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

Percentage Accurate: 95.3% → 98.6%

Time: 14.6s

Alternatives: 14

Speedup: 0.8×

• 27.6% 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: 95.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{-95}:\\ \;\;\;\;y \cdot \left(\left(2 \cdot \frac{x}{y} + 27 \cdot \frac{a \cdot b}{y}\right) - 9 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, t \cdot \left(y \cdot \left(z \cdot -9\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -2.15e-95)
   (* y (- (+ (* 2.0 (/ x y)) (* 27.0 (/ (* a b) y))) (* 9.0 (* z t))))
   (fma a (* 27.0 b) (fma x 2.0 (* t (* y (* z -9.0)))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.15e-95) {
		tmp = y * (((2.0 * (x / y)) + (27.0 * ((a * b) / y))) - (9.0 * (z * t)));
	} else {
		tmp = fma(a, (27.0 * b), fma(x, 2.0, (t * (y * (z * -9.0)))));
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -2.15e-95)
		tmp = Float64(y * Float64(Float64(Float64(2.0 * Float64(x / y)) + Float64(27.0 * Float64(Float64(a * b) / y))) - Float64(9.0 * Float64(z * t))));
	else
		tmp = fma(a, Float64(27.0 * b), fma(x, 2.0, Float64(t * Float64(y * Float64(z * -9.0)))));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -2.15e-95], N[(y * N[(N[(N[(2.0 * N[(x / y), $MachinePrecision]), $MachinePrecision] + N[(27.0 * N[(N[(a * b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(9.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(27.0 * b), $MachinePrecision] + N[(x * 2.0 + N[(t * N[(y * N[(z * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.14999999999999999e-95

   1. Initial program 94.2%

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

      1. associate-+l- 94.2%

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

      2. *-commutative 94.2%

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

      3. *-commutative 94.2%

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

      4. associate-*l* 93.1%

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

      5. associate-+l- 93.1%

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

      6. associate-*l* 94.2%

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

      7. *-commutative 94.2%

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

      8. *-commutative 94.2%

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

      9. associate-*l* 90.1%

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

      10. associate-*l* 89.0%

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

   3. Simplified 89.0%

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

   5. Taylor expanded in y around inf 65.4%

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

   if -2.14999999999999999e-95 < z

   1. Initial program 96.4%

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

      1. +-commutative 96.4%

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

      2. associate-+r- 96.4%

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

      3. *-commutative 96.4%

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

      4. cancel-sign-sub-inv 96.4%

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

      5. associate-*r* 94.7%

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

      6. distribute-lft-neg-in 94.7%

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

      7. *-commutative 94.7%

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

      8. cancel-sign-sub-inv 94.7%

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

      9. associate-+r- 94.7%

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

      10. associate-*l* 94.8%

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

      11. fma-define 95.4%

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

      12. cancel-sign-sub-inv 95.4%

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

      13. fma-define 95.4%

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

      14. distribute-lft-neg-in 95.4%

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

      15. distribute-rgt-neg-in 95.4%

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

      16. *-commutative 95.4%

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

      17. associate-*r* 97.0%

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

      18. associate-*l* 97.1%

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

      19. neg-mul-1 97.1%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, t \cdot \left(y \cdot \left(9 \cdot \color{blue}{\left(-1 \cdot z\right)}\right)\right)\right)\right) \]

      20. associate-*r* 97.1%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, t \cdot \left(y \cdot \color{blue}{\left(\left(9 \cdot -1\right) \cdot z\right)}\right)\right)\right) \]

   3. Simplified 97.1%

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

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{-95}:\\ \;\;\;\;y \cdot \left(\left(2 \cdot \frac{x}{y} + 27 \cdot \frac{a \cdot b}{y}\right) - 9 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, t \cdot \left(y \cdot \left(z \cdot -9\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 49.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := b \cdot \left(27 \cdot a\right)\\ \mathbf{if}\;t \leq -1.3 \cdot 10^{-104}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{-260}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.72 \cdot 10^{-230}:\\ \;\;\;\;2 \cdot x\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-37}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+52}:\\ \;\;\;\;2 \cdot x\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+81}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (* 27.0 a))))
   (if (<= t -1.3e-104)
     (* -9.0 (* y (* z t)))
     (if (<= t 3.1e-260)
       t_1
       (if (<= t 1.72e-230)
         (* 2.0 x)
         (if (<= t 2.3e-37)
           t_1
           (if (<= t 1.2e+52)
             (* 2.0 x)
             (if (<= t 4e+81) (* 27.0 (* a b)) (* -9.0 (* t (* z y)))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (27.0 * a);
	double tmp;
	if (t <= -1.3e-104) {
		tmp = -9.0 * (y * (z * t));
	} else if (t <= 3.1e-260) {
		tmp = t_1;
	} else if (t <= 1.72e-230) {
		tmp = 2.0 * x;
	} else if (t <= 2.3e-37) {
		tmp = t_1;
	} else if (t <= 1.2e+52) {
		tmp = 2.0 * x;
	} else if (t <= 4e+81) {
		tmp = 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.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (27.0d0 * a)
    if (t <= (-1.3d-104)) then
        tmp = (-9.0d0) * (y * (z * t))
    else if (t <= 3.1d-260) then
        tmp = t_1
    else if (t <= 1.72d-230) then
        tmp = 2.0d0 * x
    else if (t <= 2.3d-37) then
        tmp = t_1
    else if (t <= 1.2d+52) then
        tmp = 2.0d0 * x
    else if (t <= 4d+81) then
        tmp = 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;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (27.0 * a);
	double tmp;
	if (t <= -1.3e-104) {
		tmp = -9.0 * (y * (z * t));
	} else if (t <= 3.1e-260) {
		tmp = t_1;
	} else if (t <= 1.72e-230) {
		tmp = 2.0 * x;
	} else if (t <= 2.3e-37) {
		tmp = t_1;
	} else if (t <= 1.2e+52) {
		tmp = 2.0 * x;
	} else if (t <= 4e+81) {
		tmp = 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])
def code(x, y, z, t, a, b):
	t_1 = b * (27.0 * a)
	tmp = 0
	if t <= -1.3e-104:
		tmp = -9.0 * (y * (z * t))
	elif t <= 3.1e-260:
		tmp = t_1
	elif t <= 1.72e-230:
		tmp = 2.0 * x
	elif t <= 2.3e-37:
		tmp = t_1
	elif t <= 1.2e+52:
		tmp = 2.0 * x
	elif t <= 4e+81:
		tmp = 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])
function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(27.0 * a))
	tmp = 0.0
	if (t <= -1.3e-104)
		tmp = Float64(-9.0 * Float64(y * Float64(z * t)));
	elseif (t <= 3.1e-260)
		tmp = t_1;
	elseif (t <= 1.72e-230)
		tmp = Float64(2.0 * x);
	elseif (t <= 2.3e-37)
		tmp = t_1;
	elseif (t <= 1.2e+52)
		tmp = Float64(2.0 * x);
	elseif (t <= 4e+81)
		tmp = 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])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (27.0 * a);
	tmp = 0.0;
	if (t <= -1.3e-104)
		tmp = -9.0 * (y * (z * t));
	elseif (t <= 3.1e-260)
		tmp = t_1;
	elseif (t <= 1.72e-230)
		tmp = 2.0 * x;
	elseif (t <= 2.3e-37)
		tmp = t_1;
	elseif (t <= 1.2e+52)
		tmp = 2.0 * x;
	elseif (t <= 4e+81)
		tmp = 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.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(27.0 * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.3e-104], N[(-9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.1e-260], t$95$1, If[LessEqual[t, 1.72e-230], N[(2.0 * x), $MachinePrecision], If[LessEqual[t, 2.3e-37], t$95$1, If[LessEqual[t, 1.2e+52], N[(2.0 * x), $MachinePrecision], If[LessEqual[t, 4e+81], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], N[(-9.0 * N[(t * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.30000000000000001e-104

   1. Initial program 97.8%

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

      1. associate-+l- 97.8%

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

      2. *-commutative 97.8%

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

      3. *-commutative 97.8%

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

      4. associate-*l* 97.8%

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

      5. associate-+l- 97.8%

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

      6. associate-*l* 97.8%

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

      7. *-commutative 97.8%

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

      8. *-commutative 97.8%

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

      9. associate-*l* 94.9%

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

      10. associate-*l* 94.9%

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

   3. Simplified 94.9%

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

   5. Taylor expanded in x around inf 84.9%

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

   6. Taylor expanded in t around inf 46.7%

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

      1. associate-*r* 43.8%

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

      2. *-commutative 43.8%

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

      3. associate-*r* 44.7%

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

   8. Simplified 44.7%

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

   if -1.30000000000000001e-104 < t < 3.09999999999999983e-260 or 1.71999999999999999e-230 < t < 2.3e-37

   1. Initial program 94.0%

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

      1. associate-+l- 94.0%

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

      2. *-commutative 94.0%

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

      3. *-commutative 94.0%

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

      4. associate-*l* 94.0%

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

      5. associate-+l- 94.0%

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

      6. associate-*l* 94.0%

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

      7. *-commutative 94.0%

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

      8. *-commutative 94.0%

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

      9. associate-*l* 98.9%

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

      10. associate-*l* 98.0%

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

   3. Simplified 98.0%

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

   5. Taylor expanded in a around inf 50.5%

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

      1. associate-*r* 50.4%

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

   7. Simplified 50.4%

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

   if 3.09999999999999983e-260 < t < 1.71999999999999999e-230 or 2.3e-37 < t < 1.2e52

   1. Initial program 95.9%

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

      1. associate-+l- 95.9%

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

      2. *-commutative 95.9%

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

      3. *-commutative 95.9%

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

      4. associate-*l* 92.2%

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

      5. associate-+l- 92.2%

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

      6. associate-*l* 95.9%

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

      7. *-commutative 95.9%

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

      8. *-commutative 95.9%

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

      9. associate-*l* 99.9%

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

      10. associate-*l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 45.7%

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

   if 1.2e52 < t < 3.99999999999999969e81

   1. Initial program 99.6%

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

      1. associate-+l- 99.6%

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

      2. *-commutative 99.6%

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

      3. *-commutative 99.6%

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

      4. associate-*l* 99.6%

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

      5. associate-+l- 99.6%

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

      6. associate-*l* 99.6%

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

      7. *-commutative 99.6%

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

      8. *-commutative 99.6%

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

      9. associate-*l* 99.6%

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

      10. associate-*l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in a around inf 51.8%

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

   if 3.99999999999999969e81 < t

   1. Initial program 94.0%

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

      1. associate-+l- 94.0%

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

      2. *-commutative 94.0%

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

      3. *-commutative 94.0%

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

      4. associate-*l* 93.8%

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

      5. associate-+l- 93.8%

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

      6. associate-*l* 94.0%

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

      7. *-commutative 94.0%

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

      8. *-commutative 94.0%

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

      9. associate-*l* 74.8%

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

      10. associate-*l* 74.8%

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

   3. Simplified 74.8%

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

   5. Taylor expanded in y around inf 79.5%

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

4. Final simplification 51.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{-104}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{-260}:\\ \;\;\;\;b \cdot \left(27 \cdot a\right)\\ \mathbf{elif}\;t \leq 1.72 \cdot 10^{-230}:\\ \;\;\;\;2 \cdot x\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-37}:\\ \;\;\;\;b \cdot \left(27 \cdot a\right)\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+52}:\\ \;\;\;\;2 \cdot x\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+81}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 48.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := b \cdot \left(27 \cdot a\right)\\ t_2 := -9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \mathbf{if}\;t \leq -2.4 \cdot 10^{-100}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{-260}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.56 \cdot 10^{-229}:\\ \;\;\;\;2 \cdot x\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-37}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+52}:\\ \;\;\;\;2 \cdot x\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{+81}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (* 27.0 a))) (t_2 (* -9.0 (* t (* z y)))))
   (if (<= t -2.4e-100)
     t_2
     (if (<= t 4.1e-260)
       t_1
       (if (<= t 1.56e-229)
         (* 2.0 x)
         (if (<= t 3.5e-37)
           t_1
           (if (<= t 1.7e+52)
             (* 2.0 x)
             (if (<= t 5.8e+81) (* 27.0 (* a b)) t_2))))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (27.0 * a);
	double t_2 = -9.0 * (t * (z * y));
	double tmp;
	if (t <= -2.4e-100) {
		tmp = t_2;
	} else if (t <= 4.1e-260) {
		tmp = t_1;
	} else if (t <= 1.56e-229) {
		tmp = 2.0 * x;
	} else if (t <= 3.5e-37) {
		tmp = t_1;
	} else if (t <= 1.7e+52) {
		tmp = 2.0 * x;
	} else if (t <= 5.8e+81) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * (27.0d0 * a)
    t_2 = (-9.0d0) * (t * (z * y))
    if (t <= (-2.4d-100)) then
        tmp = t_2
    else if (t <= 4.1d-260) then
        tmp = t_1
    else if (t <= 1.56d-229) then
        tmp = 2.0d0 * x
    else if (t <= 3.5d-37) then
        tmp = t_1
    else if (t <= 1.7d+52) then
        tmp = 2.0d0 * x
    else if (t <= 5.8d+81) then
        tmp = 27.0d0 * (a * b)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (27.0 * a);
	double t_2 = -9.0 * (t * (z * y));
	double tmp;
	if (t <= -2.4e-100) {
		tmp = t_2;
	} else if (t <= 4.1e-260) {
		tmp = t_1;
	} else if (t <= 1.56e-229) {
		tmp = 2.0 * x;
	} else if (t <= 3.5e-37) {
		tmp = t_1;
	} else if (t <= 1.7e+52) {
		tmp = 2.0 * x;
	} else if (t <= 5.8e+81) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = b * (27.0 * a)
	t_2 = -9.0 * (t * (z * y))
	tmp = 0
	if t <= -2.4e-100:
		tmp = t_2
	elif t <= 4.1e-260:
		tmp = t_1
	elif t <= 1.56e-229:
		tmp = 2.0 * x
	elif t <= 3.5e-37:
		tmp = t_1
	elif t <= 1.7e+52:
		tmp = 2.0 * x
	elif t <= 5.8e+81:
		tmp = 27.0 * (a * b)
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(27.0 * a))
	t_2 = Float64(-9.0 * Float64(t * Float64(z * y)))
	tmp = 0.0
	if (t <= -2.4e-100)
		tmp = t_2;
	elseif (t <= 4.1e-260)
		tmp = t_1;
	elseif (t <= 1.56e-229)
		tmp = Float64(2.0 * x);
	elseif (t <= 3.5e-37)
		tmp = t_1;
	elseif (t <= 1.7e+52)
		tmp = Float64(2.0 * x);
	elseif (t <= 5.8e+81)
		tmp = Float64(27.0 * Float64(a * b));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (27.0 * a);
	t_2 = -9.0 * (t * (z * y));
	tmp = 0.0;
	if (t <= -2.4e-100)
		tmp = t_2;
	elseif (t <= 4.1e-260)
		tmp = t_1;
	elseif (t <= 1.56e-229)
		tmp = 2.0 * x;
	elseif (t <= 3.5e-37)
		tmp = t_1;
	elseif (t <= 1.7e+52)
		tmp = 2.0 * x;
	elseif (t <= 5.8e+81)
		tmp = 27.0 * (a * b);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(27.0 * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-9.0 * N[(t * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.4e-100], t$95$2, If[LessEqual[t, 4.1e-260], t$95$1, If[LessEqual[t, 1.56e-229], N[(2.0 * x), $MachinePrecision], If[LessEqual[t, 3.5e-37], t$95$1, If[LessEqual[t, 1.7e+52], N[(2.0 * x), $MachinePrecision], If[LessEqual[t, 5.8e+81], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.4000000000000003e-100 or 5.7999999999999999e81 < t

   1. Initial program 96.7%

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

      1. associate-+l- 96.7%

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

      2. *-commutative 96.7%

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

      3. *-commutative 96.7%

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

      4. associate-*l* 96.7%

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

      5. associate-+l- 96.7%

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

      6. associate-*l* 96.7%

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

      7. *-commutative 96.7%

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

      8. *-commutative 96.7%

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

      9. associate-*l* 89.5%

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

      10. associate-*l* 89.5%

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

   3. Simplified 89.5%

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

   5. Taylor expanded in y around inf 55.7%

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

   if -2.4000000000000003e-100 < t < 4.09999999999999997e-260 or 1.5600000000000001e-229 < t < 3.5000000000000001e-37

   1. Initial program 94.1%

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

      1. associate-+l- 94.1%

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

      2. *-commutative 94.1%

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

      3. *-commutative 94.1%

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

      4. associate-*l* 94.1%

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

      5. associate-+l- 94.1%

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

      6. associate-*l* 94.1%

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

      7. *-commutative 94.1%

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

      8. *-commutative 94.1%

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

      9. associate-*l* 98.9%

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

      10. associate-*l* 98.0%

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

   3. Simplified 98.0%

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

   5. Taylor expanded in a around inf 51.0%

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

      1. associate-*r* 50.9%

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

   7. Simplified 50.9%

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

   if 4.09999999999999997e-260 < t < 1.5600000000000001e-229 or 3.5000000000000001e-37 < t < 1.7e52

   1. Initial program 95.9%

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

      1. associate-+l- 95.9%

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

      2. *-commutative 95.9%

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

      3. *-commutative 95.9%

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

      4. associate-*l* 92.2%

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

      5. associate-+l- 92.2%

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

      6. associate-*l* 95.9%

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

      7. *-commutative 95.9%

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

      8. *-commutative 95.9%

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

      9. associate-*l* 99.9%

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

      10. associate-*l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 45.7%

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

   if 1.7e52 < t < 5.7999999999999999e81

   1. Initial program 99.6%

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

      1. associate-+l- 99.6%

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

      2. *-commutative 99.6%

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

      3. *-commutative 99.6%

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

      4. associate-*l* 99.6%

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

      5. associate-+l- 99.6%

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

      6. associate-*l* 99.6%

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

      7. *-commutative 99.6%

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

      8. *-commutative 99.6%

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

      9. associate-*l* 99.6%

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

      10. associate-*l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in a around inf 51.8%

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

4. Final simplification 52.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{-100}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{-260}:\\ \;\;\;\;b \cdot \left(27 \cdot a\right)\\ \mathbf{elif}\;t \leq 1.56 \cdot 10^{-229}:\\ \;\;\;\;2 \cdot x\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-37}:\\ \;\;\;\;b \cdot \left(27 \cdot a\right)\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+52}:\\ \;\;\;\;2 \cdot x\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{+81}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 78.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+75} \lor \neg \left(z \leq -2.7 \cdot 10^{+15} \lor \neg \left(z \leq -1.9 \cdot 10^{-64}\right) \land z \leq 1.5 \cdot 10^{-91}\right):\\ \;\;\;\;2 \cdot x + z \cdot \left(-9 \cdot \left(y \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot x + 27 \cdot \left(a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.2e+75)
         (not (or (<= z -2.7e+15) (and (not (<= z -1.9e-64)) (<= z 1.5e-91)))))
   (+ (* 2.0 x) (* z (* -9.0 (* y t))))
   (+ (* 2.0 x) (* 27.0 (* a b)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.2e+75) || !((z <= -2.7e+15) || (!(z <= -1.9e-64) && (z <= 1.5e-91)))) {
		tmp = (2.0 * x) + (z * (-9.0 * (y * t)));
	} else {
		tmp = (2.0 * x) + (27.0 * (a * b));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-1.2d+75)) .or. (.not. (z <= (-2.7d+15)) .or. (.not. (z <= (-1.9d-64))) .and. (z <= 1.5d-91))) then
        tmp = (2.0d0 * x) + (z * ((-9.0d0) * (y * t)))
    else
        tmp = (2.0d0 * x) + (27.0d0 * (a * b))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.2e+75) || !((z <= -2.7e+15) || (!(z <= -1.9e-64) && (z <= 1.5e-91)))) {
		tmp = (2.0 * x) + (z * (-9.0 * (y * t)));
	} else {
		tmp = (2.0 * x) + (27.0 * (a * b));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.2e+75) or not ((z <= -2.7e+15) or (not (z <= -1.9e-64) and (z <= 1.5e-91))):
		tmp = (2.0 * x) + (z * (-9.0 * (y * t)))
	else:
		tmp = (2.0 * x) + (27.0 * (a * b))
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.2e+75) || !((z <= -2.7e+15) || (!(z <= -1.9e-64) && (z <= 1.5e-91))))
		tmp = Float64(Float64(2.0 * x) + Float64(z * Float64(-9.0 * Float64(y * t))));
	else
		tmp = Float64(Float64(2.0 * x) + Float64(27.0 * Float64(a * b)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.2e+75) || ~(((z <= -2.7e+15) || (~((z <= -1.9e-64)) && (z <= 1.5e-91)))))
		tmp = (2.0 * x) + (z * (-9.0 * (y * t)));
	else
		tmp = (2.0 * x) + (27.0 * (a * b));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.2e+75], N[Not[Or[LessEqual[z, -2.7e+15], And[N[Not[LessEqual[z, -1.9e-64]], $MachinePrecision], LessEqual[z, 1.5e-91]]]], $MachinePrecision]], N[(N[(2.0 * x), $MachinePrecision] + N[(z * N[(-9.0 * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 * x), $MachinePrecision] + N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.2e75 or -2.7e15 < z < -1.9000000000000001e-64 or 1.5000000000000001e-91 < z

   1. Initial program 92.7%

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

      1. associate-+l- 92.7%

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

      2. *-commutative 92.7%

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

      3. *-commutative 92.7%

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

      4. associate-*l* 92.1%

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

      5. associate-+l- 92.1%

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

      6. associate-*l* 92.7%

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

      7. *-commutative 92.7%

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

      8. *-commutative 92.7%

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

      9. associate-*l* 90.4%

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

      10. associate-*l* 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. Taylor expanded in a around 0 73.4%

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

      1. cancel-sign-sub-inv 73.4%

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

      2. *-commutative 73.4%

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

      3. associate-*r* 75.9%

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

      4. associate-*r* 75.9%

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

      5. distribute-lft-neg-in 75.9%

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

      6. *-commutative 75.9%

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

      7. distribute-rgt-neg-in 75.9%

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

      8. *-commutative 75.9%

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

      9. metadata-eval 75.9%

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

   7. Applied egg-rr 75.9%

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

   if -1.2e75 < z < -2.7e15 or -1.9000000000000001e-64 < z < 1.5000000000000001e-91

   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. associate-+l- 99.8%

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

      2. *-commutative 99.8%

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

      3. *-commutative 99.8%

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

      4. associate-*l* 99.8%

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

      5. associate-+l- 99.8%

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

      6. associate-*l* 99.8%

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

      7. *-commutative 99.8%

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

      8. *-commutative 99.8%

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

      9. associate-*l* 99.8%

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

      10. associate-*l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 87.2%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+75} \lor \neg \left(z \leq -2.7 \cdot 10^{+15} \lor \neg \left(z \leq -1.9 \cdot 10^{-64}\right) \land z \leq 1.5 \cdot 10^{-91}\right):\\ \;\;\;\;2 \cdot x + z \cdot \left(-9 \cdot \left(y \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot x + 27 \cdot \left(a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 98.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot \left(y \cdot 9\right) \leq 4 \cdot 10^{+223}:\\ \;\;\;\;\left(2 \cdot x - t \cdot \left(y \cdot \left(z \cdot 9\right)\right)\right) + b \cdot \left(27 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\left(2 \cdot \frac{x}{y} + 27 \cdot \frac{a \cdot b}{y}\right) - 9 \cdot \left(z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* z (* y 9.0)) 4e+223)
   (+ (- (* 2.0 x) (* t (* y (* z 9.0)))) (* b (* 27.0 a)))
   (* y (- (+ (* 2.0 (/ x y)) (* 27.0 (/ (* a b) y))) (* 9.0 (* z t))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z * (y * 9.0)) <= 4e+223) {
		tmp = ((2.0 * x) - (t * (y * (z * 9.0)))) + (b * (27.0 * a));
	} else {
		tmp = y * (((2.0 * (x / y)) + (27.0 * ((a * b) / y))) - (9.0 * (z * t)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z * (y * 9.0d0)) <= 4d+223) then
        tmp = ((2.0d0 * x) - (t * (y * (z * 9.0d0)))) + (b * (27.0d0 * a))
    else
        tmp = y * (((2.0d0 * (x / y)) + (27.0d0 * ((a * b) / y))) - (9.0d0 * (z * t)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z * (y * 9.0)) <= 4e+223) {
		tmp = ((2.0 * x) - (t * (y * (z * 9.0)))) + (b * (27.0 * a));
	} else {
		tmp = y * (((2.0 * (x / y)) + (27.0 * ((a * b) / y))) - (9.0 * (z * t)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if (z * (y * 9.0)) <= 4e+223:
		tmp = ((2.0 * x) - (t * (y * (z * 9.0)))) + (b * (27.0 * a))
	else:
		tmp = y * (((2.0 * (x / y)) + (27.0 * ((a * b) / y))) - (9.0 * (z * t)))
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(z * Float64(y * 9.0)) <= 4e+223)
		tmp = Float64(Float64(Float64(2.0 * x) - Float64(t * Float64(y * Float64(z * 9.0)))) + Float64(b * Float64(27.0 * a)));
	else
		tmp = Float64(y * Float64(Float64(Float64(2.0 * Float64(x / y)) + Float64(27.0 * Float64(Float64(a * b) / y))) - Float64(9.0 * Float64(z * t))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z * (y * 9.0)) <= 4e+223)
		tmp = ((2.0 * x) - (t * (y * (z * 9.0)))) + (b * (27.0 * a));
	else
		tmp = y * (((2.0 * (x / y)) + (27.0 * ((a * b) / y))) - (9.0 * (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.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(z * N[(y * 9.0), $MachinePrecision]), $MachinePrecision], 4e+223], N[(N[(N[(2.0 * x), $MachinePrecision] - N[(t * N[(y * N[(z * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(27.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(N[(2.0 * N[(x / y), $MachinePrecision]), $MachinePrecision] + N[(27.0 * N[(N[(a * b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(9.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 y #s(literal 9 binary64)) z) < 4.00000000000000019e223

   1. Initial program 97.6%

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

   3. Taylor expanded in y around 0 97.6%

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

      1. pow1 97.6%

         \[\leadsto \left(x \cdot 2 - \color{blue}{{\left(9 \cdot \left(y \cdot z\right)\right)}^{1}} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      2. associate-*r* 97.6%

         \[\leadsto \left(x \cdot 2 - {\color{blue}{\left(\left(9 \cdot y\right) \cdot z\right)}}^{1} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

   5. Applied egg-rr 97.6%

      \[\leadsto \left(x \cdot 2 - \color{blue}{{\left(\left(9 \cdot y\right) \cdot z\right)}^{1}} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   6. Step-by-step derivation

      1. unpow1 97.6%

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

      2. *-commutative 97.6%

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

      3. associate-*l* 97.6%

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

   7. Simplified 97.6%

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

   if 4.00000000000000019e223 < (*.f64 (*.f64 y #s(literal 9 binary64)) z)

   1. Initial program 82.2%

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

      1. associate-+l- 82.2%

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

      2. *-commutative 82.2%

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

      3. *-commutative 82.2%

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

      4. associate-*l* 79.3%

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

      5. associate-+l- 79.3%

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

      6. associate-*l* 82.2%

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

      7. *-commutative 82.2%

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

      8. *-commutative 82.2%

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

      9. associate-*l* 96.6%

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

      10. associate-*l* 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 inf 96.8%

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

4. Final simplification 97.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot \left(y \cdot 9\right) \leq 4 \cdot 10^{+223}:\\ \;\;\;\;\left(2 \cdot x - t \cdot \left(y \cdot \left(z \cdot 9\right)\right)\right) + b \cdot \left(27 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\left(2 \cdot \frac{x}{y} + 27 \cdot \frac{a \cdot b}{y}\right) - 9 \cdot \left(z \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 98.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot \left(y \cdot 9\right) \leq 10^{+275}:\\ \;\;\;\;\left(2 \cdot x - t \cdot \left(9 \cdot \left(z \cdot y\right)\right)\right) + b \cdot \left(27 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot \left(z \cdot \left(t \cdot -9\right)\right) + 2 \cdot x\right) + a \cdot \left(27 \cdot b\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* z (* y 9.0)) 1e+275)
   (+ (- (* 2.0 x) (* t (* 9.0 (* z y)))) (* b (* 27.0 a)))
   (+ (+ (* y (* z (* t -9.0))) (* 2.0 x)) (* a (* 27.0 b)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z * (y * 9.0)) <= 1e+275) {
		tmp = ((2.0 * x) - (t * (9.0 * (z * y)))) + (b * (27.0 * a));
	} else {
		tmp = ((y * (z * (t * -9.0))) + (2.0 * x)) + (a * (27.0 * b));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z * (y * 9.0d0)) <= 1d+275) then
        tmp = ((2.0d0 * x) - (t * (9.0d0 * (z * y)))) + (b * (27.0d0 * a))
    else
        tmp = ((y * (z * (t * (-9.0d0)))) + (2.0d0 * x)) + (a * (27.0d0 * b))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z * (y * 9.0)) <= 1e+275) {
		tmp = ((2.0 * x) - (t * (9.0 * (z * y)))) + (b * (27.0 * a));
	} else {
		tmp = ((y * (z * (t * -9.0))) + (2.0 * x)) + (a * (27.0 * b));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if (z * (y * 9.0)) <= 1e+275:
		tmp = ((2.0 * x) - (t * (9.0 * (z * y)))) + (b * (27.0 * a))
	else:
		tmp = ((y * (z * (t * -9.0))) + (2.0 * x)) + (a * (27.0 * b))
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(z * Float64(y * 9.0)) <= 1e+275)
		tmp = Float64(Float64(Float64(2.0 * x) - Float64(t * Float64(9.0 * Float64(z * y)))) + Float64(b * Float64(27.0 * a)));
	else
		tmp = Float64(Float64(Float64(y * Float64(z * Float64(t * -9.0))) + Float64(2.0 * x)) + Float64(a * Float64(27.0 * b)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z * (y * 9.0)) <= 1e+275)
		tmp = ((2.0 * x) - (t * (9.0 * (z * y)))) + (b * (27.0 * a));
	else
		tmp = ((y * (z * (t * -9.0))) + (2.0 * x)) + (a * (27.0 * b));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(z * N[(y * 9.0), $MachinePrecision]), $MachinePrecision], 1e+275], N[(N[(N[(2.0 * x), $MachinePrecision] - N[(t * N[(9.0 * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(27.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y * N[(z * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(2.0 * x), $MachinePrecision]), $MachinePrecision] + N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 y #s(literal 9 binary64)) z) < 9.9999999999999996e274

   1. Initial program 97.7%

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

   3. Taylor expanded in y around 0 97.7%

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

   if 9.9999999999999996e274 < (*.f64 (*.f64 y #s(literal 9 binary64)) z)

   1. Initial program 75.4%

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

      1. associate-+l- 75.4%

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

      2. *-commutative 75.4%

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

      3. *-commutative 75.4%

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

      4. associate-*l* 75.4%

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

      5. associate-+l- 75.4%

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

      6. associate-*l* 75.4%

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

      7. *-commutative 75.4%

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

      8. *-commutative 75.4%

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

      9. associate-*l* 95.4%

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

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

      1. sub-neg 95.4%

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

      2. *-commutative 95.4%

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

      3. distribute-rgt-neg-in 95.4%

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

      4. *-commutative 95.4%

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

      5. distribute-lft-neg-in 95.4%

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

      6. metadata-eval 95.4%

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

      7. associate-*l* 95.6%

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

      8. associate-*r* 95.6%

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

      9. *-commutative 95.6%

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

   6. Applied egg-rr 95.6%

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

4. Final simplification 97.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot \left(y \cdot 9\right) \leq 10^{+275}:\\ \;\;\;\;\left(2 \cdot x - t \cdot \left(9 \cdot \left(z \cdot y\right)\right)\right) + b \cdot \left(27 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot \left(z \cdot \left(t \cdot -9\right)\right) + 2 \cdot x\right) + a \cdot \left(27 \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 96.9% accurate, 0.8× speedup

Math

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

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z 2e+96)
   (+ (+ (* y (* z (* t -9.0))) (* 2.0 x)) (* a (* 27.0 b)))
   (* t (+ (* -9.0 (* z y)) (* 2.0 (/ x t))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 2e+96) {
		tmp = ((y * (z * (t * -9.0))) + (2.0 * x)) + (a * (27.0 * b));
	} else {
		tmp = t * ((-9.0 * (z * y)) + (2.0 * (x / t)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= 2d+96) then
        tmp = ((y * (z * (t * (-9.0d0)))) + (2.0d0 * x)) + (a * (27.0d0 * b))
    else
        tmp = t * (((-9.0d0) * (z * y)) + (2.0d0 * (x / t)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 2e+96) {
		tmp = ((y * (z * (t * -9.0))) + (2.0 * x)) + (a * (27.0 * b));
	} else {
		tmp = t * ((-9.0 * (z * y)) + (2.0 * (x / t)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= 2e+96:
		tmp = ((y * (z * (t * -9.0))) + (2.0 * x)) + (a * (27.0 * b))
	else:
		tmp = t * ((-9.0 * (z * y)) + (2.0 * (x / t)))
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= 2e+96)
		tmp = Float64(Float64(Float64(y * Float64(z * Float64(t * -9.0))) + Float64(2.0 * x)) + Float64(a * Float64(27.0 * b)));
	else
		tmp = Float64(t * Float64(Float64(-9.0 * Float64(z * y)) + Float64(2.0 * Float64(x / t))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= 2e+96)
		tmp = ((y * (z * (t * -9.0))) + (2.0 * x)) + (a * (27.0 * b));
	else
		tmp = t * ((-9.0 * (z * y)) + (2.0 * (x / t)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, 2e+96], N[(N[(N[(y * N[(z * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(2.0 * x), $MachinePrecision]), $MachinePrecision] + N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(-9.0 * N[(z * y), $MachinePrecision]), $MachinePrecision] + N[(2.0 * N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 2.0000000000000001e96

   1. Initial program 97.4%

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

      1. associate-+l- 97.4%

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

      2. *-commutative 97.4%

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

      3. *-commutative 97.4%

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

      4. associate-*l* 97.0%

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

      5. associate-+l- 97.0%

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

      6. associate-*l* 97.4%

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

      7. *-commutative 97.4%

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

      8. *-commutative 97.4%

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

      9. associate-*l* 95.4%

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

      10. associate-*l* 94.9%

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

   3. Simplified 94.9%

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

      1. sub-neg 94.9%

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

      2. *-commutative 94.9%

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

      3. distribute-rgt-neg-in 94.9%

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

      4. *-commutative 94.9%

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

      5. distribute-lft-neg-in 94.9%

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

      6. metadata-eval 94.9%

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

      7. associate-*l* 95.0%

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

      8. associate-*r* 95.0%

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

      9. *-commutative 95.0%

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

   6. Applied egg-rr 95.0%

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

   if 2.0000000000000001e96 < 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. associate-+l- 87.6%

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

      2. *-commutative 87.6%

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

      3. *-commutative 87.6%

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

      4. associate-*l* 87.6%

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

      5. associate-+l- 87.6%

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

      6. associate-*l* 87.6%

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

      7. *-commutative 87.6%

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

      8. *-commutative 87.6%

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

      9. associate-*l* 89.6%

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

      10. associate-*l* 89.6%

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

   3. Simplified 89.6%

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

   5. Taylor expanded in a around 0 81.2%

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

      1. cancel-sign-sub-inv 81.2%

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

      2. *-commutative 81.2%

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

      3. associate-*r* 91.4%

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

      4. associate-*r* 91.4%

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

      5. distribute-lft-neg-in 91.4%

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

      6. *-commutative 91.4%

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

      7. distribute-rgt-neg-in 91.4%

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

      8. *-commutative 91.4%

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

      9. metadata-eval 91.4%

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

   7. Applied egg-rr 91.4%

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

   8. Taylor expanded in x around inf 77.2%

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

      1. *-commutative 77.2%

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

      2. associate-/l* 77.3%

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

   10. Simplified 77.3%

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

   11. Taylor expanded in t around inf 71.1%

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

4. Final simplification 90.7%

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

Alternative 8: 80.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-96}:\\ \;\;\;\;y \cdot \left(27 \cdot \frac{a \cdot b}{y} + \left(z \cdot t\right) \cdot -9\right)\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-90}:\\ \;\;\;\;2 \cdot x + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot x + z \cdot \left(-9 \cdot \left(y \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -4.8e-96)
   (* y (+ (* 27.0 (/ (* a b) y)) (* (* z t) -9.0)))
   (if (<= z 2.1e-90)
     (+ (* 2.0 x) (* 27.0 (* a b)))
     (+ (* 2.0 x) (* z (* -9.0 (* y t)))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -4.8e-96) {
		tmp = y * ((27.0 * ((a * b) / y)) + ((z * t) * -9.0));
	} else if (z <= 2.1e-90) {
		tmp = (2.0 * x) + (27.0 * (a * b));
	} else {
		tmp = (2.0 * x) + (z * (-9.0 * (y * t)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-4.8d-96)) then
        tmp = y * ((27.0d0 * ((a * b) / y)) + ((z * t) * (-9.0d0)))
    else if (z <= 2.1d-90) then
        tmp = (2.0d0 * x) + (27.0d0 * (a * b))
    else
        tmp = (2.0d0 * x) + (z * ((-9.0d0) * (y * t)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -4.8e-96) {
		tmp = y * ((27.0 * ((a * b) / y)) + ((z * t) * -9.0));
	} else if (z <= 2.1e-90) {
		tmp = (2.0 * x) + (27.0 * (a * b));
	} else {
		tmp = (2.0 * x) + (z * (-9.0 * (y * t)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -4.8e-96:
		tmp = y * ((27.0 * ((a * b) / y)) + ((z * t) * -9.0))
	elif z <= 2.1e-90:
		tmp = (2.0 * x) + (27.0 * (a * b))
	else:
		tmp = (2.0 * x) + (z * (-9.0 * (y * t)))
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -4.8e-96)
		tmp = Float64(y * Float64(Float64(27.0 * Float64(Float64(a * b) / y)) + Float64(Float64(z * t) * -9.0)));
	elseif (z <= 2.1e-90)
		tmp = Float64(Float64(2.0 * x) + Float64(27.0 * Float64(a * b)));
	else
		tmp = Float64(Float64(2.0 * x) + Float64(z * Float64(-9.0 * Float64(y * t))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -4.8e-96)
		tmp = y * ((27.0 * ((a * b) / y)) + ((z * t) * -9.0));
	elseif (z <= 2.1e-90)
		tmp = (2.0 * x) + (27.0 * (a * b));
	else
		tmp = (2.0 * x) + (z * (-9.0 * (y * t)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -4.8e-96], N[(y * N[(N[(27.0 * N[(N[(a * b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.1e-90], N[(N[(2.0 * x), $MachinePrecision] + N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 * x), $MachinePrecision] + N[(z * N[(-9.0 * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.80000000000000038e-96

   1. Initial program 94.2%

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

      1. associate-+l- 94.2%

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

      2. *-commutative 94.2%

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

      3. *-commutative 94.2%

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

      4. associate-*l* 93.1%

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

      5. associate-+l- 93.1%

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

      6. associate-*l* 94.2%

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

      7. *-commutative 94.2%

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

      8. *-commutative 94.2%

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

      9. associate-*l* 90.1%

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

      10. associate-*l* 89.0%

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

   3. Simplified 89.0%

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

   5. Taylor expanded in z around inf 93.2%

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

   6. Taylor expanded in x around 0 71.5%

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

      1. *-commutative 71.5%

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

      2. *-commutative 71.5%

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

      3. associate-*l* 71.5%

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

   8. Simplified 71.5%

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

   9. Taylor expanded in y around inf 56.1%

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

   if -4.80000000000000038e-96 < z < 2.0999999999999999e-90

   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. associate-+l- 99.8%

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

      2. *-commutative 99.8%

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

      3. *-commutative 99.8%

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

      4. associate-*l* 99.8%

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

      5. associate-+l- 99.8%

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

      6. associate-*l* 99.8%

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

      7. *-commutative 99.8%

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

      8. *-commutative 99.8%

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

      9. associate-*l* 99.8%

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

      10. associate-*l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 85.6%

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

   if 2.0999999999999999e-90 < z

   1. Initial program 92.8%

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

      1. associate-+l- 92.8%

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

      2. *-commutative 92.8%

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

      3. *-commutative 92.8%

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

      4. associate-*l* 92.7%

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

      5. associate-+l- 92.7%

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

      6. associate-*l* 92.8%

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

      7. *-commutative 92.8%

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

      8. *-commutative 92.8%

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

      9. associate-*l* 93.0%

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

      10. associate-*l* 93.1%

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

   3. Simplified 93.1%

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

   5. Taylor expanded in a around 0 75.8%

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

      1. cancel-sign-sub-inv 75.8%

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

      2. *-commutative 75.8%

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

      3. associate-*r* 81.7%

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

      4. associate-*r* 81.6%

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

      5. distribute-lft-neg-in 81.6%

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

      6. *-commutative 81.6%

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

      7. distribute-rgt-neg-in 81.6%

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

      8. *-commutative 81.6%

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

      9. metadata-eval 81.6%

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

   7. Applied egg-rr 81.6%

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

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-96}:\\ \;\;\;\;y \cdot \left(27 \cdot \frac{a \cdot b}{y} + \left(z \cdot t\right) \cdot -9\right)\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-90}:\\ \;\;\;\;2 \cdot x + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot x + z \cdot \left(-9 \cdot \left(y \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 79.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{-91}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right) + z \cdot \left(y \cdot \left(t \cdot -9\right)\right)\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-88}:\\ \;\;\;\;2 \cdot x + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot x + z \cdot \left(-9 \cdot \left(y \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -3.3e-91)
   (+ (* a (* 27.0 b)) (* z (* y (* t -9.0))))
   (if (<= z 1.8e-88)
     (+ (* 2.0 x) (* 27.0 (* a b)))
     (+ (* 2.0 x) (* z (* -9.0 (* y t)))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -3.3e-91) {
		tmp = (a * (27.0 * b)) + (z * (y * (t * -9.0)));
	} else if (z <= 1.8e-88) {
		tmp = (2.0 * x) + (27.0 * (a * b));
	} else {
		tmp = (2.0 * x) + (z * (-9.0 * (y * t)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-3.3d-91)) then
        tmp = (a * (27.0d0 * b)) + (z * (y * (t * (-9.0d0))))
    else if (z <= 1.8d-88) then
        tmp = (2.0d0 * x) + (27.0d0 * (a * b))
    else
        tmp = (2.0d0 * x) + (z * ((-9.0d0) * (y * t)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -3.3e-91) {
		tmp = (a * (27.0 * b)) + (z * (y * (t * -9.0)));
	} else if (z <= 1.8e-88) {
		tmp = (2.0 * x) + (27.0 * (a * b));
	} else {
		tmp = (2.0 * x) + (z * (-9.0 * (y * t)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -3.3e-91:
		tmp = (a * (27.0 * b)) + (z * (y * (t * -9.0)))
	elif z <= 1.8e-88:
		tmp = (2.0 * x) + (27.0 * (a * b))
	else:
		tmp = (2.0 * x) + (z * (-9.0 * (y * t)))
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -3.3e-91)
		tmp = Float64(Float64(a * Float64(27.0 * b)) + Float64(z * Float64(y * Float64(t * -9.0))));
	elseif (z <= 1.8e-88)
		tmp = Float64(Float64(2.0 * x) + Float64(27.0 * Float64(a * b)));
	else
		tmp = Float64(Float64(2.0 * x) + Float64(z * Float64(-9.0 * Float64(y * t))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -3.3e-91)
		tmp = (a * (27.0 * b)) + (z * (y * (t * -9.0)));
	elseif (z <= 1.8e-88)
		tmp = (2.0 * x) + (27.0 * (a * b));
	else
		tmp = (2.0 * x) + (z * (-9.0 * (y * t)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -3.3e-91], N[(N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision] + N[(z * N[(y * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.8e-88], N[(N[(2.0 * x), $MachinePrecision] + N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 * x), $MachinePrecision] + N[(z * N[(-9.0 * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.30000000000000011e-91

   1. Initial program 94.1%

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

      1. associate-+l- 94.1%

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

      2. *-commutative 94.1%

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

      3. *-commutative 94.1%

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

      4. associate-*l* 93.0%

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

      5. associate-+l- 93.0%

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

      6. associate-*l* 94.1%

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

      7. *-commutative 94.1%

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

      8. *-commutative 94.1%

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

      9. associate-*l* 89.9%

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

      10. associate-*l* 88.8%

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

   3. Simplified 88.8%

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

   5. Taylor expanded in z around inf 94.1%

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

   6. Taylor expanded in x around 0 73.1%

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

      1. *-commutative 73.1%

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

      2. *-commutative 73.1%

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

      3. associate-*l* 73.1%

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

   8. Simplified 73.1%

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

   if -3.30000000000000011e-91 < z < 1.8e-88

   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. associate-+l- 99.8%

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

      2. *-commutative 99.8%

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

      3. *-commutative 99.8%

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

      4. associate-*l* 99.8%

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

      5. associate-+l- 99.8%

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

      6. associate-*l* 99.8%

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

      7. *-commutative 99.8%

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

      8. *-commutative 99.8%

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

      9. associate-*l* 99.8%

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

      10. associate-*l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 85.9%

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

   if 1.8e-88 < z

   1. Initial program 92.8%

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

      1. associate-+l- 92.8%

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

      2. *-commutative 92.8%

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

      3. *-commutative 92.8%

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

      4. associate-*l* 92.7%

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

      5. associate-+l- 92.7%

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

      6. associate-*l* 92.8%

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

      7. *-commutative 92.8%

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

      8. *-commutative 92.8%

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

      9. associate-*l* 93.0%

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

      10. associate-*l* 93.1%

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

   3. Simplified 93.1%

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

   5. Taylor expanded in a around 0 75.8%

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

      1. cancel-sign-sub-inv 75.8%

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

      2. *-commutative 75.8%

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

      3. associate-*r* 81.7%

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

      4. associate-*r* 81.6%

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

      5. distribute-lft-neg-in 81.6%

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

      6. *-commutative 81.6%

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

      7. distribute-rgt-neg-in 81.6%

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

      8. *-commutative 81.6%

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

      9. metadata-eval 81.6%

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

   7. Applied egg-rr 81.6%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{-91}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right) + z \cdot \left(y \cdot \left(t \cdot -9\right)\right)\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-88}:\\ \;\;\;\;2 \cdot x + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot x + z \cdot \left(-9 \cdot \left(y \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 75.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{-100}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-36}:\\ \;\;\;\;2 \cdot x + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot x - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -2.4e-100)
   (* -9.0 (* y (* z t)))
   (if (<= t 1.15e-36)
     (+ (* 2.0 x) (* 27.0 (* a b)))
     (- (* 2.0 x) (* 9.0 (* t (* z y)))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.4e-100) {
		tmp = -9.0 * (y * (z * t));
	} else if (t <= 1.15e-36) {
		tmp = (2.0 * x) + (27.0 * (a * b));
	} else {
		tmp = (2.0 * x) - (9.0 * (t * (z * y)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-2.4d-100)) then
        tmp = (-9.0d0) * (y * (z * t))
    else if (t <= 1.15d-36) then
        tmp = (2.0d0 * x) + (27.0d0 * (a * b))
    else
        tmp = (2.0d0 * x) - (9.0d0 * (t * (z * y)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.4e-100) {
		tmp = -9.0 * (y * (z * t));
	} else if (t <= 1.15e-36) {
		tmp = (2.0 * x) + (27.0 * (a * b));
	} else {
		tmp = (2.0 * x) - (9.0 * (t * (z * y)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -2.4e-100:
		tmp = -9.0 * (y * (z * t))
	elif t <= 1.15e-36:
		tmp = (2.0 * x) + (27.0 * (a * b))
	else:
		tmp = (2.0 * x) - (9.0 * (t * (z * y)))
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -2.4e-100)
		tmp = Float64(-9.0 * Float64(y * Float64(z * t)));
	elseif (t <= 1.15e-36)
		tmp = Float64(Float64(2.0 * x) + Float64(27.0 * Float64(a * b)));
	else
		tmp = Float64(Float64(2.0 * x) - Float64(9.0 * Float64(t * Float64(z * y))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -2.4e-100)
		tmp = -9.0 * (y * (z * t));
	elseif (t <= 1.15e-36)
		tmp = (2.0 * x) + (27.0 * (a * b));
	else
		tmp = (2.0 * x) - (9.0 * (t * (z * y)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -2.4e-100], N[(-9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.15e-36], N[(N[(2.0 * x), $MachinePrecision] + N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 * x), $MachinePrecision] - N[(9.0 * N[(t * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.4000000000000003e-100

   1. Initial program 97.7%

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

      1. associate-+l- 97.7%

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

      2. *-commutative 97.7%

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

      3. *-commutative 97.7%

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

      4. associate-*l* 97.8%

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

      5. associate-+l- 97.8%

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

      6. associate-*l* 97.7%

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

      7. *-commutative 97.7%

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

      8. *-commutative 97.7%

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

      9. associate-*l* 94.9%

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

      10. associate-*l* 94.9%

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

   3. Simplified 94.9%

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

   5. Taylor expanded in x around inf 84.7%

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

   6. Taylor expanded in t around inf 47.1%

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

      1. associate-*r* 44.2%

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

      2. *-commutative 44.2%

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

      3. associate-*r* 45.2%

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

   8. Simplified 45.2%

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

   if -2.4000000000000003e-100 < t < 1.14999999999999998e-36

   1. Initial program 93.6%

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

      1. associate-+l- 93.6%

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

      2. *-commutative 93.6%

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

      3. *-commutative 93.6%

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

      4. associate-*l* 93.7%

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

      5. associate-+l- 93.7%

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

      6. associate-*l* 93.6%

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

      7. *-commutative 93.6%

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

      8. *-commutative 93.6%

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

      9. associate-*l* 99.0%

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

      10. associate-*l* 98.2%

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

   3. Simplified 98.2%

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

   5. Taylor expanded in y around 0 86.5%

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

   if 1.14999999999999998e-36 < t

   1. Initial program 96.2%

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

      1. associate-+l- 96.2%

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

      2. *-commutative 96.2%

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

      3. *-commutative 96.2%

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

      4. associate-*l* 94.3%

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

      5. associate-+l- 94.3%

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

      6. associate-*l* 96.2%

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

      7. *-commutative 96.2%

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

      8. *-commutative 96.2%

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

      9. associate-*l* 84.1%

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

      10. associate-*l* 84.1%

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

   3. Simplified 84.1%

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

   5. Taylor expanded in a around 0 91.0%

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

4. Final simplification 72.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{-100}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-36}:\\ \;\;\;\;2 \cdot x + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot x - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 75.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{+91}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+25}:\\ \;\;\;\;2 \cdot x + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot \left(t \cdot -9\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -6.4e+91)
   (* -9.0 (* y (* z t)))
   (if (<= z 4.8e+25) (+ (* 2.0 x) (* 27.0 (* a b))) (* z (* y (* t -9.0))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -6.4e+91) {
		tmp = -9.0 * (y * (z * t));
	} else if (z <= 4.8e+25) {
		tmp = (2.0 * x) + (27.0 * (a * b));
	} else {
		tmp = z * (y * (t * -9.0));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-6.4d+91)) then
        tmp = (-9.0d0) * (y * (z * t))
    else if (z <= 4.8d+25) then
        tmp = (2.0d0 * x) + (27.0d0 * (a * b))
    else
        tmp = z * (y * (t * (-9.0d0)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -6.4e+91) {
		tmp = -9.0 * (y * (z * t));
	} else if (z <= 4.8e+25) {
		tmp = (2.0 * x) + (27.0 * (a * b));
	} else {
		tmp = z * (y * (t * -9.0));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -6.4e+91:
		tmp = -9.0 * (y * (z * t))
	elif z <= 4.8e+25:
		tmp = (2.0 * x) + (27.0 * (a * b))
	else:
		tmp = z * (y * (t * -9.0))
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -6.4e+91)
		tmp = Float64(-9.0 * Float64(y * Float64(z * t)));
	elseif (z <= 4.8e+25)
		tmp = Float64(Float64(2.0 * x) + Float64(27.0 * Float64(a * b)));
	else
		tmp = Float64(z * Float64(y * Float64(t * -9.0)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -6.4e+91)
		tmp = -9.0 * (y * (z * t));
	elseif (z <= 4.8e+25)
		tmp = (2.0 * x) + (27.0 * (a * b));
	else
		tmp = z * (y * (t * -9.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -6.4e+91], N[(-9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.8e+25], N[(N[(2.0 * x), $MachinePrecision] + N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(y * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.39999999999999979e91

   1. Initial program 92.5%

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

      1. associate-+l- 92.5%

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

      2. *-commutative 92.5%

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

      3. *-commutative 92.5%

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

      4. associate-*l* 90.7%

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

      5. associate-+l- 90.7%

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

      6. associate-*l* 92.5%

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

      7. *-commutative 92.5%

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

      8. *-commutative 92.5%

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

      9. associate-*l* 84.1%

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

      10. associate-*l* 82.3%

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

   3. Simplified 82.3%

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

   5. Taylor expanded in x around inf 76.8%

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

   6. Taylor expanded in t around inf 52.6%

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

      1. associate-*r* 52.2%

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

      2. *-commutative 52.2%

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

      3. associate-*r* 44.1%

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

   8. Simplified 44.1%

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

   if -6.39999999999999979e91 < z < 4.79999999999999992e25

   1. Initial program 99.1%

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

      1. associate-+l- 99.1%

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

      2. *-commutative 99.1%

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

      3. *-commutative 99.1%

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

      4. associate-*l* 99.1%

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

      5. associate-+l- 99.1%

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

      6. associate-*l* 99.1%

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

      7. *-commutative 99.1%

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

      8. *-commutative 99.1%

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

      9. associate-*l* 99.2%

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

      10. associate-*l* 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in y around 0 83.7%

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

   if 4.79999999999999992e25 < z

   1. Initial program 90.2%

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

   3. Taylor expanded in y around 0 90.3%

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

   4. Taylor expanded in y around inf 63.4%

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

      1. *-commutative 63.4%

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

      2. associate-*r* 65.1%

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

      3. associate-*l* 65.1%

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

      4. *-commutative 65.1%

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

      5. *-commutative 65.1%

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

      6. associate-*l* 65.1%

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

      7. *-commutative 65.1%

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

      8. associate-*r* 69.6%

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

      9. *-commutative 69.6%

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

      10. associate-*l* 69.7%

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

      11. *-commutative 69.7%

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

   6. Simplified 69.7%

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

   7. Taylor expanded in t around 0 69.6%

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

      1. *-commutative 69.6%

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

      2. *-commutative 69.6%

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

      3. associate-*r* 69.6%

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

   9. Simplified 69.6%

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

4. Final simplification 72.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{+91}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+25}:\\ \;\;\;\;2 \cdot x + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot \left(t \cdot -9\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 46.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -1.15 \cdot 10^{-79} \lor \neg \left(b \leq 5.5 \cdot 10^{+45}\right):\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot x\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.15e-79) (not (<= b 5.5e+45))) (* 27.0 (* a b)) (* 2.0 x)))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.15e-79) || !(b <= 5.5e+45)) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = 2.0 * x;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-1.15d-79)) .or. (.not. (b <= 5.5d+45))) then
        tmp = 27.0d0 * (a * b)
    else
        tmp = 2.0d0 * x
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.15e-79) || !(b <= 5.5e+45)) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = 2.0 * x;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -1.15e-79) or not (b <= 5.5e+45):
		tmp = 27.0 * (a * b)
	else:
		tmp = 2.0 * x
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1.15e-79) || !(b <= 5.5e+45))
		tmp = Float64(27.0 * Float64(a * b));
	else
		tmp = Float64(2.0 * x);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -1.15e-79) || ~((b <= 5.5e+45)))
		tmp = 27.0 * (a * b);
	else
		tmp = 2.0 * x;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1.15e-79], N[Not[LessEqual[b, 5.5e+45]], $MachinePrecision]], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], N[(2.0 * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.15000000000000006e-79 or 5.5000000000000001e45 < b

   1. Initial program 95.3%

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

      1. associate-+l- 95.3%

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

      2. *-commutative 95.3%

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

      3. *-commutative 95.3%

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

      4. associate-*l* 95.3%

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

      5. associate-+l- 95.3%

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

      6. associate-*l* 95.3%

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

      7. *-commutative 95.3%

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

      8. *-commutative 95.3%

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

      9. associate-*l* 94.7%

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

      10. associate-*l* 94.0%

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

   3. Simplified 94.0%

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

   5. Taylor expanded in a around inf 51.5%

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

   if -1.15000000000000006e-79 < b < 5.5000000000000001e45

   1. Initial program 96.1%

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

      1. associate-+l- 96.1%

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

      2. *-commutative 96.1%

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

      3. *-commutative 96.1%

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

      4. associate-*l* 95.3%

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

      5. associate-+l- 95.3%

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

      6. associate-*l* 96.1%

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

      7. *-commutative 96.1%

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

      8. *-commutative 96.1%

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

      9. associate-*l* 93.9%

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

      10. associate-*l* 93.9%

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

   3. Simplified 93.9%

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

   5. Taylor expanded in x around inf 43.8%

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

4. Final simplification 47.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.15 \cdot 10^{-79} \lor \neg \left(b \leq 5.5 \cdot 10^{+45}\right):\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 46.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -1.7 \cdot 10^{-79}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;b \leq 1.65 \cdot 10^{+45}:\\ \;\;\;\;2 \cdot x\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(27 \cdot a\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.7e-79)
   (* 27.0 (* a b))
   (if (<= b 1.65e+45) (* 2.0 x) (* b (* 27.0 a)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.7e-79) {
		tmp = 27.0 * (a * b);
	} else if (b <= 1.65e+45) {
		tmp = 2.0 * x;
	} else {
		tmp = b * (27.0 * a);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1.7d-79)) then
        tmp = 27.0d0 * (a * b)
    else if (b <= 1.65d+45) then
        tmp = 2.0d0 * x
    else
        tmp = b * (27.0d0 * a)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.7e-79) {
		tmp = 27.0 * (a * b);
	} else if (b <= 1.65e+45) {
		tmp = 2.0 * x;
	} else {
		tmp = b * (27.0 * a);
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.7e-79:
		tmp = 27.0 * (a * b)
	elif b <= 1.65e+45:
		tmp = 2.0 * x
	else:
		tmp = b * (27.0 * a)
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.7e-79)
		tmp = Float64(27.0 * Float64(a * b));
	elseif (b <= 1.65e+45)
		tmp = Float64(2.0 * x);
	else
		tmp = Float64(b * Float64(27.0 * a));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.7e-79)
		tmp = 27.0 * (a * b);
	elseif (b <= 1.65e+45)
		tmp = 2.0 * x;
	else
		tmp = b * (27.0 * a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.7e-79], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.65e+45], N[(2.0 * x), $MachinePrecision], N[(b * N[(27.0 * a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.69999999999999988e-79

   1. Initial program 95.1%

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

      1. associate-+l- 95.1%

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

      2. *-commutative 95.1%

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

      3. *-commutative 95.1%

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

      4. associate-*l* 95.1%

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

      5. associate-+l- 95.1%

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

      6. associate-*l* 95.1%

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

      7. *-commutative 95.1%

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

      8. *-commutative 95.1%

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

      9. associate-*l* 94.0%

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

      10. associate-*l* 94.0%

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

   3. Simplified 94.0%

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

   5. Taylor expanded in a around inf 46.7%

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

   if -1.69999999999999988e-79 < b < 1.65e45

   1. Initial program 96.1%

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

      1. associate-+l- 96.1%

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

      2. *-commutative 96.1%

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

      3. *-commutative 96.1%

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

      4. associate-*l* 95.3%

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

      5. associate-+l- 95.3%

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

      6. associate-*l* 96.1%

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

      7. *-commutative 96.1%

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

      8. *-commutative 96.1%

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

      9. associate-*l* 93.9%

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

      10. associate-*l* 93.9%

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

   3. Simplified 93.9%

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

   5. Taylor expanded in x around inf 43.8%

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

   if 1.65e45 < b

   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. associate-+l- 95.7%

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

      2. *-commutative 95.7%

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

      3. *-commutative 95.7%

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

      4. associate-*l* 95.6%

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

      5. associate-+l- 95.6%

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

      6. associate-*l* 95.7%

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

      7. *-commutative 95.7%

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

      8. *-commutative 95.7%

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

      9. associate-*l* 96.0%

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

      10. associate-*l* 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 a around inf 59.6%

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

      1. associate-*r* 59.7%

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

   7. Simplified 59.7%

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

4. Final simplification 47.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.7 \cdot 10^{-79}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;b \leq 1.65 \cdot 10^{+45}:\\ \;\;\;\;2 \cdot x\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(27 \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 30.5% accurate, 5.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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. associate-+l- 95.7%

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

   2. *-commutative 95.7%

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

   3. *-commutative 95.7%

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

   4. associate-*l* 95.3%

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

   5. associate-+l- 95.3%

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

   6. associate-*l* 95.7%

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

   7. *-commutative 95.7%

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

   8. *-commutative 95.7%

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

   9. associate-*l* 94.3%

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

   10. associate-*l* 94.0%

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

3. Simplified 94.0%

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

5. Taylor expanded in x around inf 31.9%

   \[\leadsto \color{blue}{2 \cdot x} \]
6. Add Preprocessing

Developer target: 94.9% 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 2024085 
(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)))