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

Percentage Accurate: 100.0% → 100.0%

Time: 3.1s

Alternatives: 6

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

\[\begin{array}{l} \\ \mathsf{fma}\left(x, 2, y\right) \end{array} \]

FPCore

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

C

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

Julia

function code(x, y)
	return fma(x, 2.0, y)
end

Wolfram

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

Derivation

1. Initial program 100.0%

   \[\left(x + y\right) + x \]
2. Add Preprocessing

3. Taylor expanded in x around 0

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

   1. +-commutative N/A

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

   2. *-rgt-identity N/A

      \[\leadsto \left(2 \cdot x\right) \cdot 1 + y \]

   3. *-inverses N/A

      \[\leadsto \left(2 \cdot x\right) \cdot \frac{y}{y} + y \]

   4. associate-/l* N/A

      \[\leadsto \frac{\left(2 \cdot x\right) \cdot y}{y} + y \]

   5. associate-*l/ N/A

      \[\leadsto \frac{2 \cdot x}{y} \cdot y + y \]

   6. associate-*r/ N/A

      \[\leadsto \left(2 \cdot \frac{x}{y}\right) \cdot y + y \]

   7. associate-*r/ N/A

      \[\leadsto \frac{2 \cdot x}{y} \cdot y + y \]

   8. *-commutative N/A

      \[\leadsto \frac{x \cdot 2}{y} \cdot y + y \]

   9. associate-/l* N/A

      \[\leadsto \left(x \cdot \frac{2}{y}\right) \cdot y + y \]

   10. associate-*l* N/A

       \[\leadsto x \cdot \left(\frac{2}{y} \cdot y\right) + y \]

   11. accelerator-lowering-fma.f64 N/A

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

   12. associate-*l/ N/A

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

   13. *-rgt-identity N/A

       \[\leadsto \mathsf{fma.f64}\left(x, \left(\frac{2 \cdot y}{y \cdot \color{blue}{1}}\right), y\right) \]

   14. *-inverses N/A

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

   15. associate-/l* N/A

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

   16. associate-/r/ N/A

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

   17. associate-*l/ N/A

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

   18. associate-*r* N/A

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

   19. associate-/l* N/A

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

   20. *-inverses N/A

       \[\leadsto \mathsf{fma.f64}\left(x, \left(2 \cdot 1\right), y\right) \]

   21. metadata-eval 100.0%

       \[\leadsto \mathsf{fma.f64}\left(x, 2, y\right) \]

5. Simplified 100.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(x, 2, y\right)} \]
6. Add Preprocessing

Alternative 2: 76.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.35 \cdot 10^{-50}:\\ \;\;\;\;x + x\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+85}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -2.35e-50) (+ x x) (if (<= x 4e+85) (+ x y) (+ x x))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2.35e-50) {
		tmp = x + x;
	} else if (x <= 4e+85) {
		tmp = x + y;
	} else {
		tmp = x + 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 <= (-2.35d-50)) then
        tmp = x + x
    else if (x <= 4d+85) then
        tmp = x + y
    else
        tmp = x + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -2.35e-50) {
		tmp = x + x;
	} else if (x <= 4e+85) {
		tmp = x + y;
	} else {
		tmp = x + x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2.35e-50:
		tmp = x + x
	elif x <= 4e+85:
		tmp = x + y
	else:
		tmp = x + x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2.35e-50)
		tmp = Float64(x + x);
	elseif (x <= 4e+85)
		tmp = Float64(x + y);
	else
		tmp = Float64(x + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -2.35e-50)
		tmp = x + x;
	elseif (x <= 4e+85)
		tmp = x + y;
	else
		tmp = x + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2.35e-50], N[(x + x), $MachinePrecision], If[LessEqual[x, 4e+85], N[(x + y), $MachinePrecision], N[(x + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.3500000000000001e-50 or 4.0000000000000001e85 < x

   1. Initial program 100.0%

      \[\left(x + y\right) + x \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{x}, x\right) \]
   4. Step-by-step derivation

   5. Simplified 75.5%

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

   if -2.3500000000000001e-50 < x < 4.0000000000000001e85

   1. Initial program 99.9%

      \[\left(x + y\right) + x \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{y}, x\right) \]
   4. Step-by-step derivation

   5. Simplified 81.4%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.35 \cdot 10^{-50}:\\ \;\;\;\;x + x\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+85}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{-51}:\\ \;\;\;\;x + x\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+89}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -4.2e-51) (+ x x) (if (<= x 2.6e+89) y (+ x x))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -4.2e-51) {
		tmp = x + x;
	} else if (x <= 2.6e+89) {
		tmp = y;
	} else {
		tmp = x + 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 <= (-4.2d-51)) then
        tmp = x + x
    else if (x <= 2.6d+89) then
        tmp = y
    else
        tmp = x + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -4.2e-51) {
		tmp = x + x;
	} else if (x <= 2.6e+89) {
		tmp = y;
	} else {
		tmp = x + x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -4.2e-51:
		tmp = x + x
	elif x <= 2.6e+89:
		tmp = y
	else:
		tmp = x + x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -4.2e-51)
		tmp = Float64(x + x);
	elseif (x <= 2.6e+89)
		tmp = y;
	else
		tmp = Float64(x + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -4.2e-51)
		tmp = x + x;
	elseif (x <= 2.6e+89)
		tmp = y;
	else
		tmp = x + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -4.2e-51], N[(x + x), $MachinePrecision], If[LessEqual[x, 2.6e+89], y, N[(x + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -4.20000000000000003e-51 or 2.6000000000000001e89 < x

   1. Initial program 100.0%

      \[\left(x + y\right) + x \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{x}, x\right) \]
   4. Step-by-step derivation

   5. Simplified 75.5%

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

   if -4.20000000000000003e-51 < x < 2.6000000000000001e89

   1. Initial program 99.9%

      \[\left(x + y\right) + x \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

   5. Simplified 78.3%

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

Alternative 4: 50.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+186}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= x -2.5e+186) x y))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2.5e+186) {
		tmp = 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 <= (-2.5d+186)) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -2.5e+186) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2.5e+186:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2.5e+186)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -2.5e+186)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2.5e+186], x, y]

Derivation

1. Split input into 2 regimes

2. if x < -2.49999999999999977e186

   1. Initial program 100.0%

      \[\left(x + y\right) + x \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{y}, x\right) \]
   4. Step-by-step derivation

   5. Simplified 21.1%

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

   6. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x} \]
   7. Step-by-step derivation

   8. Simplified 18.4%

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

   if -2.49999999999999977e186 < x

   1. Initial program 99.9%

      \[\left(x + y\right) + x \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

   5. Simplified 60.8%

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

Alternative 5: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[\left(x + y\right) + x \]
2. Add Preprocessing

3. Final simplification 100.0%

   \[\leadsto x + \left(x + y\right) \]
4. Add Preprocessing

Alternative 6: 11.1% accurate, 7.0× 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 100.0%

   \[\left(x + y\right) + x \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \mathsf{+.f64}\left(\color{blue}{y}, x\right) \]
4. Step-by-step derivation

5. Simplified 60.7%

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

6. Taylor expanded in y around 0

   \[\leadsto \color{blue}{x} \]
7. Step-by-step derivation

8. Simplified 10.8%

   \[\leadsto \color{blue}{x} \]
9. Add Preprocessing

Developer Target 1: 100.0% accurate, 0.8× 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 2024193 
(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))