Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendOutside from plot-0.2.3.4, A

Percentage Accurate: 100.0% → 100.0%

Time: 1.3s

Alternatives: 3

Speedup: 1.0×

Specification

Math

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

FPCore

(FPCore (x y) :precision binary64 (+ (+ x y) x))

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return (x + y) + x

Julia

function code(x, y)
	return Float64(Float64(x + y) + x)
end

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y) :precision binary64 (+ (+ x y) x))

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return (x + y) + x

Julia

function code(x, y)
	return Float64(Float64(x + y) + x)
end

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 2 \cdot x + y \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (+ (* 2.0 x) y))

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return (2.0 * x) + y

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[\left(x + y\right) + x \]

2. Taylor expanded in x around 0 100.0%

   \[\leadsto \color{blue}{2 \cdot x + y} \]

3. Final simplification 100.0%

   \[\leadsto 2 \cdot x + y \]

Alternative 2: 74.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+17}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-58}:\\ \;\;\;\;x + x\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+96}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+105}:\\ \;\;\;\;x + x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -2.2e+17)
   y
   (if (<= y 9e-58)
     (+ x x)
     (if (<= y 6e+96) y (if (<= y 6.8e+105) (+ x x) y)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -2.2e+17) {
		tmp = y;
	} else if (y <= 9e-58) {
		tmp = x + x;
	} else if (y <= 6e+96) {
		tmp = y;
	} else if (y <= 6.8e+105) {
		tmp = x + x;
	} else {
		tmp = 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 <= (-2.2d+17)) then
        tmp = y
    else if (y <= 9d-58) then
        tmp = x + x
    else if (y <= 6d+96) then
        tmp = y
    else if (y <= 6.8d+105) then
        tmp = x + x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -2.2e+17) {
		tmp = y;
	} else if (y <= 9e-58) {
		tmp = x + x;
	} else if (y <= 6e+96) {
		tmp = y;
	} else if (y <= 6.8e+105) {
		tmp = x + x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -2.2e+17:
		tmp = y
	elif y <= 9e-58:
		tmp = x + x
	elif y <= 6e+96:
		tmp = y
	elif y <= 6.8e+105:
		tmp = x + x
	else:
		tmp = y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -2.2e+17)
		tmp = y;
	elseif (y <= 9e-58)
		tmp = Float64(x + x);
	elseif (y <= 6e+96)
		tmp = y;
	elseif (y <= 6.8e+105)
		tmp = Float64(x + x);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -2.2e+17)
		tmp = y;
	elseif (y <= 9e-58)
		tmp = x + x;
	elseif (y <= 6e+96)
		tmp = y;
	elseif (y <= 6.8e+105)
		tmp = x + x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -2.2e+17], y, If[LessEqual[y, 9e-58], N[(x + x), $MachinePrecision], If[LessEqual[y, 6e+96], y, If[LessEqual[y, 6.8e+105], N[(x + x), $MachinePrecision], y]]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.2e17 or 9.0000000000000006e-58 < y < 6.0000000000000001e96 or 6.7999999999999999e105 < y

   1. Initial program 100.0%

      \[\left(x + y\right) + x \]

   2. Taylor expanded in x around 0 84.2%

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

   if -2.2e17 < y < 9.0000000000000006e-58 or 6.0000000000000001e96 < y < 6.7999999999999999e105

   1. Initial program 100.0%

      \[\left(x + y\right) + x \]

   2. Taylor expanded in x around inf 78.0%

      \[\leadsto \color{blue}{2 \cdot x} \]
   3. Step-by-step derivation

      1. count-2 78.0%

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

   4. Simplified 78.0%

      \[\leadsto \color{blue}{x + x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+17}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-58}:\\ \;\;\;\;x + x\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+96}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+105}:\\ \;\;\;\;x + x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 3: 51.1% accurate, 5.0× speedup

Math

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

FPCore

(FPCore (x y) :precision binary64 y)

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return y

Julia

function code(x, y)
	return y
end

MATLAB

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

Wolfram

code[x_, y_] := y

Derivation

1. Initial program 100.0%

   \[\left(x + y\right) + x \]

2. Taylor expanded in x around 0 55.1%

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

3. Final simplification 55.1%

   \[\leadsto y \]

Developer target: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ y + 2 \cdot x \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (+ y (* 2.0 x)))

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return y + (2.0 * x)

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023224 
(FPCore (x y)
  :name "Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendOutside from plot-0.2.3.4, A"
  :precision binary64

  :herbie-target
  (+ y (* 2.0 x))

  (+ (+ x y) x))