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

Percentage Accurate: 99.9% → 99.9%

Time: 24.3s

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: 76.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + \frac{\left|y\right|}{2}\\ \mathbf{if}\;y \leq -1.5 \cdot 10^{-103}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-25}:\\ \;\;\;\;\frac{\left|x\right|}{2} + x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ x (/ (fabs y) 2.0))))
   (if (<= y -1.5e-103) t_0 (if (<= y 6.2e-25) (+ (/ (fabs x) 2.0) x) t_0))))

C

double code(double x, double y) {
	double t_0 = x + (fabs(y) / 2.0);
	double tmp;
	if (y <= -1.5e-103) {
		tmp = t_0;
	} else if (y <= 6.2e-25) {
		tmp = (fabs(x) / 2.0) + x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x + (abs(y) / 2.0d0)
    if (y <= (-1.5d-103)) then
        tmp = t_0
    else if (y <= 6.2d-25) then
        tmp = (abs(x) / 2.0d0) + x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = x + (Math.abs(y) / 2.0);
	double tmp;
	if (y <= -1.5e-103) {
		tmp = t_0;
	} else if (y <= 6.2e-25) {
		tmp = (Math.abs(x) / 2.0) + x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x + (math.fabs(y) / 2.0)
	tmp = 0
	if y <= -1.5e-103:
		tmp = t_0
	elif y <= 6.2e-25:
		tmp = (math.fabs(x) / 2.0) + x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x + Float64(abs(y) / 2.0))
	tmp = 0.0
	if (y <= -1.5e-103)
		tmp = t_0;
	elseif (y <= 6.2e-25)
		tmp = Float64(Float64(abs(x) / 2.0) + x);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x + (abs(y) / 2.0);
	tmp = 0.0;
	if (y <= -1.5e-103)
		tmp = t_0;
	elseif (y <= 6.2e-25)
		tmp = (abs(x) / 2.0) + x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x + N[(N[Abs[y], $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.5e-103], t$95$0, If[LessEqual[y, 6.2e-25], N[(N[(N[Abs[x], $MachinePrecision] / 2.0), $MachinePrecision] + x), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.5e-103 or 6.19999999999999989e-25 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -1.5e-103 < y < 6.19999999999999989e-25

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 76.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{-24}:\\ \;\;\;\;\frac{x}{2}\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{+20}:\\ \;\;\;\;x + \frac{\left|y\right|}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{2} + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.2e-24)
   (/ x 2.0)
   (if (<= x 2.1e+20) (+ x (/ (fabs y) 2.0)) (+ (/ x 2.0) x))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.2e-24) {
		tmp = x / 2.0;
	} else if (x <= 2.1e+20) {
		tmp = x + (fabs(y) / 2.0);
	} else {
		tmp = (x / 2.0) + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-1.2d-24)) then
        tmp = x / 2.0d0
    else if (x <= 2.1d+20) then
        tmp = x + (abs(y) / 2.0d0)
    else
        tmp = (x / 2.0d0) + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -1.2e-24) {
		tmp = x / 2.0;
	} else if (x <= 2.1e+20) {
		tmp = x + (Math.abs(y) / 2.0);
	} else {
		tmp = (x / 2.0) + x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.2e-24:
		tmp = x / 2.0
	elif x <= 2.1e+20:
		tmp = x + (math.fabs(y) / 2.0)
	else:
		tmp = (x / 2.0) + x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.2e-24)
		tmp = Float64(x / 2.0);
	elseif (x <= 2.1e+20)
		tmp = Float64(x + Float64(abs(y) / 2.0));
	else
		tmp = Float64(Float64(x / 2.0) + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.2e-24)
		tmp = x / 2.0;
	elseif (x <= 2.1e+20)
		tmp = x + (abs(y) / 2.0);
	else
		tmp = (x / 2.0) + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.2e-24], N[(x / 2.0), $MachinePrecision], If[LessEqual[x, 2.1e+20], N[(x + N[(N[Abs[y], $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(x / 2.0), $MachinePrecision] + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.1999999999999999e-24

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   10. Applied egg-rr 0

       \[\leadsto expr\]

   if -1.1999999999999999e-24 < x < 2.1e20

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if 2.1e20 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 4: 50.4% accurate, 10.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{-310}:\\ \;\;\;\;\frac{x}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{2} + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -5e-310) (/ x 2.0) (+ (/ x 2.0) x)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -5e-310) {
		tmp = x / 2.0;
	} else {
		tmp = (x / 2.0) + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-5d-310)) then
        tmp = x / 2.0d0
    else
        tmp = (x / 2.0d0) + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -5e-310) {
		tmp = x / 2.0;
	} else {
		tmp = (x / 2.0) + x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -5e-310:
		tmp = x / 2.0
	else:
		tmp = (x / 2.0) + x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -5e-310)
		tmp = Float64(x / 2.0);
	else
		tmp = Float64(Float64(x / 2.0) + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -5e-310)
		tmp = x / 2.0;
	else
		tmp = (x / 2.0) + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -5e-310], N[(x / 2.0), $MachinePrecision], N[(N[(x / 2.0), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.999999999999985e-310

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   10. Applied egg-rr 0

       \[\leadsto expr\]

   if -4.999999999999985e-310 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 30.9% accurate, 35.7× speedup

Math

\[\begin{array}{l} \\ \frac{x}{2} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

public static double code(double x, double y) {
	return x / 2.0;
}

Python

def code(x, y):
	return x / 2.0

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in y around 0 0

   \[\leadsto expr\]

5. Simplified 0

   \[\leadsto expr\]

6. Taylor expanded in x around 0 0

   \[\leadsto expr\]

8. Simplified 0

   \[\leadsto expr\]

10. Applied egg-rr 0

    \[\leadsto expr\]
11. 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 0

   \[\leadsto expr\]

5. Simplified 0

   \[\leadsto expr\]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024111 
(FPCore (x y)
  :name "Graphics.Rendering.Chart.Plot.AreaSpots:renderSpotLegend from Chart-1.5.3"
  :precision binary64
  (+ x (/ (fabs (- y x)) 2.0)))