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

Percentage Accurate: 100.0% → 100.0%

Time: 1.2s

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: 74.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -12.5 \lor \neg \left(x \leq 4.3 \cdot 10^{+58}\right):\\ \;\;\;\;x + x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -12.5) (not (<= x 4.3e+58))) (+ x x) y))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -12.5) || !(x <= 4.3e+58)) {
		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 ((x <= (-12.5d0)) .or. (.not. (x <= 4.3d+58))) 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 ((x <= -12.5) || !(x <= 4.3e+58)) {
		tmp = x + x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -12.5) or not (x <= 4.3e+58):
		tmp = x + x
	else:
		tmp = y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -12.5) || !(x <= 4.3e+58))
		tmp = Float64(x + x);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -12.5) || ~((x <= 4.3e+58)))
		tmp = x + x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -12.5], N[Not[LessEqual[x, 4.3e+58]], $MachinePrecision]], N[(x + x), $MachinePrecision], y]

Derivation

1. Split input into 2 regimes

2. if x < -12.5 or 4.29999999999999991e58 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 78.4%

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

      1. count-2 78.4%

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

   4. Simplified 78.4%

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

   if -12.5 < x < 4.29999999999999991e58

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 80.5%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -12.5 \lor \neg \left(x \leq 4.3 \cdot 10^{+58}\right):\\ \;\;\;\;x + x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 3: 50.5% 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 55.0%

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

3. Final simplification 55.0%

   \[\leadsto y \]

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 2023240 
(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))