Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendInside from plot-0.2.3.4

Percentage Accurate: 99.9% → 99.9%

Time: 8.2s

Alternatives: 5

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Final simplification 99.9%

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

Alternative 2: 84.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+133}:\\ \;\;\;\;\mathsf{fma}\left(2, y, z\right)\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+97}:\\ \;\;\;\;\mathsf{fma}\left(x, 3, z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(2, y, z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -4e+133)
   (fma 2.0 y z)
   (if (<= y 3.2e+97) (fma x 3.0 z) (fma 2.0 y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -4e+133) {
		tmp = fma(2.0, y, z);
	} else if (y <= 3.2e+97) {
		tmp = fma(x, 3.0, z);
	} else {
		tmp = fma(2.0, y, z);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -4e+133)
		tmp = fma(2.0, y, z);
	elseif (y <= 3.2e+97)
		tmp = fma(x, 3.0, z);
	else
		tmp = fma(2.0, y, z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -4e+133], N[(2.0 * y + z), $MachinePrecision], If[LessEqual[y, 3.2e+97], N[(x * 3.0 + z), $MachinePrecision], N[(2.0 * y + z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.0000000000000001e133 or 3.20000000000000016e97 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 94.8

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

   5. Applied rewrites 94.8%

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

   if -4.0000000000000001e133 < y < 3.20000000000000016e97

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x + \left(z + 2 \cdot x\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

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

      2. associate-+r+ N/A

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

      3. distribute-rgt1-in N/A

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

      4. metadata-eval N/A

         \[\leadsto \color{blue}{3} \cdot x + z \]

      5. *-commutative N/A

         \[\leadsto \color{blue}{x \cdot 3} + z \]

      6. lower-fma.f64 91.1

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, 3, z\right)} \]

   5. Applied rewrites 91.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, 3, z\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 79.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+68}:\\ \;\;\;\;x \cdot 3\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{+181}:\\ \;\;\;\;\mathsf{fma}\left(2, y, z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2.5e+68) (* x 3.0) (if (<= x 1.5e+181) (fma 2.0 y z) (* x 3.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.5e+68) {
		tmp = x * 3.0;
	} else if (x <= 1.5e+181) {
		tmp = fma(2.0, y, z);
	} else {
		tmp = x * 3.0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.5e+68)
		tmp = Float64(x * 3.0);
	elseif (x <= 1.5e+181)
		tmp = fma(2.0, y, z);
	else
		tmp = Float64(x * 3.0);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2.5e+68], N[(x * 3.0), $MachinePrecision], If[LessEqual[x, 1.5e+181], N[(2.0 * y + z), $MachinePrecision], N[(x * 3.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.5000000000000002e68 or 1.50000000000000006e181 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

         \[\leadsto \color{blue}{x \cdot 3} \]

      2. lower-*.f64 76.6

         \[\leadsto \color{blue}{x \cdot 3} \]

   5. Applied rewrites 76.6%

      \[\leadsto \color{blue}{x \cdot 3} \]

   if -2.5000000000000002e68 < x < 1.50000000000000006e181

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 89.0

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

   5. Applied rewrites 89.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(2, y, z\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 51.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+133}:\\ \;\;\;\;y \cdot 2\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+101}:\\ \;\;\;\;x \cdot 3\\ \mathbf{else}:\\ \;\;\;\;y \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -4e+133) (* y 2.0) (if (<= y 1.5e+101) (* x 3.0) (* y 2.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -4e+133) {
		tmp = y * 2.0;
	} else if (y <= 1.5e+101) {
		tmp = x * 3.0;
	} else {
		tmp = y * 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-4d+133)) then
        tmp = y * 2.0d0
    else if (y <= 1.5d+101) then
        tmp = x * 3.0d0
    else
        tmp = y * 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -4e+133) {
		tmp = y * 2.0;
	} else if (y <= 1.5e+101) {
		tmp = x * 3.0;
	} else {
		tmp = y * 2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -4e+133:
		tmp = y * 2.0
	elif y <= 1.5e+101:
		tmp = x * 3.0
	else:
		tmp = y * 2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -4e+133)
		tmp = Float64(y * 2.0);
	elseif (y <= 1.5e+101)
		tmp = Float64(x * 3.0);
	else
		tmp = Float64(y * 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -4e+133)
		tmp = y * 2.0;
	elseif (y <= 1.5e+101)
		tmp = x * 3.0;
	else
		tmp = y * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -4e+133], N[(y * 2.0), $MachinePrecision], If[LessEqual[y, 1.5e+101], N[(x * 3.0), $MachinePrecision], N[(y * 2.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.0000000000000001e133 or 1.49999999999999997e101 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

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

      1. lower-*.f64 78.9

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

   5. Applied rewrites 78.9%

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

   if -4.0000000000000001e133 < y < 1.49999999999999997e101

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

         \[\leadsto \color{blue}{x \cdot 3} \]

      2. lower-*.f64 47.5

         \[\leadsto \color{blue}{x \cdot 3} \]

   5. Applied rewrites 47.5%

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

4. Final simplification 57.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+133}:\\ \;\;\;\;y \cdot 2\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+101}:\\ \;\;\;\;x \cdot 3\\ \mathbf{else}:\\ \;\;\;\;y \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 33.9% accurate, 2.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in y around inf

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

   1. lower-*.f64 33.1

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

5. Applied rewrites 33.1%

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

6. Final simplification 33.1%

   \[\leadsto y \cdot 2 \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024219 
(FPCore (x y z)
  :name "Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendInside from plot-0.2.3.4"
  :precision binary64
  (+ (+ (+ (+ (+ x y) y) x) z) x))