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

Percentage Accurate: 95.6% → 98.2%

Time: 13.6s

Alternatives: 20

Speedup: 0.8×

• 27.2% 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: 95.6% 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: 98.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 4.4 \cdot 10^{-7}:\\ \;\;\;\;\left(x \cdot 2 + z \cdot \left(\left(t \cdot -9\right) \cdot y\right)\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\left(2 \cdot \frac{x}{t} + 27 \cdot \frac{a \cdot b}{t}\right) - 9 \cdot \left(z \cdot y\right)\right)\\ \end{array} \end{array} \]

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 (<= t 4.4e-7)
   (+ (+ (* x 2.0) (* z (* (* t -9.0) y))) (* a (* 27.0 b)))
   (* t (- (+ (* 2.0 (/ x t)) (* 27.0 (/ (* a b) t))) (* 9.0 (* z y))))))

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 (t <= 4.4e-7) {
		tmp = ((x * 2.0) + (z * ((t * -9.0) * y))) + (a * (27.0 * b));
	} else {
		tmp = t * (((2.0 * (x / t)) + (27.0 * ((a * b) / t))) - (9.0 * (z * y)));
	}
	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 (t <= 4.4d-7) then
        tmp = ((x * 2.0d0) + (z * ((t * (-9.0d0)) * y))) + (a * (27.0d0 * b))
    else
        tmp = t * (((2.0d0 * (x / t)) + (27.0d0 * ((a * b) / t))) - (9.0d0 * (z * y)))
    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 (t <= 4.4e-7) {
		tmp = ((x * 2.0) + (z * ((t * -9.0) * y))) + (a * (27.0 * b));
	} else {
		tmp = t * (((2.0 * (x / t)) + (27.0 * ((a * b) / t))) - (9.0 * (z * y)));
	}
	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 t <= 4.4e-7:
		tmp = ((x * 2.0) + (z * ((t * -9.0) * y))) + (a * (27.0 * b))
	else:
		tmp = t * (((2.0 * (x / t)) + (27.0 * ((a * b) / t))) - (9.0 * (z * y)))
	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 (t <= 4.4e-7)
		tmp = Float64(Float64(Float64(x * 2.0) + Float64(z * Float64(Float64(t * -9.0) * y))) + Float64(a * Float64(27.0 * b)));
	else
		tmp = Float64(t * Float64(Float64(Float64(2.0 * Float64(x / t)) + Float64(27.0 * Float64(Float64(a * b) / t))) - Float64(9.0 * Float64(z * y))));
	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 (t <= 4.4e-7)
		tmp = ((x * 2.0) + (z * ((t * -9.0) * y))) + (a * (27.0 * b));
	else
		tmp = t * (((2.0 * (x / t)) + (27.0 * ((a * b) / t))) - (9.0 * (z * y)));
	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[t, 4.4e-7], N[(N[(N[(x * 2.0), $MachinePrecision] + N[(z * N[(N[(t * -9.0), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(N[(2.0 * N[(x / t), $MachinePrecision]), $MachinePrecision] + N[(27.0 * N[(N[(a * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(9.0 * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 4.4000000000000002e-7

   1. Initial program 94.7%

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

      1. sub-neg 94.7%

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

      2. sub-neg 94.7%

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

      3. associate-*l* 96.4%

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

      4. associate-*l* 96.4%

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

   3. Simplified 96.4%

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

      1. sub-neg 96.4%

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

      2. *-commutative 96.4%

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

      3. distribute-rgt-neg-in 96.4%

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

      4. *-commutative 96.4%

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

      5. distribute-lft-neg-in 96.4%

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

      6. metadata-eval 96.4%

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

      7. associate-*l* 96.4%

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

      8. associate-*r* 96.4%

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

      9. associate-*l* 97.9%

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

   6. Applied egg-rr 97.9%

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

   if 4.4000000000000002e-7 < t

   1. Initial program 96.3%

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

      1. sub-neg 96.3%

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

      2. sub-neg 96.3%

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

      3. associate-*l* 88.5%

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

      4. associate-*l* 88.4%

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

   3. Simplified 88.4%

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

   5. Taylor expanded in t around inf 99.6%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 4.4 \cdot 10^{-7}:\\ \;\;\;\;\left(x \cdot 2 + z \cdot \left(\left(t \cdot -9\right) \cdot y\right)\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\left(2 \cdot \frac{x}{t} + 27 \cdot \frac{a \cdot b}{t}\right) - 9 \cdot \left(z \cdot y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 78.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{-138}:\\ \;\;\;\;y \cdot \left(2 \cdot \frac{x}{y} - 9 \cdot \left(t \cdot z\right)\right)\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+72}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \mathbf{elif}\;t \leq 1.06 \cdot 10^{+184} \lor \neg \left(t \leq 3.2 \cdot 10^{+233}\right):\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(27 \cdot \frac{a \cdot b}{t} - 9 \cdot \left(z \cdot y\right)\right)\\ \end{array} \end{array} \]

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 (<= t -1.35e-138)
   (* y (- (* 2.0 (/ x y)) (* 9.0 (* t z))))
   (if (<= t 6e+72)
     (+ (* 27.0 (* a b)) (* x 2.0))
     (if (or (<= t 1.06e+184) (not (<= t 3.2e+233)))
       (- (* x 2.0) (* 9.0 (* t (* z y))))
       (* t (- (* 27.0 (/ (* a b) t)) (* 9.0 (* z y))))))))

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 (t <= -1.35e-138) {
		tmp = y * ((2.0 * (x / y)) - (9.0 * (t * z)));
	} else if (t <= 6e+72) {
		tmp = (27.0 * (a * b)) + (x * 2.0);
	} else if ((t <= 1.06e+184) || !(t <= 3.2e+233)) {
		tmp = (x * 2.0) - (9.0 * (t * (z * y)));
	} else {
		tmp = t * ((27.0 * ((a * b) / t)) - (9.0 * (z * y)));
	}
	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 (t <= (-1.35d-138)) then
        tmp = y * ((2.0d0 * (x / y)) - (9.0d0 * (t * z)))
    else if (t <= 6d+72) then
        tmp = (27.0d0 * (a * b)) + (x * 2.0d0)
    else if ((t <= 1.06d+184) .or. (.not. (t <= 3.2d+233))) then
        tmp = (x * 2.0d0) - (9.0d0 * (t * (z * y)))
    else
        tmp = t * ((27.0d0 * ((a * b) / t)) - (9.0d0 * (z * y)))
    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 (t <= -1.35e-138) {
		tmp = y * ((2.0 * (x / y)) - (9.0 * (t * z)));
	} else if (t <= 6e+72) {
		tmp = (27.0 * (a * b)) + (x * 2.0);
	} else if ((t <= 1.06e+184) || !(t <= 3.2e+233)) {
		tmp = (x * 2.0) - (9.0 * (t * (z * y)));
	} else {
		tmp = t * ((27.0 * ((a * b) / t)) - (9.0 * (z * y)));
	}
	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 t <= -1.35e-138:
		tmp = y * ((2.0 * (x / y)) - (9.0 * (t * z)))
	elif t <= 6e+72:
		tmp = (27.0 * (a * b)) + (x * 2.0)
	elif (t <= 1.06e+184) or not (t <= 3.2e+233):
		tmp = (x * 2.0) - (9.0 * (t * (z * y)))
	else:
		tmp = t * ((27.0 * ((a * b) / t)) - (9.0 * (z * y)))
	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 (t <= -1.35e-138)
		tmp = Float64(y * Float64(Float64(2.0 * Float64(x / y)) - Float64(9.0 * Float64(t * z))));
	elseif (t <= 6e+72)
		tmp = Float64(Float64(27.0 * Float64(a * b)) + Float64(x * 2.0));
	elseif ((t <= 1.06e+184) || !(t <= 3.2e+233))
		tmp = Float64(Float64(x * 2.0) - Float64(9.0 * Float64(t * Float64(z * y))));
	else
		tmp = Float64(t * Float64(Float64(27.0 * Float64(Float64(a * b) / t)) - Float64(9.0 * Float64(z * y))));
	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 (t <= -1.35e-138)
		tmp = y * ((2.0 * (x / y)) - (9.0 * (t * z)));
	elseif (t <= 6e+72)
		tmp = (27.0 * (a * b)) + (x * 2.0);
	elseif ((t <= 1.06e+184) || ~((t <= 3.2e+233)))
		tmp = (x * 2.0) - (9.0 * (t * (z * y)));
	else
		tmp = t * ((27.0 * ((a * b) / t)) - (9.0 * (z * y)));
	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[t, -1.35e-138], N[(y * N[(N[(2.0 * N[(x / y), $MachinePrecision]), $MachinePrecision] - N[(9.0 * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6e+72], N[(N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, 1.06e+184], N[Not[LessEqual[t, 3.2e+233]], $MachinePrecision]], N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(t * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(27.0 * N[(N[(a * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] - N[(9.0 * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.35000000000000014e-138

   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* 92.6%

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

      4. associate-*l* 92.7%

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

   3. Simplified 92.7%

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

   5. Taylor expanded in a around 0 70.0%

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

   6. Taylor expanded in y around inf 64.6%

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

   if -1.35000000000000014e-138 < t < 6.00000000000000006e72

   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* 99.7%

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

      4. associate-*l* 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in y around 0 80.4%

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

   if 6.00000000000000006e72 < t < 1.06e184 or 3.20000000000000018e233 < t

   1. Initial program 96.6%

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

      1. sub-neg 96.6%

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

      2. sub-neg 96.6%

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

      3. associate-*l* 84.8%

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

      4. associate-*l* 84.8%

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

   3. Simplified 84.8%

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

   5. Taylor expanded in a around 0 89.2%

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

   if 1.06e184 < t < 3.20000000000000018e233

   1. Initial program 87.3%

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

      1. sub-neg 87.3%

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

      2. sub-neg 87.3%

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

      3. associate-*l* 76.3%

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

      4. associate-*l* 76.3%

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

   3. Simplified 76.3%

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

   5. Taylor expanded in t around inf 99.8%

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

   6. Taylor expanded in x around 0 99.8%

      \[\leadsto \color{blue}{t \cdot \left(27 \cdot \frac{a \cdot b}{t} - 9 \cdot \left(y \cdot z\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{-138}:\\ \;\;\;\;y \cdot \left(2 \cdot \frac{x}{y} - 9 \cdot \left(t \cdot z\right)\right)\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+72}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \mathbf{elif}\;t \leq 1.06 \cdot 10^{+184} \lor \neg \left(t \leq 3.2 \cdot 10^{+233}\right):\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(27 \cdot \frac{a \cdot b}{t} - 9 \cdot \left(z \cdot y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 47.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{-144}:\\ \;\;\;\;\left(t \cdot z\right) \cdot \left(-9 \cdot y\right)\\ \mathbf{elif}\;t \leq 2.55 \cdot 10^{-195}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{-72}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+52}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t \leq 9.6 \cdot 10^{+160}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-9 \cdot \left(z \cdot y\right)\right)\\ \end{array} \end{array} \]

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 (<= t -1.1e-144)
   (* (* t z) (* -9.0 y))
   (if (<= t 2.55e-195)
     (* a (* 27.0 b))
     (if (<= t 7.8e-72)
       (* x 2.0)
       (if (<= t 3e+52)
         (* 27.0 (* a b))
         (if (<= t 9.6e+160) (* x 2.0) (* t (* -9.0 (* z y)))))))))

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 (t <= -1.1e-144) {
		tmp = (t * z) * (-9.0 * y);
	} else if (t <= 2.55e-195) {
		tmp = a * (27.0 * b);
	} else if (t <= 7.8e-72) {
		tmp = x * 2.0;
	} else if (t <= 3e+52) {
		tmp = 27.0 * (a * b);
	} else if (t <= 9.6e+160) {
		tmp = x * 2.0;
	} else {
		tmp = t * (-9.0 * (z * y));
	}
	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 (t <= (-1.1d-144)) then
        tmp = (t * z) * ((-9.0d0) * y)
    else if (t <= 2.55d-195) then
        tmp = a * (27.0d0 * b)
    else if (t <= 7.8d-72) then
        tmp = x * 2.0d0
    else if (t <= 3d+52) then
        tmp = 27.0d0 * (a * b)
    else if (t <= 9.6d+160) then
        tmp = x * 2.0d0
    else
        tmp = t * ((-9.0d0) * (z * y))
    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 (t <= -1.1e-144) {
		tmp = (t * z) * (-9.0 * y);
	} else if (t <= 2.55e-195) {
		tmp = a * (27.0 * b);
	} else if (t <= 7.8e-72) {
		tmp = x * 2.0;
	} else if (t <= 3e+52) {
		tmp = 27.0 * (a * b);
	} else if (t <= 9.6e+160) {
		tmp = x * 2.0;
	} else {
		tmp = t * (-9.0 * (z * y));
	}
	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 t <= -1.1e-144:
		tmp = (t * z) * (-9.0 * y)
	elif t <= 2.55e-195:
		tmp = a * (27.0 * b)
	elif t <= 7.8e-72:
		tmp = x * 2.0
	elif t <= 3e+52:
		tmp = 27.0 * (a * b)
	elif t <= 9.6e+160:
		tmp = x * 2.0
	else:
		tmp = t * (-9.0 * (z * y))
	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 (t <= -1.1e-144)
		tmp = Float64(Float64(t * z) * Float64(-9.0 * y));
	elseif (t <= 2.55e-195)
		tmp = Float64(a * Float64(27.0 * b));
	elseif (t <= 7.8e-72)
		tmp = Float64(x * 2.0);
	elseif (t <= 3e+52)
		tmp = Float64(27.0 * Float64(a * b));
	elseif (t <= 9.6e+160)
		tmp = Float64(x * 2.0);
	else
		tmp = Float64(t * Float64(-9.0 * Float64(z * y)));
	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 (t <= -1.1e-144)
		tmp = (t * z) * (-9.0 * y);
	elseif (t <= 2.55e-195)
		tmp = a * (27.0 * b);
	elseif (t <= 7.8e-72)
		tmp = x * 2.0;
	elseif (t <= 3e+52)
		tmp = 27.0 * (a * b);
	elseif (t <= 9.6e+160)
		tmp = x * 2.0;
	else
		tmp = t * (-9.0 * (z * y));
	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[t, -1.1e-144], N[(N[(t * z), $MachinePrecision] * N[(-9.0 * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.55e-195], N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.8e-72], N[(x * 2.0), $MachinePrecision], If[LessEqual[t, 3e+52], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.6e+160], N[(x * 2.0), $MachinePrecision], N[(t * N[(-9.0 * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.10000000000000003e-144

   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* 92.6%

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

      4. associate-*l* 92.7%

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

   3. Simplified 92.7%

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

      1. +-commutative 92.7%

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

      2. associate-+r- 92.7%

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

      3. associate-*r* 92.6%

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

      4. *-commutative 92.6%

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

      5. associate-*l* 92.6%

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

      6. associate-*l* 92.6%

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

      7. associate-*r* 92.6%

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

   6. Applied egg-rr 92.6%

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

   7. Taylor expanded in y around 0 96.9%

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

      1. associate-*r* 96.8%

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

      2. *-commutative 96.8%

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

      3. associate-*l* 96.8%

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

      4. *-commutative 96.8%

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

      5. associate-*r* 96.9%

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

      6. *-commutative 96.9%

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

   9. Simplified 96.9%

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

   10. Taylor expanded in t around inf 41.7%

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

       1. associate-*r* 41.6%

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

       2. associate-*r* 41.6%

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

       3. metadata-eval 41.6%

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

       4. distribute-lft-neg-in 41.6%

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

       5. distribute-lft-neg-in 41.6%

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

       6. *-commutative 41.6%

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

       7. associate-*r* 41.7%

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

       8. associate-*l* 41.7%

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

       9. distribute-rgt-neg-in 41.7%

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

       10. distribute-rgt-neg-in 41.7%

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

       11. distribute-lft-neg-in 41.7%

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

       12. metadata-eval 41.7%

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

       13. *-commutative 41.7%

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

   12. Simplified 41.7%

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

       1. pow1 41.7%

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

   14. Applied egg-rr 41.7%

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

       1. unpow1 41.7%

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

       2. associate-*r* 41.7%

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

       3. *-commutative 41.7%

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

       4. associate-*r* 41.7%

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

       5. associate-*r* 38.5%

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

       6. *-commutative 38.5%

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

   16. Simplified 38.5%

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

   if -1.10000000000000003e-144 < t < 2.55e-195

   1. Initial program 89.7%

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

      1. sub-neg 89.7%

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

      2. sub-neg 89.7%

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

      3. associate-*l* 99.6%

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

      4. associate-*l* 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in a around inf 47.6%

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

      1. associate-*r* 47.7%

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

      2. *-commutative 47.7%

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

      3. associate-*r* 47.6%

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

   7. Simplified 47.6%

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

   if 2.55e-195 < t < 7.8e-72 or 3e52 < t < 9.6000000000000006e160

   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* 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* 92.3%

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

   3. Simplified 92.3%

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

   5. Taylor expanded in x around inf 40.3%

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

   if 7.8e-72 < t < 3e52

   1. Initial program 96.4%

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

      1. sub-neg 96.4%

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

      2. sub-neg 96.4%

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

      3. associate-*l* 99.7%

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

      4. associate-*l* 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in a around inf 37.2%

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

   if 9.6000000000000006e160 < t

   1. Initial program 95.4%

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

      1. sub-neg 95.4%

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

      2. sub-neg 95.4%

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

      3. associate-*l* 87.1%

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

      4. associate-*l* 87.0%

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

   3. Simplified 87.0%

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

   5. Taylor expanded in a around 0 88.3%

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

   6. Taylor expanded in t around inf 88.2%

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

   7. Taylor expanded in x around 0 79.4%

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

4. Final simplification 44.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{-144}:\\ \;\;\;\;\left(t \cdot z\right) \cdot \left(-9 \cdot y\right)\\ \mathbf{elif}\;t \leq 2.55 \cdot 10^{-195}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{-72}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+52}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t \leq 9.6 \cdot 10^{+160}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-9 \cdot \left(z \cdot y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 47.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{-144}:\\ \;\;\;\;-9 \cdot \left(z \cdot \left(t \cdot y\right)\right)\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-195}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;t \leq 1.56 \cdot 10^{-72}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{+51}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t \leq 10^{+161}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-9 \cdot \left(z \cdot y\right)\right)\\ \end{array} \end{array} \]

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 (<= t -1.1e-144)
   (* -9.0 (* z (* t y)))
   (if (<= t 7e-195)
     (* a (* 27.0 b))
     (if (<= t 1.56e-72)
       (* x 2.0)
       (if (<= t 7.2e+51)
         (* 27.0 (* a b))
         (if (<= t 1e+161) (* x 2.0) (* t (* -9.0 (* z y)))))))))

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 (t <= -1.1e-144) {
		tmp = -9.0 * (z * (t * y));
	} else if (t <= 7e-195) {
		tmp = a * (27.0 * b);
	} else if (t <= 1.56e-72) {
		tmp = x * 2.0;
	} else if (t <= 7.2e+51) {
		tmp = 27.0 * (a * b);
	} else if (t <= 1e+161) {
		tmp = x * 2.0;
	} else {
		tmp = t * (-9.0 * (z * y));
	}
	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 (t <= (-1.1d-144)) then
        tmp = (-9.0d0) * (z * (t * y))
    else if (t <= 7d-195) then
        tmp = a * (27.0d0 * b)
    else if (t <= 1.56d-72) then
        tmp = x * 2.0d0
    else if (t <= 7.2d+51) then
        tmp = 27.0d0 * (a * b)
    else if (t <= 1d+161) then
        tmp = x * 2.0d0
    else
        tmp = t * ((-9.0d0) * (z * y))
    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 (t <= -1.1e-144) {
		tmp = -9.0 * (z * (t * y));
	} else if (t <= 7e-195) {
		tmp = a * (27.0 * b);
	} else if (t <= 1.56e-72) {
		tmp = x * 2.0;
	} else if (t <= 7.2e+51) {
		tmp = 27.0 * (a * b);
	} else if (t <= 1e+161) {
		tmp = x * 2.0;
	} else {
		tmp = t * (-9.0 * (z * y));
	}
	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 t <= -1.1e-144:
		tmp = -9.0 * (z * (t * y))
	elif t <= 7e-195:
		tmp = a * (27.0 * b)
	elif t <= 1.56e-72:
		tmp = x * 2.0
	elif t <= 7.2e+51:
		tmp = 27.0 * (a * b)
	elif t <= 1e+161:
		tmp = x * 2.0
	else:
		tmp = t * (-9.0 * (z * y))
	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 (t <= -1.1e-144)
		tmp = Float64(-9.0 * Float64(z * Float64(t * y)));
	elseif (t <= 7e-195)
		tmp = Float64(a * Float64(27.0 * b));
	elseif (t <= 1.56e-72)
		tmp = Float64(x * 2.0);
	elseif (t <= 7.2e+51)
		tmp = Float64(27.0 * Float64(a * b));
	elseif (t <= 1e+161)
		tmp = Float64(x * 2.0);
	else
		tmp = Float64(t * Float64(-9.0 * Float64(z * y)));
	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 (t <= -1.1e-144)
		tmp = -9.0 * (z * (t * y));
	elseif (t <= 7e-195)
		tmp = a * (27.0 * b);
	elseif (t <= 1.56e-72)
		tmp = x * 2.0;
	elseif (t <= 7.2e+51)
		tmp = 27.0 * (a * b);
	elseif (t <= 1e+161)
		tmp = x * 2.0;
	else
		tmp = t * (-9.0 * (z * y));
	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[t, -1.1e-144], N[(-9.0 * N[(z * N[(t * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7e-195], N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.56e-72], N[(x * 2.0), $MachinePrecision], If[LessEqual[t, 7.2e+51], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1e+161], N[(x * 2.0), $MachinePrecision], N[(t * N[(-9.0 * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.10000000000000003e-144

   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* 92.6%

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

      4. associate-*l* 92.7%

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

   3. Simplified 92.7%

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

   5. Taylor expanded in y around inf 41.7%

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

      1. pow1 41.7%

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

      2. *-commutative 41.7%

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

      3. associate-*l* 38.5%

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

   7. Applied egg-rr 38.5%

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

      1. unpow1 38.5%

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

      2. associate-*r* 41.7%

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

      3. *-commutative 41.7%

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

      4. associate-*r* 41.6%

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

   9. Simplified 41.6%

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

   if -1.10000000000000003e-144 < t < 7.00000000000000028e-195

   1. Initial program 89.7%

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

      1. sub-neg 89.7%

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

      2. sub-neg 89.7%

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

      3. associate-*l* 99.6%

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

      4. associate-*l* 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in a around inf 47.6%

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

      1. associate-*r* 47.7%

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

      2. *-commutative 47.7%

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

      3. associate-*r* 47.6%

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

   7. Simplified 47.6%

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

   if 7.00000000000000028e-195 < t < 1.55999999999999993e-72 or 7.20000000000000022e51 < t < 1e161

   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* 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* 92.3%

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

   3. Simplified 92.3%

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

   5. Taylor expanded in x around inf 40.3%

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

   if 1.55999999999999993e-72 < t < 7.20000000000000022e51

   1. Initial program 96.4%

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

      1. sub-neg 96.4%

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

      2. sub-neg 96.4%

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

      3. associate-*l* 99.7%

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

      4. associate-*l* 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in a around inf 37.2%

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

   if 1e161 < t

   1. Initial program 95.4%

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

      1. sub-neg 95.4%

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

      2. sub-neg 95.4%

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

      3. associate-*l* 87.1%

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

      4. associate-*l* 87.0%

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

   3. Simplified 87.0%

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

   5. Taylor expanded in a around 0 88.3%

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

   6. Taylor expanded in t around inf 88.2%

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

   7. Taylor expanded in x around 0 79.4%

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

4. Final simplification 45.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{-144}:\\ \;\;\;\;-9 \cdot \left(z \cdot \left(t \cdot y\right)\right)\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-195}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;t \leq 1.56 \cdot 10^{-72}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{+51}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t \leq 10^{+161}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-9 \cdot \left(z \cdot y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 47.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{-144}:\\ \;\;\;\;-9 \cdot \left(z \cdot \left(t \cdot y\right)\right)\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-195}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;t \leq 6.4 \cdot 10^{-71}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{+53}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+161}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \end{array} \end{array} \]

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 (<= t -1.1e-144)
   (* -9.0 (* z (* t y)))
   (if (<= t 4.6e-195)
     (* a (* 27.0 b))
     (if (<= t 6.4e-71)
       (* x 2.0)
       (if (<= t 3.7e+53)
         (* 27.0 (* a b))
         (if (<= t 1.1e+161) (* x 2.0) (* -9.0 (* t (* z y)))))))))

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 (t <= -1.1e-144) {
		tmp = -9.0 * (z * (t * y));
	} else if (t <= 4.6e-195) {
		tmp = a * (27.0 * b);
	} else if (t <= 6.4e-71) {
		tmp = x * 2.0;
	} else if (t <= 3.7e+53) {
		tmp = 27.0 * (a * b);
	} else if (t <= 1.1e+161) {
		tmp = x * 2.0;
	} else {
		tmp = -9.0 * (t * (z * y));
	}
	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 (t <= (-1.1d-144)) then
        tmp = (-9.0d0) * (z * (t * y))
    else if (t <= 4.6d-195) then
        tmp = a * (27.0d0 * b)
    else if (t <= 6.4d-71) then
        tmp = x * 2.0d0
    else if (t <= 3.7d+53) then
        tmp = 27.0d0 * (a * b)
    else if (t <= 1.1d+161) then
        tmp = x * 2.0d0
    else
        tmp = (-9.0d0) * (t * (z * y))
    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 (t <= -1.1e-144) {
		tmp = -9.0 * (z * (t * y));
	} else if (t <= 4.6e-195) {
		tmp = a * (27.0 * b);
	} else if (t <= 6.4e-71) {
		tmp = x * 2.0;
	} else if (t <= 3.7e+53) {
		tmp = 27.0 * (a * b);
	} else if (t <= 1.1e+161) {
		tmp = x * 2.0;
	} else {
		tmp = -9.0 * (t * (z * y));
	}
	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 t <= -1.1e-144:
		tmp = -9.0 * (z * (t * y))
	elif t <= 4.6e-195:
		tmp = a * (27.0 * b)
	elif t <= 6.4e-71:
		tmp = x * 2.0
	elif t <= 3.7e+53:
		tmp = 27.0 * (a * b)
	elif t <= 1.1e+161:
		tmp = x * 2.0
	else:
		tmp = -9.0 * (t * (z * y))
	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 (t <= -1.1e-144)
		tmp = Float64(-9.0 * Float64(z * Float64(t * y)));
	elseif (t <= 4.6e-195)
		tmp = Float64(a * Float64(27.0 * b));
	elseif (t <= 6.4e-71)
		tmp = Float64(x * 2.0);
	elseif (t <= 3.7e+53)
		tmp = Float64(27.0 * Float64(a * b));
	elseif (t <= 1.1e+161)
		tmp = Float64(x * 2.0);
	else
		tmp = Float64(-9.0 * Float64(t * Float64(z * y)));
	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 (t <= -1.1e-144)
		tmp = -9.0 * (z * (t * y));
	elseif (t <= 4.6e-195)
		tmp = a * (27.0 * b);
	elseif (t <= 6.4e-71)
		tmp = x * 2.0;
	elseif (t <= 3.7e+53)
		tmp = 27.0 * (a * b);
	elseif (t <= 1.1e+161)
		tmp = x * 2.0;
	else
		tmp = -9.0 * (t * (z * y));
	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[t, -1.1e-144], N[(-9.0 * N[(z * N[(t * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.6e-195], N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.4e-71], N[(x * 2.0), $MachinePrecision], If[LessEqual[t, 3.7e+53], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.1e+161], N[(x * 2.0), $MachinePrecision], N[(-9.0 * N[(t * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.10000000000000003e-144

   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* 92.6%

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

      4. associate-*l* 92.7%

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

   3. Simplified 92.7%

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

   5. Taylor expanded in y around inf 41.7%

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

      1. pow1 41.7%

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

      2. *-commutative 41.7%

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

      3. associate-*l* 38.5%

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

   7. Applied egg-rr 38.5%

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

      1. unpow1 38.5%

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

      2. associate-*r* 41.7%

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

      3. *-commutative 41.7%

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

      4. associate-*r* 41.6%

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

   9. Simplified 41.6%

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

   if -1.10000000000000003e-144 < t < 4.6000000000000004e-195

   1. Initial program 89.7%

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

      1. sub-neg 89.7%

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

      2. sub-neg 89.7%

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

      3. associate-*l* 99.6%

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

      4. associate-*l* 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in a around inf 47.6%

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

      1. associate-*r* 47.7%

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

      2. *-commutative 47.7%

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

      3. associate-*r* 47.6%

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

   7. Simplified 47.6%

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

   if 4.6000000000000004e-195 < t < 6.3999999999999998e-71 or 3.7e53 < t < 1.1e161

   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* 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* 92.3%

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

   3. Simplified 92.3%

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

   5. Taylor expanded in x around inf 40.3%

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

   if 6.3999999999999998e-71 < t < 3.7e53

   1. Initial program 96.4%

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

      1. sub-neg 96.4%

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

      2. sub-neg 96.4%

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

      3. associate-*l* 99.7%

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

      4. associate-*l* 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in a around inf 37.2%

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

   if 1.1e161 < t

   1. Initial program 95.4%

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

      1. sub-neg 95.4%

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

      2. sub-neg 95.4%

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

      3. associate-*l* 87.1%

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

      4. associate-*l* 87.0%

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

   3. Simplified 87.0%

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

   5. Taylor expanded in y around inf 79.5%

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

4. Final simplification 45.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{-144}:\\ \;\;\;\;-9 \cdot \left(z \cdot \left(t \cdot y\right)\right)\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-195}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;t \leq 6.4 \cdot 10^{-71}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{+53}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+161}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 47.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := -9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \mathbf{if}\;t \leq -7 \cdot 10^{-74}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-195}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-71}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{+51}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t \leq 9.6 \cdot 10^{+160}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (* -9.0 (* t (* z y)))))
   (if (<= t -7e-74)
     t_1
     (if (<= t 2.2e-195)
       (* a (* 27.0 b))
       (if (<= t 2.8e-71)
         (* x 2.0)
         (if (<= t 4.8e+51)
           (* 27.0 (* a b))
           (if (<= t 9.6e+160) (* x 2.0) t_1)))))))

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 = -9.0 * (t * (z * y));
	double tmp;
	if (t <= -7e-74) {
		tmp = t_1;
	} else if (t <= 2.2e-195) {
		tmp = a * (27.0 * b);
	} else if (t <= 2.8e-71) {
		tmp = x * 2.0;
	} else if (t <= 4.8e+51) {
		tmp = 27.0 * (a * b);
	} else if (t <= 9.6e+160) {
		tmp = x * 2.0;
	} else {
		tmp = t_1;
	}
	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 = (-9.0d0) * (t * (z * y))
    if (t <= (-7d-74)) then
        tmp = t_1
    else if (t <= 2.2d-195) then
        tmp = a * (27.0d0 * b)
    else if (t <= 2.8d-71) then
        tmp = x * 2.0d0
    else if (t <= 4.8d+51) then
        tmp = 27.0d0 * (a * b)
    else if (t <= 9.6d+160) then
        tmp = x * 2.0d0
    else
        tmp = t_1
    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 = -9.0 * (t * (z * y));
	double tmp;
	if (t <= -7e-74) {
		tmp = t_1;
	} else if (t <= 2.2e-195) {
		tmp = a * (27.0 * b);
	} else if (t <= 2.8e-71) {
		tmp = x * 2.0;
	} else if (t <= 4.8e+51) {
		tmp = 27.0 * (a * b);
	} else if (t <= 9.6e+160) {
		tmp = x * 2.0;
	} else {
		tmp = t_1;
	}
	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 = -9.0 * (t * (z * y))
	tmp = 0
	if t <= -7e-74:
		tmp = t_1
	elif t <= 2.2e-195:
		tmp = a * (27.0 * b)
	elif t <= 2.8e-71:
		tmp = x * 2.0
	elif t <= 4.8e+51:
		tmp = 27.0 * (a * b)
	elif t <= 9.6e+160:
		tmp = x * 2.0
	else:
		tmp = t_1
	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(-9.0 * Float64(t * Float64(z * y)))
	tmp = 0.0
	if (t <= -7e-74)
		tmp = t_1;
	elseif (t <= 2.2e-195)
		tmp = Float64(a * Float64(27.0 * b));
	elseif (t <= 2.8e-71)
		tmp = Float64(x * 2.0);
	elseif (t <= 4.8e+51)
		tmp = Float64(27.0 * Float64(a * b));
	elseif (t <= 9.6e+160)
		tmp = Float64(x * 2.0);
	else
		tmp = t_1;
	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 = -9.0 * (t * (z * y));
	tmp = 0.0;
	if (t <= -7e-74)
		tmp = t_1;
	elseif (t <= 2.2e-195)
		tmp = a * (27.0 * b);
	elseif (t <= 2.8e-71)
		tmp = x * 2.0;
	elseif (t <= 4.8e+51)
		tmp = 27.0 * (a * b);
	elseif (t <= 9.6e+160)
		tmp = x * 2.0;
	else
		tmp = t_1;
	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[(-9.0 * N[(t * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7e-74], t$95$1, If[LessEqual[t, 2.2e-195], N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.8e-71], N[(x * 2.0), $MachinePrecision], If[LessEqual[t, 4.8e+51], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.6e+160], N[(x * 2.0), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -7.00000000000000029e-74 or 9.6000000000000006e160 < t

   1. Initial program 98.0%

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

      1. sub-neg 98.0%

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

      2. sub-neg 98.0%

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

      3. associate-*l* 90.6%

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

      4. associate-*l* 90.6%

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

   3. Simplified 90.6%

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

   5. Taylor expanded in y around inf 52.4%

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

   if -7.00000000000000029e-74 < t < 2.20000000000000005e-195

   1. Initial program 88.9%

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

      1. sub-neg 88.9%

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

      2. sub-neg 88.9%

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

      3. associate-*l* 99.6%

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

      4. associate-*l* 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in a around inf 46.9%

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

      1. associate-*r* 47.0%

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

      2. *-commutative 47.0%

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

      3. associate-*r* 47.0%

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

   7. Simplified 47.0%

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

   if 2.20000000000000005e-195 < t < 2.8e-71 or 4.7999999999999997e51 < t < 9.6000000000000006e160

   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* 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* 92.3%

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

   3. Simplified 92.3%

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

   5. Taylor expanded in x around inf 40.3%

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

   if 2.8e-71 < t < 4.7999999999999997e51

   1. Initial program 96.4%

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

      1. sub-neg 96.4%

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

      2. sub-neg 96.4%

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

      3. associate-*l* 99.7%

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

      4. associate-*l* 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in a around inf 37.2%

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 46.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{-74}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-195}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-71}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{+51}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t \leq 9.6 \cdot 10^{+160}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 98.3% accurate, 0.7× speedup

Math

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

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 (<= (* y 9.0) -5e-9)
   (- (+ (* 27.0 (* a b)) (* x 2.0)) (* y (* t (* z 9.0))))
   (+ (+ (* x 2.0) (* z (* (* t -9.0) y))) (* 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 ((y * 9.0) <= -5e-9) {
		tmp = ((27.0 * (a * b)) + (x * 2.0)) - (y * (t * (z * 9.0)));
	} else {
		tmp = ((x * 2.0) + (z * ((t * -9.0) * y))) + (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 ((y * 9.0d0) <= (-5d-9)) then
        tmp = ((27.0d0 * (a * b)) + (x * 2.0d0)) - (y * (t * (z * 9.0d0)))
    else
        tmp = ((x * 2.0d0) + (z * ((t * (-9.0d0)) * y))) + (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 ((y * 9.0) <= -5e-9) {
		tmp = ((27.0 * (a * b)) + (x * 2.0)) - (y * (t * (z * 9.0)));
	} else {
		tmp = ((x * 2.0) + (z * ((t * -9.0) * y))) + (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 (y * 9.0) <= -5e-9:
		tmp = ((27.0 * (a * b)) + (x * 2.0)) - (y * (t * (z * 9.0)))
	else:
		tmp = ((x * 2.0) + (z * ((t * -9.0) * y))) + (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 (Float64(y * 9.0) <= -5e-9)
		tmp = Float64(Float64(Float64(27.0 * Float64(a * b)) + Float64(x * 2.0)) - Float64(y * Float64(t * Float64(z * 9.0))));
	else
		tmp = Float64(Float64(Float64(x * 2.0) + Float64(z * Float64(Float64(t * -9.0) * y))) + 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 ((y * 9.0) <= -5e-9)
		tmp = ((27.0 * (a * b)) + (x * 2.0)) - (y * (t * (z * 9.0)));
	else
		tmp = ((x * 2.0) + (z * ((t * -9.0) * y))) + (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[LessEqual[N[(y * 9.0), $MachinePrecision], -5e-9], N[(N[(N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision] - N[(y * N[(t * N[(z * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * 2.0), $MachinePrecision] + N[(z * N[(N[(t * -9.0), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y #s(literal 9 binary64)) < -5.0000000000000001e-9

   1. Initial program 90.6%

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

      1. sub-neg 90.6%

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

      2. sub-neg 90.6%

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

      3. associate-*l* 97.9%

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

      4. associate-*l* 97.9%

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

   3. Simplified 97.9%

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

      1. +-commutative 97.9%

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

      2. associate-+r- 97.9%

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

      3. associate-*r* 97.9%

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

      4. *-commutative 97.9%

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

      5. associate-*l* 97.9%

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

      6. associate-*l* 99.4%

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

      7. associate-*r* 99.4%

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

   6. Applied egg-rr 99.4%

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

   if -5.0000000000000001e-9 < (*.f64 y #s(literal 9 binary64))

   1. Initial program 96.4%

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

      1. sub-neg 96.4%

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

      2. sub-neg 96.4%

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

      3. associate-*l* 93.6%

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

      4. associate-*l* 93.6%

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

   3. Simplified 93.6%

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

      1. sub-neg 93.6%

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

      2. *-commutative 93.6%

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

      3. distribute-rgt-neg-in 93.6%

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

      4. *-commutative 93.6%

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

      5. distribute-lft-neg-in 93.6%

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

      6. metadata-eval 93.6%

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

      7. associate-*l* 93.6%

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

      8. associate-*r* 93.6%

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

      9. associate-*l* 96.4%

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

   6. Applied egg-rr 96.4%

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

4. Final simplification 97.1%

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

Alternative 8: 97.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := a \cdot \left(27 \cdot b\right)\\ \mathbf{if}\;y \cdot 9 \leq -5 \cdot 10^{+84}:\\ \;\;\;\;t\_1 + \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(t \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 + z \cdot \left(\left(t \cdot -9\right) \cdot y\right)\right) + t\_1\\ \end{array} \end{array} \]

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+84)
     (+ t_1 (- (* x 2.0) (* (* y 9.0) (* t z))))
     (+ (+ (* x 2.0) (* z (* (* t -9.0) y))) t_1))))

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+84) {
		tmp = t_1 + ((x * 2.0) - ((y * 9.0) * (t * z)));
	} else {
		tmp = ((x * 2.0) + (z * ((t * -9.0) * y))) + t_1;
	}
	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+84)) then
        tmp = t_1 + ((x * 2.0d0) - ((y * 9.0d0) * (t * z)))
    else
        tmp = ((x * 2.0d0) + (z * ((t * (-9.0d0)) * y))) + t_1
    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+84) {
		tmp = t_1 + ((x * 2.0) - ((y * 9.0) * (t * z)));
	} else {
		tmp = ((x * 2.0) + (z * ((t * -9.0) * y))) + t_1;
	}
	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+84:
		tmp = t_1 + ((x * 2.0) - ((y * 9.0) * (t * z)))
	else:
		tmp = ((x * 2.0) + (z * ((t * -9.0) * y))) + t_1
	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+84)
		tmp = Float64(t_1 + Float64(Float64(x * 2.0) - Float64(Float64(y * 9.0) * Float64(t * z))));
	else
		tmp = Float64(Float64(Float64(x * 2.0) + Float64(z * Float64(Float64(t * -9.0) * y))) + t_1);
	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+84)
		tmp = t_1 + ((x * 2.0) - ((y * 9.0) * (t * z)));
	else
		tmp = ((x * 2.0) + (z * ((t * -9.0) * y))) + t_1;
	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+84], N[(t$95$1 + N[(N[(x * 2.0), $MachinePrecision] - N[(N[(y * 9.0), $MachinePrecision] * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * 2.0), $MachinePrecision] + N[(z * N[(N[(t * -9.0), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y #s(literal 9 binary64)) < -5.0000000000000001e84

   1. Initial program 87.5%

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

      1. sub-neg 87.5%

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

      2. sub-neg 87.5%

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

      3. associate-*l* 97.3%

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

      4. associate-*l* 97.3%

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

   3. Simplified 97.3%

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

   if -5.0000000000000001e84 < (*.f64 y #s(literal 9 binary64))

   1. Initial program 96.7%

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

      1. sub-neg 96.7%

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

      2. sub-neg 96.7%

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

      3. associate-*l* 94.0%

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

      4. associate-*l* 94.0%

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

   3. Simplified 94.0%

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

      1. sub-neg 94.0%

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

      2. *-commutative 94.0%

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

      3. distribute-rgt-neg-in 94.0%

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

      4. *-commutative 94.0%

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

      5. distribute-lft-neg-in 94.0%

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

      6. metadata-eval 94.0%

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

      7. associate-*l* 94.0%

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

      8. associate-*r* 94.0%

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

      9. associate-*l* 96.6%

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

   6. Applied egg-rr 96.6%

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

4. Final simplification 96.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot 9 \leq -5 \cdot 10^{+84}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right) + \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(t \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 + z \cdot \left(\left(t \cdot -9\right) \cdot y\right)\right) + a \cdot \left(27 \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 98.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-225}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right) + \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(t \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(27 \cdot \left(a \cdot b\right) + x \cdot 2\right) - t \cdot \left(y \cdot \left(z \cdot 9\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -3.5e-225)
   (+ (* a (* 27.0 b)) (- (* x 2.0) (* (* y 9.0) (* t z))))
   (- (+ (* 27.0 (* a b)) (* x 2.0)) (* 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 <= -3.5e-225) {
		tmp = (a * (27.0 * b)) + ((x * 2.0) - ((y * 9.0) * (t * z)));
	} else {
		tmp = ((27.0 * (a * b)) + (x * 2.0)) - (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 <= (-3.5d-225)) then
        tmp = (a * (27.0d0 * b)) + ((x * 2.0d0) - ((y * 9.0d0) * (t * z)))
    else
        tmp = ((27.0d0 * (a * b)) + (x * 2.0d0)) - (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 <= -3.5e-225) {
		tmp = (a * (27.0 * b)) + ((x * 2.0) - ((y * 9.0) * (t * z)));
	} else {
		tmp = ((27.0 * (a * b)) + (x * 2.0)) - (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 <= -3.5e-225:
		tmp = (a * (27.0 * b)) + ((x * 2.0) - ((y * 9.0) * (t * z)))
	else:
		tmp = ((27.0 * (a * b)) + (x * 2.0)) - (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 <= -3.5e-225)
		tmp = Float64(Float64(a * Float64(27.0 * b)) + Float64(Float64(x * 2.0) - Float64(Float64(y * 9.0) * Float64(t * z))));
	else
		tmp = Float64(Float64(Float64(27.0 * Float64(a * b)) + Float64(x * 2.0)) - Float64(t * Float64(y * Float64(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 <= -3.5e-225)
		tmp = (a * (27.0 * b)) + ((x * 2.0) - ((y * 9.0) * (t * z)));
	else
		tmp = ((27.0 * (a * b)) + (x * 2.0)) - (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, -3.5e-225], N[(N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision] + N[(N[(x * 2.0), $MachinePrecision] - N[(N[(y * 9.0), $MachinePrecision] * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision] - N[(t * N[(y * N[(z * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.4999999999999997e-225

   1. Initial program 93.4%

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

      1. sub-neg 93.4%

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

      2. sub-neg 93.4%

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

      3. associate-*l* 91.3%

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

      4. associate-*l* 91.3%

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

   3. Simplified 91.3%

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

   if -3.4999999999999997e-225 < 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* 96.7%

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

      4. associate-*l* 96.7%

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

   3. Simplified 96.7%

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

      1. +-commutative 96.7%

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

      2. associate-+r- 96.7%

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

      3. associate-*r* 96.7%

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

      4. *-commutative 96.7%

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

      5. associate-*l* 96.6%

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

      6. associate-*l* 97.3%

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

      7. associate-*r* 97.2%

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

   6. Applied egg-rr 97.2%

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

   7. Taylor expanded in y around 0 96.7%

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

      1. associate-*r* 96.6%

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

      2. *-commutative 96.6%

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

      3. associate-*l* 96.6%

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

      4. *-commutative 96.6%

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

      5. associate-*r* 96.7%

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

      6. *-commutative 96.7%

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

   9. Simplified 96.7%

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

4. Final simplification 94.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-225}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right) + \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(t \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(27 \cdot \left(a \cdot b\right) + x \cdot 2\right) - t \cdot \left(y \cdot \left(z \cdot 9\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 98.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-246}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right) + \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(t \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - t \cdot \left(z \cdot \left(y \cdot 9\right)\right)\right) + b \cdot \left(a \cdot 27\right)\\ \end{array} \end{array} \]

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 (<= z -5e-246)
   (+ (* a (* 27.0 b)) (- (* x 2.0) (* (* y 9.0) (* t z))))
   (+ (- (* x 2.0) (* t (* z (* y 9.0)))) (* 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 (z <= -5e-246) {
		tmp = (a * (27.0 * b)) + ((x * 2.0) - ((y * 9.0) * (t * z)));
	} else {
		tmp = ((x * 2.0) - (t * (z * (y * 9.0)))) + (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 (z <= (-5d-246)) then
        tmp = (a * (27.0d0 * b)) + ((x * 2.0d0) - ((y * 9.0d0) * (t * z)))
    else
        tmp = ((x * 2.0d0) - (t * (z * (y * 9.0d0)))) + (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 (z <= -5e-246) {
		tmp = (a * (27.0 * b)) + ((x * 2.0) - ((y * 9.0) * (t * z)));
	} else {
		tmp = ((x * 2.0) - (t * (z * (y * 9.0)))) + (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 z <= -5e-246:
		tmp = (a * (27.0 * b)) + ((x * 2.0) - ((y * 9.0) * (t * z)))
	else:
		tmp = ((x * 2.0) - (t * (z * (y * 9.0)))) + (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 (z <= -5e-246)
		tmp = Float64(Float64(a * Float64(27.0 * b)) + Float64(Float64(x * 2.0) - Float64(Float64(y * 9.0) * Float64(t * z))));
	else
		tmp = Float64(Float64(Float64(x * 2.0) - Float64(t * Float64(z * Float64(y * 9.0)))) + 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 (z <= -5e-246)
		tmp = (a * (27.0 * b)) + ((x * 2.0) - ((y * 9.0) * (t * z)));
	else
		tmp = ((x * 2.0) - (t * (z * (y * 9.0)))) + (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[LessEqual[z, -5e-246], N[(N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision] + N[(N[(x * 2.0), $MachinePrecision] - N[(N[(y * 9.0), $MachinePrecision] * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * 2.0), $MachinePrecision] - N[(t * N[(z * N[(y * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.9999999999999997e-246

   1. Initial program 93.7%

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

      1. sub-neg 93.7%

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

      2. sub-neg 93.7%

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

      3. associate-*l* 91.8%

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

      4. associate-*l* 91.8%

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

   3. Simplified 91.8%

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

   if -4.9999999999999997e-246 < z

   1. Initial program 96.0%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 94.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-246}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right) + \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(t \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - t \cdot \left(z \cdot \left(y \cdot 9\right)\right)\right) + b \cdot \left(a \cdot 27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 78.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{-138}:\\ \;\;\;\;y \cdot \left(2 \cdot \frac{x}{y} - 9 \cdot \left(t \cdot z\right)\right)\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{+72}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \end{array} \end{array} \]

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 (<= t -1.35e-138)
   (* y (- (* 2.0 (/ x y)) (* 9.0 (* t z))))
   (if (<= t 2.2e+72)
     (+ (* 27.0 (* a b)) (* x 2.0))
     (- (* x 2.0) (* 9.0 (* t (* z y)))))))

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 (t <= -1.35e-138) {
		tmp = y * ((2.0 * (x / y)) - (9.0 * (t * z)));
	} else if (t <= 2.2e+72) {
		tmp = (27.0 * (a * b)) + (x * 2.0);
	} else {
		tmp = (x * 2.0) - (9.0 * (t * (z * y)));
	}
	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 (t <= (-1.35d-138)) then
        tmp = y * ((2.0d0 * (x / y)) - (9.0d0 * (t * z)))
    else if (t <= 2.2d+72) then
        tmp = (27.0d0 * (a * b)) + (x * 2.0d0)
    else
        tmp = (x * 2.0d0) - (9.0d0 * (t * (z * y)))
    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 (t <= -1.35e-138) {
		tmp = y * ((2.0 * (x / y)) - (9.0 * (t * z)));
	} else if (t <= 2.2e+72) {
		tmp = (27.0 * (a * b)) + (x * 2.0);
	} else {
		tmp = (x * 2.0) - (9.0 * (t * (z * y)));
	}
	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 t <= -1.35e-138:
		tmp = y * ((2.0 * (x / y)) - (9.0 * (t * z)))
	elif t <= 2.2e+72:
		tmp = (27.0 * (a * b)) + (x * 2.0)
	else:
		tmp = (x * 2.0) - (9.0 * (t * (z * y)))
	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 (t <= -1.35e-138)
		tmp = Float64(y * Float64(Float64(2.0 * Float64(x / y)) - Float64(9.0 * Float64(t * z))));
	elseif (t <= 2.2e+72)
		tmp = Float64(Float64(27.0 * Float64(a * b)) + Float64(x * 2.0));
	else
		tmp = Float64(Float64(x * 2.0) - Float64(9.0 * Float64(t * Float64(z * y))));
	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 (t <= -1.35e-138)
		tmp = y * ((2.0 * (x / y)) - (9.0 * (t * z)));
	elseif (t <= 2.2e+72)
		tmp = (27.0 * (a * b)) + (x * 2.0);
	else
		tmp = (x * 2.0) - (9.0 * (t * (z * y)));
	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[t, -1.35e-138], N[(y * N[(N[(2.0 * N[(x / y), $MachinePrecision]), $MachinePrecision] - N[(9.0 * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.2e+72], N[(N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(t * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.35000000000000014e-138

   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* 92.6%

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

      4. associate-*l* 92.7%

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

   3. Simplified 92.7%

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

   5. Taylor expanded in a around 0 70.0%

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

   6. Taylor expanded in y around inf 64.6%

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

   if -1.35000000000000014e-138 < t < 2.2e72

   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* 99.7%

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

      4. associate-*l* 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in y around 0 80.4%

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

   if 2.2e72 < t

   1. Initial program 94.7%

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

      1. sub-neg 94.7%

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

      2. sub-neg 94.7%

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

      3. associate-*l* 83.1%

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

      4. associate-*l* 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. Taylor expanded in a around 0 88.8%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{-138}:\\ \;\;\;\;y \cdot \left(2 \cdot \frac{x}{y} - 9 \cdot \left(t \cdot z\right)\right)\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{+72}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 78.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{-138}:\\ \;\;\;\;\left(t \cdot z\right) \cdot \left(-9 \cdot y\right)\\ \mathbf{elif}\;t \leq 1.08 \cdot 10^{+72}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \end{array} \end{array} \]

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 (<= t -1.35e-138)
   (* (* t z) (* -9.0 y))
   (if (<= t 1.08e+72)
     (+ (* 27.0 (* a b)) (* x 2.0))
     (- (* x 2.0) (* 9.0 (* t (* z y)))))))

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 (t <= -1.35e-138) {
		tmp = (t * z) * (-9.0 * y);
	} else if (t <= 1.08e+72) {
		tmp = (27.0 * (a * b)) + (x * 2.0);
	} else {
		tmp = (x * 2.0) - (9.0 * (t * (z * y)));
	}
	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 (t <= (-1.35d-138)) then
        tmp = (t * z) * ((-9.0d0) * y)
    else if (t <= 1.08d+72) then
        tmp = (27.0d0 * (a * b)) + (x * 2.0d0)
    else
        tmp = (x * 2.0d0) - (9.0d0 * (t * (z * y)))
    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 (t <= -1.35e-138) {
		tmp = (t * z) * (-9.0 * y);
	} else if (t <= 1.08e+72) {
		tmp = (27.0 * (a * b)) + (x * 2.0);
	} else {
		tmp = (x * 2.0) - (9.0 * (t * (z * y)));
	}
	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 t <= -1.35e-138:
		tmp = (t * z) * (-9.0 * y)
	elif t <= 1.08e+72:
		tmp = (27.0 * (a * b)) + (x * 2.0)
	else:
		tmp = (x * 2.0) - (9.0 * (t * (z * y)))
	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 (t <= -1.35e-138)
		tmp = Float64(Float64(t * z) * Float64(-9.0 * y));
	elseif (t <= 1.08e+72)
		tmp = Float64(Float64(27.0 * Float64(a * b)) + Float64(x * 2.0));
	else
		tmp = Float64(Float64(x * 2.0) - Float64(9.0 * Float64(t * Float64(z * y))));
	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 (t <= -1.35e-138)
		tmp = (t * z) * (-9.0 * y);
	elseif (t <= 1.08e+72)
		tmp = (27.0 * (a * b)) + (x * 2.0);
	else
		tmp = (x * 2.0) - (9.0 * (t * (z * y)));
	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[t, -1.35e-138], N[(N[(t * z), $MachinePrecision] * N[(-9.0 * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.08e+72], N[(N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(t * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.35000000000000014e-138

   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* 92.6%

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

      4. associate-*l* 92.7%

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

   3. Simplified 92.7%

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

      1. +-commutative 92.7%

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

      2. associate-+r- 92.7%

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

      3. associate-*r* 92.6%

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

      4. *-commutative 92.6%

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

      5. associate-*l* 92.6%

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

      6. associate-*l* 92.6%

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

      7. associate-*r* 92.6%

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

   6. Applied egg-rr 92.6%

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

   7. Taylor expanded in y around 0 96.9%

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

      1. associate-*r* 96.8%

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

      2. *-commutative 96.8%

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

      3. associate-*l* 96.8%

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

      4. *-commutative 96.8%

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

      5. associate-*r* 96.9%

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

      6. *-commutative 96.9%

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

   9. Simplified 96.9%

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

   10. Taylor expanded in t around inf 41.7%

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

       1. associate-*r* 41.6%

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

       2. associate-*r* 41.6%

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

       3. metadata-eval 41.6%

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

       4. distribute-lft-neg-in 41.6%

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

       5. distribute-lft-neg-in 41.6%

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

       6. *-commutative 41.6%

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

       7. associate-*r* 41.7%

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

       8. associate-*l* 41.7%

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

       9. distribute-rgt-neg-in 41.7%

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

       10. distribute-rgt-neg-in 41.7%

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

       11. distribute-lft-neg-in 41.7%

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

       12. metadata-eval 41.7%

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

       13. *-commutative 41.7%

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

   12. Simplified 41.7%

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

       1. pow1 41.7%

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

   14. Applied egg-rr 41.7%

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

       1. unpow1 41.7%

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

       2. associate-*r* 41.7%

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

       3. *-commutative 41.7%

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

       4. associate-*r* 41.7%

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

       5. associate-*r* 38.5%

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

       6. *-commutative 38.5%

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

   16. Simplified 38.5%

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

   if -1.35000000000000014e-138 < t < 1.07999999999999999e72

   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* 99.7%

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

      4. associate-*l* 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in y around 0 80.4%

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

   if 1.07999999999999999e72 < t

   1. Initial program 94.7%

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

      1. sub-neg 94.7%

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

      2. sub-neg 94.7%

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

      3. associate-*l* 83.1%

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

      4. associate-*l* 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. Taylor expanded in a around 0 88.8%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{-138}:\\ \;\;\;\;\left(t \cdot z\right) \cdot \left(-9 \cdot y\right)\\ \mathbf{elif}\;t \leq 1.08 \cdot 10^{+72}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 75.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{-138}:\\ \;\;\;\;\left(t \cdot z\right) \cdot \left(-9 \cdot y\right)\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+137}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + z \cdot \left(\left(t \cdot -9\right) \cdot y\right)\\ \end{array} \end{array} \]

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 (<= t -1.35e-138)
   (* (* t z) (* -9.0 y))
   (if (<= t 8.5e+137)
     (+ (* 27.0 (* a b)) (* x 2.0))
     (+ (* x 2.0) (* z (* (* t -9.0) y))))))

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 (t <= -1.35e-138) {
		tmp = (t * z) * (-9.0 * y);
	} else if (t <= 8.5e+137) {
		tmp = (27.0 * (a * b)) + (x * 2.0);
	} else {
		tmp = (x * 2.0) + (z * ((t * -9.0) * y));
	}
	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 (t <= (-1.35d-138)) then
        tmp = (t * z) * ((-9.0d0) * y)
    else if (t <= 8.5d+137) then
        tmp = (27.0d0 * (a * b)) + (x * 2.0d0)
    else
        tmp = (x * 2.0d0) + (z * ((t * (-9.0d0)) * y))
    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 (t <= -1.35e-138) {
		tmp = (t * z) * (-9.0 * y);
	} else if (t <= 8.5e+137) {
		tmp = (27.0 * (a * b)) + (x * 2.0);
	} else {
		tmp = (x * 2.0) + (z * ((t * -9.0) * y));
	}
	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 t <= -1.35e-138:
		tmp = (t * z) * (-9.0 * y)
	elif t <= 8.5e+137:
		tmp = (27.0 * (a * b)) + (x * 2.0)
	else:
		tmp = (x * 2.0) + (z * ((t * -9.0) * y))
	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 (t <= -1.35e-138)
		tmp = Float64(Float64(t * z) * Float64(-9.0 * y));
	elseif (t <= 8.5e+137)
		tmp = Float64(Float64(27.0 * Float64(a * b)) + Float64(x * 2.0));
	else
		tmp = Float64(Float64(x * 2.0) + Float64(z * Float64(Float64(t * -9.0) * y)));
	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 (t <= -1.35e-138)
		tmp = (t * z) * (-9.0 * y);
	elseif (t <= 8.5e+137)
		tmp = (27.0 * (a * b)) + (x * 2.0);
	else
		tmp = (x * 2.0) + (z * ((t * -9.0) * y));
	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[t, -1.35e-138], N[(N[(t * z), $MachinePrecision] * N[(-9.0 * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.5e+137], N[(N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] + N[(z * N[(N[(t * -9.0), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.35000000000000014e-138

   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* 92.6%

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

      4. associate-*l* 92.7%

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

   3. Simplified 92.7%

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

      1. +-commutative 92.7%

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

      2. associate-+r- 92.7%

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

      3. associate-*r* 92.6%

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

      4. *-commutative 92.6%

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

      5. associate-*l* 92.6%

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

      6. associate-*l* 92.6%

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

      7. associate-*r* 92.6%

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

   6. Applied egg-rr 92.6%

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

   7. Taylor expanded in y around 0 96.9%

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

      1. associate-*r* 96.8%

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

      2. *-commutative 96.8%

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

      3. associate-*l* 96.8%

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

      4. *-commutative 96.8%

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

      5. associate-*r* 96.9%

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

      6. *-commutative 96.9%

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

   9. Simplified 96.9%

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

   10. Taylor expanded in t around inf 41.7%

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

       1. associate-*r* 41.6%

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

       2. associate-*r* 41.6%

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

       3. metadata-eval 41.6%

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

       4. distribute-lft-neg-in 41.6%

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

       5. distribute-lft-neg-in 41.6%

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

       6. *-commutative 41.6%

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

       7. associate-*r* 41.7%

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

       8. associate-*l* 41.7%

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

       9. distribute-rgt-neg-in 41.7%

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

       10. distribute-rgt-neg-in 41.7%

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

       11. distribute-lft-neg-in 41.7%

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

       12. metadata-eval 41.7%

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

       13. *-commutative 41.7%

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

   12. Simplified 41.7%

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

       1. pow1 41.7%

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

   14. Applied egg-rr 41.7%

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

       1. unpow1 41.7%

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

       2. associate-*r* 41.7%

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

       3. *-commutative 41.7%

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

       4. associate-*r* 41.7%

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

       5. associate-*r* 38.5%

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

       6. *-commutative 38.5%

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

   16. Simplified 38.5%

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

   if -1.35000000000000014e-138 < t < 8.50000000000000028e137

   1. Initial program 93.6%

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

      1. sub-neg 93.6%

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

      2. sub-neg 93.6%

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

      3. associate-*l* 98.3%

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

      4. associate-*l* 98.2%

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

   3. Simplified 98.2%

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

   5. Taylor expanded in y around 0 77.1%

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

   if 8.50000000000000028e137 < t

   1. Initial program 96.0%

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

      1. sub-neg 96.0%

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

      2. sub-neg 96.0%

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

      3. associate-*l* 82.7%

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

      4. associate-*l* 82.6%

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

   3. Simplified 82.6%

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

   5. Taylor expanded in a around 0 86.8%

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

      1. cancel-sign-sub-inv 86.8%

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

      2. *-commutative 86.8%

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

      3. metadata-eval 86.8%

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

      4. +-commutative 86.8%

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

      5. associate-*r* 86.6%

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

      6. associate-*r* 75.0%

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

      7. *-commutative 75.0%

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

   7. Applied egg-rr 75.0%

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

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{-138}:\\ \;\;\;\;\left(t \cdot z\right) \cdot \left(-9 \cdot y\right)\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+137}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + z \cdot \left(\left(t \cdot -9\right) \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 75.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{-138}:\\ \;\;\;\;\left(t \cdot z\right) \cdot \left(-9 \cdot y\right)\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{+138}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + z \cdot \left(-9 \cdot \left(t \cdot y\right)\right)\\ \end{array} \end{array} \]

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 (<= t -1.35e-138)
   (* (* t z) (* -9.0 y))
   (if (<= t 1.75e+138)
     (+ (* 27.0 (* a b)) (* x 2.0))
     (+ (* x 2.0) (* z (* -9.0 (* t y)))))))

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 (t <= -1.35e-138) {
		tmp = (t * z) * (-9.0 * y);
	} else if (t <= 1.75e+138) {
		tmp = (27.0 * (a * b)) + (x * 2.0);
	} else {
		tmp = (x * 2.0) + (z * (-9.0 * (t * y)));
	}
	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 (t <= (-1.35d-138)) then
        tmp = (t * z) * ((-9.0d0) * y)
    else if (t <= 1.75d+138) then
        tmp = (27.0d0 * (a * b)) + (x * 2.0d0)
    else
        tmp = (x * 2.0d0) + (z * ((-9.0d0) * (t * y)))
    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 (t <= -1.35e-138) {
		tmp = (t * z) * (-9.0 * y);
	} else if (t <= 1.75e+138) {
		tmp = (27.0 * (a * b)) + (x * 2.0);
	} else {
		tmp = (x * 2.0) + (z * (-9.0 * (t * y)));
	}
	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 t <= -1.35e-138:
		tmp = (t * z) * (-9.0 * y)
	elif t <= 1.75e+138:
		tmp = (27.0 * (a * b)) + (x * 2.0)
	else:
		tmp = (x * 2.0) + (z * (-9.0 * (t * y)))
	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 (t <= -1.35e-138)
		tmp = Float64(Float64(t * z) * Float64(-9.0 * y));
	elseif (t <= 1.75e+138)
		tmp = Float64(Float64(27.0 * Float64(a * b)) + Float64(x * 2.0));
	else
		tmp = Float64(Float64(x * 2.0) + Float64(z * Float64(-9.0 * Float64(t * y))));
	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 (t <= -1.35e-138)
		tmp = (t * z) * (-9.0 * y);
	elseif (t <= 1.75e+138)
		tmp = (27.0 * (a * b)) + (x * 2.0);
	else
		tmp = (x * 2.0) + (z * (-9.0 * (t * y)));
	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[t, -1.35e-138], N[(N[(t * z), $MachinePrecision] * N[(-9.0 * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.75e+138], N[(N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] + N[(z * N[(-9.0 * N[(t * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.35000000000000014e-138

   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* 92.6%

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

      4. associate-*l* 92.7%

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

   3. Simplified 92.7%

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

      1. +-commutative 92.7%

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

      2. associate-+r- 92.7%

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

      3. associate-*r* 92.6%

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

      4. *-commutative 92.6%

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

      5. associate-*l* 92.6%

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

      6. associate-*l* 92.6%

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

      7. associate-*r* 92.6%

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

   6. Applied egg-rr 92.6%

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

   7. Taylor expanded in y around 0 96.9%

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

      1. associate-*r* 96.8%

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

      2. *-commutative 96.8%

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

      3. associate-*l* 96.8%

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

      4. *-commutative 96.8%

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

      5. associate-*r* 96.9%

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

      6. *-commutative 96.9%

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

   9. Simplified 96.9%

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

   10. Taylor expanded in t around inf 41.7%

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

       1. associate-*r* 41.6%

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

       2. associate-*r* 41.6%

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

       3. metadata-eval 41.6%

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

       4. distribute-lft-neg-in 41.6%

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

       5. distribute-lft-neg-in 41.6%

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

       6. *-commutative 41.6%

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

       7. associate-*r* 41.7%

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

       8. associate-*l* 41.7%

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

       9. distribute-rgt-neg-in 41.7%

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

       10. distribute-rgt-neg-in 41.7%

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

       11. distribute-lft-neg-in 41.7%

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

       12. metadata-eval 41.7%

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

       13. *-commutative 41.7%

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

   12. Simplified 41.7%

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

       1. pow1 41.7%

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

   14. Applied egg-rr 41.7%

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

       1. unpow1 41.7%

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

       2. associate-*r* 41.7%

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

       3. *-commutative 41.7%

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

       4. associate-*r* 41.7%

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

       5. associate-*r* 38.5%

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

       6. *-commutative 38.5%

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

   16. Simplified 38.5%

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

   if -1.35000000000000014e-138 < t < 1.7499999999999999e138

   1. Initial program 93.6%

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

      1. sub-neg 93.6%

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

      2. sub-neg 93.6%

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

      3. associate-*l* 98.3%

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

      4. associate-*l* 98.2%

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

   3. Simplified 98.2%

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

   5. Taylor expanded in y around 0 77.1%

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

   if 1.7499999999999999e138 < t

   1. Initial program 96.0%

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

      1. sub-neg 96.0%

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

      2. sub-neg 96.0%

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

      3. associate-*l* 82.7%

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

      4. associate-*l* 82.6%

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

   3. Simplified 82.6%

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

   5. Taylor expanded in a around 0 86.8%

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

      1. cancel-sign-sub-inv 86.8%

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

      2. *-commutative 86.8%

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

      3. metadata-eval 86.8%

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

      4. +-commutative 86.8%

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

      5. associate-*r* 86.6%

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

      6. associate-*r* 75.0%

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

      7. *-commutative 75.0%

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

   7. Applied egg-rr 75.0%

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

   8. Taylor expanded in t around 0 75.0%

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

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{-138}:\\ \;\;\;\;\left(t \cdot z\right) \cdot \left(-9 \cdot y\right)\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{+138}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + z \cdot \left(-9 \cdot \left(t \cdot y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 71.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{-138}:\\ \;\;\;\;\left(t \cdot z\right) \cdot \left(-9 \cdot y\right)\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+161}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-9 \cdot \left(z \cdot y\right)\right)\\ \end{array} \end{array} \]

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 (<= t -1.35e-138)
   (* (* t z) (* -9.0 y))
   (if (<= t 9e+161) (+ (* 27.0 (* a b)) (* x 2.0)) (* t (* -9.0 (* z y))))))

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 (t <= -1.35e-138) {
		tmp = (t * z) * (-9.0 * y);
	} else if (t <= 9e+161) {
		tmp = (27.0 * (a * b)) + (x * 2.0);
	} else {
		tmp = t * (-9.0 * (z * y));
	}
	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 (t <= (-1.35d-138)) then
        tmp = (t * z) * ((-9.0d0) * y)
    else if (t <= 9d+161) then
        tmp = (27.0d0 * (a * b)) + (x * 2.0d0)
    else
        tmp = t * ((-9.0d0) * (z * y))
    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 (t <= -1.35e-138) {
		tmp = (t * z) * (-9.0 * y);
	} else if (t <= 9e+161) {
		tmp = (27.0 * (a * b)) + (x * 2.0);
	} else {
		tmp = t * (-9.0 * (z * y));
	}
	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 t <= -1.35e-138:
		tmp = (t * z) * (-9.0 * y)
	elif t <= 9e+161:
		tmp = (27.0 * (a * b)) + (x * 2.0)
	else:
		tmp = t * (-9.0 * (z * y))
	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 (t <= -1.35e-138)
		tmp = Float64(Float64(t * z) * Float64(-9.0 * y));
	elseif (t <= 9e+161)
		tmp = Float64(Float64(27.0 * Float64(a * b)) + Float64(x * 2.0));
	else
		tmp = Float64(t * Float64(-9.0 * Float64(z * y)));
	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 (t <= -1.35e-138)
		tmp = (t * z) * (-9.0 * y);
	elseif (t <= 9e+161)
		tmp = (27.0 * (a * b)) + (x * 2.0);
	else
		tmp = t * (-9.0 * (z * y));
	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[t, -1.35e-138], N[(N[(t * z), $MachinePrecision] * N[(-9.0 * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9e+161], N[(N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], N[(t * N[(-9.0 * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.35000000000000014e-138

   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* 92.6%

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

      4. associate-*l* 92.7%

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

   3. Simplified 92.7%

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

      1. +-commutative 92.7%

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

      2. associate-+r- 92.7%

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

      3. associate-*r* 92.6%

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

      4. *-commutative 92.6%

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

      5. associate-*l* 92.6%

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

      6. associate-*l* 92.6%

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

      7. associate-*r* 92.6%

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

   6. Applied egg-rr 92.6%

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

   7. Taylor expanded in y around 0 96.9%

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

      1. associate-*r* 96.8%

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

      2. *-commutative 96.8%

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

      3. associate-*l* 96.8%

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

      4. *-commutative 96.8%

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

      5. associate-*r* 96.9%

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

      6. *-commutative 96.9%

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

   9. Simplified 96.9%

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

   10. Taylor expanded in t around inf 41.7%

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

       1. associate-*r* 41.6%

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

       2. associate-*r* 41.6%

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

       3. metadata-eval 41.6%

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

       4. distribute-lft-neg-in 41.6%

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

       5. distribute-lft-neg-in 41.6%

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

       6. *-commutative 41.6%

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

       7. associate-*r* 41.7%

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

       8. associate-*l* 41.7%

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

       9. distribute-rgt-neg-in 41.7%

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

       10. distribute-rgt-neg-in 41.7%

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

       11. distribute-lft-neg-in 41.7%

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

       12. metadata-eval 41.7%

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

       13. *-commutative 41.7%

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

   12. Simplified 41.7%

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

       1. pow1 41.7%

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

   14. Applied egg-rr 41.7%

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

       1. unpow1 41.7%

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

       2. associate-*r* 41.7%

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

       3. *-commutative 41.7%

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

       4. associate-*r* 41.7%

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

       5. associate-*r* 38.5%

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

       6. *-commutative 38.5%

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

   16. Simplified 38.5%

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

   if -1.35000000000000014e-138 < t < 8.99999999999999984e161

   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* 97.1%

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

      4. associate-*l* 97.0%

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

   3. Simplified 97.0%

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

   5. Taylor expanded in y around 0 75.2%

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

   if 8.99999999999999984e161 < t

   1. Initial program 95.4%

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

      1. sub-neg 95.4%

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

      2. sub-neg 95.4%

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

      3. associate-*l* 87.1%

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

      4. associate-*l* 87.0%

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

   3. Simplified 87.0%

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

   5. Taylor expanded in a around 0 88.3%

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

   6. Taylor expanded in t around inf 88.2%

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

   7. Taylor expanded in x around 0 79.4%

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

4. Final simplification 62.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{-138}:\\ \;\;\;\;\left(t \cdot z\right) \cdot \left(-9 \cdot y\right)\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+161}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-9 \cdot \left(z \cdot y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 93.1% accurate, 1.0× speedup

Math

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

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

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) + (z * ((t * (-9.0d0)) * y))) + (a * (27.0d0 * b))
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) + (z * ((t * -9.0) * y))) + (a * (27.0 * b));
}

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

Julia

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

Derivation

1. Initial program 95.1%

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

   1. sub-neg 95.1%

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

   2. sub-neg 95.1%

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

   3. associate-*l* 94.6%

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

   4. associate-*l* 94.6%

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

3. Simplified 94.6%

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

   1. sub-neg 94.6%

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

   2. *-commutative 94.6%

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

   3. distribute-rgt-neg-in 94.6%

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

   4. *-commutative 94.6%

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

   5. distribute-lft-neg-in 94.6%

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

   6. metadata-eval 94.6%

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

   7. associate-*l* 95.0%

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

   8. associate-*r* 94.9%

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

   9. associate-*l* 94.6%

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

6. Applied egg-rr 94.6%

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

Alternative 17: 46.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -1.05 \cdot 10^{-49} \lor \neg \left(b \leq 2700000000\right):\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.05e-49) (not (<= b 2700000000.0)))
   (* a (* 27.0 b))
   (* 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 tmp;
	if ((b <= -1.05e-49) || !(b <= 2700000000.0)) {
		tmp = a * (27.0 * b);
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-1.05d-49)) .or. (.not. (b <= 2700000000.0d0))) then
        tmp = a * (27.0d0 * b)
    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 tmp;
	if ((b <= -1.05e-49) || !(b <= 2700000000.0)) {
		tmp = a * (27.0 * b);
	} 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):
	tmp = 0
	if (b <= -1.05e-49) or not (b <= 2700000000.0):
		tmp = a * (27.0 * b)
	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)
	tmp = 0.0
	if ((b <= -1.05e-49) || !(b <= 2700000000.0))
		tmp = Float64(a * Float64(27.0 * b));
	else
		tmp = Float64(x * 2.0);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -1.05e-49) || ~((b <= 2700000000.0)))
		tmp = a * (27.0 * b);
	else
		tmp = x * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1.05e-49], N[Not[LessEqual[b, 2700000000.0]], $MachinePrecision]], N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision], N[(x * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.0499999999999999e-49 or 2.7e9 < b

   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* 94.6%

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

      4. associate-*l* 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 a around inf 46.7%

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

      1. associate-*r* 46.8%

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

      2. *-commutative 46.8%

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

      3. associate-*r* 46.8%

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

   7. Simplified 46.8%

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

   if -1.0499999999999999e-49 < b < 2.7e9

   1. Initial program 95.3%

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

      1. sub-neg 95.3%

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

      2. sub-neg 95.3%

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

      3. associate-*l* 94.6%

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

      4. associate-*l* 94.6%

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

   3. Simplified 94.6%

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

   5. Taylor expanded in x around inf 46.1%

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

4. Final simplification 46.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.05 \cdot 10^{-49} \lor \neg \left(b \leq 2700000000\right):\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 46.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -1.15 \cdot 10^{-49} \lor \neg \left(b \leq 1500000000000\right):\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.15e-49) (not (<= b 1500000000000.0)))
   (* 27.0 (* a b))
   (* 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 tmp;
	if ((b <= -1.15e-49) || !(b <= 1500000000000.0)) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-1.15d-49)) .or. (.not. (b <= 1500000000000.0d0))) then
        tmp = 27.0d0 * (a * b)
    else
        tmp = x * 2.0d0
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.15e-49) || !(b <= 1500000000000.0)) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -1.15e-49) or not (b <= 1500000000000.0):
		tmp = 27.0 * (a * b)
	else:
		tmp = x * 2.0
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1.15e-49) || !(b <= 1500000000000.0))
		tmp = Float64(27.0 * Float64(a * b));
	else
		tmp = Float64(x * 2.0);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -1.15e-49) || ~((b <= 1500000000000.0)))
		tmp = 27.0 * (a * b);
	else
		tmp = x * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1.15e-49], N[Not[LessEqual[b, 1500000000000.0]], $MachinePrecision]], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], N[(x * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.15e-49 or 1.5e12 < b

   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* 94.6%

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

      4. associate-*l* 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 a around inf 46.7%

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

   if -1.15e-49 < b < 1.5e12

   1. Initial program 95.3%

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

      1. sub-neg 95.3%

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

      2. sub-neg 95.3%

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

      3. associate-*l* 94.6%

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

      4. associate-*l* 94.6%

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

   3. Simplified 94.6%

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

   5. Taylor expanded in x around inf 46.1%

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

4. Final simplification 46.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.15 \cdot 10^{-49} \lor \neg \left(b \leq 1500000000000\right):\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 46.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -7 \cdot 10^{-50}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;b \leq 7 \cdot 10^{+15}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \end{array} \end{array} \]

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 (<= b -7e-50)
   (* a (* 27.0 b))
   (if (<= b 7e+15) (* 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 (b <= -7e-50) {
		tmp = a * (27.0 * b);
	} else if (b <= 7e+15) {
		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 (b <= (-7d-50)) then
        tmp = a * (27.0d0 * b)
    else if (b <= 7d+15) 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 (b <= -7e-50) {
		tmp = a * (27.0 * b);
	} else if (b <= 7e+15) {
		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 b <= -7e-50:
		tmp = a * (27.0 * b)
	elif b <= 7e+15:
		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 (b <= -7e-50)
		tmp = Float64(a * Float64(27.0 * b));
	elseif (b <= 7e+15)
		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 (b <= -7e-50)
		tmp = a * (27.0 * b);
	elseif (b <= 7e+15)
		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[LessEqual[b, -7e-50], N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7e+15], N[(x * 2.0), $MachinePrecision], N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -6.99999999999999993e-50

   1. Initial program 95.5%

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

      1. sub-neg 95.5%

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

      2. sub-neg 95.5%

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

      3. associate-*l* 95.2%

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

      4. associate-*l* 95.2%

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

   3. Simplified 95.2%

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

   5. Taylor expanded in a around inf 47.8%

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

      1. associate-*r* 47.9%

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

      2. *-commutative 47.9%

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

      3. associate-*r* 47.9%

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

   7. Simplified 47.9%

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

   if -6.99999999999999993e-50 < b < 7e15

   1. Initial program 95.3%

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

      1. sub-neg 95.3%

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

      2. sub-neg 95.3%

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

      3. associate-*l* 94.6%

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

      4. associate-*l* 94.6%

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

   3. Simplified 94.6%

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

   5. Taylor expanded in x around inf 46.1%

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

   if 7e15 < b

   1. Initial program 94.1%

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

      1. sub-neg 94.1%

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

      2. sub-neg 94.1%

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

      3. associate-*l* 93.9%

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

      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 a around inf 45.7%

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

      1. associate-*r* 45.7%

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

   7. Simplified 45.7%

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

4. Final simplification 46.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7 \cdot 10^{-50}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;b \leq 7 \cdot 10^{+15}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 30.2% 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 95.1%

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

   1. sub-neg 95.1%

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

   2. sub-neg 95.1%

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

   3. associate-*l* 94.6%

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

   4. associate-*l* 94.6%

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

3. Simplified 94.6%

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

5. Taylor expanded in x around inf 32.8%

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

6. Final simplification 32.8%

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

Developer target: 95.3% 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 2024100 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, A"
  :precision binary64

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

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