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

Percentage Accurate: 99.9% → 99.9%

Time: 5.1s

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. Add Preprocessing

3. Final simplification 99.9%

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

Alternative 2: 70.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{-34}:\\ \;\;\;\;\left|y - x\right| \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(x + y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -3.5e-34) (* (fabs (- y x)) 0.5) (* 0.5 (+ x y))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -3.5e-34) {
		tmp = fabs((y - x)) * 0.5;
	} else {
		tmp = 0.5 * (x + y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-3.5d-34)) then
        tmp = abs((y - x)) * 0.5d0
    else
        tmp = 0.5d0 * (x + y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -3.5e-34) {
		tmp = Math.abs((y - x)) * 0.5;
	} else {
		tmp = 0.5 * (x + y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -3.5e-34:
		tmp = math.fabs((y - x)) * 0.5
	else:
		tmp = 0.5 * (x + y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -3.5e-34)
		tmp = Float64(abs(Float64(y - x)) * 0.5);
	else
		tmp = Float64(0.5 * Float64(x + y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -3.5e-34)
		tmp = abs((y - x)) * 0.5;
	else
		tmp = 0.5 * (x + y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -3.5e-34], N[(N[Abs[N[(y - x), $MachinePrecision]], $MachinePrecision] * 0.5), $MachinePrecision], N[(0.5 * N[(x + y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.5e-34

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 77.7%

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

   if -3.5e-34 < y

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. div-inv 99.9%

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

      3. fma-def 99.9%

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

      4. add-sqr-sqrt 69.0%

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

      5. fabs-sqr 69.0%

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

      6. add-sqr-sqrt 74.2%

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

      7. metadata-eval 74.2%

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

   4. Applied egg-rr 74.2%

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

   5. Taylor expanded in y around 0 74.2%

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

      1. associate-+r+ 74.2%

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

      2. distribute-rgt1-in 74.2%

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

      3. metadata-eval 74.2%

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

      4. distribute-lft-out 74.2%

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

   7. Simplified 74.2%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{-34}:\\ \;\;\;\;\left|y - x\right| \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(x + y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 45.5% accurate, 13.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 4.4 \cdot 10^{-8}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;y \cdot 0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y 4.4e-8) (* x 0.5) (* y 0.5)))

C

double code(double x, double y) {
	double tmp;
	if (y <= 4.4e-8) {
		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 <= 4.4d-8) 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 <= 4.4e-8) {
		tmp = x * 0.5;
	} else {
		tmp = y * 0.5;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 4.4e-8:
		tmp = x * 0.5
	else:
		tmp = y * 0.5
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 4.4e-8)
		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 <= 4.4e-8)
		tmp = x * 0.5;
	else
		tmp = y * 0.5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 4.4e-8], N[(x * 0.5), $MachinePrecision], N[(y * 0.5), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 4.3999999999999997e-8

   1. Initial program 99.9%

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

      1. add-cube-cbrt 97.8%

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

      2. pow3 97.9%

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

      3. +-commutative 97.9%

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

      4. div-inv 97.9%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\left|y - x\right| \cdot \frac{1}{2}} + x}\right)}^{3} \]

      5. fma-def 97.9%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\mathsf{fma}\left(\left|y - x\right|, \frac{1}{2}, x\right)}}\right)}^{3} \]

      6. add-sqr-sqrt 40.3%

         \[\leadsto {\left(\sqrt[3]{\mathsf{fma}\left(\left|\color{blue}{\sqrt{y - x} \cdot \sqrt{y - x}}\right|, \frac{1}{2}, x\right)}\right)}^{3} \]

      7. fabs-sqr 40.3%

         \[\leadsto {\left(\sqrt[3]{\mathsf{fma}\left(\color{blue}{\sqrt{y - x} \cdot \sqrt{y - x}}, \frac{1}{2}, x\right)}\right)}^{3} \]

      8. add-sqr-sqrt 45.0%

         \[\leadsto {\left(\sqrt[3]{\mathsf{fma}\left(\color{blue}{y - x}, \frac{1}{2}, x\right)}\right)}^{3} \]

      9. metadata-eval 45.0%

         \[\leadsto {\left(\sqrt[3]{\mathsf{fma}\left(y - x, \color{blue}{0.5}, x\right)}\right)}^{3} \]

   4. Applied egg-rr 45.0%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(y - x, 0.5, x\right)}\right)}^{3}} \]

   5. Taylor expanded in y around 0 39.7%

      \[\leadsto \color{blue}{{1}^{0.3333333333333333} \cdot \left(x + -0.5 \cdot x\right)} \]
   6. Step-by-step derivation

      1. pow-base-1 39.7%

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

      2. *-lft-identity 39.7%

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

      3. distribute-rgt1-in 39.7%

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

      4. metadata-eval 39.7%

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

      5. *-commutative 39.7%

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

   7. Simplified 39.7%

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

   if 4.3999999999999997e-8 < y

   1. Initial program 99.9%

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

      1. add-cube-cbrt 98.1%

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

      2. pow3 98.1%

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

      3. +-commutative 98.1%

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

      4. div-inv 98.1%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\left|y - x\right| \cdot \frac{1}{2}} + x}\right)}^{3} \]

      5. fma-def 98.1%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\mathsf{fma}\left(\left|y - x\right|, \frac{1}{2}, x\right)}}\right)}^{3} \]

      6. add-sqr-sqrt 84.5%

         \[\leadsto {\left(\sqrt[3]{\mathsf{fma}\left(\left|\color{blue}{\sqrt{y - x} \cdot \sqrt{y - x}}\right|, \frac{1}{2}, x\right)}\right)}^{3} \]

      7. fabs-sqr 84.5%

         \[\leadsto {\left(\sqrt[3]{\mathsf{fma}\left(\color{blue}{\sqrt{y - x} \cdot \sqrt{y - x}}, \frac{1}{2}, x\right)}\right)}^{3} \]

      8. add-sqr-sqrt 87.2%

         \[\leadsto {\left(\sqrt[3]{\mathsf{fma}\left(\color{blue}{y - x}, \frac{1}{2}, x\right)}\right)}^{3} \]

      9. metadata-eval 87.2%

         \[\leadsto {\left(\sqrt[3]{\mathsf{fma}\left(y - x, \color{blue}{0.5}, x\right)}\right)}^{3} \]

   4. Applied egg-rr 87.2%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(y - x, 0.5, x\right)}\right)}^{3}} \]

   5. Taylor expanded in x around 0 71.6%

      \[\leadsto \color{blue}{0.5 \cdot \left({1}^{0.3333333333333333} \cdot y\right)} \]
   6. Step-by-step derivation

      1. *-commutative 71.6%

         \[\leadsto \color{blue}{\left({1}^{0.3333333333333333} \cdot y\right) \cdot 0.5} \]

      2. pow-base-1 71.6%

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

      3. *-lft-identity 71.6%

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

   7. Simplified 71.6%

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

4. Final simplification 47.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 4.4 \cdot 10^{-8}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;y \cdot 0.5\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 54.7% 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. Add Preprocessing
3. Step-by-step derivation

   1. +-commutative 99.9%

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

   2. div-inv 99.9%

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

   3. fma-def 99.9%

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

   4. add-sqr-sqrt 52.3%

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

   5. fabs-sqr 52.3%

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

   6. add-sqr-sqrt 56.9%

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

   7. metadata-eval 56.9%

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

4. Applied egg-rr 56.9%

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

5. Taylor expanded in y around 0 56.9%

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

   1. associate-+r+ 56.9%

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

   2. distribute-rgt1-in 56.9%

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

   3. metadata-eval 56.9%

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

   4. distribute-lft-out 56.9%

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

7. Simplified 56.9%

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

8. Final simplification 56.9%

   \[\leadsto 0.5 \cdot \left(x + y\right) \]
9. Add Preprocessing

Alternative 5: 30.6% 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. add-cube-cbrt 97.9%

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

   2. pow3 98.0%

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

   3. +-commutative 98.0%

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

   4. div-inv 98.0%

      \[\leadsto {\left(\sqrt[3]{\color{blue}{\left|y - x\right| \cdot \frac{1}{2}} + x}\right)}^{3} \]

   5. fma-def 98.0%

      \[\leadsto {\left(\sqrt[3]{\color{blue}{\mathsf{fma}\left(\left|y - x\right|, \frac{1}{2}, x\right)}}\right)}^{3} \]

   6. add-sqr-sqrt 51.7%

      \[\leadsto {\left(\sqrt[3]{\mathsf{fma}\left(\left|\color{blue}{\sqrt{y - x} \cdot \sqrt{y - x}}\right|, \frac{1}{2}, x\right)}\right)}^{3} \]

   7. fabs-sqr 51.7%

      \[\leadsto {\left(\sqrt[3]{\mathsf{fma}\left(\color{blue}{\sqrt{y - x} \cdot \sqrt{y - x}}, \frac{1}{2}, x\right)}\right)}^{3} \]

   8. add-sqr-sqrt 55.8%

      \[\leadsto {\left(\sqrt[3]{\mathsf{fma}\left(\color{blue}{y - x}, \frac{1}{2}, x\right)}\right)}^{3} \]

   9. metadata-eval 55.8%

      \[\leadsto {\left(\sqrt[3]{\mathsf{fma}\left(y - x, \color{blue}{0.5}, x\right)}\right)}^{3} \]

4. Applied egg-rr 55.8%

   \[\leadsto \color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(y - x, 0.5, x\right)}\right)}^{3}} \]

5. Taylor expanded in y around 0 34.0%

   \[\leadsto \color{blue}{{1}^{0.3333333333333333} \cdot \left(x + -0.5 \cdot x\right)} \]
6. Step-by-step derivation

   1. pow-base-1 34.0%

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

   2. *-lft-identity 34.0%

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

   3. distribute-rgt1-in 34.0%

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

   4. metadata-eval 34.0%

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

   5. *-commutative 34.0%

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

7. Simplified 34.0%

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

8. Final simplification 34.0%

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

Alternative 6: 11.3% accurate, 107.0× speedup

Math

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

FPCore

(FPCore (x y) :precision binary64 x)

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return x

Julia

function code(x, y)
	return x
end

MATLAB

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

Wolfram

code[x_, y_] := x

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in x around inf 11.5%

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

4. Final simplification 11.5%

   \[\leadsto x \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024019 
(FPCore (x y)
  :name "Graphics.Rendering.Chart.Plot.AreaSpots:renderSpotLegend from Chart-1.5.3"
  :precision binary64
  (+ x (/ (fabs (- y x)) 2.0)))