Diagrams.Solve.Polynomial:cubForm from diagrams-solve-0.1, A

Percentage Accurate: 95.4% → 97.2%

Time: 12.7s

Alternatives: 11

Speedup: 1.0×

• 28.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (+ (- (* x 2.0) (* (* (* y 9.0) z) t)) (* (* a 27.0) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return ((x * 2.0) - (((y * 9.0) * z) * t)) + ((a * 27.0) * b);
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = ((x * 2.0d0) - (((y * 9.0d0) * z) * t)) + ((a * 27.0d0) * b)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return ((x * 2.0) - (((y * 9.0) * z) * t)) + ((a * 27.0) * b);
}

Python

def code(x, y, z, t, a, b):
	return ((x * 2.0) - (((y * 9.0) * z) * t)) + ((a * 27.0) * b)

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(x * 2.0) - Float64(Float64(Float64(y * 9.0) * z) * t)) + Float64(Float64(a * 27.0) * b))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = ((x * 2.0) - (((y * 9.0) * z) * t)) + ((a * 27.0) * b);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(x * 2.0), $MachinePrecision] - N[(N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]

Initial Program: 95.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (+ (- (* x 2.0) (* (* (* y 9.0) z) t)) (* (* a 27.0) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return ((x * 2.0) - (((y * 9.0) * z) * t)) + ((a * 27.0) * b);
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = ((x * 2.0d0) - (((y * 9.0d0) * z) * t)) + ((a * 27.0d0) * b)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return ((x * 2.0) - (((y * 9.0) * z) * t)) + ((a * 27.0) * b);
}

Python

def code(x, y, z, t, a, b):
	return ((x * 2.0) - (((y * 9.0) * z) * t)) + ((a * 27.0) * b)

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(x * 2.0) - Float64(Float64(Float64(y * 9.0) * z) * t)) + Float64(Float64(a * 27.0) * b))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = ((x * 2.0) - (((y * 9.0) * z) * t)) + ((a * 27.0) * b);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(x * 2.0), $MachinePrecision] - N[(N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]

Alternative 1: 97.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 1.85 \cdot 10^{+75}:\\ \;\;\;\;\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(27 \cdot \frac{a \cdot b}{t} - 9 \cdot \left(y \cdot z\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z 1.85e+75)
   (+ (- (* x 2.0) (* (* y 9.0) (* z t))) (* a (* 27.0 b)))
   (* t (- (* 27.0 (/ (* a b) t)) (* 9.0 (* y z))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 1.85e+75) {
		tmp = ((x * 2.0) - ((y * 9.0) * (z * t))) + (a * (27.0 * b));
	} else {
		tmp = t * ((27.0 * ((a * b) / t)) - (9.0 * (y * z)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= 1.85d+75) then
        tmp = ((x * 2.0d0) - ((y * 9.0d0) * (z * t))) + (a * (27.0d0 * b))
    else
        tmp = t * ((27.0d0 * ((a * b) / t)) - (9.0d0 * (y * z)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 1.85e+75) {
		tmp = ((x * 2.0) - ((y * 9.0) * (z * t))) + (a * (27.0 * b));
	} else {
		tmp = t * ((27.0 * ((a * b) / t)) - (9.0 * (y * z)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= 1.85e+75:
		tmp = ((x * 2.0) - ((y * 9.0) * (z * t))) + (a * (27.0 * b))
	else:
		tmp = t * ((27.0 * ((a * b) / t)) - (9.0 * (y * z)))
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= 1.85e+75)
		tmp = Float64(Float64(Float64(x * 2.0) - Float64(Float64(y * 9.0) * Float64(z * t))) + Float64(a * Float64(27.0 * b)));
	else
		tmp = Float64(t * Float64(Float64(27.0 * Float64(Float64(a * b) / t)) - Float64(9.0 * Float64(y * z))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= 1.85e+75)
		tmp = ((x * 2.0) - ((y * 9.0) * (z * t))) + (a * (27.0 * b));
	else
		tmp = t * ((27.0 * ((a * b) / t)) - (9.0 * (y * z)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, 1.85e+75], N[(N[(N[(x * 2.0), $MachinePrecision] - N[(N[(y * 9.0), $MachinePrecision] * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(27.0 * N[(N[(a * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] - N[(9.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 1.85000000000000005e75

   1. Initial program 98.9%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 98.9%

         \[\leadsto \color{blue}{x \cdot 2 - \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)} \]

      2. *-commutative 98.9%

         \[\leadsto x \cdot 2 - \left(\color{blue}{\left(z \cdot \left(y \cdot 9\right)\right)} \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      3. *-commutative 98.9%

         \[\leadsto x \cdot 2 - \left(\left(z \cdot \color{blue}{\left(9 \cdot y\right)}\right) \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      4. associate-*l* 98.9%

         \[\leadsto x \cdot 2 - \left(\color{blue}{\left(\left(z \cdot 9\right) \cdot y\right)} \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      5. associate-+l- 98.9%

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(z \cdot 9\right) \cdot y\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b} \]

      6. associate-*l* 98.9%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(z \cdot \left(9 \cdot y\right)\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      7. *-commutative 98.9%

         \[\leadsto \left(x \cdot 2 - \left(z \cdot \color{blue}{\left(y \cdot 9\right)}\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      8. *-commutative 98.9%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(\left(y \cdot 9\right) \cdot z\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      9. associate-*l* 98.4%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      10. associate-*l* 98.4%

          \[\leadsto \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \color{blue}{a \cdot \left(27 \cdot b\right)} \]

   3. Simplified 98.4%

      \[\leadsto \color{blue}{\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)} \]
   4. Add Preprocessing

   if 1.85000000000000005e75 < z

   1. Initial program 86.7%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 86.7%

         \[\leadsto \color{blue}{x \cdot 2 - \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)} \]

      2. *-commutative 86.7%

         \[\leadsto x \cdot 2 - \left(\color{blue}{\left(z \cdot \left(y \cdot 9\right)\right)} \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      3. *-commutative 86.7%

         \[\leadsto x \cdot 2 - \left(\left(z \cdot \color{blue}{\left(9 \cdot y\right)}\right) \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      4. associate-*l* 86.7%

         \[\leadsto x \cdot 2 - \left(\color{blue}{\left(\left(z \cdot 9\right) \cdot y\right)} \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      5. associate-+l- 86.7%

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(z \cdot 9\right) \cdot y\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b} \]

      6. associate-*l* 86.7%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(z \cdot \left(9 \cdot y\right)\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      7. *-commutative 86.7%

         \[\leadsto \left(x \cdot 2 - \left(z \cdot \color{blue}{\left(y \cdot 9\right)}\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      8. *-commutative 86.7%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(\left(y \cdot 9\right) \cdot z\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      9. associate-*l* 88.7%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      10. associate-*l* 86.8%

          \[\leadsto \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \color{blue}{a \cdot \left(27 \cdot b\right)} \]

   3. Simplified 86.8%

      \[\leadsto \color{blue}{\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 64.3%

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right) - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]

   6. Taylor expanded in t around inf 56.1%

      \[\leadsto \color{blue}{t \cdot \left(27 \cdot \frac{a \cdot b}{t} - 9 \cdot \left(y \cdot z\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 1.85 \cdot 10^{+75}:\\ \;\;\;\;\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(27 \cdot \frac{a \cdot b}{t} - 9 \cdot \left(y \cdot z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 51.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := 27 \cdot \left(a \cdot b\right)\\ t_2 := -9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{if}\;z \leq -8.8 \cdot 10^{-110}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.32 \cdot 10^{-213}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-268}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-260}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-91}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-52}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-16}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* 27.0 (* a b))) (t_2 (* -9.0 (* y (* z t)))))
   (if (<= z -8.8e-110)
     t_2
     (if (<= z -1.32e-213)
       t_1
       (if (<= z -9.2e-268)
         (* x 2.0)
         (if (<= z 4.2e-260)
           t_1
           (if (<= z 1.6e-91)
             (* x 2.0)
             (if (<= z 1.35e-52)
               t_2
               (if (<= z 2.1e-16)
                 (* a (* 27.0 b))
                 (* -9.0 (* t (* y z))))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 27.0 * (a * b);
	double t_2 = -9.0 * (y * (z * t));
	double tmp;
	if (z <= -8.8e-110) {
		tmp = t_2;
	} else if (z <= -1.32e-213) {
		tmp = t_1;
	} else if (z <= -9.2e-268) {
		tmp = x * 2.0;
	} else if (z <= 4.2e-260) {
		tmp = t_1;
	} else if (z <= 1.6e-91) {
		tmp = x * 2.0;
	} else if (z <= 1.35e-52) {
		tmp = t_2;
	} else if (z <= 2.1e-16) {
		tmp = a * (27.0 * b);
	} else {
		tmp = -9.0 * (t * (y * z));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 27.0d0 * (a * b)
    t_2 = (-9.0d0) * (y * (z * t))
    if (z <= (-8.8d-110)) then
        tmp = t_2
    else if (z <= (-1.32d-213)) then
        tmp = t_1
    else if (z <= (-9.2d-268)) then
        tmp = x * 2.0d0
    else if (z <= 4.2d-260) then
        tmp = t_1
    else if (z <= 1.6d-91) then
        tmp = x * 2.0d0
    else if (z <= 1.35d-52) then
        tmp = t_2
    else if (z <= 2.1d-16) then
        tmp = a * (27.0d0 * b)
    else
        tmp = (-9.0d0) * (t * (y * z))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 27.0 * (a * b);
	double t_2 = -9.0 * (y * (z * t));
	double tmp;
	if (z <= -8.8e-110) {
		tmp = t_2;
	} else if (z <= -1.32e-213) {
		tmp = t_1;
	} else if (z <= -9.2e-268) {
		tmp = x * 2.0;
	} else if (z <= 4.2e-260) {
		tmp = t_1;
	} else if (z <= 1.6e-91) {
		tmp = x * 2.0;
	} else if (z <= 1.35e-52) {
		tmp = t_2;
	} else if (z <= 2.1e-16) {
		tmp = a * (27.0 * b);
	} else {
		tmp = -9.0 * (t * (y * z));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = 27.0 * (a * b)
	t_2 = -9.0 * (y * (z * t))
	tmp = 0
	if z <= -8.8e-110:
		tmp = t_2
	elif z <= -1.32e-213:
		tmp = t_1
	elif z <= -9.2e-268:
		tmp = x * 2.0
	elif z <= 4.2e-260:
		tmp = t_1
	elif z <= 1.6e-91:
		tmp = x * 2.0
	elif z <= 1.35e-52:
		tmp = t_2
	elif z <= 2.1e-16:
		tmp = a * (27.0 * b)
	else:
		tmp = -9.0 * (t * (y * z))
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(27.0 * Float64(a * b))
	t_2 = Float64(-9.0 * Float64(y * Float64(z * t)))
	tmp = 0.0
	if (z <= -8.8e-110)
		tmp = t_2;
	elseif (z <= -1.32e-213)
		tmp = t_1;
	elseif (z <= -9.2e-268)
		tmp = Float64(x * 2.0);
	elseif (z <= 4.2e-260)
		tmp = t_1;
	elseif (z <= 1.6e-91)
		tmp = Float64(x * 2.0);
	elseif (z <= 1.35e-52)
		tmp = t_2;
	elseif (z <= 2.1e-16)
		tmp = Float64(a * Float64(27.0 * b));
	else
		tmp = Float64(-9.0 * Float64(t * Float64(y * z)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 27.0 * (a * b);
	t_2 = -9.0 * (y * (z * t));
	tmp = 0.0;
	if (z <= -8.8e-110)
		tmp = t_2;
	elseif (z <= -1.32e-213)
		tmp = t_1;
	elseif (z <= -9.2e-268)
		tmp = x * 2.0;
	elseif (z <= 4.2e-260)
		tmp = t_1;
	elseif (z <= 1.6e-91)
		tmp = x * 2.0;
	elseif (z <= 1.35e-52)
		tmp = t_2;
	elseif (z <= 2.1e-16)
		tmp = a * (27.0 * b);
	else
		tmp = -9.0 * (t * (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8.8e-110], t$95$2, If[LessEqual[z, -1.32e-213], t$95$1, If[LessEqual[z, -9.2e-268], N[(x * 2.0), $MachinePrecision], If[LessEqual[z, 4.2e-260], t$95$1, If[LessEqual[z, 1.6e-91], N[(x * 2.0), $MachinePrecision], If[LessEqual[z, 1.35e-52], t$95$2, If[LessEqual[z, 2.1e-16], N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision], N[(-9.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -8.7999999999999997e-110 or 1.59999999999999998e-91 < z < 1.35000000000000005e-52

   1. Initial program 97.4%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 97.4%

         \[\leadsto \color{blue}{x \cdot 2 - \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)} \]

      2. *-commutative 97.4%

         \[\leadsto x \cdot 2 - \left(\color{blue}{\left(z \cdot \left(y \cdot 9\right)\right)} \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      3. *-commutative 97.4%

         \[\leadsto x \cdot 2 - \left(\left(z \cdot \color{blue}{\left(9 \cdot y\right)}\right) \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      4. associate-*l* 97.4%

         \[\leadsto x \cdot 2 - \left(\color{blue}{\left(\left(z \cdot 9\right) \cdot y\right)} \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      5. associate-+l- 97.4%

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(z \cdot 9\right) \cdot y\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b} \]

      6. associate-*l* 97.4%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(z \cdot \left(9 \cdot y\right)\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      7. *-commutative 97.4%

         \[\leadsto \left(x \cdot 2 - \left(z \cdot \color{blue}{\left(y \cdot 9\right)}\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      8. *-commutative 97.4%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(\left(y \cdot 9\right) \cdot z\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      9. associate-*l* 96.4%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      10. associate-*l* 96.4%

          \[\leadsto \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \color{blue}{a \cdot \left(27 \cdot b\right)} \]

   3. Simplified 96.4%

      \[\leadsto \color{blue}{\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 75.7%

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right) - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]

   6. Taylor expanded in a around 0 53.4%

      \[\leadsto \color{blue}{-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 53.4%

         \[\leadsto -9 \cdot \color{blue}{\left(\left(y \cdot z\right) \cdot t\right)} \]

      2. associate-*l* 52.2%

         \[\leadsto -9 \cdot \color{blue}{\left(y \cdot \left(z \cdot t\right)\right)} \]

      3. *-commutative 52.2%

         \[\leadsto -9 \cdot \left(y \cdot \color{blue}{\left(t \cdot z\right)}\right) \]

   8. Simplified 52.2%

      \[\leadsto \color{blue}{-9 \cdot \left(y \cdot \left(t \cdot z\right)\right)} \]

   if -8.7999999999999997e-110 < z < -1.3199999999999999e-213 or -9.20000000000000042e-268 < z < 4.20000000000000009e-260

   1. Initial program 99.9%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 99.9%

         \[\leadsto \color{blue}{x \cdot 2 - \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)} \]

      2. *-commutative 99.9%

         \[\leadsto x \cdot 2 - \left(\color{blue}{\left(z \cdot \left(y \cdot 9\right)\right)} \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      3. *-commutative 99.9%

         \[\leadsto x \cdot 2 - \left(\left(z \cdot \color{blue}{\left(9 \cdot y\right)}\right) \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      4. associate-*l* 99.8%

         \[\leadsto x \cdot 2 - \left(\color{blue}{\left(\left(z \cdot 9\right) \cdot y\right)} \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      5. associate-+l- 99.8%

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(z \cdot 9\right) \cdot y\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b} \]

      6. associate-*l* 99.9%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(z \cdot \left(9 \cdot y\right)\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      7. *-commutative 99.9%

         \[\leadsto \left(x \cdot 2 - \left(z \cdot \color{blue}{\left(y \cdot 9\right)}\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      8. *-commutative 99.9%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(\left(y \cdot 9\right) \cdot z\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      9. associate-*l* 99.8%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      10. associate-*l* 99.7%

          \[\leadsto \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \color{blue}{a \cdot \left(27 \cdot b\right)} \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 70.7%

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right) - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]

   6. Taylor expanded in a around inf 50.3%

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right)} \]

   if -1.3199999999999999e-213 < z < -9.20000000000000042e-268 or 4.20000000000000009e-260 < z < 1.59999999999999998e-91

   1. Initial program 99.9%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 99.9%

         \[\leadsto \color{blue}{x \cdot 2 - \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)} \]

      2. *-commutative 99.9%

         \[\leadsto x \cdot 2 - \left(\color{blue}{\left(z \cdot \left(y \cdot 9\right)\right)} \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      3. *-commutative 99.9%

         \[\leadsto x \cdot 2 - \left(\left(z \cdot \color{blue}{\left(9 \cdot y\right)}\right) \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      4. associate-*l* 99.8%

         \[\leadsto x \cdot 2 - \left(\color{blue}{\left(\left(z \cdot 9\right) \cdot y\right)} \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      5. associate-+l- 99.8%

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(z \cdot 9\right) \cdot y\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b} \]

      6. associate-*l* 99.9%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(z \cdot \left(9 \cdot y\right)\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      7. *-commutative 99.9%

         \[\leadsto \left(x \cdot 2 - \left(z \cdot \color{blue}{\left(y \cdot 9\right)}\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      8. *-commutative 99.9%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(\left(y \cdot 9\right) \cdot z\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      9. associate-*l* 99.9%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      10. associate-*l* 99.8%

          \[\leadsto \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \color{blue}{a \cdot \left(27 \cdot b\right)} \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 43.5%

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

   if 1.35000000000000005e-52 < z < 2.1000000000000001e-16

   1. Initial program 100.0%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 100.0%

         \[\leadsto \color{blue}{x \cdot 2 - \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)} \]

      2. *-commutative 100.0%

         \[\leadsto x \cdot 2 - \left(\color{blue}{\left(z \cdot \left(y \cdot 9\right)\right)} \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      3. *-commutative 100.0%

         \[\leadsto x \cdot 2 - \left(\left(z \cdot \color{blue}{\left(9 \cdot y\right)}\right) \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      4. associate-*l* 99.7%

         \[\leadsto x \cdot 2 - \left(\color{blue}{\left(\left(z \cdot 9\right) \cdot y\right)} \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      5. associate-+l- 99.7%

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(z \cdot 9\right) \cdot y\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b} \]

      6. associate-*l* 100.0%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(z \cdot \left(9 \cdot y\right)\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      7. *-commutative 100.0%

         \[\leadsto \left(x \cdot 2 - \left(z \cdot \color{blue}{\left(y \cdot 9\right)}\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      8. *-commutative 100.0%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(\left(y \cdot 9\right) \cdot z\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      9. associate-*l* 99.7%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      10. associate-*l* 99.7%

          \[\leadsto \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \color{blue}{a \cdot \left(27 \cdot b\right)} \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 89.3%

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right) - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]

   6. Taylor expanded in a around inf 57.3%

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right)} \]
   7. Step-by-step derivation

      1. *-commutative 57.3%

         \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot 27} \]

      2. associate-*r* 57.3%

         \[\leadsto \color{blue}{a \cdot \left(b \cdot 27\right)} \]

      3. *-commutative 57.3%

         \[\leadsto a \cdot \color{blue}{\left(27 \cdot b\right)} \]

   8. Simplified 57.3%

      \[\leadsto \color{blue}{a \cdot \left(27 \cdot b\right)} \]

   if 2.1000000000000001e-16 < z

   1. Initial program 90.1%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 90.1%

         \[\leadsto \color{blue}{x \cdot 2 - \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)} \]

      2. *-commutative 90.1%

         \[\leadsto x \cdot 2 - \left(\color{blue}{\left(z \cdot \left(y \cdot 9\right)\right)} \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      3. *-commutative 90.1%

         \[\leadsto x \cdot 2 - \left(\left(z \cdot \color{blue}{\left(9 \cdot y\right)}\right) \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      4. associate-*l* 90.1%

         \[\leadsto x \cdot 2 - \left(\color{blue}{\left(\left(z \cdot 9\right) \cdot y\right)} \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      5. associate-+l- 90.1%

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(z \cdot 9\right) \cdot y\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b} \]

      6. associate-*l* 90.1%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(z \cdot \left(9 \cdot y\right)\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      7. *-commutative 90.1%

         \[\leadsto \left(x \cdot 2 - \left(z \cdot \color{blue}{\left(y \cdot 9\right)}\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      8. *-commutative 90.1%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(\left(y \cdot 9\right) \cdot z\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      9. associate-*l* 91.6%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      10. associate-*l* 90.2%

          \[\leadsto \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \color{blue}{a \cdot \left(27 \cdot b\right)} \]

   3. Simplified 90.2%

      \[\leadsto \color{blue}{\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 47.6%

      \[\leadsto \color{blue}{-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 49.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{-110}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq -1.32 \cdot 10^{-213}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-268}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-260}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-91}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-52}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-16}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 50.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := 27 \cdot \left(a \cdot b\right)\\ t_2 := -9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{if}\;z \leq -2.35 \cdot 10^{-116}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-215}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-268}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-260}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{-95}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-53}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{-17}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(z \cdot \left(y \cdot -9\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* 27.0 (* a b))) (t_2 (* -9.0 (* y (* z t)))))
   (if (<= z -2.35e-116)
     t_2
     (if (<= z -8e-215)
       t_1
       (if (<= z -7e-268)
         (* x 2.0)
         (if (<= z 1.2e-260)
           t_1
           (if (<= z 1.06e-95)
             (* x 2.0)
             (if (<= z 9.2e-53)
               t_2
               (if (<= z 2.05e-17)
                 (* a (* 27.0 b))
                 (* t (* z (* y -9.0))))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 27.0 * (a * b);
	double t_2 = -9.0 * (y * (z * t));
	double tmp;
	if (z <= -2.35e-116) {
		tmp = t_2;
	} else if (z <= -8e-215) {
		tmp = t_1;
	} else if (z <= -7e-268) {
		tmp = x * 2.0;
	} else if (z <= 1.2e-260) {
		tmp = t_1;
	} else if (z <= 1.06e-95) {
		tmp = x * 2.0;
	} else if (z <= 9.2e-53) {
		tmp = t_2;
	} else if (z <= 2.05e-17) {
		tmp = a * (27.0 * b);
	} else {
		tmp = t * (z * (y * -9.0));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 27.0d0 * (a * b)
    t_2 = (-9.0d0) * (y * (z * t))
    if (z <= (-2.35d-116)) then
        tmp = t_2
    else if (z <= (-8d-215)) then
        tmp = t_1
    else if (z <= (-7d-268)) then
        tmp = x * 2.0d0
    else if (z <= 1.2d-260) then
        tmp = t_1
    else if (z <= 1.06d-95) then
        tmp = x * 2.0d0
    else if (z <= 9.2d-53) then
        tmp = t_2
    else if (z <= 2.05d-17) then
        tmp = a * (27.0d0 * b)
    else
        tmp = t * (z * (y * (-9.0d0)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 27.0 * (a * b);
	double t_2 = -9.0 * (y * (z * t));
	double tmp;
	if (z <= -2.35e-116) {
		tmp = t_2;
	} else if (z <= -8e-215) {
		tmp = t_1;
	} else if (z <= -7e-268) {
		tmp = x * 2.0;
	} else if (z <= 1.2e-260) {
		tmp = t_1;
	} else if (z <= 1.06e-95) {
		tmp = x * 2.0;
	} else if (z <= 9.2e-53) {
		tmp = t_2;
	} else if (z <= 2.05e-17) {
		tmp = a * (27.0 * b);
	} else {
		tmp = t * (z * (y * -9.0));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = 27.0 * (a * b)
	t_2 = -9.0 * (y * (z * t))
	tmp = 0
	if z <= -2.35e-116:
		tmp = t_2
	elif z <= -8e-215:
		tmp = t_1
	elif z <= -7e-268:
		tmp = x * 2.0
	elif z <= 1.2e-260:
		tmp = t_1
	elif z <= 1.06e-95:
		tmp = x * 2.0
	elif z <= 9.2e-53:
		tmp = t_2
	elif z <= 2.05e-17:
		tmp = a * (27.0 * b)
	else:
		tmp = t * (z * (y * -9.0))
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(27.0 * Float64(a * b))
	t_2 = Float64(-9.0 * Float64(y * Float64(z * t)))
	tmp = 0.0
	if (z <= -2.35e-116)
		tmp = t_2;
	elseif (z <= -8e-215)
		tmp = t_1;
	elseif (z <= -7e-268)
		tmp = Float64(x * 2.0);
	elseif (z <= 1.2e-260)
		tmp = t_1;
	elseif (z <= 1.06e-95)
		tmp = Float64(x * 2.0);
	elseif (z <= 9.2e-53)
		tmp = t_2;
	elseif (z <= 2.05e-17)
		tmp = Float64(a * Float64(27.0 * b));
	else
		tmp = Float64(t * Float64(z * Float64(y * -9.0)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 27.0 * (a * b);
	t_2 = -9.0 * (y * (z * t));
	tmp = 0.0;
	if (z <= -2.35e-116)
		tmp = t_2;
	elseif (z <= -8e-215)
		tmp = t_1;
	elseif (z <= -7e-268)
		tmp = x * 2.0;
	elseif (z <= 1.2e-260)
		tmp = t_1;
	elseif (z <= 1.06e-95)
		tmp = x * 2.0;
	elseif (z <= 9.2e-53)
		tmp = t_2;
	elseif (z <= 2.05e-17)
		tmp = a * (27.0 * b);
	else
		tmp = t * (z * (y * -9.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.35e-116], t$95$2, If[LessEqual[z, -8e-215], t$95$1, If[LessEqual[z, -7e-268], N[(x * 2.0), $MachinePrecision], If[LessEqual[z, 1.2e-260], t$95$1, If[LessEqual[z, 1.06e-95], N[(x * 2.0), $MachinePrecision], If[LessEqual[z, 9.2e-53], t$95$2, If[LessEqual[z, 2.05e-17], N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision], N[(t * N[(z * N[(y * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.34999999999999997e-116 or 1.06e-95 < z < 9.2000000000000005e-53

   1. Initial program 97.4%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 97.4%

         \[\leadsto \color{blue}{x \cdot 2 - \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)} \]

      2. *-commutative 97.4%

         \[\leadsto x \cdot 2 - \left(\color{blue}{\left(z \cdot \left(y \cdot 9\right)\right)} \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      3. *-commutative 97.4%

         \[\leadsto x \cdot 2 - \left(\left(z \cdot \color{blue}{\left(9 \cdot y\right)}\right) \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      4. associate-*l* 97.4%

         \[\leadsto x \cdot 2 - \left(\color{blue}{\left(\left(z \cdot 9\right) \cdot y\right)} \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      5. associate-+l- 97.4%

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(z \cdot 9\right) \cdot y\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b} \]

      6. associate-*l* 97.4%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(z \cdot \left(9 \cdot y\right)\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      7. *-commutative 97.4%

         \[\leadsto \left(x \cdot 2 - \left(z \cdot \color{blue}{\left(y \cdot 9\right)}\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      8. *-commutative 97.4%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(\left(y \cdot 9\right) \cdot z\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      9. associate-*l* 96.4%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      10. associate-*l* 96.4%

          \[\leadsto \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \color{blue}{a \cdot \left(27 \cdot b\right)} \]

   3. Simplified 96.4%

      \[\leadsto \color{blue}{\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 76.0%

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right) - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]

   6. Taylor expanded in a around 0 52.8%

      \[\leadsto \color{blue}{-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 52.8%

         \[\leadsto -9 \cdot \color{blue}{\left(\left(y \cdot z\right) \cdot t\right)} \]

      2. associate-*l* 51.6%

         \[\leadsto -9 \cdot \color{blue}{\left(y \cdot \left(z \cdot t\right)\right)} \]

      3. *-commutative 51.6%

         \[\leadsto -9 \cdot \left(y \cdot \color{blue}{\left(t \cdot z\right)}\right) \]

   8. Simplified 51.6%

      \[\leadsto \color{blue}{-9 \cdot \left(y \cdot \left(t \cdot z\right)\right)} \]

   if -2.34999999999999997e-116 < z < -8.00000000000000033e-215 or -7.00000000000000011e-268 < z < 1.2e-260

   1. Initial program 99.9%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 99.9%

         \[\leadsto \color{blue}{x \cdot 2 - \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)} \]

      2. *-commutative 99.9%

         \[\leadsto x \cdot 2 - \left(\color{blue}{\left(z \cdot \left(y \cdot 9\right)\right)} \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      3. *-commutative 99.9%

         \[\leadsto x \cdot 2 - \left(\left(z \cdot \color{blue}{\left(9 \cdot y\right)}\right) \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      4. associate-*l* 99.8%

         \[\leadsto x \cdot 2 - \left(\color{blue}{\left(\left(z \cdot 9\right) \cdot y\right)} \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      5. associate-+l- 99.8%

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(z \cdot 9\right) \cdot y\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b} \]

      6. associate-*l* 99.9%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(z \cdot \left(9 \cdot y\right)\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      7. *-commutative 99.9%

         \[\leadsto \left(x \cdot 2 - \left(z \cdot \color{blue}{\left(y \cdot 9\right)}\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      8. *-commutative 99.9%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(\left(y \cdot 9\right) \cdot z\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      9. associate-*l* 99.8%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      10. associate-*l* 99.7%

          \[\leadsto \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \color{blue}{a \cdot \left(27 \cdot b\right)} \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 70.1%

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right) - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]

   6. Taylor expanded in a around inf 49.2%

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right)} \]

   if -8.00000000000000033e-215 < z < -7.00000000000000011e-268 or 1.2e-260 < z < 1.06e-95

   1. Initial program 99.9%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 99.9%

         \[\leadsto \color{blue}{x \cdot 2 - \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)} \]

      2. *-commutative 99.9%

         \[\leadsto x \cdot 2 - \left(\color{blue}{\left(z \cdot \left(y \cdot 9\right)\right)} \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      3. *-commutative 99.9%

         \[\leadsto x \cdot 2 - \left(\left(z \cdot \color{blue}{\left(9 \cdot y\right)}\right) \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      4. associate-*l* 99.8%

         \[\leadsto x \cdot 2 - \left(\color{blue}{\left(\left(z \cdot 9\right) \cdot y\right)} \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      5. associate-+l- 99.8%

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(z \cdot 9\right) \cdot y\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b} \]

      6. associate-*l* 99.9%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(z \cdot \left(9 \cdot y\right)\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      7. *-commutative 99.9%

         \[\leadsto \left(x \cdot 2 - \left(z \cdot \color{blue}{\left(y \cdot 9\right)}\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      8. *-commutative 99.9%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(\left(y \cdot 9\right) \cdot z\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      9. associate-*l* 99.9%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      10. associate-*l* 99.8%

          \[\leadsto \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \color{blue}{a \cdot \left(27 \cdot b\right)} \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 43.5%

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

   if 9.2000000000000005e-53 < z < 2.05e-17

   1. Initial program 100.0%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 100.0%

         \[\leadsto \color{blue}{x \cdot 2 - \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)} \]

      2. *-commutative 100.0%

         \[\leadsto x \cdot 2 - \left(\color{blue}{\left(z \cdot \left(y \cdot 9\right)\right)} \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      3. *-commutative 100.0%

         \[\leadsto x \cdot 2 - \left(\left(z \cdot \color{blue}{\left(9 \cdot y\right)}\right) \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      4. associate-*l* 99.8%

         \[\leadsto x \cdot 2 - \left(\color{blue}{\left(\left(z \cdot 9\right) \cdot y\right)} \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      5. associate-+l- 99.8%

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(z \cdot 9\right) \cdot y\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b} \]

      6. associate-*l* 100.0%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(z \cdot \left(9 \cdot y\right)\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      7. *-commutative 100.0%

         \[\leadsto \left(x \cdot 2 - \left(z \cdot \color{blue}{\left(y \cdot 9\right)}\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      8. *-commutative 100.0%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(\left(y \cdot 9\right) \cdot z\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      9. associate-*l* 99.8%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      10. associate-*l* 99.8%

          \[\leadsto \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \color{blue}{a \cdot \left(27 \cdot b\right)} \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 87.9%

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right) - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]

   6. Taylor expanded in a around inf 63.7%

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right)} \]
   7. Step-by-step derivation

      1. *-commutative 63.7%

         \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot 27} \]

      2. associate-*r* 63.7%

         \[\leadsto \color{blue}{a \cdot \left(b \cdot 27\right)} \]

      3. *-commutative 63.7%

         \[\leadsto a \cdot \color{blue}{\left(27 \cdot b\right)} \]

   8. Simplified 63.7%

      \[\leadsto \color{blue}{a \cdot \left(27 \cdot b\right)} \]

   if 2.05e-17 < z

   1. Initial program 90.3%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 90.3%

         \[\leadsto \color{blue}{x \cdot 2 - \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)} \]

      2. *-commutative 90.3%

         \[\leadsto x \cdot 2 - \left(\color{blue}{\left(z \cdot \left(y \cdot 9\right)\right)} \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      3. *-commutative 90.3%

         \[\leadsto x \cdot 2 - \left(\left(z \cdot \color{blue}{\left(9 \cdot y\right)}\right) \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      4. associate-*l* 90.3%

         \[\leadsto x \cdot 2 - \left(\color{blue}{\left(\left(z \cdot 9\right) \cdot y\right)} \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      5. associate-+l- 90.3%

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(z \cdot 9\right) \cdot y\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b} \]

      6. associate-*l* 90.3%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(z \cdot \left(9 \cdot y\right)\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      7. *-commutative 90.3%

         \[\leadsto \left(x \cdot 2 - \left(z \cdot \color{blue}{\left(y \cdot 9\right)}\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      8. *-commutative 90.3%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(\left(y \cdot 9\right) \cdot z\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      9. associate-*l* 91.7%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      10. associate-*l* 90.3%

          \[\leadsto \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \color{blue}{a \cdot \left(27 \cdot b\right)} \]

   3. Simplified 90.3%

      \[\leadsto \color{blue}{\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around 0 70.8%

      \[\leadsto \color{blue}{2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]

   6. Taylor expanded in x around 0 48.3%

      \[\leadsto \color{blue}{-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 48.3%

         \[\leadsto \color{blue}{\left(t \cdot \left(y \cdot z\right)\right) \cdot -9} \]

      2. associate-*l* 48.3%

         \[\leadsto \color{blue}{t \cdot \left(\left(y \cdot z\right) \cdot -9\right)} \]

      3. *-commutative 48.3%

         \[\leadsto t \cdot \left(\color{blue}{\left(z \cdot y\right)} \cdot -9\right) \]

      4. associate-*l* 48.3%

         \[\leadsto t \cdot \color{blue}{\left(z \cdot \left(y \cdot -9\right)\right)} \]

   8. Simplified 48.3%

      \[\leadsto \color{blue}{t \cdot \left(z \cdot \left(y \cdot -9\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 49.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.35 \cdot 10^{-116}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-215}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-268}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-260}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{-95}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-53}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{-17}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(z \cdot \left(y \cdot -9\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := 27 \cdot \left(a \cdot b\right) + x \cdot 2\\ t_2 := t \cdot \left(z \cdot \left(y \cdot -9\right)\right)\\ \mathbf{if}\;z \leq -1.05 \cdot 10^{+14}:\\ \;\;\;\;-9 \cdot \left(z \cdot \left(y \cdot t\right)\right)\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-62}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.48 \cdot 10^{-108}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+42}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq 10^{+83}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* 27.0 (* a b)) (* x 2.0))) (t_2 (* t (* z (* y -9.0)))))
   (if (<= z -1.05e+14)
     (* -9.0 (* z (* y t)))
     (if (<= z -1.15e-62)
       t_1
       (if (<= z -1.48e-108)
         t_2
         (if (<= z 1.6e-16)
           t_1
           (if (<= z 4.4e+42)
             (* -9.0 (* y (* z t)))
             (if (<= z 1e+83) t_1 t_2))))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (27.0 * (a * b)) + (x * 2.0);
	double t_2 = t * (z * (y * -9.0));
	double tmp;
	if (z <= -1.05e+14) {
		tmp = -9.0 * (z * (y * t));
	} else if (z <= -1.15e-62) {
		tmp = t_1;
	} else if (z <= -1.48e-108) {
		tmp = t_2;
	} else if (z <= 1.6e-16) {
		tmp = t_1;
	} else if (z <= 4.4e+42) {
		tmp = -9.0 * (y * (z * t));
	} else if (z <= 1e+83) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (27.0d0 * (a * b)) + (x * 2.0d0)
    t_2 = t * (z * (y * (-9.0d0)))
    if (z <= (-1.05d+14)) then
        tmp = (-9.0d0) * (z * (y * t))
    else if (z <= (-1.15d-62)) then
        tmp = t_1
    else if (z <= (-1.48d-108)) then
        tmp = t_2
    else if (z <= 1.6d-16) then
        tmp = t_1
    else if (z <= 4.4d+42) then
        tmp = (-9.0d0) * (y * (z * t))
    else if (z <= 1d+83) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (27.0 * (a * b)) + (x * 2.0);
	double t_2 = t * (z * (y * -9.0));
	double tmp;
	if (z <= -1.05e+14) {
		tmp = -9.0 * (z * (y * t));
	} else if (z <= -1.15e-62) {
		tmp = t_1;
	} else if (z <= -1.48e-108) {
		tmp = t_2;
	} else if (z <= 1.6e-16) {
		tmp = t_1;
	} else if (z <= 4.4e+42) {
		tmp = -9.0 * (y * (z * t));
	} else if (z <= 1e+83) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = (27.0 * (a * b)) + (x * 2.0)
	t_2 = t * (z * (y * -9.0))
	tmp = 0
	if z <= -1.05e+14:
		tmp = -9.0 * (z * (y * t))
	elif z <= -1.15e-62:
		tmp = t_1
	elif z <= -1.48e-108:
		tmp = t_2
	elif z <= 1.6e-16:
		tmp = t_1
	elif z <= 4.4e+42:
		tmp = -9.0 * (y * (z * t))
	elif z <= 1e+83:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(27.0 * Float64(a * b)) + Float64(x * 2.0))
	t_2 = Float64(t * Float64(z * Float64(y * -9.0)))
	tmp = 0.0
	if (z <= -1.05e+14)
		tmp = Float64(-9.0 * Float64(z * Float64(y * t)));
	elseif (z <= -1.15e-62)
		tmp = t_1;
	elseif (z <= -1.48e-108)
		tmp = t_2;
	elseif (z <= 1.6e-16)
		tmp = t_1;
	elseif (z <= 4.4e+42)
		tmp = Float64(-9.0 * Float64(y * Float64(z * t)));
	elseif (z <= 1e+83)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (27.0 * (a * b)) + (x * 2.0);
	t_2 = t * (z * (y * -9.0));
	tmp = 0.0;
	if (z <= -1.05e+14)
		tmp = -9.0 * (z * (y * t));
	elseif (z <= -1.15e-62)
		tmp = t_1;
	elseif (z <= -1.48e-108)
		tmp = t_2;
	elseif (z <= 1.6e-16)
		tmp = t_1;
	elseif (z <= 4.4e+42)
		tmp = -9.0 * (y * (z * t));
	elseif (z <= 1e+83)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(z * N[(y * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.05e+14], N[(-9.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.15e-62], t$95$1, If[LessEqual[z, -1.48e-108], t$95$2, If[LessEqual[z, 1.6e-16], t$95$1, If[LessEqual[z, 4.4e+42], N[(-9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1e+83], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.05e14

   1. Initial program 95.5%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 95.5%

         \[\leadsto \color{blue}{x \cdot 2 - \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)} \]

      2. *-commutative 95.5%

         \[\leadsto x \cdot 2 - \left(\color{blue}{\left(z \cdot \left(y \cdot 9\right)\right)} \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      3. *-commutative 95.5%

         \[\leadsto x \cdot 2 - \left(\left(z \cdot \color{blue}{\left(9 \cdot y\right)}\right) \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      4. associate-*l* 95.5%

         \[\leadsto x \cdot 2 - \left(\color{blue}{\left(\left(z \cdot 9\right) \cdot y\right)} \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      5. associate-+l- 95.5%

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(z \cdot 9\right) \cdot y\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b} \]

      6. associate-*l* 95.5%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(z \cdot \left(9 \cdot y\right)\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      7. *-commutative 95.5%

         \[\leadsto \left(x \cdot 2 - \left(z \cdot \color{blue}{\left(y \cdot 9\right)}\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      8. *-commutative 95.5%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(\left(y \cdot 9\right) \cdot z\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      9. associate-*l* 93.5%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      10. associate-*l* 93.6%

          \[\leadsto \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \color{blue}{a \cdot \left(27 \cdot b\right)} \]

   3. Simplified 93.6%

      \[\leadsto \color{blue}{\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 55.1%

      \[\leadsto \color{blue}{-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. pow1 55.1%

         \[\leadsto -9 \cdot \color{blue}{{\left(t \cdot \left(y \cdot z\right)\right)}^{1}} \]

      2. *-commutative 55.1%

         \[\leadsto -9 \cdot {\color{blue}{\left(\left(y \cdot z\right) \cdot t\right)}}^{1} \]

      3. *-commutative 55.1%

         \[\leadsto -9 \cdot {\left(\color{blue}{\left(z \cdot y\right)} \cdot t\right)}^{1} \]

      4. associate-*l* 57.2%

         \[\leadsto -9 \cdot {\color{blue}{\left(z \cdot \left(y \cdot t\right)\right)}}^{1} \]

   7. Applied egg-rr 57.2%

      \[\leadsto -9 \cdot \color{blue}{{\left(z \cdot \left(y \cdot t\right)\right)}^{1}} \]
   8. Step-by-step derivation

      1. unpow1 57.2%

         \[\leadsto -9 \cdot \color{blue}{\left(z \cdot \left(y \cdot t\right)\right)} \]

      2. *-commutative 57.2%

         \[\leadsto -9 \cdot \left(z \cdot \color{blue}{\left(t \cdot y\right)}\right) \]

   9. Simplified 57.2%

      \[\leadsto -9 \cdot \color{blue}{\left(z \cdot \left(t \cdot y\right)\right)} \]

   if -1.05e14 < z < -1.15e-62 or -1.47999999999999992e-108 < z < 1.60000000000000011e-16 or 4.4000000000000003e42 < z < 1.00000000000000003e83

   1. Initial program 99.1%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 99.1%

         \[\leadsto \color{blue}{x \cdot 2 - \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)} \]

      2. *-commutative 99.1%

         \[\leadsto x \cdot 2 - \left(\color{blue}{\left(z \cdot \left(y \cdot 9\right)\right)} \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      3. *-commutative 99.1%

         \[\leadsto x \cdot 2 - \left(\left(z \cdot \color{blue}{\left(9 \cdot y\right)}\right) \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      4. associate-*l* 99.1%

         \[\leadsto x \cdot 2 - \left(\color{blue}{\left(\left(z \cdot 9\right) \cdot y\right)} \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      5. associate-+l- 99.1%

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(z \cdot 9\right) \cdot y\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b} \]

      6. associate-*l* 99.1%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(z \cdot \left(9 \cdot y\right)\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      7. *-commutative 99.1%

         \[\leadsto \left(x \cdot 2 - \left(z \cdot \color{blue}{\left(y \cdot 9\right)}\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      8. *-commutative 99.1%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(\left(y \cdot 9\right) \cdot z\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      9. associate-*l* 99.8%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      10. associate-*l* 99.7%

          \[\leadsto \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \color{blue}{a \cdot \left(27 \cdot b\right)} \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 76.7%

      \[\leadsto \color{blue}{2 \cdot x + 27 \cdot \left(a \cdot b\right)} \]

   if -1.15e-62 < z < -1.47999999999999992e-108 or 1.00000000000000003e83 < z

   1. Initial program 89.3%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 89.3%

         \[\leadsto \color{blue}{x \cdot 2 - \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)} \]

      2. *-commutative 89.3%

         \[\leadsto x \cdot 2 - \left(\color{blue}{\left(z \cdot \left(y \cdot 9\right)\right)} \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      3. *-commutative 89.3%

         \[\leadsto x \cdot 2 - \left(\left(z \cdot \color{blue}{\left(9 \cdot y\right)}\right) \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      4. associate-*l* 89.3%

         \[\leadsto x \cdot 2 - \left(\color{blue}{\left(\left(z \cdot 9\right) \cdot y\right)} \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      5. associate-+l- 89.3%

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(z \cdot 9\right) \cdot y\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b} \]

      6. associate-*l* 89.3%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(z \cdot \left(9 \cdot y\right)\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      7. *-commutative 89.3%

         \[\leadsto \left(x \cdot 2 - \left(z \cdot \color{blue}{\left(y \cdot 9\right)}\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      8. *-commutative 89.3%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(\left(y \cdot 9\right) \cdot z\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      9. associate-*l* 89.3%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      10. associate-*l* 87.6%

          \[\leadsto \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \color{blue}{a \cdot \left(27 \cdot b\right)} \]

   3. Simplified 87.6%

      \[\leadsto \color{blue}{\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around 0 73.0%

      \[\leadsto \color{blue}{2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]

   6. Taylor expanded in x around 0 47.5%

      \[\leadsto \color{blue}{-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 47.5%

         \[\leadsto \color{blue}{\left(t \cdot \left(y \cdot z\right)\right) \cdot -9} \]

      2. associate-*l* 47.5%

         \[\leadsto \color{blue}{t \cdot \left(\left(y \cdot z\right) \cdot -9\right)} \]

      3. *-commutative 47.5%

         \[\leadsto t \cdot \left(\color{blue}{\left(z \cdot y\right)} \cdot -9\right) \]

      4. associate-*l* 47.5%

         \[\leadsto t \cdot \color{blue}{\left(z \cdot \left(y \cdot -9\right)\right)} \]

   8. Simplified 47.5%

      \[\leadsto \color{blue}{t \cdot \left(z \cdot \left(y \cdot -9\right)\right)} \]

   if 1.60000000000000011e-16 < z < 4.4000000000000003e42

   1. Initial program 99.7%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 99.7%

         \[\leadsto \color{blue}{x \cdot 2 - \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)} \]

      2. *-commutative 99.7%

         \[\leadsto x \cdot 2 - \left(\color{blue}{\left(z \cdot \left(y \cdot 9\right)\right)} \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      3. *-commutative 99.7%

         \[\leadsto x \cdot 2 - \left(\left(z \cdot \color{blue}{\left(9 \cdot y\right)}\right) \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      4. associate-*l* 99.9%

         \[\leadsto x \cdot 2 - \left(\color{blue}{\left(\left(z \cdot 9\right) \cdot y\right)} \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      5. associate-+l- 99.9%

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(z \cdot 9\right) \cdot y\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b} \]

      6. associate-*l* 99.7%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(z \cdot \left(9 \cdot y\right)\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      7. *-commutative 99.7%

         \[\leadsto \left(x \cdot 2 - \left(z \cdot \color{blue}{\left(y \cdot 9\right)}\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      8. *-commutative 99.7%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(\left(y \cdot 9\right) \cdot z\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      9. associate-*l* 99.9%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      10. associate-*l* 99.7%

          \[\leadsto \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \color{blue}{a \cdot \left(27 \cdot b\right)} \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 99.7%

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right) - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]

   6. Taylor expanded in a around 0 75.4%

      \[\leadsto \color{blue}{-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 75.4%

         \[\leadsto -9 \cdot \color{blue}{\left(\left(y \cdot z\right) \cdot t\right)} \]

      2. associate-*l* 75.4%

         \[\leadsto -9 \cdot \color{blue}{\left(y \cdot \left(z \cdot t\right)\right)} \]

      3. *-commutative 75.4%

         \[\leadsto -9 \cdot \left(y \cdot \color{blue}{\left(t \cdot z\right)}\right) \]

   8. Simplified 75.4%

      \[\leadsto \color{blue}{-9 \cdot \left(y \cdot \left(t \cdot z\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+14}:\\ \;\;\;\;-9 \cdot \left(z \cdot \left(y \cdot t\right)\right)\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-62}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \mathbf{elif}\;z \leq -1.48 \cdot 10^{-108}:\\ \;\;\;\;t \cdot \left(z \cdot \left(y \cdot -9\right)\right)\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-16}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+42}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq 10^{+83}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(z \cdot \left(y \cdot -9\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 78.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := 27 \cdot \left(a \cdot b\right)\\ t_2 := 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ t_3 := t\_1 - t\_2\\ \mathbf{if}\;b \leq -1.3 \cdot 10^{-164}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq 3.75 \cdot 10^{-22}:\\ \;\;\;\;x \cdot 2 - t\_2\\ \mathbf{elif}\;b \leq 1.02 \cdot 10^{+77} \lor \neg \left(b \leq 3.3 \cdot 10^{+100}\right):\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_1 + x \cdot 2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* 27.0 (* a b))) (t_2 (* 9.0 (* t (* y z)))) (t_3 (- t_1 t_2)))
   (if (<= b -1.3e-164)
     t_3
     (if (<= b 3.75e-22)
       (- (* x 2.0) t_2)
       (if (or (<= b 1.02e+77) (not (<= b 3.3e+100)))
         t_3
         (+ t_1 (* x 2.0)))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 27.0 * (a * b);
	double t_2 = 9.0 * (t * (y * z));
	double t_3 = t_1 - t_2;
	double tmp;
	if (b <= -1.3e-164) {
		tmp = t_3;
	} else if (b <= 3.75e-22) {
		tmp = (x * 2.0) - t_2;
	} else if ((b <= 1.02e+77) || !(b <= 3.3e+100)) {
		tmp = t_3;
	} else {
		tmp = t_1 + (x * 2.0);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = 27.0d0 * (a * b)
    t_2 = 9.0d0 * (t * (y * z))
    t_3 = t_1 - t_2
    if (b <= (-1.3d-164)) then
        tmp = t_3
    else if (b <= 3.75d-22) then
        tmp = (x * 2.0d0) - t_2
    else if ((b <= 1.02d+77) .or. (.not. (b <= 3.3d+100))) then
        tmp = t_3
    else
        tmp = t_1 + (x * 2.0d0)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 27.0 * (a * b);
	double t_2 = 9.0 * (t * (y * z));
	double t_3 = t_1 - t_2;
	double tmp;
	if (b <= -1.3e-164) {
		tmp = t_3;
	} else if (b <= 3.75e-22) {
		tmp = (x * 2.0) - t_2;
	} else if ((b <= 1.02e+77) || !(b <= 3.3e+100)) {
		tmp = t_3;
	} else {
		tmp = t_1 + (x * 2.0);
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = 27.0 * (a * b)
	t_2 = 9.0 * (t * (y * z))
	t_3 = t_1 - t_2
	tmp = 0
	if b <= -1.3e-164:
		tmp = t_3
	elif b <= 3.75e-22:
		tmp = (x * 2.0) - t_2
	elif (b <= 1.02e+77) or not (b <= 3.3e+100):
		tmp = t_3
	else:
		tmp = t_1 + (x * 2.0)
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(27.0 * Float64(a * b))
	t_2 = Float64(9.0 * Float64(t * Float64(y * z)))
	t_3 = Float64(t_1 - t_2)
	tmp = 0.0
	if (b <= -1.3e-164)
		tmp = t_3;
	elseif (b <= 3.75e-22)
		tmp = Float64(Float64(x * 2.0) - t_2);
	elseif ((b <= 1.02e+77) || !(b <= 3.3e+100))
		tmp = t_3;
	else
		tmp = Float64(t_1 + Float64(x * 2.0));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 27.0 * (a * b);
	t_2 = 9.0 * (t * (y * z));
	t_3 = t_1 - t_2;
	tmp = 0.0;
	if (b <= -1.3e-164)
		tmp = t_3;
	elseif (b <= 3.75e-22)
		tmp = (x * 2.0) - t_2;
	elseif ((b <= 1.02e+77) || ~((b <= 3.3e+100)))
		tmp = t_3;
	else
		tmp = t_1 + (x * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(9.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$1 - t$95$2), $MachinePrecision]}, If[LessEqual[b, -1.3e-164], t$95$3, If[LessEqual[b, 3.75e-22], N[(N[(x * 2.0), $MachinePrecision] - t$95$2), $MachinePrecision], If[Or[LessEqual[b, 1.02e+77], N[Not[LessEqual[b, 3.3e+100]], $MachinePrecision]], t$95$3, N[(t$95$1 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.3000000000000001e-164 or 3.74999999999999989e-22 < b < 1.02e77 or 3.3000000000000001e100 < b

   1. Initial program 96.6%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 96.6%

         \[\leadsto \color{blue}{x \cdot 2 - \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)} \]

      2. *-commutative 96.6%

         \[\leadsto x \cdot 2 - \left(\color{blue}{\left(z \cdot \left(y \cdot 9\right)\right)} \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      3. *-commutative 96.6%

         \[\leadsto x \cdot 2 - \left(\left(z \cdot \color{blue}{\left(9 \cdot y\right)}\right) \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      4. associate-*l* 96.6%

         \[\leadsto x \cdot 2 - \left(\color{blue}{\left(\left(z \cdot 9\right) \cdot y\right)} \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      5. associate-+l- 96.6%

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(z \cdot 9\right) \cdot y\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b} \]

      6. associate-*l* 96.6%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(z \cdot \left(9 \cdot y\right)\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      7. *-commutative 96.6%

         \[\leadsto \left(x \cdot 2 - \left(z \cdot \color{blue}{\left(y \cdot 9\right)}\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      8. *-commutative 96.6%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(\left(y \cdot 9\right) \cdot z\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      9. associate-*l* 96.5%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      10. associate-*l* 95.8%

          \[\leadsto \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \color{blue}{a \cdot \left(27 \cdot b\right)} \]

   3. Simplified 95.8%

      \[\leadsto \color{blue}{\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 78.8%

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right) - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]

   if -1.3000000000000001e-164 < b < 3.74999999999999989e-22

   1. Initial program 96.0%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 96.0%

         \[\leadsto \color{blue}{x \cdot 2 - \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)} \]

      2. *-commutative 96.0%

         \[\leadsto x \cdot 2 - \left(\color{blue}{\left(z \cdot \left(y \cdot 9\right)\right)} \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      3. *-commutative 96.0%

         \[\leadsto x \cdot 2 - \left(\left(z \cdot \color{blue}{\left(9 \cdot y\right)}\right) \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      4. associate-*l* 96.0%

         \[\leadsto x \cdot 2 - \left(\color{blue}{\left(\left(z \cdot 9\right) \cdot y\right)} \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      5. associate-+l- 96.0%

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(z \cdot 9\right) \cdot y\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b} \]

      6. associate-*l* 96.0%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(z \cdot \left(9 \cdot y\right)\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      7. *-commutative 96.0%

         \[\leadsto \left(x \cdot 2 - \left(z \cdot \color{blue}{\left(y \cdot 9\right)}\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      8. *-commutative 96.0%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(\left(y \cdot 9\right) \cdot z\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      9. associate-*l* 96.3%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      10. associate-*l* 96.2%

          \[\leadsto \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \color{blue}{a \cdot \left(27 \cdot b\right)} \]

   3. Simplified 96.2%

      \[\leadsto \color{blue}{\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around 0 90.0%

      \[\leadsto \color{blue}{2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]

   if 1.02e77 < b < 3.3000000000000001e100

   1. Initial program 100.0%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 100.0%

         \[\leadsto \color{blue}{x \cdot 2 - \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)} \]

      2. *-commutative 100.0%

         \[\leadsto x \cdot 2 - \left(\color{blue}{\left(z \cdot \left(y \cdot 9\right)\right)} \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      3. *-commutative 100.0%

         \[\leadsto x \cdot 2 - \left(\left(z \cdot \color{blue}{\left(9 \cdot y\right)}\right) \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      4. associate-*l* 100.0%

         \[\leadsto x \cdot 2 - \left(\color{blue}{\left(\left(z \cdot 9\right) \cdot y\right)} \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      5. associate-+l- 100.0%

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(z \cdot 9\right) \cdot y\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b} \]

      6. associate-*l* 100.0%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(z \cdot \left(9 \cdot y\right)\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      7. *-commutative 100.0%

         \[\leadsto \left(x \cdot 2 - \left(z \cdot \color{blue}{\left(y \cdot 9\right)}\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      8. *-commutative 100.0%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(\left(y \cdot 9\right) \cdot z\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      9. associate-*l* 100.0%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      10. associate-*l* 100.0%

          \[\leadsto \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \color{blue}{a \cdot \left(27 \cdot b\right)} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 100.0%

      \[\leadsto \color{blue}{2 \cdot x + 27 \cdot \left(a \cdot b\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 83.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.3 \cdot 10^{-164}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \mathbf{elif}\;b \leq 3.75 \cdot 10^{-22}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \mathbf{elif}\;b \leq 1.02 \cdot 10^{+77} \lor \neg \left(b \leq 3.3 \cdot 10^{+100}\right):\\ \;\;\;\;27 \cdot \left(a \cdot b\right) - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 49.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := -9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ t_2 := 27 \cdot \left(a \cdot b\right)\\ \mathbf{if}\;b \leq -1.3 \cdot 10^{-164}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{-211}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{-150}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;b \leq 3.3 \cdot 10^{+71}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* -9.0 (* t (* y z)))) (t_2 (* 27.0 (* a b))))
   (if (<= b -1.3e-164)
     t_2
     (if (<= b 2.5e-211)
       t_1
       (if (<= b 1.05e-150) (* x 2.0) (if (<= b 3.3e+71) t_1 t_2))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -9.0 * (t * (y * z));
	double t_2 = 27.0 * (a * b);
	double tmp;
	if (b <= -1.3e-164) {
		tmp = t_2;
	} else if (b <= 2.5e-211) {
		tmp = t_1;
	} else if (b <= 1.05e-150) {
		tmp = x * 2.0;
	} else if (b <= 3.3e+71) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (-9.0d0) * (t * (y * z))
    t_2 = 27.0d0 * (a * b)
    if (b <= (-1.3d-164)) then
        tmp = t_2
    else if (b <= 2.5d-211) then
        tmp = t_1
    else if (b <= 1.05d-150) then
        tmp = x * 2.0d0
    else if (b <= 3.3d+71) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -9.0 * (t * (y * z));
	double t_2 = 27.0 * (a * b);
	double tmp;
	if (b <= -1.3e-164) {
		tmp = t_2;
	} else if (b <= 2.5e-211) {
		tmp = t_1;
	} else if (b <= 1.05e-150) {
		tmp = x * 2.0;
	} else if (b <= 3.3e+71) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = -9.0 * (t * (y * z))
	t_2 = 27.0 * (a * b)
	tmp = 0
	if b <= -1.3e-164:
		tmp = t_2
	elif b <= 2.5e-211:
		tmp = t_1
	elif b <= 1.05e-150:
		tmp = x * 2.0
	elif b <= 3.3e+71:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(-9.0 * Float64(t * Float64(y * z)))
	t_2 = Float64(27.0 * Float64(a * b))
	tmp = 0.0
	if (b <= -1.3e-164)
		tmp = t_2;
	elseif (b <= 2.5e-211)
		tmp = t_1;
	elseif (b <= 1.05e-150)
		tmp = Float64(x * 2.0);
	elseif (b <= 3.3e+71)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = -9.0 * (t * (y * z));
	t_2 = 27.0 * (a * b);
	tmp = 0.0;
	if (b <= -1.3e-164)
		tmp = t_2;
	elseif (b <= 2.5e-211)
		tmp = t_1;
	elseif (b <= 1.05e-150)
		tmp = x * 2.0;
	elseif (b <= 3.3e+71)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(-9.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.3e-164], t$95$2, If[LessEqual[b, 2.5e-211], t$95$1, If[LessEqual[b, 1.05e-150], N[(x * 2.0), $MachinePrecision], If[LessEqual[b, 3.3e+71], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.3000000000000001e-164 or 3.2999999999999998e71 < b

   1. Initial program 97.1%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 97.1%

         \[\leadsto \color{blue}{x \cdot 2 - \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)} \]

      2. *-commutative 97.1%

         \[\leadsto x \cdot 2 - \left(\color{blue}{\left(z \cdot \left(y \cdot 9\right)\right)} \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      3. *-commutative 97.1%

         \[\leadsto x \cdot 2 - \left(\left(z \cdot \color{blue}{\left(9 \cdot y\right)}\right) \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      4. associate-*l* 97.1%

         \[\leadsto x \cdot 2 - \left(\color{blue}{\left(\left(z \cdot 9\right) \cdot y\right)} \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      5. associate-+l- 97.1%

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(z \cdot 9\right) \cdot y\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b} \]

      6. associate-*l* 97.1%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(z \cdot \left(9 \cdot y\right)\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      7. *-commutative 97.1%

         \[\leadsto \left(x \cdot 2 - \left(z \cdot \color{blue}{\left(y \cdot 9\right)}\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      8. *-commutative 97.1%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(\left(y \cdot 9\right) \cdot z\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      9. associate-*l* 97.1%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      10. associate-*l* 96.4%

          \[\leadsto \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \color{blue}{a \cdot \left(27 \cdot b\right)} \]

   3. Simplified 96.4%

      \[\leadsto \color{blue}{\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 77.9%

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right) - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]

   6. Taylor expanded in a around inf 52.8%

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right)} \]

   if -1.3000000000000001e-164 < b < 2.5000000000000001e-211 or 1.0500000000000001e-150 < b < 3.2999999999999998e71

   1. Initial program 95.1%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 95.1%

         \[\leadsto \color{blue}{x \cdot 2 - \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)} \]

      2. *-commutative 95.1%

         \[\leadsto x \cdot 2 - \left(\color{blue}{\left(z \cdot \left(y \cdot 9\right)\right)} \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      3. *-commutative 95.1%

         \[\leadsto x \cdot 2 - \left(\left(z \cdot \color{blue}{\left(9 \cdot y\right)}\right) \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      4. associate-*l* 95.0%

         \[\leadsto x \cdot 2 - \left(\color{blue}{\left(\left(z \cdot 9\right) \cdot y\right)} \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      5. associate-+l- 95.0%

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(z \cdot 9\right) \cdot y\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b} \]

      6. associate-*l* 95.1%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(z \cdot \left(9 \cdot y\right)\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      7. *-commutative 95.1%

         \[\leadsto \left(x \cdot 2 - \left(z \cdot \color{blue}{\left(y \cdot 9\right)}\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      8. *-commutative 95.1%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(\left(y \cdot 9\right) \cdot z\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      9. associate-*l* 95.2%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      10. associate-*l* 95.1%

          \[\leadsto \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \color{blue}{a \cdot \left(27 \cdot b\right)} \]

   3. Simplified 95.1%

      \[\leadsto \color{blue}{\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 48.3%

      \[\leadsto \color{blue}{-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]

   if 2.5000000000000001e-211 < b < 1.0500000000000001e-150

   1. Initial program 99.6%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 99.6%

         \[\leadsto \color{blue}{x \cdot 2 - \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)} \]

      2. *-commutative 99.6%

         \[\leadsto x \cdot 2 - \left(\color{blue}{\left(z \cdot \left(y \cdot 9\right)\right)} \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      3. *-commutative 99.6%

         \[\leadsto x \cdot 2 - \left(\left(z \cdot \color{blue}{\left(9 \cdot y\right)}\right) \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      4. associate-*l* 99.7%

         \[\leadsto x \cdot 2 - \left(\color{blue}{\left(\left(z \cdot 9\right) \cdot y\right)} \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      5. associate-+l- 99.7%

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(z \cdot 9\right) \cdot y\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b} \]

      6. associate-*l* 99.6%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(z \cdot \left(9 \cdot y\right)\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      7. *-commutative 99.6%

         \[\leadsto \left(x \cdot 2 - \left(z \cdot \color{blue}{\left(y \cdot 9\right)}\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      8. *-commutative 99.6%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(\left(y \cdot 9\right) \cdot z\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      9. associate-*l* 99.9%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      10. associate-*l* 100.0%

          \[\leadsto \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \color{blue}{a \cdot \left(27 \cdot b\right)} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 49.3%

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

4. Final simplification 50.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.3 \cdot 10^{-164}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{-211}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{-150}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;b \leq 3.3 \cdot 10^{+71}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 45.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -3.8 \cdot 10^{-180} \lor \neg \left(b \leq 1.35 \cdot 10^{-20}\right) \land \left(b \leq 1.75 \cdot 10^{+78} \lor \neg \left(b \leq 1.32 \cdot 10^{+101}\right)\right):\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -3.8e-180)
         (and (not (<= b 1.35e-20))
              (or (<= b 1.75e+78) (not (<= b 1.32e+101)))))
   (* 27.0 (* a b))
   (* x 2.0)))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -3.8e-180) || (!(b <= 1.35e-20) && ((b <= 1.75e+78) || !(b <= 1.32e+101)))) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-3.8d-180)) .or. (.not. (b <= 1.35d-20)) .and. (b <= 1.75d+78) .or. (.not. (b <= 1.32d+101))) then
        tmp = 27.0d0 * (a * b)
    else
        tmp = x * 2.0d0
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -3.8e-180) || (!(b <= 1.35e-20) && ((b <= 1.75e+78) || !(b <= 1.32e+101)))) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -3.8e-180) or (not (b <= 1.35e-20) and ((b <= 1.75e+78) or not (b <= 1.32e+101))):
		tmp = 27.0 * (a * b)
	else:
		tmp = x * 2.0
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -3.8e-180) || (!(b <= 1.35e-20) && ((b <= 1.75e+78) || !(b <= 1.32e+101))))
		tmp = Float64(27.0 * Float64(a * b));
	else
		tmp = Float64(x * 2.0);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -3.8e-180) || (~((b <= 1.35e-20)) && ((b <= 1.75e+78) || ~((b <= 1.32e+101)))))
		tmp = 27.0 * (a * b);
	else
		tmp = x * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -3.8e-180], And[N[Not[LessEqual[b, 1.35e-20]], $MachinePrecision], Or[LessEqual[b, 1.75e+78], N[Not[LessEqual[b, 1.32e+101]], $MachinePrecision]]]], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], N[(x * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -3.79999999999999999e-180 or 1.35e-20 < b < 1.7500000000000001e78 or 1.32e101 < b

   1. Initial program 96.7%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 96.7%

         \[\leadsto \color{blue}{x \cdot 2 - \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)} \]

      2. *-commutative 96.7%

         \[\leadsto x \cdot 2 - \left(\color{blue}{\left(z \cdot \left(y \cdot 9\right)\right)} \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      3. *-commutative 96.7%

         \[\leadsto x \cdot 2 - \left(\left(z \cdot \color{blue}{\left(9 \cdot y\right)}\right) \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      4. associate-*l* 96.7%

         \[\leadsto x \cdot 2 - \left(\color{blue}{\left(\left(z \cdot 9\right) \cdot y\right)} \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      5. associate-+l- 96.7%

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(z \cdot 9\right) \cdot y\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b} \]

      6. associate-*l* 96.7%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(z \cdot \left(9 \cdot y\right)\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      7. *-commutative 96.7%

         \[\leadsto \left(x \cdot 2 - \left(z \cdot \color{blue}{\left(y \cdot 9\right)}\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      8. *-commutative 96.7%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(\left(y \cdot 9\right) \cdot z\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      9. associate-*l* 96.6%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      10. associate-*l* 95.9%

          \[\leadsto \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \color{blue}{a \cdot \left(27 \cdot b\right)} \]

   3. Simplified 95.9%

      \[\leadsto \color{blue}{\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 78.1%

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right) - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]

   6. Taylor expanded in a around inf 52.3%

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right)} \]

   if -3.79999999999999999e-180 < b < 1.35e-20 or 1.7500000000000001e78 < b < 1.32e101

   1. Initial program 96.1%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 96.1%

         \[\leadsto \color{blue}{x \cdot 2 - \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)} \]

      2. *-commutative 96.1%

         \[\leadsto x \cdot 2 - \left(\color{blue}{\left(z \cdot \left(y \cdot 9\right)\right)} \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      3. *-commutative 96.1%

         \[\leadsto x \cdot 2 - \left(\left(z \cdot \color{blue}{\left(9 \cdot y\right)}\right) \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      4. associate-*l* 96.1%

         \[\leadsto x \cdot 2 - \left(\color{blue}{\left(\left(z \cdot 9\right) \cdot y\right)} \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      5. associate-+l- 96.1%

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(z \cdot 9\right) \cdot y\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b} \]

      6. associate-*l* 96.1%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(z \cdot \left(9 \cdot y\right)\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      7. *-commutative 96.1%

         \[\leadsto \left(x \cdot 2 - \left(z \cdot \color{blue}{\left(y \cdot 9\right)}\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      8. *-commutative 96.1%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(\left(y \cdot 9\right) \cdot z\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      9. associate-*l* 96.4%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      10. associate-*l* 96.4%

          \[\leadsto \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \color{blue}{a \cdot \left(27 \cdot b\right)} \]

   3. Simplified 96.4%

      \[\leadsto \color{blue}{\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 41.2%

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

4. Final simplification 47.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.8 \cdot 10^{-180} \lor \neg \left(b \leq 1.35 \cdot 10^{-20}\right) \land \left(b \leq 1.75 \cdot 10^{+78} \lor \neg \left(b \leq 1.32 \cdot 10^{+101}\right)\right):\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 97.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 1.85 \cdot 10^{+75}:\\ \;\;\;\;\left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) + y \cdot \left(z \cdot \left(t \cdot -9\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(27 \cdot \frac{a \cdot b}{t} - 9 \cdot \left(y \cdot z\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z 1.85e+75)
   (+ (+ (* (* a 27.0) b) (* x 2.0)) (* y (* z (* t -9.0))))
   (* t (- (* 27.0 (/ (* a b) t)) (* 9.0 (* y z))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 1.85e+75) {
		tmp = (((a * 27.0) * b) + (x * 2.0)) + (y * (z * (t * -9.0)));
	} else {
		tmp = t * ((27.0 * ((a * b) / t)) - (9.0 * (y * z)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= 1.85d+75) then
        tmp = (((a * 27.0d0) * b) + (x * 2.0d0)) + (y * (z * (t * (-9.0d0))))
    else
        tmp = t * ((27.0d0 * ((a * b) / t)) - (9.0d0 * (y * z)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 1.85e+75) {
		tmp = (((a * 27.0) * b) + (x * 2.0)) + (y * (z * (t * -9.0)));
	} else {
		tmp = t * ((27.0 * ((a * b) / t)) - (9.0 * (y * z)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= 1.85e+75:
		tmp = (((a * 27.0) * b) + (x * 2.0)) + (y * (z * (t * -9.0)))
	else:
		tmp = t * ((27.0 * ((a * b) / t)) - (9.0 * (y * z)))
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= 1.85e+75)
		tmp = Float64(Float64(Float64(Float64(a * 27.0) * b) + Float64(x * 2.0)) + Float64(y * Float64(z * Float64(t * -9.0))));
	else
		tmp = Float64(t * Float64(Float64(27.0 * Float64(Float64(a * b) / t)) - Float64(9.0 * Float64(y * z))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= 1.85e+75)
		tmp = (((a * 27.0) * b) + (x * 2.0)) + (y * (z * (t * -9.0)));
	else
		tmp = t * ((27.0 * ((a * b) / t)) - (9.0 * (y * z)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, 1.85e+75], N[(N[(N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision] + N[(y * N[(z * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(27.0 * N[(N[(a * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] - N[(9.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 1.85000000000000005e75

   1. Initial program 98.9%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. +-commutative 98.9%

         \[\leadsto \color{blue}{\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} \]

      2. associate-+r- 98.9%

         \[\leadsto \color{blue}{\left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t} \]

      3. *-commutative 98.9%

         \[\leadsto \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) - \color{blue}{t \cdot \left(\left(y \cdot 9\right) \cdot z\right)} \]

      4. cancel-sign-sub-inv 98.9%

         \[\leadsto \color{blue}{\left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) + \left(-t\right) \cdot \left(\left(y \cdot 9\right) \cdot z\right)} \]

      5. associate-*r* 96.2%

         \[\leadsto \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) + \color{blue}{\left(\left(-t\right) \cdot \left(y \cdot 9\right)\right) \cdot z} \]

      6. distribute-lft-neg-in 96.2%

         \[\leadsto \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) + \color{blue}{\left(-t \cdot \left(y \cdot 9\right)\right)} \cdot z \]

      7. *-commutative 96.2%

         \[\leadsto \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) + \left(-\color{blue}{\left(y \cdot 9\right) \cdot t}\right) \cdot z \]

      8. cancel-sign-sub-inv 96.2%

         \[\leadsto \color{blue}{\left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) - \left(\left(y \cdot 9\right) \cdot t\right) \cdot z} \]

      9. associate-+r- 96.2%

         \[\leadsto \color{blue}{\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot t\right) \cdot z\right)} \]

      10. associate-*l* 96.2%

          \[\leadsto \color{blue}{a \cdot \left(27 \cdot b\right)} + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot t\right) \cdot z\right) \]

      11. fma-define 96.2%

          \[\leadsto \color{blue}{\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - \left(\left(y \cdot 9\right) \cdot t\right) \cdot z\right)} \]

      12. fma-neg 96.2%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \color{blue}{\mathsf{fma}\left(x, 2, -\left(\left(y \cdot 9\right) \cdot t\right) \cdot z\right)}\right) \]

      13. associate-*l* 98.4%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, -\color{blue}{\left(y \cdot 9\right) \cdot \left(t \cdot z\right)}\right)\right) \]

      14. distribute-rgt-neg-in 98.4%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, \color{blue}{\left(y \cdot 9\right) \cdot \left(-t \cdot z\right)}\right)\right) \]

      15. *-commutative 98.4%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, \left(y \cdot 9\right) \cdot \left(-\color{blue}{z \cdot t}\right)\right)\right) \]

      16. associate-*l* 98.3%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, \color{blue}{y \cdot \left(9 \cdot \left(-z \cdot t\right)\right)}\right)\right) \]

      17. *-commutative 98.3%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, y \cdot \color{blue}{\left(\left(-z \cdot t\right) \cdot 9\right)}\right)\right) \]

      18. distribute-lft-neg-in 98.3%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, y \cdot \color{blue}{\left(-\left(z \cdot t\right) \cdot 9\right)}\right)\right) \]

      19. associate-*r* 97.9%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, y \cdot \left(-\color{blue}{z \cdot \left(t \cdot 9\right)}\right)\right)\right) \]

   3. Simplified 97.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, y \cdot \left(z \cdot \left(t \cdot -9\right)\right)\right)\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-undefine 97.9%

         \[\leadsto \color{blue}{a \cdot \left(27 \cdot b\right) + \mathsf{fma}\left(x, 2, y \cdot \left(z \cdot \left(t \cdot -9\right)\right)\right)} \]

      2. fma-undefine 97.9%

         \[\leadsto a \cdot \left(27 \cdot b\right) + \color{blue}{\left(x \cdot 2 + y \cdot \left(z \cdot \left(t \cdot -9\right)\right)\right)} \]

      3. associate-+r+ 97.9%

         \[\leadsto \color{blue}{\left(a \cdot \left(27 \cdot b\right) + x \cdot 2\right) + y \cdot \left(z \cdot \left(t \cdot -9\right)\right)} \]

      4. associate-*r* 98.0%

         \[\leadsto \left(\color{blue}{\left(a \cdot 27\right) \cdot b} + x \cdot 2\right) + y \cdot \left(z \cdot \left(t \cdot -9\right)\right) \]

      5. *-commutative 98.0%

         \[\leadsto \left(\color{blue}{b \cdot \left(a \cdot 27\right)} + x \cdot 2\right) + y \cdot \left(z \cdot \left(t \cdot -9\right)\right) \]

   6. Applied egg-rr 98.0%

      \[\leadsto \color{blue}{\left(b \cdot \left(a \cdot 27\right) + x \cdot 2\right) + y \cdot \left(z \cdot \left(t \cdot -9\right)\right)} \]

   if 1.85000000000000005e75 < z

   1. Initial program 86.7%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 86.7%

         \[\leadsto \color{blue}{x \cdot 2 - \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)} \]

      2. *-commutative 86.7%

         \[\leadsto x \cdot 2 - \left(\color{blue}{\left(z \cdot \left(y \cdot 9\right)\right)} \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      3. *-commutative 86.7%

         \[\leadsto x \cdot 2 - \left(\left(z \cdot \color{blue}{\left(9 \cdot y\right)}\right) \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      4. associate-*l* 86.7%

         \[\leadsto x \cdot 2 - \left(\color{blue}{\left(\left(z \cdot 9\right) \cdot y\right)} \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      5. associate-+l- 86.7%

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(z \cdot 9\right) \cdot y\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b} \]

      6. associate-*l* 86.7%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(z \cdot \left(9 \cdot y\right)\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      7. *-commutative 86.7%

         \[\leadsto \left(x \cdot 2 - \left(z \cdot \color{blue}{\left(y \cdot 9\right)}\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      8. *-commutative 86.7%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(\left(y \cdot 9\right) \cdot z\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      9. associate-*l* 88.7%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      10. associate-*l* 86.8%

          \[\leadsto \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \color{blue}{a \cdot \left(27 \cdot b\right)} \]

   3. Simplified 86.8%

      \[\leadsto \color{blue}{\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 64.3%

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right) - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]

   6. Taylor expanded in t around inf 56.1%

      \[\leadsto \color{blue}{t \cdot \left(27 \cdot \frac{a \cdot b}{t} - 9 \cdot \left(y \cdot z\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 1.85 \cdot 10^{+75}:\\ \;\;\;\;\left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) + y \cdot \left(z \cdot \left(t \cdot -9\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(27 \cdot \frac{a \cdot b}{t} - 9 \cdot \left(y \cdot z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 77.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -1.3 \cdot 10^{-164} \lor \neg \left(b \leq 3.8 \cdot 10^{+71}\right):\\ \;\;\;\;27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.3e-164) (not (<= b 3.8e+71)))
   (+ (* 27.0 (* a b)) (* x 2.0))
   (- (* x 2.0) (* 9.0 (* t (* y z))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.3e-164) || !(b <= 3.8e+71)) {
		tmp = (27.0 * (a * b)) + (x * 2.0);
	} else {
		tmp = (x * 2.0) - (9.0 * (t * (y * z)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-1.3d-164)) .or. (.not. (b <= 3.8d+71))) then
        tmp = (27.0d0 * (a * b)) + (x * 2.0d0)
    else
        tmp = (x * 2.0d0) - (9.0d0 * (t * (y * z)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.3e-164) || !(b <= 3.8e+71)) {
		tmp = (27.0 * (a * b)) + (x * 2.0);
	} else {
		tmp = (x * 2.0) - (9.0 * (t * (y * z)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -1.3e-164) or not (b <= 3.8e+71):
		tmp = (27.0 * (a * b)) + (x * 2.0)
	else:
		tmp = (x * 2.0) - (9.0 * (t * (y * z)))
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1.3e-164) || !(b <= 3.8e+71))
		tmp = Float64(Float64(27.0 * Float64(a * b)) + Float64(x * 2.0));
	else
		tmp = Float64(Float64(x * 2.0) - Float64(9.0 * Float64(t * Float64(y * z))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -1.3e-164) || ~((b <= 3.8e+71)))
		tmp = (27.0 * (a * b)) + (x * 2.0);
	else
		tmp = (x * 2.0) - (9.0 * (t * (y * z)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1.3e-164], N[Not[LessEqual[b, 3.8e+71]], $MachinePrecision]], N[(N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.3000000000000001e-164 or 3.8000000000000001e71 < b

   1. Initial program 97.1%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 97.1%

         \[\leadsto \color{blue}{x \cdot 2 - \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)} \]

      2. *-commutative 97.1%

         \[\leadsto x \cdot 2 - \left(\color{blue}{\left(z \cdot \left(y \cdot 9\right)\right)} \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      3. *-commutative 97.1%

         \[\leadsto x \cdot 2 - \left(\left(z \cdot \color{blue}{\left(9 \cdot y\right)}\right) \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      4. associate-*l* 97.1%

         \[\leadsto x \cdot 2 - \left(\color{blue}{\left(\left(z \cdot 9\right) \cdot y\right)} \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      5. associate-+l- 97.1%

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(z \cdot 9\right) \cdot y\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b} \]

      6. associate-*l* 97.1%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(z \cdot \left(9 \cdot y\right)\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      7. *-commutative 97.1%

         \[\leadsto \left(x \cdot 2 - \left(z \cdot \color{blue}{\left(y \cdot 9\right)}\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      8. *-commutative 97.1%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(\left(y \cdot 9\right) \cdot z\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      9. associate-*l* 97.1%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      10. associate-*l* 96.4%

          \[\leadsto \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \color{blue}{a \cdot \left(27 \cdot b\right)} \]

   3. Simplified 96.4%

      \[\leadsto \color{blue}{\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 72.3%

      \[\leadsto \color{blue}{2 \cdot x + 27 \cdot \left(a \cdot b\right)} \]

   if -1.3000000000000001e-164 < b < 3.8000000000000001e71

   1. Initial program 95.6%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 95.6%

         \[\leadsto \color{blue}{x \cdot 2 - \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)} \]

      2. *-commutative 95.6%

         \[\leadsto x \cdot 2 - \left(\color{blue}{\left(z \cdot \left(y \cdot 9\right)\right)} \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      3. *-commutative 95.6%

         \[\leadsto x \cdot 2 - \left(\left(z \cdot \color{blue}{\left(9 \cdot y\right)}\right) \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      4. associate-*l* 95.6%

         \[\leadsto x \cdot 2 - \left(\color{blue}{\left(\left(z \cdot 9\right) \cdot y\right)} \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      5. associate-+l- 95.6%

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(z \cdot 9\right) \cdot y\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b} \]

      6. associate-*l* 95.6%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(z \cdot \left(9 \cdot y\right)\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      7. *-commutative 95.6%

         \[\leadsto \left(x \cdot 2 - \left(z \cdot \color{blue}{\left(y \cdot 9\right)}\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      8. *-commutative 95.6%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(\left(y \cdot 9\right) \cdot z\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      9. associate-*l* 95.8%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      10. associate-*l* 95.7%

          \[\leadsto \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \color{blue}{a \cdot \left(27 \cdot b\right)} \]

   3. Simplified 95.7%

      \[\leadsto \color{blue}{\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around 0 84.4%

      \[\leadsto \color{blue}{2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.3 \cdot 10^{-164} \lor \neg \left(b \leq 3.8 \cdot 10^{+71}\right):\\ \;\;\;\;27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 95.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (+ (- (* x 2.0) (* (* (* y 9.0) z) t)) (* (* a 27.0) b)))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	return ((x * 2.0) - (((y * 9.0) * z) * t)) + ((a * 27.0) * b);
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = ((x * 2.0d0) - (((y * 9.0d0) * z) * t)) + ((a * 27.0d0) * b)
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	return ((x * 2.0) - (((y * 9.0) * z) * t)) + ((a * 27.0) * b);
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	return ((x * 2.0) - (((y * 9.0) * z) * t)) + ((a * 27.0) * b)

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(x * 2.0) - Float64(Float64(Float64(y * 9.0) * z) * t)) + Float64(Float64(a * 27.0) * b))
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp = code(x, y, z, t, a, b)
	tmp = ((x * 2.0) - (((y * 9.0) * z) * t)) + ((a * 27.0) * b);
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(x * 2.0), $MachinePrecision] - N[(N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 96.4%

   \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
2. Add Preprocessing

3. Final simplification 96.4%

   \[\leadsto \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
4. Add Preprocessing

Alternative 11: 30.7% accurate, 5.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ x \cdot 2 \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b) :precision binary64 (* x 2.0))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	return x * 2.0;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = x * 2.0d0
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	return x * 2.0;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	return x * 2.0

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	return Float64(x * 2.0)
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp = code(x, y, z, t, a, b)
	tmp = x * 2.0;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := N[(x * 2.0), $MachinePrecision]

Derivation

1. Initial program 96.4%

   \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
2. Step-by-step derivation

   1. associate-+l- 96.4%

      \[\leadsto \color{blue}{x \cdot 2 - \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)} \]

   2. *-commutative 96.4%

      \[\leadsto x \cdot 2 - \left(\color{blue}{\left(z \cdot \left(y \cdot 9\right)\right)} \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

   3. *-commutative 96.4%

      \[\leadsto x \cdot 2 - \left(\left(z \cdot \color{blue}{\left(9 \cdot y\right)}\right) \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

   4. associate-*l* 96.4%

      \[\leadsto x \cdot 2 - \left(\color{blue}{\left(\left(z \cdot 9\right) \cdot y\right)} \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

   5. associate-+l- 96.4%

      \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(z \cdot 9\right) \cdot y\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b} \]

   6. associate-*l* 96.4%

      \[\leadsto \left(x \cdot 2 - \color{blue}{\left(z \cdot \left(9 \cdot y\right)\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

   7. *-commutative 96.4%

      \[\leadsto \left(x \cdot 2 - \left(z \cdot \color{blue}{\left(y \cdot 9\right)}\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

   8. *-commutative 96.4%

      \[\leadsto \left(x \cdot 2 - \color{blue}{\left(\left(y \cdot 9\right) \cdot z\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

   9. associate-*l* 96.5%

      \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]

   10. associate-*l* 96.1%

       \[\leadsto \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \color{blue}{a \cdot \left(27 \cdot b\right)} \]

3. Simplified 96.1%

   \[\leadsto \color{blue}{\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)} \]
4. Add Preprocessing

5. Taylor expanded in x around inf 29.2%

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

6. Final simplification 29.2%

   \[\leadsto x \cdot 2 \]
7. Add Preprocessing

Developer target: 95.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y < 7.590524218811189 \cdot 10^{-161}:\\ \;\;\;\;\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) + \left(a \cdot 27\right) \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (< y 7.590524218811189e-161)
   (+ (- (* x 2.0) (* (* (* y 9.0) z) t)) (* a (* 27.0 b)))
   (+ (- (* x 2.0) (* 9.0 (* y (* t z)))) (* (* a 27.0) b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y < 7.590524218811189e-161) {
		tmp = ((x * 2.0) - (((y * 9.0) * z) * t)) + (a * (27.0 * b));
	} else {
		tmp = ((x * 2.0) - (9.0 * (y * (t * z)))) + ((a * 27.0) * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y < 7.590524218811189d-161) then
        tmp = ((x * 2.0d0) - (((y * 9.0d0) * z) * t)) + (a * (27.0d0 * b))
    else
        tmp = ((x * 2.0d0) - (9.0d0 * (y * (t * z)))) + ((a * 27.0d0) * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y < 7.590524218811189e-161) {
		tmp = ((x * 2.0) - (((y * 9.0) * z) * t)) + (a * (27.0 * b));
	} else {
		tmp = ((x * 2.0) - (9.0 * (y * (t * z)))) + ((a * 27.0) * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y < 7.590524218811189e-161:
		tmp = ((x * 2.0) - (((y * 9.0) * z) * t)) + (a * (27.0 * b))
	else:
		tmp = ((x * 2.0) - (9.0 * (y * (t * z)))) + ((a * 27.0) * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y < 7.590524218811189e-161)
		tmp = Float64(Float64(Float64(x * 2.0) - Float64(Float64(Float64(y * 9.0) * z) * t)) + Float64(a * Float64(27.0 * b)));
	else
		tmp = Float64(Float64(Float64(x * 2.0) - Float64(9.0 * Float64(y * Float64(t * z)))) + Float64(Float64(a * 27.0) * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y < 7.590524218811189e-161)
		tmp = ((x * 2.0) - (((y * 9.0) * z) * t)) + (a * (27.0 * b));
	else
		tmp = ((x * 2.0) - (9.0 * (y * (t * z)))) + ((a * 27.0) * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Less[y, 7.590524218811189e-161], N[(N[(N[(x * 2.0), $MachinePrecision] - N[(N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(y * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]]

Reproduce

herbie shell --seed 2024071 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, A"
  :precision binary64

  :alt
  (if (< y 7.590524218811189e-161) (+ (- (* x 2.0) (* (* (* y 9.0) z) t)) (* a (* 27.0 b))) (+ (- (* x 2.0) (* 9.0 (* y (* t z)))) (* (* a 27.0) b)))

  (+ (- (* x 2.0) (* (* (* y 9.0) z) t)) (* (* a 27.0) b)))