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

Percentage Accurate: 100.0% → 100.0%

Time: 1.5s

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: 74.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{+62}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq -25000000000:\\ \;\;\;\;x + x\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{-48}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-5}:\\ \;\;\;\;x + x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.35e+62)
   y
   (if (<= y -25000000000.0)
     (+ x x)
     (if (<= y -4.6e-48) y (if (<= y 1.15e-5) (+ x x) y)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.35e+62) {
		tmp = y;
	} else if (y <= -25000000000.0) {
		tmp = x + x;
	} else if (y <= -4.6e-48) {
		tmp = y;
	} else if (y <= 1.15e-5) {
		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 <= (-1.35d+62)) then
        tmp = y
    else if (y <= (-25000000000.0d0)) then
        tmp = x + x
    else if (y <= (-4.6d-48)) then
        tmp = y
    else if (y <= 1.15d-5) 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 <= -1.35e+62) {
		tmp = y;
	} else if (y <= -25000000000.0) {
		tmp = x + x;
	} else if (y <= -4.6e-48) {
		tmp = y;
	} else if (y <= 1.15e-5) {
		tmp = x + x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.35e+62:
		tmp = y
	elif y <= -25000000000.0:
		tmp = x + x
	elif y <= -4.6e-48:
		tmp = y
	elif y <= 1.15e-5:
		tmp = x + x
	else:
		tmp = y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.35e+62)
		tmp = y;
	elseif (y <= -25000000000.0)
		tmp = Float64(x + x);
	elseif (y <= -4.6e-48)
		tmp = y;
	elseif (y <= 1.15e-5)
		tmp = Float64(x + x);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.35e+62)
		tmp = y;
	elseif (y <= -25000000000.0)
		tmp = x + x;
	elseif (y <= -4.6e-48)
		tmp = y;
	elseif (y <= 1.15e-5)
		tmp = x + x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.35e+62], y, If[LessEqual[y, -25000000000.0], N[(x + x), $MachinePrecision], If[LessEqual[y, -4.6e-48], y, If[LessEqual[y, 1.15e-5], N[(x + x), $MachinePrecision], y]]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.35e62 or -2.5e10 < y < -4.6000000000000001e-48 or 1.15e-5 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 75.1%

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

   if -1.35e62 < y < -2.5e10 or -4.6000000000000001e-48 < y < 1.15e-5

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 81.7%

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

      1. count-2 81.7%

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

   4. Simplified 81.7%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{+62}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq -25000000000:\\ \;\;\;\;x + x\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{-48}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-5}:\\ \;\;\;\;x + x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 3: 51.4% 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 46.0%

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

3. Final simplification 46.0%

   \[\leadsto y \]

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 2023171 
(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))