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

Percentage Accurate: 99.9% → 99.9%

Time: 10.9s

Alternatives: 5

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. Add Preprocessing

Alternative 2: 58.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in y around inf

   \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{fabs.f64}\left(\color{blue}{y}\right), 2\right)\right) \]
4. Step-by-step derivation

5. Simplified 58.9%

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

Alternative 3: 13.9% accurate, 11.9× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(0.75 + \frac{y \cdot 0.2}{x}\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* x (+ 0.75 (/ (* y 0.2) x))))

C

double code(double x, double y) {
	return x * (0.75 + ((y * 0.2) / x));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x * (0.75d0 + ((y * 0.2d0) / x))
end function

Java

public static double code(double x, double y) {
	return x * (0.75 + ((y * 0.2) / x));
}

Python

def code(x, y):
	return x * (0.75 + ((y * 0.2) / x))

Julia

function code(x, y)
	return Float64(x * Float64(0.75 + Float64(Float64(y * 0.2) / x)))
end

MATLAB

function tmp = code(x, y)
	tmp = x * (0.75 + ((y * 0.2) / x));
end

Wolfram

code[x_, y_] := N[(x * N[(0.75 + N[(N[(y * 0.2), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

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

   1. flip-+ N/A

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

   2. flip-- N/A

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

   3. associate-/l/ N/A

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

   4. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right) - \left(\frac{\left|y - x\right|}{2} \cdot \frac{\left|y - x\right|}{2}\right) \cdot \left(\frac{\left|y - x\right|}{2} \cdot \frac{\left|y - x\right|}{2}\right)\right), \color{blue}{\left(\left(x - \frac{\left|y - x\right|}{2}\right) \cdot \left(x \cdot x + \frac{\left|y - x\right|}{2} \cdot \frac{\left|y - x\right|}{2}\right)\right)}\right) \]

4. Applied egg-rr 28.6%

   \[\leadsto \color{blue}{\frac{x \cdot \left(x \cdot \left(x \cdot x\right)\right) - \frac{\left(\left(y - x\right) \cdot \left(y - x\right)\right) \cdot \left(\left(y - x\right) \cdot \left(y - x\right)\right)}{16}}{\left(x + \frac{\left|y - x\right|}{-2}\right) \cdot \left(x \cdot x + \frac{\left(y - x\right) \cdot \left(y - x\right)}{4}\right)}} \]

5. Taylor expanded in x around inf

   \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, x\right)\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{\_.f64}\left(y, x\right)\right)\right), 16\right)\right), \color{blue}{\left(\frac{5}{4} \cdot {x}^{3}\right)}\right) \]
6. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, x\right)\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{\_.f64}\left(y, x\right)\right)\right), 16\right)\right), \left({x}^{3} \cdot \color{blue}{\frac{5}{4}}\right)\right) \]

   2. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, x\right)\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{\_.f64}\left(y, x\right)\right)\right), 16\right)\right), \mathsf{*.f64}\left(\left({x}^{3}\right), \color{blue}{\frac{5}{4}}\right)\right) \]

   3. cube-mult N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, x\right)\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{\_.f64}\left(y, x\right)\right)\right), 16\right)\right), \mathsf{*.f64}\left(\left(x \cdot \left(x \cdot x\right)\right), \frac{5}{4}\right)\right) \]

   4. unpow2 N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, x\right)\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{\_.f64}\left(y, x\right)\right)\right), 16\right)\right), \mathsf{*.f64}\left(\left(x \cdot {x}^{2}\right), \frac{5}{4}\right)\right) \]

   5. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, x\right)\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{\_.f64}\left(y, x\right)\right)\right), 16\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \left({x}^{2}\right)\right), \frac{5}{4}\right)\right) \]

   6. unpow2 N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, x\right)\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{\_.f64}\left(y, x\right)\right)\right), 16\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \left(x \cdot x\right)\right), \frac{5}{4}\right)\right) \]

   7. *-lowering-*.f64 3.8%

      \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, x\right)\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{\_.f64}\left(y, x\right)\right)\right), 16\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, x\right)\right), \frac{5}{4}\right)\right) \]

7. Simplified 3.8%

   \[\leadsto \frac{x \cdot \left(x \cdot \left(x \cdot x\right)\right) - \frac{\left(\left(y - x\right) \cdot \left(y - x\right)\right) \cdot \left(\left(y - x\right) \cdot \left(y - x\right)\right)}{16}}{\color{blue}{\left(x \cdot \left(x \cdot x\right)\right) \cdot 1.25}} \]

8. Taylor expanded in x around inf

   \[\leadsto \color{blue}{x \cdot \left(\frac{3}{4} + \frac{1}{5} \cdot \frac{y}{x}\right)} \]
9. Step-by-step derivation

   1. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{3}{4} + \frac{1}{5} \cdot \frac{y}{x}\right)}\right) \]

   2. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{3}{4}, \color{blue}{\left(\frac{1}{5} \cdot \frac{y}{x}\right)}\right)\right) \]

   3. associate-*r/ N/A

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{3}{4}, \left(\frac{\frac{1}{5} \cdot y}{\color{blue}{x}}\right)\right)\right) \]

   4. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{3}{4}, \mathsf{/.f64}\left(\left(\frac{1}{5} \cdot y\right), \color{blue}{x}\right)\right)\right) \]

   5. *-commutative N/A

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{3}{4}, \mathsf{/.f64}\left(\left(y \cdot \frac{1}{5}\right), x\right)\right)\right) \]

   6. *-lowering-*.f64 13.4%

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{3}{4}, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \frac{1}{5}\right), x\right)\right)\right) \]

10. Simplified 13.4%

    \[\leadsto \color{blue}{x \cdot \left(0.75 + \frac{y \cdot 0.2}{x}\right)} \]
11. Add Preprocessing

Alternative 4: 11.5% accurate, 35.7× speedup

Math

\[\begin{array}{l} \\ x \cdot 0.75 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* x 0.75))

C

double code(double x, double y) {
	return x * 0.75;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x * 0.75d0
end function

Java

public static double code(double x, double y) {
	return x * 0.75;
}

Python

def code(x, y):
	return x * 0.75

Julia

function code(x, y)
	return Float64(x * 0.75)
end

MATLAB

function tmp = code(x, y)
	tmp = x * 0.75;
end

Wolfram

code[x_, y_] := N[(x * 0.75), $MachinePrecision]

Derivation

1. Initial program 99.9%

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

   1. +-commutative N/A

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

   2. flip-+ N/A

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

   3. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\left(\frac{\left|y - x\right|}{2} \cdot \frac{\left|y - x\right|}{2} - x \cdot x\right), \color{blue}{\left(\frac{\left|y - x\right|}{2} - x\right)}\right) \]

   4. --lowering--.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\left(\frac{\left|y - x\right|}{2} \cdot \frac{\left|y - x\right|}{2}\right), \left(x \cdot x\right)\right), \left(\color{blue}{\frac{\left|y - x\right|}{2}} - x\right)\right) \]

   5. frac-times N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\left(\frac{\left|y - x\right| \cdot \left|y - x\right|}{2 \cdot 2}\right), \left(x \cdot x\right)\right), \left(\frac{\color{blue}{\left|y - x\right|}}{2} - x\right)\right) \]

   6. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(\left|y - x\right| \cdot \left|y - x\right|\right), \left(2 \cdot 2\right)\right), \left(x \cdot x\right)\right), \left(\frac{\color{blue}{\left|y - x\right|}}{2} - x\right)\right) \]

   7. sqr-abs N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(\left(y - x\right) \cdot \left(y - x\right)\right), \left(2 \cdot 2\right)\right), \left(x \cdot x\right)\right), \left(\frac{\left|\color{blue}{y - x}\right|}{2} - x\right)\right) \]

   8. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(y - x\right), \left(y - x\right)\right), \left(2 \cdot 2\right)\right), \left(x \cdot x\right)\right), \left(\frac{\left|\color{blue}{y - x}\right|}{2} - x\right)\right) \]

   9. --lowering--.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(y - x\right)\right), \left(2 \cdot 2\right)\right), \left(x \cdot x\right)\right), \left(\frac{\left|\color{blue}{y} - x\right|}{2} - x\right)\right) \]

   10. --lowering--.f64 N/A

       \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{\_.f64}\left(y, x\right)\right), \left(2 \cdot 2\right)\right), \left(x \cdot x\right)\right), \left(\frac{\left|y - \color{blue}{x}\right|}{2} - x\right)\right) \]

   11. metadata-eval N/A

       \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{\_.f64}\left(y, x\right)\right), 4\right), \left(x \cdot x\right)\right), \left(\frac{\left|y - x\right|}{2} - x\right)\right) \]

   12. *-lowering-*.f64 N/A

       \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{\_.f64}\left(y, x\right)\right), 4\right), \mathsf{*.f64}\left(x, x\right)\right), \left(\frac{\left|y - x\right|}{\color{blue}{2}} - x\right)\right) \]

   13. --lowering--.f64 N/A

       \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{\_.f64}\left(y, x\right)\right), 4\right), \mathsf{*.f64}\left(x, x\right)\right), \mathsf{\_.f64}\left(\left(\frac{\left|y - x\right|}{2}\right), \color{blue}{x}\right)\right) \]

   14. /-lowering-/.f64 N/A

       \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{\_.f64}\left(y, x\right)\right), 4\right), \mathsf{*.f64}\left(x, x\right)\right), \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(\left|y - x\right|\right), 2\right), x\right)\right) \]

   15. fabs-lowering-fabs.f64 N/A

       \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{\_.f64}\left(y, x\right)\right), 4\right), \mathsf{*.f64}\left(x, x\right)\right), \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{fabs.f64}\left(\left(y - x\right)\right), 2\right), x\right)\right) \]

   16. --lowering--.f64 58.7%

       \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{\_.f64}\left(y, x\right)\right), 4\right), \mathsf{*.f64}\left(x, x\right)\right), \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{fabs.f64}\left(\mathsf{\_.f64}\left(y, x\right)\right), 2\right), x\right)\right) \]

4. Applied egg-rr 58.7%

   \[\leadsto \color{blue}{\frac{\frac{\left(y - x\right) \cdot \left(y - x\right)}{4} - x \cdot x}{\frac{\left|y - x\right|}{2} - x}} \]

5. Taylor expanded in x around inf

   \[\leadsto \color{blue}{\frac{3}{4} \cdot x} \]
6. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto x \cdot \color{blue}{\frac{3}{4}} \]

   2. *-lowering-*.f64 11.3%

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\frac{3}{4}}\right) \]

7. Simplified 11.3%

   \[\leadsto \color{blue}{x \cdot 0.75} \]
8. Add Preprocessing

Alternative 5: 11.5% 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

   \[\leadsto \color{blue}{x} \]
4. Step-by-step derivation

5. Simplified 11.3%

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

Reproduce

herbie shell --seed 2024160 
(FPCore (x y)
  :name "Graphics.Rendering.Chart.Plot.AreaSpots:renderSpotLegend from Chart-1.5.3"
  :precision binary64
  (+ x (/ (fabs (- y x)) 2.0)))