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

Percentage Accurate: 99.9% → 99.9%

Time: 7.9s

Alternatives: 9

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

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Final simplification 100.0%

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

Alternative 2: 80.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{-21}:\\ \;\;\;\;x + \frac{\left|y\right|}{2}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-145}:\\ \;\;\;\;x + \frac{\left|x\right|}{2}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(x + y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.05e-21)
   (+ x (/ (fabs y) 2.0))
   (if (<= y 2.2e-145) (+ x (/ (fabs x) 2.0)) (* 0.5 (+ x y)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.05e-21) {
		tmp = x + (fabs(y) / 2.0);
	} else if (y <= 2.2e-145) {
		tmp = x + (fabs(x) / 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 <= (-1.05d-21)) then
        tmp = x + (abs(y) / 2.0d0)
    else if (y <= 2.2d-145) then
        tmp = x + (abs(x) / 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 <= -1.05e-21) {
		tmp = x + (Math.abs(y) / 2.0);
	} else if (y <= 2.2e-145) {
		tmp = x + (Math.abs(x) / 2.0);
	} else {
		tmp = 0.5 * (x + y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.05e-21:
		tmp = x + (math.fabs(y) / 2.0)
	elif y <= 2.2e-145:
		tmp = x + (math.fabs(x) / 2.0)
	else:
		tmp = 0.5 * (x + y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.05e-21)
		tmp = Float64(x + Float64(abs(y) / 2.0));
	elseif (y <= 2.2e-145)
		tmp = Float64(x + Float64(abs(x) / 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 <= -1.05e-21)
		tmp = x + (abs(y) / 2.0);
	elseif (y <= 2.2e-145)
		tmp = x + (abs(x) / 2.0);
	else
		tmp = 0.5 * (x + y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.05e-21], N[(x + N[(N[Abs[y], $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.2e-145], N[(x + N[(N[Abs[x], $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(x + y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.05000000000000006e-21

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 86.0%

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

   if -1.05000000000000006e-21 < y < 2.19999999999999999e-145

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 89.2%

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

      1. neg-mul-1 89.2%

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

   5. Simplified 89.2%

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

   if 2.19999999999999999e-145 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around -inf 100.0%

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

      1. fabs-neg 100.0%

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

      2. mul-1-neg 100.0%

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

      3. sub-neg 100.0%

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

      4. fabs-sub 100.0%

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

      5. rem-square-sqrt 82.1%

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

      6. fabs-sqr 82.1%

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

      7. rem-square-sqrt 85.7%

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

   5. Simplified 85.7%

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

   6. Taylor expanded in x around 0 85.7%

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

      1. distribute-lft-out 85.7%

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

   8. Simplified 85.7%

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

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{-21}:\\ \;\;\;\;x + \frac{\left|y\right|}{2}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-145}:\\ \;\;\;\;x + \frac{\left|x\right|}{2}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(x + y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 77.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.7 \cdot 10^{-192}:\\ \;\;\;\;0.5 \cdot \left(x + y\right)\\ \mathbf{elif}\;x \leq 9.4 \cdot 10^{-95}:\\ \;\;\;\;x + \frac{\left|y\right|}{2}\\ \mathbf{else}:\\ \;\;\;\;x \cdot 1.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -6.7e-192)
   (* 0.5 (+ x y))
   (if (<= x 9.4e-95) (+ x (/ (fabs y) 2.0)) (* x 1.5))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -6.7e-192) {
		tmp = 0.5 * (x + y);
	} else if (x <= 9.4e-95) {
		tmp = x + (fabs(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 <= (-6.7d-192)) then
        tmp = 0.5d0 * (x + y)
    else if (x <= 9.4d-95) then
        tmp = x + (abs(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 <= -6.7e-192) {
		tmp = 0.5 * (x + y);
	} else if (x <= 9.4e-95) {
		tmp = x + (Math.abs(y) / 2.0);
	} else {
		tmp = x * 1.5;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -6.7e-192:
		tmp = 0.5 * (x + y)
	elif x <= 9.4e-95:
		tmp = x + (math.fabs(y) / 2.0)
	else:
		tmp = x * 1.5
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -6.7e-192)
		tmp = Float64(0.5 * Float64(x + y));
	elseif (x <= 9.4e-95)
		tmp = Float64(x + Float64(abs(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 <= -6.7e-192)
		tmp = 0.5 * (x + y);
	elseif (x <= 9.4e-95)
		tmp = x + (abs(y) / 2.0);
	else
		tmp = x * 1.5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -6.7e-192], N[(0.5 * N[(x + y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9.4e-95], N[(x + N[(N[Abs[y], $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision], N[(x * 1.5), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.69999999999999991e-192

   1. Initial program 100.0%

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

   3. Taylor expanded in y around -inf 100.0%

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

      1. fabs-neg 100.0%

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

      2. mul-1-neg 100.0%

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

      3. sub-neg 100.0%

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

      4. fabs-sub 100.0%

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

      5. rem-square-sqrt 80.6%

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

      6. fabs-sqr 80.6%

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

      7. rem-square-sqrt 81.4%

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

   5. Simplified 81.4%

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

   6. Taylor expanded in x around 0 81.4%

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

      1. distribute-lft-out 81.4%

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

   8. Simplified 81.4%

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

   if -6.69999999999999991e-192 < x < 9.3999999999999995e-95

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 92.1%

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

   if 9.3999999999999995e-95 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 71.4%

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

      1. neg-mul-1 71.4%

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

   5. Simplified 71.4%

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

   6. Taylor expanded in x around 0 71.4%

      \[\leadsto \color{blue}{x + 0.5 \cdot \left|-x\right|} \]
   7. Step-by-step derivation

      1. *-rgt-identity 71.4%

         \[\leadsto \color{blue}{x \cdot 1} + 0.5 \cdot \left|-x\right| \]

      2. *-commutative 71.4%

         \[\leadsto x \cdot 1 + \color{blue}{\left|-x\right| \cdot 0.5} \]

      3. fabs-neg 71.4%

         \[\leadsto x \cdot 1 + \color{blue}{\left|x\right|} \cdot 0.5 \]

      4. rem-square-sqrt 71.3%

         \[\leadsto x \cdot 1 + \left|\color{blue}{\sqrt{x} \cdot \sqrt{x}}\right| \cdot 0.5 \]

      5. fabs-sqr 71.3%

         \[\leadsto x \cdot 1 + \color{blue}{\left(\sqrt{x} \cdot \sqrt{x}\right)} \cdot 0.5 \]

      6. rem-square-sqrt 71.4%

         \[\leadsto x \cdot 1 + \color{blue}{x} \cdot 0.5 \]

      7. distribute-lft-out 71.4%

         \[\leadsto \color{blue}{x \cdot \left(1 + 0.5\right)} \]

      8. metadata-eval 71.4%

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

   8. Simplified 71.4%

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

Alternative 4: 77.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{-191}:\\ \;\;\;\;0.5 \cdot \left(x + y\right)\\ \mathbf{elif}\;x \leq 9.8 \cdot 10^{-95}:\\ \;\;\;\;\left|y\right| \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;x \cdot 1.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -2.4e-191)
   (* 0.5 (+ x y))
   (if (<= x 9.8e-95) (* (fabs y) 0.5) (* x 1.5))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2.4e-191) {
		tmp = 0.5 * (x + y);
	} else if (x <= 9.8e-95) {
		tmp = fabs(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 <= (-2.4d-191)) then
        tmp = 0.5d0 * (x + y)
    else if (x <= 9.8d-95) then
        tmp = abs(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 <= -2.4e-191) {
		tmp = 0.5 * (x + y);
	} else if (x <= 9.8e-95) {
		tmp = Math.abs(y) * 0.5;
	} else {
		tmp = x * 1.5;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2.4e-191:
		tmp = 0.5 * (x + y)
	elif x <= 9.8e-95:
		tmp = math.fabs(y) * 0.5
	else:
		tmp = x * 1.5
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2.4e-191)
		tmp = Float64(0.5 * Float64(x + y));
	elseif (x <= 9.8e-95)
		tmp = Float64(abs(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 <= -2.4e-191)
		tmp = 0.5 * (x + y);
	elseif (x <= 9.8e-95)
		tmp = abs(y) * 0.5;
	else
		tmp = x * 1.5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2.4e-191], N[(0.5 * N[(x + y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9.8e-95], N[(N[Abs[y], $MachinePrecision] * 0.5), $MachinePrecision], N[(x * 1.5), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.3999999999999999e-191

   1. Initial program 100.0%

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

   3. Taylor expanded in y around -inf 100.0%

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

      1. fabs-neg 100.0%

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

      2. mul-1-neg 100.0%

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

      3. sub-neg 100.0%

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

      4. fabs-sub 100.0%

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

      5. rem-square-sqrt 80.6%

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

      6. fabs-sqr 80.6%

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

      7. rem-square-sqrt 81.4%

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

   5. Simplified 81.4%

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

   6. Taylor expanded in x around 0 81.4%

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

      1. distribute-lft-out 81.4%

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

   8. Simplified 81.4%

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

   if -2.3999999999999999e-191 < x < 9.8e-95

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 92.1%

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

   4. Taylor expanded in x around 0 90.9%

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

   if 9.8e-95 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 71.4%

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

      1. neg-mul-1 71.4%

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

   5. Simplified 71.4%

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

   6. Taylor expanded in x around 0 71.4%

      \[\leadsto \color{blue}{x + 0.5 \cdot \left|-x\right|} \]
   7. Step-by-step derivation

      1. *-rgt-identity 71.4%

         \[\leadsto \color{blue}{x \cdot 1} + 0.5 \cdot \left|-x\right| \]

      2. *-commutative 71.4%

         \[\leadsto x \cdot 1 + \color{blue}{\left|-x\right| \cdot 0.5} \]

      3. fabs-neg 71.4%

         \[\leadsto x \cdot 1 + \color{blue}{\left|x\right|} \cdot 0.5 \]

      4. rem-square-sqrt 71.3%

         \[\leadsto x \cdot 1 + \left|\color{blue}{\sqrt{x} \cdot \sqrt{x}}\right| \cdot 0.5 \]

      5. fabs-sqr 71.3%

         \[\leadsto x \cdot 1 + \color{blue}{\left(\sqrt{x} \cdot \sqrt{x}\right)} \cdot 0.5 \]

      6. rem-square-sqrt 71.4%

         \[\leadsto x \cdot 1 + \color{blue}{x} \cdot 0.5 \]

      7. distribute-lft-out 71.4%

         \[\leadsto \color{blue}{x \cdot \left(1 + 0.5\right)} \]

      8. metadata-eval 71.4%

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

   8. Simplified 71.4%

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

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{-191}:\\ \;\;\;\;0.5 \cdot \left(x + y\right)\\ \mathbf{elif}\;x \leq 9.8 \cdot 10^{-95}:\\ \;\;\;\;\left|y\right| \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;x \cdot 1.5\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 58.3% accurate, 8.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{-175}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-107}:\\ \;\;\;\;y \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;x \cdot 1.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -8.5e-175) (* x 0.5) (if (<= x 1.2e-107) (* y 0.5) (* x 1.5))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -8.5e-175) {
		tmp = x * 0.5;
	} else if (x <= 1.2e-107) {
		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 <= (-8.5d-175)) then
        tmp = x * 0.5d0
    else if (x <= 1.2d-107) 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 <= -8.5e-175) {
		tmp = x * 0.5;
	} else if (x <= 1.2e-107) {
		tmp = y * 0.5;
	} else {
		tmp = x * 1.5;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -8.5e-175:
		tmp = x * 0.5
	elif x <= 1.2e-107:
		tmp = y * 0.5
	else:
		tmp = x * 1.5
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -8.5e-175)
		tmp = Float64(x * 0.5);
	elseif (x <= 1.2e-107)
		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 <= -8.5e-175)
		tmp = x * 0.5;
	elseif (x <= 1.2e-107)
		tmp = y * 0.5;
	else
		tmp = x * 1.5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -8.5e-175], N[(x * 0.5), $MachinePrecision], If[LessEqual[x, 1.2e-107], N[(y * 0.5), $MachinePrecision], N[(x * 1.5), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -8.5000000000000005e-175

   1. Initial program 100.0%

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

   3. Taylor expanded in y around -inf 100.0%

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

      1. fabs-neg 100.0%

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

      2. mul-1-neg 100.0%

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

      3. sub-neg 100.0%

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

      4. fabs-sub 100.0%

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

      5. rem-square-sqrt 79.9%

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

      6. fabs-sqr 79.9%

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

      7. rem-square-sqrt 80.7%

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

   5. Simplified 80.7%

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

   6. Taylor expanded in x around inf 61.3%

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

      1. *-commutative 61.3%

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

   8. Simplified 61.3%

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

   if -8.5000000000000005e-175 < x < 1.19999999999999997e-107

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 88.9%

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

      1. metadata-eval 88.9%

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

      2. fabs-mul 88.9%

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

      3. *-commutative 88.9%

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

      4. rem-square-sqrt 53.4%

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

      5. fabs-sqr 53.4%

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

      6. rem-square-sqrt 54.4%

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

      7. *-commutative 54.4%

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

   5. Simplified 54.4%

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

   6. Taylor expanded in y around inf 54.7%

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

      1. *-commutative 54.7%

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

   8. Simplified 54.7%

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

   if 1.19999999999999997e-107 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 69.8%

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

      1. neg-mul-1 69.8%

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

   5. Simplified 69.8%

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

   6. Taylor expanded in x around 0 69.8%

      \[\leadsto \color{blue}{x + 0.5 \cdot \left|-x\right|} \]
   7. Step-by-step derivation

      1. *-rgt-identity 69.8%

         \[\leadsto \color{blue}{x \cdot 1} + 0.5 \cdot \left|-x\right| \]

      2. *-commutative 69.8%

         \[\leadsto x \cdot 1 + \color{blue}{\left|-x\right| \cdot 0.5} \]

      3. fabs-neg 69.8%

         \[\leadsto x \cdot 1 + \color{blue}{\left|x\right|} \cdot 0.5 \]

      4. rem-square-sqrt 69.7%

         \[\leadsto x \cdot 1 + \left|\color{blue}{\sqrt{x} \cdot \sqrt{x}}\right| \cdot 0.5 \]

      5. fabs-sqr 69.7%

         \[\leadsto x \cdot 1 + \color{blue}{\left(\sqrt{x} \cdot \sqrt{x}\right)} \cdot 0.5 \]

      6. rem-square-sqrt 69.8%

         \[\leadsto x \cdot 1 + \color{blue}{x} \cdot 0.5 \]

      7. distribute-lft-out 69.8%

         \[\leadsto \color{blue}{x \cdot \left(1 + 0.5\right)} \]

      8. metadata-eval 69.8%

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

   8. Simplified 69.8%

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

Alternative 6: 67.3% accurate, 10.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 9.5 \cdot 10^{-104}:\\ \;\;\;\;0.5 \cdot \left(x + y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 1.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 9.5e-104) (* 0.5 (+ x y)) (* x 1.5)))

C

double code(double x, double y) {
	double tmp;
	if (x <= 9.5e-104) {
		tmp = 0.5 * (x + y);
	} 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 <= 9.5d-104) then
        tmp = 0.5d0 * (x + y)
    else
        tmp = x * 1.5d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= 9.5e-104) {
		tmp = 0.5 * (x + y);
	} else {
		tmp = x * 1.5;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 9.5e-104:
		tmp = 0.5 * (x + y)
	else:
		tmp = x * 1.5
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 9.5e-104)
		tmp = Float64(0.5 * Float64(x + y));
	else
		tmp = Float64(x * 1.5);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 9.5e-104)
		tmp = 0.5 * (x + y);
	else
		tmp = x * 1.5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 9.5e-104], N[(0.5 * N[(x + y), $MachinePrecision]), $MachinePrecision], N[(x * 1.5), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 9.5000000000000002e-104

   1. Initial program 100.0%

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

   3. Taylor expanded in y around -inf 100.0%

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

      1. fabs-neg 100.0%

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

      2. mul-1-neg 100.0%

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

      3. sub-neg 100.0%

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

      4. fabs-sub 100.0%

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

      5. rem-square-sqrt 71.9%

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

      6. fabs-sqr 71.9%

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

      7. rem-square-sqrt 73.0%

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

   5. Simplified 73.0%

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

   6. Taylor expanded in x around 0 73.0%

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

      1. distribute-lft-out 73.0%

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

   8. Simplified 73.0%

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

   if 9.5000000000000002e-104 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 69.8%

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

      1. neg-mul-1 69.8%

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

   5. Simplified 69.8%

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

   6. Taylor expanded in x around 0 69.8%

      \[\leadsto \color{blue}{x + 0.5 \cdot \left|-x\right|} \]
   7. Step-by-step derivation

      1. *-rgt-identity 69.8%

         \[\leadsto \color{blue}{x \cdot 1} + 0.5 \cdot \left|-x\right| \]

      2. *-commutative 69.8%

         \[\leadsto x \cdot 1 + \color{blue}{\left|-x\right| \cdot 0.5} \]

      3. fabs-neg 69.8%

         \[\leadsto x \cdot 1 + \color{blue}{\left|x\right|} \cdot 0.5 \]

      4. rem-square-sqrt 69.7%

         \[\leadsto x \cdot 1 + \left|\color{blue}{\sqrt{x} \cdot \sqrt{x}}\right| \cdot 0.5 \]

      5. fabs-sqr 69.7%

         \[\leadsto x \cdot 1 + \color{blue}{\left(\sqrt{x} \cdot \sqrt{x}\right)} \cdot 0.5 \]

      6. rem-square-sqrt 69.8%

         \[\leadsto x \cdot 1 + \color{blue}{x} \cdot 0.5 \]

      7. distribute-lft-out 69.8%

         \[\leadsto \color{blue}{x \cdot \left(1 + 0.5\right)} \]

      8. metadata-eval 69.8%

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

   8. Simplified 69.8%

      \[\leadsto \color{blue}{x \cdot 1.5} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 50.8% accurate, 13.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{-310}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;x \cdot 1.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= x -2e-310) (* x 0.5) (* x 1.5)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2e-310) {
		tmp = x * 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 <= (-2d-310)) then
        tmp = x * 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 <= -2e-310) {
		tmp = x * 0.5;
	} else {
		tmp = x * 1.5;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2e-310:
		tmp = x * 0.5
	else:
		tmp = x * 1.5
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2e-310)
		tmp = Float64(x * 0.5);
	else
		tmp = Float64(x * 1.5);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -2e-310)
		tmp = x * 0.5;
	else
		tmp = x * 1.5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2e-310], N[(x * 0.5), $MachinePrecision], N[(x * 1.5), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.999999999999994e-310

   1. Initial program 100.0%

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

   3. Taylor expanded in y around -inf 100.0%

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

      1. fabs-neg 100.0%

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

      2. mul-1-neg 100.0%

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

      3. sub-neg 100.0%

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

      4. fabs-sub 100.0%

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

      5. rem-square-sqrt 79.7%

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

      6. fabs-sqr 79.7%

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

      7. rem-square-sqrt 80.5%

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

   5. Simplified 80.5%

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

   6. Taylor expanded in x around inf 51.6%

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

      1. *-commutative 51.6%

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

   8. Simplified 51.6%

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

   if -1.999999999999994e-310 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 49.9%

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

      1. neg-mul-1 49.9%

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

   5. Simplified 49.9%

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

   6. Taylor expanded in x around 0 49.9%

      \[\leadsto \color{blue}{x + 0.5 \cdot \left|-x\right|} \]
   7. Step-by-step derivation

      1. *-rgt-identity 49.9%

         \[\leadsto \color{blue}{x \cdot 1} + 0.5 \cdot \left|-x\right| \]

      2. *-commutative 49.9%

         \[\leadsto x \cdot 1 + \color{blue}{\left|-x\right| \cdot 0.5} \]

      3. fabs-neg 49.9%

         \[\leadsto x \cdot 1 + \color{blue}{\left|x\right|} \cdot 0.5 \]

      4. rem-square-sqrt 49.8%

         \[\leadsto x \cdot 1 + \left|\color{blue}{\sqrt{x} \cdot \sqrt{x}}\right| \cdot 0.5 \]

      5. fabs-sqr 49.8%

         \[\leadsto x \cdot 1 + \color{blue}{\left(\sqrt{x} \cdot \sqrt{x}\right)} \cdot 0.5 \]

      6. rem-square-sqrt 49.9%

         \[\leadsto x \cdot 1 + \color{blue}{x} \cdot 0.5 \]

      7. distribute-lft-out 49.9%

         \[\leadsto \color{blue}{x \cdot \left(1 + 0.5\right)} \]

      8. metadata-eval 49.9%

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

   8. Simplified 49.9%

      \[\leadsto \color{blue}{x \cdot 1.5} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 8: 30.5% 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 100.0%

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

3. Taylor expanded in y around -inf 100.0%

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

   1. fabs-neg 100.0%

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

   2. mul-1-neg 100.0%

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

   3. sub-neg 100.0%

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

   4. fabs-sub 100.0%

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

   5. rem-square-sqrt 54.3%

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

   6. fabs-sqr 54.3%

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

   7. rem-square-sqrt 59.0%

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

5. Simplified 59.0%

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

6. Taylor expanded in x around inf 31.9%

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

   1. *-commutative 31.9%

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

8. Simplified 31.9%

   \[\leadsto \color{blue}{x \cdot 0.5} \]
9. Add Preprocessing

Alternative 9: 11.4% 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 100.0%

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

3. Taylor expanded in x around inf 11.2%

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

Reproduce

herbie shell --seed 2024116 
(FPCore (x y)
  :name "Graphics.Rendering.Chart.Plot.AreaSpots:renderSpotLegend from Chart-1.5.3"
  :precision binary64
  (+ x (/ (fabs (- y x)) 2.0)))