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

Percentage Accurate: 100.0% → 100.0%

Time: 2.8s

Alternatives: 7

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

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

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y) :precision binary64 (+ y (- x (* y x))))

C

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

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = y + (x - (y * x))
end function

Java

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

Python

[x, y] = sort([x, y])
def code(x, y):
	return y + (x - (y * x))

Julia

x, y = sort([x, y])
function code(x, y)
	return Float64(y + Float64(x - Float64(y * x)))
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp = code(x, y)
	tmp = y + (x - (y * x));
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
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. Add Preprocessing
3. Step-by-step derivation

   1. +-commutative 100.0%

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

   2. associate--l+ 100.0%

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

4. Applied egg-rr 100.0%

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

5. Final simplification 100.0%

   \[\leadsto y + \left(x - y \cdot x\right) \]
6. Add Preprocessing

Alternative 2: 99.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \lor \neg \left(x \leq 1\right):\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y)
 :precision binary64
 (if (or (<= x -1.0) (not (<= x 1.0))) (* x (- 1.0 y)) (+ y x)))

C

assert(x < y);
double code(double x, double y) {
	double tmp;
	if ((x <= -1.0) || !(x <= 1.0)) {
		tmp = x * (1.0 - y);
	} else {
		tmp = y + x;
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x <= (-1.0d0)) .or. (.not. (x <= 1.0d0))) then
        tmp = x * (1.0d0 - y)
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y) {
	double tmp;
	if ((x <= -1.0) || !(x <= 1.0)) {
		tmp = x * (1.0 - y);
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y):
	tmp = 0
	if (x <= -1.0) or not (x <= 1.0):
		tmp = x * (1.0 - y)
	else:
		tmp = y + x
	return tmp

Julia

x, y = sort([x, y])
function code(x, y)
	tmp = 0.0
	if ((x <= -1.0) || !(x <= 1.0))
		tmp = Float64(x * Float64(1.0 - y));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -1.0) || ~((x <= 1.0)))
		tmp = x * (1.0 - y);
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_] := If[Or[LessEqual[x, -1.0], N[Not[LessEqual[x, 1.0]], $MachinePrecision]], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1 or 1 < x

   1. Initial program 100.0%

      \[\left(x + y\right) - x \cdot y \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 97.2%

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

   if -1 < x < 1

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. associate--l+ 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in y around 0 99.9%

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

4. Final simplification 98.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \lor \neg \left(x \leq 1\right):\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{-6}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;y - y \cdot x\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y)
 :precision binary64
 (if (<= y -6e-6) (* x (- 1.0 y)) (if (<= y 1.0) (+ y x) (- y (* y x)))))

C

assert(x < y);
double code(double x, double y) {
	double tmp;
	if (y <= -6e-6) {
		tmp = x * (1.0 - y);
	} else if (y <= 1.0) {
		tmp = y + x;
	} else {
		tmp = y - (y * x);
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-6d-6)) then
        tmp = x * (1.0d0 - y)
    else if (y <= 1.0d0) then
        tmp = y + x
    else
        tmp = y - (y * x)
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y) {
	double tmp;
	if (y <= -6e-6) {
		tmp = x * (1.0 - y);
	} else if (y <= 1.0) {
		tmp = y + x;
	} else {
		tmp = y - (y * x);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y):
	tmp = 0
	if y <= -6e-6:
		tmp = x * (1.0 - y)
	elif y <= 1.0:
		tmp = y + x
	else:
		tmp = y - (y * x)
	return tmp

Julia

x, y = sort([x, y])
function code(x, y)
	tmp = 0.0
	if (y <= -6e-6)
		tmp = Float64(x * Float64(1.0 - y));
	elseif (y <= 1.0)
		tmp = Float64(y + x);
	else
		tmp = Float64(y - Float64(y * x));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -6e-6)
		tmp = x * (1.0 - y);
	elseif (y <= 1.0)
		tmp = y + x;
	else
		tmp = y - (y * x);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_] := If[LessEqual[y, -6e-6], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.0], N[(y + x), $MachinePrecision], N[(y - N[(y * x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.0000000000000002e-6

   1. Initial program 100.0%

      \[\left(x + y\right) - x \cdot y \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 46.4%

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

   if -6.0000000000000002e-6 < y < 1

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. associate--l+ 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in y around 0 98.9%

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

   if 1 < y

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. associate--l+ 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in y around inf 98.9%

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

      1. mul-1-neg 98.9%

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

      2. distribute-rgt-neg-out 98.9%

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

   7. Simplified 98.9%

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

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{-6}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;y - y \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -0.00027:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - x\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y)
 :precision binary64
 (if (<= y -0.00027) (* x (- 1.0 y)) (if (<= y 1.0) (+ y x) (* y (- 1.0 x)))))

C

assert(x < y);
double code(double x, double y) {
	double tmp;
	if (y <= -0.00027) {
		tmp = x * (1.0 - y);
	} else if (y <= 1.0) {
		tmp = y + x;
	} else {
		tmp = y * (1.0 - x);
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-0.00027d0)) then
        tmp = x * (1.0d0 - y)
    else if (y <= 1.0d0) then
        tmp = y + x
    else
        tmp = y * (1.0d0 - x)
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y) {
	double tmp;
	if (y <= -0.00027) {
		tmp = x * (1.0 - y);
	} else if (y <= 1.0) {
		tmp = y + x;
	} else {
		tmp = y * (1.0 - x);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y):
	tmp = 0
	if y <= -0.00027:
		tmp = x * (1.0 - y)
	elif y <= 1.0:
		tmp = y + x
	else:
		tmp = y * (1.0 - x)
	return tmp

Julia

x, y = sort([x, y])
function code(x, y)
	tmp = 0.0
	if (y <= -0.00027)
		tmp = Float64(x * Float64(1.0 - y));
	elseif (y <= 1.0)
		tmp = Float64(y + x);
	else
		tmp = Float64(y * Float64(1.0 - x));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -0.00027)
		tmp = x * (1.0 - y);
	elseif (y <= 1.0)
		tmp = y + x;
	else
		tmp = y * (1.0 - x);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_] := If[LessEqual[y, -0.00027], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.0], N[(y + x), $MachinePrecision], N[(y * N[(1.0 - x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.70000000000000003e-4

   1. Initial program 100.0%

      \[\left(x + y\right) - x \cdot y \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 46.4%

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

   if -2.70000000000000003e-4 < y < 1

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. associate--l+ 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in y around 0 98.9%

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

   if 1 < y

   1. Initial program 100.0%

      \[\left(x + y\right) - x \cdot y \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 98.9%

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

Alternative 5: 63.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{-114}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y) :precision binary64 (if (<= x -4.6e-114) x y))

C

assert(x < y);
double code(double x, double y) {
	double tmp;
	if (x <= -4.6e-114) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-4.6d-114)) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y) {
	double tmp;
	if (x <= -4.6e-114) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y):
	tmp = 0
	if x <= -4.6e-114:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

x, y = sort([x, y])
function code(x, y)
	tmp = 0.0
	if (x <= -4.6e-114)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -4.6e-114)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_] := If[LessEqual[x, -4.6e-114], x, y]

Derivation

1. Split input into 2 regimes

2. if x < -4.5999999999999999e-114

   1. Initial program 100.0%

      \[\left(x + y\right) - x \cdot y \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 55.6%

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

   if -4.5999999999999999e-114 < x

   1. Initial program 100.0%

      \[\left(x + y\right) - x \cdot y \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 45.6%

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

Alternative 6: 74.4% accurate, 2.3× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ y + x \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y) :precision binary64 (+ y x))

C

assert(x < y);
double code(double x, double y) {
	return y + x;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = y + x
end function

Java

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

Python

[x, y] = sort([x, y])
def code(x, y):
	return y + x

Julia

x, y = sort([x, y])
function code(x, y)
	return Float64(y + x)
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp = code(x, y)
	tmp = y + x;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_] := N[(y + x), $MachinePrecision]

Derivation

1. Initial program 100.0%

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

   1. +-commutative 100.0%

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

   2. associate--l+ 100.0%

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

4. Applied egg-rr 100.0%

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

5. Taylor expanded in y around 0 77.1%

   \[\leadsto y + \color{blue}{x} \]
6. Add Preprocessing

Alternative 7: 37.7% accurate, 7.0× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ x \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y) :precision binary64 x)

C

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

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x
end function

Java

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

Python

[x, y] = sort([x, y])
def code(x, y):
	return x

Julia

x, y = sort([x, y])
function code(x, y)
	return x
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp = code(x, y)
	tmp = x;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_] := x

Derivation

1. Initial program 100.0%

   \[\left(x + y\right) - x \cdot y \]
2. Add Preprocessing

3. Taylor expanded in y around 0 43.6%

   \[\leadsto \color{blue}{x} \]
4. Add Preprocessing

Reproduce

herbie shell --seed 2024096 
(FPCore (x y)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, A"
  :precision binary64
  (- (+ x y) (* x y)))