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

Percentage Accurate: 95.6% → 96.5%

Time: 14.6s

Alternatives: 17

Speedup: 0.8×

• 27.9% 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: 96.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 3.5 \cdot 10^{+68}:\\ \;\;\;\;\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot 27 + -9 \cdot \left(t \cdot \left(y \cdot \frac{z}{b}\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z 3.5e+68)
   (+ (- (* x 2.0) (* (* y 9.0) (* z t))) (* a (* 27.0 b)))
   (* b (+ (* a 27.0) (* -9.0 (* t (* y (/ z b))))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 3.5e+68) {
		tmp = ((x * 2.0) - ((y * 9.0) * (z * t))) + (a * (27.0 * b));
	} else {
		tmp = b * ((a * 27.0) + (-9.0 * (t * (y * (z / b)))));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= 3.5d+68) then
        tmp = ((x * 2.0d0) - ((y * 9.0d0) * (z * t))) + (a * (27.0d0 * b))
    else
        tmp = b * ((a * 27.0d0) + ((-9.0d0) * (t * (y * (z / b)))))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 3.5e+68) {
		tmp = ((x * 2.0) - ((y * 9.0) * (z * t))) + (a * (27.0 * b));
	} else {
		tmp = b * ((a * 27.0) + (-9.0 * (t * (y * (z / b)))));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= 3.5e+68:
		tmp = ((x * 2.0) - ((y * 9.0) * (z * t))) + (a * (27.0 * b))
	else:
		tmp = b * ((a * 27.0) + (-9.0 * (t * (y * (z / b)))))
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= 3.5e+68)
		tmp = Float64(Float64(Float64(x * 2.0) - Float64(Float64(y * 9.0) * Float64(z * t))) + Float64(a * Float64(27.0 * b)));
	else
		tmp = Float64(b * Float64(Float64(a * 27.0) + Float64(-9.0 * Float64(t * Float64(y * Float64(z / b))))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= 3.5e+68)
		tmp = ((x * 2.0) - ((y * 9.0) * (z * t))) + (a * (27.0 * b));
	else
		tmp = b * ((a * 27.0) + (-9.0 * (t * (y * (z / 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.
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+68], N[(N[(N[(x * 2.0), $MachinePrecision] - N[(N[(y * 9.0), $MachinePrecision] * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(N[(a * 27.0), $MachinePrecision] + N[(-9.0 * N[(t * N[(y * N[(z / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 3.49999999999999977e68

   1. Initial program 95.2%

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

      1. sub-neg 95.2%

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

      2. sub-neg 95.2%

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

      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

   if 3.49999999999999977e68 < z

   1. Initial program 87.6%

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

      1. sub-neg 87.6%

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

      2. sub-neg 87.6%

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

      3. associate-*l* 83.6%

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

      4. associate-*l* 83.6%

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

   3. Simplified 83.6%

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

      1. +-commutative 83.6%

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

      2. associate-+r- 83.6%

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

      3. associate-*r* 83.6%

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

      4. *-commutative 83.6%

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

      5. associate-*l* 83.6%

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

      6. associate-*l* 83.5%

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

      7. associate-*r* 83.5%

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

   6. Applied egg-rr 83.5%

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

      1. add-cube-cbrt 83.1%

         \[\leadsto \left(\color{blue}{\left(\sqrt[3]{27 \cdot \left(a \cdot b\right)} \cdot \sqrt[3]{27 \cdot \left(a \cdot b\right)}\right) \cdot \sqrt[3]{27 \cdot \left(a \cdot b\right)}} + x \cdot 2\right) - y \cdot \left(\left(9 \cdot z\right) \cdot t\right) \]

      2. pow3 83.1%

         \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{27 \cdot \left(a \cdot b\right)}\right)}^{3}} + x \cdot 2\right) - y \cdot \left(\left(9 \cdot z\right) \cdot t\right) \]

   8. Applied egg-rr 83.1%

      \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{27 \cdot \left(a \cdot b\right)}\right)}^{3}} + x \cdot 2\right) - y \cdot \left(\left(9 \cdot z\right) \cdot t\right) \]

   9. Taylor expanded in b around inf 73.6%

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

       1. +-commutative 73.6%

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

       2. associate--l+ 73.6%

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

       3. *-commutative 73.6%

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

       4. associate-*r/ 73.6%

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

       5. associate-*r/ 73.6%

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

       6. div-sub 75.7%

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

   11. Simplified 75.6%

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

   12. Taylor expanded in x around 0 67.5%

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

       1. associate-/l* 71.7%

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

       2. associate-/l* 73.8%

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

   14. Simplified 73.8%

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

Alternative 2: 79.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := t \cdot \left(z \cdot y\right)\\ t_2 := 27 \cdot \left(a \cdot b\right)\\ \mathbf{if}\;x \leq -8.8 \cdot 10^{+49}:\\ \;\;\;\;x \cdot 2 + t\_2\\ \mathbf{elif}\;x \leq 0.0001:\\ \;\;\;\;t\_2 - 9 \cdot t\_1\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{+74}:\\ \;\;\;\;x \cdot \left(2 + 27 \cdot \left(a \cdot \frac{b}{x}\right)\right)\\ \mathbf{elif}\;x \leq 1.12 \cdot 10^{+105}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right) + -9 \cdot t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (* z y))) (t_2 (* 27.0 (* a b))))
   (if (<= x -8.8e+49)
     (+ (* x 2.0) t_2)
     (if (<= x 0.0001)
       (- t_2 (* 9.0 t_1))
       (if (<= x 2.05e+74)
         (* x (+ 2.0 (* 27.0 (* a (/ b x)))))
         (if (<= x 1.12e+105)
           (+ (* b (* a 27.0)) (* -9.0 t_1))
           (- (* x 2.0) (* 9.0 (* y (* z t))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (z * y);
	double t_2 = 27.0 * (a * b);
	double tmp;
	if (x <= -8.8e+49) {
		tmp = (x * 2.0) + t_2;
	} else if (x <= 0.0001) {
		tmp = t_2 - (9.0 * t_1);
	} else if (x <= 2.05e+74) {
		tmp = x * (2.0 + (27.0 * (a * (b / x))));
	} else if (x <= 1.12e+105) {
		tmp = (b * (a * 27.0)) + (-9.0 * t_1);
	} else {
		tmp = (x * 2.0) - (9.0 * (y * (z * t)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * (z * y)
    t_2 = 27.0d0 * (a * b)
    if (x <= (-8.8d+49)) then
        tmp = (x * 2.0d0) + t_2
    else if (x <= 0.0001d0) then
        tmp = t_2 - (9.0d0 * t_1)
    else if (x <= 2.05d+74) then
        tmp = x * (2.0d0 + (27.0d0 * (a * (b / x))))
    else if (x <= 1.12d+105) then
        tmp = (b * (a * 27.0d0)) + ((-9.0d0) * t_1)
    else
        tmp = (x * 2.0d0) - (9.0d0 * (y * (z * t)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (z * y);
	double t_2 = 27.0 * (a * b);
	double tmp;
	if (x <= -8.8e+49) {
		tmp = (x * 2.0) + t_2;
	} else if (x <= 0.0001) {
		tmp = t_2 - (9.0 * t_1);
	} else if (x <= 2.05e+74) {
		tmp = x * (2.0 + (27.0 * (a * (b / x))));
	} else if (x <= 1.12e+105) {
		tmp = (b * (a * 27.0)) + (-9.0 * t_1);
	} else {
		tmp = (x * 2.0) - (9.0 * (y * (z * t)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = t * (z * y)
	t_2 = 27.0 * (a * b)
	tmp = 0
	if x <= -8.8e+49:
		tmp = (x * 2.0) + t_2
	elif x <= 0.0001:
		tmp = t_2 - (9.0 * t_1)
	elif x <= 2.05e+74:
		tmp = x * (2.0 + (27.0 * (a * (b / x))))
	elif x <= 1.12e+105:
		tmp = (b * (a * 27.0)) + (-9.0 * t_1)
	else:
		tmp = (x * 2.0) - (9.0 * (y * (z * t)))
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(z * y))
	t_2 = Float64(27.0 * Float64(a * b))
	tmp = 0.0
	if (x <= -8.8e+49)
		tmp = Float64(Float64(x * 2.0) + t_2);
	elseif (x <= 0.0001)
		tmp = Float64(t_2 - Float64(9.0 * t_1));
	elseif (x <= 2.05e+74)
		tmp = Float64(x * Float64(2.0 + Float64(27.0 * Float64(a * Float64(b / x)))));
	elseif (x <= 1.12e+105)
		tmp = Float64(Float64(b * Float64(a * 27.0)) + Float64(-9.0 * t_1));
	else
		tmp = Float64(Float64(x * 2.0) - Float64(9.0 * Float64(y * Float64(z * t))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (z * y);
	t_2 = 27.0 * (a * b);
	tmp = 0.0;
	if (x <= -8.8e+49)
		tmp = (x * 2.0) + t_2;
	elseif (x <= 0.0001)
		tmp = t_2 - (9.0 * t_1);
	elseif (x <= 2.05e+74)
		tmp = x * (2.0 + (27.0 * (a * (b / x))));
	elseif (x <= 1.12e+105)
		tmp = (b * (a * 27.0)) + (-9.0 * t_1);
	else
		tmp = (x * 2.0) - (9.0 * (y * (z * t)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
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[(t * N[(z * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -8.8e+49], N[(N[(x * 2.0), $MachinePrecision] + t$95$2), $MachinePrecision], If[LessEqual[x, 0.0001], N[(t$95$2 - N[(9.0 * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.05e+74], N[(x * N[(2.0 + N[(27.0 * N[(a * N[(b / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.12e+105], N[(N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision] + N[(-9.0 * t$95$1), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -8.8000000000000003e49

   1. Initial program 98.1%

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

      1. sub-neg 98.1%

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

      2. sub-neg 98.1%

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

      3. associate-*l* 96.5%

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

      4. associate-*l* 96.5%

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

   3. Simplified 96.5%

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

   5. Taylor expanded in y around 0 84.2%

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

   if -8.8000000000000003e49 < x < 1.00000000000000005e-4

   1. Initial program 93.2%

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

      1. sub-neg 93.2%

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

      2. sub-neg 93.2%

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

      3. associate-*l* 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* 94.5%

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

   3. Simplified 94.5%

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

   5. Taylor expanded in x around 0 87.3%

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

   if 1.00000000000000005e-4 < x < 2.05e74

   1. Initial program 86.5%

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

      1. sub-neg 86.5%

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

      2. sub-neg 86.5%

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

      3. associate-*l* 86.5%

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

      4. associate-*l* 80.2%

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

   3. Simplified 80.2%

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

   5. Taylor expanded in y around 0 86.6%

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

   6. Taylor expanded in x around inf 86.6%

      \[\leadsto \color{blue}{x \cdot \left(2 + 27 \cdot \frac{a \cdot b}{x}\right)} \]
   7. Step-by-step derivation

      1. associate-/l* 86.7%

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

   8. Simplified 86.7%

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

   if 2.05e74 < x < 1.12e105

   1. Initial program 78.2%

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

      1. sub-neg 78.2%

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

      2. sub-neg 78.2%

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

      3. associate-*l* 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. Step-by-step derivation

      1. +-commutative 99.5%

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

      2. associate-+r- 99.5%

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

      3. associate-*r* 99.7%

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

      4. *-commutative 99.7%

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

      5. associate-*l* 99.5%

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

      6. associate-*l* 99.8%

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

      7. associate-*r* 99.5%

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

   6. Applied egg-rr 99.5%

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

   7. Taylor expanded in x around 0 63.8%

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

      1. cancel-sign-sub-inv 63.8%

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

      2. metadata-eval 63.8%

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

      3. associate-*r* 63.8%

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

      4. *-commutative 63.8%

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

   9. Simplified 63.8%

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

   if 1.12e105 < x

   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* 93.8%

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

      4. associate-*l* 93.8%

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

   3. Simplified 93.8%

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

   5. Taylor expanded in a around 0 81.8%

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

      1. pow1 81.8%

         \[\leadsto 2 \cdot x - 9 \cdot \color{blue}{{\left(t \cdot \left(y \cdot z\right)\right)}^{1}} \]

   7. Applied egg-rr 81.8%

      \[\leadsto 2 \cdot x - 9 \cdot \color{blue}{{\left(t \cdot \left(y \cdot z\right)\right)}^{1}} \]
   8. Step-by-step derivation

      1. unpow1 81.8%

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

      2. *-commutative 81.8%

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

      3. associate-*l* 78.9%

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

      4. *-commutative 78.9%

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

   9. Simplified 78.9%

      \[\leadsto 2 \cdot x - 9 \cdot \color{blue}{\left(y \cdot \left(t \cdot z\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 84.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.8 \cdot 10^{+49}:\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;x \leq 0.0001:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{+74}:\\ \;\;\;\;x \cdot \left(2 + 27 \cdot \left(a \cdot \frac{b}{x}\right)\right)\\ \mathbf{elif}\;x \leq 1.12 \cdot 10^{+105}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right) + -9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 76.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -1.38 \cdot 10^{-45} \lor \neg \left(b \leq 3.7 \cdot 10^{-59} \lor \neg \left(b \leq 9.5 \cdot 10^{+70}\right) \land b \leq 8.5 \cdot 10^{+96}\right):\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
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 -1.38e-45)
         (not (or (<= b 3.7e-59) (and (not (<= b 9.5e+70)) (<= b 8.5e+96)))))
   (+ (* x 2.0) (* 27.0 (* a b)))
   (- (* x 2.0) (* 9.0 (* t (* z y))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.38e-45) || !((b <= 3.7e-59) || (!(b <= 9.5e+70) && (b <= 8.5e+96)))) {
		tmp = (x * 2.0) + (27.0 * (a * b));
	} 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.
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 <= (-1.38d-45)) .or. (.not. (b <= 3.7d-59) .or. (.not. (b <= 9.5d+70)) .and. (b <= 8.5d+96))) then
        tmp = (x * 2.0d0) + (27.0d0 * (a * b))
    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;
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 <= -1.38e-45) || !((b <= 3.7e-59) || (!(b <= 9.5e+70) && (b <= 8.5e+96)))) {
		tmp = (x * 2.0) + (27.0 * (a * b));
	} 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])
[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 <= -1.38e-45) or not ((b <= 3.7e-59) or (not (b <= 9.5e+70) and (b <= 8.5e+96))):
		tmp = (x * 2.0) + (27.0 * (a * b))
	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])
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 <= -1.38e-45) || !((b <= 3.7e-59) || (!(b <= 9.5e+70) && (b <= 8.5e+96))))
		tmp = Float64(Float64(x * 2.0) + Float64(27.0 * Float64(a * b)));
	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])){:}
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 <= -1.38e-45) || ~(((b <= 3.7e-59) || (~((b <= 9.5e+70)) && (b <= 8.5e+96)))))
		tmp = (x * 2.0) + (27.0 * (a * b));
	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.
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, -1.38e-45], N[Not[Or[LessEqual[b, 3.7e-59], And[N[Not[LessEqual[b, 9.5e+70]], $MachinePrecision], LessEqual[b, 8.5e+96]]]], $MachinePrecision]], N[(N[(x * 2.0), $MachinePrecision] + N[(27.0 * N[(a * b), $MachinePrecision]), $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 2 regimes

2. if b < -1.38e-45 or 3.6999999999999999e-59 < b < 9.5000000000000002e70 or 8.50000000000000025e96 < b

   1. Initial program 92.2%

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

      1. sub-neg 92.2%

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

      2. sub-neg 92.2%

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

      3. associate-*l* 93.0%

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

      4. associate-*l* 92.4%

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

   3. Simplified 92.4%

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

   5. Taylor expanded in y around 0 75.2%

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

   if -1.38e-45 < b < 3.6999999999999999e-59 or 9.5000000000000002e70 < b < 8.50000000000000025e96

   1. Initial program 95.7%

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

      1. sub-neg 95.7%

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

      2. sub-neg 95.7%

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

      3. associate-*l* 95.7%

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

      4. associate-*l* 96.5%

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

   3. Simplified 96.5%

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

   5. Taylor expanded in a around 0 86.2%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.38 \cdot 10^{-45} \lor \neg \left(b \leq 3.7 \cdot 10^{-59} \lor \neg \left(b \leq 9.5 \cdot 10^{+70}\right) \land b \leq 8.5 \cdot 10^{+96}\right):\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 76.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \mathbf{if}\;b \leq -7 \cdot 10^{-46}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 5 \cdot 10^{-59}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \mathbf{elif}\;b \leq 1.35 \cdot 10^{+17} \lor \neg \left(b \leq 3.8 \cdot 10^{+98}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* x 2.0) (* 27.0 (* a b)))))
   (if (<= b -7e-46)
     t_1
     (if (<= b 5e-59)
       (- (* x 2.0) (* 9.0 (* t (* z y))))
       (if (or (<= b 1.35e+17) (not (<= b 3.8e+98)))
         t_1
         (- (* x 2.0) (* 9.0 (* y (* z t)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * 2.0) + (27.0 * (a * b));
	double tmp;
	if (b <= -7e-46) {
		tmp = t_1;
	} else if (b <= 5e-59) {
		tmp = (x * 2.0) - (9.0 * (t * (z * y)));
	} else if ((b <= 1.35e+17) || !(b <= 3.8e+98)) {
		tmp = t_1;
	} else {
		tmp = (x * 2.0) - (9.0 * (y * (z * t)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * 2.0d0) + (27.0d0 * (a * b))
    if (b <= (-7d-46)) then
        tmp = t_1
    else if (b <= 5d-59) then
        tmp = (x * 2.0d0) - (9.0d0 * (t * (z * y)))
    else if ((b <= 1.35d+17) .or. (.not. (b <= 3.8d+98))) then
        tmp = t_1
    else
        tmp = (x * 2.0d0) - (9.0d0 * (y * (z * t)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * 2.0) + (27.0 * (a * b));
	double tmp;
	if (b <= -7e-46) {
		tmp = t_1;
	} else if (b <= 5e-59) {
		tmp = (x * 2.0) - (9.0 * (t * (z * y)));
	} else if ((b <= 1.35e+17) || !(b <= 3.8e+98)) {
		tmp = t_1;
	} else {
		tmp = (x * 2.0) - (9.0 * (y * (z * t)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = (x * 2.0) + (27.0 * (a * b))
	tmp = 0
	if b <= -7e-46:
		tmp = t_1
	elif b <= 5e-59:
		tmp = (x * 2.0) - (9.0 * (t * (z * y)))
	elif (b <= 1.35e+17) or not (b <= 3.8e+98):
		tmp = t_1
	else:
		tmp = (x * 2.0) - (9.0 * (y * (z * t)))
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * 2.0) + Float64(27.0 * Float64(a * b)))
	tmp = 0.0
	if (b <= -7e-46)
		tmp = t_1;
	elseif (b <= 5e-59)
		tmp = Float64(Float64(x * 2.0) - Float64(9.0 * Float64(t * Float64(z * y))));
	elseif ((b <= 1.35e+17) || !(b <= 3.8e+98))
		tmp = t_1;
	else
		tmp = Float64(Float64(x * 2.0) - Float64(9.0 * Float64(y * Float64(z * t))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * 2.0) + (27.0 * (a * b));
	tmp = 0.0;
	if (b <= -7e-46)
		tmp = t_1;
	elseif (b <= 5e-59)
		tmp = (x * 2.0) - (9.0 * (t * (z * y)));
	elseif ((b <= 1.35e+17) || ~((b <= 3.8e+98)))
		tmp = t_1;
	else
		tmp = (x * 2.0) - (9.0 * (y * (z * t)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * 2.0), $MachinePrecision] + N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -7e-46], t$95$1, If[LessEqual[b, 5e-59], N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(t * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[b, 1.35e+17], N[Not[LessEqual[b, 3.8e+98]], $MachinePrecision]], t$95$1, N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -7.0000000000000004e-46 or 5.0000000000000001e-59 < b < 1.35e17 or 3.7999999999999999e98 < b

   1. Initial program 92.4%

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

      1. sub-neg 92.4%

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

      2. sub-neg 92.4%

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

      3. associate-*l* 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* 93.3%

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

   3. Simplified 93.3%

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

   5. Taylor expanded in y around 0 76.2%

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

   if -7.0000000000000004e-46 < b < 5.0000000000000001e-59

   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* 95.5%

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

      4. associate-*l* 96.3%

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

   3. Simplified 96.3%

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

   5. Taylor expanded in a around 0 85.5%

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

   if 1.35e17 < b < 3.7999999999999999e98

   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* 87.7%

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

      4. associate-*l* 87.7%

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

   3. Simplified 87.7%

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

   5. Taylor expanded in a around 0 69.1%

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

      1. pow1 69.1%

         \[\leadsto 2 \cdot x - 9 \cdot \color{blue}{{\left(t \cdot \left(y \cdot z\right)\right)}^{1}} \]

   7. Applied egg-rr 69.1%

      \[\leadsto 2 \cdot x - 9 \cdot \color{blue}{{\left(t \cdot \left(y \cdot z\right)\right)}^{1}} \]
   8. Step-by-step derivation

      1. unpow1 69.1%

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

      2. *-commutative 69.1%

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

      3. associate-*l* 69.2%

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

      4. *-commutative 69.2%

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

   9. Simplified 69.2%

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

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7 \cdot 10^{-46}:\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;b \leq 5 \cdot 10^{-59}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \mathbf{elif}\;b \leq 1.35 \cdot 10^{+17} \lor \neg \left(b \leq 3.8 \cdot 10^{+98}\right):\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 47.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -4.1 \cdot 10^{+49}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{-196}:\\ \;\;\;\;\left(z \cdot t\right) \cdot \left(y \cdot -9\right)\\ \mathbf{elif}\;x \leq -2.9 \cdot 10^{-260}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;x \leq 2.75 \cdot 10^{-271}:\\ \;\;\;\;t \cdot \left(y \cdot \left(z \cdot -9\right)\right)\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{+19}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -4.1e+49)
   (* x 2.0)
   (if (<= x -2.5e-196)
     (* (* z t) (* y -9.0))
     (if (<= x -2.9e-260)
       (* a (* 27.0 b))
       (if (<= x 2.75e-271)
         (* t (* y (* z -9.0)))
         (if (<= x 2.2e+19) (* 27.0 (* a b)) (* x 2.0)))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -4.1e+49) {
		tmp = x * 2.0;
	} else if (x <= -2.5e-196) {
		tmp = (z * t) * (y * -9.0);
	} else if (x <= -2.9e-260) {
		tmp = a * (27.0 * b);
	} else if (x <= 2.75e-271) {
		tmp = t * (y * (z * -9.0));
	} else if (x <= 2.2e+19) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-4.1d+49)) then
        tmp = x * 2.0d0
    else if (x <= (-2.5d-196)) then
        tmp = (z * t) * (y * (-9.0d0))
    else if (x <= (-2.9d-260)) then
        tmp = a * (27.0d0 * b)
    else if (x <= 2.75d-271) then
        tmp = t * (y * (z * (-9.0d0)))
    else if (x <= 2.2d+19) then
        tmp = 27.0d0 * (a * b)
    else
        tmp = x * 2.0d0
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -4.1e+49) {
		tmp = x * 2.0;
	} else if (x <= -2.5e-196) {
		tmp = (z * t) * (y * -9.0);
	} else if (x <= -2.9e-260) {
		tmp = a * (27.0 * b);
	} else if (x <= 2.75e-271) {
		tmp = t * (y * (z * -9.0));
	} else if (x <= 2.2e+19) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -4.1e+49:
		tmp = x * 2.0
	elif x <= -2.5e-196:
		tmp = (z * t) * (y * -9.0)
	elif x <= -2.9e-260:
		tmp = a * (27.0 * b)
	elif x <= 2.75e-271:
		tmp = t * (y * (z * -9.0))
	elif x <= 2.2e+19:
		tmp = 27.0 * (a * b)
	else:
		tmp = x * 2.0
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -4.1e+49)
		tmp = Float64(x * 2.0);
	elseif (x <= -2.5e-196)
		tmp = Float64(Float64(z * t) * Float64(y * -9.0));
	elseif (x <= -2.9e-260)
		tmp = Float64(a * Float64(27.0 * b));
	elseif (x <= 2.75e-271)
		tmp = Float64(t * Float64(y * Float64(z * -9.0)));
	elseif (x <= 2.2e+19)
		tmp = Float64(27.0 * Float64(a * b));
	else
		tmp = Float64(x * 2.0);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -4.1e+49)
		tmp = x * 2.0;
	elseif (x <= -2.5e-196)
		tmp = (z * t) * (y * -9.0);
	elseif (x <= -2.9e-260)
		tmp = a * (27.0 * b);
	elseif (x <= 2.75e-271)
		tmp = t * (y * (z * -9.0));
	elseif (x <= 2.2e+19)
		tmp = 27.0 * (a * b);
	else
		tmp = x * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -4.1e+49], N[(x * 2.0), $MachinePrecision], If[LessEqual[x, -2.5e-196], N[(N[(z * t), $MachinePrecision] * N[(y * -9.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.9e-260], N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.75e-271], N[(t * N[(y * N[(z * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.2e+19], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], N[(x * 2.0), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -4.1e49 or 2.2e19 < x

   1. Initial program 96.1%

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

      1. sub-neg 96.1%

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

      2. sub-neg 96.1%

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

      3. associate-*l* 96.3%

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

      4. associate-*l* 95.4%

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

   3. Simplified 95.4%

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

   5. Taylor expanded in x around inf 58.5%

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

   if -4.1e49 < x < -2.5000000000000002e-196

   1. Initial program 92.1%

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

      1. sub-neg 92.1%

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

      2. sub-neg 92.1%

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

      3. associate-*l* 96.0%

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

      4. associate-*l* 95.9%

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

   3. Simplified 95.9%

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

      1. +-commutative 95.9%

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

      2. associate-+r- 95.9%

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

      3. associate-*r* 96.0%

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

      4. *-commutative 96.0%

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

      5. associate-*l* 95.9%

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

      6. associate-*l* 94.0%

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

      7. associate-*r* 94.0%

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

   6. Applied egg-rr 94.0%

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

      1. add-cube-cbrt 93.7%

         \[\leadsto \left(\color{blue}{\left(\sqrt[3]{27 \cdot \left(a \cdot b\right)} \cdot \sqrt[3]{27 \cdot \left(a \cdot b\right)}\right) \cdot \sqrt[3]{27 \cdot \left(a \cdot b\right)}} + x \cdot 2\right) - y \cdot \left(\left(9 \cdot z\right) \cdot t\right) \]

      2. pow3 93.7%

         \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{27 \cdot \left(a \cdot b\right)}\right)}^{3}} + x \cdot 2\right) - y \cdot \left(\left(9 \cdot z\right) \cdot t\right) \]

   8. Applied egg-rr 93.7%

      \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{27 \cdot \left(a \cdot b\right)}\right)}^{3}} + x \cdot 2\right) - y \cdot \left(\left(9 \cdot z\right) \cdot t\right) \]

   9. Taylor expanded in y around inf 55.3%

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

       1. *-commutative 55.3%

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

       2. associate-*r* 55.3%

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

       3. *-commutative 55.3%

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

       4. associate-*l* 53.4%

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

       5. *-commutative 53.4%

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

       6. associate-*l* 55.3%

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

       7. *-commutative 55.3%

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

       8. *-commutative 55.3%

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

   11. Simplified 55.3%

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

   if -2.5000000000000002e-196 < x < -2.8999999999999999e-260

   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* 90.8%

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

      4. associate-*l* 95.1%

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

   3. Simplified 95.1%

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

   5. Taylor expanded in a around inf 68.2%

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

      1. associate-*r* 63.8%

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

      2. *-commutative 63.8%

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

      3. associate-*r* 68.1%

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

   7. Simplified 68.1%

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

   if -2.8999999999999999e-260 < x < 2.7499999999999998e-271

   1. Initial program 91.1%

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

      1. sub-neg 91.1%

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

      2. sub-neg 91.1%

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

      3. associate-*l* 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* 90.7%

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

   3. Simplified 90.7%

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

      1. +-commutative 90.7%

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

      2. associate-+r- 90.7%

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

      3. associate-*r* 90.6%

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

      4. *-commutative 90.6%

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

      5. associate-*l* 90.7%

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

      6. associate-*l* 90.5%

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

      7. associate-*r* 90.4%

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

   6. Applied egg-rr 90.4%

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

   7. Taylor expanded in y around inf 58.8%

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

      1. associate-*r* 58.9%

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

      2. *-commutative 58.9%

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

      3. associate-*r* 58.8%

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

      4. *-commutative 58.8%

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

      5. associate-*r* 58.8%

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

   9. Simplified 58.8%

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

   if 2.7499999999999998e-271 < x < 2.2e19

   1. Initial program 91.4%

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

      1. sub-neg 91.4%

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

      2. sub-neg 91.4%

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

      3. associate-*l* 91.7%

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

      4. associate-*l* 91.8%

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

   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

   5. Taylor expanded in a around inf 56.0%

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 58.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.1 \cdot 10^{+49}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{-196}:\\ \;\;\;\;\left(z \cdot t\right) \cdot \left(y \cdot -9\right)\\ \mathbf{elif}\;x \leq -2.9 \cdot 10^{-260}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;x \leq 2.75 \cdot 10^{-271}:\\ \;\;\;\;t \cdot \left(y \cdot \left(z \cdot -9\right)\right)\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{+19}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 47.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -8.4 \cdot 10^{+49}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \leq -1.22 \cdot 10^{-194}:\\ \;\;\;\;y \cdot \left(z \cdot \left(t \cdot -9\right)\right)\\ \mathbf{elif}\;x \leq -9.8 \cdot 10^{-261}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-271}:\\ \;\;\;\;t \cdot \left(y \cdot \left(z \cdot -9\right)\right)\\ \mathbf{elif}\;x \leq 10^{+20}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -8.4e+49)
   (* x 2.0)
   (if (<= x -1.22e-194)
     (* y (* z (* t -9.0)))
     (if (<= x -9.8e-261)
       (* a (* 27.0 b))
       (if (<= x 5.8e-271)
         (* t (* y (* z -9.0)))
         (if (<= x 1e+20) (* 27.0 (* a b)) (* x 2.0)))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -8.4e+49) {
		tmp = x * 2.0;
	} else if (x <= -1.22e-194) {
		tmp = y * (z * (t * -9.0));
	} else if (x <= -9.8e-261) {
		tmp = a * (27.0 * b);
	} else if (x <= 5.8e-271) {
		tmp = t * (y * (z * -9.0));
	} else if (x <= 1e+20) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-8.4d+49)) then
        tmp = x * 2.0d0
    else if (x <= (-1.22d-194)) then
        tmp = y * (z * (t * (-9.0d0)))
    else if (x <= (-9.8d-261)) then
        tmp = a * (27.0d0 * b)
    else if (x <= 5.8d-271) then
        tmp = t * (y * (z * (-9.0d0)))
    else if (x <= 1d+20) then
        tmp = 27.0d0 * (a * b)
    else
        tmp = x * 2.0d0
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -8.4e+49) {
		tmp = x * 2.0;
	} else if (x <= -1.22e-194) {
		tmp = y * (z * (t * -9.0));
	} else if (x <= -9.8e-261) {
		tmp = a * (27.0 * b);
	} else if (x <= 5.8e-271) {
		tmp = t * (y * (z * -9.0));
	} else if (x <= 1e+20) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -8.4e+49:
		tmp = x * 2.0
	elif x <= -1.22e-194:
		tmp = y * (z * (t * -9.0))
	elif x <= -9.8e-261:
		tmp = a * (27.0 * b)
	elif x <= 5.8e-271:
		tmp = t * (y * (z * -9.0))
	elif x <= 1e+20:
		tmp = 27.0 * (a * b)
	else:
		tmp = x * 2.0
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -8.4e+49)
		tmp = Float64(x * 2.0);
	elseif (x <= -1.22e-194)
		tmp = Float64(y * Float64(z * Float64(t * -9.0)));
	elseif (x <= -9.8e-261)
		tmp = Float64(a * Float64(27.0 * b));
	elseif (x <= 5.8e-271)
		tmp = Float64(t * Float64(y * Float64(z * -9.0)));
	elseif (x <= 1e+20)
		tmp = Float64(27.0 * Float64(a * b));
	else
		tmp = Float64(x * 2.0);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -8.4e+49)
		tmp = x * 2.0;
	elseif (x <= -1.22e-194)
		tmp = y * (z * (t * -9.0));
	elseif (x <= -9.8e-261)
		tmp = a * (27.0 * b);
	elseif (x <= 5.8e-271)
		tmp = t * (y * (z * -9.0));
	elseif (x <= 1e+20)
		tmp = 27.0 * (a * b);
	else
		tmp = x * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -8.4e+49], N[(x * 2.0), $MachinePrecision], If[LessEqual[x, -1.22e-194], N[(y * N[(z * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -9.8e-261], N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.8e-271], N[(t * N[(y * N[(z * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1e+20], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], N[(x * 2.0), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -8.40000000000000043e49 or 1e20 < x

   1. Initial program 96.1%

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

      1. sub-neg 96.1%

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

      2. sub-neg 96.1%

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

      3. associate-*l* 96.3%

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

      4. associate-*l* 95.4%

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

   3. Simplified 95.4%

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

   5. Taylor expanded in x around inf 58.5%

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

   if -8.40000000000000043e49 < x < -1.2200000000000001e-194

   1. Initial program 92.1%

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

      1. sub-neg 92.1%

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

      2. sub-neg 92.1%

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

      3. associate-*l* 96.0%

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

      4. associate-*l* 95.9%

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

   3. Simplified 95.9%

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

   5. Taylor expanded in y around inf 91.9%

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

   6. Taylor expanded in y around inf 53.4%

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

      1. *-commutative 53.4%

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

      2. *-commutative 53.4%

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

      3. associate-*l* 53.4%

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

   8. Simplified 53.4%

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

   if -1.2200000000000001e-194 < x < -9.80000000000000009e-261

   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* 90.8%

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

      4. associate-*l* 95.1%

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

   3. Simplified 95.1%

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

   5. Taylor expanded in a around inf 68.2%

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

      1. associate-*r* 63.8%

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

      2. *-commutative 63.8%

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

      3. associate-*r* 68.1%

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

   7. Simplified 68.1%

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

   if -9.80000000000000009e-261 < x < 5.80000000000000028e-271

   1. Initial program 91.1%

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

      1. sub-neg 91.1%

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

      2. sub-neg 91.1%

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

      3. associate-*l* 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* 90.7%

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

   3. Simplified 90.7%

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

      1. +-commutative 90.7%

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

      2. associate-+r- 90.7%

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

      3. associate-*r* 90.6%

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

      4. *-commutative 90.6%

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

      5. associate-*l* 90.7%

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

      6. associate-*l* 90.5%

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

      7. associate-*r* 90.4%

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

   6. Applied egg-rr 90.4%

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

   7. Taylor expanded in y around inf 58.8%

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

      1. associate-*r* 58.9%

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

      2. *-commutative 58.9%

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

      3. associate-*r* 58.8%

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

      4. *-commutative 58.8%

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

      5. associate-*r* 58.8%

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

   9. Simplified 58.8%

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

   if 5.80000000000000028e-271 < x < 1e20

   1. Initial program 91.4%

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

      1. sub-neg 91.4%

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

      2. sub-neg 91.4%

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

      3. associate-*l* 91.7%

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

      4. associate-*l* 91.8%

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

   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

   5. Taylor expanded in a around inf 56.0%

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 57.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.4 \cdot 10^{+49}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \leq -1.22 \cdot 10^{-194}:\\ \;\;\;\;y \cdot \left(z \cdot \left(t \cdot -9\right)\right)\\ \mathbf{elif}\;x \leq -9.8 \cdot 10^{-261}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-271}:\\ \;\;\;\;t \cdot \left(y \cdot \left(z \cdot -9\right)\right)\\ \mathbf{elif}\;x \leq 10^{+20}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 47.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -9.8 \cdot 10^{+48}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \leq -3 \cdot 10^{-195}:\\ \;\;\;\;y \cdot \left(t \cdot \left(z \cdot -9\right)\right)\\ \mathbf{elif}\;x \leq -2.05 \cdot 10^{-260}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;x \leq 2.18 \cdot 10^{-271}:\\ \;\;\;\;t \cdot \left(y \cdot \left(z \cdot -9\right)\right)\\ \mathbf{elif}\;x \leq 2.65 \cdot 10^{+17}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -9.8e+48)
   (* x 2.0)
   (if (<= x -3e-195)
     (* y (* t (* z -9.0)))
     (if (<= x -2.05e-260)
       (* a (* 27.0 b))
       (if (<= x 2.18e-271)
         (* t (* y (* z -9.0)))
         (if (<= x 2.65e+17) (* 27.0 (* a b)) (* x 2.0)))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -9.8e+48) {
		tmp = x * 2.0;
	} else if (x <= -3e-195) {
		tmp = y * (t * (z * -9.0));
	} else if (x <= -2.05e-260) {
		tmp = a * (27.0 * b);
	} else if (x <= 2.18e-271) {
		tmp = t * (y * (z * -9.0));
	} else if (x <= 2.65e+17) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-9.8d+48)) then
        tmp = x * 2.0d0
    else if (x <= (-3d-195)) then
        tmp = y * (t * (z * (-9.0d0)))
    else if (x <= (-2.05d-260)) then
        tmp = a * (27.0d0 * b)
    else if (x <= 2.18d-271) then
        tmp = t * (y * (z * (-9.0d0)))
    else if (x <= 2.65d+17) then
        tmp = 27.0d0 * (a * b)
    else
        tmp = x * 2.0d0
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -9.8e+48) {
		tmp = x * 2.0;
	} else if (x <= -3e-195) {
		tmp = y * (t * (z * -9.0));
	} else if (x <= -2.05e-260) {
		tmp = a * (27.0 * b);
	} else if (x <= 2.18e-271) {
		tmp = t * (y * (z * -9.0));
	} else if (x <= 2.65e+17) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -9.8e+48:
		tmp = x * 2.0
	elif x <= -3e-195:
		tmp = y * (t * (z * -9.0))
	elif x <= -2.05e-260:
		tmp = a * (27.0 * b)
	elif x <= 2.18e-271:
		tmp = t * (y * (z * -9.0))
	elif x <= 2.65e+17:
		tmp = 27.0 * (a * b)
	else:
		tmp = x * 2.0
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -9.8e+48)
		tmp = Float64(x * 2.0);
	elseif (x <= -3e-195)
		tmp = Float64(y * Float64(t * Float64(z * -9.0)));
	elseif (x <= -2.05e-260)
		tmp = Float64(a * Float64(27.0 * b));
	elseif (x <= 2.18e-271)
		tmp = Float64(t * Float64(y * Float64(z * -9.0)));
	elseif (x <= 2.65e+17)
		tmp = Float64(27.0 * Float64(a * b));
	else
		tmp = Float64(x * 2.0);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -9.8e+48)
		tmp = x * 2.0;
	elseif (x <= -3e-195)
		tmp = y * (t * (z * -9.0));
	elseif (x <= -2.05e-260)
		tmp = a * (27.0 * b);
	elseif (x <= 2.18e-271)
		tmp = t * (y * (z * -9.0));
	elseif (x <= 2.65e+17)
		tmp = 27.0 * (a * b);
	else
		tmp = x * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -9.8e+48], N[(x * 2.0), $MachinePrecision], If[LessEqual[x, -3e-195], N[(y * N[(t * N[(z * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.05e-260], N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.18e-271], N[(t * N[(y * N[(z * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.65e+17], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], N[(x * 2.0), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -9.80000000000000059e48 or 2.65e17 < x

   1. Initial program 96.1%

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

      1. sub-neg 96.1%

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

      2. sub-neg 96.1%

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

      3. associate-*l* 96.3%

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

      4. associate-*l* 95.4%

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

   3. Simplified 95.4%

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

   5. Taylor expanded in x around inf 58.5%

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

   if -9.80000000000000059e48 < x < -3e-195

   1. Initial program 92.1%

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

      1. sub-neg 92.1%

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

      2. sub-neg 92.1%

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

      3. associate-*l* 96.0%

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

      4. associate-*l* 95.9%

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

   3. Simplified 95.9%

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

   5. Taylor expanded in y around inf 91.9%

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

   6. Taylor expanded in y around inf 53.4%

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

      1. *-commutative 53.4%

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

      2. *-commutative 53.4%

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

      3. associate-*l* 53.4%

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

   8. Simplified 53.4%

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

   9. Taylor expanded in z around 0 53.4%

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

       1. *-commutative 53.4%

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

       2. associate-*l* 53.4%

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

   11. Simplified 53.4%

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

   if -3e-195 < x < -2.04999999999999998e-260

   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* 90.8%

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

      4. associate-*l* 95.1%

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

   3. Simplified 95.1%

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

   5. Taylor expanded in a around inf 68.2%

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

      1. associate-*r* 63.8%

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

      2. *-commutative 63.8%

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

      3. associate-*r* 68.1%

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

   7. Simplified 68.1%

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

   if -2.04999999999999998e-260 < x < 2.1800000000000001e-271

   1. Initial program 91.1%

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

      1. sub-neg 91.1%

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

      2. sub-neg 91.1%

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

      3. associate-*l* 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* 90.7%

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

   3. Simplified 90.7%

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

      1. +-commutative 90.7%

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

      2. associate-+r- 90.7%

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

      3. associate-*r* 90.6%

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

      4. *-commutative 90.6%

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

      5. associate-*l* 90.7%

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

      6. associate-*l* 90.5%

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

      7. associate-*r* 90.4%

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

   6. Applied egg-rr 90.4%

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

   7. Taylor expanded in y around inf 58.8%

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

      1. associate-*r* 58.9%

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

      2. *-commutative 58.9%

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

      3. associate-*r* 58.8%

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

      4. *-commutative 58.8%

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

      5. associate-*r* 58.8%

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

   9. Simplified 58.8%

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

   if 2.1800000000000001e-271 < x < 2.65e17

   1. Initial program 91.4%

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

      1. sub-neg 91.4%

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

      2. sub-neg 91.4%

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

      3. associate-*l* 91.7%

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

      4. associate-*l* 91.8%

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

   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

   5. Taylor expanded in a around inf 56.0%

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 57.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.8 \cdot 10^{+48}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \leq -3 \cdot 10^{-195}:\\ \;\;\;\;y \cdot \left(t \cdot \left(z \cdot -9\right)\right)\\ \mathbf{elif}\;x \leq -2.05 \cdot 10^{-260}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;x \leq 2.18 \cdot 10^{-271}:\\ \;\;\;\;t \cdot \left(y \cdot \left(z \cdot -9\right)\right)\\ \mathbf{elif}\;x \leq 2.65 \cdot 10^{+17}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 47.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+49}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \leq -1.45 \cdot 10^{-195}:\\ \;\;\;\;y \cdot \left(-9 \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;x \leq -3.1 \cdot 10^{-260}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;x \leq 2.15 \cdot 10^{-271}:\\ \;\;\;\;t \cdot \left(y \cdot \left(z \cdot -9\right)\right)\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+18}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -2.5e+49)
   (* x 2.0)
   (if (<= x -1.45e-195)
     (* y (* -9.0 (* z t)))
     (if (<= x -3.1e-260)
       (* a (* 27.0 b))
       (if (<= x 2.15e-271)
         (* t (* y (* z -9.0)))
         (if (<= x 2.6e+18) (* 27.0 (* a b)) (* x 2.0)))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -2.5e+49) {
		tmp = x * 2.0;
	} else if (x <= -1.45e-195) {
		tmp = y * (-9.0 * (z * t));
	} else if (x <= -3.1e-260) {
		tmp = a * (27.0 * b);
	} else if (x <= 2.15e-271) {
		tmp = t * (y * (z * -9.0));
	} else if (x <= 2.6e+18) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-2.5d+49)) then
        tmp = x * 2.0d0
    else if (x <= (-1.45d-195)) then
        tmp = y * ((-9.0d0) * (z * t))
    else if (x <= (-3.1d-260)) then
        tmp = a * (27.0d0 * b)
    else if (x <= 2.15d-271) then
        tmp = t * (y * (z * (-9.0d0)))
    else if (x <= 2.6d+18) then
        tmp = 27.0d0 * (a * b)
    else
        tmp = x * 2.0d0
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -2.5e+49) {
		tmp = x * 2.0;
	} else if (x <= -1.45e-195) {
		tmp = y * (-9.0 * (z * t));
	} else if (x <= -3.1e-260) {
		tmp = a * (27.0 * b);
	} else if (x <= 2.15e-271) {
		tmp = t * (y * (z * -9.0));
	} else if (x <= 2.6e+18) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -2.5e+49:
		tmp = x * 2.0
	elif x <= -1.45e-195:
		tmp = y * (-9.0 * (z * t))
	elif x <= -3.1e-260:
		tmp = a * (27.0 * b)
	elif x <= 2.15e-271:
		tmp = t * (y * (z * -9.0))
	elif x <= 2.6e+18:
		tmp = 27.0 * (a * b)
	else:
		tmp = x * 2.0
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -2.5e+49)
		tmp = Float64(x * 2.0);
	elseif (x <= -1.45e-195)
		tmp = Float64(y * Float64(-9.0 * Float64(z * t)));
	elseif (x <= -3.1e-260)
		tmp = Float64(a * Float64(27.0 * b));
	elseif (x <= 2.15e-271)
		tmp = Float64(t * Float64(y * Float64(z * -9.0)));
	elseif (x <= 2.6e+18)
		tmp = Float64(27.0 * Float64(a * b));
	else
		tmp = Float64(x * 2.0);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -2.5e+49)
		tmp = x * 2.0;
	elseif (x <= -1.45e-195)
		tmp = y * (-9.0 * (z * t));
	elseif (x <= -3.1e-260)
		tmp = a * (27.0 * b);
	elseif (x <= 2.15e-271)
		tmp = t * (y * (z * -9.0));
	elseif (x <= 2.6e+18)
		tmp = 27.0 * (a * b);
	else
		tmp = x * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -2.5e+49], N[(x * 2.0), $MachinePrecision], If[LessEqual[x, -1.45e-195], N[(y * N[(-9.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3.1e-260], N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.15e-271], N[(t * N[(y * N[(z * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.6e+18], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], N[(x * 2.0), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -2.5000000000000002e49 or 2.6e18 < x

   1. Initial program 96.1%

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

      1. sub-neg 96.1%

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

      2. sub-neg 96.1%

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

      3. associate-*l* 96.3%

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

      4. associate-*l* 95.4%

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

   3. Simplified 95.4%

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

   5. Taylor expanded in x around inf 58.5%

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

   if -2.5000000000000002e49 < x < -1.4500000000000001e-195

   1. Initial program 92.1%

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

      1. sub-neg 92.1%

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

      2. sub-neg 92.1%

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

      3. associate-*l* 96.0%

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

      4. associate-*l* 95.9%

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

   3. Simplified 95.9%

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

   5. Taylor expanded in y around inf 91.9%

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

   6. Taylor expanded in y around inf 53.4%

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

   if -1.4500000000000001e-195 < x < -3.09999999999999983e-260

   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* 90.8%

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

      4. associate-*l* 95.1%

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

   3. Simplified 95.1%

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

   5. Taylor expanded in a around inf 68.2%

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

      1. associate-*r* 63.8%

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

      2. *-commutative 63.8%

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

      3. associate-*r* 68.1%

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

   7. Simplified 68.1%

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

   if -3.09999999999999983e-260 < x < 2.15e-271

   1. Initial program 91.1%

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

      1. sub-neg 91.1%

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

      2. sub-neg 91.1%

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

      3. associate-*l* 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* 90.7%

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

   3. Simplified 90.7%

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

      1. +-commutative 90.7%

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

      2. associate-+r- 90.7%

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

      3. associate-*r* 90.6%

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

      4. *-commutative 90.6%

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

      5. associate-*l* 90.7%

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

      6. associate-*l* 90.5%

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

      7. associate-*r* 90.4%

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

   6. Applied egg-rr 90.4%

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

   7. Taylor expanded in y around inf 58.8%

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

      1. associate-*r* 58.9%

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

      2. *-commutative 58.9%

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

      3. associate-*r* 58.8%

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

      4. *-commutative 58.8%

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

      5. associate-*r* 58.8%

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

   9. Simplified 58.8%

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

   if 2.15e-271 < x < 2.6e18

   1. Initial program 91.4%

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

      1. sub-neg 91.4%

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

      2. sub-neg 91.4%

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

      3. associate-*l* 91.7%

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

      4. associate-*l* 91.8%

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

   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

   5. Taylor expanded in a around inf 56.0%

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 57.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+49}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \leq -1.45 \cdot 10^{-195}:\\ \;\;\;\;y \cdot \left(-9 \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;x \leq -3.1 \cdot 10^{-260}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;x \leq 2.15 \cdot 10^{-271}:\\ \;\;\;\;t \cdot \left(y \cdot \left(z \cdot -9\right)\right)\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+18}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 47.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.95 \cdot 10^{+48}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \leq -1.05 \cdot 10^{-194}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \mathbf{elif}\;x \leq -2.8 \cdot 10^{-260}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{-271}:\\ \;\;\;\;t \cdot \left(y \cdot \left(z \cdot -9\right)\right)\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{+18}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -1.95e+48)
   (* x 2.0)
   (if (<= x -1.05e-194)
     (* -9.0 (* t (* z y)))
     (if (<= x -2.8e-260)
       (* a (* 27.0 b))
       (if (<= x 4.6e-271)
         (* t (* y (* z -9.0)))
         (if (<= x 4.5e+18) (* 27.0 (* a b)) (* x 2.0)))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.95e+48) {
		tmp = x * 2.0;
	} else if (x <= -1.05e-194) {
		tmp = -9.0 * (t * (z * y));
	} else if (x <= -2.8e-260) {
		tmp = a * (27.0 * b);
	} else if (x <= 4.6e-271) {
		tmp = t * (y * (z * -9.0));
	} else if (x <= 4.5e+18) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-1.95d+48)) then
        tmp = x * 2.0d0
    else if (x <= (-1.05d-194)) then
        tmp = (-9.0d0) * (t * (z * y))
    else if (x <= (-2.8d-260)) then
        tmp = a * (27.0d0 * b)
    else if (x <= 4.6d-271) then
        tmp = t * (y * (z * (-9.0d0)))
    else if (x <= 4.5d+18) then
        tmp = 27.0d0 * (a * b)
    else
        tmp = x * 2.0d0
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.95e+48) {
		tmp = x * 2.0;
	} else if (x <= -1.05e-194) {
		tmp = -9.0 * (t * (z * y));
	} else if (x <= -2.8e-260) {
		tmp = a * (27.0 * b);
	} else if (x <= 4.6e-271) {
		tmp = t * (y * (z * -9.0));
	} else if (x <= 4.5e+18) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -1.95e+48:
		tmp = x * 2.0
	elif x <= -1.05e-194:
		tmp = -9.0 * (t * (z * y))
	elif x <= -2.8e-260:
		tmp = a * (27.0 * b)
	elif x <= 4.6e-271:
		tmp = t * (y * (z * -9.0))
	elif x <= 4.5e+18:
		tmp = 27.0 * (a * b)
	else:
		tmp = x * 2.0
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -1.95e+48)
		tmp = Float64(x * 2.0);
	elseif (x <= -1.05e-194)
		tmp = Float64(-9.0 * Float64(t * Float64(z * y)));
	elseif (x <= -2.8e-260)
		tmp = Float64(a * Float64(27.0 * b));
	elseif (x <= 4.6e-271)
		tmp = Float64(t * Float64(y * Float64(z * -9.0)));
	elseif (x <= 4.5e+18)
		tmp = Float64(27.0 * Float64(a * b));
	else
		tmp = Float64(x * 2.0);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -1.95e+48)
		tmp = x * 2.0;
	elseif (x <= -1.05e-194)
		tmp = -9.0 * (t * (z * y));
	elseif (x <= -2.8e-260)
		tmp = a * (27.0 * b);
	elseif (x <= 4.6e-271)
		tmp = t * (y * (z * -9.0));
	elseif (x <= 4.5e+18)
		tmp = 27.0 * (a * b);
	else
		tmp = x * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -1.95e+48], N[(x * 2.0), $MachinePrecision], If[LessEqual[x, -1.05e-194], N[(-9.0 * N[(t * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.8e-260], N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.6e-271], N[(t * N[(y * N[(z * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.5e+18], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], N[(x * 2.0), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -1.95e48 or 4.5e18 < x

   1. Initial program 96.1%

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

      1. sub-neg 96.1%

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

      2. sub-neg 96.1%

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

      3. associate-*l* 96.3%

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

      4. associate-*l* 95.4%

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

   3. Simplified 95.4%

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

   5. Taylor expanded in x around inf 58.5%

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

   if -1.95e48 < x < -1.05e-194

   1. Initial program 92.1%

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

      1. sub-neg 92.1%

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

      2. sub-neg 92.1%

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

      3. associate-*l* 96.0%

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

      4. associate-*l* 95.9%

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

   3. Simplified 95.9%

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

   5. Taylor expanded in y around inf 55.3%

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

   if -1.05e-194 < x < -2.7999999999999998e-260

   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* 90.8%

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

      4. associate-*l* 95.1%

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

   3. Simplified 95.1%

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

   5. Taylor expanded in a around inf 68.2%

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

      1. associate-*r* 63.8%

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

      2. *-commutative 63.8%

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

      3. associate-*r* 68.1%

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

   7. Simplified 68.1%

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

   if -2.7999999999999998e-260 < x < 4.60000000000000017e-271

   1. Initial program 91.1%

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

      1. sub-neg 91.1%

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

      2. sub-neg 91.1%

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

      3. associate-*l* 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* 90.7%

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

   3. Simplified 90.7%

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

      1. +-commutative 90.7%

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

      2. associate-+r- 90.7%

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

      3. associate-*r* 90.6%

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

      4. *-commutative 90.6%

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

      5. associate-*l* 90.7%

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

      6. associate-*l* 90.5%

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

      7. associate-*r* 90.4%

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

   6. Applied egg-rr 90.4%

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

   7. Taylor expanded in y around inf 58.8%

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

      1. associate-*r* 58.9%

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

      2. *-commutative 58.9%

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

      3. associate-*r* 58.8%

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

      4. *-commutative 58.8%

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

      5. associate-*r* 58.8%

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

   9. Simplified 58.8%

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

   if 4.60000000000000017e-271 < x < 4.5e18

   1. Initial program 91.4%

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

      1. sub-neg 91.4%

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

      2. sub-neg 91.4%

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

      3. associate-*l* 91.7%

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

      4. associate-*l* 91.8%

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

   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

   5. Taylor expanded in a around inf 56.0%

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 58.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.95 \cdot 10^{+48}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \leq -1.05 \cdot 10^{-194}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \mathbf{elif}\;x \leq -2.8 \cdot 10^{-260}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{-271}:\\ \;\;\;\;t \cdot \left(y \cdot \left(z \cdot -9\right)\right)\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{+18}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 47.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := -9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \mathbf{if}\;x \leq -2.65 \cdot 10^{+48}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \leq -3.1 \cdot 10^{-196}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -9.5 \cdot 10^{-261}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;x \leq 9.8 \cdot 10^{-271}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{+18}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* -9.0 (* t (* z y)))))
   (if (<= x -2.65e+48)
     (* x 2.0)
     (if (<= x -3.1e-196)
       t_1
       (if (<= x -9.5e-261)
         (* a (* 27.0 b))
         (if (<= x 9.8e-271)
           t_1
           (if (<= x 1.75e+18) (* 27.0 (* a b)) (* x 2.0))))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -9.0 * (t * (z * y));
	double tmp;
	if (x <= -2.65e+48) {
		tmp = x * 2.0;
	} else if (x <= -3.1e-196) {
		tmp = t_1;
	} else if (x <= -9.5e-261) {
		tmp = a * (27.0 * b);
	} else if (x <= 9.8e-271) {
		tmp = t_1;
	} else if (x <= 1.75e+18) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-9.0d0) * (t * (z * y))
    if (x <= (-2.65d+48)) then
        tmp = x * 2.0d0
    else if (x <= (-3.1d-196)) then
        tmp = t_1
    else if (x <= (-9.5d-261)) then
        tmp = a * (27.0d0 * b)
    else if (x <= 9.8d-271) then
        tmp = t_1
    else if (x <= 1.75d+18) then
        tmp = 27.0d0 * (a * b)
    else
        tmp = x * 2.0d0
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -9.0 * (t * (z * y));
	double tmp;
	if (x <= -2.65e+48) {
		tmp = x * 2.0;
	} else if (x <= -3.1e-196) {
		tmp = t_1;
	} else if (x <= -9.5e-261) {
		tmp = a * (27.0 * b);
	} else if (x <= 9.8e-271) {
		tmp = t_1;
	} else if (x <= 1.75e+18) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = -9.0 * (t * (z * y))
	tmp = 0
	if x <= -2.65e+48:
		tmp = x * 2.0
	elif x <= -3.1e-196:
		tmp = t_1
	elif x <= -9.5e-261:
		tmp = a * (27.0 * b)
	elif x <= 9.8e-271:
		tmp = t_1
	elif x <= 1.75e+18:
		tmp = 27.0 * (a * b)
	else:
		tmp = x * 2.0
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(-9.0 * Float64(t * Float64(z * y)))
	tmp = 0.0
	if (x <= -2.65e+48)
		tmp = Float64(x * 2.0);
	elseif (x <= -3.1e-196)
		tmp = t_1;
	elseif (x <= -9.5e-261)
		tmp = Float64(a * Float64(27.0 * b));
	elseif (x <= 9.8e-271)
		tmp = t_1;
	elseif (x <= 1.75e+18)
		tmp = Float64(27.0 * Float64(a * b));
	else
		tmp = Float64(x * 2.0);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = -9.0 * (t * (z * y));
	tmp = 0.0;
	if (x <= -2.65e+48)
		tmp = x * 2.0;
	elseif (x <= -3.1e-196)
		tmp = t_1;
	elseif (x <= -9.5e-261)
		tmp = a * (27.0 * b);
	elseif (x <= 9.8e-271)
		tmp = t_1;
	elseif (x <= 1.75e+18)
		tmp = 27.0 * (a * b);
	else
		tmp = x * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(-9.0 * N[(t * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.65e+48], N[(x * 2.0), $MachinePrecision], If[LessEqual[x, -3.1e-196], t$95$1, If[LessEqual[x, -9.5e-261], N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9.8e-271], t$95$1, If[LessEqual[x, 1.75e+18], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], N[(x * 2.0), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.65e48 or 1.75e18 < x

   1. Initial program 96.1%

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

      1. sub-neg 96.1%

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

      2. sub-neg 96.1%

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

      3. associate-*l* 96.3%

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

      4. associate-*l* 95.4%

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

   3. Simplified 95.4%

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

   5. Taylor expanded in x around inf 58.5%

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

   if -2.65e48 < x < -3.09999999999999993e-196 or -9.5000000000000008e-261 < x < 9.8000000000000007e-271

   1. Initial program 91.8%

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

      1. sub-neg 91.8%

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

      2. sub-neg 91.8%

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

      3. associate-*l* 94.3%

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

      4. associate-*l* 94.3%

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

   3. Simplified 94.3%

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

   5. Taylor expanded in y around inf 56.4%

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

   if -3.09999999999999993e-196 < x < -9.5000000000000008e-261

   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* 90.8%

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

      4. associate-*l* 95.1%

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

   3. Simplified 95.1%

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

   5. Taylor expanded in a around inf 68.2%

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

      1. associate-*r* 63.8%

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

      2. *-commutative 63.8%

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

      3. associate-*r* 68.1%

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

   7. Simplified 68.1%

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

   if 9.8000000000000007e-271 < x < 1.75e18

   1. Initial program 91.4%

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

      1. sub-neg 91.4%

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

      2. sub-neg 91.4%

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

      3. associate-*l* 91.7%

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

      4. associate-*l* 91.8%

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

   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

   5. Taylor expanded in a around inf 56.0%

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

4. Final simplification 58.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.65 \cdot 10^{+48}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \leq -3.1 \cdot 10^{-196}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \mathbf{elif}\;x \leq -9.5 \cdot 10^{-261}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;x \leq 9.8 \cdot 10^{-271}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{+18}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 80.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := t \cdot \left(z \cdot y\right)\\ \mathbf{if}\;z \leq -6.8 \cdot 10^{-12}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right) + -9 \cdot \left(z \cdot \left(y \cdot t\right)\right)\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-131}:\\ \;\;\;\;x \cdot 2 - 9 \cdot t\_1\\ \mathbf{elif}\;z \leq 7.7 \cdot 10^{-50}:\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right) + -9 \cdot t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (* z y))))
   (if (<= z -6.8e-12)
     (+ (* a (* 27.0 b)) (* -9.0 (* z (* y t))))
     (if (<= z -1.2e-131)
       (- (* x 2.0) (* 9.0 t_1))
       (if (<= z 7.7e-50)
         (+ (* x 2.0) (* 27.0 (* a b)))
         (+ (* b (* a 27.0)) (* -9.0 t_1)))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (z * y);
	double tmp;
	if (z <= -6.8e-12) {
		tmp = (a * (27.0 * b)) + (-9.0 * (z * (y * t)));
	} else if (z <= -1.2e-131) {
		tmp = (x * 2.0) - (9.0 * t_1);
	} else if (z <= 7.7e-50) {
		tmp = (x * 2.0) + (27.0 * (a * b));
	} else {
		tmp = (b * (a * 27.0)) + (-9.0 * t_1);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (z * y)
    if (z <= (-6.8d-12)) then
        tmp = (a * (27.0d0 * b)) + ((-9.0d0) * (z * (y * t)))
    else if (z <= (-1.2d-131)) then
        tmp = (x * 2.0d0) - (9.0d0 * t_1)
    else if (z <= 7.7d-50) then
        tmp = (x * 2.0d0) + (27.0d0 * (a * b))
    else
        tmp = (b * (a * 27.0d0)) + ((-9.0d0) * t_1)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (z * y);
	double tmp;
	if (z <= -6.8e-12) {
		tmp = (a * (27.0 * b)) + (-9.0 * (z * (y * t)));
	} else if (z <= -1.2e-131) {
		tmp = (x * 2.0) - (9.0 * t_1);
	} else if (z <= 7.7e-50) {
		tmp = (x * 2.0) + (27.0 * (a * b));
	} else {
		tmp = (b * (a * 27.0)) + (-9.0 * t_1);
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = t * (z * y)
	tmp = 0
	if z <= -6.8e-12:
		tmp = (a * (27.0 * b)) + (-9.0 * (z * (y * t)))
	elif z <= -1.2e-131:
		tmp = (x * 2.0) - (9.0 * t_1)
	elif z <= 7.7e-50:
		tmp = (x * 2.0) + (27.0 * (a * b))
	else:
		tmp = (b * (a * 27.0)) + (-9.0 * t_1)
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(z * y))
	tmp = 0.0
	if (z <= -6.8e-12)
		tmp = Float64(Float64(a * Float64(27.0 * b)) + Float64(-9.0 * Float64(z * Float64(y * t))));
	elseif (z <= -1.2e-131)
		tmp = Float64(Float64(x * 2.0) - Float64(9.0 * t_1));
	elseif (z <= 7.7e-50)
		tmp = Float64(Float64(x * 2.0) + Float64(27.0 * Float64(a * b)));
	else
		tmp = Float64(Float64(b * Float64(a * 27.0)) + Float64(-9.0 * t_1));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (z * y);
	tmp = 0.0;
	if (z <= -6.8e-12)
		tmp = (a * (27.0 * b)) + (-9.0 * (z * (y * t)));
	elseif (z <= -1.2e-131)
		tmp = (x * 2.0) - (9.0 * t_1);
	elseif (z <= 7.7e-50)
		tmp = (x * 2.0) + (27.0 * (a * b));
	else
		tmp = (b * (a * 27.0)) + (-9.0 * 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.
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[(t * N[(z * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.8e-12], N[(N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision] + N[(-9.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.2e-131], N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.7e-50], N[(N[(x * 2.0), $MachinePrecision] + N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision] + N[(-9.0 * t$95$1), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.8000000000000001e-12

   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* 90.2%

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

      4. associate-*l* 91.7%

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

   3. Simplified 91.7%

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

      1. +-commutative 91.7%

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

      2. associate-+r- 91.7%

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

      3. associate-*r* 90.2%

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

      4. *-commutative 90.2%

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

      5. associate-*l* 91.8%

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

      6. associate-*l* 90.2%

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

      7. associate-*r* 90.1%

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

   6. Applied egg-rr 90.1%

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

      1. add-cube-cbrt 89.8%

         \[\leadsto \left(\color{blue}{\left(\sqrt[3]{27 \cdot \left(a \cdot b\right)} \cdot \sqrt[3]{27 \cdot \left(a \cdot b\right)}\right) \cdot \sqrt[3]{27 \cdot \left(a \cdot b\right)}} + x \cdot 2\right) - y \cdot \left(\left(9 \cdot z\right) \cdot t\right) \]

      2. pow3 89.7%

         \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{27 \cdot \left(a \cdot b\right)}\right)}^{3}} + x \cdot 2\right) - y \cdot \left(\left(9 \cdot z\right) \cdot t\right) \]

   8. Applied egg-rr 89.7%

      \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{27 \cdot \left(a \cdot b\right)}\right)}^{3}} + x \cdot 2\right) - y \cdot \left(\left(9 \cdot z\right) \cdot t\right) \]

   9. Taylor expanded in x around 0 75.1%

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

       1. cancel-sign-sub-inv 75.1%

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

       2. metadata-eval 75.1%

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

       3. *-commutative 75.1%

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

       4. associate-*r* 75.1%

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

       5. *-commutative 75.1%

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

       6. associate-*r* 78.5%

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

   11. Simplified 78.5%

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

   if -6.8000000000000001e-12 < z < -1.2e-131

   1. Initial program 99.8%

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

      1. sub-neg 99.8%

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

      2. sub-neg 99.8%

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

      3. associate-*l* 99.8%

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

      4. associate-*l* 95.3%

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

   3. Simplified 95.3%

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

   5. Taylor expanded in a around 0 62.5%

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

   if -1.2e-131 < z < 7.69999999999999964e-50

   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* 98.9%

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

      4. associate-*l* 98.9%

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

   3. Simplified 98.9%

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

   5. Taylor expanded in y around 0 85.2%

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

   if 7.69999999999999964e-50 < z

   1. Initial program 89.8%

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

      1. sub-neg 89.8%

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

      2. sub-neg 89.8%

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

      3. associate-*l* 89.7%

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

      4. associate-*l* 89.8%

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

   3. Simplified 89.8%

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

      1. +-commutative 89.8%

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

      2. associate-+r- 89.8%

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

      3. associate-*r* 89.7%

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

      4. *-commutative 89.7%

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

      5. associate-*l* 89.8%

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

      6. associate-*l* 89.8%

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

      7. associate-*r* 89.8%

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

   6. Applied egg-rr 89.8%

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

   7. Taylor expanded in x around 0 71.3%

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

      1. cancel-sign-sub-inv 71.3%

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

      2. metadata-eval 71.3%

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

      3. associate-*r* 71.2%

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

      4. *-commutative 71.2%

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

   9. Simplified 71.2%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{-12}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right) + -9 \cdot \left(z \cdot \left(y \cdot t\right)\right)\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-131}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \mathbf{elif}\;z \leq 7.7 \cdot 10^{-50}:\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right) + -9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 80.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := a \cdot \left(27 \cdot b\right) + -9 \cdot \left(z \cdot \left(y \cdot t\right)\right)\\ \mathbf{if}\;z \leq -7 \cdot 10^{-11}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-131}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-49}:\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
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)) (* -9.0 (* z (* y t))))))
   (if (<= z -7e-11)
     t_1
     (if (<= z -4.4e-131)
       (- (* x 2.0) (* 9.0 (* t (* z y))))
       (if (<= z 1.4e-49) (+ (* x 2.0) (* 27.0 (* a b))) t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a * (27.0 * b)) + (-9.0 * (z * (y * t)));
	double tmp;
	if (z <= -7e-11) {
		tmp = t_1;
	} else if (z <= -4.4e-131) {
		tmp = (x * 2.0) - (9.0 * (t * (z * y)));
	} else if (z <= 1.4e-49) {
		tmp = (x * 2.0) + (27.0 * (a * b));
	} 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.
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)) + ((-9.0d0) * (z * (y * t)))
    if (z <= (-7d-11)) then
        tmp = t_1
    else if (z <= (-4.4d-131)) then
        tmp = (x * 2.0d0) - (9.0d0 * (t * (z * y)))
    else if (z <= 1.4d-49) then
        tmp = (x * 2.0d0) + (27.0d0 * (a * b))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a * (27.0 * b)) + (-9.0 * (z * (y * t)));
	double tmp;
	if (z <= -7e-11) {
		tmp = t_1;
	} else if (z <= -4.4e-131) {
		tmp = (x * 2.0) - (9.0 * (t * (z * y)));
	} else if (z <= 1.4e-49) {
		tmp = (x * 2.0) + (27.0 * (a * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = (a * (27.0 * b)) + (-9.0 * (z * (y * t)))
	tmp = 0
	if z <= -7e-11:
		tmp = t_1
	elif z <= -4.4e-131:
		tmp = (x * 2.0) - (9.0 * (t * (z * y)))
	elif z <= 1.4e-49:
		tmp = (x * 2.0) + (27.0 * (a * b))
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a * Float64(27.0 * b)) + Float64(-9.0 * Float64(z * Float64(y * t))))
	tmp = 0.0
	if (z <= -7e-11)
		tmp = t_1;
	elseif (z <= -4.4e-131)
		tmp = Float64(Float64(x * 2.0) - Float64(9.0 * Float64(t * Float64(z * y))));
	elseif (z <= 1.4e-49)
		tmp = Float64(Float64(x * 2.0) + Float64(27.0 * Float64(a * b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a * (27.0 * b)) + (-9.0 * (z * (y * t)));
	tmp = 0.0;
	if (z <= -7e-11)
		tmp = t_1;
	elseif (z <= -4.4e-131)
		tmp = (x * 2.0) - (9.0 * (t * (z * y)));
	elseif (z <= 1.4e-49)
		tmp = (x * 2.0) + (27.0 * (a * b));
	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.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision] + N[(-9.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7e-11], t$95$1, If[LessEqual[z, -4.4e-131], N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(t * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.4e-49], N[(N[(x * 2.0), $MachinePrecision] + N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.00000000000000038e-11 or 1.39999999999999999e-49 < z

   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* 89.9%

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

      4. associate-*l* 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. Step-by-step derivation

      1. +-commutative 90.6%

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

      2. associate-+r- 90.6%

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

      3. associate-*r* 89.9%

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

      4. *-commutative 89.9%

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

      5. associate-*l* 90.7%

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

      6. associate-*l* 89.9%

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

      7. associate-*r* 89.9%

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

   6. Applied egg-rr 89.9%

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

      1. add-cube-cbrt 89.6%

         \[\leadsto \left(\color{blue}{\left(\sqrt[3]{27 \cdot \left(a \cdot b\right)} \cdot \sqrt[3]{27 \cdot \left(a \cdot b\right)}\right) \cdot \sqrt[3]{27 \cdot \left(a \cdot b\right)}} + x \cdot 2\right) - y \cdot \left(\left(9 \cdot z\right) \cdot t\right) \]

      2. pow3 89.6%

         \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{27 \cdot \left(a \cdot b\right)}\right)}^{3}} + x \cdot 2\right) - y \cdot \left(\left(9 \cdot z\right) \cdot t\right) \]

   8. Applied egg-rr 89.6%

      \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{27 \cdot \left(a \cdot b\right)}\right)}^{3}} + x \cdot 2\right) - y \cdot \left(\left(9 \cdot z\right) \cdot t\right) \]

   9. Taylor expanded in x around 0 72.9%

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

       1. cancel-sign-sub-inv 72.9%

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

       2. metadata-eval 72.9%

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

       3. *-commutative 72.9%

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

       4. associate-*r* 72.9%

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

       5. *-commutative 72.9%

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

       6. associate-*r* 77.5%

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

   11. Simplified 77.5%

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

   if -7.00000000000000038e-11 < z < -4.3999999999999999e-131

   1. Initial program 99.8%

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

      1. sub-neg 99.8%

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

      2. sub-neg 99.8%

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

      3. associate-*l* 99.8%

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

      4. associate-*l* 95.3%

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

   3. Simplified 95.3%

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

   5. Taylor expanded in a around 0 62.5%

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

   if -4.3999999999999999e-131 < z < 1.39999999999999999e-49

   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* 98.9%

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

      4. associate-*l* 98.9%

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

   3. Simplified 98.9%

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

   5. Taylor expanded in y around 0 85.2%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{-11}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right) + -9 \cdot \left(z \cdot \left(y \cdot t\right)\right)\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-131}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-49}:\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right) + -9 \cdot \left(z \cdot \left(y \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 97.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.12 \cdot 10^{+52}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right) + -9 \cdot \left(z \cdot \left(y \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - t \cdot \left(9 \cdot \left(z \cdot y\right)\right)\right) + b \cdot \left(a \cdot 27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.12e+52)
   (+ (* a (* 27.0 b)) (* -9.0 (* z (* y t))))
   (+ (- (* x 2.0) (* t (* 9.0 (* z y)))) (* b (* a 27.0)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.12e+52) {
		tmp = (a * (27.0 * b)) + (-9.0 * (z * (y * t)));
	} else {
		tmp = ((x * 2.0) - (t * (9.0 * (z * y)))) + (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.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-1.12d+52)) then
        tmp = (a * (27.0d0 * b)) + ((-9.0d0) * (z * (y * t)))
    else
        tmp = ((x * 2.0d0) - (t * (9.0d0 * (z * y)))) + (b * (a * 27.0d0))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.12e+52) {
		tmp = (a * (27.0 * b)) + (-9.0 * (z * (y * t)));
	} else {
		tmp = ((x * 2.0) - (t * (9.0 * (z * y)))) + (b * (a * 27.0));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.12e+52:
		tmp = (a * (27.0 * b)) + (-9.0 * (z * (y * t)))
	else:
		tmp = ((x * 2.0) - (t * (9.0 * (z * y)))) + (b * (a * 27.0))
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.12e+52)
		tmp = Float64(Float64(a * Float64(27.0 * b)) + Float64(-9.0 * Float64(z * Float64(y * t))));
	else
		tmp = Float64(Float64(Float64(x * 2.0) - Float64(t * Float64(9.0 * Float64(z * y)))) + 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])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1.12e+52)
		tmp = (a * (27.0 * b)) + (-9.0 * (z * (y * t)));
	else
		tmp = ((x * 2.0) - (t * (9.0 * (z * y)))) + (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.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.12e+52], N[(N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision] + N[(-9.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * 2.0), $MachinePrecision] - N[(t * N[(9.0 * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.12000000000000002e52

   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* 88.1%

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

      4. associate-*l* 90.0%

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

   3. Simplified 90.0%

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

      1. +-commutative 90.0%

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

      2. associate-+r- 90.0%

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

      3. associate-*r* 88.1%

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

      4. *-commutative 88.1%

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

      5. associate-*l* 90.2%

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

      6. associate-*l* 88.1%

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

      7. associate-*r* 88.0%

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

   6. Applied egg-rr 88.0%

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

      1. add-cube-cbrt 87.7%

         \[\leadsto \left(\color{blue}{\left(\sqrt[3]{27 \cdot \left(a \cdot b\right)} \cdot \sqrt[3]{27 \cdot \left(a \cdot b\right)}\right) \cdot \sqrt[3]{27 \cdot \left(a \cdot b\right)}} + x \cdot 2\right) - y \cdot \left(\left(9 \cdot z\right) \cdot t\right) \]

      2. pow3 87.7%

         \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{27 \cdot \left(a \cdot b\right)}\right)}^{3}} + x \cdot 2\right) - y \cdot \left(\left(9 \cdot z\right) \cdot t\right) \]

   8. Applied egg-rr 87.7%

      \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{27 \cdot \left(a \cdot b\right)}\right)}^{3}} + x \cdot 2\right) - y \cdot \left(\left(9 \cdot z\right) \cdot t\right) \]

   9. Taylor expanded in x around 0 74.0%

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

       1. cancel-sign-sub-inv 74.0%

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

       2. metadata-eval 74.0%

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

       3. *-commutative 74.0%

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

       4. associate-*r* 74.0%

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

       5. *-commutative 74.0%

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

       6. associate-*r* 78.2%

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

   11. Simplified 78.2%

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

   if -1.12000000000000002e52 < z

   1. Initial program 95.2%

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

   3. Taylor expanded in y around 0 95.1%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.12 \cdot 10^{+52}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right) + -9 \cdot \left(z \cdot \left(y \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - t \cdot \left(9 \cdot \left(z \cdot y\right)\right)\right) + b \cdot \left(a \cdot 27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 74.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{-42}:\\ \;\;\;\;\left(z \cdot t\right) \cdot \left(y \cdot -9\right)\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+96}:\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.25e-42)
   (* (* z t) (* y -9.0))
   (if (<= z 5.2e+96) (+ (* x 2.0) (* 27.0 (* a b))) (* -9.0 (* t (* z y))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.25e-42) {
		tmp = (z * t) * (y * -9.0);
	} else if (z <= 5.2e+96) {
		tmp = (x * 2.0) + (27.0 * (a * b));
	} 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.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-1.25d-42)) then
        tmp = (z * t) * (y * (-9.0d0))
    else if (z <= 5.2d+96) then
        tmp = (x * 2.0d0) + (27.0d0 * (a * b))
    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;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.25e-42) {
		tmp = (z * t) * (y * -9.0);
	} else if (z <= 5.2e+96) {
		tmp = (x * 2.0) + (27.0 * (a * b));
	} else {
		tmp = -9.0 * (t * (z * y));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.25e-42:
		tmp = (z * t) * (y * -9.0)
	elif z <= 5.2e+96:
		tmp = (x * 2.0) + (27.0 * (a * b))
	else:
		tmp = -9.0 * (t * (z * y))
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.25e-42)
		tmp = Float64(Float64(z * t) * Float64(y * -9.0));
	elseif (z <= 5.2e+96)
		tmp = Float64(Float64(x * 2.0) + Float64(27.0 * Float64(a * b)));
	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])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1.25e-42)
		tmp = (z * t) * (y * -9.0);
	elseif (z <= 5.2e+96)
		tmp = (x * 2.0) + (27.0 * (a * b));
	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.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.25e-42], N[(N[(z * t), $MachinePrecision] * N[(y * -9.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.2e+96], N[(N[(x * 2.0), $MachinePrecision] + N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-9.0 * N[(t * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.25000000000000001e-42

   1. Initial program 90.4%

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

      1. sub-neg 90.4%

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

      2. sub-neg 90.4%

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

      3. associate-*l* 90.8%

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

      4. associate-*l* 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. Step-by-step derivation

      1. +-commutative 92.3%

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

      2. associate-+r- 92.3%

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

      3. associate-*r* 90.8%

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

      4. *-commutative 90.8%

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

      5. associate-*l* 92.4%

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

      6. associate-*l* 90.8%

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

      7. associate-*r* 90.7%

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

   6. Applied egg-rr 90.7%

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

      1. add-cube-cbrt 90.4%

         \[\leadsto \left(\color{blue}{\left(\sqrt[3]{27 \cdot \left(a \cdot b\right)} \cdot \sqrt[3]{27 \cdot \left(a \cdot b\right)}\right) \cdot \sqrt[3]{27 \cdot \left(a \cdot b\right)}} + x \cdot 2\right) - y \cdot \left(\left(9 \cdot z\right) \cdot t\right) \]

      2. pow3 90.4%

         \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{27 \cdot \left(a \cdot b\right)}\right)}^{3}} + x \cdot 2\right) - y \cdot \left(\left(9 \cdot z\right) \cdot t\right) \]

   8. Applied egg-rr 90.4%

      \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{27 \cdot \left(a \cdot b\right)}\right)}^{3}} + x \cdot 2\right) - y \cdot \left(\left(9 \cdot z\right) \cdot t\right) \]

   9. Taylor expanded in y around inf 56.0%

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

       1. *-commutative 56.0%

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

       2. associate-*r* 53.4%

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

       3. *-commutative 53.4%

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

       4. associate-*l* 51.8%

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

       5. *-commutative 51.8%

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

       6. associate-*l* 53.4%

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

       7. *-commutative 53.4%

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

       8. *-commutative 53.4%

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

   11. Simplified 53.4%

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

   if -1.25000000000000001e-42 < z < 5.2e96

   1. Initial program 97.3%

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

      1. sub-neg 97.3%

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

      2. sub-neg 97.3%

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

      3. associate-*l* 99.1%

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

      4. associate-*l* 98.6%

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

   3. Simplified 98.6%

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

   5. Taylor expanded in y around 0 77.6%

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

   if 5.2e96 < z

   1. Initial program 85.8%

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

      1. sub-neg 85.8%

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

      2. sub-neg 85.8%

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

      3. associate-*l* 81.2%

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

      4. associate-*l* 81.2%

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

   3. Simplified 81.2%

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

   5. Taylor expanded in y around inf 51.3%

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

4. Final simplification 67.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{-42}:\\ \;\;\;\;\left(z \cdot t\right) \cdot \left(y \cdot -9\right)\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+96}:\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 48.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{+17} \lor \neg \left(x \leq 8.5 \cdot 10^{+19}\right):\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= x -1.3e+17) (not (<= x 8.5e+19))) (* x 2.0) (* a (* 27.0 b))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -1.3e+17) || !(x <= 8.5e+19)) {
		tmp = x * 2.0;
	} else {
		tmp = a * (27.0 * b);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((x <= (-1.3d+17)) .or. (.not. (x <= 8.5d+19))) then
        tmp = x * 2.0d0
    else
        tmp = a * (27.0d0 * b)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -1.3e+17) || !(x <= 8.5e+19)) {
		tmp = x * 2.0;
	} else {
		tmp = a * (27.0 * b);
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if (x <= -1.3e+17) or not (x <= 8.5e+19):
		tmp = x * 2.0
	else:
		tmp = a * (27.0 * b)
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((x <= -1.3e+17) || !(x <= 8.5e+19))
		tmp = Float64(x * 2.0);
	else
		tmp = Float64(a * Float64(27.0 * b));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((x <= -1.3e+17) || ~((x <= 8.5e+19)))
		tmp = x * 2.0;
	else
		tmp = a * (27.0 * b);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[x, -1.3e+17], N[Not[LessEqual[x, 8.5e+19]], $MachinePrecision]], N[(x * 2.0), $MachinePrecision], N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.3e17 or 8.5e19 < x

   1. Initial program 95.6%

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

      1. sub-neg 95.6%

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

      2. sub-neg 95.6%

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

      3. associate-*l* 94.9%

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

      4. associate-*l* 94.1%

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

   3. Simplified 94.1%

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

   5. Taylor expanded in x around inf 56.3%

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

   if -1.3e17 < x < 8.5e19

   1. Initial program 92.4%

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

      1. sub-neg 92.4%

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

      2. sub-neg 92.4%

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

      3. associate-*l* 93.7%

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

      4. associate-*l* 94.4%

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

   3. Simplified 94.4%

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

   5. Taylor expanded in a around inf 49.9%

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

      1. associate-*r* 49.8%

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

      2. *-commutative 49.8%

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

      3. associate-*r* 49.8%

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

   7. Simplified 49.8%

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

4. Final simplification 52.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{+17} \lor \neg \left(x \leq 8.5 \cdot 10^{+19}\right):\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 47.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -2 \cdot 10^{-32} \lor \neg \left(a \leq 1.5 \cdot 10^{-109}\right):\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -2e-32) (not (<= a 1.5e-109))) (* 27.0 (* a b)) (* x 2.0)))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -2e-32) || !(a <= 1.5e-109)) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((a <= (-2d-32)) .or. (.not. (a <= 1.5d-109))) then
        tmp = 27.0d0 * (a * b)
    else
        tmp = x * 2.0d0
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -2e-32) || !(a <= 1.5e-109)) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -2e-32) or not (a <= 1.5e-109):
		tmp = 27.0 * (a * b)
	else:
		tmp = x * 2.0
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -2e-32) || !(a <= 1.5e-109))
		tmp = Float64(27.0 * Float64(a * b));
	else
		tmp = Float64(x * 2.0);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -2e-32) || ~((a <= 1.5e-109)))
		tmp = 27.0 * (a * b);
	else
		tmp = x * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -2e-32], N[Not[LessEqual[a, 1.5e-109]], $MachinePrecision]], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], N[(x * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.00000000000000011e-32 or 1.50000000000000011e-109 < a

   1. Initial program 92.0%

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

      1. sub-neg 92.0%

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

      2. sub-neg 92.0%

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

      3. associate-*l* 93.3%

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

      4. associate-*l* 93.9%

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

   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 50.5%

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

   if -2.00000000000000011e-32 < a < 1.50000000000000011e-109

   1. Initial program 96.9%

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

      1. sub-neg 96.9%

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

      2. sub-neg 96.9%

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

      3. associate-*l* 95.7%

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

      4. associate-*l* 94.7%

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

   3. Simplified 94.7%

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

   5. Taylor expanded in x around inf 44.8%

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

4. Final simplification 48.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2 \cdot 10^{-32} \lor \neg \left(a \leq 1.5 \cdot 10^{-109}\right):\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 30.4% accurate, 5.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 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* 94.2%

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

   4. associate-*l* 94.2%

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

3. Simplified 94.2%

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

5. Taylor expanded in x around inf 30.1%

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

6. Final simplification 30.1%

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

Developer target: 95.0% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024088 
(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)))