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

Percentage Accurate: 100.0% → 100.0%

Time: 2.7s

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, 0.1× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \mathsf{fma}\left(x, 1 - y, y\right) \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y) :precision binary64 (fma x (- 1.0 y) y))

C

assert(x < y);
double code(double x, double y) {
	return fma(x, (1.0 - y), y);
}

Julia

x, y = sort([x, y])
function code(x, y)
	return fma(x, Float64(1.0 - y), y)
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_] := N[(x * N[(1.0 - y), $MachinePrecision] + y), $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-+r- 100.0%

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

   3. *-commutative 100.0%

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

   4. +-commutative 100.0%

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

   5. *-lft-identity 100.0%

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

   6. metadata-eval 100.0%

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

   7. distribute-rgt-out-- 100.0%

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

   8. fma-def 100.0%

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

   9. metadata-eval 100.0%

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

3. Simplified 100.0%

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

4. Final simplification 100.0%

   \[\leadsto \mathsf{fma}\left(x, 1 - y, y\right) \]

Alternative 2: 67.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} t_0 := x \cdot \left(-y\right)\\ \mathbf{if}\;x \leq -2.4 \cdot 10^{+190}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -6 \cdot 10^{-15}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* x (- y))))
   (if (<= x -2.4e+190) t_0 (if (<= x -6e-15) x (if (<= x 1.0) y t_0)))))

C

assert(x < y);
double code(double x, double y) {
	double t_0 = x * -y;
	double tmp;
	if (x <= -2.4e+190) {
		tmp = t_0;
	} else if (x <= -6e-15) {
		tmp = x;
	} else if (x <= 1.0) {
		tmp = y;
	} else {
		tmp = t_0;
	}
	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) :: t_0
    real(8) :: tmp
    t_0 = x * -y
    if (x <= (-2.4d+190)) then
        tmp = t_0
    else if (x <= (-6d-15)) then
        tmp = x
    else if (x <= 1.0d0) then
        tmp = y
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y) {
	double t_0 = x * -y;
	double tmp;
	if (x <= -2.4e+190) {
		tmp = t_0;
	} else if (x <= -6e-15) {
		tmp = x;
	} else if (x <= 1.0) {
		tmp = y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y):
	t_0 = x * -y
	tmp = 0
	if x <= -2.4e+190:
		tmp = t_0
	elif x <= -6e-15:
		tmp = x
	elif x <= 1.0:
		tmp = y
	else:
		tmp = t_0
	return tmp

Julia

x, y = sort([x, y])
function code(x, y)
	t_0 = Float64(x * Float64(-y))
	tmp = 0.0
	if (x <= -2.4e+190)
		tmp = t_0;
	elseif (x <= -6e-15)
		tmp = x;
	elseif (x <= 1.0)
		tmp = y;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y)
	t_0 = x * -y;
	tmp = 0.0;
	if (x <= -2.4e+190)
		tmp = t_0;
	elseif (x <= -6e-15)
		tmp = x;
	elseif (x <= 1.0)
		tmp = y;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_] := Block[{t$95$0 = N[(x * (-y)), $MachinePrecision]}, If[LessEqual[x, -2.4e+190], t$95$0, If[LessEqual[x, -6e-15], x, If[LessEqual[x, 1.0], y, t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.3999999999999999e190 or 1 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 53.7%

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

   3. Taylor expanded in x around inf 53.0%

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

      1. mul-1-neg 53.0%

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

      2. distribute-rgt-neg-in 53.0%

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

   5. Simplified 53.0%

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

   if -2.3999999999999999e190 < x < -6e-15

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 53.1%

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

   if -6e-15 < x < 1

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 78.5%

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

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{+190}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;x \leq -6 \cdot 10^{-15}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \end{array} \]

Alternative 3: 86.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{-20}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y)
 :precision binary64
 (if (<= x -4e-20) (* x (- 1.0 y)) (if (<= x 1.0) y (* x (- y)))))

C

assert(x < y);
double code(double x, double y) {
	double tmp;
	if (x <= -4e-20) {
		tmp = x * (1.0 - y);
	} else if (x <= 1.0) {
		tmp = y;
	} else {
		tmp = x * -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 <= (-4d-20)) then
        tmp = x * (1.0d0 - y)
    else if (x <= 1.0d0) then
        tmp = y
    else
        tmp = x * -y
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y) {
	double tmp;
	if (x <= -4e-20) {
		tmp = x * (1.0 - y);
	} else if (x <= 1.0) {
		tmp = y;
	} else {
		tmp = x * -y;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y):
	tmp = 0
	if x <= -4e-20:
		tmp = x * (1.0 - y)
	elif x <= 1.0:
		tmp = y
	else:
		tmp = x * -y
	return tmp

Julia

x, y = sort([x, y])
function code(x, y)
	tmp = 0.0
	if (x <= -4e-20)
		tmp = Float64(x * Float64(1.0 - y));
	elseif (x <= 1.0)
		tmp = y;
	else
		tmp = Float64(x * Float64(-y));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -4e-20)
		tmp = x * (1.0 - y);
	elseif (x <= 1.0)
		tmp = y;
	else
		tmp = x * -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, -4e-20], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.0], y, N[(x * (-y)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.99999999999999978e-20

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 98.0%

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

   if -3.99999999999999978e-20 < x < 1

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 79.2%

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

   if 1 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 50.0%

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

   3. Taylor expanded in x around inf 48.9%

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

      1. mul-1-neg 48.9%

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

      2. distribute-rgt-neg-in 48.9%

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

   5. Simplified 48.9%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{-20}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \end{array} \]

Alternative 4: 87.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{-20}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - x\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y)
 :precision binary64
 (if (<= x -6.8e-20) (* x (- 1.0 y)) (* y (- 1.0 x))))

C

assert(x < y);
double code(double x, double y) {
	double tmp;
	if (x <= -6.8e-20) {
		tmp = x * (1.0 - y);
	} 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 (x <= (-6.8d-20)) then
        tmp = x * (1.0d0 - y)
    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 (x <= -6.8e-20) {
		tmp = x * (1.0 - y);
	} else {
		tmp = y * (1.0 - x);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y):
	tmp = 0
	if x <= -6.8e-20:
		tmp = x * (1.0 - y)
	else:
		tmp = y * (1.0 - x)
	return tmp

Julia

x, y = sort([x, y])
function code(x, y)
	tmp = 0.0
	if (x <= -6.8e-20)
		tmp = Float64(x * Float64(1.0 - y));
	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 (x <= -6.8e-20)
		tmp = x * (1.0 - y);
	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[x, -6.8e-20], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], N[(y * N[(1.0 - x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.7999999999999994e-20

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 98.0%

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

   if -6.7999999999999994e-20 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 69.0%

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

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{-20}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - x\right)\\ \end{array} \]

Alternative 5: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 + y) - (x * y)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

2. Final simplification 100.0%

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

Alternative 6: 62.1% accurate, 2.3× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{-16}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y) :precision binary64 (if (<= x -2.1e-16) x y))

C

assert(x < y);
double code(double x, double y) {
	double tmp;
	if (x <= -2.1e-16) {
		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 <= (-2.1d-16)) 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 <= -2.1e-16) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y):
	tmp = 0
	if x <= -2.1e-16:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

x, y = sort([x, y])
function code(x, y)
	tmp = 0.0
	if (x <= -2.1e-16)
		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 <= -2.1e-16)
		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, -2.1e-16], x, y]

Derivation

1. Split input into 2 regimes

2. if x < -2.1000000000000001e-16

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 47.7%

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

   if -2.1000000000000001e-16 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 50.3%

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

4. Final simplification 49.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{-16}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 7: 38.8% 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. Taylor expanded in y around 0 37.7%

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

3. Final simplification 37.7%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023332 
(FPCore (x y)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, A"
  :precision binary64
  (- (+ x y) (* x y)))