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

Percentage Accurate: 100.0% → 100.0%

Time: 3.1s

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

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. lift-+.f64 N/A

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

   2. +-commutative N/A

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

   3. lift-+.f64 N/A

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

   4. associate-+r+ N/A

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

   5. count-2 N/A

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

   6. lower-fma.f64 100.0

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

4. Applied rewrites 100.0%

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

Alternative 2: 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 3: 50.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ x + x \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in x around inf

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

   1. *-rgt-identity N/A

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

   2. *-inverses N/A

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

   3. associate-/l* N/A

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

   4. *-commutative N/A

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

   5. associate-*l* N/A

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

   6. associate-/l* N/A

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

   7. associate-*l/ N/A

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

   8. lower-*.f64 N/A

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

   9. associate-*l/ N/A

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

   10. *-rgt-identity N/A

       \[\leadsto x \cdot \frac{2 \cdot y}{\color{blue}{y \cdot 1}} \]

   11. *-inverses N/A

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

   12. associate-/l* N/A

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

   13. associate-/r/ N/A

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

   14. associate-*l/ N/A

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

   15. associate-*r* N/A

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

   16. associate-/l* N/A

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

   17. *-inverses N/A

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

   18. metadata-eval 53.1

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

5. Applied rewrites 53.1%

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

7. Applied rewrites 53.1%

   \[\leadsto x + \color{blue}{x} \]
8. 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 2024234 
(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))