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

Percentage Accurate: 100.0% → 100.0%

Time: 5.9s

Alternatives: 9

Speedup: 1.2×

• could not determine a ground truth

  1. x = -2.282608770082e+166
  2. y = 4.798762470553445e-81
  3. z = -1.0083907073872857e-287

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: 100.0% 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

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

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%

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

   2. associate-+l+ 100.0%

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

   3. remove-double-neg 100.0%

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

   4. unsub-neg 100.0%

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

   5. +-commutative 100.0%

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

   6. +-commutative 100.0%

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

   7. associate-+l+ 100.0%

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

   8. associate-+r+ 100.0%

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

   9. associate-+r+ 100.0%

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

   10. distribute-neg-in 100.0%

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

   11. distribute-neg-out 100.0%

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

   12. neg-mul-1 100.0%

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

   13. count-2 100.0%

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

   14. distribute-lft-neg-in 100.0%

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

   15. metadata-eval 100.0%

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

   16. metadata-eval 100.0%

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

   17. distribute-rgt-out 100.0%

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

   18. distribute-neg-out 100.0%

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

   19. fma-define 100.0%

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

3. Simplified 100.0%

   \[\leadsto \color{blue}{z - \mathsf{fma}\left(x, -3, y \cdot -2\right)} \]
4. Add Preprocessing

5. Final simplification 100.0%

   \[\leadsto z - \mathsf{fma}\left(x, -3, y \cdot -2\right) \]
6. Add Preprocessing

Alternative 2: 55.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.1 \cdot 10^{+53}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 1.32 \cdot 10^{-213}:\\ \;\;\;\;y \cdot 2\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-106}:\\ \;\;\;\;x \cdot 3\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-51}:\\ \;\;\;\;y \cdot 2\\ \mathbf{elif}\;z \leq 1.38 \cdot 10^{+29}:\\ \;\;\;\;x \cdot 3\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -7.1e+53)
   z
   (if (<= z 1.32e-213)
     (* y 2.0)
     (if (<= z 2e-106)
       (* x 3.0)
       (if (<= z 3.3e-51) (* y 2.0) (if (<= z 1.38e+29) (* x 3.0) z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -7.1e+53) {
		tmp = z;
	} else if (z <= 1.32e-213) {
		tmp = y * 2.0;
	} else if (z <= 2e-106) {
		tmp = x * 3.0;
	} else if (z <= 3.3e-51) {
		tmp = y * 2.0;
	} else if (z <= 1.38e+29) {
		tmp = x * 3.0;
	} 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 <= (-7.1d+53)) then
        tmp = z
    else if (z <= 1.32d-213) then
        tmp = y * 2.0d0
    else if (z <= 2d-106) then
        tmp = x * 3.0d0
    else if (z <= 3.3d-51) then
        tmp = y * 2.0d0
    else if (z <= 1.38d+29) then
        tmp = x * 3.0d0
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -7.1e+53) {
		tmp = z;
	} else if (z <= 1.32e-213) {
		tmp = y * 2.0;
	} else if (z <= 2e-106) {
		tmp = x * 3.0;
	} else if (z <= 3.3e-51) {
		tmp = y * 2.0;
	} else if (z <= 1.38e+29) {
		tmp = x * 3.0;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -7.1e+53:
		tmp = z
	elif z <= 1.32e-213:
		tmp = y * 2.0
	elif z <= 2e-106:
		tmp = x * 3.0
	elif z <= 3.3e-51:
		tmp = y * 2.0
	elif z <= 1.38e+29:
		tmp = x * 3.0
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -7.1e+53)
		tmp = z;
	elseif (z <= 1.32e-213)
		tmp = Float64(y * 2.0);
	elseif (z <= 2e-106)
		tmp = Float64(x * 3.0);
	elseif (z <= 3.3e-51)
		tmp = Float64(y * 2.0);
	elseif (z <= 1.38e+29)
		tmp = Float64(x * 3.0);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -7.1e+53)
		tmp = z;
	elseif (z <= 1.32e-213)
		tmp = y * 2.0;
	elseif (z <= 2e-106)
		tmp = x * 3.0;
	elseif (z <= 3.3e-51)
		tmp = y * 2.0;
	elseif (z <= 1.38e+29)
		tmp = x * 3.0;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -7.1e+53], z, If[LessEqual[z, 1.32e-213], N[(y * 2.0), $MachinePrecision], If[LessEqual[z, 2e-106], N[(x * 3.0), $MachinePrecision], If[LessEqual[z, 3.3e-51], N[(y * 2.0), $MachinePrecision], If[LessEqual[z, 1.38e+29], N[(x * 3.0), $MachinePrecision], z]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.09999999999999974e53 or 1.38e29 < 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. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

      5. +-commutative 100.0%

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

      6. +-commutative 100.0%

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

   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 76.1%

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

   if -7.09999999999999974e53 < z < 1.3199999999999999e-213 or 1.99999999999999988e-106 < z < 3.29999999999999973e-51

   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. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

      5. +-commutative 100.0%

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

      6. +-commutative 100.0%

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

   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 60.4%

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

   if 1.3199999999999999e-213 < z < 1.99999999999999988e-106 or 3.29999999999999973e-51 < z < 1.38e29

   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. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

      5. +-commutative 100.0%

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

      6. +-commutative 100.0%

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

   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 inf 56.7%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.1 \cdot 10^{+53}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 1.32 \cdot 10^{-213}:\\ \;\;\;\;y \cdot 2\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-106}:\\ \;\;\;\;x \cdot 3\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-51}:\\ \;\;\;\;y \cdot 2\\ \mathbf{elif}\;z \leq 1.38 \cdot 10^{+29}:\\ \;\;\;\;x \cdot 3\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 86.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+64} \lor \neg \left(z \leq 1.9 \cdot 10^{+29}\right):\\ \;\;\;\;z + y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x + 2 \cdot \left(x + y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -3.2e+64) (not (<= z 1.9e+29)))
   (+ z (* y 2.0))
   (+ x (* 2.0 (+ x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.2e+64) || !(z <= 1.9e+29)) {
		tmp = z + (y * 2.0);
	} else {
		tmp = x + (2.0 * (x + 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 ((z <= (-3.2d+64)) .or. (.not. (z <= 1.9d+29))) then
        tmp = z + (y * 2.0d0)
    else
        tmp = x + (2.0d0 * (x + y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.2e+64) || !(z <= 1.9e+29)) {
		tmp = z + (y * 2.0);
	} else {
		tmp = x + (2.0 * (x + y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -3.2e+64) or not (z <= 1.9e+29):
		tmp = z + (y * 2.0)
	else:
		tmp = x + (2.0 * (x + y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -3.2e+64) || !(z <= 1.9e+29))
		tmp = Float64(z + Float64(y * 2.0));
	else
		tmp = Float64(x + Float64(2.0 * Float64(x + y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -3.2e+64) || ~((z <= 1.9e+29)))
		tmp = z + (y * 2.0);
	else
		tmp = x + (2.0 * (x + y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -3.2e+64], N[Not[LessEqual[z, 1.9e+29]], $MachinePrecision]], N[(z + N[(y * 2.0), $MachinePrecision]), $MachinePrecision], N[(x + N[(2.0 * N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.20000000000000019e64 or 1.89999999999999985e29 < 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. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

      5. +-commutative 100.0%

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

      6. +-commutative 100.0%

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

   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 90.3%

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

   if -3.20000000000000019e64 < z < 1.89999999999999985e29

   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. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

      5. +-commutative 100.0%

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

      6. +-commutative 100.0%

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

   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 89.8%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+64} \lor \neg \left(z \leq 1.9 \cdot 10^{+29}\right):\\ \;\;\;\;z + y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x + 2 \cdot \left(x + y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 86.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+53} \lor \neg \left(z \leq 1.3 \cdot 10^{+29}\right):\\ \;\;\;\;z + y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;y \cdot 2 + x \cdot 3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -7.5e+53) (not (<= z 1.3e+29)))
   (+ z (* y 2.0))
   (+ (* y 2.0) (* x 3.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -7.5e+53) || !(z <= 1.3e+29)) {
		tmp = z + (y * 2.0);
	} else {
		tmp = (y * 2.0) + (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 ((z <= (-7.5d+53)) .or. (.not. (z <= 1.3d+29))) then
        tmp = z + (y * 2.0d0)
    else
        tmp = (y * 2.0d0) + (x * 3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -7.5e+53) || !(z <= 1.3e+29)) {
		tmp = z + (y * 2.0);
	} else {
		tmp = (y * 2.0) + (x * 3.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -7.5e+53) or not (z <= 1.3e+29):
		tmp = z + (y * 2.0)
	else:
		tmp = (y * 2.0) + (x * 3.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -7.5e+53) || !(z <= 1.3e+29))
		tmp = Float64(z + Float64(y * 2.0));
	else
		tmp = Float64(Float64(y * 2.0) + Float64(x * 3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -7.5e+53) || ~((z <= 1.3e+29)))
		tmp = z + (y * 2.0);
	else
		tmp = (y * 2.0) + (x * 3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -7.5e+53], N[Not[LessEqual[z, 1.3e+29]], $MachinePrecision]], N[(z + N[(y * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(y * 2.0), $MachinePrecision] + N[(x * 3.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.4999999999999997e53 or 1.3e29 < 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. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

      5. +-commutative 100.0%

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

      6. +-commutative 100.0%

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

   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 90.3%

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

   if -7.4999999999999997e53 < z < 1.3e29

   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. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

      5. +-commutative 100.0%

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

      6. +-commutative 100.0%

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

   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 89.8%

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

   6. Taylor expanded in x around 0 89.8%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+53} \lor \neg \left(z \leq 1.3 \cdot 10^{+29}\right):\\ \;\;\;\;z + y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;y \cdot 2 + x \cdot 3\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 80.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{+117} \lor \neg \left(x \leq 3.6 \cdot 10^{+98}\right):\\ \;\;\;\;x \cdot 3\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -6.8e+117) (not (<= x 3.6e+98))) (* x 3.0) (+ z (* y 2.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -6.8e+117) || !(x <= 3.6e+98)) {
		tmp = 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 <= (-6.8d+117)) .or. (.not. (x <= 3.6d+98))) then
        tmp = 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 <= -6.8e+117) || !(x <= 3.6e+98)) {
		tmp = x * 3.0;
	} else {
		tmp = z + (y * 2.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -6.8e+117) or not (x <= 3.6e+98):
		tmp = x * 3.0
	else:
		tmp = z + (y * 2.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -6.8e+117) || !(x <= 3.6e+98))
		tmp = 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 <= -6.8e+117) || ~((x <= 3.6e+98)))
		tmp = x * 3.0;
	else
		tmp = z + (y * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -6.8e+117], N[Not[LessEqual[x, 3.6e+98]], $MachinePrecision]], N[(x * 3.0), $MachinePrecision], N[(z + N[(y * 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.8000000000000002e117 or 3.59999999999999981e98 < x

   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. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

      5. +-commutative 100.0%

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

      6. +-commutative 100.0%

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

   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 inf 63.1%

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

   if -6.8000000000000002e117 < x < 3.59999999999999981e98

   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. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

      5. +-commutative 100.0%

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

      6. +-commutative 100.0%

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

   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 86.1%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{+117} \lor \neg \left(x \leq 3.6 \cdot 10^{+98}\right):\\ \;\;\;\;x \cdot 3\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 86.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+42} \lor \neg \left(y \leq 9 \cdot 10^{+69}\right):\\ \;\;\;\;z + y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;z + x \cdot 3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -5.2e+42) (not (<= y 9e+69))) (+ z (* y 2.0)) (+ z (* x 3.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5.2e+42) || !(y <= 9e+69)) {
		tmp = z + (y * 2.0);
	} else {
		tmp = z + (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 ((y <= (-5.2d+42)) .or. (.not. (y <= 9d+69))) then
        tmp = z + (y * 2.0d0)
    else
        tmp = z + (x * 3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5.2e+42) || !(y <= 9e+69)) {
		tmp = z + (y * 2.0);
	} else {
		tmp = z + (x * 3.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -5.2e+42) or not (y <= 9e+69):
		tmp = z + (y * 2.0)
	else:
		tmp = z + (x * 3.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -5.2e+42) || !(y <= 9e+69))
		tmp = Float64(z + Float64(y * 2.0));
	else
		tmp = Float64(z + Float64(x * 3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -5.2e+42) || ~((y <= 9e+69)))
		tmp = z + (y * 2.0);
	else
		tmp = z + (x * 3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -5.2e+42], N[Not[LessEqual[y, 9e+69]], $MachinePrecision]], N[(z + N[(y * 2.0), $MachinePrecision]), $MachinePrecision], N[(z + N[(x * 3.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.1999999999999998e42 or 8.9999999999999999e69 < 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. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

      5. +-commutative 100.0%

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

      6. +-commutative 100.0%

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

   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 88.0%

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

   if -5.1999999999999998e42 < y < 8.9999999999999999e69

   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. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

      5. +-commutative 100.0%

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

      6. +-commutative 100.0%

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

   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 0 100.0%

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

   6. Taylor expanded in y around 0 87.4%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+42} \lor \neg \left(y \leq 9 \cdot 10^{+69}\right):\\ \;\;\;\;z + y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;z + x \cdot 3\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 56.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{+58}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-21}:\\ \;\;\;\;y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -4.3e+58) z (if (<= z 7.5e-21) (* y 2.0) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -4.3e+58) {
		tmp = z;
	} else if (z <= 7.5e-21) {
		tmp = y * 2.0;
	} 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 <= (-4.3d+58)) then
        tmp = z
    else if (z <= 7.5d-21) then
        tmp = y * 2.0d0
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -4.3e+58) {
		tmp = z;
	} else if (z <= 7.5e-21) {
		tmp = y * 2.0;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -4.3e+58:
		tmp = z
	elif z <= 7.5e-21:
		tmp = y * 2.0
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -4.3e+58)
		tmp = z;
	elseif (z <= 7.5e-21)
		tmp = Float64(y * 2.0);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -4.3e+58)
		tmp = z;
	elseif (z <= 7.5e-21)
		tmp = y * 2.0;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -4.3e+58], z, If[LessEqual[z, 7.5e-21], N[(y * 2.0), $MachinePrecision], z]]

Derivation

1. Split input into 2 regimes

2. if z < -4.29999999999999991e58 or 7.50000000000000072e-21 < 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. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

      5. +-commutative 100.0%

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

      6. +-commutative 100.0%

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

   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 69.4%

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

   if -4.29999999999999991e58 < z < 7.50000000000000072e-21

   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. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

      5. +-commutative 100.0%

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

      6. +-commutative 100.0%

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

   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 53.6%

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

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{+58}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-21}:\\ \;\;\;\;y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 100.0% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = z + ((y * 2.0d0) + (x * 3.0d0))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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. associate-+l+ 100.0%

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

   3. +-commutative 100.0%

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

   4. count-2 100.0%

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

   5. +-commutative 100.0%

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

   6. +-commutative 100.0%

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

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 0 100.0%

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

6. Final simplification 100.0%

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

Alternative 9: 37.5% 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 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. associate-+l+ 100.0%

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

   3. +-commutative 100.0%

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

   4. count-2 100.0%

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

   5. +-commutative 100.0%

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

   6. +-commutative 100.0%

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

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 35.2%

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

6. Final simplification 35.2%

   \[\leadsto z \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024062 
(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))