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

Percentage Accurate: 99.9% → 99.9%

Time: 1.1s

Alternatives: 6

Speedup: 1.0×

Specification

\[\mathsf{TRUE}\left(\right)\]

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

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

FPCore

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

C

double code(double x, double y, double z) {
	return ((((x + y) + y) + x) + x) + 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 + y) + y) + x) + x) + z
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(N[(N[(N[(N[(x + y), $MachinePrecision] + y), $MachinePrecision] + x), $MachinePrecision] + x), $MachinePrecision] + z), $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 x around 0

   \[\leadsto \color{blue}{z + \left(2 \cdot y + 3 \cdot x\right)} \]

5. Applied rewrites 70.9%

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

6. Taylor expanded in x around 0

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

8. Applied rewrites 99.9%

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

Alternative 2: 84.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(\left(x + y\right) + y\right) + x\\ t_1 := t\_0 + x\\ \mathbf{if}\;x \leq -3.1 \cdot 10^{-34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 5.7 \cdot 10^{-47}:\\ \;\;\;\;t\_0 + z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (+ (+ x y) y) x)) (t_1 (+ t_0 x)))
   (if (<= x -3.1e-34) t_1 (if (<= x 5.7e-47) (+ t_0 z) t_1))))

C

double code(double x, double y, double z) {
	double t_0 = ((x + y) + y) + x;
	double t_1 = t_0 + x;
	double tmp;
	if (x <= -3.1e-34) {
		tmp = t_1;
	} else if (x <= 5.7e-47) {
		tmp = t_0 + z;
	} else {
		tmp = t_1;
	}
	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) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = ((x + y) + y) + x
    t_1 = t_0 + x
    if (x <= (-3.1d-34)) then
        tmp = t_1
    else if (x <= 5.7d-47) then
        tmp = t_0 + z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = ((x + y) + y) + x;
	double t_1 = t_0 + x;
	double tmp;
	if (x <= -3.1e-34) {
		tmp = t_1;
	} else if (x <= 5.7e-47) {
		tmp = t_0 + z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = ((x + y) + y) + x
	t_1 = t_0 + x
	tmp = 0
	if x <= -3.1e-34:
		tmp = t_1
	elif x <= 5.7e-47:
		tmp = t_0 + z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(x + y) + y) + x)
	t_1 = Float64(t_0 + x)
	tmp = 0.0
	if (x <= -3.1e-34)
		tmp = t_1;
	elseif (x <= 5.7e-47)
		tmp = Float64(t_0 + z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = ((x + y) + y) + x;
	t_1 = t_0 + x;
	tmp = 0.0;
	if (x <= -3.1e-34)
		tmp = t_1;
	elseif (x <= 5.7e-47)
		tmp = t_0 + z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(x + y), $MachinePrecision] + y), $MachinePrecision] + x), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 + x), $MachinePrecision]}, If[LessEqual[x, -3.1e-34], t$95$1, If[LessEqual[x, 5.7e-47], N[(t$95$0 + z), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if x < -3.0999999999999998e-34 or 5.70000000000000046e-47 < 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 0

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

   5. Applied rewrites 83.5%

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

   if -3.0999999999999998e-34 < x < 5.70000000000000046e-47

   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

      \[\leadsto \color{blue}{z + \left(2 \cdot y + 3 \cdot x\right)} \]

   5. Applied rewrites 97.2%

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

Alternative 3: 72.8% accurate, 1.2× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return (((x + y) + y) + x) + 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 + y) + y) + x) + z
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(N[(N[(N[(x + y), $MachinePrecision] + y), $MachinePrecision] + x), $MachinePrecision] + z), $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 x around 0

   \[\leadsto \color{blue}{z + \left(2 \cdot y + 3 \cdot x\right)} \]

5. Applied rewrites 70.9%

   \[\leadsto \color{blue}{\left(\left(\left(x + y\right) + y\right) + x\right) + z} \]
6. Add Preprocessing

Alternative 4: 71.9% accurate, 1.6× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return ((x + y) + 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 + y) + y) + z
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(N[(N[(x + y), $MachinePrecision] + y), $MachinePrecision] + z), $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 x around 0

   \[\leadsto \color{blue}{z + \left(2 \cdot y + 3 \cdot x\right)} \]

5. Applied rewrites 70.9%

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

6. Taylor expanded in x around 0

   \[\leadsto 2 \cdot y + z \]

8. Applied rewrites 70.0%

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

Alternative 5: 39.5% accurate, 2.3× speedup

Math

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

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(N[(x + y), $MachinePrecision] + y), $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 x around 0

   \[\leadsto \color{blue}{z + \left(2 \cdot y + 3 \cdot x\right)} \]

5. Applied rewrites 70.9%

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

6. Taylor expanded in x around 0

   \[\leadsto 2 \cdot y + z \]

8. Applied rewrites 70.0%

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

9. Taylor expanded in x around 0

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

11. Applied rewrites 39.8%

    \[\leadsto \left(x + y\right) + \color{blue}{y} \]
12. Add Preprocessing

Alternative 6: 13.2% accurate, 4.0× speedup

Math

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

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(x + y), $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 x around 0

   \[\leadsto \color{blue}{z + \left(2 \cdot y + 3 \cdot x\right)} \]

5. Applied rewrites 70.9%

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

6. Taylor expanded in x around inf

   \[\leadsto \color{blue}{x \cdot \left(3 + \left(2 \cdot \frac{y}{x} + \frac{z}{x}\right)\right)} \]

8. Applied rewrites 13.7%

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

Reproduce

herbie shell --seed 2024321 
(FPCore (x y z)
  :name "Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendInside from plot-0.2.3.4"
  :precision binary64
  :pre (TRUE)
  (+ (+ (+ (+ (+ x y) y) x) z) x))