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

Average Accuracy: 79.2% → 79.3%

Time: 12.0s

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	79.2%
Target	79.3%
Herbie	79.3%

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

Derivation

1. Initial program 76.8%

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

2. Simplified 76.8%

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

   [Start] 76.8	\[ x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   associate-*l* [=>] 76.8	\[ x + \color{blue}{\left(y - x\right) \cdot \left(6 \cdot z\right)} \]

3. Final simplification 76.8%

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

Alternatives

Alternative 1
Accuracy	46.9%
Cost	1244

\[\begin{array}{l} t_0 := z \cdot \left(x \cdot -6\right)\\ \mathbf{if}\;x \leq -1.22 \cdot 10^{+88}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -6.2 \cdot 10^{-13}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-93}:\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \mathbf{elif}\;x \leq 2 \cdot 10^{-56}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{-39}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+17}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.65 \cdot 10^{+69}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 2
Accuracy	47.0%
Cost	1244

\[\begin{array}{l} t_0 := z \cdot \left(x \cdot -6\right)\\ \mathbf{if}\;x \leq -1.8 \cdot 10^{+84}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -6.8 \cdot 10^{-13}:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{-92}:\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-62}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-40}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{+18}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{+69}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3
Accuracy	69.2%
Cost	713

\[\begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{-74} \lor \neg \left(y \leq 170000000\right):\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + z \cdot -6\right)\\ \end{array} \]

Alternative 4
Accuracy	69.2%
Cost	713

\[\begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{-77} \lor \neg \left(y \leq 170000000\right):\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(x \cdot -6\right)\\ \end{array} \]

Alternative 5
Accuracy	69.2%
Cost	713

\[\begin{array}{l} \mathbf{if}\;y \leq -1.06 \cdot 10^{-75} \lor \neg \left(y \leq 170000000\right):\\ \;\;\;\;x + z \cdot \left(y \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(x \cdot -6\right)\\ \end{array} \]

Alternative 6
Accuracy	69.2%
Cost	713

\[\begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{-77} \lor \neg \left(y \leq 170000000\right):\\ \;\;\;\;x + z \cdot \left(y \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;x + -6 \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 7
Accuracy	55.4%
Cost	712

\[\begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{-39}:\\ \;\;\;\;y \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;y \leq 180000000:\\ \;\;\;\;x \cdot \left(1 + z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \end{array} \]

Alternative 8
Accuracy	49.9%
Cost	585

\[\begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{-20} \lor \neg \left(z \leq 5.8 \cdot 10^{-67}\right):\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9
Accuracy	49.9%
Cost	585

\[\begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{-19} \lor \neg \left(z \leq 1.35 \cdot 10^{-67}\right):\\ \;\;\;\;y \cdot \left(6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10
Accuracy	49.9%
Cost	584

\[\begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{-19}:\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-67}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(6 \cdot z\right)\\ \end{array} \]

Alternative 11
Accuracy	79.2%
Cost	576

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

Alternative 12
Accuracy	36.5%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023157 
(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)))