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

Percentage Accurate: 99.9% → 99.9%

Time: 8.2s

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

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

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 99.9%

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

3. Final simplification 99.9%

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

Alternative 2: 80.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{-103}:\\ \;\;\;\;x + \frac{\left|y\right|}{2}\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{-150}:\\ \;\;\;\;x + \frac{\left|x\right|}{2}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(x + y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.5e-103)
   (+ x (/ (fabs y) 2.0))
   (if (<= y 2.05e-150) (+ x (/ (fabs x) 2.0)) (* 0.5 (+ x y)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.5e-103) {
		tmp = x + (fabs(y) / 2.0);
	} else if (y <= 2.05e-150) {
		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 <= (-1.5d-103)) then
        tmp = x + (abs(y) / 2.0d0)
    else if (y <= 2.05d-150) 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 <= -1.5e-103) {
		tmp = x + (Math.abs(y) / 2.0);
	} else if (y <= 2.05e-150) {
		tmp = x + (Math.abs(x) / 2.0);
	} else {
		tmp = 0.5 * (x + y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.5e-103:
		tmp = x + (math.fabs(y) / 2.0)
	elif y <= 2.05e-150:
		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 <= -1.5e-103)
		tmp = Float64(x + Float64(abs(y) / 2.0));
	elseif (y <= 2.05e-150)
		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 <= -1.5e-103)
		tmp = x + (abs(y) / 2.0);
	elseif (y <= 2.05e-150)
		tmp = x + (abs(x) / 2.0);
	else
		tmp = 0.5 * (x + y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.5e-103], N[(x + N[(N[Abs[y], $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.05e-150], 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 < -1.5e-103

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 80.6%

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

   if -1.5e-103 < y < 2.0499999999999999e-150

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 92.1%

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

      1. neg-mul-1 92.1%

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

   5. Simplified 92.1%

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

   if 2.0499999999999999e-150 < 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 86.5%

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

      6. fabs-sqr 86.5%

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

      7. rem-square-sqrt 89.5%

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

   5. Simplified 89.5%

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

   6. Taylor expanded in x around 0 89.5%

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

      1. distribute-lft-out 89.5%

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

      2. +-commutative 89.5%

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

   8. Simplified 89.5%

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

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{-103}:\\ \;\;\;\;x + \frac{\left|y\right|}{2}\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{-150}:\\ \;\;\;\;x + \frac{\left|x\right|}{2}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(x + y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 80.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{-28}:\\ \;\;\;\;0.5 \cdot \left(x + y\right)\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{+19}:\\ \;\;\;\;x + \frac{\left|y\right|}{2}\\ \mathbf{else}:\\ \;\;\;\;\left|x \cdot 1.5\right|\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -3.2e-28)
   (* 0.5 (+ x y))
   (if (<= x 1.9e+19) (+ x (/ (fabs y) 2.0)) (fabs (* x 1.5)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -3.2e-28) {
		tmp = 0.5 * (x + y);
	} else if (x <= 1.9e+19) {
		tmp = x + (fabs(y) / 2.0);
	} else {
		tmp = fabs((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 <= (-3.2d-28)) then
        tmp = 0.5d0 * (x + y)
    else if (x <= 1.9d+19) then
        tmp = x + (abs(y) / 2.0d0)
    else
        tmp = abs((x * 1.5d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -3.2e-28) {
		tmp = 0.5 * (x + y);
	} else if (x <= 1.9e+19) {
		tmp = x + (Math.abs(y) / 2.0);
	} else {
		tmp = Math.abs((x * 1.5));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -3.2e-28:
		tmp = 0.5 * (x + y)
	elif x <= 1.9e+19:
		tmp = x + (math.fabs(y) / 2.0)
	else:
		tmp = math.fabs((x * 1.5))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -3.2e-28)
		tmp = Float64(0.5 * Float64(x + y));
	elseif (x <= 1.9e+19)
		tmp = Float64(x + Float64(abs(y) / 2.0));
	else
		tmp = abs(Float64(x * 1.5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -3.2e-28)
		tmp = 0.5 * (x + y);
	elseif (x <= 1.9e+19)
		tmp = x + (abs(y) / 2.0);
	else
		tmp = abs((x * 1.5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -3.2e-28], N[(0.5 * N[(x + y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.9e+19], N[(x + N[(N[Abs[y], $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision], N[Abs[N[(x * 1.5), $MachinePrecision]], $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.19999999999999982e-28

   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 87.7%

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

      6. fabs-sqr 87.7%

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

      7. rem-square-sqrt 88.3%

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

   5. Simplified 88.3%

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

   6. Taylor expanded in x around 0 88.4%

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

      1. distribute-lft-out 88.4%

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

      2. +-commutative 88.4%

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

   8. Simplified 88.4%

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

   if -3.19999999999999982e-28 < x < 1.9e19

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 82.8%

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

   if 1.9e19 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 81.3%

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

      1. neg-mul-1 81.3%

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

   5. Simplified 81.3%

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

      1. add-sqr-sqrt 81.1%

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

      2. pow2 81.1%

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

      3. div-inv 81.1%

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

      4. fabs-neg 81.1%

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

      5. add-sqr-sqrt 81.0%

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

      6. fabs-sqr 81.0%

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

      7. add-sqr-sqrt 81.1%

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

      8. metadata-eval 81.1%

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

   7. Applied egg-rr 81.1%

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

      1. flip-+ 40.4%

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

      2. div-inv 40.2%

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

   9. Applied egg-rr 43.8%

      \[\leadsto \color{blue}{\left(\left(x \cdot 1.5\right) \cdot \left(x \cdot 0.5\right)\right) \cdot \frac{2}{x}} \]
   10. Step-by-step derivation

       1. metadata-eval 43.8%

          \[\leadsto \left(\left(x \cdot 1.5\right) \cdot \left(x \cdot 0.5\right)\right) \cdot \frac{\color{blue}{\frac{1}{0.5}}}{x} \]

       2. associate-/r* 43.8%

          \[\leadsto \left(\left(x \cdot 1.5\right) \cdot \left(x \cdot 0.5\right)\right) \cdot \color{blue}{\frac{1}{0.5 \cdot x}} \]

       3. *-commutative 43.8%

          \[\leadsto \left(\left(x \cdot 1.5\right) \cdot \left(x \cdot 0.5\right)\right) \cdot \frac{1}{\color{blue}{x \cdot 0.5}} \]

       4. div-inv 44.0%

          \[\leadsto \color{blue}{\frac{\left(x \cdot 1.5\right) \cdot \left(x \cdot 0.5\right)}{x \cdot 0.5}} \]

       5. associate-/l* 81.3%

          \[\leadsto \color{blue}{\left(x \cdot 1.5\right) \cdot \frac{x \cdot 0.5}{x \cdot 0.5}} \]

       6. *-inverses 81.3%

          \[\leadsto \left(x \cdot 1.5\right) \cdot \color{blue}{1} \]

       7. associate-*l* 81.3%

          \[\leadsto \color{blue}{x \cdot \left(1.5 \cdot 1\right)} \]

       8. metadata-eval 81.3%

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

       9. add-sqr-sqrt 80.8%

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

       10. sqrt-unprod 44.0%

           \[\leadsto \color{blue}{\sqrt{\left(x \cdot 1.5\right) \cdot \left(x \cdot 1.5\right)}} \]

       11. swap-sqr 43.9%

           \[\leadsto \sqrt{\color{blue}{\left(x \cdot x\right) \cdot \left(1.5 \cdot 1.5\right)}} \]

       12. pow2 43.9%

           \[\leadsto \sqrt{\color{blue}{{x}^{2}} \cdot \left(1.5 \cdot 1.5\right)} \]

       13. metadata-eval 43.9%

           \[\leadsto \sqrt{{x}^{2} \cdot \color{blue}{2.25}} \]

   11. Applied egg-rr 43.9%

       \[\leadsto \color{blue}{\sqrt{{x}^{2} \cdot 2.25}} \]
   12. Step-by-step derivation

       1. unpow2 43.9%

          \[\leadsto \sqrt{\color{blue}{\left(x \cdot x\right)} \cdot 2.25} \]

       2. metadata-eval 43.9%

          \[\leadsto \sqrt{\left(x \cdot x\right) \cdot \color{blue}{\left(1.5 \cdot 1.5\right)}} \]

       3. swap-sqr 44.0%

          \[\leadsto \sqrt{\color{blue}{\left(x \cdot 1.5\right) \cdot \left(x \cdot 1.5\right)}} \]

       4. rem-sqrt-square 81.3%

          \[\leadsto \color{blue}{\left|x \cdot 1.5\right|} \]

       5. *-commutative 81.3%

          \[\leadsto \left|\color{blue}{1.5 \cdot x}\right| \]

   13. Simplified 81.3%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{-28}:\\ \;\;\;\;0.5 \cdot \left(x + y\right)\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{+19}:\\ \;\;\;\;x + \frac{\left|y\right|}{2}\\ \mathbf{else}:\\ \;\;\;\;\left|x \cdot 1.5\right|\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 57.1% accurate, 8.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.22 \cdot 10^{-27}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{-109}:\\ \;\;\;\;y \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;x \cdot 1.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.22e-27) (* x 0.5) (if (<= x 1.45e-109) (* y 0.5) (* x 1.5))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.22e-27) {
		tmp = x * 0.5;
	} else if (x <= 1.45e-109) {
		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 <= (-1.22d-27)) then
        tmp = x * 0.5d0
    else if (x <= 1.45d-109) 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 <= -1.22e-27) {
		tmp = x * 0.5;
	} else if (x <= 1.45e-109) {
		tmp = y * 0.5;
	} else {
		tmp = x * 1.5;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.22e-27:
		tmp = x * 0.5
	elif x <= 1.45e-109:
		tmp = y * 0.5
	else:
		tmp = x * 1.5
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.22e-27)
		tmp = Float64(x * 0.5);
	elseif (x <= 1.45e-109)
		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 <= -1.22e-27)
		tmp = x * 0.5;
	elseif (x <= 1.45e-109)
		tmp = y * 0.5;
	else
		tmp = x * 1.5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.22e-27], N[(x * 0.5), $MachinePrecision], If[LessEqual[x, 1.45e-109], N[(y * 0.5), $MachinePrecision], N[(x * 1.5), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.22e-27

   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 87.7%

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

      6. fabs-sqr 87.7%

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

      7. rem-square-sqrt 88.3%

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

   5. Simplified 88.3%

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

   6. Taylor expanded in x around inf 73.9%

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

   if -1.22e-27 < x < 1.45e-109

   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 48.6%

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

      6. fabs-sqr 48.6%

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

      7. rem-square-sqrt 50.3%

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

   5. Simplified 50.3%

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

   6. Taylor expanded in x around 0 41.2%

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

   if 1.45e-109 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 65.8%

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

      1. neg-mul-1 65.8%

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

   5. Simplified 65.8%

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

      1. add-sqr-sqrt 65.6%

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

      2. pow2 65.6%

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

      3. div-inv 65.6%

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

      4. fabs-neg 65.6%

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

      5. add-sqr-sqrt 65.6%

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

      6. fabs-sqr 65.6%

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

      7. add-sqr-sqrt 65.6%

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

      8. metadata-eval 65.6%

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

   7. Applied egg-rr 65.6%

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

   8. Taylor expanded in x around 0 65.8%

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

      1. +-commutative 65.8%

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

      2. unpow2 65.8%

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

      3. rem-square-sqrt 65.8%

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

      4. metadata-eval 65.8%

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

   10. Simplified 65.8%

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

4. Final simplification 59.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.22 \cdot 10^{-27}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{-109}:\\ \;\;\;\;y \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;x \cdot 1.5\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 66.8% accurate, 10.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.35 \cdot 10^{-71}:\\ \;\;\;\;0.5 \cdot \left(x + y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 1.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 1.35e-71) (* 0.5 (+ x y)) (* x 1.5)))

C

double code(double x, double y) {
	double tmp;
	if (x <= 1.35e-71) {
		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 <= 1.35d-71) 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 <= 1.35e-71) {
		tmp = 0.5 * (x + y);
	} else {
		tmp = x * 1.5;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 1.35e-71:
		tmp = 0.5 * (x + y)
	else:
		tmp = x * 1.5
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 1.35e-71)
		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 <= 1.35e-71)
		tmp = 0.5 * (x + y);
	else
		tmp = x * 1.5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 1.35e-71], N[(0.5 * N[(x + y), $MachinePrecision]), $MachinePrecision], N[(x * 1.5), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1.3500000000000001e-71

   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 65.1%

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

      6. fabs-sqr 65.1%

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

      7. rem-square-sqrt 66.6%

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

   5. Simplified 66.6%

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

   6. Taylor expanded in x around 0 66.6%

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

      1. distribute-lft-out 66.6%

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

      2. +-commutative 66.6%

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

   8. Simplified 66.6%

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

   if 1.3500000000000001e-71 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 67.6%

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

      1. neg-mul-1 67.6%

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

   5. Simplified 67.6%

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

      1. add-sqr-sqrt 67.5%

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

      2. pow2 67.5%

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

      3. div-inv 67.5%

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

      4. fabs-neg 67.5%

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

      5. add-sqr-sqrt 67.4%

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

      6. fabs-sqr 67.4%

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

      7. add-sqr-sqrt 67.5%

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

      8. metadata-eval 67.5%

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

   7. Applied egg-rr 67.5%

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

   8. Taylor expanded in x around 0 67.6%

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

      1. +-commutative 67.6%

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

      2. unpow2 67.6%

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

      3. rem-square-sqrt 67.6%

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

      4. metadata-eval 67.6%

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

   10. Simplified 67.6%

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

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.35 \cdot 10^{-71}:\\ \;\;\;\;0.5 \cdot \left(x + y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 1.5\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 45.8% accurate, 13.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 8.4 \cdot 10^{-128}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;y \cdot 0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y 8.4e-128) (* x 0.5) (* y 0.5)))

C

double code(double x, double y) {
	double tmp;
	if (y <= 8.4e-128) {
		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 <= 8.4d-128) 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 <= 8.4e-128) {
		tmp = x * 0.5;
	} else {
		tmp = y * 0.5;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 8.4e-128:
		tmp = x * 0.5
	else:
		tmp = y * 0.5
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 8.4e-128)
		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 <= 8.4e-128)
		tmp = x * 0.5;
	else
		tmp = y * 0.5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 8.4e-128], N[(x * 0.5), $MachinePrecision], N[(y * 0.5), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 8.4000000000000004e-128

   1. Initial program 99.9%

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

   3. Taylor expanded in y around -inf 99.9%

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

      1. fabs-neg 99.9%

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

      2. mul-1-neg 99.9%

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

      3. sub-neg 99.9%

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

      4. fabs-sub 99.9%

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

      5. rem-square-sqrt 31.7%

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

      6. fabs-sqr 31.7%

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

      7. rem-square-sqrt 37.2%

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

   5. Simplified 37.2%

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

   6. Taylor expanded in x around inf 36.4%

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

   if 8.4000000000000004e-128 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around -inf 99.9%

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

      1. fabs-neg 99.9%

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

      2. mul-1-neg 99.9%

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

      3. sub-neg 99.9%

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

      4. fabs-sub 99.9%

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

      5. rem-square-sqrt 85.9%

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

      6. fabs-sqr 85.9%

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

      7. rem-square-sqrt 89.0%

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

   5. Simplified 89.0%

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

   6. Taylor expanded in x around 0 69.5%

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

4. Final simplification 48.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 8.4 \cdot 10^{-128}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;y \cdot 0.5\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 30.9% 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. Taylor expanded in y around -inf 99.9%

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

   1. fabs-neg 99.9%

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

   2. mul-1-neg 99.9%

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

   3. sub-neg 99.9%

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

   4. fabs-sub 99.9%

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

   5. rem-square-sqrt 50.8%

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

   6. fabs-sqr 50.8%

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

   7. rem-square-sqrt 55.4%

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

5. Simplified 55.4%

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

6. Taylor expanded in x around inf 31.0%

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

7. Final simplification 31.0%

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

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. Add Preprocessing

3. Taylor expanded in x around inf 10.9%

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

Reproduce

herbie shell --seed 2024111 
(FPCore (x y)
  :name "Graphics.Rendering.Chart.Plot.AreaSpots:renderSpotLegend from Chart-1.5.3"
  :precision binary64
  (+ x (/ (fabs (- y x)) 2.0)))