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

Percentage Accurate: 100.0% → 100.0%

Time: 5.5s

Alternatives: 6

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. associate--l+ N/A

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

   2. +-commutative N/A

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

   3. associate-+l- N/A

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

   4. --lowering--.f64 N/A

      \[\leadsto \mathsf{\_.f64}\left(y, \color{blue}{\left(x \cdot y - x\right)}\right) \]

   5. --lowering--.f64 N/A

      \[\leadsto \mathsf{\_.f64}\left(y, \mathsf{\_.f64}\left(\left(x \cdot y\right), \color{blue}{x}\right)\right) \]

   6. *-lowering-*.f64 100.0%

      \[\leadsto \mathsf{\_.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), x\right)\right) \]

4. Applied egg-rr 100.0%

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

5. Final simplification 100.0%

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

Alternative 2: 99.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;x \leq 1.16 \cdot 10^{-60}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;y - y \cdot x\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y)
 :precision binary64
 (if (<= x -1.0) (* x (- 1.0 y)) (if (<= x 1.16e-60) (+ y x) (- y (* y x)))))

C

assert(x < y);
double code(double x, double y) {
	double tmp;
	if (x <= -1.0) {
		tmp = x * (1.0 - y);
	} else if (x <= 1.16e-60) {
		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 (x <= (-1.0d0)) then
        tmp = x * (1.0d0 - y)
    else if (x <= 1.16d-60) 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 (x <= -1.0) {
		tmp = x * (1.0 - y);
	} else if (x <= 1.16e-60) {
		tmp = y + x;
	} else {
		tmp = y - (y * x);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y):
	tmp = 0
	if x <= -1.0:
		tmp = x * (1.0 - y)
	elif x <= 1.16e-60:
		tmp = y + x
	else:
		tmp = y - (y * x)
	return tmp

Julia

x, y = sort([x, y])
function code(x, y)
	tmp = 0.0
	if (x <= -1.0)
		tmp = Float64(x * Float64(1.0 - y));
	elseif (x <= 1.16e-60)
		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 (x <= -1.0)
		tmp = x * (1.0 - y);
	elseif (x <= 1.16e-60)
		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[x, -1.0], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.16e-60], N[(y + x), $MachinePrecision], N[(y - N[(y * x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

      1. sub-neg N/A

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

      2. mul-1-neg N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + -1 \cdot y\right)}\right) \]

      4. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 + \left(\mathsf{neg}\left(y\right)\right)\right)\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 - \color{blue}{y}\right)\right) \]

      6. --lowering--.f64 99.9%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \color{blue}{y}\right)\right) \]

   5. Simplified 99.9%

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

   if -1 < x < 1.16e-60

   1. Initial program 100.0%

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

      1. associate--l+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l- N/A

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

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(y, \color{blue}{\left(x \cdot y - x\right)}\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(y, \mathsf{\_.f64}\left(\left(x \cdot y\right), \color{blue}{x}\right)\right) \]

      6. *-lowering-*.f64 100.0%

         \[\leadsto \mathsf{\_.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), x\right)\right) \]

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in y around 0

      \[\leadsto \mathsf{\_.f64}\left(y, \color{blue}{\left(-1 \cdot x\right)}\right) \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(y, \left(\mathsf{neg}\left(x\right)\right)\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{\_.f64}\left(y, \left(0 - \color{blue}{x}\right)\right) \]

      3. --lowering--.f64 99.3%

         \[\leadsto \mathsf{\_.f64}\left(y, \mathsf{\_.f64}\left(0, \color{blue}{x}\right)\right) \]

   7. Simplified 99.3%

      \[\leadsto y - \color{blue}{\left(0 - x\right)} \]
   8. Step-by-step derivation

      1. associate--r- N/A

         \[\leadsto \left(y - 0\right) + \color{blue}{x} \]

      2. --rgt-identity N/A

         \[\leadsto y + x \]

      3. +-lowering-+.f64 99.3%

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{x}\right) \]

   9. Applied egg-rr 99.3%

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

   if 1.16e-60 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{y}, \mathsf{*.f64}\left(x, y\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 47.0%

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

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;x \leq 1.16 \cdot 10^{-60}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;y - y \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.8% accurate, 0.5× speedup

Math

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

FPCore

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

C

assert(x < y);
double code(double x, double y) {
	double t_0 = x * (1.0 - y);
	double tmp;
	if (x <= -1.0) {
		tmp = t_0;
	} else if (x <= 1.0) {
		tmp = y + x;
	} 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 * (1.0d0 - y)
    if (x <= (-1.0d0)) then
        tmp = t_0
    else if (x <= 1.0d0) then
        tmp = y + x
    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 * (1.0 - y);
	double tmp;
	if (x <= -1.0) {
		tmp = t_0;
	} else if (x <= 1.0) {
		tmp = y + x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

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

Julia

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

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y)
	t_0 = x * (1.0 - y);
	tmp = 0.0;
	if (x <= -1.0)
		tmp = t_0;
	elseif (x <= 1.0)
		tmp = y + x;
	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 * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.0], t$95$0, If[LessEqual[x, 1.0], N[(y + x), $MachinePrecision], t$95$0]]]

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

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

      1. sub-neg N/A

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

      2. mul-1-neg N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + -1 \cdot y\right)}\right) \]

      4. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 + \left(\mathsf{neg}\left(y\right)\right)\right)\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 - \color{blue}{y}\right)\right) \]

      6. --lowering--.f64 99.3%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \color{blue}{y}\right)\right) \]

   5. Simplified 99.3%

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

   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. associate--l+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l- N/A

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

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(y, \color{blue}{\left(x \cdot y - x\right)}\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(y, \mathsf{\_.f64}\left(\left(x \cdot y\right), \color{blue}{x}\right)\right) \]

      6. *-lowering-*.f64 100.0%

         \[\leadsto \mathsf{\_.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), x\right)\right) \]

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in y around 0

      \[\leadsto \mathsf{\_.f64}\left(y, \color{blue}{\left(-1 \cdot x\right)}\right) \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(y, \left(\mathsf{neg}\left(x\right)\right)\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{\_.f64}\left(y, \left(0 - \color{blue}{x}\right)\right) \]

      3. --lowering--.f64 98.7%

         \[\leadsto \mathsf{\_.f64}\left(y, \mathsf{\_.f64}\left(0, \color{blue}{x}\right)\right) \]

   7. Simplified 98.7%

      \[\leadsto y - \color{blue}{\left(0 - x\right)} \]
   8. Step-by-step derivation

      1. associate--r- N/A

         \[\leadsto \left(y - 0\right) + \color{blue}{x} \]

      2. --rgt-identity N/A

         \[\leadsto y + x \]

      3. +-lowering-+.f64 98.7%

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{x}\right) \]

   9. Applied egg-rr 98.7%

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

Alternative 4: 64.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 6.4 \cdot 10^{-93}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y) :precision binary64 (if (<= y 6.4e-93) x y))

C

assert(x < y);
double code(double x, double y) {
	double tmp;
	if (y <= 6.4e-93) {
		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 <= 6.4d-93) 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 <= 6.4e-93) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y):
	tmp = 0
	if y <= 6.4e-93:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

x, y = sort([x, y])
function code(x, y)
	tmp = 0.0
	if (y <= 6.4e-93)
		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 <= 6.4e-93)
		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, 6.4e-93], x, y]

Derivation

1. Split input into 2 regimes

2. if y < 6.3999999999999997e-93

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 51.6%

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

   if 6.3999999999999997e-93 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{y} \]
   4. Step-by-step derivation

   5. Simplified 50.6%

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

Alternative 5: 75.0% 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. associate--l+ N/A

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

   2. +-commutative N/A

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

   3. associate-+l- N/A

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

   4. --lowering--.f64 N/A

      \[\leadsto \mathsf{\_.f64}\left(y, \color{blue}{\left(x \cdot y - x\right)}\right) \]

   5. --lowering--.f64 N/A

      \[\leadsto \mathsf{\_.f64}\left(y, \mathsf{\_.f64}\left(\left(x \cdot y\right), \color{blue}{x}\right)\right) \]

   6. *-lowering-*.f64 100.0%

      \[\leadsto \mathsf{\_.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), x\right)\right) \]

4. Applied egg-rr 100.0%

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

5. Taylor expanded in y around 0

   \[\leadsto \mathsf{\_.f64}\left(y, \color{blue}{\left(-1 \cdot x\right)}\right) \]
6. Step-by-step derivation

   1. mul-1-neg N/A

      \[\leadsto \mathsf{\_.f64}\left(y, \left(\mathsf{neg}\left(x\right)\right)\right) \]

   2. neg-sub0 N/A

      \[\leadsto \mathsf{\_.f64}\left(y, \left(0 - \color{blue}{x}\right)\right) \]

   3. --lowering--.f64 75.6%

      \[\leadsto \mathsf{\_.f64}\left(y, \mathsf{\_.f64}\left(0, \color{blue}{x}\right)\right) \]

7. Simplified 75.6%

   \[\leadsto y - \color{blue}{\left(0 - x\right)} \]
8. Step-by-step derivation

   1. associate--r- N/A

      \[\leadsto \left(y - 0\right) + \color{blue}{x} \]

   2. --rgt-identity N/A

      \[\leadsto y + x \]

   3. +-lowering-+.f64 75.6%

      \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{x}\right) \]

9. Applied egg-rr 75.6%

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

Alternative 6: 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. Add Preprocessing

3. Taylor expanded in y around 0

   \[\leadsto \color{blue}{x} \]
4. Step-by-step derivation

5. Simplified 41.1%

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

Reproduce

herbie shell --seed 2024161 
(FPCore (x y)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, A"
  :precision binary64
  (- (+ x y) (* x y)))