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

Percentage Accurate: 100.0% → 100.0%

Time: 1.8s

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

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[\left(x + y\right) + x \]
2. Step-by-step derivation

   1. +-commutative N/A

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

   2. associate-+l+ N/A

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

   3. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{\left(x + x\right)}\right) \]

   4. count-2 N/A

      \[\leadsto \mathsf{+.f64}\left(y, \left(2 \cdot \color{blue}{x}\right)\right) \]

   5. *-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(y, \left(x \cdot \color{blue}{2}\right)\right) \]

   6. *-lowering-*.f64 100.0%

      \[\leadsto \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(x, \color{blue}{2}\right)\right) \]

3. Simplified 100.0%

   \[\leadsto \color{blue}{y + x \cdot 2} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 2: 74.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{-63}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{+19}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -4.2e-63) (* x 2.0) (if (<= x 1.65e+19) y (* x 2.0))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -4.2e-63) {
		tmp = x * 2.0;
	} else if (x <= 1.65e+19) {
		tmp = y;
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-4.2d-63)) then
        tmp = x * 2.0d0
    else if (x <= 1.65d+19) then
        tmp = y
    else
        tmp = x * 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -4.2e-63) {
		tmp = x * 2.0;
	} else if (x <= 1.65e+19) {
		tmp = y;
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -4.2e-63:
		tmp = x * 2.0
	elif x <= 1.65e+19:
		tmp = y
	else:
		tmp = x * 2.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -4.2e-63)
		tmp = Float64(x * 2.0);
	elseif (x <= 1.65e+19)
		tmp = y;
	else
		tmp = Float64(x * 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -4.2e-63)
		tmp = x * 2.0;
	elseif (x <= 1.65e+19)
		tmp = y;
	else
		tmp = x * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -4.2e-63], N[(x * 2.0), $MachinePrecision], If[LessEqual[x, 1.65e+19], y, N[(x * 2.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -4.2e-63 or 1.65e19 < x

   1. Initial program 100.0%

      \[\left(x + y\right) + x \]
   2. Step-by-step derivation

      1. +-commutative N/A

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

      2. associate-+l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{\left(x + x\right)}\right) \]

      4. count-2 N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(2 \cdot \color{blue}{x}\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(x \cdot \color{blue}{2}\right)\right) \]

      6. *-lowering-*.f64 100.0%

         \[\leadsto \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(x, \color{blue}{2}\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{y + x \cdot 2} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0

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

      1. *-lowering-*.f64 80.6%

         \[\leadsto \mathsf{*.f64}\left(2, \color{blue}{x}\right) \]

   7. Simplified 80.6%

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

   if -4.2e-63 < x < 1.65e19

   1. Initial program 100.0%

      \[\left(x + y\right) + x \]
   2. Step-by-step derivation

      1. +-commutative N/A

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

      2. associate-+l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{\left(x + x\right)}\right) \]

      4. count-2 N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(2 \cdot \color{blue}{x}\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(x \cdot \color{blue}{2}\right)\right) \]

      6. *-lowering-*.f64 100.0%

         \[\leadsto \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(x, \color{blue}{2}\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{y + x \cdot 2} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y} \]
   6. Step-by-step derivation

   7. Simplified 78.0%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{-63}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{+19}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 51.2% 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. Step-by-step derivation

   1. +-commutative N/A

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

   2. associate-+l+ N/A

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

   3. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{\left(x + x\right)}\right) \]

   4. count-2 N/A

      \[\leadsto \mathsf{+.f64}\left(y, \left(2 \cdot \color{blue}{x}\right)\right) \]

   5. *-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(y, \left(x \cdot \color{blue}{2}\right)\right) \]

   6. *-lowering-*.f64 100.0%

      \[\leadsto \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(x, \color{blue}{2}\right)\right) \]

3. Simplified 100.0%

   \[\leadsto \color{blue}{y + x \cdot 2} \]
4. Add Preprocessing

5. Taylor expanded in y around inf

   \[\leadsto \color{blue}{y} \]
6. Step-by-step derivation

7. Simplified 46.6%

   \[\leadsto \color{blue}{y} \]
8. Add Preprocessing

Developer Target 1: 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 2024161 
(FPCore (x y)
  :name "Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendOutside from plot-0.2.3.4, A"
  :precision binary64

  :alt
  (! :herbie-platform default (+ y (* 2 x)))

  (+ (+ x y) x))