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

Percentage Accurate: 99.9% → 99.9%

Time: 2.8s

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. Add Preprocessing

Alternative 2: 69.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+37}:\\ \;\;\;\;\left|y - x\right| \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(x + y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -6e+37) (* (fabs (- y x)) 0.5) (* 0.5 (+ x y))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -6e+37) {
		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 <= (-6d+37)) 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 <= -6e+37) {
		tmp = Math.abs((y - x)) * 0.5;
	} else {
		tmp = 0.5 * (x + y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -6e+37:
		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 <= -6e+37)
		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 <= -6e+37)
		tmp = abs((y - x)) * 0.5;
	else
		tmp = 0.5 * (x + y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -6e+37], 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 < -6.00000000000000043e37

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 92.0%

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

   if -6.00000000000000043e37 < y

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. div-inv 99.8%

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

      3. add-sqr-sqrt 62.1%

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

      4. fabs-sqr 62.1%

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

      5. add-sqr-sqrt 68.5%

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

      6. metadata-eval 68.5%

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

   4. Applied egg-rr 68.5%

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

   5. Taylor expanded in y around 0 68.5%

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

      1. associate-+r+ 68.6%

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

      2. distribute-rgt1-in 68.6%

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

      3. metadata-eval 68.6%

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

      4. distribute-lft-out 68.6%

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

   7. Simplified 68.6%

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

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+37}:\\ \;\;\;\;\left|y - x\right| \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(x + y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 45.7% accurate, 13.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 6.8 \cdot 10^{-75}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;y \cdot 0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y 6.8e-75) (* x 0.5) (* y 0.5)))

C

double code(double x, double y) {
	double tmp;
	if (y <= 6.8e-75) {
		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 <= 6.8d-75) 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 <= 6.8e-75) {
		tmp = x * 0.5;
	} else {
		tmp = y * 0.5;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 6.8e-75:
		tmp = x * 0.5
	else:
		tmp = y * 0.5
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 6.8e-75)
		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 <= 6.8e-75)
		tmp = x * 0.5;
	else
		tmp = y * 0.5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 6.8e-75], N[(x * 0.5), $MachinePrecision], N[(y * 0.5), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 6.8000000000000003e-75

   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. add-sqr-sqrt 32.3%

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

      4. fabs-sqr 32.3%

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

      5. add-sqr-sqrt 38.6%

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

      6. metadata-eval 38.6%

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

   4. Applied egg-rr 38.6%

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

   5. Taylor expanded in y around 0 36.6%

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

      1. distribute-rgt1-in 36.6%

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

      2. metadata-eval 36.6%

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

      3. *-commutative 36.6%

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

   7. Simplified 36.6%

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

   if 6.8000000000000003e-75 < 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. add-sqr-sqrt 87.7%

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

      4. fabs-sqr 87.7%

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

      5. add-sqr-sqrt 90.5%

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

      6. metadata-eval 90.5%

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

   4. Applied egg-rr 90.5%

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

   5. Taylor expanded in y around inf 76.0%

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

4. Final simplification 48.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 6.8 \cdot 10^{-75}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;y \cdot 0.5\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 31.1% accurate, 13.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 3.75 \cdot 10^{-121}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot 0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y 3.75e-121) x (* y 0.5)))

C

double code(double x, double y) {
	double tmp;
	if (y <= 3.75e-121) {
		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 <= 3.75d-121) 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 <= 3.75e-121) {
		tmp = x;
	} else {
		tmp = y * 0.5;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 3.75e-121:
		tmp = x
	else:
		tmp = y * 0.5
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 3.75e-121)
		tmp = x;
	else
		tmp = Float64(y * 0.5);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 3.75e-121)
		tmp = x;
	else
		tmp = y * 0.5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 3.75e-121], x, N[(y * 0.5), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 3.75000000000000013e-121

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 13.3%

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

   if 3.75000000000000013e-121 < 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. add-sqr-sqrt 86.7%

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

      4. fabs-sqr 86.7%

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

      5. add-sqr-sqrt 89.6%

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

      6. metadata-eval 89.6%

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

   4. Applied egg-rr 89.6%

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

   5. Taylor expanded in y around inf 71.8%

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

4. Final simplification 33.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 3.75 \cdot 10^{-121}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot 0.5\\ \end{array} \]
5. Add Preprocessing

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. 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. add-sqr-sqrt 49.2%

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

   4. fabs-sqr 49.2%

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

   5. add-sqr-sqrt 54.4%

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

   6. metadata-eval 54.4%

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

4. Applied egg-rr 54.4%

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

5. Taylor expanded in y around 0 54.4%

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

   1. associate-+r+ 54.4%

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

   2. distribute-rgt1-in 54.4%

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

   3. metadata-eval 54.4%

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

   4. distribute-lft-out 54.4%

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

7. Simplified 54.4%

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

Reproduce

herbie shell --seed 2024096 
(FPCore (x y)
  :name "Graphics.Rendering.Chart.Plot.AreaSpots:renderSpotLegend from Chart-1.5.3"
  :precision binary64
  (+ x (/ (fabs (- y x)) 2.0)))