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

Percentage Accurate: 99.9% → 99.9%

Time: 8.2s

Alternatives: 6

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: 85.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{-24}:\\ \;\;\;\;\mathsf{fma}\left(2, x + y, x\right)\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+56}:\\ \;\;\;\;\mathsf{fma}\left(x, 3, z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(2, y, z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -5.2e-24)
   (fma 2.0 (+ x y) x)
   (if (<= y 5.2e+56) (fma x 3.0 z) (fma 2.0 y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -5.2e-24) {
		tmp = fma(2.0, (x + y), x);
	} else if (y <= 5.2e+56) {
		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 <= -5.2e-24)
		tmp = fma(2.0, Float64(x + y), x);
	elseif (y <= 5.2e+56)
		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, -5.2e-24], N[(2.0 * N[(x + y), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[y, 5.2e+56], N[(x * 3.0 + z), $MachinePrecision], N[(2.0 * y + z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.2e-24

   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 z around 0

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

      1. +-commutative N/A

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

      2. distribute-lft-out N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-+.f64 85.1

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

   5. Applied rewrites 85.1%

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

   if -5.2e-24 < y < 5.20000000000000022e56

   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 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 95.7

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

   5. Applied rewrites 95.7%

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

   if 5.20000000000000022e56 < 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 90.2

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

   5. Applied rewrites 90.2%

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

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{-24}:\\ \;\;\;\;\mathsf{fma}\left(2, x + y, x\right)\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+56}:\\ \;\;\;\;\mathsf{fma}\left(x, 3, z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(2, y, z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{-28}:\\ \;\;\;\;\mathsf{fma}\left(2, y, z\right)\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+56}:\\ \;\;\;\;\mathsf{fma}\left(x, 3, z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(2, y, z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.9e-28)
   (fma 2.0 y z)
   (if (<= y 5.2e+56) (fma x 3.0 z) (fma 2.0 y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.9e-28) {
		tmp = fma(2.0, y, z);
	} else if (y <= 5.2e+56) {
		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 <= -1.9e-28)
		tmp = fma(2.0, y, z);
	elseif (y <= 5.2e+56)
		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, -1.9e-28], N[(2.0 * y + z), $MachinePrecision], If[LessEqual[y, 5.2e+56], N[(x * 3.0 + z), $MachinePrecision], N[(2.0 * y + z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.90000000000000005e-28 or 5.20000000000000022e56 < 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 84.4

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

   5. Applied rewrites 84.4%

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

   if -1.90000000000000005e-28 < y < 5.20000000000000022e56

   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 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 95.7

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

   5. Applied rewrites 95.7%

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

Alternative 4: 79.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{+169}:\\ \;\;\;\;x \cdot 3\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{+161}:\\ \;\;\;\;\mathsf{fma}\left(2, y, z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -3.6e+169) (* x 3.0) (if (<= x 8.5e+161) (fma 2.0 y z) (* x 3.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.6e+169) {
		tmp = x * 3.0;
	} else if (x <= 8.5e+161) {
		tmp = fma(2.0, y, z);
	} else {
		tmp = x * 3.0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -3.6e+169)
		tmp = Float64(x * 3.0);
	elseif (x <= 8.5e+161)
		tmp = fma(2.0, y, z);
	else
		tmp = Float64(x * 3.0);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -3.6e+169], N[(x * 3.0), $MachinePrecision], If[LessEqual[x, 8.5e+161], N[(2.0 * y + z), $MachinePrecision], N[(x * 3.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -3.6000000000000001e169 or 8.50000000000000007e161 < 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 80.0

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

   5. Applied rewrites 80.0%

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

   if -3.6000000000000001e169 < x < 8.50000000000000007e161

   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

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

      1. +-commutative N/A

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

      2. lower-fma.f64 83.9

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

   5. Applied rewrites 83.9%

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

Alternative 5: 52.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{-28}:\\ \;\;\;\;y + y\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+56}:\\ \;\;\;\;x \cdot 3\\ \mathbf{else}:\\ \;\;\;\;y + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.9e-28) (+ y y) (if (<= y 5.2e+56) (* x 3.0) (+ y y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.9e-28) {
		tmp = y + y;
	} else if (y <= 5.2e+56) {
		tmp = x * 3.0;
	} else {
		tmp = y + y;
	}
	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 <= (-1.9d-28)) then
        tmp = y + y
    else if (y <= 5.2d+56) then
        tmp = x * 3.0d0
    else
        tmp = y + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.9e-28) {
		tmp = y + y;
	} else if (y <= 5.2e+56) {
		tmp = x * 3.0;
	} else {
		tmp = y + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.9e-28:
		tmp = y + y
	elif y <= 5.2e+56:
		tmp = x * 3.0
	else:
		tmp = y + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.9e-28)
		tmp = Float64(y + y);
	elseif (y <= 5.2e+56)
		tmp = Float64(x * 3.0);
	else
		tmp = Float64(y + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.9e-28)
		tmp = y + y;
	elseif (y <= 5.2e+56)
		tmp = x * 3.0;
	else
		tmp = y + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.9e-28], N[(y + y), $MachinePrecision], If[LessEqual[y, 5.2e+56], N[(x * 3.0), $MachinePrecision], N[(y + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.90000000000000005e-28 or 5.20000000000000022e56 < 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 70.8

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

   5. Applied rewrites 70.8%

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

   7. Applied rewrites 70.8%

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

   if -1.90000000000000005e-28 < y < 5.20000000000000022e56

   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 40.3

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

   5. Applied rewrites 40.3%

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

Alternative 6: 34.1% accurate, 4.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(y + 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 y around inf

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

   1. lower-*.f64 36.0

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

5. Applied rewrites 36.0%

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

7. Applied rewrites 36.0%

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

Reproduce

herbie shell --seed 2024238 
(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))