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

Percentage Accurate: 99.9% → 100.0%

Time: 3.8s

Alternatives: 10

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: 100.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(x, 3, \mathsf{fma}\left(y, 2, z\right)\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (fma x 3.0 (fma y 2.0 z)))

C

double code(double x, double y, double z) {
	return fma(x, 3.0, fma(y, 2.0, z));
}

Julia

function code(x, y, z)
	return fma(x, 3.0, fma(y, 2.0, z))
end

Wolfram

code[x_, y_, z_] := N[(x * 3.0 + N[(y * 2.0 + z), $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. +-commutative 99.9%

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

   2. +-commutative 99.9%

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

   3. associate-+l+ 99.9%

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

   4. associate-+r+ 99.9%

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

   5. count-2 99.9%

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

   6. associate-+l+ 99.9%

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

   7. associate-+r+ 99.9%

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

   8. distribute-rgt1-in 99.9%

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

   9. *-commutative 99.9%

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

   10. fma-def 100.0%

       \[\leadsto \color{blue}{\mathsf{fma}\left(x, 2 + 1, \left(y + y\right) + z\right)} \]

   11. metadata-eval 100.0%

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

   12. count-2 100.0%

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

   13. *-commutative 100.0%

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

   14. fma-def 100.0%

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

3. Simplified 100.0%

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

4. Final simplification 100.0%

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

Alternative 2: 53.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+53}:\\ \;\;\;\;x \cdot 3\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{-33}:\\ \;\;\;\;y \cdot 2\\ \mathbf{elif}\;x \leq -8 \cdot 10^{-73}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{-227}:\\ \;\;\;\;y \cdot 2\\ \mathbf{elif}\;x \leq 8.8 \cdot 10^{+55}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x \cdot 3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2.5e+53)
   (* x 3.0)
   (if (<= x -1.6e-33)
     (* y 2.0)
     (if (<= x -8e-73)
       z
       (if (<= x 1.9e-227) (* y 2.0) (if (<= x 8.8e+55) z (* x 3.0)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.5e+53) {
		tmp = x * 3.0;
	} else if (x <= -1.6e-33) {
		tmp = y * 2.0;
	} else if (x <= -8e-73) {
		tmp = z;
	} else if (x <= 1.9e-227) {
		tmp = y * 2.0;
	} else if (x <= 8.8e+55) {
		tmp = z;
	} else {
		tmp = x * 3.0;
	}
	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 <= (-2.5d+53)) then
        tmp = x * 3.0d0
    else if (x <= (-1.6d-33)) then
        tmp = y * 2.0d0
    else if (x <= (-8d-73)) then
        tmp = z
    else if (x <= 1.9d-227) then
        tmp = y * 2.0d0
    else if (x <= 8.8d+55) then
        tmp = z
    else
        tmp = x * 3.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.5e+53) {
		tmp = x * 3.0;
	} else if (x <= -1.6e-33) {
		tmp = y * 2.0;
	} else if (x <= -8e-73) {
		tmp = z;
	} else if (x <= 1.9e-227) {
		tmp = y * 2.0;
	} else if (x <= 8.8e+55) {
		tmp = z;
	} else {
		tmp = x * 3.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2.5e+53:
		tmp = x * 3.0
	elif x <= -1.6e-33:
		tmp = y * 2.0
	elif x <= -8e-73:
		tmp = z
	elif x <= 1.9e-227:
		tmp = y * 2.0
	elif x <= 8.8e+55:
		tmp = z
	else:
		tmp = x * 3.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.5e+53)
		tmp = Float64(x * 3.0);
	elseif (x <= -1.6e-33)
		tmp = Float64(y * 2.0);
	elseif (x <= -8e-73)
		tmp = z;
	elseif (x <= 1.9e-227)
		tmp = Float64(y * 2.0);
	elseif (x <= 8.8e+55)
		tmp = z;
	else
		tmp = Float64(x * 3.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -2.5e+53)
		tmp = x * 3.0;
	elseif (x <= -1.6e-33)
		tmp = y * 2.0;
	elseif (x <= -8e-73)
		tmp = z;
	elseif (x <= 1.9e-227)
		tmp = y * 2.0;
	elseif (x <= 8.8e+55)
		tmp = z;
	else
		tmp = x * 3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2.5e+53], N[(x * 3.0), $MachinePrecision], If[LessEqual[x, -1.6e-33], N[(y * 2.0), $MachinePrecision], If[LessEqual[x, -8e-73], z, If[LessEqual[x, 1.9e-227], N[(y * 2.0), $MachinePrecision], If[LessEqual[x, 8.8e+55], z, N[(x * 3.0), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.5000000000000002e53 or 8.80000000000000042e55 < 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. +-commutative 99.8%

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

      2. associate-+l+ 99.8%

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

      3. +-commutative 99.8%

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

      4. count-2 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 68.6%

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

   if -2.5000000000000002e53 < x < -1.59999999999999988e-33 or -7.99999999999999998e-73 < x < 1.90000000000000005e-227

   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. +-commutative 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. count-2 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 57.8%

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

   if -1.59999999999999988e-33 < x < -7.99999999999999998e-73 or 1.90000000000000005e-227 < x < 8.80000000000000042e55

   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. +-commutative 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around inf 55.4%

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

4. Final simplification 61.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+53}:\\ \;\;\;\;x \cdot 3\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{-33}:\\ \;\;\;\;y \cdot 2\\ \mathbf{elif}\;x \leq -8 \cdot 10^{-73}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{-227}:\\ \;\;\;\;y \cdot 2\\ \mathbf{elif}\;x \leq 8.8 \cdot 10^{+55}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x \cdot 3\\ \end{array} \]

Alternative 3: 84.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{-22}:\\ \;\;\;\;z + x \cdot 3\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-26}:\\ \;\;\;\;x + 2 \cdot \left(x + y\right)\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -4e-22)
   (+ z (* x 3.0))
   (if (<= z 2.1e-26) (+ x (* 2.0 (+ x y))) (+ z (* y 2.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -4e-22) {
		tmp = z + (x * 3.0);
	} else if (z <= 2.1e-26) {
		tmp = x + (2.0 * (x + y));
	} else {
		tmp = z + (y * 2.0);
	}
	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 <= (-4d-22)) then
        tmp = z + (x * 3.0d0)
    else if (z <= 2.1d-26) then
        tmp = x + (2.0d0 * (x + y))
    else
        tmp = z + (y * 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -4e-22) {
		tmp = z + (x * 3.0);
	} else if (z <= 2.1e-26) {
		tmp = x + (2.0 * (x + y));
	} else {
		tmp = z + (y * 2.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -4e-22:
		tmp = z + (x * 3.0)
	elif z <= 2.1e-26:
		tmp = x + (2.0 * (x + y))
	else:
		tmp = z + (y * 2.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -4e-22)
		tmp = Float64(z + Float64(x * 3.0));
	elseif (z <= 2.1e-26)
		tmp = Float64(x + Float64(2.0 * Float64(x + y)));
	else
		tmp = Float64(z + Float64(y * 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -4e-22)
		tmp = z + (x * 3.0);
	elseif (z <= 2.1e-26)
		tmp = x + (2.0 * (x + y));
	else
		tmp = z + (y * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -4e-22], N[(z + N[(x * 3.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.1e-26], N[(x + N[(2.0 * N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z + N[(y * 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.0000000000000002e-22

   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. +-commutative 99.8%

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

      2. associate-+l+ 99.8%

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

      3. +-commutative 99.8%

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

      4. count-2 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around 0 87.2%

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

      1. +-commutative 87.2%

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

      2. associate-+l+ 87.3%

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

      3. distribute-rgt1-in 87.3%

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

      4. metadata-eval 87.3%

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

   6. Simplified 87.3%

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

   if -4.0000000000000002e-22 < z < 2.10000000000000008e-26

   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. +-commutative 99.8%

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

      2. associate-+l+ 99.8%

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

      3. +-commutative 99.8%

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

      4. count-2 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around 0 93.7%

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

   if 2.10000000000000008e-26 < 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. +-commutative 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 85.4%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{-22}:\\ \;\;\;\;z + x \cdot 3\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-26}:\\ \;\;\;\;x + 2 \cdot \left(x + y\right)\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot 2\\ \end{array} \]

Alternative 4: 84.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{-18}:\\ \;\;\;\;z + x \cdot 3\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-27}:\\ \;\;\;\;x \cdot 3 + y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -8.5e-18)
   (+ z (* x 3.0))
   (if (<= z 4.2e-27) (+ (* x 3.0) (* y 2.0)) (+ z (* y 2.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -8.5e-18) {
		tmp = z + (x * 3.0);
	} else if (z <= 4.2e-27) {
		tmp = (x * 3.0) + (y * 2.0);
	} else {
		tmp = z + (y * 2.0);
	}
	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 <= (-8.5d-18)) then
        tmp = z + (x * 3.0d0)
    else if (z <= 4.2d-27) then
        tmp = (x * 3.0d0) + (y * 2.0d0)
    else
        tmp = z + (y * 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -8.5e-18) {
		tmp = z + (x * 3.0);
	} else if (z <= 4.2e-27) {
		tmp = (x * 3.0) + (y * 2.0);
	} else {
		tmp = z + (y * 2.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -8.5e-18:
		tmp = z + (x * 3.0)
	elif z <= 4.2e-27:
		tmp = (x * 3.0) + (y * 2.0)
	else:
		tmp = z + (y * 2.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -8.5e-18)
		tmp = Float64(z + Float64(x * 3.0));
	elseif (z <= 4.2e-27)
		tmp = Float64(Float64(x * 3.0) + Float64(y * 2.0));
	else
		tmp = Float64(z + Float64(y * 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -8.5e-18)
		tmp = z + (x * 3.0);
	elseif (z <= 4.2e-27)
		tmp = (x * 3.0) + (y * 2.0);
	else
		tmp = z + (y * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -8.5e-18], N[(z + N[(x * 3.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.2e-27], N[(N[(x * 3.0), $MachinePrecision] + N[(y * 2.0), $MachinePrecision]), $MachinePrecision], N[(z + N[(y * 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.4999999999999995e-18

   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. +-commutative 99.8%

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

      2. associate-+l+ 99.8%

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

      3. +-commutative 99.8%

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

      4. count-2 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around 0 87.2%

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

      1. +-commutative 87.2%

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

      2. associate-+l+ 87.3%

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

      3. distribute-rgt1-in 87.3%

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

      4. metadata-eval 87.3%

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

   6. Simplified 87.3%

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

   if -8.4999999999999995e-18 < z < 4.20000000000000031e-27

   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. +-commutative 99.8%

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

      2. associate-+l+ 99.8%

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

      3. +-commutative 99.8%

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

      4. count-2 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around 0 99.9%

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

   5. Taylor expanded in z around 0 93.7%

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

   if 4.20000000000000031e-27 < 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. +-commutative 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 85.4%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{-18}:\\ \;\;\;\;z + x \cdot 3\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-27}:\\ \;\;\;\;x \cdot 3 + y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot 2\\ \end{array} \]

Alternative 5: 85.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{+53} \lor \neg \left(x \leq 1.5 \cdot 10^{+40}\right):\\ \;\;\;\;z + x \cdot 3\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -6e+53) (not (<= x 1.5e+40))) (+ z (* x 3.0)) (+ z (* y 2.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -6e+53) || !(x <= 1.5e+40)) {
		tmp = z + (x * 3.0);
	} else {
		tmp = z + (y * 2.0);
	}
	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 <= (-6d+53)) .or. (.not. (x <= 1.5d+40))) then
        tmp = z + (x * 3.0d0)
    else
        tmp = z + (y * 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -6e+53) || !(x <= 1.5e+40)) {
		tmp = z + (x * 3.0);
	} else {
		tmp = z + (y * 2.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -6e+53) or not (x <= 1.5e+40):
		tmp = z + (x * 3.0)
	else:
		tmp = z + (y * 2.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -6e+53) || !(x <= 1.5e+40))
		tmp = Float64(z + Float64(x * 3.0));
	else
		tmp = Float64(z + Float64(y * 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -6e+53) || ~((x <= 1.5e+40)))
		tmp = z + (x * 3.0);
	else
		tmp = z + (y * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -6e+53], N[Not[LessEqual[x, 1.5e+40]], $MachinePrecision]], N[(z + N[(x * 3.0), $MachinePrecision]), $MachinePrecision], N[(z + N[(y * 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.99999999999999996e53 or 1.5000000000000001e40 < 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. +-commutative 99.8%

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

      2. associate-+l+ 99.8%

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

      3. +-commutative 99.8%

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

      4. count-2 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around 0 83.1%

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

      1. +-commutative 83.1%

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

      2. associate-+l+ 83.1%

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

      3. distribute-rgt1-in 83.1%

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

      4. metadata-eval 83.1%

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

   6. Simplified 83.1%

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

   if -5.99999999999999996e53 < x < 1.5000000000000001e40

   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. +-commutative 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 88.5%

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

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{+53} \lor \neg \left(x \leq 1.5 \cdot 10^{+40}\right):\\ \;\;\;\;z + x \cdot 3\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot 2\\ \end{array} \]

Alternative 6: 79.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.45 \cdot 10^{+164}:\\ \;\;\;\;y \cdot 2\\ \mathbf{elif}\;y \leq 6.7 \cdot 10^{+158}:\\ \;\;\;\;z + x \cdot 3\\ \mathbf{else}:\\ \;\;\;\;y \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.45e+164)
   (* y 2.0)
   (if (<= y 6.7e+158) (+ z (* x 3.0)) (* y 2.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.45e+164) {
		tmp = y * 2.0;
	} else if (y <= 6.7e+158) {
		tmp = z + (x * 3.0);
	} else {
		tmp = y * 2.0;
	}
	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+164)) then
        tmp = y * 2.0d0
    else if (y <= 6.7d+158) then
        tmp = z + (x * 3.0d0)
    else
        tmp = y * 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.45e+164) {
		tmp = y * 2.0;
	} else if (y <= 6.7e+158) {
		tmp = z + (x * 3.0);
	} else {
		tmp = y * 2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3.45e+164:
		tmp = y * 2.0
	elif y <= 6.7e+158:
		tmp = z + (x * 3.0)
	else:
		tmp = y * 2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.45e+164)
		tmp = Float64(y * 2.0);
	elseif (y <= 6.7e+158)
		tmp = Float64(z + Float64(x * 3.0));
	else
		tmp = Float64(y * 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -3.45e+164)
		tmp = y * 2.0;
	elseif (y <= 6.7e+158)
		tmp = z + (x * 3.0);
	else
		tmp = y * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.45e+164], N[(y * 2.0), $MachinePrecision], If[LessEqual[y, 6.7e+158], N[(z + N[(x * 3.0), $MachinePrecision]), $MachinePrecision], N[(y * 2.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.44999999999999993e164 or 6.6999999999999996e158 < 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. +-commutative 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. count-2 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 82.5%

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

   if -3.44999999999999993e164 < y < 6.6999999999999996e158

   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. +-commutative 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. count-2 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 79.9%

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

      1. +-commutative 79.9%

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

      2. associate-+l+ 79.9%

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

      3. distribute-rgt1-in 79.9%

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

      4. metadata-eval 79.9%

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

   6. Simplified 79.9%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.45 \cdot 10^{+164}:\\ \;\;\;\;y \cdot 2\\ \mathbf{elif}\;y \leq 6.7 \cdot 10^{+158}:\\ \;\;\;\;z + x \cdot 3\\ \mathbf{else}:\\ \;\;\;\;y \cdot 2\\ \end{array} \]

Alternative 7: 99.9% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + (z + (2.0d0 * (x + y)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(x + N[(z + N[(2.0 * N[(x + y), $MachinePrecision]), $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. +-commutative 99.9%

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

   2. associate-+l+ 99.9%

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

   3. +-commutative 99.9%

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

   4. count-2 99.9%

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

3. Simplified 99.9%

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

4. Final simplification 99.9%

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

Alternative 8: 99.9% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

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 * 3.0d0) + (z + (y * 2.0d0))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(N[(x * 3.0), $MachinePrecision] + N[(z + N[(y * 2.0), $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. +-commutative 99.9%

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

   2. associate-+l+ 99.9%

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

   3. +-commutative 99.9%

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

   4. count-2 99.9%

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

3. Simplified 99.9%

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

4. Taylor expanded in x around 0 99.9%

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

5. Final simplification 99.9%

   \[\leadsto x \cdot 3 + \left(z + y \cdot 2\right) \]

Alternative 9: 52.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+28}:\\ \;\;\;\;y \cdot 2\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+63}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.8e+28) (* y 2.0) (if (<= y 9e+63) z (* y 2.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.8e+28) {
		tmp = y * 2.0;
	} else if (y <= 9e+63) {
		tmp = z;
	} else {
		tmp = y * 2.0;
	}
	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 <= (-3.8d+28)) then
        tmp = y * 2.0d0
    else if (y <= 9d+63) then
        tmp = z
    else
        tmp = y * 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.8e+28) {
		tmp = y * 2.0;
	} else if (y <= 9e+63) {
		tmp = z;
	} else {
		tmp = y * 2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3.8e+28:
		tmp = y * 2.0
	elif y <= 9e+63:
		tmp = z
	else:
		tmp = y * 2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.8e+28)
		tmp = Float64(y * 2.0);
	elseif (y <= 9e+63)
		tmp = z;
	else
		tmp = Float64(y * 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -3.8e+28)
		tmp = y * 2.0;
	elseif (y <= 9e+63)
		tmp = z;
	else
		tmp = y * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.8e+28], N[(y * 2.0), $MachinePrecision], If[LessEqual[y, 9e+63], z, N[(y * 2.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.7999999999999999e28 or 9.00000000000000034e63 < 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. +-commutative 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. count-2 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 64.1%

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

   if -3.7999999999999999e28 < y < 9.00000000000000034e63

   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. +-commutative 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. count-2 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 46.6%

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

4. Final simplification 53.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+28}:\\ \;\;\;\;y \cdot 2\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+63}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y \cdot 2\\ \end{array} \]

Alternative 10: 33.0% 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. +-commutative 99.9%

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

   2. associate-+l+ 99.9%

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

   3. +-commutative 99.9%

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

   4. count-2 99.9%

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

3. Simplified 99.9%

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

4. Taylor expanded in z around inf 33.5%

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

5. Final simplification 33.5%

   \[\leadsto z \]

Reproduce

herbie shell --seed 2023238 
(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))