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

Percentage Accurate: 99.9% → 99.9%

Time: 3.9s

Alternatives: 6

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

2. Final simplification 99.9%

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

Alternative 2: 70.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{-87}:\\ \;\;\;\;0.5 \cdot \left(x + y\right)\\ \mathbf{else}:\\ \;\;\;\;\left|y - x\right| \cdot 0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -5.8e-87) (* 0.5 (+ x y)) (* (fabs (- y x)) 0.5)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -5.8e-87) {
		tmp = 0.5 * (x + y);
	} else {
		tmp = fabs((y - x)) * 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 (x <= (-5.8d-87)) then
        tmp = 0.5d0 * (x + y)
    else
        tmp = abs((y - x)) * 0.5d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -5.8e-87) {
		tmp = 0.5 * (x + y);
	} else {
		tmp = Math.abs((y - x)) * 0.5;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -5.8e-87:
		tmp = 0.5 * (x + y)
	else:
		tmp = math.fabs((y - x)) * 0.5
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -5.8e-87)
		tmp = Float64(0.5 * Float64(x + y));
	else
		tmp = Float64(abs(Float64(y - x)) * 0.5);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -5.8e-87)
		tmp = 0.5 * (x + y);
	else
		tmp = abs((y - x)) * 0.5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -5.8e-87], N[(0.5 * N[(x + y), $MachinePrecision]), $MachinePrecision], N[(N[Abs[N[(y - x), $MachinePrecision]], $MachinePrecision] * 0.5), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.7999999999999998e-87

   1. Initial program 100.0%

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

      1. add-sqr-sqrt 27.0%

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

      2. pow2 27.0%

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

      3. +-commutative 27.0%

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

      4. div-inv 27.0%

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

      5. fma-def 27.0%

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

      6. add-sqr-sqrt 10.9%

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

      7. fabs-sqr 10.9%

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

      8. add-sqr-sqrt 11.0%

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

      9. metadata-eval 11.0%

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

   3. Applied egg-rr 11.0%

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

   4. Taylor expanded in y around 0 84.0%

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

      1. +-commutative 84.0%

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

      2. associate-+r+ 84.0%

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

      3. distribute-lft1-in 84.0%

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

      4. metadata-eval 84.0%

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

      5. distribute-lft-out 84.0%

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

   6. Simplified 84.0%

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

   if -5.7999999999999998e-87 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 67.2%

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

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{-87}:\\ \;\;\;\;0.5 \cdot \left(x + y\right)\\ \mathbf{else}:\\ \;\;\;\;\left|y - x\right| \cdot 0.5\\ \end{array} \]

Alternative 3: 30.8% accurate, 21.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 6.5 \cdot 10^{-291}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot 0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y 6.5e-291) x (* y 0.5)))

C

double code(double x, double y) {
	double tmp;
	if (y <= 6.5e-291) {
		tmp = x;
	} else {
		tmp = y * 0.5;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= 6.5d-291) then
        tmp = x
    else
        tmp = y * 0.5d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= 6.5e-291) {
		tmp = x;
	} else {
		tmp = y * 0.5;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 6.5e-291:
		tmp = x
	else:
		tmp = y * 0.5
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 6.5e-291)
		tmp = x;
	else
		tmp = Float64(y * 0.5);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 6.5e-291)
		tmp = x;
	else
		tmp = y * 0.5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 6.5e-291], x, N[(y * 0.5), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 6.50000000000000002e-291

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 11.3%

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

   if 6.50000000000000002e-291 < y

   1. Initial program 100.0%

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

      1. add-sqr-sqrt 71.6%

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

      2. pow2 71.6%

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

      3. +-commutative 71.6%

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

      4. div-inv 71.6%

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

      5. fma-def 71.6%

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

      6. add-sqr-sqrt 50.8%

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

      7. fabs-sqr 50.8%

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

      8. add-sqr-sqrt 54.6%

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

      9. metadata-eval 54.6%

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

   3. Applied egg-rr 54.6%

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

   4. Taylor expanded in x around 0 51.2%

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

      1. unpow2 51.2%

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

      2. rem-square-sqrt 52.1%

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

   6. Simplified 52.1%

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

4. Final simplification 29.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 6.5 \cdot 10^{-291}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot 0.5\\ \end{array} \]

Alternative 4: 44.9% accurate, 21.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 3.25 \cdot 10^{-15}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;y \cdot 0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y 3.25e-15) (* x 0.5) (* y 0.5)))

C

double code(double x, double y) {
	double tmp;
	if (y <= 3.25e-15) {
		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 <= 3.25d-15) 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 <= 3.25e-15) {
		tmp = x * 0.5;
	} else {
		tmp = y * 0.5;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 3.25e-15:
		tmp = x * 0.5
	else:
		tmp = y * 0.5
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 3.25e-15)
		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 <= 3.25e-15)
		tmp = x * 0.5;
	else
		tmp = y * 0.5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 3.25e-15], N[(x * 0.5), $MachinePrecision], N[(y * 0.5), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 3.24999999999999996e-15

   1. Initial program 99.9%

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

      1. add-sqr-sqrt 70.4%

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

      2. pow2 70.4%

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

      3. +-commutative 70.4%

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

      4. div-inv 70.4%

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

      5. fma-def 70.4%

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

      6. add-sqr-sqrt 7.1%

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

      7. fabs-sqr 7.1%

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

      8. add-sqr-sqrt 12.1%

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

      9. metadata-eval 12.1%

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

   3. Applied egg-rr 12.1%

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

   4. Taylor expanded in y around 0 35.0%

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

      1. distribute-lft1-in 35.0%

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

      2. metadata-eval 35.0%

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

      3. *-commutative 35.0%

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

   6. Simplified 35.0%

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

   if 3.24999999999999996e-15 < y

   1. Initial program 100.0%

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

      1. add-sqr-sqrt 87.6%

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

      2. pow2 87.6%

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

      3. +-commutative 87.6%

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

      4. div-inv 87.6%

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

      5. fma-def 87.6%

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

      6. add-sqr-sqrt 74.2%

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

      7. fabs-sqr 74.2%

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

      8. add-sqr-sqrt 76.7%

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

      9. metadata-eval 76.7%

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

   3. Applied egg-rr 76.7%

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

   4. Taylor expanded in x around 0 73.4%

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

      1. unpow2 73.4%

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

      2. rem-square-sqrt 74.8%

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

   6. Simplified 74.8%

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

4. Final simplification 44.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 3.25 \cdot 10^{-15}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;y \cdot 0.5\\ \end{array} \]

Alternative 5: 54.5% accurate, 21.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. add-sqr-sqrt 74.4%

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

   2. pow2 74.4%

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

   3. +-commutative 74.4%

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

   4. div-inv 74.4%

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

   5. fma-def 74.4%

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

   6. add-sqr-sqrt 22.8%

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

   7. fabs-sqr 22.8%

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

   8. add-sqr-sqrt 27.2%

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

   9. metadata-eval 27.2%

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

3. Applied egg-rr 27.2%

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

4. Taylor expanded in y around 0 52.7%

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

   1. +-commutative 52.7%

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

   2. associate-+r+ 52.7%

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

   3. distribute-lft1-in 52.7%

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

   4. metadata-eval 52.7%

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

   5. distribute-lft-out 52.7%

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

6. Simplified 52.7%

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

7. Final simplification 52.7%

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

Alternative 6: 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. Taylor expanded in x around inf 11.3%

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

3. Final simplification 11.3%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023279 
(FPCore (x y)
  :name "Graphics.Rendering.Chart.Plot.AreaSpots:renderSpotLegend from Chart-1.5.3"
  :precision binary64
  (+ x (/ (fabs (- y x)) 2.0)))