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

Percentage Accurate: 99.9% → 100.0%

Time: 7.0s

Alternatives: 9

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

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

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 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%

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

   2. associate-+l+ 99.9%

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

   3. remove-double-neg 99.9%

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

   4. unsub-neg 99.9%

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

   5. +-commutative 99.9%

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

   6. +-commutative 99.9%

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

   7. associate-+l+ 99.9%

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

   8. associate-+r+ 99.9%

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

   9. associate-+r+ 99.9%

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

   10. distribute-neg-in 99.9%

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

   11. distribute-neg-out 99.9%

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

   12. neg-mul-1 99.9%

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

   13. count-2 99.9%

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

   14. distribute-lft-neg-in 99.9%

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

   15. metadata-eval 99.9%

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

   16. metadata-eval 99.9%

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

   17. distribute-rgt-out 99.9%

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

   18. distribute-neg-out 99.9%

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

   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. Add Preprocessing

Alternative 2: 52.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+15}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-129}:\\ \;\;\;\;y \cdot 2\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-255}:\\ \;\;\;\;x \cdot 3\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-264}:\\ \;\;\;\;y \cdot 2\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-116}:\\ \;\;\;\;x \cdot 3\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-20}:\\ \;\;\;\;y \cdot 2\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{+36}:\\ \;\;\;\;x \cdot 3\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -8e+15)
   z
   (if (<= z -1.8e-129)
     (* y 2.0)
     (if (<= z -7e-255)
       (* x 3.0)
       (if (<= z 3.2e-264)
         (* y 2.0)
         (if (<= z 2.2e-116)
           (* x 3.0)
           (if (<= z 5.2e-20) (* y 2.0) (if (<= z 1.22e+36) (* x 3.0) z))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -8e+15) {
		tmp = z;
	} else if (z <= -1.8e-129) {
		tmp = y * 2.0;
	} else if (z <= -7e-255) {
		tmp = x * 3.0;
	} else if (z <= 3.2e-264) {
		tmp = y * 2.0;
	} else if (z <= 2.2e-116) {
		tmp = x * 3.0;
	} else if (z <= 5.2e-20) {
		tmp = y * 2.0;
	} else if (z <= 1.22e+36) {
		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 <= (-8d+15)) then
        tmp = z
    else if (z <= (-1.8d-129)) then
        tmp = y * 2.0d0
    else if (z <= (-7d-255)) then
        tmp = x * 3.0d0
    else if (z <= 3.2d-264) then
        tmp = y * 2.0d0
    else if (z <= 2.2d-116) then
        tmp = x * 3.0d0
    else if (z <= 5.2d-20) then
        tmp = y * 2.0d0
    else if (z <= 1.22d+36) 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 <= -8e+15) {
		tmp = z;
	} else if (z <= -1.8e-129) {
		tmp = y * 2.0;
	} else if (z <= -7e-255) {
		tmp = x * 3.0;
	} else if (z <= 3.2e-264) {
		tmp = y * 2.0;
	} else if (z <= 2.2e-116) {
		tmp = x * 3.0;
	} else if (z <= 5.2e-20) {
		tmp = y * 2.0;
	} else if (z <= 1.22e+36) {
		tmp = x * 3.0;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -8e+15:
		tmp = z
	elif z <= -1.8e-129:
		tmp = y * 2.0
	elif z <= -7e-255:
		tmp = x * 3.0
	elif z <= 3.2e-264:
		tmp = y * 2.0
	elif z <= 2.2e-116:
		tmp = x * 3.0
	elif z <= 5.2e-20:
		tmp = y * 2.0
	elif z <= 1.22e+36:
		tmp = x * 3.0
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -8e+15)
		tmp = z;
	elseif (z <= -1.8e-129)
		tmp = Float64(y * 2.0);
	elseif (z <= -7e-255)
		tmp = Float64(x * 3.0);
	elseif (z <= 3.2e-264)
		tmp = Float64(y * 2.0);
	elseif (z <= 2.2e-116)
		tmp = Float64(x * 3.0);
	elseif (z <= 5.2e-20)
		tmp = Float64(y * 2.0);
	elseif (z <= 1.22e+36)
		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 <= -8e+15)
		tmp = z;
	elseif (z <= -1.8e-129)
		tmp = y * 2.0;
	elseif (z <= -7e-255)
		tmp = x * 3.0;
	elseif (z <= 3.2e-264)
		tmp = y * 2.0;
	elseif (z <= 2.2e-116)
		tmp = x * 3.0;
	elseif (z <= 5.2e-20)
		tmp = y * 2.0;
	elseif (z <= 1.22e+36)
		tmp = x * 3.0;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -8e+15], z, If[LessEqual[z, -1.8e-129], N[(y * 2.0), $MachinePrecision], If[LessEqual[z, -7e-255], N[(x * 3.0), $MachinePrecision], If[LessEqual[z, 3.2e-264], N[(y * 2.0), $MachinePrecision], If[LessEqual[z, 2.2e-116], N[(x * 3.0), $MachinePrecision], If[LessEqual[z, 5.2e-20], N[(y * 2.0), $MachinePrecision], If[LessEqual[z, 1.22e+36], N[(x * 3.0), $MachinePrecision], z]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8e15 or 1.21999999999999995e36 < 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%

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

      3. associate-+l+ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 65.8%

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

   if -8e15 < z < -1.8e-129 or -6.99999999999999958e-255 < z < 3.19999999999999995e-264 or 2.2000000000000001e-116 < z < 5.1999999999999999e-20

   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%

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

      3. associate-+l+ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 65.3%

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

   if -1.8e-129 < z < -6.99999999999999958e-255 or 3.19999999999999995e-264 < z < 2.2000000000000001e-116 or 5.1999999999999999e-20 < z < 1.21999999999999995e36

   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%

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

      3. associate-+l+ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 72.4%

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

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+15}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-129}:\\ \;\;\;\;y \cdot 2\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-255}:\\ \;\;\;\;x \cdot 3\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-264}:\\ \;\;\;\;y \cdot 2\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-116}:\\ \;\;\;\;x \cdot 3\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-20}:\\ \;\;\;\;y \cdot 2\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{+36}:\\ \;\;\;\;x \cdot 3\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 78.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.8 \cdot 10^{+162} \lor \neg \left(y \leq 3 \cdot 10^{+51} \lor \neg \left(y \leq 2.6 \cdot 10^{+92}\right) \land y \leq 1.2 \cdot 10^{+137}\right):\\ \;\;\;\;y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;z - x \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -7.8e+162)
         (not (or (<= y 3e+51) (and (not (<= y 2.6e+92)) (<= y 1.2e+137)))))
   (* y 2.0)
   (- z (* x -3.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -7.8e+162) || !((y <= 3e+51) || (!(y <= 2.6e+92) && (y <= 1.2e+137)))) {
		tmp = 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 <= (-7.8d+162)) .or. (.not. (y <= 3d+51) .or. (.not. (y <= 2.6d+92)) .and. (y <= 1.2d+137))) then
        tmp = 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 <= -7.8e+162) || !((y <= 3e+51) || (!(y <= 2.6e+92) && (y <= 1.2e+137)))) {
		tmp = y * 2.0;
	} else {
		tmp = z - (x * -3.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -7.8e+162) or not ((y <= 3e+51) or (not (y <= 2.6e+92) and (y <= 1.2e+137))):
		tmp = y * 2.0
	else:
		tmp = z - (x * -3.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -7.8e+162) || !((y <= 3e+51) || (!(y <= 2.6e+92) && (y <= 1.2e+137))))
		tmp = 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 <= -7.8e+162) || ~(((y <= 3e+51) || (~((y <= 2.6e+92)) && (y <= 1.2e+137)))))
		tmp = y * 2.0;
	else
		tmp = z - (x * -3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -7.8e+162], N[Not[Or[LessEqual[y, 3e+51], And[N[Not[LessEqual[y, 2.6e+92]], $MachinePrecision], LessEqual[y, 1.2e+137]]]], $MachinePrecision]], N[(y * 2.0), $MachinePrecision], N[(z - N[(x * -3.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.80000000000000079e162 or 3e51 < y < 2.5999999999999999e92 or 1.19999999999999992e137 < 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. +-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%

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

      3. associate-+l+ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 79.5%

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

   if -7.80000000000000079e162 < y < 3e51 or 2.5999999999999999e92 < y < 1.19999999999999992e137

   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%

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

      2. associate-+l+ 99.9%

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

      3. remove-double-neg 99.9%

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

      4. unsub-neg 99.9%

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

      5. +-commutative 99.9%

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

      6. +-commutative 99.9%

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

      7. associate-+l+ 99.9%

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

      8. associate-+r+ 99.9%

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

      9. associate-+r+ 99.9%

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

      10. distribute-neg-in 99.9%

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

      11. distribute-neg-out 99.9%

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

      12. neg-mul-1 99.9%

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

      13. count-2 99.9%

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

      14. distribute-lft-neg-in 99.9%

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

      15. metadata-eval 99.9%

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

      16. metadata-eval 99.9%

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

      17. distribute-rgt-out 99.9%

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

      18. distribute-neg-out 99.9%

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

      19. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 86.6%

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

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.8 \cdot 10^{+162} \lor \neg \left(y \leq 3 \cdot 10^{+51} \lor \neg \left(y \leq 2.6 \cdot 10^{+92}\right) \land y \leq 1.2 \cdot 10^{+137}\right):\\ \;\;\;\;y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;z - x \cdot -3\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 86.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6000000000 \lor \neg \left(z \leq 1.56 \cdot 10^{+35}\right):\\ \;\;\;\;z - y \cdot -2\\ \mathbf{else}:\\ \;\;\;\;x + 2 \cdot \left(x + y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -6000000000.0) (not (<= z 1.56e+35)))
   (- z (* y -2.0))
   (+ x (* 2.0 (+ x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -6000000000.0) || !(z <= 1.56e+35)) {
		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 <= (-6000000000.0d0)) .or. (.not. (z <= 1.56d+35))) 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 <= -6000000000.0) || !(z <= 1.56e+35)) {
		tmp = z - (y * -2.0);
	} else {
		tmp = x + (2.0 * (x + y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -6000000000.0) or not (z <= 1.56e+35):
		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 <= -6000000000.0) || !(z <= 1.56e+35))
		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 <= -6000000000.0) || ~((z <= 1.56e+35)))
		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, -6000000000.0], N[Not[LessEqual[z, 1.56e+35]], $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 < -6e9 or 1.56000000000000008e35 < 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%

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

      3. associate-+l+ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 85.7%

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

   7. Simplified 85.7%

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

   if -6e9 < z < 1.56000000000000008e35

   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%

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

      3. associate-+l+ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 93.1%

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

   7. Simplified 93.1%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6000000000 \lor \neg \left(z \leq 1.56 \cdot 10^{+35}\right):\\ \;\;\;\;z - y \cdot -2\\ \mathbf{else}:\\ \;\;\;\;x + 2 \cdot \left(x + y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.85 \cdot 10^{+123} \lor \neg \left(x \leq 7600\right):\\ \;\;\;\;z - x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;z - y \cdot -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.85e+123) (not (<= x 7600.0)))
   (- z (* x -3.0))
   (- z (* y -2.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.85e+123) || !(x <= 7600.0)) {
		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 <= (-1.85d+123)) .or. (.not. (x <= 7600.0d0))) 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 <= -1.85e+123) || !(x <= 7600.0)) {
		tmp = z - (x * -3.0);
	} else {
		tmp = z - (y * -2.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.85e+123) or not (x <= 7600.0):
		tmp = z - (x * -3.0)
	else:
		tmp = z - (y * -2.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.85e+123) || !(x <= 7600.0))
		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 <= -1.85e+123) || ~((x <= 7600.0)))
		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, -1.85e+123], N[Not[LessEqual[x, 7600.0]], $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 < -1.84999999999999998e123 or 7600 < x

   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%

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

      2. associate-+l+ 99.9%

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

      3. remove-double-neg 99.9%

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

      4. unsub-neg 99.9%

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

      5. +-commutative 99.9%

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

      6. +-commutative 99.9%

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

      7. associate-+l+ 99.9%

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

      8. associate-+r+ 99.9%

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

      9. associate-+r+ 99.9%

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

      10. distribute-neg-in 99.9%

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

      11. distribute-neg-out 99.9%

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

      12. neg-mul-1 99.9%

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

      13. count-2 99.9%

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

      14. distribute-lft-neg-in 99.9%

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

      15. metadata-eval 99.9%

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

      16. metadata-eval 99.9%

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

      17. distribute-rgt-out 99.9%

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

      18. distribute-neg-out 99.9%

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

      19. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 81.6%

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

   if -1.84999999999999998e123 < x < 7600

   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+ 99.9%

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

      3. associate-+l+ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 90.1%

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

   7. Simplified 90.1%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.85 \cdot 10^{+123} \lor \neg \left(x \leq 7600\right):\\ \;\;\;\;z - x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;z - y \cdot -2\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 52.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6000000000000:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+78}:\\ \;\;\;\;y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -6000000000000.0) z (if (<= z 3.6e+78) (* y 2.0) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -6000000000000.0) {
		tmp = z;
	} else if (z <= 3.6e+78) {
		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 <= (-6000000000000.0d0)) then
        tmp = z
    else if (z <= 3.6d+78) 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 <= -6000000000000.0) {
		tmp = z;
	} else if (z <= 3.6e+78) {
		tmp = y * 2.0;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -6000000000000.0:
		tmp = z
	elif z <= 3.6e+78:
		tmp = y * 2.0
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -6000000000000.0)
		tmp = z;
	elseif (z <= 3.6e+78)
		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 <= -6000000000000.0)
		tmp = z;
	elseif (z <= 3.6e+78)
		tmp = y * 2.0;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -6000000000000.0], z, If[LessEqual[z, 3.6e+78], N[(y * 2.0), $MachinePrecision], z]]

Derivation

1. Split input into 2 regimes

2. if z < -6e12 or 3.6000000000000002e78 < 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%

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

      3. associate-+l+ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 68.9%

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

   if -6e12 < z < 3.6000000000000002e78

   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%

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

      3. associate-+l+ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 45.0%

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

4. Final simplification 56.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6000000000000:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+78}:\\ \;\;\;\;y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 99.9% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

   2. associate-+l+ 99.9%

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

   3. remove-double-neg 99.9%

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

   4. unsub-neg 99.9%

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

   5. +-commutative 99.9%

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

   6. +-commutative 99.9%

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

   7. associate-+l+ 99.9%

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

   8. associate-+r+ 99.9%

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

   9. associate-+r+ 99.9%

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

   10. distribute-neg-in 99.9%

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

   11. distribute-neg-out 99.9%

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

   12. neg-mul-1 99.9%

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

   13. count-2 99.9%

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

   14. distribute-lft-neg-in 99.9%

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

   15. metadata-eval 99.9%

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

   16. metadata-eval 99.9%

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

   17. distribute-rgt-out 99.9%

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

   18. distribute-neg-out 99.9%

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

   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. Taylor expanded in x around 0 99.9%

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

6. Final simplification 99.9%

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

Alternative 8: 99.9% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

   3. +-commutative 99.9%

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

   4. count-2 99.9%

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

   5. +-commutative 99.9%

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

   6. +-commutative 99.9%

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

3. Simplified 99.9%

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

5. Final simplification 99.9%

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

Alternative 9: 33.5% 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 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%

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

   3. associate-+l+ 99.9%

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

3. Simplified 99.9%

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

5. Taylor expanded in z around inf 38.4%

   \[\leadsto \color{blue}{z} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024085 
(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))