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

Percentage Accurate: 100.0% → 100.0%

Time: 2.1s

Alternatives: 8

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--l+ 100.0%

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

   3. +-commutative 100.0%

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

   4. *-rgt-identity 100.0%

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

   5. distribute-lft-out-- 100.0%

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

   6. unsub-neg 100.0%

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

   7. +-commutative 100.0%

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

   8. fma-def 100.0%

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

   9. +-commutative 100.0%

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

   10. unsub-neg 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: 68.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} t_0 := x \cdot \left(-y\right)\\ \mathbf{if}\;y \leq -1:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-164}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+173}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+234}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* x (- y))))
   (if (<= y -1.0)
     t_0
     (if (<= y 2.7e-164)
       x
       (if (<= y 3.6e+173) y (if (<= y 1.25e+234) t_0 y))))))

C

assert(x < y);
double code(double x, double y) {
	double t_0 = x * -y;
	double tmp;
	if (y <= -1.0) {
		tmp = t_0;
	} else if (y <= 2.7e-164) {
		tmp = x;
	} else if (y <= 3.6e+173) {
		tmp = y;
	} else if (y <= 1.25e+234) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = x * -y
    if (y <= (-1.0d0)) then
        tmp = t_0
    else if (y <= 2.7d-164) then
        tmp = x
    else if (y <= 3.6d+173) then
        tmp = y
    else if (y <= 1.25d+234) then
        tmp = t_0
    else
        tmp = y
    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 (y <= -1.0) {
		tmp = t_0;
	} else if (y <= 2.7e-164) {
		tmp = x;
	} else if (y <= 3.6e+173) {
		tmp = y;
	} else if (y <= 1.25e+234) {
		tmp = t_0;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y):
	t_0 = x * -y
	tmp = 0
	if y <= -1.0:
		tmp = t_0
	elif y <= 2.7e-164:
		tmp = x
	elif y <= 3.6e+173:
		tmp = y
	elif y <= 1.25e+234:
		tmp = t_0
	else:
		tmp = y
	return tmp

Julia

x, y = sort([x, y])
function code(x, y)
	t_0 = Float64(x * Float64(-y))
	tmp = 0.0
	if (y <= -1.0)
		tmp = t_0;
	elseif (y <= 2.7e-164)
		tmp = x;
	elseif (y <= 3.6e+173)
		tmp = y;
	elseif (y <= 1.25e+234)
		tmp = t_0;
	else
		tmp = y;
	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 (y <= -1.0)
		tmp = t_0;
	elseif (y <= 2.7e-164)
		tmp = x;
	elseif (y <= 3.6e+173)
		tmp = y;
	elseif (y <= 1.25e+234)
		tmp = t_0;
	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_] := Block[{t$95$0 = N[(x * (-y)), $MachinePrecision]}, If[LessEqual[y, -1.0], t$95$0, If[LessEqual[y, 2.7e-164], x, If[LessEqual[y, 3.6e+173], y, If[LessEqual[y, 1.25e+234], t$95$0, y]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1 or 3.6000000000000002e173 < y < 1.2500000000000001e234

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 99.5%

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

   3. Taylor expanded in x around inf 51.7%

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

      1. mul-1-neg 51.7%

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

      2. distribute-rgt-neg-out 51.7%

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

   5. Simplified 51.7%

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

   if -1 < y < 2.7000000000000001e-164

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 82.1%

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

   if 2.7000000000000001e-164 < y < 3.6000000000000002e173 or 1.2500000000000001e234 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 57.9%

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

4. Final simplification 65.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-164}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+173}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+234}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 3: 87.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-164}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - x\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y)
 :precision binary64
 (if (<= y -1.0) (* x (- y)) (if (<= y 2.7e-164) x (* y (- 1.0 x)))))

C

assert(x < y);
double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x * -y;
	} else if (y <= 2.7e-164) {
		tmp = 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 <= (-1.0d0)) then
        tmp = x * -y
    else if (y <= 2.7d-164) then
        tmp = 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 <= -1.0) {
		tmp = x * -y;
	} else if (y <= 2.7e-164) {
		tmp = x;
	} else {
		tmp = y * (1.0 - x);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = x * -y
	elif y <= 2.7e-164:
		tmp = x
	else:
		tmp = y * (1.0 - x)
	return tmp

Julia

x, y = sort([x, y])
function code(x, y)
	tmp = 0.0
	if (y <= -1.0)
		tmp = Float64(x * Float64(-y));
	elseif (y <= 2.7e-164)
		tmp = 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 <= -1.0)
		tmp = x * -y;
	elseif (y <= 2.7e-164)
		tmp = 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, -1.0], N[(x * (-y)), $MachinePrecision], If[LessEqual[y, 2.7e-164], x, N[(y * N[(1.0 - x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 99.4%

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

   3. Taylor expanded in x around inf 46.5%

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

      1. mul-1-neg 46.5%

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

      2. distribute-rgt-neg-out 46.5%

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

   5. Simplified 46.5%

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

   if -1 < y < 2.7000000000000001e-164

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 82.1%

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

   if 2.7000000000000001e-164 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 84.5%

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

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-164}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - x\right)\\ \end{array} \]

Alternative 4: 88.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 2.7 \cdot 10^{-164}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - x\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y)
 :precision binary64
 (if (<= y 2.7e-164) (* x (- 1.0 y)) (* y (- 1.0 x))))

C

assert(x < y);
double code(double x, double y) {
	double tmp;
	if (y <= 2.7e-164) {
		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 (y <= 2.7d-164) 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 (y <= 2.7e-164) {
		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 y <= 2.7e-164:
		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 (y <= 2.7e-164)
		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 (y <= 2.7e-164)
		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[y, 2.7e-164], 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 y < 2.7000000000000001e-164

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 68.4%

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

   if 2.7000000000000001e-164 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 84.5%

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

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.7 \cdot 10^{-164}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - x\right)\\ \end{array} \]

Alternative 5: 88.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 2.7 \cdot 10^{-164}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;y - x \cdot y\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y)
 :precision binary64
 (if (<= y 2.7e-164) (* x (- 1.0 y)) (- y (* x y))))

C

assert(x < y);
double code(double x, double y) {
	double tmp;
	if (y <= 2.7e-164) {
		tmp = x * (1.0 - y);
	} else {
		tmp = y - (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 (y <= 2.7d-164) then
        tmp = x * (1.0d0 - y)
    else
        tmp = y - (x * y)
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y) {
	double tmp;
	if (y <= 2.7e-164) {
		tmp = x * (1.0 - y);
	} else {
		tmp = y - (x * y);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y):
	tmp = 0
	if y <= 2.7e-164:
		tmp = x * (1.0 - y)
	else:
		tmp = y - (x * y)
	return tmp

Julia

x, y = sort([x, y])
function code(x, y)
	tmp = 0.0
	if (y <= 2.7e-164)
		tmp = Float64(x * Float64(1.0 - y));
	else
		tmp = Float64(y - Float64(x * y));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 2.7e-164)
		tmp = x * (1.0 - y);
	else
		tmp = y - (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[y, 2.7e-164], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], N[(y - N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2.7000000000000001e-164

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 68.4%

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

   if 2.7000000000000001e-164 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 84.5%

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

   3. Taylor expanded in x around 0 84.5%

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

      1. mul-1-neg 84.5%

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

      2. unsub-neg 84.5%

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

   5. Simplified 84.5%

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

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.7 \cdot 10^{-164}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;y - x \cdot y\\ \end{array} \]

Alternative 6: 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 7: 64.5% accurate, 2.3× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 2.7 \cdot 10^{-164}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y) :precision binary64 (if (<= y 2.7e-164) x y))

C

assert(x < y);
double code(double x, double y) {
	double tmp;
	if (y <= 2.7e-164) {
		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 (y <= 2.7d-164) 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 (y <= 2.7e-164) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y):
	tmp = 0
	if y <= 2.7e-164:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

x, y = sort([x, y])
function code(x, y)
	tmp = 0.0
	if (y <= 2.7e-164)
		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 (y <= 2.7e-164)
		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[y, 2.7e-164], x, y]

Derivation

1. Split input into 2 regimes

2. if y < 2.7000000000000001e-164

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 51.3%

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

   if 2.7000000000000001e-164 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 53.3%

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

4. Final simplification 52.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.7 \cdot 10^{-164}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 8: 38.9% 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 38.2%

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

3. Final simplification 38.2%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023224 
(FPCore (x y)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, A"
  :precision binary64
  (- (+ x y) (* x y)))