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

Percentage Accurate: 100.0% → 100.0%

Time: 3.1s

Alternatives: 8

Speedup: N/A×

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

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

FPCore

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

C

assert(x < y);
double code(double x, double y) {
	return y + (x * (1.0 - 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 = y + (x * (1.0d0 - y))
end function

Java

assert x < y;
public static double code(double x, double y) {
	return y + (x * (1.0 - y));
}

Python

[x, y] = sort([x, y])
def code(x, y):
	return y + (x * (1.0 - y))

Julia

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

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp = code(x, y)
	tmp = y + (x * (1.0 - y));
end

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. associate--l+ 100.0%

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

   2. +-commutative 100.0%

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

   3. remove-double-neg 100.0%

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

   4. unsub-neg 100.0%

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

   5. cancel-sign-sub-inv 100.0%

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

   6. associate--l+ 100.0%

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

   7. neg-mul-1 100.0%

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

   8. cancel-sign-sub-inv 100.0%

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

   9. distribute-lft-neg-out 100.0%

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

   10. distribute-rgt-neg-out 100.0%

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

   11. *-commutative 100.0%

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

   12. distribute-rgt-out 100.0%

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

   13. +-commutative 100.0%

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

   14. sub-neg 100.0%

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

   15. metadata-eval 100.0%

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

3. Simplified 100.0%

   \[\leadsto \color{blue}{y + x \cdot \left(1 - y\right)} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 2: 67.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} t_0 := y \cdot \left(-x\right)\\ \mathbf{if}\;y \leq -1:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-171}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-99}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-27}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+229}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* y (- x))))
   (if (<= y -1.0)
     t_0
     (if (<= y 5.2e-171)
       x
       (if (<= y 1.45e-99)
         y
         (if (<= y 9.5e-27) x (if (<= y 7.5e+229) y t_0)))))))

C

assert(x < y);
double code(double x, double y) {
	double t_0 = y * -x;
	double tmp;
	if (y <= -1.0) {
		tmp = t_0;
	} else if (y <= 5.2e-171) {
		tmp = x;
	} else if (y <= 1.45e-99) {
		tmp = y;
	} else if (y <= 9.5e-27) {
		tmp = x;
	} else if (y <= 7.5e+229) {
		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 = y * -x
    if (y <= (-1.0d0)) then
        tmp = t_0
    else if (y <= 5.2d-171) then
        tmp = x
    else if (y <= 1.45d-99) then
        tmp = y
    else if (y <= 9.5d-27) then
        tmp = x
    else if (y <= 7.5d+229) 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 = y * -x;
	double tmp;
	if (y <= -1.0) {
		tmp = t_0;
	} else if (y <= 5.2e-171) {
		tmp = x;
	} else if (y <= 1.45e-99) {
		tmp = y;
	} else if (y <= 9.5e-27) {
		tmp = x;
	} else if (y <= 7.5e+229) {
		tmp = y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y):
	t_0 = y * -x
	tmp = 0
	if y <= -1.0:
		tmp = t_0
	elif y <= 5.2e-171:
		tmp = x
	elif y <= 1.45e-99:
		tmp = y
	elif y <= 9.5e-27:
		tmp = x
	elif y <= 7.5e+229:
		tmp = y
	else:
		tmp = t_0
	return tmp

Julia

x, y = sort([x, y])
function code(x, y)
	t_0 = Float64(y * Float64(-x))
	tmp = 0.0
	if (y <= -1.0)
		tmp = t_0;
	elseif (y <= 5.2e-171)
		tmp = x;
	elseif (y <= 1.45e-99)
		tmp = y;
	elseif (y <= 9.5e-27)
		tmp = x;
	elseif (y <= 7.5e+229)
		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 = y * -x;
	tmp = 0.0;
	if (y <= -1.0)
		tmp = t_0;
	elseif (y <= 5.2e-171)
		tmp = x;
	elseif (y <= 1.45e-99)
		tmp = y;
	elseif (y <= 9.5e-27)
		tmp = x;
	elseif (y <= 7.5e+229)
		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[(y * (-x)), $MachinePrecision]}, If[LessEqual[y, -1.0], t$95$0, If[LessEqual[y, 5.2e-171], x, If[LessEqual[y, 1.45e-99], y, If[LessEqual[y, 9.5e-27], x, If[LessEqual[y, 7.5e+229], y, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1 or 7.50000000000000021e229 < y

   1. Initial program 99.9%

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

      1. associate--l+ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 99.5%

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

   6. Taylor expanded in x around inf 50.9%

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

      1. mul-1-neg 50.9%

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

      2. distribute-lft-neg-out 50.9%

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

      3. *-commutative 50.9%

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

   8. Simplified 50.9%

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

   if -1 < y < 5.2000000000000001e-171 or 1.44999999999999993e-99 < y < 9.50000000000000037e-27

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 85.2%

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

   if 5.2000000000000001e-171 < y < 1.44999999999999993e-99 or 9.50000000000000037e-27 < y < 7.50000000000000021e229

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 51.8%

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

Alternative 3: 62.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 5.2 \cdot 10^{-171}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-99}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-28}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y)
 :precision binary64
 (if (<= y 5.2e-171) x (if (<= y 1.15e-99) y (if (<= y 5.5e-28) x y))))

C

assert(x < y);
double code(double x, double y) {
	double tmp;
	if (y <= 5.2e-171) {
		tmp = x;
	} else if (y <= 1.15e-99) {
		tmp = y;
	} else if (y <= 5.5e-28) {
		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 <= 5.2d-171) then
        tmp = x
    else if (y <= 1.15d-99) then
        tmp = y
    else if (y <= 5.5d-28) 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 <= 5.2e-171) {
		tmp = x;
	} else if (y <= 1.15e-99) {
		tmp = y;
	} else if (y <= 5.5e-28) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y):
	tmp = 0
	if y <= 5.2e-171:
		tmp = x
	elif y <= 1.15e-99:
		tmp = y
	elif y <= 5.5e-28:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

x, y = sort([x, y])
function code(x, y)
	tmp = 0.0
	if (y <= 5.2e-171)
		tmp = x;
	elseif (y <= 1.15e-99)
		tmp = y;
	elseif (y <= 5.5e-28)
		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 <= 5.2e-171)
		tmp = x;
	elseif (y <= 1.15e-99)
		tmp = y;
	elseif (y <= 5.5e-28)
		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, 5.2e-171], x, If[LessEqual[y, 1.15e-99], y, If[LessEqual[y, 5.5e-28], x, y]]]

Derivation

1. Split input into 2 regimes

2. if y < 5.2000000000000001e-171 or 1.1499999999999999e-99 < y < 5.49999999999999967e-28

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 61.4%

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

   if 5.2000000000000001e-171 < y < 1.1499999999999999e-99 or 5.49999999999999967e-28 < y

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 48.1%

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

Alternative 4: 88.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{-118}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y)
 :precision binary64
 (if (<= x -1.65e-118) (* x (- 1.0 y)) (if (<= x 1.0) y (* y (- x)))))

C

assert(x < y);
double code(double x, double y) {
	double tmp;
	if (x <= -1.65e-118) {
		tmp = x * (1.0 - y);
	} else if (x <= 1.0) {
		tmp = 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 <= (-1.65d-118)) then
        tmp = x * (1.0d0 - y)
    else if (x <= 1.0d0) then
        tmp = 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 <= -1.65e-118) {
		tmp = x * (1.0 - y);
	} else if (x <= 1.0) {
		tmp = y;
	} else {
		tmp = y * -x;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y):
	tmp = 0
	if x <= -1.65e-118:
		tmp = x * (1.0 - y)
	elif x <= 1.0:
		tmp = y
	else:
		tmp = y * -x
	return tmp

Julia

x, y = sort([x, y])
function code(x, y)
	tmp = 0.0
	if (x <= -1.65e-118)
		tmp = Float64(x * Float64(1.0 - y));
	elseif (x <= 1.0)
		tmp = y;
	else
		tmp = Float64(y * Float64(-x));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.65e-118)
		tmp = x * (1.0 - y);
	elseif (x <= 1.0)
		tmp = 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[LessEqual[x, -1.65e-118], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.0], y, N[(y * (-x)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.65e-118

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 86.0%

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

   if -1.65e-118 < x < 1

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 74.0%

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

   if 1 < x

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 38.3%

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

   6. Taylor expanded in x around inf 37.2%

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

      1. mul-1-neg 37.2%

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

      2. distribute-lft-neg-out 37.2%

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

      3. *-commutative 37.2%

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

   8. Simplified 37.2%

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

Alternative 5: 88.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{-118}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;y - y \cdot x\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y)
 :precision binary64
 (if (<= x -1.65e-118) (* x (- 1.0 y)) (- y (* y x))))

C

assert(x < y);
double code(double x, double y) {
	double tmp;
	if (x <= -1.65e-118) {
		tmp = x * (1.0 - y);
	} 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 (x <= (-1.65d-118)) then
        tmp = x * (1.0d0 - y)
    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 (x <= -1.65e-118) {
		tmp = x * (1.0 - y);
	} else {
		tmp = y - (y * x);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y):
	tmp = 0
	if x <= -1.65e-118:
		tmp = x * (1.0 - y)
	else:
		tmp = y - (y * x)
	return tmp

Julia

x, y = sort([x, y])
function code(x, y)
	tmp = 0.0
	if (x <= -1.65e-118)
		tmp = Float64(x * Float64(1.0 - y));
	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 (x <= -1.65e-118)
		tmp = x * (1.0 - y);
	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[x, -1.65e-118], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], N[(y - N[(y * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.65e-118

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 86.0%

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

   if -1.65e-118 < x

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 61.1%

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

      1. sub-neg 61.1%

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

      2. distribute-rgt-in 61.1%

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

      3. *-un-lft-identity 61.1%

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

   7. Applied egg-rr 61.1%

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

      1. distribute-lft-neg-out 61.1%

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

      2. unsub-neg 61.1%

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

      3. *-commutative 61.1%

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

   9. Applied egg-rr 61.1%

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

Alternative 6: 88.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{-118}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - x\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y)
 :precision binary64
 (if (<= x -1.65e-118) (* x (- 1.0 y)) (* y (- 1.0 x))))

C

assert(x < y);
double code(double x, double y) {
	double tmp;
	if (x <= -1.65e-118) {
		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 <= (-1.65d-118)) 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 <= -1.65e-118) {
		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 <= -1.65e-118:
		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 <= -1.65e-118)
		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 <= -1.65e-118)
		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, -1.65e-118], 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 < -1.65e-118

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 86.0%

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

   if -1.65e-118 < x

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 61.1%

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

Alternative 7: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

assert(x < y);
double code(double x, double y) {
	return x + (y - (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 = x + (y - (y * x))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_] := N[(x + N[(y - 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. associate--l+ 100.0%

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

3. Simplified 100.0%

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

5. Final simplification 100.0%

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

Alternative 8: 38.5% 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. Step-by-step derivation

   1. associate--l+ 100.0%

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

3. Simplified 100.0%

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

5. Taylor expanded in y around 0 45.7%

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

Reproduce

herbie shell --seed 2024108 
(FPCore (x y)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, A"
  :precision binary64
  (- (+ x y) (* x y)))