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

Percentage Accurate: 100.0% → 100.0%

Time: 3.3s

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 99.9%

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

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

   2. *-rgt-identity N/A

      \[\leadsto \color{blue}{\left(2 \cdot x\right) \cdot 1} + y \]

   3. *-inverses N/A

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

   4. associate-/l* N/A

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

   5. associate-*l/ N/A

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

   6. associate-*r/ N/A

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

   7. associate-*r/ N/A

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

   8. *-commutative N/A

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

   9. associate-/l* N/A

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

   10. associate-*l* N/A

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

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

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

   12. associate-*l/ N/A

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

   13. *-rgt-identity N/A

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

   14. *-inverses N/A

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

   15. associate-/l* N/A

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

   16. associate-/r/ N/A

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

   17. associate-*l/ N/A

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

   18. associate-*r* N/A

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

   19. associate-/l* N/A

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

   20. *-inverses N/A

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

   21. metadata-eval 100.0

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

5. Simplified 100.0%

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

Alternative 2: 76.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.26:\\ \;\;\;\;x + x\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+63}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -0.26) (+ x x) (if (<= x 4.2e+63) (+ x y) (+ x x))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -0.26) {
		tmp = x + x;
	} else if (x <= 4.2e+63) {
		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 <= (-0.26d0)) then
        tmp = x + x
    else if (x <= 4.2d+63) 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 <= -0.26) {
		tmp = x + x;
	} else if (x <= 4.2e+63) {
		tmp = x + y;
	} else {
		tmp = x + x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -0.26:
		tmp = x + x
	elif x <= 4.2e+63:
		tmp = x + y
	else:
		tmp = x + x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -0.26)
		tmp = Float64(x + x);
	elseif (x <= 4.2e+63)
		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 <= -0.26)
		tmp = x + x;
	elseif (x <= 4.2e+63)
		tmp = x + y;
	else
		tmp = x + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -0.26], N[(x + x), $MachinePrecision], If[LessEqual[x, 4.2e+63], N[(x + y), $MachinePrecision], N[(x + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -0.26000000000000001 or 4.2000000000000004e63 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 84.7%

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

   if -0.26000000000000001 < x < 4.2000000000000004e63

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

   5. Simplified 77.7%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.26:\\ \;\;\;\;x + x\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+63}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.45:\\ \;\;\;\;x + x\\ \mathbf{elif}\;x \leq 2.35 \cdot 10^{+64}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.45) (+ x x) (if (<= x 2.35e+64) y (+ x x))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.45) {
		tmp = x + x;
	} else if (x <= 2.35e+64) {
		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 <= (-1.45d0)) then
        tmp = x + x
    else if (x <= 2.35d+64) 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 <= -1.45) {
		tmp = x + x;
	} else if (x <= 2.35e+64) {
		tmp = y;
	} else {
		tmp = x + x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.45:
		tmp = x + x
	elif x <= 2.35e+64:
		tmp = y
	else:
		tmp = x + x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.45)
		tmp = Float64(x + x);
	elseif (x <= 2.35e+64)
		tmp = y;
	else
		tmp = Float64(x + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.45)
		tmp = x + x;
	elseif (x <= 2.35e+64)
		tmp = y;
	else
		tmp = x + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.45], N[(x + x), $MachinePrecision], If[LessEqual[x, 2.35e+64], y, N[(x + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.44999999999999996 or 2.35000000000000015e64 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 84.7%

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

   if -1.44999999999999996 < x < 2.35000000000000015e64

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

   5. Simplified 74.4%

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

Alternative 4: 49.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.38 \cdot 10^{+107}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= x 1.38e+107) y x))

C

double code(double x, double y) {
	double tmp;
	if (x <= 1.38e+107) {
		tmp = y;
	} else {
		tmp = 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 <= 1.38d+107) then
        tmp = y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= 1.38e+107) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 1.38e+107:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 1.38e+107)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 1.38e+107)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 1.38e+107], y, x]

Derivation

1. Split input into 2 regimes

2. if x < 1.38e107

   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 59.4%

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

   if 1.38e107 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

   5. Simplified 18.8%

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

   6. Taylor expanded in y around 0

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

   8. Simplified 18.7%

      \[\leadsto \color{blue}{x} \]
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 99.9%

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

3. Final simplification 99.9%

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

Alternative 6: 11.2% 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 99.9%

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

3. Taylor expanded in x around 0

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

5. Simplified 58.4%

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

6. Taylor expanded in y around 0

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

8. Simplified 11.1%

   \[\leadsto \color{blue}{x} \]
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 2024196 
(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))