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

Percentage Accurate: 95.7% → 98.3%

Time: 14.1s

Alternatives: 15

Speedup: 0.8×

• 27.3% 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: 95.7% 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: 98.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := a \cdot \left(27 \cdot b\right)\\ \mathbf{if}\;y \cdot 9 \leq -5 \cdot 10^{+22}:\\ \;\;\;\;\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + t_1\\ \mathbf{else}:\\ \;\;\;\;t_1 + \left(x \cdot 2 - z \cdot \left(\left(y \cdot 9\right) \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (* 27.0 b))))
   (if (<= (* y 9.0) -5e+22)
     (+ (- (* x 2.0) (* (* y 9.0) (* z t))) t_1)
     (+ t_1 (- (* x 2.0) (* z (* (* y 9.0) t)))))))

C

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 = a * (27.0 * b);
	double tmp;
	if ((y * 9.0) <= -5e+22) {
		tmp = ((x * 2.0) - ((y * 9.0) * (z * t))) + t_1;
	} else {
		tmp = t_1 + ((x * 2.0) - (z * ((y * 9.0) * t)));
	}
	return tmp;
}

Fortran

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) :: tmp
    t_1 = a * (27.0d0 * b)
    if ((y * 9.0d0) <= (-5d+22)) then
        tmp = ((x * 2.0d0) - ((y * 9.0d0) * (z * t))) + t_1
    else
        tmp = t_1 + ((x * 2.0d0) - (z * ((y * 9.0d0) * t)))
    end if
    code = tmp
end function

Java

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 = a * (27.0 * b);
	double tmp;
	if ((y * 9.0) <= -5e+22) {
		tmp = ((x * 2.0) - ((y * 9.0) * (z * t))) + t_1;
	} else {
		tmp = t_1 + ((x * 2.0) - (z * ((y * 9.0) * t)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = a * (27.0 * b)
	tmp = 0
	if (y * 9.0) <= -5e+22:
		tmp = ((x * 2.0) - ((y * 9.0) * (z * t))) + t_1
	else:
		tmp = t_1 + ((x * 2.0) - (z * ((y * 9.0) * t)))
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(27.0 * b))
	tmp = 0.0
	if (Float64(y * 9.0) <= -5e+22)
		tmp = Float64(Float64(Float64(x * 2.0) - Float64(Float64(y * 9.0) * Float64(z * t))) + t_1);
	else
		tmp = Float64(t_1 + Float64(Float64(x * 2.0) - Float64(z * Float64(Float64(y * 9.0) * t))));
	end
	return tmp
end

MATLAB

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 = a * (27.0 * b);
	tmp = 0.0;
	if ((y * 9.0) <= -5e+22)
		tmp = ((x * 2.0) - ((y * 9.0) * (z * t))) + t_1;
	else
		tmp = t_1 + ((x * 2.0) - (z * ((y * 9.0) * t)));
	end
	tmp_2 = tmp;
end

Wolfram

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[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(y * 9.0), $MachinePrecision], -5e+22], N[(N[(N[(x * 2.0), $MachinePrecision] - N[(N[(y * 9.0), $MachinePrecision] * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(t$95$1 + N[(N[(x * 2.0), $MachinePrecision] - N[(z * N[(N[(y * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y 9) < -4.9999999999999996e22

   1. Initial program 92.6%

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

      1. sub-neg 92.6%

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

      2. sub-neg 92.6%

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

      3. associate-*l* 99.8%

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

      4. 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

   if -4.9999999999999996e22 < (*.f64 y 9)

   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. sub-neg 98.9%

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

      2. sub-neg 98.9%

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

      3. associate-*l* 93.3%

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

      4. associate-*l* 93.3%

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

   3. Simplified 93.3%

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

   5. Taylor expanded in y around 0 98.8%

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

      1. *-commutative 98.8%

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

      2. associate-*l* 98.9%

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

      3. *-commutative 98.9%

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

      4. associate-*r* 98.9%

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

      5. *-commutative 98.9%

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

      6. associate-*r* 95.2%

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

      7. *-commutative 95.2%

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

   7. Simplified 95.2%

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

4. Final simplification 96.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot 9 \leq -5 \cdot 10^{+22}:\\ \;\;\;\;\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right) + \left(x \cdot 2 - z \cdot \left(\left(y \cdot 9\right) \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 72.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := x \cdot 2 - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ t_2 := x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \mathbf{if}\;a \leq -1.26 \cdot 10^{+194}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.7 \cdot 10^{+89}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{+65}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -5.4 \cdot 10^{+32}:\\ \;\;\;\;y \cdot \left(z \cdot \left(t \cdot -9\right)\right)\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-129}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (* x 2.0) (* 9.0 (* t (* y z)))))
        (t_2 (+ (* x 2.0) (* 27.0 (* a b)))))
   (if (<= a -1.26e+194)
     t_2
     (if (<= a -1.7e+89)
       t_1
       (if (<= a -2.4e+65)
         t_2
         (if (<= a -5.4e+32)
           (* y (* z (* t -9.0)))
           (if (<= a 3.5e-129) t_1 t_2)))))))

C

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 = (x * 2.0) - (9.0 * (t * (y * z)));
	double t_2 = (x * 2.0) + (27.0 * (a * b));
	double tmp;
	if (a <= -1.26e+194) {
		tmp = t_2;
	} else if (a <= -1.7e+89) {
		tmp = t_1;
	} else if (a <= -2.4e+65) {
		tmp = t_2;
	} else if (a <= -5.4e+32) {
		tmp = y * (z * (t * -9.0));
	} else if (a <= 3.5e-129) {
		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.
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 = (x * 2.0d0) - (9.0d0 * (t * (y * z)))
    t_2 = (x * 2.0d0) + (27.0d0 * (a * b))
    if (a <= (-1.26d+194)) then
        tmp = t_2
    else if (a <= (-1.7d+89)) then
        tmp = t_1
    else if (a <= (-2.4d+65)) then
        tmp = t_2
    else if (a <= (-5.4d+32)) then
        tmp = y * (z * (t * (-9.0d0)))
    else if (a <= 3.5d-129) 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;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * 2.0) - (9.0 * (t * (y * z)));
	double t_2 = (x * 2.0) + (27.0 * (a * b));
	double tmp;
	if (a <= -1.26e+194) {
		tmp = t_2;
	} else if (a <= -1.7e+89) {
		tmp = t_1;
	} else if (a <= -2.4e+65) {
		tmp = t_2;
	} else if (a <= -5.4e+32) {
		tmp = y * (z * (t * -9.0));
	} else if (a <= 3.5e-129) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = (x * 2.0) - (9.0 * (t * (y * z)))
	t_2 = (x * 2.0) + (27.0 * (a * b))
	tmp = 0
	if a <= -1.26e+194:
		tmp = t_2
	elif a <= -1.7e+89:
		tmp = t_1
	elif a <= -2.4e+65:
		tmp = t_2
	elif a <= -5.4e+32:
		tmp = y * (z * (t * -9.0))
	elif a <= 3.5e-129:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

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(x * 2.0) - Float64(9.0 * Float64(t * Float64(y * z))))
	t_2 = Float64(Float64(x * 2.0) + Float64(27.0 * Float64(a * b)))
	tmp = 0.0
	if (a <= -1.26e+194)
		tmp = t_2;
	elseif (a <= -1.7e+89)
		tmp = t_1;
	elseif (a <= -2.4e+65)
		tmp = t_2;
	elseif (a <= -5.4e+32)
		tmp = Float64(y * Float64(z * Float64(t * -9.0)));
	elseif (a <= 3.5e-129)
		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])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * 2.0) - (9.0 * (t * (y * z)));
	t_2 = (x * 2.0) + (27.0 * (a * b));
	tmp = 0.0;
	if (a <= -1.26e+194)
		tmp = t_2;
	elseif (a <= -1.7e+89)
		tmp = t_1;
	elseif (a <= -2.4e+65)
		tmp = t_2;
	elseif (a <= -5.4e+32)
		tmp = y * (z * (t * -9.0));
	elseif (a <= 3.5e-129)
		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.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * 2.0), $MachinePrecision] + N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.26e+194], t$95$2, If[LessEqual[a, -1.7e+89], t$95$1, If[LessEqual[a, -2.4e+65], t$95$2, If[LessEqual[a, -5.4e+32], N[(y * N[(z * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.5e-129], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.26e194 or -1.7000000000000001e89 < a < -2.4000000000000002e65 or 3.4999999999999997e-129 < a

   1. Initial program 97.3%

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

      1. sub-neg 97.3%

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

      2. sub-neg 97.3%

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

      3. associate-*l* 96.6%

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

      4. associate-*l* 96.6%

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

   3. Simplified 96.6%

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

   5. Taylor expanded in y around 0 73.4%

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

   if -1.26e194 < a < -1.7000000000000001e89 or -5.40000000000000025e32 < a < 3.4999999999999997e-129

   1. Initial program 97.7%

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

      1. sub-neg 97.7%

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

      2. sub-neg 97.7%

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

      3. associate-*l* 93.0%

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

      4. associate-*l* 92.9%

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

   3. Simplified 92.9%

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

   5. Taylor expanded in a around 0 85.3%

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

   if -2.4000000000000002e65 < a < -5.40000000000000025e32

   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. sub-neg 100.0%

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

      2. sub-neg 100.0%

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

      3. associate-*l* 100.0%

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

      4. 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 0 100.0%

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

   6. Taylor expanded in a around 0 75.5%

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

      1. associate-*r* 75.5%

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

      2. *-commutative 75.5%

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

      3. associate-*l* 75.5%

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

      4. *-commutative 75.5%

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

   8. Simplified 75.5%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.26 \cdot 10^{+194}:\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;a \leq -1.7 \cdot 10^{+89}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{+65}:\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;a \leq -5.4 \cdot 10^{+32}:\\ \;\;\;\;y \cdot \left(z \cdot \left(t \cdot -9\right)\right)\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-129}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 47.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(t \cdot \left(y \cdot z\right)\right) \cdot -9\\ t_2 := b \cdot \left(a \cdot 27\right)\\ \mathbf{if}\;x \leq -1.7 \cdot 10^{+76}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{-163}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 3.25 \cdot 10^{-223}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{-113}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 9 \cdot 10^{+43}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* t (* y z)) -9.0)) (t_2 (* b (* a 27.0))))
   (if (<= x -1.7e+76)
     (* x 2.0)
     (if (<= x -1.5e-163)
       t_2
       (if (<= x 3.25e-223)
         t_1
         (if (<= x 4.8e-113) t_2 (if (<= x 9e+43) t_1 (* x 2.0))))))))

C

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 = (t * (y * z)) * -9.0;
	double t_2 = b * (a * 27.0);
	double tmp;
	if (x <= -1.7e+76) {
		tmp = x * 2.0;
	} else if (x <= -1.5e-163) {
		tmp = t_2;
	} else if (x <= 3.25e-223) {
		tmp = t_1;
	} else if (x <= 4.8e-113) {
		tmp = t_2;
	} else if (x <= 9e+43) {
		tmp = t_1;
	} 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.
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 = (t * (y * z)) * (-9.0d0)
    t_2 = b * (a * 27.0d0)
    if (x <= (-1.7d+76)) then
        tmp = x * 2.0d0
    else if (x <= (-1.5d-163)) then
        tmp = t_2
    else if (x <= 3.25d-223) then
        tmp = t_1
    else if (x <= 4.8d-113) then
        tmp = t_2
    else if (x <= 9d+43) then
        tmp = t_1
    else
        tmp = x * 2.0d0
    end if
    code = tmp
end function

Java

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 = (t * (y * z)) * -9.0;
	double t_2 = b * (a * 27.0);
	double tmp;
	if (x <= -1.7e+76) {
		tmp = x * 2.0;
	} else if (x <= -1.5e-163) {
		tmp = t_2;
	} else if (x <= 3.25e-223) {
		tmp = t_1;
	} else if (x <= 4.8e-113) {
		tmp = t_2;
	} else if (x <= 9e+43) {
		tmp = t_1;
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = (t * (y * z)) * -9.0
	t_2 = b * (a * 27.0)
	tmp = 0
	if x <= -1.7e+76:
		tmp = x * 2.0
	elif x <= -1.5e-163:
		tmp = t_2
	elif x <= 3.25e-223:
		tmp = t_1
	elif x <= 4.8e-113:
		tmp = t_2
	elif x <= 9e+43:
		tmp = t_1
	else:
		tmp = x * 2.0
	return tmp

Julia

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(t * Float64(y * z)) * -9.0)
	t_2 = Float64(b * Float64(a * 27.0))
	tmp = 0.0
	if (x <= -1.7e+76)
		tmp = Float64(x * 2.0);
	elseif (x <= -1.5e-163)
		tmp = t_2;
	elseif (x <= 3.25e-223)
		tmp = t_1;
	elseif (x <= 4.8e-113)
		tmp = t_2;
	elseif (x <= 9e+43)
		tmp = t_1;
	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])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t * (y * z)) * -9.0;
	t_2 = b * (a * 27.0);
	tmp = 0.0;
	if (x <= -1.7e+76)
		tmp = x * 2.0;
	elseif (x <= -1.5e-163)
		tmp = t_2;
	elseif (x <= 3.25e-223)
		tmp = t_1;
	elseif (x <= 4.8e-113)
		tmp = t_2;
	elseif (x <= 9e+43)
		tmp = t_1;
	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.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision] * -9.0), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.7e+76], N[(x * 2.0), $MachinePrecision], If[LessEqual[x, -1.5e-163], t$95$2, If[LessEqual[x, 3.25e-223], t$95$1, If[LessEqual[x, 4.8e-113], t$95$2, If[LessEqual[x, 9e+43], t$95$1, N[(x * 2.0), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.6999999999999999e76 or 9e43 < x

   1. Initial program 98.1%

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

      1. sub-neg 98.1%

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

      2. sub-neg 98.1%

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

      3. associate-*l* 94.5%

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

      4. associate-*l* 94.5%

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

   3. Simplified 94.5%

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

   5. Taylor expanded in x around inf 58.0%

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

   if -1.6999999999999999e76 < x < -1.5000000000000001e-163 or 3.2499999999999998e-223 < x < 4.80000000000000024e-113

   1. Initial program 97.2%

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

      1. sub-neg 97.2%

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

      2. sub-neg 97.2%

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

      3. associate-*l* 96.1%

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

      4. 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 y around 0 97.1%

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

      1. *-commutative 97.1%

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

      2. associate-*l* 97.2%

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

      3. *-commutative 97.2%

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

      4. associate-*r* 97.2%

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

      5. *-commutative 97.2%

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

      6. associate-*r* 96.1%

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

      7. *-commutative 96.1%

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

   7. Simplified 96.1%

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

   8. Taylor expanded in t around 0 96.1%

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

   9. Taylor expanded in a around inf 52.9%

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

       1. *-commutative 52.9%

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

       2. *-commutative 52.9%

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

       3. associate-*l* 52.9%

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

       4. *-commutative 52.9%

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

   11. Simplified 52.9%

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

   if -1.5000000000000001e-163 < x < 3.2499999999999998e-223 or 4.80000000000000024e-113 < x < 9e43

   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. sub-neg 97.1%

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

      2. sub-neg 97.1%

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

      3. associate-*l* 93.4%

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

      4. associate-*l* 93.4%

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

   3. Simplified 93.4%

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

   5. Taylor expanded in y around inf 65.2%

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

4. Final simplification 58.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{+76}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{-163}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \mathbf{elif}\;x \leq 3.25 \cdot 10^{-223}:\\ \;\;\;\;\left(t \cdot \left(y \cdot z\right)\right) \cdot -9\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{-113}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \mathbf{elif}\;x \leq 9 \cdot 10^{+43}:\\ \;\;\;\;\left(t \cdot \left(y \cdot z\right)\right) \cdot -9\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 47.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot 27\right)\\ \mathbf{if}\;x \leq -2.4 \cdot 10^{+76}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \leq -1.35 \cdot 10^{-163}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-224}:\\ \;\;\;\;y \cdot \left(z \cdot \left(t \cdot -9\right)\right)\\ \mathbf{elif}\;x \leq 9.8 \cdot 10^{-113}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.75 \cdot 10^{+42}:\\ \;\;\;\;\left(t \cdot \left(y \cdot z\right)\right) \cdot -9\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (* a 27.0))))
   (if (<= x -2.4e+76)
     (* x 2.0)
     (if (<= x -1.35e-163)
       t_1
       (if (<= x 8e-224)
         (* y (* z (* t -9.0)))
         (if (<= x 9.8e-113)
           t_1
           (if (<= x 2.75e+42) (* (* t (* y z)) -9.0) (* x 2.0))))))))

C

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 = b * (a * 27.0);
	double tmp;
	if (x <= -2.4e+76) {
		tmp = x * 2.0;
	} else if (x <= -1.35e-163) {
		tmp = t_1;
	} else if (x <= 8e-224) {
		tmp = y * (z * (t * -9.0));
	} else if (x <= 9.8e-113) {
		tmp = t_1;
	} else if (x <= 2.75e+42) {
		tmp = (t * (y * z)) * -9.0;
	} 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.
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) :: tmp
    t_1 = b * (a * 27.0d0)
    if (x <= (-2.4d+76)) then
        tmp = x * 2.0d0
    else if (x <= (-1.35d-163)) then
        tmp = t_1
    else if (x <= 8d-224) then
        tmp = y * (z * (t * (-9.0d0)))
    else if (x <= 9.8d-113) then
        tmp = t_1
    else if (x <= 2.75d+42) then
        tmp = (t * (y * z)) * (-9.0d0)
    else
        tmp = x * 2.0d0
    end if
    code = tmp
end function

Java

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 = b * (a * 27.0);
	double tmp;
	if (x <= -2.4e+76) {
		tmp = x * 2.0;
	} else if (x <= -1.35e-163) {
		tmp = t_1;
	} else if (x <= 8e-224) {
		tmp = y * (z * (t * -9.0));
	} else if (x <= 9.8e-113) {
		tmp = t_1;
	} else if (x <= 2.75e+42) {
		tmp = (t * (y * z)) * -9.0;
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = b * (a * 27.0)
	tmp = 0
	if x <= -2.4e+76:
		tmp = x * 2.0
	elif x <= -1.35e-163:
		tmp = t_1
	elif x <= 8e-224:
		tmp = y * (z * (t * -9.0))
	elif x <= 9.8e-113:
		tmp = t_1
	elif x <= 2.75e+42:
		tmp = (t * (y * z)) * -9.0
	else:
		tmp = x * 2.0
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a * 27.0))
	tmp = 0.0
	if (x <= -2.4e+76)
		tmp = Float64(x * 2.0);
	elseif (x <= -1.35e-163)
		tmp = t_1;
	elseif (x <= 8e-224)
		tmp = Float64(y * Float64(z * Float64(t * -9.0)));
	elseif (x <= 9.8e-113)
		tmp = t_1;
	elseif (x <= 2.75e+42)
		tmp = Float64(Float64(t * Float64(y * z)) * -9.0);
	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])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (a * 27.0);
	tmp = 0.0;
	if (x <= -2.4e+76)
		tmp = x * 2.0;
	elseif (x <= -1.35e-163)
		tmp = t_1;
	elseif (x <= 8e-224)
		tmp = y * (z * (t * -9.0));
	elseif (x <= 9.8e-113)
		tmp = t_1;
	elseif (x <= 2.75e+42)
		tmp = (t * (y * z)) * -9.0;
	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.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.4e+76], N[(x * 2.0), $MachinePrecision], If[LessEqual[x, -1.35e-163], t$95$1, If[LessEqual[x, 8e-224], N[(y * N[(z * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9.8e-113], t$95$1, If[LessEqual[x, 2.75e+42], N[(N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision] * -9.0), $MachinePrecision], N[(x * 2.0), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.4e76 or 2.75000000000000001e42 < x

   1. Initial program 98.1%

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

      1. sub-neg 98.1%

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

      2. sub-neg 98.1%

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

      3. associate-*l* 94.5%

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

      4. associate-*l* 94.5%

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

   3. Simplified 94.5%

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

   5. Taylor expanded in x around inf 58.0%

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

   if -2.4e76 < x < -1.35000000000000007e-163 or 8.0000000000000002e-224 < x < 9.8000000000000006e-113

   1. Initial program 97.2%

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

      1. sub-neg 97.2%

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

      2. sub-neg 97.2%

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

      3. associate-*l* 96.1%

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

      4. 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 y around 0 97.1%

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

      1. *-commutative 97.1%

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

      2. associate-*l* 97.2%

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

      3. *-commutative 97.2%

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

      4. associate-*r* 97.2%

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

      5. *-commutative 97.2%

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

      6. associate-*r* 96.1%

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

      7. *-commutative 96.1%

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

   7. Simplified 96.1%

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

   8. Taylor expanded in t around 0 96.1%

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

   9. Taylor expanded in a around inf 52.9%

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

       1. *-commutative 52.9%

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

       2. *-commutative 52.9%

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

       3. associate-*l* 52.9%

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

       4. *-commutative 52.9%

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

   11. Simplified 52.9%

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

   if -1.35000000000000007e-163 < x < 8.0000000000000002e-224

   1. Initial program 94.8%

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

      1. sub-neg 94.8%

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

      2. sub-neg 94.8%

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

      3. associate-*l* 94.9%

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

      4. associate-*l* 94.9%

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

   3. Simplified 94.9%

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

   5. Taylor expanded in x around 0 94.8%

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

   6. Taylor expanded in a around 0 64.4%

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

      1. associate-*r* 64.4%

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

      2. *-commutative 64.4%

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

      3. associate-*l* 64.5%

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

      4. *-commutative 64.5%

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

   8. Simplified 64.5%

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

   if 9.8000000000000006e-113 < x < 2.75000000000000001e42

   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. sub-neg 99.7%

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

      2. sub-neg 99.7%

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

      3. associate-*l* 91.7%

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

      4. associate-*l* 91.7%

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

   3. Simplified 91.7%

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

   5. Taylor expanded in y around inf 66.1%

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

4. Final simplification 58.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{+76}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \leq -1.35 \cdot 10^{-163}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-224}:\\ \;\;\;\;y \cdot \left(z \cdot \left(t \cdot -9\right)\right)\\ \mathbf{elif}\;x \leq 9.8 \cdot 10^{-113}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \mathbf{elif}\;x \leq 2.75 \cdot 10^{+42}:\\ \;\;\;\;\left(t \cdot \left(y \cdot z\right)\right) \cdot -9\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 47.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot 27\right)\\ \mathbf{if}\;x \leq -5.2 \cdot 10^{+78}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \leq -1.36 \cdot 10^{-163}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 3.95 \cdot 10^{-224}:\\ \;\;\;\;y \cdot \left(z \cdot \left(t \cdot -9\right)\right)\\ \mathbf{elif}\;x \leq 9.4 \cdot 10^{-113}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{+45}:\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(t \cdot -9\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (* a 27.0))))
   (if (<= x -5.2e+78)
     (* x 2.0)
     (if (<= x -1.36e-163)
       t_1
       (if (<= x 3.95e-224)
         (* y (* z (* t -9.0)))
         (if (<= x 9.4e-113)
           t_1
           (if (<= x 1.35e+45) (* (* y z) (* t -9.0)) (* x 2.0))))))))

C

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 = b * (a * 27.0);
	double tmp;
	if (x <= -5.2e+78) {
		tmp = x * 2.0;
	} else if (x <= -1.36e-163) {
		tmp = t_1;
	} else if (x <= 3.95e-224) {
		tmp = y * (z * (t * -9.0));
	} else if (x <= 9.4e-113) {
		tmp = t_1;
	} else if (x <= 1.35e+45) {
		tmp = (y * z) * (t * -9.0);
	} 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.
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) :: tmp
    t_1 = b * (a * 27.0d0)
    if (x <= (-5.2d+78)) then
        tmp = x * 2.0d0
    else if (x <= (-1.36d-163)) then
        tmp = t_1
    else if (x <= 3.95d-224) then
        tmp = y * (z * (t * (-9.0d0)))
    else if (x <= 9.4d-113) then
        tmp = t_1
    else if (x <= 1.35d+45) then
        tmp = (y * z) * (t * (-9.0d0))
    else
        tmp = x * 2.0d0
    end if
    code = tmp
end function

Java

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 = b * (a * 27.0);
	double tmp;
	if (x <= -5.2e+78) {
		tmp = x * 2.0;
	} else if (x <= -1.36e-163) {
		tmp = t_1;
	} else if (x <= 3.95e-224) {
		tmp = y * (z * (t * -9.0));
	} else if (x <= 9.4e-113) {
		tmp = t_1;
	} else if (x <= 1.35e+45) {
		tmp = (y * z) * (t * -9.0);
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = b * (a * 27.0)
	tmp = 0
	if x <= -5.2e+78:
		tmp = x * 2.0
	elif x <= -1.36e-163:
		tmp = t_1
	elif x <= 3.95e-224:
		tmp = y * (z * (t * -9.0))
	elif x <= 9.4e-113:
		tmp = t_1
	elif x <= 1.35e+45:
		tmp = (y * z) * (t * -9.0)
	else:
		tmp = x * 2.0
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a * 27.0))
	tmp = 0.0
	if (x <= -5.2e+78)
		tmp = Float64(x * 2.0);
	elseif (x <= -1.36e-163)
		tmp = t_1;
	elseif (x <= 3.95e-224)
		tmp = Float64(y * Float64(z * Float64(t * -9.0)));
	elseif (x <= 9.4e-113)
		tmp = t_1;
	elseif (x <= 1.35e+45)
		tmp = Float64(Float64(y * z) * Float64(t * -9.0));
	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])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (a * 27.0);
	tmp = 0.0;
	if (x <= -5.2e+78)
		tmp = x * 2.0;
	elseif (x <= -1.36e-163)
		tmp = t_1;
	elseif (x <= 3.95e-224)
		tmp = y * (z * (t * -9.0));
	elseif (x <= 9.4e-113)
		tmp = t_1;
	elseif (x <= 1.35e+45)
		tmp = (y * z) * (t * -9.0);
	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.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5.2e+78], N[(x * 2.0), $MachinePrecision], If[LessEqual[x, -1.36e-163], t$95$1, If[LessEqual[x, 3.95e-224], N[(y * N[(z * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9.4e-113], t$95$1, If[LessEqual[x, 1.35e+45], N[(N[(y * z), $MachinePrecision] * N[(t * -9.0), $MachinePrecision]), $MachinePrecision], N[(x * 2.0), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -5.2e78 or 1.34999999999999992e45 < x

   1. Initial program 98.1%

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

      1. sub-neg 98.1%

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

      2. sub-neg 98.1%

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

      3. associate-*l* 94.5%

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

      4. associate-*l* 94.5%

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

   3. Simplified 94.5%

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

   5. Taylor expanded in x around inf 58.0%

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

   if -5.2e78 < x < -1.36e-163 or 3.9499999999999999e-224 < x < 9.4000000000000004e-113

   1. Initial program 97.2%

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

      1. sub-neg 97.2%

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

      2. sub-neg 97.2%

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

      3. associate-*l* 96.1%

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

      4. 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 y around 0 97.1%

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

      1. *-commutative 97.1%

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

      2. associate-*l* 97.2%

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

      3. *-commutative 97.2%

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

      4. associate-*r* 97.2%

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

      5. *-commutative 97.2%

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

      6. associate-*r* 96.1%

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

      7. *-commutative 96.1%

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

   7. Simplified 96.1%

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

   8. Taylor expanded in t around 0 96.1%

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

   9. Taylor expanded in a around inf 52.9%

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

       1. *-commutative 52.9%

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

       2. *-commutative 52.9%

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

       3. associate-*l* 52.9%

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

       4. *-commutative 52.9%

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

   11. Simplified 52.9%

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

   if -1.36e-163 < x < 3.9499999999999999e-224

   1. Initial program 94.8%

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

      1. sub-neg 94.8%

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

      2. sub-neg 94.8%

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

      3. associate-*l* 94.9%

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

      4. associate-*l* 94.9%

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

   3. Simplified 94.9%

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

   5. Taylor expanded in x around 0 94.8%

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

   6. Taylor expanded in a around 0 64.4%

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

      1. associate-*r* 64.4%

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

      2. *-commutative 64.4%

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

      3. associate-*l* 64.5%

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

      4. *-commutative 64.5%

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

   8. Simplified 64.5%

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

   if 9.4000000000000004e-113 < x < 1.34999999999999992e45

   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. sub-neg 99.7%

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

      2. sub-neg 99.7%

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

      3. associate-*l* 91.7%

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

      4. associate-*l* 91.7%

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

   3. Simplified 91.7%

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

   5. Taylor expanded in x around 0 85.5%

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

   6. Taylor expanded in a around 0 66.1%

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

      1. associate-*r* 66.1%

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

   8. Simplified 66.1%

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

4. Final simplification 58.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{+78}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \leq -1.36 \cdot 10^{-163}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \mathbf{elif}\;x \leq 3.95 \cdot 10^{-224}:\\ \;\;\;\;y \cdot \left(z \cdot \left(t \cdot -9\right)\right)\\ \mathbf{elif}\;x \leq 9.4 \cdot 10^{-113}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{+45}:\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(t \cdot -9\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 78.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -2.7 \cdot 10^{-98} \lor \neg \left(b \leq 2.7 \cdot 10^{+60}\right):\\ \;\;\;\;27 \cdot \left(a \cdot b\right) - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - y \cdot \left(t \cdot \left(9 \cdot z\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -2.7e-98) (not (<= b 2.7e+60)))
   (- (* 27.0 (* a b)) (* 9.0 (* t (* y z))))
   (- (* x 2.0) (* y (* t (* 9.0 z))))))

C

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 <= -2.7e-98) || !(b <= 2.7e+60)) {
		tmp = (27.0 * (a * b)) - (9.0 * (t * (y * z)));
	} else {
		tmp = (x * 2.0) - (y * (t * (9.0 * z)));
	}
	return tmp;
}

Fortran

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 <= (-2.7d-98)) .or. (.not. (b <= 2.7d+60))) then
        tmp = (27.0d0 * (a * b)) - (9.0d0 * (t * (y * z)))
    else
        tmp = (x * 2.0d0) - (y * (t * (9.0d0 * z)))
    end if
    code = tmp
end function

Java

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 <= -2.7e-98) || !(b <= 2.7e+60)) {
		tmp = (27.0 * (a * b)) - (9.0 * (t * (y * z)));
	} else {
		tmp = (x * 2.0) - (y * (t * (9.0 * z)));
	}
	return tmp;
}

Python

[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 <= -2.7e-98) or not (b <= 2.7e+60):
		tmp = (27.0 * (a * b)) - (9.0 * (t * (y * z)))
	else:
		tmp = (x * 2.0) - (y * (t * (9.0 * z)))
	return tmp

Julia

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 <= -2.7e-98) || !(b <= 2.7e+60))
		tmp = Float64(Float64(27.0 * Float64(a * b)) - Float64(9.0 * Float64(t * Float64(y * z))));
	else
		tmp = Float64(Float64(x * 2.0) - Float64(y * Float64(t * Float64(9.0 * z))));
	end
	return tmp
end

MATLAB

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 <= -2.7e-98) || ~((b <= 2.7e+60)))
		tmp = (27.0 * (a * b)) - (9.0 * (t * (y * z)));
	else
		tmp = (x * 2.0) - (y * (t * (9.0 * 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.
code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -2.7e-98], N[Not[LessEqual[b, 2.7e+60]], $MachinePrecision]], N[(N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision] - N[(9.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] - N[(y * N[(t * N[(9.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.6999999999999999e-98 or 2.6999999999999999e60 < b

   1. Initial program 96.8%

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

      1. sub-neg 96.8%

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

      2. sub-neg 96.8%

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

      3. associate-*l* 92.4%

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

      4. associate-*l* 92.4%

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

   3. Simplified 92.4%

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

   5. Taylor expanded in x around 0 76.8%

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

   if -2.6999999999999999e-98 < b < 2.6999999999999999e60

   1. Initial program 98.3%

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

      1. sub-neg 98.3%

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

      2. sub-neg 98.3%

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

      3. associate-*l* 96.8%

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

      4. associate-*l* 96.9%

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

   3. Simplified 96.9%

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

      1. +-commutative 96.9%

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

      2. associate-+r- 96.9%

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

      3. *-commutative 96.9%

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

      4. associate-*l* 96.8%

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

      5. associate-*l* 96.8%

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

      6. associate-*r* 96.9%

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

   6. Applied egg-rr 96.9%

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

   7. Taylor expanded in b around 0 82.9%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.7 \cdot 10^{-98} \lor \neg \left(b \leq 2.7 \cdot 10^{+60}\right):\\ \;\;\;\;27 \cdot \left(a \cdot b\right) - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - y \cdot \left(t \cdot \left(9 \cdot z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 97.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+83}:\\ \;\;\;\;x \cdot 2 - y \cdot \left(t \cdot \left(9 \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right) + \left(x \cdot 2 - \left(9 \cdot t\right) \cdot \left(y \cdot z\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.75e+83)
   (- (* x 2.0) (* y (* t (* 9.0 z))))
   (+ (* a (* 27.0 b)) (- (* x 2.0) (* (* 9.0 t) (* y z))))))

C

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 <= -1.75e+83) {
		tmp = (x * 2.0) - (y * (t * (9.0 * z)));
	} else {
		tmp = (a * (27.0 * b)) + ((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.
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 <= (-1.75d+83)) then
        tmp = (x * 2.0d0) - (y * (t * (9.0d0 * z)))
    else
        tmp = (a * (27.0d0 * b)) + ((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;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.75e+83) {
		tmp = (x * 2.0) - (y * (t * (9.0 * z)));
	} else {
		tmp = (a * (27.0 * b)) + ((x * 2.0) - ((9.0 * t) * (y * z)));
	}
	return tmp;
}

Python

[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 <= -1.75e+83:
		tmp = (x * 2.0) - (y * (t * (9.0 * z)))
	else:
		tmp = (a * (27.0 * b)) + ((x * 2.0) - ((9.0 * t) * (y * z)))
	return tmp

Julia

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 <= -1.75e+83)
		tmp = Float64(Float64(x * 2.0) - Float64(y * Float64(t * Float64(9.0 * z))));
	else
		tmp = Float64(Float64(a * Float64(27.0 * b)) + Float64(Float64(x * 2.0) - Float64(Float64(9.0 * t) * Float64(y * z))));
	end
	return tmp
end

MATLAB

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 <= -1.75e+83)
		tmp = (x * 2.0) - (y * (t * (9.0 * z)));
	else
		tmp = (a * (27.0 * b)) + ((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.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.75e+83], N[(N[(x * 2.0), $MachinePrecision] - N[(y * N[(t * N[(9.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision] + N[(N[(x * 2.0), $MachinePrecision] - N[(N[(9.0 * t), $MachinePrecision] * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.74999999999999989e83

   1. Initial program 92.1%

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

      1. sub-neg 92.1%

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

      2. sub-neg 92.1%

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

      3. associate-*l* 82.9%

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

      4. associate-*l* 83.0%

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

   3. Simplified 83.0%

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

      1. +-commutative 83.0%

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

      2. associate-+r- 83.0%

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

      3. *-commutative 83.0%

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

      4. associate-*l* 82.9%

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

      5. associate-*l* 82.8%

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

      6. associate-*r* 82.9%

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

   6. Applied egg-rr 82.9%

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

   7. Taylor expanded in b around 0 56.1%

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

   if -1.74999999999999989e83 < z

   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. sub-neg 98.9%

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

      2. sub-neg 98.9%

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

      3. associate-*l* 97.5%

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

      4. associate-*l* 97.5%

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

   3. Simplified 97.5%

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

   5. Taylor expanded in y around 0 98.9%

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

      1. associate-*r* 98.9%

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

   7. Simplified 98.9%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+83}:\\ \;\;\;\;x \cdot 2 - y \cdot \left(t \cdot \left(9 \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right) + \left(x \cdot 2 - \left(9 \cdot t\right) \cdot \left(y \cdot z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 98.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := a \cdot \left(27 \cdot b\right)\\ \mathbf{if}\;t \leq 2 \cdot 10^{-135}:\\ \;\;\;\;t_1 + \left(x \cdot 2 - z \cdot \left(9 \cdot \left(y \cdot t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1 + \left(x \cdot 2 - \left(9 \cdot t\right) \cdot \left(y \cdot z\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (* 27.0 b))))
   (if (<= t 2e-135)
     (+ t_1 (- (* x 2.0) (* z (* 9.0 (* y t)))))
     (+ t_1 (- (* x 2.0) (* (* 9.0 t) (* y z)))))))

C

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 = a * (27.0 * b);
	double tmp;
	if (t <= 2e-135) {
		tmp = t_1 + ((x * 2.0) - (z * (9.0 * (y * t))));
	} else {
		tmp = t_1 + ((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.
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) :: tmp
    t_1 = a * (27.0d0 * b)
    if (t <= 2d-135) then
        tmp = t_1 + ((x * 2.0d0) - (z * (9.0d0 * (y * t))))
    else
        tmp = t_1 + ((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;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (27.0 * b);
	double tmp;
	if (t <= 2e-135) {
		tmp = t_1 + ((x * 2.0) - (z * (9.0 * (y * t))));
	} else {
		tmp = t_1 + ((x * 2.0) - ((9.0 * t) * (y * z)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = a * (27.0 * b)
	tmp = 0
	if t <= 2e-135:
		tmp = t_1 + ((x * 2.0) - (z * (9.0 * (y * t))))
	else:
		tmp = t_1 + ((x * 2.0) - ((9.0 * t) * (y * z)))
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(27.0 * b))
	tmp = 0.0
	if (t <= 2e-135)
		tmp = Float64(t_1 + Float64(Float64(x * 2.0) - Float64(z * Float64(9.0 * Float64(y * t)))));
	else
		tmp = Float64(t_1 + Float64(Float64(x * 2.0) - Float64(Float64(9.0 * t) * Float64(y * z))));
	end
	return tmp
end

MATLAB

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 = a * (27.0 * b);
	tmp = 0.0;
	if (t <= 2e-135)
		tmp = t_1 + ((x * 2.0) - (z * (9.0 * (y * t))));
	else
		tmp = t_1 + ((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.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, 2e-135], N[(t$95$1 + N[(N[(x * 2.0), $MachinePrecision] - N[(z * N[(9.0 * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(N[(x * 2.0), $MachinePrecision] - N[(N[(9.0 * t), $MachinePrecision] * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < 2.0000000000000001e-135

   1. Initial program 96.9%

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

      1. sub-neg 96.9%

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

      2. sub-neg 96.9%

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

      3. associate-*l* 95.3%

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

      4. associate-*l* 95.3%

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

   3. Simplified 95.3%

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

   5. Taylor expanded in y around 0 96.9%

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

      1. *-commutative 96.9%

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

      2. associate-*l* 96.9%

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

      3. *-commutative 96.9%

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

      4. associate-*r* 96.9%

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

      5. *-commutative 96.9%

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

      6. associate-*r* 95.9%

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

      7. *-commutative 95.9%

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

   7. Simplified 95.9%

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

   8. Taylor expanded in t around 0 95.9%

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

   if 2.0000000000000001e-135 < t

   1. Initial program 98.8%

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

      1. sub-neg 98.8%

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

      2. sub-neg 98.8%

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

      3. associate-*l* 93.5%

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

      4. associate-*l* 93.5%

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

   3. Simplified 93.5%

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

   5. Taylor expanded in y around 0 98.7%

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

      1. associate-*r* 98.7%

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

   7. Simplified 98.7%

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

4. Final simplification 96.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 2 \cdot 10^{-135}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right) + \left(x \cdot 2 - z \cdot \left(9 \cdot \left(y \cdot t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right) + \left(x \cdot 2 - \left(9 \cdot t\right) \cdot \left(y \cdot z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 73.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -5.2 \cdot 10^{+193} \lor \neg \left(a \leq 3.5 \cdot 10^{-129}\right):\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - y \cdot \left(z \cdot \left(9 \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -5.2e+193) (not (<= a 3.5e-129)))
   (+ (* x 2.0) (* 27.0 (* a b)))
   (- (* x 2.0) (* y (* z (* 9.0 t))))))

C

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 ((a <= -5.2e+193) || !(a <= 3.5e-129)) {
		tmp = (x * 2.0) + (27.0 * (a * b));
	} else {
		tmp = (x * 2.0) - (y * (z * (9.0 * t)));
	}
	return tmp;
}

Fortran

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 ((a <= (-5.2d+193)) .or. (.not. (a <= 3.5d-129))) then
        tmp = (x * 2.0d0) + (27.0d0 * (a * b))
    else
        tmp = (x * 2.0d0) - (y * (z * (9.0d0 * t)))
    end if
    code = tmp
end function

Java

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 ((a <= -5.2e+193) || !(a <= 3.5e-129)) {
		tmp = (x * 2.0) + (27.0 * (a * b));
	} else {
		tmp = (x * 2.0) - (y * (z * (9.0 * t)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -5.2e+193) or not (a <= 3.5e-129):
		tmp = (x * 2.0) + (27.0 * (a * b))
	else:
		tmp = (x * 2.0) - (y * (z * (9.0 * t)))
	return tmp

Julia

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 ((a <= -5.2e+193) || !(a <= 3.5e-129))
		tmp = Float64(Float64(x * 2.0) + Float64(27.0 * Float64(a * b)));
	else
		tmp = Float64(Float64(x * 2.0) - Float64(y * Float64(z * Float64(9.0 * t))));
	end
	return tmp
end

MATLAB

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 ((a <= -5.2e+193) || ~((a <= 3.5e-129)))
		tmp = (x * 2.0) + (27.0 * (a * b));
	else
		tmp = (x * 2.0) - (y * (z * (9.0 * t)));
	end
	tmp_2 = tmp;
end

Wolfram

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[a, -5.2e+193], N[Not[LessEqual[a, 3.5e-129]], $MachinePrecision]], N[(N[(x * 2.0), $MachinePrecision] + N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] - N[(y * N[(z * N[(9.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -5.20000000000000026e193 or 3.4999999999999997e-129 < a

   1. Initial program 97.2%

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

      1. sub-neg 97.2%

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

      2. sub-neg 97.2%

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

      3. associate-*l* 96.5%

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

      4. associate-*l* 96.5%

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

   3. Simplified 96.5%

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

   5. Taylor expanded in y around 0 73.6%

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

   if -5.20000000000000026e193 < a < 3.4999999999999997e-129

   1. Initial program 97.8%

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

      1. sub-neg 97.8%

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

      2. sub-neg 97.8%

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

      3. associate-*l* 93.3%

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

      4. associate-*l* 93.3%

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

   3. Simplified 93.3%

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

      1. +-commutative 93.3%

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

      2. associate-+r- 93.3%

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

      3. *-commutative 93.3%

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

      4. associate-*l* 93.3%

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

      5. associate-*l* 93.2%

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

      6. associate-*r* 93.3%

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

   6. Applied egg-rr 93.3%

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

   7. Taylor expanded in b around 0 80.9%

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

   8. Taylor expanded in y around 0 84.6%

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

      1. associate-*r* 84.7%

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

      2. *-commutative 84.7%

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

      3. associate-*l* 80.8%

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

   10. Simplified 80.8%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.2 \cdot 10^{+193} \lor \neg \left(a \leq 3.5 \cdot 10^{-129}\right):\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - y \cdot \left(z \cdot \left(9 \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 73.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -4.4 \cdot 10^{+193} \lor \neg \left(a \leq 3.5 \cdot 10^{-129}\right):\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - y \cdot \left(t \cdot \left(9 \cdot z\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -4.4e+193) (not (<= a 3.5e-129)))
   (+ (* x 2.0) (* 27.0 (* a b)))
   (- (* x 2.0) (* y (* t (* 9.0 z))))))

C

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 ((a <= -4.4e+193) || !(a <= 3.5e-129)) {
		tmp = (x * 2.0) + (27.0 * (a * b));
	} else {
		tmp = (x * 2.0) - (y * (t * (9.0 * z)));
	}
	return tmp;
}

Fortran

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 ((a <= (-4.4d+193)) .or. (.not. (a <= 3.5d-129))) then
        tmp = (x * 2.0d0) + (27.0d0 * (a * b))
    else
        tmp = (x * 2.0d0) - (y * (t * (9.0d0 * z)))
    end if
    code = tmp
end function

Java

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 ((a <= -4.4e+193) || !(a <= 3.5e-129)) {
		tmp = (x * 2.0) + (27.0 * (a * b));
	} else {
		tmp = (x * 2.0) - (y * (t * (9.0 * z)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -4.4e+193) or not (a <= 3.5e-129):
		tmp = (x * 2.0) + (27.0 * (a * b))
	else:
		tmp = (x * 2.0) - (y * (t * (9.0 * z)))
	return tmp

Julia

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 ((a <= -4.4e+193) || !(a <= 3.5e-129))
		tmp = Float64(Float64(x * 2.0) + Float64(27.0 * Float64(a * b)));
	else
		tmp = Float64(Float64(x * 2.0) - Float64(y * Float64(t * Float64(9.0 * z))));
	end
	return tmp
end

MATLAB

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 ((a <= -4.4e+193) || ~((a <= 3.5e-129)))
		tmp = (x * 2.0) + (27.0 * (a * b));
	else
		tmp = (x * 2.0) - (y * (t * (9.0 * 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.
code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -4.4e+193], N[Not[LessEqual[a, 3.5e-129]], $MachinePrecision]], N[(N[(x * 2.0), $MachinePrecision] + N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] - N[(y * N[(t * N[(9.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -4.39999999999999972e193 or 3.4999999999999997e-129 < a

   1. Initial program 97.2%

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

      1. sub-neg 97.2%

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

      2. sub-neg 97.2%

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

      3. associate-*l* 96.5%

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

      4. associate-*l* 96.5%

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

   3. Simplified 96.5%

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

   5. Taylor expanded in y around 0 73.6%

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

   if -4.39999999999999972e193 < a < 3.4999999999999997e-129

   1. Initial program 97.8%

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

      1. sub-neg 97.8%

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

      2. sub-neg 97.8%

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

      3. associate-*l* 93.3%

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

      4. associate-*l* 93.3%

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

   3. Simplified 93.3%

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

      1. +-commutative 93.3%

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

      2. associate-+r- 93.3%

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

      3. *-commutative 93.3%

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

      4. associate-*l* 93.3%

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

      5. associate-*l* 93.2%

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

      6. associate-*r* 93.3%

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

   6. Applied egg-rr 93.3%

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

   7. Taylor expanded in b around 0 80.9%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.4 \cdot 10^{+193} \lor \neg \left(a \leq 3.5 \cdot 10^{-129}\right):\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - y \cdot \left(t \cdot \left(9 \cdot z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 76.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -16000000000000:\\ \;\;\;\;y \cdot \left(z \cdot \left(t \cdot -9\right)\right)\\ \mathbf{elif}\;z \leq 0.52:\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot \left(y \cdot z\right)\right) \cdot -9\\ \end{array} \end{array} \]

FPCore

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 -16000000000000.0)
   (* y (* z (* t -9.0)))
   (if (<= z 0.52) (+ (* x 2.0) (* 27.0 (* a b))) (* (* t (* y z)) -9.0))))

C

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 <= -16000000000000.0) {
		tmp = y * (z * (t * -9.0));
	} else if (z <= 0.52) {
		tmp = (x * 2.0) + (27.0 * (a * b));
	} else {
		tmp = (t * (y * z)) * -9.0;
	}
	return tmp;
}

Fortran

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 <= (-16000000000000.0d0)) then
        tmp = y * (z * (t * (-9.0d0)))
    else if (z <= 0.52d0) then
        tmp = (x * 2.0d0) + (27.0d0 * (a * b))
    else
        tmp = (t * (y * z)) * (-9.0d0)
    end if
    code = tmp
end function

Java

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 <= -16000000000000.0) {
		tmp = y * (z * (t * -9.0));
	} else if (z <= 0.52) {
		tmp = (x * 2.0) + (27.0 * (a * b));
	} else {
		tmp = (t * (y * z)) * -9.0;
	}
	return tmp;
}

Python

[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 <= -16000000000000.0:
		tmp = y * (z * (t * -9.0))
	elif z <= 0.52:
		tmp = (x * 2.0) + (27.0 * (a * b))
	else:
		tmp = (t * (y * z)) * -9.0
	return tmp

Julia

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 <= -16000000000000.0)
		tmp = Float64(y * Float64(z * Float64(t * -9.0)));
	elseif (z <= 0.52)
		tmp = Float64(Float64(x * 2.0) + Float64(27.0 * Float64(a * b)));
	else
		tmp = Float64(Float64(t * Float64(y * z)) * -9.0);
	end
	return tmp
end

MATLAB

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 <= -16000000000000.0)
		tmp = y * (z * (t * -9.0));
	elseif (z <= 0.52)
		tmp = (x * 2.0) + (27.0 * (a * b));
	else
		tmp = (t * (y * z)) * -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.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -16000000000000.0], N[(y * N[(z * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.52], N[(N[(x * 2.0), $MachinePrecision] + N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision] * -9.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.6e13

   1. Initial program 93.8%

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

      1. sub-neg 93.8%

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

      2. sub-neg 93.8%

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

      3. associate-*l* 85.1%

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

      4. associate-*l* 85.2%

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

   3. Simplified 85.2%

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

   5. Taylor expanded in x around 0 78.2%

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

   6. Taylor expanded in a around 0 58.0%

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

      1. associate-*r* 58.0%

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

      2. *-commutative 58.0%

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

      3. associate-*l* 45.7%

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

      4. *-commutative 45.7%

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

   8. Simplified 45.7%

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

   if -1.6e13 < z < 0.52000000000000002

   1. Initial program 99.8%

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

      1. sub-neg 99.8%

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

      2. sub-neg 99.8%

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

      3. associate-*l* 99.2%

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

      4. associate-*l* 99.1%

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

   3. Simplified 99.1%

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

   5. Taylor expanded in y around 0 76.2%

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

   if 0.52000000000000002 < z

   1. Initial program 96.2%

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

      1. sub-neg 96.2%

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

      2. sub-neg 96.2%

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

      3. associate-*l* 94.4%

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

      4. associate-*l* 94.4%

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

   3. Simplified 94.4%

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

   5. Taylor expanded in y around inf 63.0%

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

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -16000000000000:\\ \;\;\;\;y \cdot \left(z \cdot \left(t \cdot -9\right)\right)\\ \mathbf{elif}\;z \leq 0.52:\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot \left(y \cdot z\right)\right) \cdot -9\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 48.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{+78} \lor \neg \left(x \leq 4.1 \cdot 10^{+96}\right):\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

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 (<= x -2.8e+78) (not (<= x 4.1e+96))) (* x 2.0) (* 27.0 (* a b))))

C

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 ((x <= -2.8e+78) || !(x <= 4.1e+96)) {
		tmp = x * 2.0;
	} else {
		tmp = 27.0 * (a * b);
	}
	return tmp;
}

Fortran

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 ((x <= (-2.8d+78)) .or. (.not. (x <= 4.1d+96))) then
        tmp = x * 2.0d0
    else
        tmp = 27.0d0 * (a * b)
    end if
    code = tmp
end function

Java

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 ((x <= -2.8e+78) || !(x <= 4.1e+96)) {
		tmp = x * 2.0;
	} else {
		tmp = 27.0 * (a * b);
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if (x <= -2.8e+78) or not (x <= 4.1e+96):
		tmp = x * 2.0
	else:
		tmp = 27.0 * (a * b)
	return tmp

Julia

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 ((x <= -2.8e+78) || !(x <= 4.1e+96))
		tmp = Float64(x * 2.0);
	else
		tmp = Float64(27.0 * Float64(a * b));
	end
	return tmp
end

MATLAB

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 ((x <= -2.8e+78) || ~((x <= 4.1e+96)))
		tmp = x * 2.0;
	else
		tmp = 27.0 * (a * b);
	end
	tmp_2 = tmp;
end

Wolfram

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[x, -2.8e+78], N[Not[LessEqual[x, 4.1e+96]], $MachinePrecision]], N[(x * 2.0), $MachinePrecision], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.8000000000000001e78 or 4.09999999999999998e96 < x

   1. Initial program 97.9%

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

      1. sub-neg 97.9%

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

      2. sub-neg 97.9%

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

      3. associate-*l* 93.9%

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

      4. associate-*l* 93.9%

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

   3. Simplified 93.9%

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

   5. Taylor expanded in x around inf 60.3%

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

   if -2.8000000000000001e78 < x < 4.09999999999999998e96

   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. sub-neg 97.4%

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

      2. sub-neg 97.4%

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

      3. associate-*l* 95.1%

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

      4. 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 0 97.4%

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

      1. *-commutative 97.4%

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

      2. associate-*l* 97.4%

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

      3. *-commutative 97.4%

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

      4. associate-*r* 97.4%

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

      5. *-commutative 97.4%

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

      6. associate-*r* 95.1%

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

      7. *-commutative 95.1%

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

   7. Simplified 95.1%

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

   8. Taylor expanded in t around 0 95.1%

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

   9. Taylor expanded in a around inf 42.1%

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

4. Final simplification 48.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{+78} \lor \neg \left(x \leq 4.1 \cdot 10^{+96}\right):\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 48.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{+77} \lor \neg \left(x \leq 6.2 \cdot 10^{+101}\right):\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \end{array} \end{array} \]

FPCore

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 (<= x -2.1e+77) (not (<= x 6.2e+101))) (* x 2.0) (* a (* 27.0 b))))

C

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 ((x <= -2.1e+77) || !(x <= 6.2e+101)) {
		tmp = x * 2.0;
	} else {
		tmp = a * (27.0 * b);
	}
	return tmp;
}

Fortran

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 ((x <= (-2.1d+77)) .or. (.not. (x <= 6.2d+101))) then
        tmp = x * 2.0d0
    else
        tmp = a * (27.0d0 * b)
    end if
    code = tmp
end function

Java

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 ((x <= -2.1e+77) || !(x <= 6.2e+101)) {
		tmp = x * 2.0;
	} else {
		tmp = a * (27.0 * b);
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if (x <= -2.1e+77) or not (x <= 6.2e+101):
		tmp = x * 2.0
	else:
		tmp = a * (27.0 * b)
	return tmp

Julia

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 ((x <= -2.1e+77) || !(x <= 6.2e+101))
		tmp = Float64(x * 2.0);
	else
		tmp = Float64(a * Float64(27.0 * b));
	end
	return tmp
end

MATLAB

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 ((x <= -2.1e+77) || ~((x <= 6.2e+101)))
		tmp = x * 2.0;
	else
		tmp = a * (27.0 * b);
	end
	tmp_2 = tmp;
end

Wolfram

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[x, -2.1e+77], N[Not[LessEqual[x, 6.2e+101]], $MachinePrecision]], N[(x * 2.0), $MachinePrecision], N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.0999999999999999e77 or 6.19999999999999998e101 < x

   1. Initial program 97.9%

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

      1. sub-neg 97.9%

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

      2. sub-neg 97.9%

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

      3. associate-*l* 93.9%

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

      4. associate-*l* 93.9%

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

   3. Simplified 93.9%

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

   5. Taylor expanded in x around inf 60.3%

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

   if -2.0999999999999999e77 < x < 6.19999999999999998e101

   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. sub-neg 97.4%

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

      2. sub-neg 97.4%

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

      3. associate-*l* 95.1%

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

      4. 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 0 97.4%

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

      1. *-commutative 97.4%

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

      2. associate-*l* 97.4%

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

      3. *-commutative 97.4%

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

      4. associate-*r* 97.4%

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

      5. *-commutative 97.4%

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

      6. associate-*r* 95.1%

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

      7. *-commutative 95.1%

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

   7. Simplified 95.1%

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

   8. Taylor expanded in t around 0 95.1%

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

   9. Taylor expanded in a around inf 42.1%

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

       1. associate-*r* 42.1%

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

       2. *-commutative 42.1%

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

       3. associate-*r* 42.1%

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

   11. Simplified 42.1%

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

4. Final simplification 48.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{+77} \lor \neg \left(x \leq 6.2 \cdot 10^{+101}\right):\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 48.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{+76} \lor \neg \left(x \leq 4.7 \cdot 10^{+95}\right):\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \end{array} \end{array} \]

FPCore

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 (<= x -4.5e+76) (not (<= x 4.7e+95))) (* x 2.0) (* b (* a 27.0))))

C

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 ((x <= -4.5e+76) || !(x <= 4.7e+95)) {
		tmp = x * 2.0;
	} else {
		tmp = b * (a * 27.0);
	}
	return tmp;
}

Fortran

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 ((x <= (-4.5d+76)) .or. (.not. (x <= 4.7d+95))) then
        tmp = x * 2.0d0
    else
        tmp = b * (a * 27.0d0)
    end if
    code = tmp
end function

Java

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 ((x <= -4.5e+76) || !(x <= 4.7e+95)) {
		tmp = x * 2.0;
	} else {
		tmp = b * (a * 27.0);
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if (x <= -4.5e+76) or not (x <= 4.7e+95):
		tmp = x * 2.0
	else:
		tmp = b * (a * 27.0)
	return tmp

Julia

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 ((x <= -4.5e+76) || !(x <= 4.7e+95))
		tmp = Float64(x * 2.0);
	else
		tmp = Float64(b * Float64(a * 27.0));
	end
	return tmp
end

MATLAB

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 ((x <= -4.5e+76) || ~((x <= 4.7e+95)))
		tmp = x * 2.0;
	else
		tmp = b * (a * 27.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[x, -4.5e+76], N[Not[LessEqual[x, 4.7e+95]], $MachinePrecision]], N[(x * 2.0), $MachinePrecision], N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.4999999999999997e76 or 4.69999999999999972e95 < x

   1. Initial program 97.9%

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

      1. sub-neg 97.9%

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

      2. sub-neg 97.9%

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

      3. associate-*l* 93.9%

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

      4. associate-*l* 93.9%

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

   3. Simplified 93.9%

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

   5. Taylor expanded in x around inf 60.3%

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

   if -4.4999999999999997e76 < x < 4.69999999999999972e95

   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. sub-neg 97.4%

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

      2. sub-neg 97.4%

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

      3. associate-*l* 95.1%

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

      4. 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 0 97.4%

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

      1. *-commutative 97.4%

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

      2. associate-*l* 97.4%

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

      3. *-commutative 97.4%

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

      4. associate-*r* 97.4%

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

      5. *-commutative 97.4%

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

      6. associate-*r* 95.1%

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

      7. *-commutative 95.1%

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

   7. Simplified 95.1%

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

   8. Taylor expanded in t around 0 95.1%

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

   9. Taylor expanded in a around inf 42.1%

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

       1. *-commutative 42.1%

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

       2. *-commutative 42.1%

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

       3. associate-*l* 42.1%

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

       4. *-commutative 42.1%

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

   11. Simplified 42.1%

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

4. Final simplification 48.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{+76} \lor \neg \left(x \leq 4.7 \cdot 10^{+95}\right):\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 30.9% accurate, 5.7× speedup

Math

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

FPCore

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

C

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.
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;
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])
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])
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])){:}
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.
code[x_, y_, z_, t_, a_, b_] := N[(x * 2.0), $MachinePrecision]

Derivation

1. Initial program 97.6%

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

   1. sub-neg 97.6%

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

   2. sub-neg 97.6%

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

   3. associate-*l* 94.7%

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

   4. associate-*l* 94.7%

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

3. Simplified 94.7%

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

5. Taylor expanded in x around inf 29.9%

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

6. Final simplification 29.9%

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

Developer target: 95.2% 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 2024018 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, A"
  :precision binary64

  :herbie-target
  (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)))