

↓

def code(x, y, z):
	return x + ((-6.0 * (x * z)) + (6.0 * (z * y)))

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(-6.0 * Float64(x * z)) + Float64(6.0 * Float64(z * y))))
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 * (x * z)) + (6.0 * (z * y)));
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[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision] + N[(6.0 * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Target

Original	99.6%
Target	99.7%
Herbie	99.7%

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

Derivation

1. Initial program 99.6%

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

2. Taylor expanded in y around 0 99.7%

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

3. Final simplification 99.7%

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

Alternatives

Alternative 1
Accuracy	87.8%
Cost	713

\[\begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{-11} \lor \neg \left(y \leq 5.7 \cdot 10^{-61}\right):\\ \;\;\;\;x + 6 \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x + -6 \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 2
Accuracy	61.2%
Cost	585

\[\begin{array}{l} \mathbf{if}\;z \leq -33000000000 \lor \neg \left(z \leq 1.4 \cdot 10^{-19}\right):\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3
Accuracy	99.6%
Cost	576

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

Alternative 4
Accuracy	99.7%
Cost	576

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

Alternative 5
Accuracy	63.0%
Cost	448

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

Alternative 6
Accuracy	63.1%
Cost	448

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

Alternative 7
Accuracy	45.1%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023133 
(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)))