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

Percentage Accurate: 99.9% → 99.9%

Time: 5.9s

Alternatives: 7

Speedup: 1.2×

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, 1.2× speedup

Math

\[\begin{array}{l} \\ z + \left(2 \cdot y + 3 \cdot x\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ z (+ (* 2.0 y) (* 3.0 x))))

C

double code(double x, double y, double z) {
	return z + ((2.0 * y) + (3.0 * 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 + ((2.0d0 * y) + (3.0d0 * x))
end function

Java

public static double code(double x, double y, double z) {
	return z + ((2.0 * y) + (3.0 * x));
}

Python

def code(x, y, z):
	return z + ((2.0 * y) + (3.0 * x))

Julia

function code(x, y, z)
	return Float64(z + Float64(Float64(2.0 * y) + Float64(3.0 * x)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = z + ((2.0 * y) + (3.0 * x));
end

Wolfram

code[x_, y_, z_] := N[(z + N[(N[(2.0 * y), $MachinePrecision] + N[(3.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

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

   1. associate-+l+ 99.9%

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

   2. +-commutative 99.9%

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

   3. associate-+l+ 99.9%

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

   4. +-commutative 99.9%

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

   5. count-2 99.9%

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

   6. +-commutative 99.9%

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

3. Simplified 99.9%

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

5. Taylor expanded in x around 0 99.9%

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

6. Final simplification 99.9%

   \[\leadsto z + \left(2 \cdot y + 3 \cdot x\right) \]
7. Add Preprocessing

Alternative 2: 52.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+60}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq -1.36 \cdot 10^{-229}:\\ \;\;\;\;3 \cdot x\\ \mathbf{elif}\;z \leq -1.12 \cdot 10^{-303}:\\ \;\;\;\;2 \cdot y\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-81}:\\ \;\;\;\;3 \cdot x\\ \mathbf{elif}\;z \leq 1.52 \cdot 10^{-61}:\\ \;\;\;\;2 \cdot y\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+41}:\\ \;\;\;\;3 \cdot x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.55e+60)
   z
   (if (<= z -1.36e-229)
     (* 3.0 x)
     (if (<= z -1.12e-303)
       (* 2.0 y)
       (if (<= z 3.6e-81)
         (* 3.0 x)
         (if (<= z 1.52e-61) (* 2.0 y) (if (<= z 1.45e+41) (* 3.0 x) z)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.55e+60) {
		tmp = z;
	} else if (z <= -1.36e-229) {
		tmp = 3.0 * x;
	} else if (z <= -1.12e-303) {
		tmp = 2.0 * y;
	} else if (z <= 3.6e-81) {
		tmp = 3.0 * x;
	} else if (z <= 1.52e-61) {
		tmp = 2.0 * y;
	} else if (z <= 1.45e+41) {
		tmp = 3.0 * x;
	} else {
		tmp = z;
	}
	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 (z <= (-1.55d+60)) then
        tmp = z
    else if (z <= (-1.36d-229)) then
        tmp = 3.0d0 * x
    else if (z <= (-1.12d-303)) then
        tmp = 2.0d0 * y
    else if (z <= 3.6d-81) then
        tmp = 3.0d0 * x
    else if (z <= 1.52d-61) then
        tmp = 2.0d0 * y
    else if (z <= 1.45d+41) then
        tmp = 3.0d0 * x
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.55e+60) {
		tmp = z;
	} else if (z <= -1.36e-229) {
		tmp = 3.0 * x;
	} else if (z <= -1.12e-303) {
		tmp = 2.0 * y;
	} else if (z <= 3.6e-81) {
		tmp = 3.0 * x;
	} else if (z <= 1.52e-61) {
		tmp = 2.0 * y;
	} else if (z <= 1.45e+41) {
		tmp = 3.0 * x;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.55e+60:
		tmp = z
	elif z <= -1.36e-229:
		tmp = 3.0 * x
	elif z <= -1.12e-303:
		tmp = 2.0 * y
	elif z <= 3.6e-81:
		tmp = 3.0 * x
	elif z <= 1.52e-61:
		tmp = 2.0 * y
	elif z <= 1.45e+41:
		tmp = 3.0 * x
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.55e+60)
		tmp = z;
	elseif (z <= -1.36e-229)
		tmp = Float64(3.0 * x);
	elseif (z <= -1.12e-303)
		tmp = Float64(2.0 * y);
	elseif (z <= 3.6e-81)
		tmp = Float64(3.0 * x);
	elseif (z <= 1.52e-61)
		tmp = Float64(2.0 * y);
	elseif (z <= 1.45e+41)
		tmp = Float64(3.0 * x);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.55e+60)
		tmp = z;
	elseif (z <= -1.36e-229)
		tmp = 3.0 * x;
	elseif (z <= -1.12e-303)
		tmp = 2.0 * y;
	elseif (z <= 3.6e-81)
		tmp = 3.0 * x;
	elseif (z <= 1.52e-61)
		tmp = 2.0 * y;
	elseif (z <= 1.45e+41)
		tmp = 3.0 * x;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.55e+60], z, If[LessEqual[z, -1.36e-229], N[(3.0 * x), $MachinePrecision], If[LessEqual[z, -1.12e-303], N[(2.0 * y), $MachinePrecision], If[LessEqual[z, 3.6e-81], N[(3.0 * x), $MachinePrecision], If[LessEqual[z, 1.52e-61], N[(2.0 * y), $MachinePrecision], If[LessEqual[z, 1.45e+41], N[(3.0 * x), $MachinePrecision], z]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.55e60 or 1.44999999999999994e41 < z

   1. Initial program 100.0%

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

      1. associate-+l+ 100.0%

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

      2. +-commutative 100.0%

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

      3. associate-+l+ 100.0%

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

      4. +-commutative 100.0%

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

      5. count-2 100.0%

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

      6. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 79.9%

      \[\leadsto \color{blue}{z} \]

   if -1.55e60 < z < -1.36e-229 or -1.1199999999999999e-303 < z < 3.5999999999999999e-81 or 1.52000000000000003e-61 < z < 1.44999999999999994e41

   1. Initial program 99.8%

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

      1. associate-+l+ 99.8%

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

      2. +-commutative 99.8%

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

      3. associate-+l+ 99.9%

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

      4. +-commutative 99.9%

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

      5. count-2 99.9%

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

      6. +-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 54.1%

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

   if -1.36e-229 < z < -1.1199999999999999e-303 or 3.5999999999999999e-81 < z < 1.52000000000000003e-61

   1. Initial program 100.0%

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

      1. associate-+l+ 100.0%

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

      2. +-commutative 100.0%

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

      3. associate-+l+ 100.0%

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

      4. +-commutative 100.0%

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

      5. count-2 100.0%

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

      6. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 66.1%

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

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+60}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq -1.36 \cdot 10^{-229}:\\ \;\;\;\;3 \cdot x\\ \mathbf{elif}\;z \leq -1.12 \cdot 10^{-303}:\\ \;\;\;\;2 \cdot y\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-81}:\\ \;\;\;\;3 \cdot x\\ \mathbf{elif}\;z \leq 1.52 \cdot 10^{-61}:\\ \;\;\;\;2 \cdot y\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+41}:\\ \;\;\;\;3 \cdot x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{+61} \lor \neg \left(z \leq 9 \cdot 10^{+41}\right):\\ \;\;\;\;z + 2 \cdot y\\ \mathbf{else}:\\ \;\;\;\;x + 2 \cdot \left(y + x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.15e+61) (not (<= z 9e+41)))
   (+ z (* 2.0 y))
   (+ x (* 2.0 (+ y x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.15e+61) || !(z <= 9e+41)) {
		tmp = z + (2.0 * y);
	} else {
		tmp = x + (2.0 * (y + x));
	}
	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 ((z <= (-2.15d+61)) .or. (.not. (z <= 9d+41))) then
        tmp = z + (2.0d0 * y)
    else
        tmp = x + (2.0d0 * (y + x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.15e+61) || !(z <= 9e+41)) {
		tmp = z + (2.0 * y);
	} else {
		tmp = x + (2.0 * (y + x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.15e+61) or not (z <= 9e+41):
		tmp = z + (2.0 * y)
	else:
		tmp = x + (2.0 * (y + x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.15e+61) || !(z <= 9e+41))
		tmp = Float64(z + Float64(2.0 * y));
	else
		tmp = Float64(x + Float64(2.0 * Float64(y + x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -2.15e+61) || ~((z <= 9e+41)))
		tmp = z + (2.0 * y);
	else
		tmp = x + (2.0 * (y + x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.15e+61], N[Not[LessEqual[z, 9e+41]], $MachinePrecision]], N[(z + N[(2.0 * y), $MachinePrecision]), $MachinePrecision], N[(x + N[(2.0 * N[(y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.1500000000000001e61 or 9.0000000000000002e41 < z

   1. Initial program 100.0%

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

      1. associate-+l+ 100.0%

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

      2. +-commutative 100.0%

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

      3. associate-+l+ 100.0%

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

      4. +-commutative 100.0%

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

      5. count-2 100.0%

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

      6. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 91.9%

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

   if -2.1500000000000001e61 < z < 9.0000000000000002e41

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+l+ 99.9%

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

      4. +-commutative 99.9%

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

      5. count-2 99.9%

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

      6. +-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 91.2%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{+61} \lor \neg \left(z \leq 9 \cdot 10^{+41}\right):\\ \;\;\;\;z + 2 \cdot y\\ \mathbf{else}:\\ \;\;\;\;x + 2 \cdot \left(y + x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 78.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+232} \lor \neg \left(x \leq 5 \cdot 10^{+125}\right):\\ \;\;\;\;3 \cdot x\\ \mathbf{else}:\\ \;\;\;\;z + 2 \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -4e+232) (not (<= x 5e+125))) (* 3.0 x) (+ z (* 2.0 y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -4e+232) || !(x <= 5e+125)) {
		tmp = 3.0 * x;
	} else {
		tmp = z + (2.0 * 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 ((x <= (-4d+232)) .or. (.not. (x <= 5d+125))) then
        tmp = 3.0d0 * x
    else
        tmp = z + (2.0d0 * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -4e+232) || !(x <= 5e+125)) {
		tmp = 3.0 * x;
	} else {
		tmp = z + (2.0 * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -4e+232) or not (x <= 5e+125):
		tmp = 3.0 * x
	else:
		tmp = z + (2.0 * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -4e+232) || !(x <= 5e+125))
		tmp = Float64(3.0 * x);
	else
		tmp = Float64(z + Float64(2.0 * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -4e+232) || ~((x <= 5e+125)))
		tmp = 3.0 * x;
	else
		tmp = z + (2.0 * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -4e+232], N[Not[LessEqual[x, 5e+125]], $MachinePrecision]], N[(3.0 * x), $MachinePrecision], N[(z + N[(2.0 * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.00000000000000023e232 or 4.99999999999999962e125 < x

   1. Initial program 99.7%

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

      1. associate-+l+ 99.7%

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

      2. +-commutative 99.7%

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

      3. associate-+l+ 99.7%

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

      4. +-commutative 99.7%

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

      5. count-2 99.7%

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

      6. +-commutative 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 89.8%

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

   if -4.00000000000000023e232 < x < 4.99999999999999962e125

   1. Initial program 100.0%

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

      1. associate-+l+ 100.0%

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

      2. +-commutative 100.0%

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

      3. associate-+l+ 100.0%

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

      4. +-commutative 100.0%

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

      5. count-2 100.0%

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

      6. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 81.3%

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

4. Final simplification 83.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+232} \lor \neg \left(x \leq 5 \cdot 10^{+125}\right):\\ \;\;\;\;3 \cdot x\\ \mathbf{else}:\\ \;\;\;\;z + 2 \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+73} \lor \neg \left(y \leq 3.1 \cdot 10^{+27}\right):\\ \;\;\;\;z + 2 \cdot y\\ \mathbf{else}:\\ \;\;\;\;z + 3 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.9e+73) (not (<= y 3.1e+27)))
   (+ z (* 2.0 y))
   (+ z (* 3.0 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.9e+73) || !(y <= 3.1e+27)) {
		tmp = z + (2.0 * y);
	} else {
		tmp = z + (3.0 * x);
	}
	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+73)) .or. (.not. (y <= 3.1d+27))) then
        tmp = z + (2.0d0 * y)
    else
        tmp = z + (3.0d0 * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.9e+73) || !(y <= 3.1e+27)) {
		tmp = z + (2.0 * y);
	} else {
		tmp = z + (3.0 * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.9e+73) or not (y <= 3.1e+27):
		tmp = z + (2.0 * y)
	else:
		tmp = z + (3.0 * x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.9e+73) || !(y <= 3.1e+27))
		tmp = Float64(z + Float64(2.0 * y));
	else
		tmp = Float64(z + Float64(3.0 * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.9e+73) || ~((y <= 3.1e+27)))
		tmp = z + (2.0 * y);
	else
		tmp = z + (3.0 * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.9e+73], N[Not[LessEqual[y, 3.1e+27]], $MachinePrecision]], N[(z + N[(2.0 * y), $MachinePrecision]), $MachinePrecision], N[(z + N[(3.0 * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.90000000000000011e73 or 3.09999999999999996e27 < y

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+l+ 99.9%

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

      4. +-commutative 99.9%

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

      5. count-2 99.9%

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

      6. +-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 86.8%

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

   if -1.90000000000000011e73 < y < 3.09999999999999996e27

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+l+ 99.9%

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

      4. +-commutative 99.9%

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

      5. count-2 99.9%

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

      6. +-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 88.4%

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

      1. +-commutative 88.4%

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

      2. associate-+l+ 88.4%

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

      3. distribute-lft1-in 88.4%

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

      4. metadata-eval 88.4%

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

   7. Simplified 88.4%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+73} \lor \neg \left(y \leq 3.1 \cdot 10^{+27}\right):\\ \;\;\;\;z + 2 \cdot y\\ \mathbf{else}:\\ \;\;\;\;z + 3 \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 52.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.55 \cdot 10^{+61}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-25}:\\ \;\;\;\;2 \cdot y\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -2.55e+61) z (if (<= z 5.8e-25) (* 2.0 y) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.55e+61) {
		tmp = z;
	} else if (z <= 5.8e-25) {
		tmp = 2.0 * y;
	} else {
		tmp = z;
	}
	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 (z <= (-2.55d+61)) then
        tmp = z
    else if (z <= 5.8d-25) then
        tmp = 2.0d0 * y
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.55e+61) {
		tmp = z;
	} else if (z <= 5.8e-25) {
		tmp = 2.0 * y;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -2.55e+61:
		tmp = z
	elif z <= 5.8e-25:
		tmp = 2.0 * y
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -2.55e+61)
		tmp = z;
	elseif (z <= 5.8e-25)
		tmp = Float64(2.0 * y);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -2.55e+61)
		tmp = z;
	elseif (z <= 5.8e-25)
		tmp = 2.0 * y;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -2.55e+61], z, If[LessEqual[z, 5.8e-25], N[(2.0 * y), $MachinePrecision], z]]

Derivation

1. Split input into 2 regimes

2. if z < -2.55000000000000005e61 or 5.8000000000000001e-25 < z

   1. Initial program 100.0%

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

      1. associate-+l+ 100.0%

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

      2. +-commutative 100.0%

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

      3. associate-+l+ 100.0%

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

      4. +-commutative 100.0%

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

      5. count-2 100.0%

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

      6. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 73.9%

      \[\leadsto \color{blue}{z} \]

   if -2.55000000000000005e61 < z < 5.8000000000000001e-25

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+l+ 99.9%

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

      4. +-commutative 99.9%

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

      5. count-2 99.9%

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

      6. +-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 45.3%

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

4. Final simplification 57.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.55 \cdot 10^{+61}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-25}:\\ \;\;\;\;2 \cdot y\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 34.7% accurate, 11.0× speedup

Math

\[\begin{array}{l} \\ z \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := z

Derivation

1. Initial program 99.9%

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

   1. associate-+l+ 99.9%

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

   2. +-commutative 99.9%

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

   3. associate-+l+ 99.9%

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

   4. +-commutative 99.9%

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

   5. count-2 99.9%

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

   6. +-commutative 99.9%

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

3. Simplified 99.9%

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

5. Taylor expanded in z around inf 35.7%

   \[\leadsto \color{blue}{z} \]

6. Final simplification 35.7%

   \[\leadsto z \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024034 
(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))