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

Percentage Accurate: 99.9% → 99.9%

Time: 4.9s

Alternatives: 8

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. Final simplification 99.9%

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

Alternative 2: 73.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(y - x\right) \cdot 0.5\\ \mathbf{if}\;y \leq -9.5 \cdot 10^{+133}:\\ \;\;\;\;\left|y - x\right| \cdot 0.5\\ \mathbf{elif}\;y \leq -1.68 \cdot 10^{-181}:\\ \;\;\;\;\frac{t_0 \cdot t_0 - x \cdot x}{y \cdot -0.5 + x \cdot -0.5}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(x + y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* (- y x) 0.5)))
   (if (<= y -9.5e+133)
     (* (fabs (- y x)) 0.5)
     (if (<= y -1.68e-181)
       (/ (- (* t_0 t_0) (* x x)) (+ (* y -0.5) (* x -0.5)))
       (* 0.5 (+ x y))))))

C

double code(double x, double y) {
	double t_0 = (y - x) * 0.5;
	double tmp;
	if (y <= -9.5e+133) {
		tmp = fabs((y - x)) * 0.5;
	} else if (y <= -1.68e-181) {
		tmp = ((t_0 * t_0) - (x * x)) / ((y * -0.5) + (x * -0.5));
	} 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) :: t_0
    real(8) :: tmp
    t_0 = (y - x) * 0.5d0
    if (y <= (-9.5d+133)) then
        tmp = abs((y - x)) * 0.5d0
    else if (y <= (-1.68d-181)) then
        tmp = ((t_0 * t_0) - (x * x)) / ((y * (-0.5d0)) + (x * (-0.5d0)))
    else
        tmp = 0.5d0 * (x + y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = (y - x) * 0.5;
	double tmp;
	if (y <= -9.5e+133) {
		tmp = Math.abs((y - x)) * 0.5;
	} else if (y <= -1.68e-181) {
		tmp = ((t_0 * t_0) - (x * x)) / ((y * -0.5) + (x * -0.5));
	} else {
		tmp = 0.5 * (x + y);
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (y - x) * 0.5
	tmp = 0
	if y <= -9.5e+133:
		tmp = math.fabs((y - x)) * 0.5
	elif y <= -1.68e-181:
		tmp = ((t_0 * t_0) - (x * x)) / ((y * -0.5) + (x * -0.5))
	else:
		tmp = 0.5 * (x + y)
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(y - x) * 0.5)
	tmp = 0.0
	if (y <= -9.5e+133)
		tmp = Float64(abs(Float64(y - x)) * 0.5);
	elseif (y <= -1.68e-181)
		tmp = Float64(Float64(Float64(t_0 * t_0) - Float64(x * x)) / Float64(Float64(y * -0.5) + Float64(x * -0.5)));
	else
		tmp = Float64(0.5 * Float64(x + y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (y - x) * 0.5;
	tmp = 0.0;
	if (y <= -9.5e+133)
		tmp = abs((y - x)) * 0.5;
	elseif (y <= -1.68e-181)
		tmp = ((t_0 * t_0) - (x * x)) / ((y * -0.5) + (x * -0.5));
	else
		tmp = 0.5 * (x + y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(y - x), $MachinePrecision] * 0.5), $MachinePrecision]}, If[LessEqual[y, -9.5e+133], N[(N[Abs[N[(y - x), $MachinePrecision]], $MachinePrecision] * 0.5), $MachinePrecision], If[LessEqual[y, -1.68e-181], N[(N[(N[(t$95$0 * t$95$0), $MachinePrecision] - N[(x * x), $MachinePrecision]), $MachinePrecision] / N[(N[(y * -0.5), $MachinePrecision] + N[(x * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(x + y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.49999999999999996e133

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 97.1%

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

   if -9.49999999999999996e133 < y < -1.68e-181

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. div-inv 99.9%

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

      3. fma-def 99.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\left|y - x\right|, \frac{1}{2}, x\right)} \]

      4. add-sqr-sqrt 23.3%

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

      5. fabs-sqr 23.3%

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

      6. add-sqr-sqrt 29.2%

         \[\leadsto \mathsf{fma}\left(\color{blue}{y - x}, \frac{1}{2}, x\right) \]

      7. metadata-eval 29.2%

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

   3. Applied egg-rr 29.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 0.5, x\right)} \]
   4. Step-by-step derivation

      1. fma-udef 29.2%

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

      2. flip-+ 19.9%

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

   5. Applied egg-rr 19.9%

      \[\leadsto \color{blue}{\frac{\left(\left(y - x\right) \cdot 0.5\right) \cdot \left(\left(y - x\right) \cdot 0.5\right) - x \cdot x}{\left(y - x\right) \cdot 0.5 - x}} \]
   6. Step-by-step derivation

      1. add-sqr-sqrt 14.9%

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

      2. sqrt-prod 84.2%

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

      3. associate-*r* 84.2%

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

      4. sqrt-prod 83.8%

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

      5. fma-neg 83.8%

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

      6. *-commutative 83.8%

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

      7. associate-*l* 83.8%

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

      8. pow2 83.8%

         \[\leadsto \frac{\left(\left(y - x\right) \cdot 0.5\right) \cdot \left(\left(y - x\right) \cdot 0.5\right) - x \cdot x}{\mathsf{fma}\left(\sqrt{0.5 \cdot \color{blue}{{\left(y - x\right)}^{2}}}, \sqrt{0.5}, -x\right)} \]

   7. Applied egg-rr 83.8%

      \[\leadsto \frac{\left(\left(y - x\right) \cdot 0.5\right) \cdot \left(\left(y - x\right) \cdot 0.5\right) - x \cdot x}{\color{blue}{\mathsf{fma}\left(\sqrt{0.5 \cdot {\left(y - x\right)}^{2}}, \sqrt{0.5}, -x\right)}} \]

   8. Taylor expanded in y around -inf 70.6%

      \[\leadsto \frac{\left(\left(y - x\right) \cdot 0.5\right) \cdot \left(\left(y - x\right) \cdot 0.5\right) - x \cdot x}{\color{blue}{\left({\left(\sqrt{0.5}\right)}^{2} \cdot x + -1 \cdot \left({\left(\sqrt{0.5}\right)}^{2} \cdot y\right)\right) - x}} \]
   9. Step-by-step derivation

      1. sub-neg 70.6%

         \[\leadsto \frac{\left(\left(y - x\right) \cdot 0.5\right) \cdot \left(\left(y - x\right) \cdot 0.5\right) - x \cdot x}{\color{blue}{\left({\left(\sqrt{0.5}\right)}^{2} \cdot x + -1 \cdot \left({\left(\sqrt{0.5}\right)}^{2} \cdot y\right)\right) + \left(-x\right)}} \]

      2. +-commutative 70.6%

         \[\leadsto \frac{\left(\left(y - x\right) \cdot 0.5\right) \cdot \left(\left(y - x\right) \cdot 0.5\right) - x \cdot x}{\color{blue}{\left(-1 \cdot \left({\left(\sqrt{0.5}\right)}^{2} \cdot y\right) + {\left(\sqrt{0.5}\right)}^{2} \cdot x\right)} + \left(-x\right)} \]

      3. associate-+l+ 70.6%

         \[\leadsto \frac{\left(\left(y - x\right) \cdot 0.5\right) \cdot \left(\left(y - x\right) \cdot 0.5\right) - x \cdot x}{\color{blue}{-1 \cdot \left({\left(\sqrt{0.5}\right)}^{2} \cdot y\right) + \left({\left(\sqrt{0.5}\right)}^{2} \cdot x + \left(-x\right)\right)}} \]

      4. *-commutative 70.6%

         \[\leadsto \frac{\left(\left(y - x\right) \cdot 0.5\right) \cdot \left(\left(y - x\right) \cdot 0.5\right) - x \cdot x}{\color{blue}{\left({\left(\sqrt{0.5}\right)}^{2} \cdot y\right) \cdot -1} + \left({\left(\sqrt{0.5}\right)}^{2} \cdot x + \left(-x\right)\right)} \]

      5. *-commutative 70.6%

         \[\leadsto \frac{\left(\left(y - x\right) \cdot 0.5\right) \cdot \left(\left(y - x\right) \cdot 0.5\right) - x \cdot x}{\color{blue}{\left(y \cdot {\left(\sqrt{0.5}\right)}^{2}\right)} \cdot -1 + \left({\left(\sqrt{0.5}\right)}^{2} \cdot x + \left(-x\right)\right)} \]

      6. unpow2 70.6%

         \[\leadsto \frac{\left(\left(y - x\right) \cdot 0.5\right) \cdot \left(\left(y - x\right) \cdot 0.5\right) - x \cdot x}{\left(y \cdot \color{blue}{\left(\sqrt{0.5} \cdot \sqrt{0.5}\right)}\right) \cdot -1 + \left({\left(\sqrt{0.5}\right)}^{2} \cdot x + \left(-x\right)\right)} \]

      7. rem-square-sqrt 71.5%

         \[\leadsto \frac{\left(\left(y - x\right) \cdot 0.5\right) \cdot \left(\left(y - x\right) \cdot 0.5\right) - x \cdot x}{\left(y \cdot \color{blue}{0.5}\right) \cdot -1 + \left({\left(\sqrt{0.5}\right)}^{2} \cdot x + \left(-x\right)\right)} \]

      8. associate-*l* 71.5%

         \[\leadsto \frac{\left(\left(y - x\right) \cdot 0.5\right) \cdot \left(\left(y - x\right) \cdot 0.5\right) - x \cdot x}{\color{blue}{y \cdot \left(0.5 \cdot -1\right)} + \left({\left(\sqrt{0.5}\right)}^{2} \cdot x + \left(-x\right)\right)} \]

      9. metadata-eval 71.5%

         \[\leadsto \frac{\left(\left(y - x\right) \cdot 0.5\right) \cdot \left(\left(y - x\right) \cdot 0.5\right) - x \cdot x}{y \cdot \color{blue}{-0.5} + \left({\left(\sqrt{0.5}\right)}^{2} \cdot x + \left(-x\right)\right)} \]

      10. unpow2 71.5%

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

      11. rem-square-sqrt 71.9%

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

      12. neg-mul-1 71.9%

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

      13. distribute-rgt-out 71.9%

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

      14. metadata-eval 71.9%

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

   10. Simplified 71.9%

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

   if -1.68e-181 < y

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. div-inv 99.9%

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

      3. fma-def 99.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\left|y - x\right|, \frac{1}{2}, x\right)} \]

      4. add-sqr-sqrt 73.8%

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

      5. fabs-sqr 73.8%

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

      6. add-sqr-sqrt 78.6%

         \[\leadsto \mathsf{fma}\left(\color{blue}{y - x}, \frac{1}{2}, x\right) \]

      7. metadata-eval 78.6%

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

   3. Applied egg-rr 78.6%

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

   4. Taylor expanded in y around 0 78.6%

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

      1. +-commutative 78.6%

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

      2. associate-+r+ 78.6%

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

      3. distribute-lft1-in 78.6%

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

      4. metadata-eval 78.6%

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

      5. distribute-lft-out 78.6%

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

   6. Simplified 78.6%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+133}:\\ \;\;\;\;\left|y - x\right| \cdot 0.5\\ \mathbf{elif}\;y \leq -1.68 \cdot 10^{-181}:\\ \;\;\;\;\frac{\left(\left(y - x\right) \cdot 0.5\right) \cdot \left(\left(y - x\right) \cdot 0.5\right) - x \cdot x}{y \cdot -0.5 + x \cdot -0.5}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(x + y\right)\\ \end{array} \]

Alternative 3: 73.8% accurate, 3.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(y - x\right) \cdot 0.5\\ \mathbf{if}\;y \leq -3.6 \cdot 10^{+143}:\\ \;\;\;\;\frac{y}{0.5} \cdot -0.25\\ \mathbf{elif}\;y \leq -1.68 \cdot 10^{-181}:\\ \;\;\;\;\frac{t_0 \cdot t_0 - x \cdot x}{y \cdot -0.5 + x \cdot -0.5}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(x + y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* (- y x) 0.5)))
   (if (<= y -3.6e+143)
     (* (/ y 0.5) -0.25)
     (if (<= y -1.68e-181)
       (/ (- (* t_0 t_0) (* x x)) (+ (* y -0.5) (* x -0.5)))
       (* 0.5 (+ x y))))))

C

double code(double x, double y) {
	double t_0 = (y - x) * 0.5;
	double tmp;
	if (y <= -3.6e+143) {
		tmp = (y / 0.5) * -0.25;
	} else if (y <= -1.68e-181) {
		tmp = ((t_0 * t_0) - (x * x)) / ((y * -0.5) + (x * -0.5));
	} 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) :: t_0
    real(8) :: tmp
    t_0 = (y - x) * 0.5d0
    if (y <= (-3.6d+143)) then
        tmp = (y / 0.5d0) * (-0.25d0)
    else if (y <= (-1.68d-181)) then
        tmp = ((t_0 * t_0) - (x * x)) / ((y * (-0.5d0)) + (x * (-0.5d0)))
    else
        tmp = 0.5d0 * (x + y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = (y - x) * 0.5;
	double tmp;
	if (y <= -3.6e+143) {
		tmp = (y / 0.5) * -0.25;
	} else if (y <= -1.68e-181) {
		tmp = ((t_0 * t_0) - (x * x)) / ((y * -0.5) + (x * -0.5));
	} else {
		tmp = 0.5 * (x + y);
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (y - x) * 0.5
	tmp = 0
	if y <= -3.6e+143:
		tmp = (y / 0.5) * -0.25
	elif y <= -1.68e-181:
		tmp = ((t_0 * t_0) - (x * x)) / ((y * -0.5) + (x * -0.5))
	else:
		tmp = 0.5 * (x + y)
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(y - x) * 0.5)
	tmp = 0.0
	if (y <= -3.6e+143)
		tmp = Float64(Float64(y / 0.5) * -0.25);
	elseif (y <= -1.68e-181)
		tmp = Float64(Float64(Float64(t_0 * t_0) - Float64(x * x)) / Float64(Float64(y * -0.5) + Float64(x * -0.5)));
	else
		tmp = Float64(0.5 * Float64(x + y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (y - x) * 0.5;
	tmp = 0.0;
	if (y <= -3.6e+143)
		tmp = (y / 0.5) * -0.25;
	elseif (y <= -1.68e-181)
		tmp = ((t_0 * t_0) - (x * x)) / ((y * -0.5) + (x * -0.5));
	else
		tmp = 0.5 * (x + y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(y - x), $MachinePrecision] * 0.5), $MachinePrecision]}, If[LessEqual[y, -3.6e+143], N[(N[(y / 0.5), $MachinePrecision] * -0.25), $MachinePrecision], If[LessEqual[y, -1.68e-181], N[(N[(N[(t$95$0 * t$95$0), $MachinePrecision] - N[(x * x), $MachinePrecision]), $MachinePrecision] / N[(N[(y * -0.5), $MachinePrecision] + N[(x * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(x + y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.5999999999999999e143

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. div-inv 100.0%

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

      3. fma-def 100.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\left|y - x\right|, \frac{1}{2}, x\right)} \]

      4. add-sqr-sqrt 0.0%

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

      5. fabs-sqr 0.0%

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

      6. add-sqr-sqrt 0.7%

         \[\leadsto \mathsf{fma}\left(\color{blue}{y - x}, \frac{1}{2}, x\right) \]

      7. metadata-eval 0.7%

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

   3. Applied egg-rr 0.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 0.5, x\right)} \]
   4. Step-by-step derivation

      1. fma-udef 0.7%

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

      2. flip-+ 0.2%

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

   5. Applied egg-rr 0.2%

      \[\leadsto \color{blue}{\frac{\left(\left(y - x\right) \cdot 0.5\right) \cdot \left(\left(y - x\right) \cdot 0.5\right) - x \cdot x}{\left(y - x\right) \cdot 0.5 - x}} \]
   6. Step-by-step derivation

      1. add-sqr-sqrt 0.0%

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

      2. sqrt-prod 10.0%

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

      3. associate-*r* 10.0%

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

      4. sqrt-prod 9.9%

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

      5. fma-neg 9.9%

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

      6. *-commutative 9.9%

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

      7. associate-*l* 9.9%

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

      8. pow2 9.9%

         \[\leadsto \frac{\left(\left(y - x\right) \cdot 0.5\right) \cdot \left(\left(y - x\right) \cdot 0.5\right) - x \cdot x}{\mathsf{fma}\left(\sqrt{0.5 \cdot \color{blue}{{\left(y - x\right)}^{2}}}, \sqrt{0.5}, -x\right)} \]

   7. Applied egg-rr 9.9%

      \[\leadsto \frac{\left(\left(y - x\right) \cdot 0.5\right) \cdot \left(\left(y - x\right) \cdot 0.5\right) - x \cdot x}{\color{blue}{\mathsf{fma}\left(\sqrt{0.5 \cdot {\left(y - x\right)}^{2}}, \sqrt{0.5}, -x\right)}} \]

   8. Taylor expanded in y around -inf 94.9%

      \[\leadsto \color{blue}{-0.25 \cdot \frac{y}{{\left(\sqrt{0.5}\right)}^{2}}} \]
   9. Step-by-step derivation

      1. *-commutative 94.9%

         \[\leadsto \color{blue}{\frac{y}{{\left(\sqrt{0.5}\right)}^{2}} \cdot -0.25} \]

      2. unpow2 94.9%

         \[\leadsto \frac{y}{\color{blue}{\sqrt{0.5} \cdot \sqrt{0.5}}} \cdot -0.25 \]

      3. rem-square-sqrt 96.8%

         \[\leadsto \frac{y}{\color{blue}{0.5}} \cdot -0.25 \]

   10. Simplified 96.8%

       \[\leadsto \color{blue}{\frac{y}{0.5} \cdot -0.25} \]

   if -3.5999999999999999e143 < y < -1.68e-181

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. div-inv 99.9%

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

      3. fma-def 99.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\left|y - x\right|, \frac{1}{2}, x\right)} \]

      4. add-sqr-sqrt 23.3%

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

      5. fabs-sqr 23.3%

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

      6. add-sqr-sqrt 29.2%

         \[\leadsto \mathsf{fma}\left(\color{blue}{y - x}, \frac{1}{2}, x\right) \]

      7. metadata-eval 29.2%

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

   3. Applied egg-rr 29.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 0.5, x\right)} \]
   4. Step-by-step derivation

      1. fma-udef 29.2%

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

      2. flip-+ 19.9%

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

   5. Applied egg-rr 19.9%

      \[\leadsto \color{blue}{\frac{\left(\left(y - x\right) \cdot 0.5\right) \cdot \left(\left(y - x\right) \cdot 0.5\right) - x \cdot x}{\left(y - x\right) \cdot 0.5 - x}} \]
   6. Step-by-step derivation

      1. add-sqr-sqrt 14.9%

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

      2. sqrt-prod 84.2%

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

      3. associate-*r* 84.2%

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

      4. sqrt-prod 83.8%

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

      5. fma-neg 83.8%

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

      6. *-commutative 83.8%

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

      7. associate-*l* 83.8%

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

      8. pow2 83.8%

         \[\leadsto \frac{\left(\left(y - x\right) \cdot 0.5\right) \cdot \left(\left(y - x\right) \cdot 0.5\right) - x \cdot x}{\mathsf{fma}\left(\sqrt{0.5 \cdot \color{blue}{{\left(y - x\right)}^{2}}}, \sqrt{0.5}, -x\right)} \]

   7. Applied egg-rr 83.8%

      \[\leadsto \frac{\left(\left(y - x\right) \cdot 0.5\right) \cdot \left(\left(y - x\right) \cdot 0.5\right) - x \cdot x}{\color{blue}{\mathsf{fma}\left(\sqrt{0.5 \cdot {\left(y - x\right)}^{2}}, \sqrt{0.5}, -x\right)}} \]

   8. Taylor expanded in y around -inf 70.6%

      \[\leadsto \frac{\left(\left(y - x\right) \cdot 0.5\right) \cdot \left(\left(y - x\right) \cdot 0.5\right) - x \cdot x}{\color{blue}{\left({\left(\sqrt{0.5}\right)}^{2} \cdot x + -1 \cdot \left({\left(\sqrt{0.5}\right)}^{2} \cdot y\right)\right) - x}} \]
   9. Step-by-step derivation

      1. sub-neg 70.6%

         \[\leadsto \frac{\left(\left(y - x\right) \cdot 0.5\right) \cdot \left(\left(y - x\right) \cdot 0.5\right) - x \cdot x}{\color{blue}{\left({\left(\sqrt{0.5}\right)}^{2} \cdot x + -1 \cdot \left({\left(\sqrt{0.5}\right)}^{2} \cdot y\right)\right) + \left(-x\right)}} \]

      2. +-commutative 70.6%

         \[\leadsto \frac{\left(\left(y - x\right) \cdot 0.5\right) \cdot \left(\left(y - x\right) \cdot 0.5\right) - x \cdot x}{\color{blue}{\left(-1 \cdot \left({\left(\sqrt{0.5}\right)}^{2} \cdot y\right) + {\left(\sqrt{0.5}\right)}^{2} \cdot x\right)} + \left(-x\right)} \]

      3. associate-+l+ 70.6%

         \[\leadsto \frac{\left(\left(y - x\right) \cdot 0.5\right) \cdot \left(\left(y - x\right) \cdot 0.5\right) - x \cdot x}{\color{blue}{-1 \cdot \left({\left(\sqrt{0.5}\right)}^{2} \cdot y\right) + \left({\left(\sqrt{0.5}\right)}^{2} \cdot x + \left(-x\right)\right)}} \]

      4. *-commutative 70.6%

         \[\leadsto \frac{\left(\left(y - x\right) \cdot 0.5\right) \cdot \left(\left(y - x\right) \cdot 0.5\right) - x \cdot x}{\color{blue}{\left({\left(\sqrt{0.5}\right)}^{2} \cdot y\right) \cdot -1} + \left({\left(\sqrt{0.5}\right)}^{2} \cdot x + \left(-x\right)\right)} \]

      5. *-commutative 70.6%

         \[\leadsto \frac{\left(\left(y - x\right) \cdot 0.5\right) \cdot \left(\left(y - x\right) \cdot 0.5\right) - x \cdot x}{\color{blue}{\left(y \cdot {\left(\sqrt{0.5}\right)}^{2}\right)} \cdot -1 + \left({\left(\sqrt{0.5}\right)}^{2} \cdot x + \left(-x\right)\right)} \]

      6. unpow2 70.6%

         \[\leadsto \frac{\left(\left(y - x\right) \cdot 0.5\right) \cdot \left(\left(y - x\right) \cdot 0.5\right) - x \cdot x}{\left(y \cdot \color{blue}{\left(\sqrt{0.5} \cdot \sqrt{0.5}\right)}\right) \cdot -1 + \left({\left(\sqrt{0.5}\right)}^{2} \cdot x + \left(-x\right)\right)} \]

      7. rem-square-sqrt 71.5%

         \[\leadsto \frac{\left(\left(y - x\right) \cdot 0.5\right) \cdot \left(\left(y - x\right) \cdot 0.5\right) - x \cdot x}{\left(y \cdot \color{blue}{0.5}\right) \cdot -1 + \left({\left(\sqrt{0.5}\right)}^{2} \cdot x + \left(-x\right)\right)} \]

      8. associate-*l* 71.5%

         \[\leadsto \frac{\left(\left(y - x\right) \cdot 0.5\right) \cdot \left(\left(y - x\right) \cdot 0.5\right) - x \cdot x}{\color{blue}{y \cdot \left(0.5 \cdot -1\right)} + \left({\left(\sqrt{0.5}\right)}^{2} \cdot x + \left(-x\right)\right)} \]

      9. metadata-eval 71.5%

         \[\leadsto \frac{\left(\left(y - x\right) \cdot 0.5\right) \cdot \left(\left(y - x\right) \cdot 0.5\right) - x \cdot x}{y \cdot \color{blue}{-0.5} + \left({\left(\sqrt{0.5}\right)}^{2} \cdot x + \left(-x\right)\right)} \]

      10. unpow2 71.5%

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

      11. rem-square-sqrt 71.9%

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

      12. neg-mul-1 71.9%

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

      13. distribute-rgt-out 71.9%

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

      14. metadata-eval 71.9%

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

   10. Simplified 71.9%

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

   if -1.68e-181 < y

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. div-inv 99.9%

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

      3. fma-def 99.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\left|y - x\right|, \frac{1}{2}, x\right)} \]

      4. add-sqr-sqrt 73.8%

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

      5. fabs-sqr 73.8%

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

      6. add-sqr-sqrt 78.6%

         \[\leadsto \mathsf{fma}\left(\color{blue}{y - x}, \frac{1}{2}, x\right) \]

      7. metadata-eval 78.6%

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

   3. Applied egg-rr 78.6%

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

   4. Taylor expanded in y around 0 78.6%

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

      1. +-commutative 78.6%

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

      2. associate-+r+ 78.6%

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

      3. distribute-lft1-in 78.6%

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

      4. metadata-eval 78.6%

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

      5. distribute-lft-out 78.6%

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

   6. Simplified 78.6%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+143}:\\ \;\;\;\;\frac{y}{0.5} \cdot -0.25\\ \mathbf{elif}\;y \leq -1.68 \cdot 10^{-181}:\\ \;\;\;\;\frac{\left(\left(y - x\right) \cdot 0.5\right) \cdot \left(\left(y - x\right) \cdot 0.5\right) - x \cdot x}{y \cdot -0.5 + x \cdot -0.5}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(x + y\right)\\ \end{array} \]

Alternative 4: 70.9% accurate, 15.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{-106}:\\ \;\;\;\;\frac{y}{0.5} \cdot -0.25\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(x + y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -3.4e-106) (* (/ y 0.5) -0.25) (* 0.5 (+ x y))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -3.4e-106) {
		tmp = (y / 0.5) * -0.25;
	} 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 <= (-3.4d-106)) then
        tmp = (y / 0.5d0) * (-0.25d0)
    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 <= -3.4e-106) {
		tmp = (y / 0.5) * -0.25;
	} else {
		tmp = 0.5 * (x + y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -3.4e-106:
		tmp = (y / 0.5) * -0.25
	else:
		tmp = 0.5 * (x + y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -3.4e-106)
		tmp = Float64(Float64(y / 0.5) * -0.25);
	else
		tmp = Float64(0.5 * Float64(x + y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -3.4e-106)
		tmp = (y / 0.5) * -0.25;
	else
		tmp = 0.5 * (x + y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -3.4e-106], N[(N[(y / 0.5), $MachinePrecision] * -0.25), $MachinePrecision], N[(0.5 * N[(x + y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.39999999999999982e-106

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. div-inv 100.0%

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

      3. fma-def 100.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\left|y - x\right|, \frac{1}{2}, x\right)} \]

      4. add-sqr-sqrt 10.6%

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

      5. fabs-sqr 10.6%

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

      6. add-sqr-sqrt 13.5%

         \[\leadsto \mathsf{fma}\left(\color{blue}{y - x}, \frac{1}{2}, x\right) \]

      7. metadata-eval 13.5%

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

   3. Applied egg-rr 13.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 0.5, x\right)} \]
   4. Step-by-step derivation

      1. fma-udef 13.5%

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

      2. flip-+ 6.7%

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

   5. Applied egg-rr 6.7%

      \[\leadsto \color{blue}{\frac{\left(\left(y - x\right) \cdot 0.5\right) \cdot \left(\left(y - x\right) \cdot 0.5\right) - x \cdot x}{\left(y - x\right) \cdot 0.5 - x}} \]
   6. Step-by-step derivation

      1. add-sqr-sqrt 4.7%

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

      2. sqrt-prod 48.1%

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

      3. associate-*r* 48.1%

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

      4. sqrt-prod 47.9%

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

      5. fma-neg 47.9%

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

      6. *-commutative 47.9%

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

      7. associate-*l* 47.9%

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

      8. pow2 47.9%

         \[\leadsto \frac{\left(\left(y - x\right) \cdot 0.5\right) \cdot \left(\left(y - x\right) \cdot 0.5\right) - x \cdot x}{\mathsf{fma}\left(\sqrt{0.5 \cdot \color{blue}{{\left(y - x\right)}^{2}}}, \sqrt{0.5}, -x\right)} \]

   7. Applied egg-rr 47.9%

      \[\leadsto \frac{\left(\left(y - x\right) \cdot 0.5\right) \cdot \left(\left(y - x\right) \cdot 0.5\right) - x \cdot x}{\color{blue}{\mathsf{fma}\left(\sqrt{0.5 \cdot {\left(y - x\right)}^{2}}, \sqrt{0.5}, -x\right)}} \]

   8. Taylor expanded in y around -inf 75.3%

      \[\leadsto \color{blue}{-0.25 \cdot \frac{y}{{\left(\sqrt{0.5}\right)}^{2}}} \]
   9. Step-by-step derivation

      1. *-commutative 75.3%

         \[\leadsto \color{blue}{\frac{y}{{\left(\sqrt{0.5}\right)}^{2}} \cdot -0.25} \]

      2. unpow2 75.3%

         \[\leadsto \frac{y}{\color{blue}{\sqrt{0.5} \cdot \sqrt{0.5}}} \cdot -0.25 \]

      3. rem-square-sqrt 76.8%

         \[\leadsto \frac{y}{\color{blue}{0.5}} \cdot -0.25 \]

   10. Simplified 76.8%

       \[\leadsto \color{blue}{\frac{y}{0.5} \cdot -0.25} \]

   if -3.39999999999999982e-106 < y

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. div-inv 99.9%

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

      3. fma-def 99.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\left|y - x\right|, \frac{1}{2}, x\right)} \]

      4. add-sqr-sqrt 70.3%

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

      5. fabs-sqr 70.3%

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

      6. add-sqr-sqrt 75.4%

         \[\leadsto \mathsf{fma}\left(\color{blue}{y - x}, \frac{1}{2}, x\right) \]

      7. metadata-eval 75.4%

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

   3. Applied egg-rr 75.4%

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

   4. Taylor expanded in y around 0 75.4%

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

      1. +-commutative 75.4%

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

      2. associate-+r+ 75.5%

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

      3. distribute-lft1-in 75.5%

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

      4. metadata-eval 75.5%

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

      5. distribute-lft-out 75.5%

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

   6. Simplified 75.5%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{-106}:\\ \;\;\;\;\frac{y}{0.5} \cdot -0.25\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(x + y\right)\\ \end{array} \]

Alternative 5: 31.3% accurate, 21.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.25 \cdot 10^{-167}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot 0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y 2.25e-167) x (* y 0.5)))

C

double code(double x, double y) {
	double tmp;
	if (y <= 2.25e-167) {
		tmp = x;
	} 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 <= 2.25d-167) then
        tmp = x
    else
        tmp = y * 0.5d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= 2.25e-167) {
		tmp = x;
	} else {
		tmp = y * 0.5;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 2.25e-167:
		tmp = x
	else:
		tmp = y * 0.5
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 2.25e-167)
		tmp = x;
	else
		tmp = Float64(y * 0.5);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 2.25e-167)
		tmp = x;
	else
		tmp = y * 0.5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 2.25e-167], x, N[(y * 0.5), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2.2500000000000001e-167

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 12.0%

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

   if 2.2500000000000001e-167 < y

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. div-inv 100.0%

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

      3. fma-def 100.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\left|y - x\right|, \frac{1}{2}, x\right)} \]

      4. add-sqr-sqrt 83.4%

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

      5. fabs-sqr 83.4%

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

      6. add-sqr-sqrt 86.9%

         \[\leadsto \mathsf{fma}\left(\color{blue}{y - x}, \frac{1}{2}, x\right) \]

      7. metadata-eval 86.9%

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

   3. Applied egg-rr 86.9%

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

   4. Taylor expanded in y around inf 68.9%

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

4. Final simplification 32.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.25 \cdot 10^{-167}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot 0.5\\ \end{array} \]

Alternative 6: 44.9% accurate, 21.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.7 \cdot 10^{-164}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;y \cdot 0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y 2.7e-164) (* x 0.5) (* y 0.5)))

C

double code(double x, double y) {
	double tmp;
	if (y <= 2.7e-164) {
		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 <= 2.7d-164) 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 <= 2.7e-164) {
		tmp = x * 0.5;
	} else {
		tmp = y * 0.5;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 2.7e-164:
		tmp = x * 0.5
	else:
		tmp = y * 0.5
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 2.7e-164)
		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 <= 2.7e-164)
		tmp = x * 0.5;
	else
		tmp = y * 0.5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 2.7e-164], N[(x * 0.5), $MachinePrecision], N[(y * 0.5), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2.7000000000000001e-164

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. div-inv 99.9%

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

      3. fma-def 99.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\left|y - x\right|, \frac{1}{2}, x\right)} \]

      4. add-sqr-sqrt 31.3%

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

      5. fabs-sqr 31.3%

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

      6. add-sqr-sqrt 36.3%

         \[\leadsto \mathsf{fma}\left(\color{blue}{y - x}, \frac{1}{2}, x\right) \]

      7. metadata-eval 36.3%

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

   3. Applied egg-rr 36.3%

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

   4. Taylor expanded in y around 0 35.4%

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

      1. distribute-lft1-in 35.4%

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

      2. metadata-eval 35.4%

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

      3. *-commutative 35.4%

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

   6. Simplified 35.4%

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

   if 2.7000000000000001e-164 < y

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. div-inv 100.0%

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

      3. fma-def 100.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\left|y - x\right|, \frac{1}{2}, x\right)} \]

      4. add-sqr-sqrt 83.4%

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

      5. fabs-sqr 83.4%

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

      6. add-sqr-sqrt 86.9%

         \[\leadsto \mathsf{fma}\left(\color{blue}{y - x}, \frac{1}{2}, x\right) \]

      7. metadata-eval 86.9%

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

   3. Applied egg-rr 86.9%

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

   4. Taylor expanded in y around inf 68.9%

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

4. Final simplification 47.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.7 \cdot 10^{-164}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;y \cdot 0.5\\ \end{array} \]

Alternative 7: 54.4% accurate, 21.4× speedup

Math

\[\begin{array}{l} \\ 0.5 \cdot \left(x + y\right) \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. +-commutative 99.9%

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

   2. div-inv 99.9%

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

   3. fma-def 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left|y - x\right|, \frac{1}{2}, x\right)} \]

   4. add-sqr-sqrt 50.4%

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

   5. fabs-sqr 50.4%

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

   6. add-sqr-sqrt 54.9%

      \[\leadsto \mathsf{fma}\left(\color{blue}{y - x}, \frac{1}{2}, x\right) \]

   7. metadata-eval 54.9%

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

3. Applied egg-rr 54.9%

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

4. Taylor expanded in y around 0 54.9%

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

   1. +-commutative 54.9%

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

   2. associate-+r+ 54.9%

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

   3. distribute-lft1-in 54.9%

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

   4. metadata-eval 54.9%

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

   5. distribute-lft-out 54.9%

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

6. Simplified 54.9%

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

7. Final simplification 54.9%

   \[\leadsto 0.5 \cdot \left(x + y\right) \]

Alternative 8: 11.3% 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. Taylor expanded in x around inf 10.6%

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

3. Final simplification 10.6%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023224 
(FPCore (x y)
  :name "Graphics.Rendering.Chart.Plot.AreaSpots:renderSpotLegend from Chart-1.5.3"
  :precision binary64
  (+ x (/ (fabs (- y x)) 2.0)))