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

Percentage Accurate: 100.0% → 100.0%

Time: 3.1s

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, 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]

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 2: 61.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{-46}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{-149}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq -1.56 \cdot 10^{-190}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -2.2e-46)
   x
   (if (<= x -1.9e-149)
     y
     (if (<= x -1.56e-190) x (if (<= x 1.0) y (* x (- y)))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2.2e-46) {
		tmp = x;
	} else if (x <= -1.9e-149) {
		tmp = y;
	} else if (x <= -1.56e-190) {
		tmp = x;
	} else if (x <= 1.0) {
		tmp = y;
	} else {
		tmp = x * -y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-2.2d-46)) then
        tmp = x
    else if (x <= (-1.9d-149)) then
        tmp = y
    else if (x <= (-1.56d-190)) then
        tmp = x
    else if (x <= 1.0d0) then
        tmp = y
    else
        tmp = x * -y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -2.2e-46) {
		tmp = x;
	} else if (x <= -1.9e-149) {
		tmp = y;
	} else if (x <= -1.56e-190) {
		tmp = x;
	} else if (x <= 1.0) {
		tmp = y;
	} else {
		tmp = x * -y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2.2e-46:
		tmp = x
	elif x <= -1.9e-149:
		tmp = y
	elif x <= -1.56e-190:
		tmp = x
	elif x <= 1.0:
		tmp = y
	else:
		tmp = x * -y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2.2e-46)
		tmp = x;
	elseif (x <= -1.9e-149)
		tmp = y;
	elseif (x <= -1.56e-190)
		tmp = x;
	elseif (x <= 1.0)
		tmp = y;
	else
		tmp = Float64(x * Float64(-y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -2.2e-46)
		tmp = x;
	elseif (x <= -1.9e-149)
		tmp = y;
	elseif (x <= -1.56e-190)
		tmp = x;
	elseif (x <= 1.0)
		tmp = y;
	else
		tmp = x * -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2.2e-46], x, If[LessEqual[x, -1.9e-149], y, If[LessEqual[x, -1.56e-190], x, If[LessEqual[x, 1.0], y, N[(x * (-y)), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.2000000000000001e-46 or -1.90000000000000003e-149 < x < -1.56e-190

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 51.7%

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

   if -2.2000000000000001e-46 < x < -1.90000000000000003e-149 or -1.56e-190 < x < 1

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 69.0%

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

   if 1 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 100.0%

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

   3. Taylor expanded in y around inf 48.4%

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

      1. mul-1-neg 48.4%

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

      2. distribute-lft-neg-out 48.4%

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

      3. *-commutative 48.4%

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

   5. Simplified 48.4%

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

4. Final simplification 57.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{-46}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{-149}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq -1.56 \cdot 10^{-190}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \end{array} \]

Alternative 3: 72.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(1 - y\right)\\ \mathbf{if}\;x \leq -7 \cdot 10^{-77}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -3.6 \cdot 10^{-146}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq -1.56 \cdot 10^{-190}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* x (- 1.0 y))))
   (if (<= x -7e-77)
     t_0
     (if (<= x -3.6e-146)
       y
       (if (<= x -1.56e-190) t_0 (if (<= x 1.0) y (* x (- y))))))))

C

double code(double x, double y) {
	double t_0 = x * (1.0 - y);
	double tmp;
	if (x <= -7e-77) {
		tmp = t_0;
	} else if (x <= -3.6e-146) {
		tmp = y;
	} else if (x <= -1.56e-190) {
		tmp = t_0;
	} else if (x <= 1.0) {
		tmp = y;
	} else {
		tmp = x * -y;
	}
	return tmp;
}

Fortran

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 <= (-7d-77)) then
        tmp = t_0
    else if (x <= (-3.6d-146)) then
        tmp = y
    else if (x <= (-1.56d-190)) then
        tmp = t_0
    else if (x <= 1.0d0) then
        tmp = y
    else
        tmp = x * -y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = x * (1.0 - y);
	double tmp;
	if (x <= -7e-77) {
		tmp = t_0;
	} else if (x <= -3.6e-146) {
		tmp = y;
	} else if (x <= -1.56e-190) {
		tmp = t_0;
	} else if (x <= 1.0) {
		tmp = y;
	} else {
		tmp = x * -y;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x * (1.0 - y)
	tmp = 0
	if x <= -7e-77:
		tmp = t_0
	elif x <= -3.6e-146:
		tmp = y
	elif x <= -1.56e-190:
		tmp = t_0
	elif x <= 1.0:
		tmp = y
	else:
		tmp = x * -y
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x * Float64(1.0 - y))
	tmp = 0.0
	if (x <= -7e-77)
		tmp = t_0;
	elseif (x <= -3.6e-146)
		tmp = y;
	elseif (x <= -1.56e-190)
		tmp = t_0;
	elseif (x <= 1.0)
		tmp = y;
	else
		tmp = Float64(x * Float64(-y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x * (1.0 - y);
	tmp = 0.0;
	if (x <= -7e-77)
		tmp = t_0;
	elseif (x <= -3.6e-146)
		tmp = y;
	elseif (x <= -1.56e-190)
		tmp = t_0;
	elseif (x <= 1.0)
		tmp = y;
	else
		tmp = x * -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -7e-77], t$95$0, If[LessEqual[x, -3.6e-146], y, If[LessEqual[x, -1.56e-190], t$95$0, If[LessEqual[x, 1.0], y, N[(x * (-y)), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.00000000000000026e-77 or -3.59999999999999978e-146 < x < -1.56e-190

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 82.5%

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

   if -7.00000000000000026e-77 < x < -3.59999999999999978e-146 or -1.56e-190 < x < 1

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 70.5%

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

   if 1 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 100.0%

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

   3. Taylor expanded in y around inf 48.4%

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

      1. mul-1-neg 48.4%

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

      2. distribute-lft-neg-out 48.4%

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

      3. *-commutative 48.4%

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

   5. Simplified 48.4%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{-77}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;x \leq -3.6 \cdot 10^{-146}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq -1.56 \cdot 10^{-190}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \end{array} \]

Alternative 4: 73.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 4.4 \cdot 10^{-98}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y 4.4e-98) (* x (- 1.0 y)) (* y (- 1.0 x))))

C

double code(double x, double y) {
	double tmp;
	if (y <= 4.4e-98) {
		tmp = x * (1.0 - y);
	} else {
		tmp = y * (1.0 - x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= 4.4d-98) then
        tmp = x * (1.0d0 - y)
    else
        tmp = y * (1.0d0 - x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= 4.4e-98) {
		tmp = x * (1.0 - y);
	} else {
		tmp = y * (1.0 - x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 4.4e-98:
		tmp = x * (1.0 - y)
	else:
		tmp = y * (1.0 - x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 4.4e-98)
		tmp = Float64(x * Float64(1.0 - y));
	else
		tmp = Float64(y * Float64(1.0 - x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 4.4e-98)
		tmp = x * (1.0 - y);
	else
		tmp = y * (1.0 - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 4.4e-98], 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 < 4.39999999999999993e-98

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 73.2%

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

   if 4.39999999999999993e-98 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 80.3%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 4.4 \cdot 10^{-98}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - x\right)\\ \end{array} \]

Alternative 5: 73.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 4.3 \cdot 10^{-98}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;y - x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y 4.3e-98) (* x (- 1.0 y)) (- y (* x y))))

C

double code(double x, double y) {
	double tmp;
	if (y <= 4.3e-98) {
		tmp = x * (1.0 - y);
	} else {
		tmp = y - (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= 4.3d-98) then
        tmp = x * (1.0d0 - y)
    else
        tmp = y - (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= 4.3e-98) {
		tmp = x * (1.0 - y);
	} else {
		tmp = y - (x * y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 4.3e-98:
		tmp = x * (1.0 - y)
	else:
		tmp = y - (x * y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 4.3e-98)
		tmp = Float64(x * Float64(1.0 - y));
	else
		tmp = Float64(y - Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 4.3e-98)
		tmp = x * (1.0 - y);
	else
		tmp = y - (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 4.3e-98], 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 < 4.29999999999999988e-98

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 73.2%

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

   if 4.29999999999999988e-98 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 80.3%

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

      1. sub-neg 80.3%

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

      2. distribute-rgt-in 80.4%

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

      3. *-un-lft-identity 80.4%

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

   4. Applied egg-rr 80.4%

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

      1. distribute-lft-neg-out 80.4%

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

      2. unsub-neg 80.4%

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

      3. *-commutative 80.4%

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

   6. Applied egg-rr 80.4%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 4.3 \cdot 10^{-98}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;y - x \cdot y\\ \end{array} \]

Alternative 6: 73.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 4.4 \cdot 10^{-98}:\\ \;\;\;\;x - x \cdot y\\ \mathbf{else}:\\ \;\;\;\;y - x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y 4.4e-98) (- x (* x y)) (- y (* x y))))

C

double code(double x, double y) {
	double tmp;
	if (y <= 4.4e-98) {
		tmp = x - (x * y);
	} else {
		tmp = y - (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= 4.4d-98) then
        tmp = x - (x * y)
    else
        tmp = y - (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= 4.4e-98) {
		tmp = x - (x * y);
	} else {
		tmp = y - (x * y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 4.4e-98:
		tmp = x - (x * y)
	else:
		tmp = y - (x * y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 4.4e-98)
		tmp = Float64(x - Float64(x * y));
	else
		tmp = Float64(y - Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 4.4e-98)
		tmp = x - (x * y);
	else
		tmp = y - (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 4.4e-98], N[(x - N[(x * y), $MachinePrecision]), $MachinePrecision], N[(y - N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 4.39999999999999993e-98

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 73.2%

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

      1. sub-neg 73.2%

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

      2. distribute-rgt-in 73.2%

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

      3. *-un-lft-identity 73.2%

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

   4. Applied egg-rr 73.2%

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

   if 4.39999999999999993e-98 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 80.3%

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

      1. sub-neg 80.3%

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

      2. distribute-rgt-in 80.4%

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

      3. *-un-lft-identity 80.4%

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

   4. Applied egg-rr 80.4%

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

      1. distribute-lft-neg-out 80.4%

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

      2. unsub-neg 80.4%

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

      3. *-commutative 80.4%

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

   6. Applied egg-rr 80.4%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 4.4 \cdot 10^{-98}:\\ \;\;\;\;x - x \cdot y\\ \mathbf{else}:\\ \;\;\;\;y - x \cdot y\\ \end{array} \]

Alternative 7: 50.1% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.42 \cdot 10^{-101}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y 1.42e-101) x y))

C

double code(double x, double y) {
	double tmp;
	if (y <= 1.42e-101) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= 1.42d-101) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= 1.42e-101) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 1.42e-101:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 1.42e-101)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 1.42e-101)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 1.42e-101], x, y]

Derivation

1. Split input into 2 regimes

2. if y < 1.4200000000000001e-101

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 56.7%

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

   if 1.4200000000000001e-101 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 40.6%

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

4. Final simplification 51.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.42 \cdot 10^{-101}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 8: 38.7% accurate, 7.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y) :precision binary64 x)

C

double code(double x, double y) {
	return x;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x
end function

Java

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

Python

def code(x, y):
	return x

Julia

function code(x, y)
	return x
end

MATLAB

function tmp = code(x, y)
	tmp = x;
end

Wolfram

code[x_, y_] := x

Derivation

1. Initial program 100.0%

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

2. Taylor expanded in y around 0 44.3%

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

3. Final simplification 44.3%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023318 
(FPCore (x y)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, A"
  :precision binary64
  (- (+ x y) (* x y)))