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

Percentage Accurate: 99.9% → 99.9%

Time: 6.9s

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: 53.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+70}:\\ \;\;\;\;2 \cdot y\\ \mathbf{elif}\;y \leq -2.95 \cdot 10^{-170}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 10200000:\\ \;\;\;\;3 \cdot x\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+86}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;2 \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.6e+70)
   (* 2.0 y)
   (if (<= y -2.95e-170)
     z
     (if (<= y 10200000.0) (* 3.0 x) (if (<= y 3.1e+86) z (* 2.0 y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.6e+70) {
		tmp = 2.0 * y;
	} else if (y <= -2.95e-170) {
		tmp = z;
	} else if (y <= 10200000.0) {
		tmp = 3.0 * x;
	} else if (y <= 3.1e+86) {
		tmp = z;
	} else {
		tmp = 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 (y <= (-3.6d+70)) then
        tmp = 2.0d0 * y
    else if (y <= (-2.95d-170)) then
        tmp = z
    else if (y <= 10200000.0d0) then
        tmp = 3.0d0 * x
    else if (y <= 3.1d+86) then
        tmp = z
    else
        tmp = 2.0d0 * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.6e+70) {
		tmp = 2.0 * y;
	} else if (y <= -2.95e-170) {
		tmp = z;
	} else if (y <= 10200000.0) {
		tmp = 3.0 * x;
	} else if (y <= 3.1e+86) {
		tmp = z;
	} else {
		tmp = 2.0 * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3.6e+70:
		tmp = 2.0 * y
	elif y <= -2.95e-170:
		tmp = z
	elif y <= 10200000.0:
		tmp = 3.0 * x
	elif y <= 3.1e+86:
		tmp = z
	else:
		tmp = 2.0 * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.6e+70)
		tmp = Float64(2.0 * y);
	elseif (y <= -2.95e-170)
		tmp = z;
	elseif (y <= 10200000.0)
		tmp = Float64(3.0 * x);
	elseif (y <= 3.1e+86)
		tmp = z;
	else
		tmp = Float64(2.0 * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -3.6e+70)
		tmp = 2.0 * y;
	elseif (y <= -2.95e-170)
		tmp = z;
	elseif (y <= 10200000.0)
		tmp = 3.0 * x;
	elseif (y <= 3.1e+86)
		tmp = z;
	else
		tmp = 2.0 * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.6e+70], N[(2.0 * y), $MachinePrecision], If[LessEqual[y, -2.95e-170], z, If[LessEqual[y, 10200000.0], N[(3.0 * x), $MachinePrecision], If[LessEqual[y, 3.1e+86], z, N[(2.0 * y), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.6e70 or 3.1000000000000002e86 < 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+ 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 69.4%

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

   if -3.6e70 < y < -2.9499999999999999e-170 or 1.02e7 < y < 3.1000000000000002e86

   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 58.1%

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

   if -2.9499999999999999e-170 < y < 1.02e7

   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 inf 54.7%

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

4. Final simplification 61.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+70}:\\ \;\;\;\;2 \cdot y\\ \mathbf{elif}\;y \leq -2.95 \cdot 10^{-170}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 10200000:\\ \;\;\;\;3 \cdot x\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+86}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;2 \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 86.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+32}:\\ \;\;\;\;z + 2 \cdot y\\ \mathbf{elif}\;y \leq 2.75 \cdot 10^{+88}:\\ \;\;\;\;z + 3 \cdot x\\ \mathbf{else}:\\ \;\;\;\;x + 2 \cdot \left(y + x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.1e+32)
   (+ z (* 2.0 y))
   (if (<= y 2.75e+88) (+ z (* 3.0 x)) (+ x (* 2.0 (+ y x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.1e+32) {
		tmp = z + (2.0 * y);
	} else if (y <= 2.75e+88) {
		tmp = z + (3.0 * x);
	} 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 (y <= (-3.1d+32)) then
        tmp = z + (2.0d0 * y)
    else if (y <= 2.75d+88) then
        tmp = z + (3.0d0 * x)
    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 (y <= -3.1e+32) {
		tmp = z + (2.0 * y);
	} else if (y <= 2.75e+88) {
		tmp = z + (3.0 * x);
	} else {
		tmp = x + (2.0 * (y + x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3.1e+32:
		tmp = z + (2.0 * y)
	elif y <= 2.75e+88:
		tmp = z + (3.0 * x)
	else:
		tmp = x + (2.0 * (y + x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.1e+32)
		tmp = Float64(z + Float64(2.0 * y));
	elseif (y <= 2.75e+88)
		tmp = Float64(z + Float64(3.0 * x));
	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 (y <= -3.1e+32)
		tmp = z + (2.0 * y);
	elseif (y <= 2.75e+88)
		tmp = z + (3.0 * x);
	else
		tmp = x + (2.0 * (y + x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.1e+32], N[(z + N[(2.0 * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.75e+88], N[(z + N[(3.0 * x), $MachinePrecision]), $MachinePrecision], N[(x + N[(2.0 * N[(y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.09999999999999993e32

   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 87.8%

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

   if -3.09999999999999993e32 < y < 2.75e88

   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 93.0%

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

      1. +-commutative 93.0%

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

      2. associate-+l+ 93.0%

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

      3. distribute-lft1-in 93.0%

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

      4. metadata-eval 93.0%

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

   7. Simplified 93.0%

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

   if 2.75e88 < y

   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 0 87.0%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+32}:\\ \;\;\;\;z + 2 \cdot y\\ \mathbf{elif}\;y \leq 2.75 \cdot 10^{+88}:\\ \;\;\;\;z + 3 \cdot x\\ \mathbf{else}:\\ \;\;\;\;x + 2 \cdot \left(y + x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 80.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.3 \cdot 10^{+134} \lor \neg \left(x \leq 2.6 \cdot 10^{+104}\right):\\ \;\;\;\;3 \cdot x\\ \mathbf{else}:\\ \;\;\;\;z + 2 \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -6.3e+134) (not (<= x 2.6e+104))) (* 3.0 x) (+ z (* 2.0 y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -6.3e+134) || !(x <= 2.6e+104)) {
		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 <= (-6.3d+134)) .or. (.not. (x <= 2.6d+104))) 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 <= -6.3e+134) || !(x <= 2.6e+104)) {
		tmp = 3.0 * x;
	} else {
		tmp = z + (2.0 * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -6.3e+134) or not (x <= 2.6e+104):
		tmp = 3.0 * x
	else:
		tmp = z + (2.0 * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -6.3e+134) || !(x <= 2.6e+104))
		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 <= -6.3e+134) || ~((x <= 2.6e+104)))
		tmp = 3.0 * x;
	else
		tmp = z + (2.0 * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -6.3e+134], N[Not[LessEqual[x, 2.6e+104]], $MachinePrecision]], N[(3.0 * x), $MachinePrecision], N[(z + N[(2.0 * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.3000000000000003e134 or 2.6e104 < x

   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+ 99.8%

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

      4. +-commutative 99.8%

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

      5. count-2 99.8%

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

      6. +-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 68.4%

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

   if -6.3000000000000003e134 < x < 2.6e104

   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 84.1%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.3 \cdot 10^{+134} \lor \neg \left(x \leq 2.6 \cdot 10^{+104}\right):\\ \;\;\;\;3 \cdot x\\ \mathbf{else}:\\ \;\;\;\;z + 2 \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 86.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.45 \cdot 10^{+30} \lor \neg \left(y \leq 6.5 \cdot 10^{+77}\right):\\ \;\;\;\;z + 2 \cdot y\\ \mathbf{else}:\\ \;\;\;\;z + 3 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3.45e+30) (not (<= y 6.5e+77)))
   (+ z (* 2.0 y))
   (+ z (* 3.0 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.45e+30) || !(y <= 6.5e+77)) {
		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 <= (-3.45d+30)) .or. (.not. (y <= 6.5d+77))) 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 <= -3.45e+30) || !(y <= 6.5e+77)) {
		tmp = z + (2.0 * y);
	} else {
		tmp = z + (3.0 * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3.45e+30) or not (y <= 6.5e+77):
		tmp = z + (2.0 * y)
	else:
		tmp = z + (3.0 * x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3.45e+30) || !(y <= 6.5e+77))
		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 <= -3.45e+30) || ~((y <= 6.5e+77)))
		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, -3.45e+30], N[Not[LessEqual[y, 6.5e+77]], $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 < -3.4499999999999999e30 or 6.5e77 < 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+ 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 83.9%

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

   if -3.4499999999999999e30 < y < 6.5e77

   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 92.9%

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

      1. +-commutative 92.9%

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

      2. associate-+l+ 92.9%

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

      3. distribute-lft1-in 92.9%

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

      4. metadata-eval 92.9%

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

   7. Simplified 92.9%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.45 \cdot 10^{+30} \lor \neg \left(y \leq 6.5 \cdot 10^{+77}\right):\\ \;\;\;\;z + 2 \cdot y\\ \mathbf{else}:\\ \;\;\;\;z + 3 \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 54.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+69} \lor \neg \left(y \leq 8.5 \cdot 10^{+88}\right):\\ \;\;\;\;2 \cdot y\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1e+69) (not (<= y 8.5e+88))) (* 2.0 y) z))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1e+69) || !(y <= 8.5e+88)) {
		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 ((y <= (-1d+69)) .or. (.not. (y <= 8.5d+88))) 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 ((y <= -1e+69) || !(y <= 8.5e+88)) {
		tmp = 2.0 * y;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1e+69) or not (y <= 8.5e+88):
		tmp = 2.0 * y
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1e+69) || !(y <= 8.5e+88))
		tmp = Float64(2.0 * y);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1e+69) || ~((y <= 8.5e+88)))
		tmp = 2.0 * y;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1e+69], N[Not[LessEqual[y, 8.5e+88]], $MachinePrecision]], N[(2.0 * y), $MachinePrecision], z]

Derivation

1. Split input into 2 regimes

2. if y < -1.0000000000000001e69 or 8.5000000000000005e88 < 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+ 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 69.4%

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

   if -1.0000000000000001e69 < y < 8.5000000000000005e88

   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 48.7%

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

4. Final simplification 57.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+69} \lor \neg \left(y \leq 8.5 \cdot 10^{+88}\right):\\ \;\;\;\;2 \cdot y\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 35.0% 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 34.9%

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

6. Final simplification 34.9%

   \[\leadsto z \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024046 
(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))