Graphics.Rendering.Chart.Plot.AreaSpots:renderSpotLegend from Chart-1.5.3

Percentage Accurate: 99.9% → 99.9%

Time: 9.5s

Alternatives: 12

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ x + \frac{\left|y - x\right|}{2} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (+ x (/ (fabs (- y x)) 2.0)))

C

double code(double x, double y) {
	return x + (fabs((y - x)) / 2.0);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x + (abs((y - x)) / 2.0d0)
end function

Java

public static double code(double x, double y) {
	return x + (Math.abs((y - x)) / 2.0);
}

Python

def code(x, y):
	return x + (math.fabs((y - x)) / 2.0)

Julia

function code(x, y)
	return Float64(x + Float64(abs(Float64(y - x)) / 2.0))
end

MATLAB

function tmp = code(x, y)
	tmp = x + (abs((y - x)) / 2.0);
end

Wolfram

code[x_, y_] := N[(x + N[(N[Abs[N[(y - x), $MachinePrecision]], $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \frac{\left|y - x\right|}{2} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (+ x (/ (fabs (- y x)) 2.0)))

C

double code(double x, double y) {
	return x + (fabs((y - x)) / 2.0);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x + (abs((y - x)) / 2.0d0)
end function

Java

public static double code(double x, double y) {
	return x + (Math.abs((y - x)) / 2.0);
}

Python

def code(x, y):
	return x + (math.fabs((y - x)) / 2.0)

Julia

function code(x, y)
	return Float64(x + Float64(abs(Float64(y - x)) / 2.0))
end

MATLAB

function tmp = code(x, y)
	tmp = x + (abs((y - x)) / 2.0);
end

Wolfram

code[x_, y_] := N[(x + N[(N[Abs[N[(y - x), $MachinePrecision]], $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \frac{\left|y - x\right|}{2} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (+ x (/ (fabs (- y x)) 2.0)))

C

double code(double x, double y) {
	return x + (fabs((y - x)) / 2.0);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x + (abs((y - x)) / 2.0d0)
end function

Java

public static double code(double x, double y) {
	return x + (Math.abs((y - x)) / 2.0);
}

Python

def code(x, y):
	return x + (math.fabs((y - x)) / 2.0)

Julia

function code(x, y)
	return Float64(x + Float64(abs(Float64(y - x)) / 2.0))
end

MATLAB

function tmp = code(x, y)
	tmp = x + (abs((y - x)) / 2.0);
end

Wolfram

code[x_, y_] := N[(x + N[(N[Abs[N[(y - x), $MachinePrecision]], $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[x + \frac{\left|y - x\right|}{2} \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 2: 82.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{-27}:\\ \;\;\;\;0.5 \cdot \left(x + y\right)\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+47}:\\ \;\;\;\;x + \frac{\left|y\right|}{2}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{x - y}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -5.5e-27)
   (* 0.5 (+ x y))
   (if (<= x 2.6e+47) (+ x (/ (fabs y) 2.0)) (+ x (/ (- x y) 2.0)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -5.5e-27) {
		tmp = 0.5 * (x + y);
	} else if (x <= 2.6e+47) {
		tmp = x + (fabs(y) / 2.0);
	} else {
		tmp = x + ((x - y) / 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-5.5d-27)) then
        tmp = 0.5d0 * (x + y)
    else if (x <= 2.6d+47) then
        tmp = x + (abs(y) / 2.0d0)
    else
        tmp = x + ((x - y) / 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -5.5e-27) {
		tmp = 0.5 * (x + y);
	} else if (x <= 2.6e+47) {
		tmp = x + (Math.abs(y) / 2.0);
	} else {
		tmp = x + ((x - y) / 2.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -5.5e-27:
		tmp = 0.5 * (x + y)
	elif x <= 2.6e+47:
		tmp = x + (math.fabs(y) / 2.0)
	else:
		tmp = x + ((x - y) / 2.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -5.5e-27)
		tmp = Float64(0.5 * Float64(x + y));
	elseif (x <= 2.6e+47)
		tmp = Float64(x + Float64(abs(y) / 2.0));
	else
		tmp = Float64(x + Float64(Float64(x - y) / 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -5.5e-27)
		tmp = 0.5 * (x + y);
	elseif (x <= 2.6e+47)
		tmp = x + (abs(y) / 2.0);
	else
		tmp = x + ((x - y) / 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -5.5e-27], N[(0.5 * N[(x + y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.6e+47], N[(x + N[(N[Abs[y], $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(x - y), $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.5000000000000002e-27

   1. Initial program 100.0%

      \[x + \frac{\left|y - x\right|}{2} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num 99.8%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{2}{\left|y - x\right|}}} \]

      2. inv-pow 99.8%

         \[\leadsto x + \color{blue}{{\left(\frac{2}{\left|y - x\right|}\right)}^{-1}} \]

      3. add-sqr-sqrt 90.7%

         \[\leadsto x + {\left(\frac{2}{\left|\color{blue}{\sqrt{y - x} \cdot \sqrt{y - x}}\right|}\right)}^{-1} \]

      4. fabs-sqr 90.7%

         \[\leadsto x + {\left(\frac{2}{\color{blue}{\sqrt{y - x} \cdot \sqrt{y - x}}}\right)}^{-1} \]

      5. add-sqr-sqrt 91.2%

         \[\leadsto x + {\left(\frac{2}{\color{blue}{y - x}}\right)}^{-1} \]

   4. Applied egg-rr 91.2%

      \[\leadsto x + \color{blue}{{\left(\frac{2}{y - x}\right)}^{-1}} \]

   5. Taylor expanded in x around 0 91.4%

      \[\leadsto \color{blue}{0.5 \cdot x + 0.5 \cdot y} \]
   6. Step-by-step derivation

      1. distribute-lft-out 91.4%

         \[\leadsto \color{blue}{0.5 \cdot \left(x + y\right)} \]

      2. +-commutative 91.4%

         \[\leadsto 0.5 \cdot \color{blue}{\left(y + x\right)} \]

   7. Simplified 91.4%

      \[\leadsto \color{blue}{0.5 \cdot \left(y + x\right)} \]

   if -5.5000000000000002e-27 < x < 2.60000000000000003e47

   1. Initial program 99.9%

      \[x + \frac{\left|y - x\right|}{2} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 80.1%

      \[\leadsto x + \frac{\left|\color{blue}{y}\right|}{2} \]

   if 2.60000000000000003e47 < x

   1. Initial program 99.9%

      \[x + \frac{\left|y - x\right|}{2} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num 99.8%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{2}{\left|y - x\right|}}} \]

      2. inv-pow 99.8%

         \[\leadsto x + \color{blue}{{\left(\frac{2}{\left|y - x\right|}\right)}^{-1}} \]

      3. add-sqr-sqrt 5.6%

         \[\leadsto x + {\left(\frac{2}{\left|\color{blue}{\sqrt{y - x} \cdot \sqrt{y - x}}\right|}\right)}^{-1} \]

      4. fabs-sqr 5.6%

         \[\leadsto x + {\left(\frac{2}{\color{blue}{\sqrt{y - x} \cdot \sqrt{y - x}}}\right)}^{-1} \]

      5. add-sqr-sqrt 20.7%

         \[\leadsto x + {\left(\frac{2}{\color{blue}{y - x}}\right)}^{-1} \]

   4. Applied egg-rr 20.7%

      \[\leadsto x + \color{blue}{{\left(\frac{2}{y - x}\right)}^{-1}} \]
   5. Step-by-step derivation

      1. add-sqr-sqrt 5.6%

         \[\leadsto x + {\left(\frac{2}{\color{blue}{\sqrt{y - x} \cdot \sqrt{y - x}}}\right)}^{-1} \]

      2. fabs-sqr 5.6%

         \[\leadsto x + {\left(\frac{2}{\color{blue}{\left|\sqrt{y - x} \cdot \sqrt{y - x}\right|}}\right)}^{-1} \]

      3. add-sqr-sqrt 99.8%

         \[\leadsto x + {\left(\frac{2}{\left|\color{blue}{y - x}\right|}\right)}^{-1} \]

      4. fabs-sub 99.8%

         \[\leadsto x + {\left(\frac{2}{\color{blue}{\left|x - y\right|}}\right)}^{-1} \]

   6. Applied egg-rr 99.8%

      \[\leadsto x + {\left(\frac{2}{\color{blue}{\left|x - y\right|}}\right)}^{-1} \]
   7. Step-by-step derivation

      1. unpow-1 99.8%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{2}{\left|x - y\right|}}} \]

      2. clear-num 99.8%

         \[\leadsto x + \frac{1}{\color{blue}{\frac{1}{\frac{\left|x - y\right|}{2}}}} \]

      3. remove-double-div 99.9%

         \[\leadsto x + \color{blue}{\frac{\left|x - y\right|}{2}} \]

      4. add-sqr-sqrt 94.0%

         \[\leadsto x + \frac{\left|\color{blue}{\sqrt{x - y} \cdot \sqrt{x - y}}\right|}{2} \]

      5. fabs-sqr 94.0%

         \[\leadsto x + \frac{\color{blue}{\sqrt{x - y} \cdot \sqrt{x - y}}}{2} \]

      6. add-sqr-sqrt 94.2%

         \[\leadsto x + \frac{\color{blue}{x - y}}{2} \]

   8. Applied egg-rr 94.2%

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

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{-27}:\\ \;\;\;\;0.5 \cdot \left(x + y\right)\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+47}:\\ \;\;\;\;x + \frac{\left|y\right|}{2}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{x - y}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 80.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{-27}:\\ \;\;\;\;0.5 \cdot \left(x + y\right)\\ \mathbf{elif}\;x \leq 10^{-215}:\\ \;\;\;\;0.5 \cdot \left|y\right|\\ \mathbf{else}:\\ \;\;\;\;x + \frac{x - y}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -2.7e-27)
   (* 0.5 (+ x y))
   (if (<= x 1e-215) (* 0.5 (fabs y)) (+ x (/ (- x y) 2.0)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2.7e-27) {
		tmp = 0.5 * (x + y);
	} else if (x <= 1e-215) {
		tmp = 0.5 * fabs(y);
	} else {
		tmp = x + ((x - y) / 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-2.7d-27)) then
        tmp = 0.5d0 * (x + y)
    else if (x <= 1d-215) then
        tmp = 0.5d0 * abs(y)
    else
        tmp = x + ((x - y) / 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -2.7e-27) {
		tmp = 0.5 * (x + y);
	} else if (x <= 1e-215) {
		tmp = 0.5 * Math.abs(y);
	} else {
		tmp = x + ((x - y) / 2.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2.7e-27:
		tmp = 0.5 * (x + y)
	elif x <= 1e-215:
		tmp = 0.5 * math.fabs(y)
	else:
		tmp = x + ((x - y) / 2.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2.7e-27)
		tmp = Float64(0.5 * Float64(x + y));
	elseif (x <= 1e-215)
		tmp = Float64(0.5 * abs(y));
	else
		tmp = Float64(x + Float64(Float64(x - y) / 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -2.7e-27)
		tmp = 0.5 * (x + y);
	elseif (x <= 1e-215)
		tmp = 0.5 * abs(y);
	else
		tmp = x + ((x - y) / 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2.7e-27], N[(0.5 * N[(x + y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1e-215], N[(0.5 * N[Abs[y], $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(x - y), $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.69999999999999989e-27

   1. Initial program 100.0%

      \[x + \frac{\left|y - x\right|}{2} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num 99.8%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{2}{\left|y - x\right|}}} \]

      2. inv-pow 99.8%

         \[\leadsto x + \color{blue}{{\left(\frac{2}{\left|y - x\right|}\right)}^{-1}} \]

      3. add-sqr-sqrt 90.7%

         \[\leadsto x + {\left(\frac{2}{\left|\color{blue}{\sqrt{y - x} \cdot \sqrt{y - x}}\right|}\right)}^{-1} \]

      4. fabs-sqr 90.7%

         \[\leadsto x + {\left(\frac{2}{\color{blue}{\sqrt{y - x} \cdot \sqrt{y - x}}}\right)}^{-1} \]

      5. add-sqr-sqrt 91.2%

         \[\leadsto x + {\left(\frac{2}{\color{blue}{y - x}}\right)}^{-1} \]

   4. Applied egg-rr 91.2%

      \[\leadsto x + \color{blue}{{\left(\frac{2}{y - x}\right)}^{-1}} \]

   5. Taylor expanded in x around 0 91.4%

      \[\leadsto \color{blue}{0.5 \cdot x + 0.5 \cdot y} \]
   6. Step-by-step derivation

      1. distribute-lft-out 91.4%

         \[\leadsto \color{blue}{0.5 \cdot \left(x + y\right)} \]

      2. +-commutative 91.4%

         \[\leadsto 0.5 \cdot \color{blue}{\left(y + x\right)} \]

   7. Simplified 91.4%

      \[\leadsto \color{blue}{0.5 \cdot \left(y + x\right)} \]

   if -2.69999999999999989e-27 < x < 1.00000000000000004e-215

   1. Initial program 100.0%

      \[x + \frac{\left|y - x\right|}{2} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 86.3%

      \[\leadsto x + \frac{\left|\color{blue}{y}\right|}{2} \]

   4. Taylor expanded in x around 0 84.3%

      \[\leadsto \color{blue}{0.5 \cdot \left|y\right|} \]

   if 1.00000000000000004e-215 < x

   1. Initial program 99.8%

      \[x + \frac{\left|y - x\right|}{2} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num 99.7%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{2}{\left|y - x\right|}}} \]

      2. inv-pow 99.7%

         \[\leadsto x + \color{blue}{{\left(\frac{2}{\left|y - x\right|}\right)}^{-1}} \]

      3. add-sqr-sqrt 18.1%

         \[\leadsto x + {\left(\frac{2}{\left|\color{blue}{\sqrt{y - x} \cdot \sqrt{y - x}}\right|}\right)}^{-1} \]

      4. fabs-sqr 18.1%

         \[\leadsto x + {\left(\frac{2}{\color{blue}{\sqrt{y - x} \cdot \sqrt{y - x}}}\right)}^{-1} \]

      5. add-sqr-sqrt 29.1%

         \[\leadsto x + {\left(\frac{2}{\color{blue}{y - x}}\right)}^{-1} \]

   4. Applied egg-rr 29.1%

      \[\leadsto x + \color{blue}{{\left(\frac{2}{y - x}\right)}^{-1}} \]
   5. Step-by-step derivation

      1. add-sqr-sqrt 18.1%

         \[\leadsto x + {\left(\frac{2}{\color{blue}{\sqrt{y - x} \cdot \sqrt{y - x}}}\right)}^{-1} \]

      2. fabs-sqr 18.1%

         \[\leadsto x + {\left(\frac{2}{\color{blue}{\left|\sqrt{y - x} \cdot \sqrt{y - x}\right|}}\right)}^{-1} \]

      3. add-sqr-sqrt 99.7%

         \[\leadsto x + {\left(\frac{2}{\left|\color{blue}{y - x}\right|}\right)}^{-1} \]

      4. fabs-sub 99.7%

         \[\leadsto x + {\left(\frac{2}{\color{blue}{\left|x - y\right|}}\right)}^{-1} \]

   6. Applied egg-rr 99.7%

      \[\leadsto x + {\left(\frac{2}{\color{blue}{\left|x - y\right|}}\right)}^{-1} \]
   7. Step-by-step derivation

      1. unpow-1 99.7%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{2}{\left|x - y\right|}}} \]

      2. clear-num 99.7%

         \[\leadsto x + \frac{1}{\color{blue}{\frac{1}{\frac{\left|x - y\right|}{2}}}} \]

      3. remove-double-div 99.8%

         \[\leadsto x + \color{blue}{\frac{\left|x - y\right|}{2}} \]

      4. add-sqr-sqrt 81.4%

         \[\leadsto x + \frac{\left|\color{blue}{\sqrt{x - y} \cdot \sqrt{x - y}}\right|}{2} \]

      5. fabs-sqr 81.4%

         \[\leadsto x + \frac{\color{blue}{\sqrt{x - y} \cdot \sqrt{x - y}}}{2} \]

      6. add-sqr-sqrt 81.8%

         \[\leadsto x + \frac{\color{blue}{x - y}}{2} \]

   8. Applied egg-rr 81.8%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{-27}:\\ \;\;\;\;0.5 \cdot \left(x + y\right)\\ \mathbf{elif}\;x \leq 10^{-215}:\\ \;\;\;\;0.5 \cdot \left|y\right|\\ \mathbf{else}:\\ \;\;\;\;x + \frac{x - y}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 56.4% accurate, 5.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -230:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq -8 \cdot 10^{-247}:\\ \;\;\;\;y \cdot 0.5\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-179}:\\ \;\;\;\;\frac{y}{-2}\\ \mathbf{else}:\\ \;\;\;\;x \cdot 1.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -230.0)
   (* x 0.5)
   (if (<= x -8e-247) (* y 0.5) (if (<= x 5.8e-179) (/ y -2.0) (* x 1.5)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -230.0) {
		tmp = x * 0.5;
	} else if (x <= -8e-247) {
		tmp = y * 0.5;
	} else if (x <= 5.8e-179) {
		tmp = y / -2.0;
	} else {
		tmp = x * 1.5;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-230.0d0)) then
        tmp = x * 0.5d0
    else if (x <= (-8d-247)) then
        tmp = y * 0.5d0
    else if (x <= 5.8d-179) then
        tmp = y / (-2.0d0)
    else
        tmp = x * 1.5d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -230.0) {
		tmp = x * 0.5;
	} else if (x <= -8e-247) {
		tmp = y * 0.5;
	} else if (x <= 5.8e-179) {
		tmp = y / -2.0;
	} else {
		tmp = x * 1.5;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -230.0:
		tmp = x * 0.5
	elif x <= -8e-247:
		tmp = y * 0.5
	elif x <= 5.8e-179:
		tmp = y / -2.0
	else:
		tmp = x * 1.5
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -230.0)
		tmp = Float64(x * 0.5);
	elseif (x <= -8e-247)
		tmp = Float64(y * 0.5);
	elseif (x <= 5.8e-179)
		tmp = Float64(y / -2.0);
	else
		tmp = Float64(x * 1.5);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -230.0)
		tmp = x * 0.5;
	elseif (x <= -8e-247)
		tmp = y * 0.5;
	elseif (x <= 5.8e-179)
		tmp = y / -2.0;
	else
		tmp = x * 1.5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -230.0], N[(x * 0.5), $MachinePrecision], If[LessEqual[x, -8e-247], N[(y * 0.5), $MachinePrecision], If[LessEqual[x, 5.8e-179], N[(y / -2.0), $MachinePrecision], N[(x * 1.5), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -230

   1. Initial program 100.0%

      \[x + \frac{\left|y - x\right|}{2} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num 99.8%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{2}{\left|y - x\right|}}} \]

      2. inv-pow 99.8%

         \[\leadsto x + \color{blue}{{\left(\frac{2}{\left|y - x\right|}\right)}^{-1}} \]

      3. add-sqr-sqrt 90.0%

         \[\leadsto x + {\left(\frac{2}{\left|\color{blue}{\sqrt{y - x} \cdot \sqrt{y - x}}\right|}\right)}^{-1} \]

      4. fabs-sqr 90.0%

         \[\leadsto x + {\left(\frac{2}{\color{blue}{\sqrt{y - x} \cdot \sqrt{y - x}}}\right)}^{-1} \]

      5. add-sqr-sqrt 90.5%

         \[\leadsto x + {\left(\frac{2}{\color{blue}{y - x}}\right)}^{-1} \]

   4. Applied egg-rr 90.5%

      \[\leadsto x + \color{blue}{{\left(\frac{2}{y - x}\right)}^{-1}} \]

   5. Taylor expanded in x around inf 75.8%

      \[\leadsto \color{blue}{0.5 \cdot x} \]

   if -230 < x < -8.0000000000000002e-247

   1. Initial program 100.0%

      \[x + \frac{\left|y - x\right|}{2} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 81.5%

      \[\leadsto x + \frac{\left|\color{blue}{y}\right|}{2} \]

   4. Taylor expanded in x around 0 78.5%

      \[\leadsto \color{blue}{0.5 \cdot \left|y\right|} \]
   5. Step-by-step derivation

      1. rem-square-sqrt 46.7%

         \[\leadsto 0.5 \cdot \left|\color{blue}{\sqrt{y} \cdot \sqrt{y}}\right| \]

      2. fabs-sqr 46.7%

         \[\leadsto 0.5 \cdot \color{blue}{\left(\sqrt{y} \cdot \sqrt{y}\right)} \]

      3. rem-square-sqrt 47.9%

         \[\leadsto 0.5 \cdot \color{blue}{y} \]

   6. Simplified 47.9%

      \[\leadsto \color{blue}{0.5 \cdot y} \]

   if -8.0000000000000002e-247 < x < 5.7999999999999998e-179

   1. Initial program 99.9%

      \[x + \frac{\left|y - x\right|}{2} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 88.1%

      \[\leadsto x + \frac{\left|\color{blue}{y}\right|}{2} \]

   4. Taylor expanded in x around 0 86.5%

      \[\leadsto \color{blue}{0.5 \cdot \left|y\right|} \]
   5. Step-by-step derivation

      1. rem-square-sqrt 29.7%

         \[\leadsto 0.5 \cdot \left|\color{blue}{\sqrt{y} \cdot \sqrt{y}}\right| \]

      2. fabs-sqr 29.7%

         \[\leadsto 0.5 \cdot \color{blue}{\left(\sqrt{y} \cdot \sqrt{y}\right)} \]

      3. rem-square-sqrt 31.5%

         \[\leadsto 0.5 \cdot \color{blue}{y} \]

   6. Simplified 31.5%

      \[\leadsto \color{blue}{0.5 \cdot y} \]
   7. Step-by-step derivation

      1. *-commutative 31.5%

         \[\leadsto \color{blue}{y \cdot 0.5} \]

      2. metadata-eval 31.5%

         \[\leadsto y \cdot \color{blue}{\frac{1}{2}} \]

      3. div-inv 31.5%

         \[\leadsto \color{blue}{\frac{y}{2}} \]

      4. frac-2neg 31.5%

         \[\leadsto \color{blue}{\frac{-y}{-2}} \]

      5. add-sqr-sqrt 1.5%

         \[\leadsto \frac{\color{blue}{\sqrt{-y} \cdot \sqrt{-y}}}{-2} \]

      6. sqrt-unprod 2.9%

         \[\leadsto \frac{\color{blue}{\sqrt{\left(-y\right) \cdot \left(-y\right)}}}{-2} \]

      7. sqr-neg 2.9%

         \[\leadsto \frac{\sqrt{\color{blue}{y \cdot y}}}{-2} \]

      8. sqrt-unprod 1.2%

         \[\leadsto \frac{\color{blue}{\sqrt{y} \cdot \sqrt{y}}}{-2} \]

      9. add-sqr-sqrt 57.7%

         \[\leadsto \frac{\color{blue}{y}}{-2} \]

      10. metadata-eval 57.7%

          \[\leadsto \frac{y}{\color{blue}{-2}} \]

   8. Applied egg-rr 57.7%

      \[\leadsto \color{blue}{\frac{y}{-2}} \]

   if 5.7999999999999998e-179 < x

   1. Initial program 99.9%

      \[x + \frac{\left|y - x\right|}{2} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num 99.7%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{2}{\left|y - x\right|}}} \]

      2. inv-pow 99.7%

         \[\leadsto x + \color{blue}{{\left(\frac{2}{\left|y - x\right|}\right)}^{-1}} \]

      3. add-sqr-sqrt 18.7%

         \[\leadsto x + {\left(\frac{2}{\left|\color{blue}{\sqrt{y - x} \cdot \sqrt{y - x}}\right|}\right)}^{-1} \]

      4. fabs-sqr 18.7%

         \[\leadsto x + {\left(\frac{2}{\color{blue}{\sqrt{y - x} \cdot \sqrt{y - x}}}\right)}^{-1} \]

      5. add-sqr-sqrt 30.1%

         \[\leadsto x + {\left(\frac{2}{\color{blue}{y - x}}\right)}^{-1} \]

   4. Applied egg-rr 30.1%

      \[\leadsto x + \color{blue}{{\left(\frac{2}{y - x}\right)}^{-1}} \]
   5. Step-by-step derivation

      1. add-sqr-sqrt 18.7%

         \[\leadsto x + {\left(\frac{2}{\color{blue}{\sqrt{y - x} \cdot \sqrt{y - x}}}\right)}^{-1} \]

      2. fabs-sqr 18.7%

         \[\leadsto x + {\left(\frac{2}{\color{blue}{\left|\sqrt{y - x} \cdot \sqrt{y - x}\right|}}\right)}^{-1} \]

      3. add-sqr-sqrt 99.7%

         \[\leadsto x + {\left(\frac{2}{\left|\color{blue}{y - x}\right|}\right)}^{-1} \]

      4. fabs-sub 99.7%

         \[\leadsto x + {\left(\frac{2}{\color{blue}{\left|x - y\right|}}\right)}^{-1} \]

   6. Applied egg-rr 99.7%

      \[\leadsto x + {\left(\frac{2}{\color{blue}{\left|x - y\right|}}\right)}^{-1} \]
   7. Step-by-step derivation

      1. unpow-1 99.7%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{2}{\left|x - y\right|}}} \]

      2. clear-num 99.7%

         \[\leadsto x + \frac{1}{\color{blue}{\frac{1}{\frac{\left|x - y\right|}{2}}}} \]

      3. remove-double-div 99.9%

         \[\leadsto x + \color{blue}{\frac{\left|x - y\right|}{2}} \]

      4. add-sqr-sqrt 80.7%

         \[\leadsto x + \frac{\left|\color{blue}{\sqrt{x - y} \cdot \sqrt{x - y}}\right|}{2} \]

      5. fabs-sqr 80.7%

         \[\leadsto x + \frac{\color{blue}{\sqrt{x - y} \cdot \sqrt{x - y}}}{2} \]

      6. add-sqr-sqrt 81.1%

         \[\leadsto x + \frac{\color{blue}{x - y}}{2} \]

   8. Applied egg-rr 81.1%

      \[\leadsto x + \color{blue}{\frac{x - y}{2}} \]

   9. Taylor expanded in x around inf 63.7%

      \[\leadsto \color{blue}{1.5 \cdot x} \]
   10. Step-by-step derivation

       1. *-commutative 63.7%

          \[\leadsto \color{blue}{x \cdot 1.5} \]

   11. Simplified 63.7%

       \[\leadsto \color{blue}{x \cdot 1.5} \]
3. Recombined 4 regimes into one program.

4. Final simplification 62.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -230:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq -8 \cdot 10^{-247}:\\ \;\;\;\;y \cdot 0.5\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-179}:\\ \;\;\;\;\frac{y}{-2}\\ \mathbf{else}:\\ \;\;\;\;x \cdot 1.5\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 71.2% accurate, 6.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{-232}:\\ \;\;\;\;x - \frac{y}{2}\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-231}:\\ \;\;\;\;x + \frac{1}{\frac{2}{x}}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(x + y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -5.2e-232)
   (- x (/ y 2.0))
   (if (<= y 1.5e-231) (+ x (/ 1.0 (/ 2.0 x))) (* 0.5 (+ x y)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -5.2e-232) {
		tmp = x - (y / 2.0);
	} else if (y <= 1.5e-231) {
		tmp = x + (1.0 / (2.0 / x));
	} else {
		tmp = 0.5 * (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 <= (-5.2d-232)) then
        tmp = x - (y / 2.0d0)
    else if (y <= 1.5d-231) then
        tmp = x + (1.0d0 / (2.0d0 / x))
    else
        tmp = 0.5d0 * (x + y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -5.2e-232) {
		tmp = x - (y / 2.0);
	} else if (y <= 1.5e-231) {
		tmp = x + (1.0 / (2.0 / x));
	} else {
		tmp = 0.5 * (x + y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -5.2e-232:
		tmp = x - (y / 2.0)
	elif y <= 1.5e-231:
		tmp = x + (1.0 / (2.0 / x))
	else:
		tmp = 0.5 * (x + y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -5.2e-232)
		tmp = Float64(x - Float64(y / 2.0));
	elseif (y <= 1.5e-231)
		tmp = Float64(x + Float64(1.0 / Float64(2.0 / x)));
	else
		tmp = Float64(0.5 * Float64(x + y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -5.2e-232)
		tmp = x - (y / 2.0);
	elseif (y <= 1.5e-231)
		tmp = x + (1.0 / (2.0 / x));
	else
		tmp = 0.5 * (x + y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -5.2e-232], N[(x - N[(y / 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.5e-231], N[(x + N[(1.0 / N[(2.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(x + y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.19999999999999992e-232

   1. Initial program 100.0%

      \[x + \frac{\left|y - x\right|}{2} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num 99.7%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{2}{\left|y - x\right|}}} \]

      2. inv-pow 99.7%

         \[\leadsto x + \color{blue}{{\left(\frac{2}{\left|y - x\right|}\right)}^{-1}} \]

      3. add-sqr-sqrt 21.7%

         \[\leadsto x + {\left(\frac{2}{\left|\color{blue}{\sqrt{y - x} \cdot \sqrt{y - x}}\right|}\right)}^{-1} \]

      4. fabs-sqr 21.7%

         \[\leadsto x + {\left(\frac{2}{\color{blue}{\sqrt{y - x} \cdot \sqrt{y - x}}}\right)}^{-1} \]

      5. add-sqr-sqrt 26.3%

         \[\leadsto x + {\left(\frac{2}{\color{blue}{y - x}}\right)}^{-1} \]

   4. Applied egg-rr 26.3%

      \[\leadsto x + \color{blue}{{\left(\frac{2}{y - x}\right)}^{-1}} \]
   5. Step-by-step derivation

      1. add-sqr-sqrt 21.7%

         \[\leadsto x + {\left(\frac{2}{\color{blue}{\sqrt{y - x} \cdot \sqrt{y - x}}}\right)}^{-1} \]

      2. fabs-sqr 21.7%

         \[\leadsto x + {\left(\frac{2}{\color{blue}{\left|\sqrt{y - x} \cdot \sqrt{y - x}\right|}}\right)}^{-1} \]

      3. add-sqr-sqrt 99.7%

         \[\leadsto x + {\left(\frac{2}{\left|\color{blue}{y - x}\right|}\right)}^{-1} \]

      4. fabs-sub 99.7%

         \[\leadsto x + {\left(\frac{2}{\color{blue}{\left|x - y\right|}}\right)}^{-1} \]

   6. Applied egg-rr 99.7%

      \[\leadsto x + {\left(\frac{2}{\color{blue}{\left|x - y\right|}}\right)}^{-1} \]
   7. Step-by-step derivation

      1. unpow-1 99.7%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{2}{\left|x - y\right|}}} \]

      2. clear-num 99.7%

         \[\leadsto x + \frac{1}{\color{blue}{\frac{1}{\frac{\left|x - y\right|}{2}}}} \]

      3. remove-double-div 100.0%

         \[\leadsto x + \color{blue}{\frac{\left|x - y\right|}{2}} \]

      4. add-sqr-sqrt 77.7%

         \[\leadsto x + \frac{\left|\color{blue}{\sqrt{x - y} \cdot \sqrt{x - y}}\right|}{2} \]

      5. fabs-sqr 77.7%

         \[\leadsto x + \frac{\color{blue}{\sqrt{x - y} \cdot \sqrt{x - y}}}{2} \]

      6. add-sqr-sqrt 82.0%

         \[\leadsto x + \frac{\color{blue}{x - y}}{2} \]

   8. Applied egg-rr 82.0%

      \[\leadsto x + \color{blue}{\frac{x - y}{2}} \]

   9. Taylor expanded in x around 0 63.8%

      \[\leadsto x + \frac{\color{blue}{-1 \cdot y}}{2} \]
   10. Step-by-step derivation

       1. neg-mul-1 63.8%

          \[\leadsto x + \frac{\color{blue}{-y}}{2} \]

   11. Simplified 63.8%

       \[\leadsto x + \frac{\color{blue}{-y}}{2} \]

   if -5.19999999999999992e-232 < y < 1.5000000000000001e-231

   1. Initial program 99.7%

      \[x + \frac{\left|y - x\right|}{2} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 68.5%

      \[\leadsto x + \frac{\left|\color{blue}{y \cdot \left(1 + -1 \cdot \frac{x}{y}\right)}\right|}{2} \]
   4. Step-by-step derivation

      1. mul-1-neg 68.5%

         \[\leadsto x + \frac{\left|y \cdot \left(1 + \color{blue}{\left(-\frac{x}{y}\right)}\right)\right|}{2} \]

      2. unsub-neg 68.5%

         \[\leadsto x + \frac{\left|y \cdot \color{blue}{\left(1 - \frac{x}{y}\right)}\right|}{2} \]

   5. Simplified 68.5%

      \[\leadsto x + \frac{\left|\color{blue}{y \cdot \left(1 - \frac{x}{y}\right)}\right|}{2} \]

   6. Taylor expanded in x around inf 60.6%

      \[\leadsto x + \frac{\left|y \cdot \color{blue}{\left(-1 \cdot \frac{x}{y}\right)}\right|}{2} \]
   7. Step-by-step derivation

      1. neg-mul-1 60.6%

         \[\leadsto x + \frac{\left|y \cdot \color{blue}{\left(-\frac{x}{y}\right)}\right|}{2} \]

      2. distribute-neg-frac2 60.6%

         \[\leadsto x + \frac{\left|y \cdot \color{blue}{\frac{x}{-y}}\right|}{2} \]

   8. Simplified 60.6%

      \[\leadsto x + \frac{\left|y \cdot \color{blue}{\frac{x}{-y}}\right|}{2} \]
   9. Step-by-step derivation

      1. clear-num 60.5%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{2}{\left|y \cdot \frac{x}{-y}\right|}}} \]

      2. inv-pow 60.5%

         \[\leadsto x + \color{blue}{{\left(\frac{2}{\left|y \cdot \frac{x}{-y}\right|}\right)}^{-1}} \]

      3. add-sqr-sqrt 22.1%

         \[\leadsto x + {\left(\frac{2}{\left|\color{blue}{\sqrt{y \cdot \frac{x}{-y}} \cdot \sqrt{y \cdot \frac{x}{-y}}}\right|}\right)}^{-1} \]

      4. fabs-sqr 22.1%

         \[\leadsto x + {\left(\frac{2}{\color{blue}{\sqrt{y \cdot \frac{x}{-y}} \cdot \sqrt{y \cdot \frac{x}{-y}}}}\right)}^{-1} \]

      5. add-sqr-sqrt 29.5%

         \[\leadsto x + {\left(\frac{2}{\color{blue}{y \cdot \frac{x}{-y}}}\right)}^{-1} \]

      6. clear-num 29.5%

         \[\leadsto x + {\left(\frac{2}{y \cdot \color{blue}{\frac{1}{\frac{-y}{x}}}}\right)}^{-1} \]

      7. un-div-inv 29.5%

         \[\leadsto x + {\left(\frac{2}{\color{blue}{\frac{y}{\frac{-y}{x}}}}\right)}^{-1} \]

      8. add-sqr-sqrt 18.5%

         \[\leadsto x + {\left(\frac{2}{\frac{y}{\frac{\color{blue}{\sqrt{-y} \cdot \sqrt{-y}}}{x}}}\right)}^{-1} \]

      9. sqrt-unprod 2.1%

         \[\leadsto x + {\left(\frac{2}{\frac{y}{\frac{\color{blue}{\sqrt{\left(-y\right) \cdot \left(-y\right)}}}{x}}}\right)}^{-1} \]

      10. sqr-neg 2.1%

          \[\leadsto x + {\left(\frac{2}{\frac{y}{\frac{\sqrt{\color{blue}{y \cdot y}}}{x}}}\right)}^{-1} \]

      11. sqrt-unprod 20.4%

          \[\leadsto x + {\left(\frac{2}{\frac{y}{\frac{\color{blue}{\sqrt{y} \cdot \sqrt{y}}}{x}}}\right)}^{-1} \]

      12. add-sqr-sqrt 43.3%

          \[\leadsto x + {\left(\frac{2}{\frac{y}{\frac{\color{blue}{y}}{x}}}\right)}^{-1} \]

   10. Applied egg-rr 43.3%

       \[\leadsto x + \color{blue}{{\left(\frac{2}{\frac{y}{\frac{y}{x}}}\right)}^{-1}} \]
   11. Step-by-step derivation

       1. unpow-1 43.3%

          \[\leadsto x + \color{blue}{\frac{1}{\frac{2}{\frac{y}{\frac{y}{x}}}}} \]

       2. associate-/r/ 64.0%

          \[\leadsto x + \frac{1}{\frac{2}{\color{blue}{\frac{y}{y} \cdot x}}} \]

       3. *-inverses 64.0%

          \[\leadsto x + \frac{1}{\frac{2}{\color{blue}{1} \cdot x}} \]

       4. *-lft-identity 64.0%

          \[\leadsto x + \frac{1}{\frac{2}{\color{blue}{x}}} \]

   12. Simplified 64.0%

       \[\leadsto x + \color{blue}{\frac{1}{\frac{2}{x}}} \]

   if 1.5000000000000001e-231 < y

   1. Initial program 99.9%

      \[x + \frac{\left|y - x\right|}{2} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num 99.7%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{2}{\left|y - x\right|}}} \]

      2. inv-pow 99.7%

         \[\leadsto x + \color{blue}{{\left(\frac{2}{\left|y - x\right|}\right)}^{-1}} \]

      3. add-sqr-sqrt 79.9%

         \[\leadsto x + {\left(\frac{2}{\left|\color{blue}{\sqrt{y - x} \cdot \sqrt{y - x}}\right|}\right)}^{-1} \]

      4. fabs-sqr 79.9%

         \[\leadsto x + {\left(\frac{2}{\color{blue}{\sqrt{y - x} \cdot \sqrt{y - x}}}\right)}^{-1} \]

      5. add-sqr-sqrt 83.7%

         \[\leadsto x + {\left(\frac{2}{\color{blue}{y - x}}\right)}^{-1} \]

   4. Applied egg-rr 83.7%

      \[\leadsto x + \color{blue}{{\left(\frac{2}{y - x}\right)}^{-1}} \]

   5. Taylor expanded in x around 0 84.0%

      \[\leadsto \color{blue}{0.5 \cdot x + 0.5 \cdot y} \]
   6. Step-by-step derivation

      1. distribute-lft-out 84.0%

         \[\leadsto \color{blue}{0.5 \cdot \left(x + y\right)} \]

      2. +-commutative 84.0%

         \[\leadsto 0.5 \cdot \color{blue}{\left(y + x\right)} \]

   7. Simplified 84.0%

      \[\leadsto \color{blue}{0.5 \cdot \left(y + x\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 72.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{-232}:\\ \;\;\;\;x - \frac{y}{2}\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-231}:\\ \;\;\;\;x + \frac{1}{\frac{2}{x}}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(x + y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 71.2% accurate, 7.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{-230}:\\ \;\;\;\;x - \frac{y}{2}\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-230}:\\ \;\;\;\;x \cdot 1.5\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(x + y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.15e-230)
   (- x (/ y 2.0))
   (if (<= y 1.85e-230) (* x 1.5) (* 0.5 (+ x y)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.15e-230) {
		tmp = x - (y / 2.0);
	} else if (y <= 1.85e-230) {
		tmp = x * 1.5;
	} else {
		tmp = 0.5 * (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 <= (-1.15d-230)) then
        tmp = x - (y / 2.0d0)
    else if (y <= 1.85d-230) then
        tmp = x * 1.5d0
    else
        tmp = 0.5d0 * (x + y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.15e-230) {
		tmp = x - (y / 2.0);
	} else if (y <= 1.85e-230) {
		tmp = x * 1.5;
	} else {
		tmp = 0.5 * (x + y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.15e-230:
		tmp = x - (y / 2.0)
	elif y <= 1.85e-230:
		tmp = x * 1.5
	else:
		tmp = 0.5 * (x + y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.15e-230)
		tmp = Float64(x - Float64(y / 2.0));
	elseif (y <= 1.85e-230)
		tmp = Float64(x * 1.5);
	else
		tmp = Float64(0.5 * Float64(x + y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.15e-230)
		tmp = x - (y / 2.0);
	elseif (y <= 1.85e-230)
		tmp = x * 1.5;
	else
		tmp = 0.5 * (x + y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.15e-230], N[(x - N[(y / 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.85e-230], N[(x * 1.5), $MachinePrecision], N[(0.5 * N[(x + y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.1499999999999999e-230

   1. Initial program 100.0%

      \[x + \frac{\left|y - x\right|}{2} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num 99.7%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{2}{\left|y - x\right|}}} \]

      2. inv-pow 99.7%

         \[\leadsto x + \color{blue}{{\left(\frac{2}{\left|y - x\right|}\right)}^{-1}} \]

      3. add-sqr-sqrt 21.7%

         \[\leadsto x + {\left(\frac{2}{\left|\color{blue}{\sqrt{y - x} \cdot \sqrt{y - x}}\right|}\right)}^{-1} \]

      4. fabs-sqr 21.7%

         \[\leadsto x + {\left(\frac{2}{\color{blue}{\sqrt{y - x} \cdot \sqrt{y - x}}}\right)}^{-1} \]

      5. add-sqr-sqrt 26.3%

         \[\leadsto x + {\left(\frac{2}{\color{blue}{y - x}}\right)}^{-1} \]

   4. Applied egg-rr 26.3%

      \[\leadsto x + \color{blue}{{\left(\frac{2}{y - x}\right)}^{-1}} \]
   5. Step-by-step derivation

      1. add-sqr-sqrt 21.7%

         \[\leadsto x + {\left(\frac{2}{\color{blue}{\sqrt{y - x} \cdot \sqrt{y - x}}}\right)}^{-1} \]

      2. fabs-sqr 21.7%

         \[\leadsto x + {\left(\frac{2}{\color{blue}{\left|\sqrt{y - x} \cdot \sqrt{y - x}\right|}}\right)}^{-1} \]

      3. add-sqr-sqrt 99.7%

         \[\leadsto x + {\left(\frac{2}{\left|\color{blue}{y - x}\right|}\right)}^{-1} \]

      4. fabs-sub 99.7%

         \[\leadsto x + {\left(\frac{2}{\color{blue}{\left|x - y\right|}}\right)}^{-1} \]

   6. Applied egg-rr 99.7%

      \[\leadsto x + {\left(\frac{2}{\color{blue}{\left|x - y\right|}}\right)}^{-1} \]
   7. Step-by-step derivation

      1. unpow-1 99.7%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{2}{\left|x - y\right|}}} \]

      2. clear-num 99.7%

         \[\leadsto x + \frac{1}{\color{blue}{\frac{1}{\frac{\left|x - y\right|}{2}}}} \]

      3. remove-double-div 100.0%

         \[\leadsto x + \color{blue}{\frac{\left|x - y\right|}{2}} \]

      4. add-sqr-sqrt 77.7%

         \[\leadsto x + \frac{\left|\color{blue}{\sqrt{x - y} \cdot \sqrt{x - y}}\right|}{2} \]

      5. fabs-sqr 77.7%

         \[\leadsto x + \frac{\color{blue}{\sqrt{x - y} \cdot \sqrt{x - y}}}{2} \]

      6. add-sqr-sqrt 82.0%

         \[\leadsto x + \frac{\color{blue}{x - y}}{2} \]

   8. Applied egg-rr 82.0%

      \[\leadsto x + \color{blue}{\frac{x - y}{2}} \]

   9. Taylor expanded in x around 0 63.8%

      \[\leadsto x + \frac{\color{blue}{-1 \cdot y}}{2} \]
   10. Step-by-step derivation

       1. neg-mul-1 63.8%

          \[\leadsto x + \frac{\color{blue}{-y}}{2} \]

   11. Simplified 63.8%

       \[\leadsto x + \frac{\color{blue}{-y}}{2} \]

   if -1.1499999999999999e-230 < y < 1.84999999999999991e-230

   1. Initial program 99.7%

      \[x + \frac{\left|y - x\right|}{2} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num 99.5%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{2}{\left|y - x\right|}}} \]

      2. inv-pow 99.5%

         \[\leadsto x + \color{blue}{{\left(\frac{2}{\left|y - x\right|}\right)}^{-1}} \]

      3. add-sqr-sqrt 37.8%

         \[\leadsto x + {\left(\frac{2}{\left|\color{blue}{\sqrt{y - x} \cdot \sqrt{y - x}}\right|}\right)}^{-1} \]

      4. fabs-sqr 37.8%

         \[\leadsto x + {\left(\frac{2}{\color{blue}{\sqrt{y - x} \cdot \sqrt{y - x}}}\right)}^{-1} \]

      5. add-sqr-sqrt 48.6%

         \[\leadsto x + {\left(\frac{2}{\color{blue}{y - x}}\right)}^{-1} \]

   4. Applied egg-rr 48.6%

      \[\leadsto x + \color{blue}{{\left(\frac{2}{y - x}\right)}^{-1}} \]
   5. Step-by-step derivation

      1. add-sqr-sqrt 37.8%

         \[\leadsto x + {\left(\frac{2}{\color{blue}{\sqrt{y - x} \cdot \sqrt{y - x}}}\right)}^{-1} \]

      2. fabs-sqr 37.8%

         \[\leadsto x + {\left(\frac{2}{\color{blue}{\left|\sqrt{y - x} \cdot \sqrt{y - x}\right|}}\right)}^{-1} \]

      3. add-sqr-sqrt 99.5%

         \[\leadsto x + {\left(\frac{2}{\left|\color{blue}{y - x}\right|}\right)}^{-1} \]

      4. fabs-sub 99.5%

         \[\leadsto x + {\left(\frac{2}{\color{blue}{\left|x - y\right|}}\right)}^{-1} \]

   6. Applied egg-rr 99.5%

      \[\leadsto x + {\left(\frac{2}{\color{blue}{\left|x - y\right|}}\right)}^{-1} \]
   7. Step-by-step derivation

      1. unpow-1 99.5%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{2}{\left|x - y\right|}}} \]

      2. clear-num 99.5%

         \[\leadsto x + \frac{1}{\color{blue}{\frac{1}{\frac{\left|x - y\right|}{2}}}} \]

      3. remove-double-div 99.7%

         \[\leadsto x + \color{blue}{\frac{\left|x - y\right|}{2}} \]

      4. add-sqr-sqrt 61.5%

         \[\leadsto x + \frac{\left|\color{blue}{\sqrt{x - y} \cdot \sqrt{x - y}}\right|}{2} \]

      5. fabs-sqr 61.5%

         \[\leadsto x + \frac{\color{blue}{\sqrt{x - y} \cdot \sqrt{x - y}}}{2} \]

      6. add-sqr-sqrt 67.9%

         \[\leadsto x + \frac{\color{blue}{x - y}}{2} \]

   8. Applied egg-rr 67.9%

      \[\leadsto x + \color{blue}{\frac{x - y}{2}} \]

   9. Taylor expanded in x around inf 64.0%

      \[\leadsto \color{blue}{1.5 \cdot x} \]
   10. Step-by-step derivation

       1. *-commutative 64.0%

          \[\leadsto \color{blue}{x \cdot 1.5} \]

   11. Simplified 64.0%

       \[\leadsto \color{blue}{x \cdot 1.5} \]

   if 1.84999999999999991e-230 < y

   1. Initial program 99.9%

      \[x + \frac{\left|y - x\right|}{2} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num 99.7%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{2}{\left|y - x\right|}}} \]

      2. inv-pow 99.7%

         \[\leadsto x + \color{blue}{{\left(\frac{2}{\left|y - x\right|}\right)}^{-1}} \]

      3. add-sqr-sqrt 79.9%

         \[\leadsto x + {\left(\frac{2}{\left|\color{blue}{\sqrt{y - x} \cdot \sqrt{y - x}}\right|}\right)}^{-1} \]

      4. fabs-sqr 79.9%

         \[\leadsto x + {\left(\frac{2}{\color{blue}{\sqrt{y - x} \cdot \sqrt{y - x}}}\right)}^{-1} \]

      5. add-sqr-sqrt 83.7%

         \[\leadsto x + {\left(\frac{2}{\color{blue}{y - x}}\right)}^{-1} \]

   4. Applied egg-rr 83.7%

      \[\leadsto x + \color{blue}{{\left(\frac{2}{y - x}\right)}^{-1}} \]

   5. Taylor expanded in x around 0 84.0%

      \[\leadsto \color{blue}{0.5 \cdot x + 0.5 \cdot y} \]
   6. Step-by-step derivation

      1. distribute-lft-out 84.0%

         \[\leadsto \color{blue}{0.5 \cdot \left(x + y\right)} \]

      2. +-commutative 84.0%

         \[\leadsto 0.5 \cdot \color{blue}{\left(y + x\right)} \]

   7. Simplified 84.0%

      \[\leadsto \color{blue}{0.5 \cdot \left(y + x\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 72.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{-230}:\\ \;\;\;\;x - \frac{y}{2}\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-230}:\\ \;\;\;\;x \cdot 1.5\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(x + y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 65.6% accurate, 8.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.28 \cdot 10^{-270}:\\ \;\;\;\;0.5 \cdot \left(x + y\right)\\ \mathbf{elif}\;x \leq 9.8 \cdot 10^{-175}:\\ \;\;\;\;\frac{y}{-2}\\ \mathbf{else}:\\ \;\;\;\;x \cdot 1.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.28e-270)
   (* 0.5 (+ x y))
   (if (<= x 9.8e-175) (/ y -2.0) (* x 1.5))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.28e-270) {
		tmp = 0.5 * (x + y);
	} else if (x <= 9.8e-175) {
		tmp = y / -2.0;
	} else {
		tmp = x * 1.5;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-1.28d-270)) then
        tmp = 0.5d0 * (x + y)
    else if (x <= 9.8d-175) then
        tmp = y / (-2.0d0)
    else
        tmp = x * 1.5d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -1.28e-270) {
		tmp = 0.5 * (x + y);
	} else if (x <= 9.8e-175) {
		tmp = y / -2.0;
	} else {
		tmp = x * 1.5;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.28e-270:
		tmp = 0.5 * (x + y)
	elif x <= 9.8e-175:
		tmp = y / -2.0
	else:
		tmp = x * 1.5
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.28e-270)
		tmp = Float64(0.5 * Float64(x + y));
	elseif (x <= 9.8e-175)
		tmp = Float64(y / -2.0);
	else
		tmp = Float64(x * 1.5);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.28e-270)
		tmp = 0.5 * (x + y);
	elseif (x <= 9.8e-175)
		tmp = y / -2.0;
	else
		tmp = x * 1.5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.28e-270], N[(0.5 * N[(x + y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9.8e-175], N[(y / -2.0), $MachinePrecision], N[(x * 1.5), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.27999999999999991e-270

   1. Initial program 100.0%

      \[x + \frac{\left|y - x\right|}{2} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num 99.7%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{2}{\left|y - x\right|}}} \]

      2. inv-pow 99.7%

         \[\leadsto x + \color{blue}{{\left(\frac{2}{\left|y - x\right|}\right)}^{-1}} \]

      3. add-sqr-sqrt 79.2%

         \[\leadsto x + {\left(\frac{2}{\left|\color{blue}{\sqrt{y - x} \cdot \sqrt{y - x}}\right|}\right)}^{-1} \]

      4. fabs-sqr 79.2%

         \[\leadsto x + {\left(\frac{2}{\color{blue}{\sqrt{y - x} \cdot \sqrt{y - x}}}\right)}^{-1} \]

      5. add-sqr-sqrt 79.8%

         \[\leadsto x + {\left(\frac{2}{\color{blue}{y - x}}\right)}^{-1} \]

   4. Applied egg-rr 79.8%

      \[\leadsto x + \color{blue}{{\left(\frac{2}{y - x}\right)}^{-1}} \]

   5. Taylor expanded in x around 0 80.1%

      \[\leadsto \color{blue}{0.5 \cdot x + 0.5 \cdot y} \]
   6. Step-by-step derivation

      1. distribute-lft-out 80.1%

         \[\leadsto \color{blue}{0.5 \cdot \left(x + y\right)} \]

      2. +-commutative 80.1%

         \[\leadsto 0.5 \cdot \color{blue}{\left(y + x\right)} \]

   7. Simplified 80.1%

      \[\leadsto \color{blue}{0.5 \cdot \left(y + x\right)} \]

   if -1.27999999999999991e-270 < x < 9.79999999999999996e-175

   1. Initial program 99.9%

      \[x + \frac{\left|y - x\right|}{2} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 89.8%

      \[\leadsto x + \frac{\left|\color{blue}{y}\right|}{2} \]

   4. Taylor expanded in x around 0 88.3%

      \[\leadsto \color{blue}{0.5 \cdot \left|y\right|} \]
   5. Step-by-step derivation

      1. rem-square-sqrt 28.2%

         \[\leadsto 0.5 \cdot \left|\color{blue}{\sqrt{y} \cdot \sqrt{y}}\right| \]

      2. fabs-sqr 28.2%

         \[\leadsto 0.5 \cdot \color{blue}{\left(\sqrt{y} \cdot \sqrt{y}\right)} \]

      3. rem-square-sqrt 29.8%

         \[\leadsto 0.5 \cdot \color{blue}{y} \]

   6. Simplified 29.8%

      \[\leadsto \color{blue}{0.5 \cdot y} \]
   7. Step-by-step derivation

      1. *-commutative 29.8%

         \[\leadsto \color{blue}{y \cdot 0.5} \]

      2. metadata-eval 29.8%

         \[\leadsto y \cdot \color{blue}{\frac{1}{2}} \]

      3. div-inv 29.8%

         \[\leadsto \color{blue}{\frac{y}{2}} \]

      4. frac-2neg 29.8%

         \[\leadsto \color{blue}{\frac{-y}{-2}} \]

      5. add-sqr-sqrt 1.5%

         \[\leadsto \frac{\color{blue}{\sqrt{-y} \cdot \sqrt{-y}}}{-2} \]

      6. sqrt-unprod 2.7%

         \[\leadsto \frac{\color{blue}{\sqrt{\left(-y\right) \cdot \left(-y\right)}}}{-2} \]

      7. sqr-neg 2.7%

         \[\leadsto \frac{\sqrt{\color{blue}{y \cdot y}}}{-2} \]

      8. sqrt-unprod 0.9%

         \[\leadsto \frac{\color{blue}{\sqrt{y} \cdot \sqrt{y}}}{-2} \]

      9. add-sqr-sqrt 60.9%

         \[\leadsto \frac{\color{blue}{y}}{-2} \]

      10. metadata-eval 60.9%

          \[\leadsto \frac{y}{\color{blue}{-2}} \]

   8. Applied egg-rr 60.9%

      \[\leadsto \color{blue}{\frac{y}{-2}} \]

   if 9.79999999999999996e-175 < x

   1. Initial program 99.9%

      \[x + \frac{\left|y - x\right|}{2} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num 99.7%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{2}{\left|y - x\right|}}} \]

      2. inv-pow 99.7%

         \[\leadsto x + \color{blue}{{\left(\frac{2}{\left|y - x\right|}\right)}^{-1}} \]

      3. add-sqr-sqrt 18.7%

         \[\leadsto x + {\left(\frac{2}{\left|\color{blue}{\sqrt{y - x} \cdot \sqrt{y - x}}\right|}\right)}^{-1} \]

      4. fabs-sqr 18.7%

         \[\leadsto x + {\left(\frac{2}{\color{blue}{\sqrt{y - x} \cdot \sqrt{y - x}}}\right)}^{-1} \]

      5. add-sqr-sqrt 30.1%

         \[\leadsto x + {\left(\frac{2}{\color{blue}{y - x}}\right)}^{-1} \]

   4. Applied egg-rr 30.1%

      \[\leadsto x + \color{blue}{{\left(\frac{2}{y - x}\right)}^{-1}} \]
   5. Step-by-step derivation

      1. add-sqr-sqrt 18.7%

         \[\leadsto x + {\left(\frac{2}{\color{blue}{\sqrt{y - x} \cdot \sqrt{y - x}}}\right)}^{-1} \]

      2. fabs-sqr 18.7%

         \[\leadsto x + {\left(\frac{2}{\color{blue}{\left|\sqrt{y - x} \cdot \sqrt{y - x}\right|}}\right)}^{-1} \]

      3. add-sqr-sqrt 99.7%

         \[\leadsto x + {\left(\frac{2}{\left|\color{blue}{y - x}\right|}\right)}^{-1} \]

      4. fabs-sub 99.7%

         \[\leadsto x + {\left(\frac{2}{\color{blue}{\left|x - y\right|}}\right)}^{-1} \]

   6. Applied egg-rr 99.7%

      \[\leadsto x + {\left(\frac{2}{\color{blue}{\left|x - y\right|}}\right)}^{-1} \]
   7. Step-by-step derivation

      1. unpow-1 99.7%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{2}{\left|x - y\right|}}} \]

      2. clear-num 99.7%

         \[\leadsto x + \frac{1}{\color{blue}{\frac{1}{\frac{\left|x - y\right|}{2}}}} \]

      3. remove-double-div 99.9%

         \[\leadsto x + \color{blue}{\frac{\left|x - y\right|}{2}} \]

      4. add-sqr-sqrt 80.7%

         \[\leadsto x + \frac{\left|\color{blue}{\sqrt{x - y} \cdot \sqrt{x - y}}\right|}{2} \]

      5. fabs-sqr 80.7%

         \[\leadsto x + \frac{\color{blue}{\sqrt{x - y} \cdot \sqrt{x - y}}}{2} \]

      6. add-sqr-sqrt 81.1%

         \[\leadsto x + \frac{\color{blue}{x - y}}{2} \]

   8. Applied egg-rr 81.1%

      \[\leadsto x + \color{blue}{\frac{x - y}{2}} \]

   9. Taylor expanded in x around inf 63.7%

      \[\leadsto \color{blue}{1.5 \cdot x} \]
   10. Step-by-step derivation

       1. *-commutative 63.7%

          \[\leadsto \color{blue}{x \cdot 1.5} \]

   11. Simplified 63.7%

       \[\leadsto \color{blue}{x \cdot 1.5} \]
3. Recombined 3 regimes into one program.

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.28 \cdot 10^{-270}:\\ \;\;\;\;0.5 \cdot \left(x + y\right)\\ \mathbf{elif}\;x \leq 9.8 \cdot 10^{-175}:\\ \;\;\;\;\frac{y}{-2}\\ \mathbf{else}:\\ \;\;\;\;x \cdot 1.5\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 55.4% accurate, 8.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -61:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-217}:\\ \;\;\;\;y \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;x \cdot 1.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -61.0) (* x 0.5) (if (<= x 6e-217) (* y 0.5) (* x 1.5))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -61.0) {
		tmp = x * 0.5;
	} else if (x <= 6e-217) {
		tmp = y * 0.5;
	} else {
		tmp = x * 1.5;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-61.0d0)) then
        tmp = x * 0.5d0
    else if (x <= 6d-217) then
        tmp = y * 0.5d0
    else
        tmp = x * 1.5d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -61.0) {
		tmp = x * 0.5;
	} else if (x <= 6e-217) {
		tmp = y * 0.5;
	} else {
		tmp = x * 1.5;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -61.0:
		tmp = x * 0.5
	elif x <= 6e-217:
		tmp = y * 0.5
	else:
		tmp = x * 1.5
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -61.0)
		tmp = Float64(x * 0.5);
	elseif (x <= 6e-217)
		tmp = Float64(y * 0.5);
	else
		tmp = Float64(x * 1.5);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -61.0)
		tmp = x * 0.5;
	elseif (x <= 6e-217)
		tmp = y * 0.5;
	else
		tmp = x * 1.5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -61.0], N[(x * 0.5), $MachinePrecision], If[LessEqual[x, 6e-217], N[(y * 0.5), $MachinePrecision], N[(x * 1.5), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -61

   1. Initial program 100.0%

      \[x + \frac{\left|y - x\right|}{2} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num 99.8%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{2}{\left|y - x\right|}}} \]

      2. inv-pow 99.8%

         \[\leadsto x + \color{blue}{{\left(\frac{2}{\left|y - x\right|}\right)}^{-1}} \]

      3. add-sqr-sqrt 90.0%

         \[\leadsto x + {\left(\frac{2}{\left|\color{blue}{\sqrt{y - x} \cdot \sqrt{y - x}}\right|}\right)}^{-1} \]

      4. fabs-sqr 90.0%

         \[\leadsto x + {\left(\frac{2}{\color{blue}{\sqrt{y - x} \cdot \sqrt{y - x}}}\right)}^{-1} \]

      5. add-sqr-sqrt 90.5%

         \[\leadsto x + {\left(\frac{2}{\color{blue}{y - x}}\right)}^{-1} \]

   4. Applied egg-rr 90.5%

      \[\leadsto x + \color{blue}{{\left(\frac{2}{y - x}\right)}^{-1}} \]

   5. Taylor expanded in x around inf 75.8%

      \[\leadsto \color{blue}{0.5 \cdot x} \]

   if -61 < x < 6.00000000000000009e-217

   1. Initial program 100.0%

      \[x + \frac{\left|y - x\right|}{2} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 86.1%

      \[\leadsto x + \frac{\left|\color{blue}{y}\right|}{2} \]

   4. Taylor expanded in x around 0 84.0%

      \[\leadsto \color{blue}{0.5 \cdot \left|y\right|} \]
   5. Step-by-step derivation

      1. rem-square-sqrt 40.5%

         \[\leadsto 0.5 \cdot \left|\color{blue}{\sqrt{y} \cdot \sqrt{y}}\right| \]

      2. fabs-sqr 40.5%

         \[\leadsto 0.5 \cdot \color{blue}{\left(\sqrt{y} \cdot \sqrt{y}\right)} \]

      3. rem-square-sqrt 42.0%

         \[\leadsto 0.5 \cdot \color{blue}{y} \]

   6. Simplified 42.0%

      \[\leadsto \color{blue}{0.5 \cdot y} \]

   if 6.00000000000000009e-217 < x

   1. Initial program 99.8%

      \[x + \frac{\left|y - x\right|}{2} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num 99.7%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{2}{\left|y - x\right|}}} \]

      2. inv-pow 99.7%

         \[\leadsto x + \color{blue}{{\left(\frac{2}{\left|y - x\right|}\right)}^{-1}} \]

      3. add-sqr-sqrt 18.1%

         \[\leadsto x + {\left(\frac{2}{\left|\color{blue}{\sqrt{y - x} \cdot \sqrt{y - x}}\right|}\right)}^{-1} \]

      4. fabs-sqr 18.1%

         \[\leadsto x + {\left(\frac{2}{\color{blue}{\sqrt{y - x} \cdot \sqrt{y - x}}}\right)}^{-1} \]

      5. add-sqr-sqrt 29.1%

         \[\leadsto x + {\left(\frac{2}{\color{blue}{y - x}}\right)}^{-1} \]

   4. Applied egg-rr 29.1%

      \[\leadsto x + \color{blue}{{\left(\frac{2}{y - x}\right)}^{-1}} \]
   5. Step-by-step derivation

      1. add-sqr-sqrt 18.1%

         \[\leadsto x + {\left(\frac{2}{\color{blue}{\sqrt{y - x} \cdot \sqrt{y - x}}}\right)}^{-1} \]

      2. fabs-sqr 18.1%

         \[\leadsto x + {\left(\frac{2}{\color{blue}{\left|\sqrt{y - x} \cdot \sqrt{y - x}\right|}}\right)}^{-1} \]

      3. add-sqr-sqrt 99.7%

         \[\leadsto x + {\left(\frac{2}{\left|\color{blue}{y - x}\right|}\right)}^{-1} \]

      4. fabs-sub 99.7%

         \[\leadsto x + {\left(\frac{2}{\color{blue}{\left|x - y\right|}}\right)}^{-1} \]

   6. Applied egg-rr 99.7%

      \[\leadsto x + {\left(\frac{2}{\color{blue}{\left|x - y\right|}}\right)}^{-1} \]
   7. Step-by-step derivation

      1. unpow-1 99.7%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{2}{\left|x - y\right|}}} \]

      2. clear-num 99.7%

         \[\leadsto x + \frac{1}{\color{blue}{\frac{1}{\frac{\left|x - y\right|}{2}}}} \]

      3. remove-double-div 99.8%

         \[\leadsto x + \color{blue}{\frac{\left|x - y\right|}{2}} \]

      4. add-sqr-sqrt 81.4%

         \[\leadsto x + \frac{\left|\color{blue}{\sqrt{x - y} \cdot \sqrt{x - y}}\right|}{2} \]

      5. fabs-sqr 81.4%

         \[\leadsto x + \frac{\color{blue}{\sqrt{x - y} \cdot \sqrt{x - y}}}{2} \]

      6. add-sqr-sqrt 81.8%

         \[\leadsto x + \frac{\color{blue}{x - y}}{2} \]

   8. Applied egg-rr 81.8%

      \[\leadsto x + \color{blue}{\frac{x - y}{2}} \]

   9. Taylor expanded in x around inf 61.3%

      \[\leadsto \color{blue}{1.5 \cdot x} \]
   10. Step-by-step derivation

       1. *-commutative 61.3%

          \[\leadsto \color{blue}{x \cdot 1.5} \]

   11. Simplified 61.3%

       \[\leadsto \color{blue}{x \cdot 1.5} \]
3. Recombined 3 regimes into one program.

4. Final simplification 58.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -61:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-217}:\\ \;\;\;\;y \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;x \cdot 1.5\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 79.8% accurate, 8.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.4 \cdot 10^{-230}:\\ \;\;\;\;x + \frac{x - y}{2}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(x + y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y 1.4e-230) (+ x (/ (- x y) 2.0)) (* 0.5 (+ x y))))

C

double code(double x, double y) {
	double tmp;
	if (y <= 1.4e-230) {
		tmp = x + ((x - y) / 2.0);
	} else {
		tmp = 0.5 * (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 <= 1.4d-230) then
        tmp = x + ((x - y) / 2.0d0)
    else
        tmp = 0.5d0 * (x + y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= 1.4e-230) {
		tmp = x + ((x - y) / 2.0);
	} else {
		tmp = 0.5 * (x + y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 1.4e-230:
		tmp = x + ((x - y) / 2.0)
	else:
		tmp = 0.5 * (x + y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 1.4e-230)
		tmp = Float64(x + Float64(Float64(x - y) / 2.0));
	else
		tmp = Float64(0.5 * Float64(x + y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 1.4e-230)
		tmp = x + ((x - y) / 2.0);
	else
		tmp = 0.5 * (x + y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 1.4e-230], N[(x + N[(N[(x - y), $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(x + y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.4e-230

   1. Initial program 99.9%

      \[x + \frac{\left|y - x\right|}{2} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num 99.7%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{2}{\left|y - x\right|}}} \]

      2. inv-pow 99.7%

         \[\leadsto x + \color{blue}{{\left(\frac{2}{\left|y - x\right|}\right)}^{-1}} \]

      3. add-sqr-sqrt 25.4%

         \[\leadsto x + {\left(\frac{2}{\left|\color{blue}{\sqrt{y - x} \cdot \sqrt{y - x}}\right|}\right)}^{-1} \]

      4. fabs-sqr 25.4%

         \[\leadsto x + {\left(\frac{2}{\color{blue}{\sqrt{y - x} \cdot \sqrt{y - x}}}\right)}^{-1} \]

      5. add-sqr-sqrt 31.4%

         \[\leadsto x + {\left(\frac{2}{\color{blue}{y - x}}\right)}^{-1} \]

   4. Applied egg-rr 31.4%

      \[\leadsto x + \color{blue}{{\left(\frac{2}{y - x}\right)}^{-1}} \]
   5. Step-by-step derivation

      1. add-sqr-sqrt 25.4%

         \[\leadsto x + {\left(\frac{2}{\color{blue}{\sqrt{y - x} \cdot \sqrt{y - x}}}\right)}^{-1} \]

      2. fabs-sqr 25.4%

         \[\leadsto x + {\left(\frac{2}{\color{blue}{\left|\sqrt{y - x} \cdot \sqrt{y - x}\right|}}\right)}^{-1} \]

      3. add-sqr-sqrt 99.7%

         \[\leadsto x + {\left(\frac{2}{\left|\color{blue}{y - x}\right|}\right)}^{-1} \]

      4. fabs-sub 99.7%

         \[\leadsto x + {\left(\frac{2}{\color{blue}{\left|x - y\right|}}\right)}^{-1} \]

   6. Applied egg-rr 99.7%

      \[\leadsto x + {\left(\frac{2}{\color{blue}{\left|x - y\right|}}\right)}^{-1} \]
   7. Step-by-step derivation

      1. unpow-1 99.7%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{2}{\left|x - y\right|}}} \]

      2. clear-num 99.7%

         \[\leadsto x + \frac{1}{\color{blue}{\frac{1}{\frac{\left|x - y\right|}{2}}}} \]

      3. remove-double-div 99.9%

         \[\leadsto x + \color{blue}{\frac{\left|x - y\right|}{2}} \]

      4. add-sqr-sqrt 74.0%

         \[\leadsto x + \frac{\left|\color{blue}{\sqrt{x - y} \cdot \sqrt{x - y}}\right|}{2} \]

      5. fabs-sqr 74.0%

         \[\leadsto x + \frac{\color{blue}{\sqrt{x - y} \cdot \sqrt{x - y}}}{2} \]

      6. add-sqr-sqrt 78.7%

         \[\leadsto x + \frac{\color{blue}{x - y}}{2} \]

   8. Applied egg-rr 78.7%

      \[\leadsto x + \color{blue}{\frac{x - y}{2}} \]

   if 1.4e-230 < y

   1. Initial program 99.9%

      \[x + \frac{\left|y - x\right|}{2} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num 99.7%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{2}{\left|y - x\right|}}} \]

      2. inv-pow 99.7%

         \[\leadsto x + \color{blue}{{\left(\frac{2}{\left|y - x\right|}\right)}^{-1}} \]

      3. add-sqr-sqrt 79.9%

         \[\leadsto x + {\left(\frac{2}{\left|\color{blue}{\sqrt{y - x} \cdot \sqrt{y - x}}\right|}\right)}^{-1} \]

      4. fabs-sqr 79.9%

         \[\leadsto x + {\left(\frac{2}{\color{blue}{\sqrt{y - x} \cdot \sqrt{y - x}}}\right)}^{-1} \]

      5. add-sqr-sqrt 83.7%

         \[\leadsto x + {\left(\frac{2}{\color{blue}{y - x}}\right)}^{-1} \]

   4. Applied egg-rr 83.7%

      \[\leadsto x + \color{blue}{{\left(\frac{2}{y - x}\right)}^{-1}} \]

   5. Taylor expanded in x around 0 84.0%

      \[\leadsto \color{blue}{0.5 \cdot x + 0.5 \cdot y} \]
   6. Step-by-step derivation

      1. distribute-lft-out 84.0%

         \[\leadsto \color{blue}{0.5 \cdot \left(x + y\right)} \]

      2. +-commutative 84.0%

         \[\leadsto 0.5 \cdot \color{blue}{\left(y + x\right)} \]

   7. Simplified 84.0%

      \[\leadsto \color{blue}{0.5 \cdot \left(y + x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.4 \cdot 10^{-230}:\\ \;\;\;\;x + \frac{x - y}{2}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(x + y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 45.5% accurate, 13.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 7.4 \cdot 10^{-90}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;y \cdot 0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y 7.4e-90) (* x 0.5) (* y 0.5)))

C

double code(double x, double y) {
	double tmp;
	if (y <= 7.4e-90) {
		tmp = x * 0.5;
	} else {
		tmp = y * 0.5;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= 7.4d-90) then
        tmp = x * 0.5d0
    else
        tmp = y * 0.5d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= 7.4e-90) {
		tmp = x * 0.5;
	} else {
		tmp = y * 0.5;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 7.4e-90:
		tmp = x * 0.5
	else:
		tmp = y * 0.5
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 7.4e-90)
		tmp = Float64(x * 0.5);
	else
		tmp = Float64(y * 0.5);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 7.4e-90)
		tmp = x * 0.5;
	else
		tmp = y * 0.5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 7.4e-90], N[(x * 0.5), $MachinePrecision], N[(y * 0.5), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 7.40000000000000035e-90

   1. Initial program 99.9%

      \[x + \frac{\left|y - x\right|}{2} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num 99.7%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{2}{\left|y - x\right|}}} \]

      2. inv-pow 99.7%

         \[\leadsto x + \color{blue}{{\left(\frac{2}{\left|y - x\right|}\right)}^{-1}} \]

      3. add-sqr-sqrt 32.5%

         \[\leadsto x + {\left(\frac{2}{\left|\color{blue}{\sqrt{y - x} \cdot \sqrt{y - x}}\right|}\right)}^{-1} \]

      4. fabs-sqr 32.5%

         \[\leadsto x + {\left(\frac{2}{\color{blue}{\sqrt{y - x} \cdot \sqrt{y - x}}}\right)}^{-1} \]

      5. add-sqr-sqrt 38.3%

         \[\leadsto x + {\left(\frac{2}{\color{blue}{y - x}}\right)}^{-1} \]

   4. Applied egg-rr 38.3%

      \[\leadsto x + \color{blue}{{\left(\frac{2}{y - x}\right)}^{-1}} \]

   5. Taylor expanded in x around inf 34.7%

      \[\leadsto \color{blue}{0.5 \cdot x} \]

   if 7.40000000000000035e-90 < y

   1. Initial program 100.0%

      \[x + \frac{\left|y - x\right|}{2} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 72.2%

      \[\leadsto x + \frac{\left|\color{blue}{y}\right|}{2} \]

   4. Taylor expanded in x around 0 66.8%

      \[\leadsto \color{blue}{0.5 \cdot \left|y\right|} \]
   5. Step-by-step derivation

      1. rem-square-sqrt 66.3%

         \[\leadsto 0.5 \cdot \left|\color{blue}{\sqrt{y} \cdot \sqrt{y}}\right| \]

      2. fabs-sqr 66.3%

         \[\leadsto 0.5 \cdot \color{blue}{\left(\sqrt{y} \cdot \sqrt{y}\right)} \]

      3. rem-square-sqrt 66.8%

         \[\leadsto 0.5 \cdot \color{blue}{y} \]

   6. Simplified 66.8%

      \[\leadsto \color{blue}{0.5 \cdot y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 45.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 7.4 \cdot 10^{-90}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;y \cdot 0.5\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 29.7% accurate, 35.7× speedup

Math

\[\begin{array}{l} \\ x \cdot 0.5 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* x 0.5))

C

double code(double x, double y) {
	return x * 0.5;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x * 0.5d0
end function

Java

public static double code(double x, double y) {
	return x * 0.5;
}

Python

def code(x, y):
	return x * 0.5

Julia

function code(x, y)
	return Float64(x * 0.5)
end

MATLAB

function tmp = code(x, y)
	tmp = x * 0.5;
end

Wolfram

code[x_, y_] := N[(x * 0.5), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[x + \frac{\left|y - x\right|}{2} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. clear-num 99.7%

      \[\leadsto x + \color{blue}{\frac{1}{\frac{2}{\left|y - x\right|}}} \]

   2. inv-pow 99.7%

      \[\leadsto x + \color{blue}{{\left(\frac{2}{\left|y - x\right|}\right)}^{-1}} \]

   3. add-sqr-sqrt 48.4%

      \[\leadsto x + {\left(\frac{2}{\left|\color{blue}{\sqrt{y - x} \cdot \sqrt{y - x}}\right|}\right)}^{-1} \]

   4. fabs-sqr 48.4%

      \[\leadsto x + {\left(\frac{2}{\color{blue}{\sqrt{y - x} \cdot \sqrt{y - x}}}\right)}^{-1} \]

   5. add-sqr-sqrt 53.5%

      \[\leadsto x + {\left(\frac{2}{\color{blue}{y - x}}\right)}^{-1} \]

4. Applied egg-rr 53.5%

   \[\leadsto x + \color{blue}{{\left(\frac{2}{y - x}\right)}^{-1}} \]

5. Taylor expanded in x around inf 29.6%

   \[\leadsto \color{blue}{0.5 \cdot x} \]

6. Final simplification 29.6%

   \[\leadsto x \cdot 0.5 \]
7. Add Preprocessing

Alternative 12: 11.2% accurate, 107.0× 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 99.9%

   \[x + \frac{\left|y - x\right|}{2} \]
2. Add Preprocessing

3. Taylor expanded in x around inf 11.4%

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

Reproduce

herbie shell --seed 2024146 
(FPCore (x y)
  :name "Graphics.Rendering.Chart.Plot.AreaSpots:renderSpotLegend from Chart-1.5.3"
  :precision binary64
  (+ x (/ (fabs (- y x)) 2.0)))