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

Percentage Accurate: 100.0% → 100.0%

Time: 7.7s

Alternatives: 9

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. *-commutative 100.0%

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

   3. associate--l+ 100.0%

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

   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-define 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. Add Preprocessing
5. Add Preprocessing

Alternative 2: 69.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} t_0 := y \cdot \left(-x\right)\\ \mathbf{if}\;y \leq -1:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-130}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+219}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

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 8e-130) x (if (<= y 9e+219) 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 <= 8e-130) {
		tmp = x;
	} else if (y <= 9e+219) {
		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 <= 8d-130) then
        tmp = x
    else if (y <= 9d+219) 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 <= 8e-130) {
		tmp = x;
	} else if (y <= 9e+219) {
		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 <= 8e-130:
		tmp = x
	elif y <= 9e+219:
		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 <= 8e-130)
		tmp = x;
	elseif (y <= 9e+219)
		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 <= 8e-130)
		tmp = x;
	elseif (y <= 9e+219)
		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, 8e-130], x, If[LessEqual[y, 9e+219], y, t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1 or 9.00000000000000047e219 < 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%

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

   4. Taylor expanded in x around inf 53.5%

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

      1. associate-*r* 53.5%

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

      2. neg-mul-1 53.5%

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

      3. *-commutative 53.5%

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

   6. Simplified 53.5%

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

   if -1 < y < 8.0000000000000007e-130

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 75.4%

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

   4. Taylor expanded in y around 0 74.1%

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

   if 8.0000000000000007e-130 < y < 9.00000000000000047e219

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 82.0%

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

   4. Taylor expanded in x around 0 58.4%

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

Alternative 3: 88.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq 5.1 \cdot 10^{-130}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - x\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y)
 :precision binary64
 (if (<= y -1.0) (* y (- x)) (if (<= y 5.1e-130) x (* y (- 1.0 x)))))

C

assert(x < y);
double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = y * -x;
	} else if (y <= 5.1e-130) {
		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 = y * -x
    else if (y <= 5.1d-130) 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 = y * -x;
	} else if (y <= 5.1e-130) {
		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 = y * -x
	elif y <= 5.1e-130:
		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(y * Float64(-x));
	elseif (y <= 5.1e-130)
		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 = y * -x;
	elseif (y <= 5.1e-130)
		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[(y * (-x)), $MachinePrecision], If[LessEqual[y, 5.1e-130], 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. Add Preprocessing

   3. Taylor expanded in y around inf 98.5%

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

   4. Taylor expanded in x around inf 53.4%

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

      1. associate-*r* 53.4%

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

      2. neg-mul-1 53.4%

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

      3. *-commutative 53.4%

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

   6. Simplified 53.4%

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

   if -1 < y < 5.0999999999999999e-130

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 75.4%

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

   4. Taylor expanded in y around 0 74.1%

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

   if 5.0999999999999999e-130 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 85.6%

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

Alternative 4: 88.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 8.5 \cdot 10^{-130}:\\ \;\;\;\;x - x \cdot y\\ \mathbf{else}:\\ \;\;\;\;y - x \cdot y\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y)
 :precision binary64
 (if (<= y 8.5e-130) (- x (* x y)) (- y (* x y))))

C

assert(x < y);
double code(double x, double y) {
	double tmp;
	if (y <= 8.5e-130) {
		tmp = x - (x * 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 <= 8.5d-130) then
        tmp = x - (x * 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 <= 8.5e-130) {
		tmp = x - (x * y);
	} else {
		tmp = y - (x * y);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y):
	tmp = 0
	if y <= 8.5e-130:
		tmp = x - (x * y)
	else:
		tmp = y - (x * y)
	return tmp

Julia

x, y = sort([x, y])
function code(x, y)
	tmp = 0.0
	if (y <= 8.5e-130)
		tmp = Float64(x - Float64(x * 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 <= 8.5e-130)
		tmp = x - (x * 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, 8.5e-130], N[(x - N[(x * y), $MachinePrecision]), $MachinePrecision], N[(y - N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 8.50000000000000033e-130

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 67.5%

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

   if 8.50000000000000033e-130 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 85.6%

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

Alternative 5: 88.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 8.5 \cdot 10^{-130}:\\ \;\;\;\;x - x \cdot y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - x\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y)
 :precision binary64
 (if (<= y 8.5e-130) (- x (* x y)) (* y (- 1.0 x))))

C

assert(x < y);
double code(double x, double y) {
	double tmp;
	if (y <= 8.5e-130) {
		tmp = x - (x * 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 <= 8.5d-130) then
        tmp = x - (x * 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 <= 8.5e-130) {
		tmp = x - (x * y);
	} else {
		tmp = y * (1.0 - x);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y):
	tmp = 0
	if y <= 8.5e-130:
		tmp = x - (x * y)
	else:
		tmp = y * (1.0 - x)
	return tmp

Julia

x, y = sort([x, y])
function code(x, y)
	tmp = 0.0
	if (y <= 8.5e-130)
		tmp = Float64(x - Float64(x * 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 <= 8.5e-130)
		tmp = x - (x * 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, 8.5e-130], N[(x - N[(x * y), $MachinePrecision]), $MachinePrecision], N[(y * N[(1.0 - x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 8.50000000000000033e-130

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 67.5%

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

   if 8.50000000000000033e-130 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 85.6%

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

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. Add Preprocessing
3. Add Preprocessing

Alternative 7: 64.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 5.1 \cdot 10^{-130}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y) :precision binary64 (if (<= y 5.1e-130) x y))

C

assert(x < y);
double code(double x, double y) {
	double tmp;
	if (y <= 5.1e-130) {
		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 <= 5.1d-130) 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 <= 5.1e-130) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y):
	tmp = 0
	if y <= 5.1e-130:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

x, y = sort([x, y])
function code(x, y)
	tmp = 0.0
	if (y <= 5.1e-130)
		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 <= 5.1e-130)
		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, 5.1e-130], x, y]

Derivation

1. Split input into 2 regimes

2. if y < 5.0999999999999999e-130

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 67.5%

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

   4. Taylor expanded in y around 0 47.5%

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

   if 5.0999999999999999e-130 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 85.6%

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

   4. Taylor expanded in x around 0 55.9%

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

Alternative 8: 38.0% 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 x around inf 59.2%

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

4. Taylor expanded in y around 0 35.4%

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

Alternative 9: 2.7% accurate, 7.0× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ 0 \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y) :precision binary64 0.0)

C

assert(x < y);
double code(double x, double y) {
	return 0.0;
}

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 = 0.0d0
end function

Java

assert x < y;
public static double code(double x, double y) {
	return 0.0;
}

Python

[x, y] = sort([x, y])
def code(x, y):
	return 0.0

Julia

x, y = sort([x, y])
function code(x, y)
	return 0.0
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp = code(x, y)
	tmp = 0.0;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_] := 0.0

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in y around inf 66.1%

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

4. Taylor expanded in x around inf 26.2%

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

   1. associate-*r* 26.2%

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

   2. neg-mul-1 26.2%

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

   3. *-commutative 26.2%

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

6. Simplified 26.2%

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

   1. add-log-exp 16.4%

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

   2. add-sqr-sqrt 16.4%

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

   3. sqrt-unprod 16.4%

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

   4. exp-prod 16.4%

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

   5. add-sqr-sqrt 8.3%

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

   6. sqrt-unprod 8.7%

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

   7. sqr-neg 8.7%

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

   8. sqrt-unprod 1.7%

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

   9. add-sqr-sqrt 2.1%

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

   10. pow-flip 2.1%

       \[\leadsto \log \left(\sqrt{e^{y \cdot \left(-x\right)} \cdot \color{blue}{\frac{1}{{\left(e^{y}\right)}^{\left(-x\right)}}}}\right) \]

   11. exp-prod 1.8%

       \[\leadsto \log \left(\sqrt{e^{y \cdot \left(-x\right)} \cdot \frac{1}{\color{blue}{e^{y \cdot \left(-x\right)}}}}\right) \]

   12. rgt-mult-inverse 2.7%

       \[\leadsto \log \left(\sqrt{\color{blue}{1}}\right) \]

   13. metadata-eval 2.7%

       \[\leadsto \log \color{blue}{1} \]

   14. metadata-eval 2.7%

       \[\leadsto \color{blue}{0} \]

8. Applied egg-rr 2.7%

   \[\leadsto \color{blue}{0} \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2024181 
(FPCore (x y)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, A"
  :precision binary64
  (- (+ x y) (* x y)))