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

Percentage Accurate: 100.0% → 100.0%

Time: 2.3s

Alternatives: 6

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \left(x + y\right) - x \cdot y \end{array} \]

FPCore

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

C

double code(double x, double y) {
	return (x + y) - (x * y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x + y) - (x * y)
end function

Java

public static double code(double x, double y) {
	return (x + y) - (x * y);
}

Python

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

Julia

function code(x, y)
	return Float64(Float64(x + y) - Float64(x * y))
end

MATLAB

function tmp = code(x, y)
	tmp = (x + y) - (x * y);
end

Wolfram

code[x_, y_] := N[(N[(x + y), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x + y\right) - x \cdot y \end{array} \]

FPCore

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

C

double code(double x, double y) {
	return (x + y) - (x * y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x + y) - (x * y)
end function

Java

public static double code(double x, double y) {
	return (x + y) - (x * y);
}

Python

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

Julia

function code(x, y)
	return Float64(Float64(x + y) - Float64(x * y))
end

MATLAB

function tmp = code(x, y)
	tmp = (x + y) - (x * y);
end

Wolfram

code[x_, y_] := N[(N[(x + y), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ y + \left(x - y \cdot x\right) \end{array} \]

FPCore

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

C

double code(double x, double y) {
	return y + (x - (y * x));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = y + (x - (y * x))
end function

Java

public static double code(double x, double y) {
	return y + (x - (y * x));
}

Python

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

Julia

function code(x, y)
	return Float64(y + Float64(x - Float64(y * x)))
end

MATLAB

function tmp = code(x, y)
	tmp = y + (x - (y * x));
end

Wolfram

code[x_, y_] := N[(y + N[(x - N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\left(x + y\right) - x \cdot y \]
2. Step-by-step derivation

   1. +-commutative 100.0%

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

   2. associate--l+ 100.0%

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

3. Simplified 100.0%

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

4. Final simplification 100.0%

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

Alternative 2: 60.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(-x\right)\\ \mathbf{if}\;x \leq -4 \cdot 10^{+228}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -2.2 \cdot 10^{-91}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* y (- x))))
   (if (<= x -4e+228) t_0 (if (<= x -2.2e-91) x (if (<= x 1.0) y t_0)))))

C

double code(double x, double y) {
	double t_0 = y * -x;
	double tmp;
	if (x <= -4e+228) {
		tmp = t_0;
	} else if (x <= -2.2e-91) {
		tmp = x;
	} else if (x <= 1.0) {
		tmp = y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = y * -x
    if (x <= (-4d+228)) then
        tmp = t_0
    else if (x <= (-2.2d-91)) then
        tmp = x
    else if (x <= 1.0d0) then
        tmp = y
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = y * -x;
	double tmp;
	if (x <= -4e+228) {
		tmp = t_0;
	} else if (x <= -2.2e-91) {
		tmp = x;
	} else if (x <= 1.0) {
		tmp = y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = y * -x
	tmp = 0
	if x <= -4e+228:
		tmp = t_0
	elif x <= -2.2e-91:
		tmp = x
	elif x <= 1.0:
		tmp = y
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(y * Float64(-x))
	tmp = 0.0
	if (x <= -4e+228)
		tmp = t_0;
	elseif (x <= -2.2e-91)
		tmp = x;
	elseif (x <= 1.0)
		tmp = y;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = y * -x;
	tmp = 0.0;
	if (x <= -4e+228)
		tmp = t_0;
	elseif (x <= -2.2e-91)
		tmp = x;
	elseif (x <= 1.0)
		tmp = y;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(y * (-x)), $MachinePrecision]}, If[LessEqual[x, -4e+228], t$95$0, If[LessEqual[x, -2.2e-91], x, If[LessEqual[x, 1.0], y, t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.9999999999999997e228 or 1 < x

   1. Initial program 100.0%

      \[\left(x + y\right) - x \cdot y \]
   2. Step-by-step derivation

      1. +-commutative 100.0%

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

      2. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 54.7%

      \[\leadsto \color{blue}{y \cdot \left(1 - x\right)} \]

   5. Taylor expanded in x around inf 54.0%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot x\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 54.0%

         \[\leadsto \color{blue}{-y \cdot x} \]

      2. distribute-rgt-neg-out 54.0%

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

   7. Simplified 54.0%

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

   if -3.9999999999999997e228 < x < -2.2000000000000001e-91

   1. Initial program 99.9%

      \[\left(x + y\right) - x \cdot y \]
   2. Step-by-step derivation

      1. +-commutative 99.9%

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

      2. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 59.4%

      \[\leadsto \color{blue}{x} \]

   if -2.2000000000000001e-91 < x < 1

   1. Initial program 100.0%

      \[\left(x + y\right) - x \cdot y \]
   2. Step-by-step derivation

      1. +-commutative 100.0%

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

      2. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 78.2%

      \[\leadsto \color{blue}{y} \]
3. Recombined 3 regimes into one program.

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+228}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;x \leq -2.2 \cdot 10^{-91}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \end{array} \]

Alternative 3: 81.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.029 \lor \neg \left(y \leq 4.9 \cdot 10^{-197}\right):\\ \;\;\;\;y \cdot \left(1 - x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -0.029) (not (<= y 4.9e-197))) (* y (- 1.0 x)) x))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -0.029) || !(y <= 4.9e-197)) {
		tmp = y * (1.0 - x);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-0.029d0)) .or. (.not. (y <= 4.9d-197))) then
        tmp = y * (1.0d0 - x)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -0.029) || !(y <= 4.9e-197)) {
		tmp = y * (1.0 - x);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -0.029) or not (y <= 4.9e-197):
		tmp = y * (1.0 - x)
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -0.029) || !(y <= 4.9e-197))
		tmp = Float64(y * Float64(1.0 - x));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -0.029) || ~((y <= 4.9e-197)))
		tmp = y * (1.0 - x);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -0.029], N[Not[LessEqual[y, 4.9e-197]], $MachinePrecision]], N[(y * N[(1.0 - x), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -0.0290000000000000015 or 4.9000000000000002e-197 < y

   1. Initial program 100.0%

      \[\left(x + y\right) - x \cdot y \]
   2. Step-by-step derivation

      1. +-commutative 100.0%

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

      2. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 83.0%

      \[\leadsto \color{blue}{y \cdot \left(1 - x\right)} \]

   if -0.0290000000000000015 < y < 4.9000000000000002e-197

   1. Initial program 100.0%

      \[\left(x + y\right) - x \cdot y \]
   2. Step-by-step derivation

      1. +-commutative 100.0%

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

      2. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 74.3%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.029 \lor \neg \left(y \leq 4.9 \cdot 10^{-197}\right):\\ \;\;\;\;y \cdot \left(1 - x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 73.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{-91}:\\ \;\;\;\;x - y \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -2.1e-91) (- x (* y x)) (* y (- 1.0 x))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2.1e-91) {
		tmp = x - (y * x);
	} else {
		tmp = y * (1.0 - x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-2.1d-91)) then
        tmp = x - (y * x)
    else
        tmp = y * (1.0d0 - x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -2.1e-91) {
		tmp = x - (y * x);
	} else {
		tmp = y * (1.0 - x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2.1e-91:
		tmp = x - (y * x)
	else:
		tmp = y * (1.0 - x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2.1e-91)
		tmp = Float64(x - Float64(y * x));
	else
		tmp = Float64(y * Float64(1.0 - x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -2.1e-91)
		tmp = x - (y * x);
	else
		tmp = y * (1.0 - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2.1e-91], N[(x - N[(y * x), $MachinePrecision]), $MachinePrecision], N[(y * N[(1.0 - x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.0999999999999999e-91

   1. Initial program 100.0%

      \[\left(x + y\right) - x \cdot y \]
   2. Step-by-step derivation

      1. +-commutative 100.0%

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

      2. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 89.9%

      \[\leadsto \color{blue}{\left(1 - y\right) \cdot x} \]
   5. Step-by-step derivation

      1. *-commutative 89.9%

         \[\leadsto \color{blue}{x \cdot \left(1 - y\right)} \]

      2. distribute-lft-out-- 89.9%

         \[\leadsto \color{blue}{x \cdot 1 - x \cdot y} \]

      3. *-rgt-identity 89.9%

         \[\leadsto \color{blue}{x} - x \cdot y \]

   6. Simplified 89.9%

      \[\leadsto \color{blue}{x - x \cdot y} \]

   if -2.0999999999999999e-91 < x

   1. Initial program 100.0%

      \[\left(x + y\right) - x \cdot y \]
   2. Step-by-step derivation

      1. +-commutative 100.0%

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

      2. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 70.4%

      \[\leadsto \color{blue}{y \cdot \left(1 - x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{-91}:\\ \;\;\;\;x - y \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - x\right)\\ \end{array} \]

Alternative 5: 49.3% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{-91}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= x -2.8e-91) x y))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2.8e-91) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-2.8d-91)) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -2.8e-91) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2.8e-91:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2.8e-91)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -2.8e-91)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2.8e-91], x, y]

Derivation

1. Split input into 2 regimes

2. if x < -2.8e-91

   1. Initial program 100.0%

      \[\left(x + y\right) - x \cdot y \]
   2. Step-by-step derivation

      1. +-commutative 100.0%

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

      2. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 52.3%

      \[\leadsto \color{blue}{x} \]

   if -2.8e-91 < x

   1. Initial program 100.0%

      \[\left(x + y\right) - x \cdot y \]
   2. Step-by-step derivation

      1. +-commutative 100.0%

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

      2. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 54.3%

      \[\leadsto \color{blue}{y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 53.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{-91}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 6: 39.0% accurate, 7.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y) :precision binary64 x)

C

double code(double x, double y) {
	return x;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x
end function

Java

public static double code(double x, double y) {
	return x;
}

Python

def code(x, y):
	return x

Julia

function code(x, y)
	return x
end

MATLAB

function tmp = code(x, y)
	tmp = x;
end

Wolfram

code[x_, y_] := x

Derivation

1. Initial program 100.0%

   \[\left(x + y\right) - x \cdot y \]
2. Step-by-step derivation

   1. +-commutative 100.0%

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

   2. associate--l+ 100.0%

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

3. Simplified 100.0%

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

4. Taylor expanded in y around 0 37.6%

   \[\leadsto \color{blue}{x} \]

5. Final simplification 37.6%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023221 
(FPCore (x y)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, A"
  :precision binary64
  (- (+ x y) (* x y)))