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

Percentage Accurate: 99.9% → 99.9%

Time: 4.2s

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

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

Alternative 2: 84.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.26 \cdot 10^{+14}:\\ \;\;\;\;\mathsf{fma}\left(y, 2, z\right)\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+159}:\\ \;\;\;\;\mathsf{fma}\left(3, x, y + y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(3, x, z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.26e+14)
   (fma y 2.0 z)
   (if (<= z 6e+159) (fma 3.0 x (+ y y)) (fma 3.0 x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.26e+14) {
		tmp = fma(y, 2.0, z);
	} else if (z <= 6e+159) {
		tmp = fma(3.0, x, (y + y));
	} else {
		tmp = fma(3.0, x, z);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.26e+14)
		tmp = fma(y, 2.0, z);
	elseif (z <= 6e+159)
		tmp = fma(3.0, x, Float64(y + y));
	else
		tmp = fma(3.0, x, z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.26e+14], N[(y * 2.0 + z), $MachinePrecision], If[LessEqual[z, 6e+159], N[(3.0 * x + N[(y + y), $MachinePrecision]), $MachinePrecision], N[(3.0 * x + z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.26e14

   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. *-commutative N/A

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

      3. lower-fma.f64 89.9

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

   5. Applied rewrites 89.9%

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

   if -1.26e14 < z < 6.0000000000000004e159

   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 z around 0

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

      1. associate-+r+ N/A

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

      2. distribute-rgt1-in N/A

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

      3. metadata-eval N/A

         \[\leadsto \color{blue}{3} \cdot x + 2 \cdot y \]

      4. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(3, x, 2 \cdot y\right)} \]

      5. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(3, x, \color{blue}{y \cdot 2}\right) \]

      6. lower-*.f64 91.2

         \[\leadsto \mathsf{fma}\left(3, x, \color{blue}{y \cdot 2}\right) \]

   5. Applied rewrites 91.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(3, x, y \cdot 2\right)} \]
   6. Step-by-step derivation

   7. Applied rewrites 91.2%

      \[\leadsto \mathsf{fma}\left(3, x, y + y\right) \]

   if 6.0000000000000004e159 < z

   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 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. lower-fma.f64 95.7

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

   5. Applied rewrites 95.7%

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

Alternative 3: 85.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+59}:\\ \;\;\;\;\mathsf{fma}\left(y, 2, z\right)\\ \mathbf{elif}\;y \leq 10^{+45}:\\ \;\;\;\;\mathsf{fma}\left(3, x, z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, 2, z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.9e+59)
   (fma y 2.0 z)
   (if (<= y 1e+45) (fma 3.0 x z) (fma y 2.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.9e+59) {
		tmp = fma(y, 2.0, z);
	} else if (y <= 1e+45) {
		tmp = fma(3.0, x, z);
	} else {
		tmp = fma(y, 2.0, z);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.9e+59)
		tmp = fma(y, 2.0, z);
	elseif (y <= 1e+45)
		tmp = fma(3.0, x, z);
	else
		tmp = fma(y, 2.0, z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.9e+59], N[(y * 2.0 + z), $MachinePrecision], If[LessEqual[y, 1e+45], N[(3.0 * x + z), $MachinePrecision], N[(y * 2.0 + z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.89999999999999991e59 or 9.9999999999999993e44 < y

   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. *-commutative N/A

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

      3. lower-fma.f64 82.7

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

   5. Applied rewrites 82.7%

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

   if -2.89999999999999991e59 < y < 9.9999999999999993e44

   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. lower-fma.f64 88.9

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

   5. Applied rewrites 88.9%

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

Alternative 4: 80.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+142}:\\ \;\;\;\;y + y\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{+154}:\\ \;\;\;\;\mathsf{fma}\left(3, x, z\right)\\ \mathbf{else}:\\ \;\;\;\;y + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -9e+142) (+ y y) (if (<= y 7.4e+154) (fma 3.0 x z) (+ y y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -9e+142) {
		tmp = y + y;
	} else if (y <= 7.4e+154) {
		tmp = fma(3.0, x, z);
	} else {
		tmp = y + y;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -9e+142)
		tmp = Float64(y + y);
	elseif (y <= 7.4e+154)
		tmp = fma(3.0, x, z);
	else
		tmp = Float64(y + y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -9e+142], N[(y + y), $MachinePrecision], If[LessEqual[y, 7.4e+154], N[(3.0 * x + z), $MachinePrecision], N[(y + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -8.9999999999999998e142 or 7.39999999999999989e154 < 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. *-commutative N/A

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

      2. lower-*.f64 85.1

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

   5. Applied rewrites 85.1%

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

   7. Applied rewrites 85.1%

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

   if -8.9999999999999998e142 < y < 7.39999999999999989e154

   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. lower-fma.f64 82.8

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

   5. Applied rewrites 82.8%

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

Alternative 5: 53.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{-6}:\\ \;\;\;\;y + y\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+45}:\\ \;\;\;\;3 \cdot x\\ \mathbf{else}:\\ \;\;\;\;y + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -6.8e-6) (+ y y) (if (<= y 1.3e+45) (* 3.0 x) (+ y y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -6.8e-6) {
		tmp = y + y;
	} else if (y <= 1.3e+45) {
		tmp = 3.0 * x;
	} 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 <= (-6.8d-6)) then
        tmp = y + y
    else if (y <= 1.3d+45) then
        tmp = 3.0d0 * x
    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 <= -6.8e-6) {
		tmp = y + y;
	} else if (y <= 1.3e+45) {
		tmp = 3.0 * x;
	} else {
		tmp = y + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -6.8e-6:
		tmp = y + y
	elif y <= 1.3e+45:
		tmp = 3.0 * x
	else:
		tmp = y + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -6.8e-6)
		tmp = Float64(y + y);
	elseif (y <= 1.3e+45)
		tmp = Float64(3.0 * x);
	else
		tmp = Float64(y + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -6.8e-6)
		tmp = y + y;
	elseif (y <= 1.3e+45)
		tmp = 3.0 * x;
	else
		tmp = y + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -6.8e-6], N[(y + y), $MachinePrecision], If[LessEqual[y, 1.3e+45], N[(3.0 * x), $MachinePrecision], N[(y + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -6.80000000000000012e-6 or 1.30000000000000004e45 < y

   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. *-commutative N/A

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

      2. lower-*.f64 58.3

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

   5. Applied rewrites 58.3%

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

   7. Applied rewrites 58.3%

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

   if -6.80000000000000012e-6 < y < 1.30000000000000004e45

   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. lower-*.f64 52.5

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

   5. Applied rewrites 52.5%

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

Alternative 6: 35.1% 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. *-commutative N/A

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

   2. lower-*.f64 34.7

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

5. Applied rewrites 34.7%

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

7. Applied rewrites 34.7%

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

Reproduce

herbie shell --seed 2024244 
(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))