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

Percentage Accurate: 99.9% → 99.9%

Time: 8.1s

Alternatives: 11

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: 84.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x + y\right) \cdot 0.5\\ \mathbf{if}\;y \leq -2.1 \cdot 10^{-64}:\\ \;\;\;\;x - t\_0\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-164}:\\ \;\;\;\;x + \frac{\left|x\right|}{2}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* (+ x y) 0.5)))
   (if (<= y -2.1e-64)
     (- x t_0)
     (if (<= y 1.25e-164) (+ x (/ (fabs x) 2.0)) t_0))))

C

double code(double x, double y) {
	double t_0 = (x + y) * 0.5;
	double tmp;
	if (y <= -2.1e-64) {
		tmp = x - t_0;
	} else if (y <= 1.25e-164) {
		tmp = x + (fabs(x) / 2.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x + y) * 0.5d0
    if (y <= (-2.1d-64)) then
        tmp = x - t_0
    else if (y <= 1.25d-164) then
        tmp = x + (abs(x) / 2.0d0)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = (x + y) * 0.5;
	double tmp;
	if (y <= -2.1e-64) {
		tmp = x - t_0;
	} else if (y <= 1.25e-164) {
		tmp = x + (Math.abs(x) / 2.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (x + y) * 0.5
	tmp = 0
	if y <= -2.1e-64:
		tmp = x - t_0
	elif y <= 1.25e-164:
		tmp = x + (math.fabs(x) / 2.0)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(x + y) * 0.5)
	tmp = 0.0
	if (y <= -2.1e-64)
		tmp = Float64(x - t_0);
	elseif (y <= 1.25e-164)
		tmp = Float64(x + Float64(abs(x) / 2.0));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (x + y) * 0.5;
	tmp = 0.0;
	if (y <= -2.1e-64)
		tmp = x - t_0;
	elseif (y <= 1.25e-164)
		tmp = x + (abs(x) / 2.0);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(x + y), $MachinePrecision] * 0.5), $MachinePrecision]}, If[LessEqual[y, -2.1e-64], N[(x - t$95$0), $MachinePrecision], If[LessEqual[y, 1.25e-164], N[(x + N[(N[Abs[x], $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.10000000000000011e-64

   1. Initial program 100.0%

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

      1. add-cube-cbrt 98.1%

         \[\leadsto x + \frac{\left|\color{blue}{\left(\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}\right) \cdot \sqrt[3]{y - x}}\right|}{2} \]

      2. fabs-mul 98.1%

         \[\leadsto x + \frac{\color{blue}{\left|\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}\right| \cdot \left|\sqrt[3]{y - x}\right|}}{2} \]

      3. pow2 98.1%

         \[\leadsto x + \frac{\left|\color{blue}{{\left(\sqrt[3]{y - x}\right)}^{2}}\right| \cdot \left|\sqrt[3]{y - x}\right|}{2} \]

   4. Applied egg-rr 98.1%

      \[\leadsto x + \frac{\color{blue}{\left|{\left(\sqrt[3]{y - x}\right)}^{2}\right| \cdot \left|\sqrt[3]{y - x}\right|}}{2} \]

   6. Applied egg-rr 91.0%

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

   if -2.10000000000000011e-64 < y < 1.2499999999999999e-164

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 90.3%

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

      1. neg-mul-1 90.3%

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

   5. Simplified 90.3%

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

   if 1.2499999999999999e-164 < y

   1. Initial program 99.9%

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

      1. *-un-lft-identity 99.9%

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

      2. fma-define 99.9%

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

      3. add-sqr-sqrt 83.3%

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

      4. fabs-sqr 83.3%

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

      5. add-sqr-sqrt 86.8%

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

      6. frac-2neg 86.8%

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

      7. distribute-frac-neg 86.8%

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

      8. fmm-undef 86.8%

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

      9. *-un-lft-identity 86.8%

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

      10. metadata-eval 86.8%

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

   4. Applied egg-rr 86.8%

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

   5. Taylor expanded in x around 0 86.8%

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

      1. cancel-sign-sub-inv 86.8%

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

      2. metadata-eval 86.8%

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

      3. distribute-lft-in 86.8%

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

      4. +-commutative 86.8%

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

   7. Simplified 86.8%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{-64}:\\ \;\;\;\;x - \left(x + y\right) \cdot 0.5\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-164}:\\ \;\;\;\;x + \frac{\left|x\right|}{2}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) \cdot 0.5\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 83.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{-115}:\\ \;\;\;\;\left(x + y\right) \cdot 0.5\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{-93}:\\ \;\;\;\;x + \frac{\left|y\right|}{2}\\ \mathbf{else}:\\ \;\;\;\;y \cdot -0.5 + x \cdot 1.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1e-115)
   (* (+ x y) 0.5)
   (if (<= x 1.35e-93) (+ x (/ (fabs y) 2.0)) (+ (* y -0.5) (* x 1.5)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1e-115) {
		tmp = (x + y) * 0.5;
	} else if (x <= 1.35e-93) {
		tmp = x + (fabs(y) / 2.0);
	} else {
		tmp = (y * -0.5) + (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 <= (-1d-115)) then
        tmp = (x + y) * 0.5d0
    else if (x <= 1.35d-93) then
        tmp = x + (abs(y) / 2.0d0)
    else
        tmp = (y * (-0.5d0)) + (x * 1.5d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -1e-115) {
		tmp = (x + y) * 0.5;
	} else if (x <= 1.35e-93) {
		tmp = x + (Math.abs(y) / 2.0);
	} else {
		tmp = (y * -0.5) + (x * 1.5);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1e-115:
		tmp = (x + y) * 0.5
	elif x <= 1.35e-93:
		tmp = x + (math.fabs(y) / 2.0)
	else:
		tmp = (y * -0.5) + (x * 1.5)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1e-115)
		tmp = Float64(Float64(x + y) * 0.5);
	elseif (x <= 1.35e-93)
		tmp = Float64(x + Float64(abs(y) / 2.0));
	else
		tmp = Float64(Float64(y * -0.5) + Float64(x * 1.5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1e-115)
		tmp = (x + y) * 0.5;
	elseif (x <= 1.35e-93)
		tmp = x + (abs(y) / 2.0);
	else
		tmp = (y * -0.5) + (x * 1.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1e-115], N[(N[(x + y), $MachinePrecision] * 0.5), $MachinePrecision], If[LessEqual[x, 1.35e-93], N[(x + N[(N[Abs[y], $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(y * -0.5), $MachinePrecision] + N[(x * 1.5), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.0000000000000001e-115

   1. Initial program 100.0%

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

      1. *-un-lft-identity 100.0%

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

      2. fma-define 100.0%

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

      3. add-sqr-sqrt 81.5%

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

      4. fabs-sqr 81.5%

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

      5. add-sqr-sqrt 82.1%

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

      6. frac-2neg 82.1%

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

      7. distribute-frac-neg 82.1%

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

      8. fmm-undef 82.1%

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

      9. *-un-lft-identity 82.1%

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

      10. metadata-eval 82.1%

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

   4. Applied egg-rr 82.1%

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

   5. Taylor expanded in x around 0 82.1%

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

      1. cancel-sign-sub-inv 82.1%

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

      2. metadata-eval 82.1%

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

      3. distribute-lft-in 82.1%

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

      4. +-commutative 82.1%

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

   7. Simplified 82.1%

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

   if -1.0000000000000001e-115 < x < 1.3500000000000001e-93

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 92.8%

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

   if 1.3500000000000001e-93 < x

   1. Initial program 99.8%

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

      1. add-cube-cbrt 98.7%

         \[\leadsto x + \frac{\left|\color{blue}{\left(\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}\right) \cdot \sqrt[3]{y - x}}\right|}{2} \]

      2. fabs-mul 98.7%

         \[\leadsto x + \frac{\color{blue}{\left|\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}\right| \cdot \left|\sqrt[3]{y - x}\right|}}{2} \]

      3. pow2 98.7%

         \[\leadsto x + \frac{\left|\color{blue}{{\left(\sqrt[3]{y - x}\right)}^{2}}\right| \cdot \left|\sqrt[3]{y - x}\right|}{2} \]

   4. Applied egg-rr 98.7%

      \[\leadsto x + \frac{\color{blue}{\left|{\left(\sqrt[3]{y - x}\right)}^{2}\right| \cdot \left|\sqrt[3]{y - x}\right|}}{2} \]
   5. Step-by-step derivation

      1. add-sqr-sqrt 98.6%

         \[\leadsto x + \color{blue}{\sqrt{\frac{\left|{\left(\sqrt[3]{y - x}\right)}^{2}\right| \cdot \left|\sqrt[3]{y - x}\right|}{2}} \cdot \sqrt{\frac{\left|{\left(\sqrt[3]{y - x}\right)}^{2}\right| \cdot \left|\sqrt[3]{y - x}\right|}{2}}} \]

      2. sqrt-unprod 48.4%

         \[\leadsto x + \color{blue}{\sqrt{\frac{\left|{\left(\sqrt[3]{y - x}\right)}^{2}\right| \cdot \left|\sqrt[3]{y - x}\right|}{2} \cdot \frac{\left|{\left(\sqrt[3]{y - x}\right)}^{2}\right| \cdot \left|\sqrt[3]{y - x}\right|}{2}}} \]

      3. frac-2neg 48.4%

         \[\leadsto x + \sqrt{\color{blue}{\frac{-\left|{\left(\sqrt[3]{y - x}\right)}^{2}\right| \cdot \left|\sqrt[3]{y - x}\right|}{-2}} \cdot \frac{\left|{\left(\sqrt[3]{y - x}\right)}^{2}\right| \cdot \left|\sqrt[3]{y - x}\right|}{2}} \]

      4. metadata-eval 48.4%

         \[\leadsto x + \sqrt{\frac{-\left|{\left(\sqrt[3]{y - x}\right)}^{2}\right| \cdot \left|\sqrt[3]{y - x}\right|}{\color{blue}{-2}} \cdot \frac{\left|{\left(\sqrt[3]{y - x}\right)}^{2}\right| \cdot \left|\sqrt[3]{y - x}\right|}{2}} \]

      5. frac-2neg 48.4%

         \[\leadsto x + \sqrt{\frac{-\left|{\left(\sqrt[3]{y - x}\right)}^{2}\right| \cdot \left|\sqrt[3]{y - x}\right|}{-2} \cdot \color{blue}{\frac{-\left|{\left(\sqrt[3]{y - x}\right)}^{2}\right| \cdot \left|\sqrt[3]{y - x}\right|}{-2}}} \]

      6. metadata-eval 48.4%

         \[\leadsto x + \sqrt{\frac{-\left|{\left(\sqrt[3]{y - x}\right)}^{2}\right| \cdot \left|\sqrt[3]{y - x}\right|}{-2} \cdot \frac{-\left|{\left(\sqrt[3]{y - x}\right)}^{2}\right| \cdot \left|\sqrt[3]{y - x}\right|}{\color{blue}{-2}}} \]

      7. frac-times 48.4%

         \[\leadsto x + \sqrt{\color{blue}{\frac{\left(-\left|{\left(\sqrt[3]{y - x}\right)}^{2}\right| \cdot \left|\sqrt[3]{y - x}\right|\right) \cdot \left(-\left|{\left(\sqrt[3]{y - x}\right)}^{2}\right| \cdot \left|\sqrt[3]{y - x}\right|\right)}{-2 \cdot -2}}} \]

   6. Applied egg-rr 84.2%

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

   7. Taylor expanded in x around 0 84.2%

      \[\leadsto \color{blue}{-0.5 \cdot y + 1.5 \cdot x} \]
3. Recombined 3 regimes into one program.

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{-115}:\\ \;\;\;\;\left(x + y\right) \cdot 0.5\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{-93}:\\ \;\;\;\;x + \frac{\left|y\right|}{2}\\ \mathbf{else}:\\ \;\;\;\;y \cdot -0.5 + x \cdot 1.5\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 72.1% accurate, 7.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{-64}:\\ \;\;\;\;x - y \cdot 0.5\\ \mathbf{elif}\;y \leq -7.6 \cdot 10^{-239}:\\ \;\;\;\;x \cdot 1.5\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) \cdot 0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.45e-64)
   (- x (* y 0.5))
   (if (<= y -7.6e-239) (* x 1.5) (* (+ x y) 0.5))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.45e-64) {
		tmp = x - (y * 0.5);
	} else if (y <= -7.6e-239) {
		tmp = x * 1.5;
	} else {
		tmp = (x + 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 <= (-1.45d-64)) then
        tmp = x - (y * 0.5d0)
    else if (y <= (-7.6d-239)) then
        tmp = x * 1.5d0
    else
        tmp = (x + y) * 0.5d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.45e-64) {
		tmp = x - (y * 0.5);
	} else if (y <= -7.6e-239) {
		tmp = x * 1.5;
	} else {
		tmp = (x + y) * 0.5;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.45e-64:
		tmp = x - (y * 0.5)
	elif y <= -7.6e-239:
		tmp = x * 1.5
	else:
		tmp = (x + y) * 0.5
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.45e-64)
		tmp = Float64(x - Float64(y * 0.5));
	elseif (y <= -7.6e-239)
		tmp = Float64(x * 1.5);
	else
		tmp = Float64(Float64(x + y) * 0.5);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.45e-64)
		tmp = x - (y * 0.5);
	elseif (y <= -7.6e-239)
		tmp = x * 1.5;
	else
		tmp = (x + y) * 0.5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.45e-64], N[(x - N[(y * 0.5), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -7.6e-239], N[(x * 1.5), $MachinePrecision], N[(N[(x + y), $MachinePrecision] * 0.5), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.4499999999999999e-64

   1. Initial program 100.0%

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

      1. add-cube-cbrt 98.1%

         \[\leadsto x + \frac{\left|\color{blue}{\left(\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}\right) \cdot \sqrt[3]{y - x}}\right|}{2} \]

      2. fabs-mul 98.1%

         \[\leadsto x + \frac{\color{blue}{\left|\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}\right| \cdot \left|\sqrt[3]{y - x}\right|}}{2} \]

      3. pow2 98.1%

         \[\leadsto x + \frac{\left|\color{blue}{{\left(\sqrt[3]{y - x}\right)}^{2}}\right| \cdot \left|\sqrt[3]{y - x}\right|}{2} \]

   4. Applied egg-rr 98.1%

      \[\leadsto x + \frac{\color{blue}{\left|{\left(\sqrt[3]{y - x}\right)}^{2}\right| \cdot \left|\sqrt[3]{y - x}\right|}}{2} \]

   6. Applied egg-rr 91.1%

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

   7. Taylor expanded in y around inf 78.8%

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

   if -1.4499999999999999e-64 < y < -7.6000000000000004e-239

   1. Initial program 99.9%

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

      1. add-cube-cbrt 98.5%

         \[\leadsto x + \frac{\left|\color{blue}{\left(\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}\right) \cdot \sqrt[3]{y - x}}\right|}{2} \]

      2. fabs-mul 98.5%

         \[\leadsto x + \frac{\color{blue}{\left|\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}\right| \cdot \left|\sqrt[3]{y - x}\right|}}{2} \]

      3. pow2 98.5%

         \[\leadsto x + \frac{\left|\color{blue}{{\left(\sqrt[3]{y - x}\right)}^{2}}\right| \cdot \left|\sqrt[3]{y - x}\right|}{2} \]

   4. Applied egg-rr 98.5%

      \[\leadsto x + \frac{\color{blue}{\left|{\left(\sqrt[3]{y - x}\right)}^{2}\right| \cdot \left|\sqrt[3]{y - x}\right|}}{2} \]
   5. Step-by-step derivation

      1. mul-fabs 98.5%

         \[\leadsto x + \frac{\color{blue}{\left|{\left(\sqrt[3]{y - x}\right)}^{2} \cdot \sqrt[3]{y - x}\right|}}{2} \]

      2. unpow2 98.5%

         \[\leadsto x + \frac{\left|\color{blue}{\left(\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}\right)} \cdot \sqrt[3]{y - x}\right|}{2} \]

      3. add-cube-cbrt 99.9%

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

      4. add-sqr-sqrt 25.6%

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

      5. fabs-sqr 25.6%

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

      6. add-sqr-sqrt 37.0%

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

      7. flip-- 27.9%

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

      8. clear-num 27.7%

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

      9. difference-of-squares 27.7%

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

      10. add-sqr-sqrt 8.3%

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

      11. sqrt-unprod 12.5%

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

      12. sqr-neg 12.5%

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

      13. sqrt-unprod 4.1%

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

      14. add-sqr-sqrt 47.8%

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

      15. sub-neg 47.8%

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

      16. pow2 47.8%

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

      17. sub-neg 47.8%

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

      18. add-sqr-sqrt 4.1%

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

      19. sqrt-unprod 47.8%

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

      20. sqr-neg 47.8%

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

      21. sqrt-unprod 43.5%

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

      22. add-sqr-sqrt 47.8%

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

   6. Applied egg-rr 47.8%

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

      1. associate-/r/ 47.8%

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

   8. Simplified 47.8%

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

   9. Taylor expanded in x around inf 66.1%

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

       1. *-commutative 66.1%

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

   11. Simplified 66.1%

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

   if -7.6000000000000004e-239 < y

   1. Initial program 99.9%

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

      1. *-un-lft-identity 99.9%

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

      2. fma-define 99.9%

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

      3. add-sqr-sqrt 74.5%

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

      4. fabs-sqr 74.5%

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

      5. add-sqr-sqrt 79.3%

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

      6. frac-2neg 79.3%

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

      7. distribute-frac-neg 79.3%

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

      8. fmm-undef 79.3%

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

      9. *-un-lft-identity 79.3%

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

      10. metadata-eval 79.3%

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

   4. Applied egg-rr 79.3%

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

   5. Taylor expanded in x around 0 79.4%

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

      1. cancel-sign-sub-inv 79.4%

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

      2. metadata-eval 79.4%

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

      3. distribute-lft-in 79.4%

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

      4. +-commutative 79.4%

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

   7. Simplified 79.4%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{-64}:\\ \;\;\;\;x - y \cdot 0.5\\ \mathbf{elif}\;y \leq -7.6 \cdot 10^{-239}:\\ \;\;\;\;x \cdot 1.5\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) \cdot 0.5\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 70.5% accurate, 7.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{-63}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{-239}:\\ \;\;\;\;x \cdot 1.5\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) \cdot 0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -2.6e-63)
   (* y -0.5)
   (if (<= y -3.3e-239) (* x 1.5) (* (+ x y) 0.5))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -2.6e-63) {
		tmp = y * -0.5;
	} else if (y <= -3.3e-239) {
		tmp = x * 1.5;
	} else {
		tmp = (x + 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 <= (-2.6d-63)) then
        tmp = y * (-0.5d0)
    else if (y <= (-3.3d-239)) then
        tmp = x * 1.5d0
    else
        tmp = (x + y) * 0.5d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -2.6e-63) {
		tmp = y * -0.5;
	} else if (y <= -3.3e-239) {
		tmp = x * 1.5;
	} else {
		tmp = (x + y) * 0.5;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -2.6e-63:
		tmp = y * -0.5
	elif y <= -3.3e-239:
		tmp = x * 1.5
	else:
		tmp = (x + y) * 0.5
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -2.6e-63)
		tmp = Float64(y * -0.5);
	elseif (y <= -3.3e-239)
		tmp = Float64(x * 1.5);
	else
		tmp = Float64(Float64(x + y) * 0.5);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -2.6e-63)
		tmp = y * -0.5;
	elseif (y <= -3.3e-239)
		tmp = x * 1.5;
	else
		tmp = (x + y) * 0.5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -2.6e-63], N[(y * -0.5), $MachinePrecision], If[LessEqual[y, -3.3e-239], N[(x * 1.5), $MachinePrecision], N[(N[(x + y), $MachinePrecision] * 0.5), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.6000000000000001e-63

   1. Initial program 100.0%

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

      1. add-cube-cbrt 98.1%

         \[\leadsto x + \frac{\left|\color{blue}{\left(\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}\right) \cdot \sqrt[3]{y - x}}\right|}{2} \]

      2. fabs-mul 98.1%

         \[\leadsto x + \frac{\color{blue}{\left|\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}\right| \cdot \left|\sqrt[3]{y - x}\right|}}{2} \]

      3. pow2 98.1%

         \[\leadsto x + \frac{\left|\color{blue}{{\left(\sqrt[3]{y - x}\right)}^{2}}\right| \cdot \left|\sqrt[3]{y - x}\right|}{2} \]

   4. Applied egg-rr 98.1%

      \[\leadsto x + \frac{\color{blue}{\left|{\left(\sqrt[3]{y - x}\right)}^{2}\right| \cdot \left|\sqrt[3]{y - x}\right|}}{2} \]

   6. Applied egg-rr 91.0%

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

   7. Taylor expanded in x around 0 75.6%

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

      1. *-commutative 75.6%

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

   9. Simplified 75.6%

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

   if -2.6000000000000001e-63 < y < -3.29999999999999995e-239

   1. Initial program 99.9%

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

      1. add-cube-cbrt 98.5%

         \[\leadsto x + \frac{\left|\color{blue}{\left(\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}\right) \cdot \sqrt[3]{y - x}}\right|}{2} \]

      2. fabs-mul 98.5%

         \[\leadsto x + \frac{\color{blue}{\left|\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}\right| \cdot \left|\sqrt[3]{y - x}\right|}}{2} \]

      3. pow2 98.5%

         \[\leadsto x + \frac{\left|\color{blue}{{\left(\sqrt[3]{y - x}\right)}^{2}}\right| \cdot \left|\sqrt[3]{y - x}\right|}{2} \]

   4. Applied egg-rr 98.5%

      \[\leadsto x + \frac{\color{blue}{\left|{\left(\sqrt[3]{y - x}\right)}^{2}\right| \cdot \left|\sqrt[3]{y - x}\right|}}{2} \]
   5. Step-by-step derivation

      1. mul-fabs 98.5%

         \[\leadsto x + \frac{\color{blue}{\left|{\left(\sqrt[3]{y - x}\right)}^{2} \cdot \sqrt[3]{y - x}\right|}}{2} \]

      2. unpow2 98.5%

         \[\leadsto x + \frac{\left|\color{blue}{\left(\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}\right)} \cdot \sqrt[3]{y - x}\right|}{2} \]

      3. add-cube-cbrt 99.9%

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

      4. add-sqr-sqrt 27.9%

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

      5. fabs-sqr 27.9%

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

      6. add-sqr-sqrt 39.0%

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

      7. flip-- 30.1%

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

      8. clear-num 29.9%

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

      9. difference-of-squares 29.9%

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

      10. add-sqr-sqrt 8.1%

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

      11. sqrt-unprod 12.6%

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

      12. sqr-neg 12.6%

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

      13. sqrt-unprod 4.5%

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

      14. add-sqr-sqrt 46.8%

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

      15. sub-neg 46.8%

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

      16. pow2 46.8%

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

      17. sub-neg 46.8%

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

      18. add-sqr-sqrt 4.5%

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

      19. sqrt-unprod 46.8%

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

      20. sqr-neg 46.8%

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

      21. sqrt-unprod 42.1%

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

      22. add-sqr-sqrt 46.8%

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

   6. Applied egg-rr 46.8%

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

      1. associate-/r/ 46.9%

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

   8. Simplified 46.9%

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

   9. Taylor expanded in x around inf 64.6%

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

       1. *-commutative 64.6%

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

   11. Simplified 64.6%

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

   if -3.29999999999999995e-239 < y

   1. Initial program 99.9%

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

      1. *-un-lft-identity 99.9%

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

      2. fma-define 99.9%

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

      3. add-sqr-sqrt 74.5%

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

      4. fabs-sqr 74.5%

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

      5. add-sqr-sqrt 79.3%

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

      6. frac-2neg 79.3%

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

      7. distribute-frac-neg 79.3%

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

      8. fmm-undef 79.3%

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

      9. *-un-lft-identity 79.3%

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

      10. metadata-eval 79.3%

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

   4. Applied egg-rr 79.3%

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

   5. Taylor expanded in x around 0 79.4%

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

      1. cancel-sign-sub-inv 79.4%

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

      2. metadata-eval 79.4%

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

      3. distribute-lft-in 79.4%

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

      4. +-commutative 79.4%

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

   7. Simplified 79.4%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{-63}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{-239}:\\ \;\;\;\;x \cdot 1.5\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) \cdot 0.5\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 61.0% accurate, 8.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{-64}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-72}:\\ \;\;\;\;x \cdot 1.5\\ \mathbf{else}:\\ \;\;\;\;y \cdot 0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -3.2e-64) (* y -0.5) (if (<= y 1.4e-72) (* x 1.5) (* y 0.5))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -3.2e-64) {
		tmp = y * -0.5;
	} else if (y <= 1.4e-72) {
		tmp = x * 1.5;
	} 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 <= (-3.2d-64)) then
        tmp = y * (-0.5d0)
    else if (y <= 1.4d-72) then
        tmp = x * 1.5d0
    else
        tmp = y * 0.5d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -3.2e-64) {
		tmp = y * -0.5;
	} else if (y <= 1.4e-72) {
		tmp = x * 1.5;
	} else {
		tmp = y * 0.5;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -3.2e-64:
		tmp = y * -0.5
	elif y <= 1.4e-72:
		tmp = x * 1.5
	else:
		tmp = y * 0.5
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -3.2e-64)
		tmp = Float64(y * -0.5);
	elseif (y <= 1.4e-72)
		tmp = Float64(x * 1.5);
	else
		tmp = Float64(y * 0.5);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -3.2e-64)
		tmp = y * -0.5;
	elseif (y <= 1.4e-72)
		tmp = x * 1.5;
	else
		tmp = y * 0.5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -3.2e-64], N[(y * -0.5), $MachinePrecision], If[LessEqual[y, 1.4e-72], N[(x * 1.5), $MachinePrecision], N[(y * 0.5), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.19999999999999975e-64

   1. Initial program 100.0%

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

      1. add-cube-cbrt 98.1%

         \[\leadsto x + \frac{\left|\color{blue}{\left(\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}\right) \cdot \sqrt[3]{y - x}}\right|}{2} \]

      2. fabs-mul 98.1%

         \[\leadsto x + \frac{\color{blue}{\left|\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}\right| \cdot \left|\sqrt[3]{y - x}\right|}}{2} \]

      3. pow2 98.1%

         \[\leadsto x + \frac{\left|\color{blue}{{\left(\sqrt[3]{y - x}\right)}^{2}}\right| \cdot \left|\sqrt[3]{y - x}\right|}{2} \]

   4. Applied egg-rr 98.1%

      \[\leadsto x + \frac{\color{blue}{\left|{\left(\sqrt[3]{y - x}\right)}^{2}\right| \cdot \left|\sqrt[3]{y - x}\right|}}{2} \]

   6. Applied egg-rr 91.0%

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

   7. Taylor expanded in x around 0 75.6%

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

      1. *-commutative 75.6%

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

   9. Simplified 75.6%

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

   if -3.19999999999999975e-64 < y < 1.3999999999999999e-72

   1. Initial program 99.9%

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

      1. add-cube-cbrt 98.4%

         \[\leadsto x + \frac{\left|\color{blue}{\left(\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}\right) \cdot \sqrt[3]{y - x}}\right|}{2} \]

      2. fabs-mul 98.4%

         \[\leadsto x + \frac{\color{blue}{\left|\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}\right| \cdot \left|\sqrt[3]{y - x}\right|}}{2} \]

      3. pow2 98.4%

         \[\leadsto x + \frac{\left|\color{blue}{{\left(\sqrt[3]{y - x}\right)}^{2}}\right| \cdot \left|\sqrt[3]{y - x}\right|}{2} \]

   4. Applied egg-rr 98.4%

      \[\leadsto x + \frac{\color{blue}{\left|{\left(\sqrt[3]{y - x}\right)}^{2}\right| \cdot \left|\sqrt[3]{y - x}\right|}}{2} \]
   5. Step-by-step derivation

      1. mul-fabs 98.4%

         \[\leadsto x + \frac{\color{blue}{\left|{\left(\sqrt[3]{y - x}\right)}^{2} \cdot \sqrt[3]{y - x}\right|}}{2} \]

      2. unpow2 98.4%

         \[\leadsto x + \frac{\left|\color{blue}{\left(\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}\right)} \cdot \sqrt[3]{y - x}\right|}{2} \]

      3. add-cube-cbrt 99.9%

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

      4. add-sqr-sqrt 45.8%

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

      5. fabs-sqr 45.8%

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

      6. add-sqr-sqrt 54.9%

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

      7. flip-- 36.1%

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

      8. clear-num 36.0%

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

      9. difference-of-squares 36.0%

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

      10. add-sqr-sqrt 8.1%

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

      11. sqrt-unprod 17.2%

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

      12. sqr-neg 17.2%

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

      13. sqrt-unprod 9.1%

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

      14. add-sqr-sqrt 40.7%

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

      15. sub-neg 40.7%

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

      16. pow2 40.7%

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

      17. sub-neg 40.7%

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

      18. add-sqr-sqrt 9.1%

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

      19. sqrt-unprod 40.7%

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

      20. sqr-neg 40.7%

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

      21. sqrt-unprod 31.5%

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

      22. add-sqr-sqrt 40.7%

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

   6. Applied egg-rr 40.7%

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

      1. associate-/r/ 40.7%

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

   8. Simplified 40.7%

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

   9. Taylor expanded in x around inf 54.6%

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

       1. *-commutative 54.6%

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

   11. Simplified 54.6%

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

   if 1.3999999999999999e-72 < y

   1. Initial program 99.9%

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

      1. *-un-lft-identity 99.9%

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

      2. fma-define 99.9%

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

      3. add-sqr-sqrt 88.2%

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

      4. fabs-sqr 88.2%

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

      5. add-sqr-sqrt 90.8%

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

      6. frac-2neg 90.8%

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

      7. distribute-frac-neg 90.8%

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

      8. fmm-undef 90.8%

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

      9. *-un-lft-identity 90.8%

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

      10. metadata-eval 90.8%

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

   4. Applied egg-rr 90.8%

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

   5. Taylor expanded in x around 0 76.4%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{-64}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-72}:\\ \;\;\;\;x \cdot 1.5\\ \mathbf{else}:\\ \;\;\;\;y \cdot 0.5\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 58.9% accurate, 8.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{-90}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-102}:\\ \;\;\;\;y \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;x \cdot 1.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.4e-90) (* x 0.5) (if (<= x 6e-102) (* y 0.5) (* x 1.5))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.4e-90) {
		tmp = x * 0.5;
	} else if (x <= 6e-102) {
		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 <= (-1.4d-90)) then
        tmp = x * 0.5d0
    else if (x <= 6d-102) 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 <= -1.4e-90) {
		tmp = x * 0.5;
	} else if (x <= 6e-102) {
		tmp = y * 0.5;
	} else {
		tmp = x * 1.5;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.4e-90:
		tmp = x * 0.5
	elif x <= 6e-102:
		tmp = y * 0.5
	else:
		tmp = x * 1.5
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.4e-90)
		tmp = Float64(x * 0.5);
	elseif (x <= 6e-102)
		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 <= -1.4e-90)
		tmp = x * 0.5;
	elseif (x <= 6e-102)
		tmp = y * 0.5;
	else
		tmp = x * 1.5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.4e-90], N[(x * 0.5), $MachinePrecision], If[LessEqual[x, 6e-102], N[(y * 0.5), $MachinePrecision], N[(x * 1.5), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.3999999999999999e-90

   1. Initial program 100.0%

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

      1. *-un-lft-identity 100.0%

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

      2. fma-define 100.0%

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

      3. add-sqr-sqrt 81.4%

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

      4. fabs-sqr 81.4%

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

      5. add-sqr-sqrt 82.0%

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

      6. frac-2neg 82.0%

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

      7. distribute-frac-neg 82.0%

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

      8. fmm-undef 82.0%

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

      9. *-un-lft-identity 82.0%

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

      10. metadata-eval 82.0%

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

   4. Applied egg-rr 82.0%

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

   5. Taylor expanded in x around inf 63.3%

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

   if -1.3999999999999999e-90 < x < 6e-102

   1. Initial program 100.0%

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

      1. *-un-lft-identity 100.0%

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

      2. fma-define 100.0%

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

      3. add-sqr-sqrt 53.1%

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

      4. fabs-sqr 53.1%

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

      5. add-sqr-sqrt 55.2%

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

      6. frac-2neg 55.2%

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

      7. distribute-frac-neg 55.2%

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

      8. fmm-undef 55.2%

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

      9. *-un-lft-identity 55.2%

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

      10. metadata-eval 55.2%

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

   4. Applied egg-rr 55.2%

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

   5. Taylor expanded in x around 0 50.0%

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

   if 6e-102 < x

   1. Initial program 99.8%

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

      1. add-cube-cbrt 98.7%

         \[\leadsto x + \frac{\left|\color{blue}{\left(\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}\right) \cdot \sqrt[3]{y - x}}\right|}{2} \]

      2. fabs-mul 98.7%

         \[\leadsto x + \frac{\color{blue}{\left|\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}\right| \cdot \left|\sqrt[3]{y - x}\right|}}{2} \]

      3. pow2 98.7%

         \[\leadsto x + \frac{\left|\color{blue}{{\left(\sqrt[3]{y - x}\right)}^{2}}\right| \cdot \left|\sqrt[3]{y - x}\right|}{2} \]

   4. Applied egg-rr 98.7%

      \[\leadsto x + \frac{\color{blue}{\left|{\left(\sqrt[3]{y - x}\right)}^{2}\right| \cdot \left|\sqrt[3]{y - x}\right|}}{2} \]
   5. Step-by-step derivation

      1. mul-fabs 98.7%

         \[\leadsto x + \frac{\color{blue}{\left|{\left(\sqrt[3]{y - x}\right)}^{2} \cdot \sqrt[3]{y - x}\right|}}{2} \]

      2. unpow2 98.7%

         \[\leadsto x + \frac{\left|\color{blue}{\left(\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}\right)} \cdot \sqrt[3]{y - x}\right|}{2} \]

      3. add-cube-cbrt 99.8%

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

      4. add-sqr-sqrt 15.6%

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

      5. fabs-sqr 15.6%

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

      6. add-sqr-sqrt 26.8%

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

      7. flip-- 9.6%

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

      8. clear-num 9.6%

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

      9. difference-of-squares 9.9%

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

      10. add-sqr-sqrt 9.9%

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

      11. sqrt-unprod 10.2%

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

      12. sqr-neg 10.2%

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

      13. sqrt-unprod 0.0%

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

      14. add-sqr-sqrt 36.4%

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

      15. sub-neg 36.4%

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

      16. pow2 36.4%

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

      17. sub-neg 36.4%

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

      18. add-sqr-sqrt 0.0%

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

      19. sqrt-unprod 36.4%

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

      20. sqr-neg 36.4%

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

      21. sqrt-unprod 36.3%

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

      22. add-sqr-sqrt 36.4%

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

   6. Applied egg-rr 36.4%

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

      1. associate-/r/ 36.5%

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

   8. Simplified 36.5%

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

   9. Taylor expanded in x around inf 61.1%

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

       1. *-commutative 61.1%

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

   11. Simplified 61.1%

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

4. Final simplification 58.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{-90}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-102}:\\ \;\;\;\;y \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;x \cdot 1.5\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 79.5% accurate, 8.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.32 \cdot 10^{-285}:\\ \;\;\;\;y \cdot -0.5 + x \cdot 1.5\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) \cdot 0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.32e-285) (+ (* y -0.5) (* x 1.5)) (* (+ x y) 0.5)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.32e-285) {
		tmp = (y * -0.5) + (x * 1.5);
	} else {
		tmp = (x + 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 <= (-1.32d-285)) then
        tmp = (y * (-0.5d0)) + (x * 1.5d0)
    else
        tmp = (x + y) * 0.5d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.32e-285) {
		tmp = (y * -0.5) + (x * 1.5);
	} else {
		tmp = (x + y) * 0.5;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.32e-285:
		tmp = (y * -0.5) + (x * 1.5)
	else:
		tmp = (x + y) * 0.5
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.32e-285)
		tmp = Float64(Float64(y * -0.5) + Float64(x * 1.5));
	else
		tmp = Float64(Float64(x + y) * 0.5);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.32e-285)
		tmp = (y * -0.5) + (x * 1.5);
	else
		tmp = (x + y) * 0.5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.32e-285], N[(N[(y * -0.5), $MachinePrecision] + N[(x * 1.5), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] * 0.5), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.3199999999999999e-285

   1. Initial program 100.0%

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

      1. add-cube-cbrt 98.2%

         \[\leadsto x + \frac{\left|\color{blue}{\left(\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}\right) \cdot \sqrt[3]{y - x}}\right|}{2} \]

      2. fabs-mul 98.2%

         \[\leadsto x + \frac{\color{blue}{\left|\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}\right| \cdot \left|\sqrt[3]{y - x}\right|}}{2} \]

      3. pow2 98.2%

         \[\leadsto x + \frac{\left|\color{blue}{{\left(\sqrt[3]{y - x}\right)}^{2}}\right| \cdot \left|\sqrt[3]{y - x}\right|}{2} \]

   4. Applied egg-rr 98.2%

      \[\leadsto x + \frac{\color{blue}{\left|{\left(\sqrt[3]{y - x}\right)}^{2}\right| \cdot \left|\sqrt[3]{y - x}\right|}}{2} \]
   5. Step-by-step derivation

      1. add-sqr-sqrt 98.1%

         \[\leadsto x + \color{blue}{\sqrt{\frac{\left|{\left(\sqrt[3]{y - x}\right)}^{2}\right| \cdot \left|\sqrt[3]{y - x}\right|}{2}} \cdot \sqrt{\frac{\left|{\left(\sqrt[3]{y - x}\right)}^{2}\right| \cdot \left|\sqrt[3]{y - x}\right|}{2}}} \]

      2. sqrt-unprod 53.5%

         \[\leadsto x + \color{blue}{\sqrt{\frac{\left|{\left(\sqrt[3]{y - x}\right)}^{2}\right| \cdot \left|\sqrt[3]{y - x}\right|}{2} \cdot \frac{\left|{\left(\sqrt[3]{y - x}\right)}^{2}\right| \cdot \left|\sqrt[3]{y - x}\right|}{2}}} \]

      3. frac-2neg 53.5%

         \[\leadsto x + \sqrt{\color{blue}{\frac{-\left|{\left(\sqrt[3]{y - x}\right)}^{2}\right| \cdot \left|\sqrt[3]{y - x}\right|}{-2}} \cdot \frac{\left|{\left(\sqrt[3]{y - x}\right)}^{2}\right| \cdot \left|\sqrt[3]{y - x}\right|}{2}} \]

      4. metadata-eval 53.5%

         \[\leadsto x + \sqrt{\frac{-\left|{\left(\sqrt[3]{y - x}\right)}^{2}\right| \cdot \left|\sqrt[3]{y - x}\right|}{\color{blue}{-2}} \cdot \frac{\left|{\left(\sqrt[3]{y - x}\right)}^{2}\right| \cdot \left|\sqrt[3]{y - x}\right|}{2}} \]

      5. frac-2neg 53.5%

         \[\leadsto x + \sqrt{\frac{-\left|{\left(\sqrt[3]{y - x}\right)}^{2}\right| \cdot \left|\sqrt[3]{y - x}\right|}{-2} \cdot \color{blue}{\frac{-\left|{\left(\sqrt[3]{y - x}\right)}^{2}\right| \cdot \left|\sqrt[3]{y - x}\right|}{-2}}} \]

      6. metadata-eval 53.5%

         \[\leadsto x + \sqrt{\frac{-\left|{\left(\sqrt[3]{y - x}\right)}^{2}\right| \cdot \left|\sqrt[3]{y - x}\right|}{-2} \cdot \frac{-\left|{\left(\sqrt[3]{y - x}\right)}^{2}\right| \cdot \left|\sqrt[3]{y - x}\right|}{\color{blue}{-2}}} \]

      7. frac-times 53.5%

         \[\leadsto x + \sqrt{\color{blue}{\frac{\left(-\left|{\left(\sqrt[3]{y - x}\right)}^{2}\right| \cdot \left|\sqrt[3]{y - x}\right|\right) \cdot \left(-\left|{\left(\sqrt[3]{y - x}\right)}^{2}\right| \cdot \left|\sqrt[3]{y - x}\right|\right)}{-2 \cdot -2}}} \]

   6. Applied egg-rr 82.3%

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

   7. Taylor expanded in x around 0 82.3%

      \[\leadsto \color{blue}{-0.5 \cdot y + 1.5 \cdot x} \]

   if -1.3199999999999999e-285 < y

   1. Initial program 99.9%

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

      1. *-un-lft-identity 99.9%

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

      2. fma-define 99.9%

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

      3. add-sqr-sqrt 76.4%

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

      4. fabs-sqr 76.4%

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

      5. add-sqr-sqrt 81.0%

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

      6. frac-2neg 81.0%

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

      7. distribute-frac-neg 81.0%

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

      8. fmm-undef 81.0%

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

      9. *-un-lft-identity 81.0%

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

      10. metadata-eval 81.0%

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

   4. Applied egg-rr 81.0%

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

   5. Taylor expanded in x around 0 81.0%

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

      1. cancel-sign-sub-inv 81.0%

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

      2. metadata-eval 81.0%

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

      3. distribute-lft-in 81.0%

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

      4. +-commutative 81.0%

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

   7. Simplified 81.0%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.32 \cdot 10^{-285}:\\ \;\;\;\;y \cdot -0.5 + x \cdot 1.5\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) \cdot 0.5\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 46.2% accurate, 13.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.75 \cdot 10^{-65}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;y \cdot 0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y 1.75e-65) (* x 0.5) (* y 0.5)))

C

double code(double x, double y) {
	double tmp;
	if (y <= 1.75e-65) {
		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 <= 1.75d-65) 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 <= 1.75e-65) {
		tmp = x * 0.5;
	} else {
		tmp = y * 0.5;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 1.75e-65:
		tmp = x * 0.5
	else:
		tmp = y * 0.5
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 1.75e-65)
		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 <= 1.75e-65)
		tmp = x * 0.5;
	else
		tmp = y * 0.5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 1.75e-65], N[(x * 0.5), $MachinePrecision], N[(y * 0.5), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.75000000000000002e-65

   1. Initial program 99.9%

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

      1. *-un-lft-identity 99.9%

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

      2. fma-define 99.9%

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

      3. add-sqr-sqrt 32.5%

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

      4. fabs-sqr 32.5%

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

      5. add-sqr-sqrt 38.2%

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

      6. frac-2neg 38.2%

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

      7. distribute-frac-neg 38.2%

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

      8. fmm-undef 38.2%

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

      9. *-un-lft-identity 38.2%

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

      10. metadata-eval 38.2%

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

   4. Applied egg-rr 38.2%

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

   5. Taylor expanded in x around inf 33.2%

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

   if 1.75000000000000002e-65 < y

   1. Initial program 99.9%

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

      1. *-un-lft-identity 99.9%

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

      2. fma-define 99.9%

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

      3. add-sqr-sqrt 88.8%

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

      4. fabs-sqr 88.8%

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

      5. add-sqr-sqrt 91.3%

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

      6. frac-2neg 91.3%

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

      7. distribute-frac-neg 91.3%

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

      8. fmm-undef 91.3%

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

      9. *-un-lft-identity 91.3%

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

      10. metadata-eval 91.3%

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

   4. Applied egg-rr 91.3%

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

   5. Taylor expanded in x around 0 78.7%

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

4. Final simplification 46.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.75 \cdot 10^{-65}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;y \cdot 0.5\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 30.8% accurate, 35.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. *-un-lft-identity 99.9%

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

   2. fma-define 99.9%

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

   3. add-sqr-sqrt 49.2%

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

   4. fabs-sqr 49.2%

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

   5. add-sqr-sqrt 54.0%

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

   6. frac-2neg 54.0%

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

   7. distribute-frac-neg 54.0%

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

   8. fmm-undef 54.0%

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

   9. *-un-lft-identity 54.0%

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

   10. metadata-eval 54.0%

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

4. Applied egg-rr 54.0%

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

5. Taylor expanded in x around inf 27.7%

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

6. Final simplification 27.7%

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

Alternative 11: 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 99.9%

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

3. Taylor expanded in x around inf 10.6%

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

Reproduce

herbie shell --seed 2024184 
(FPCore (x y)
  :name "Graphics.Rendering.Chart.Plot.AreaSpots:renderSpotLegend from Chart-1.5.3"
  :precision binary64
  (+ x (/ (fabs (- y x)) 2.0)))