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: 70.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.45 \cdot 10^{-82}:\\ \;\;\;\;0.5 \cdot \left(x + y\right)\\ \mathbf{else}:\\ \;\;\;\;\left|y - x\right| \cdot 0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -3.45e-82) (* 0.5 (+ x y)) (* (fabs (- y x)) 0.5)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -3.45e-82) {
		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 <= (-3.45d-82)) 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 <= -3.45e-82) {
		tmp = 0.5 * (x + y);
	} else {
		tmp = Math.abs((y - x)) * 0.5;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -3.45e-82:
		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 <= -3.45e-82)
		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 <= -3.45e-82)
		tmp = 0.5 * (x + y);
	else
		tmp = abs((y - x)) * 0.5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -3.45e-82], 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 < -3.4500000000000001e-82

   1. Initial program 100.0%

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

      1. flip-+ 43.7%

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

      2. div-sub 43.7%

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

      3. pow2 43.7%

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

      4. div-inv 43.7%

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

      5. add-sqr-sqrt 40.6%

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

      6. fabs-sqr 40.6%

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

      7. add-sqr-sqrt 43.7%

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

      8. metadata-eval 43.7%

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

   3. Applied egg-rr 40.6%

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

   4. Taylor expanded in x around 0 91.2%

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

      1. distribute-lft-out 91.2%

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

   6. Simplified 91.2%

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

   if -3.4500000000000001e-82 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 55.5%

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

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.45 \cdot 10^{-82}:\\ \;\;\;\;0.5 \cdot \left(x + y\right)\\ \mathbf{else}:\\ \;\;\;\;\left|y - x\right| \cdot 0.5\\ \end{array} \]

Alternative 3: 45.9% accurate, 21.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 180:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;y \cdot 0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y 180.0) (* x 0.5) (* y 0.5)))

C

double code(double x, double y) {
	double tmp;
	if (y <= 180.0) {
		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 <= 180.0d0) 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 <= 180.0) {
		tmp = x * 0.5;
	} else {
		tmp = y * 0.5;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 180.0:
		tmp = x * 0.5
	else:
		tmp = y * 0.5
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 180.0)
		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 <= 180.0)
		tmp = x * 0.5;
	else
		tmp = y * 0.5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 180.0], N[(x * 0.5), $MachinePrecision], N[(y * 0.5), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 180

   1. Initial program 99.9%

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

      1. flip-+ 48.7%

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

      2. div-sub 48.7%

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

      3. pow2 48.7%

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

      4. div-inv 48.7%

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

      5. add-sqr-sqrt 17.9%

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

      6. fabs-sqr 17.9%

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

      7. add-sqr-sqrt 35.0%

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

      8. metadata-eval 35.0%

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

   3. Applied egg-rr 21.5%

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

   4. Taylor expanded in x around inf 37.0%

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

      1. *-commutative 37.0%

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

   6. Simplified 37.0%

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

   if 180 < y

   1. Initial program 99.9%

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

      1. flip-+ 32.0%

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

      2. div-sub 31.9%

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

      3. pow2 31.9%

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

      4. div-inv 31.9%

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

      5. add-sqr-sqrt 28.5%

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

      6. fabs-sqr 28.5%

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

      7. add-sqr-sqrt 29.0%

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

      8. metadata-eval 29.0%

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

   3. Applied egg-rr 29.1%

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

   4. Taylor expanded in x around 0 62.6%

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

      1. *-commutative 62.6%

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

   6. Simplified 62.6%

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

4. Final simplification 42.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 180:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;y \cdot 0.5\\ \end{array} \]

Alternative 4: 55.2% 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. flip-+ 45.0%

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

   2. div-sub 45.0%

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

   3. pow2 45.0%

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

   4. div-inv 45.0%

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

   5. add-sqr-sqrt 20.3%

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

   6. fabs-sqr 20.3%

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

   7. add-sqr-sqrt 33.7%

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

   8. metadata-eval 33.7%

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

3. Applied egg-rr 23.2%

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

4. Taylor expanded in x around 0 51.7%

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

   1. distribute-lft-out 51.7%

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

6. Simplified 51.7%

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

7. Final simplification 51.7%

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

Alternative 5: 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. Step-by-step derivation

   1. flip-+ 45.0%

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

   2. div-sub 45.0%

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

   3. pow2 45.0%

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

   4. div-inv 45.0%

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

   5. add-sqr-sqrt 20.3%

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

   6. fabs-sqr 20.3%

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

   7. add-sqr-sqrt 33.7%

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

   8. metadata-eval 33.7%

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

3. Applied egg-rr 23.2%

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

4. Taylor expanded in x around inf 33.7%

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

   1. *-commutative 33.7%

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

6. Simplified 33.7%

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

7. Final simplification 33.7%

   \[\leadsto x \cdot 0.5 \]

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 13.1%

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

3. Final simplification 13.1%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023318 
(FPCore (x y)
  :name "Graphics.Rendering.Chart.Plot.AreaSpots:renderSpotLegend from Chart-1.5.3"
  :precision binary64
  (+ x (/ (fabs (- y x)) 2.0)))