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

Percentage Accurate: 95.1% → 99.0%

Time: 14.1s

Alternatives: 16

Speedup: 0.7×

• 28.6% 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: 95.1% 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: 99.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot 9 \leq -200:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, y \cdot \left(\left(-9 \cdot z\right) \cdot t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - \left(y \cdot t\right) \cdot \left(9 \cdot z\right)\right) + a \cdot \left(27 \cdot b\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* y 9.0) -200.0)
   (fma a (* 27.0 b) (fma x 2.0 (* y (* (* -9.0 z) t))))
   (+ (- (* x 2.0) (* (* y t) (* 9.0 z))) (* a (* 27.0 b)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y * 9.0) <= -200.0) {
		tmp = fma(a, (27.0 * b), fma(x, 2.0, (y * ((-9.0 * z) * t))));
	} else {
		tmp = ((x * 2.0) - ((y * t) * (9.0 * z))) + (a * (27.0 * b));
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(y * 9.0) <= -200.0)
		tmp = fma(a, Float64(27.0 * b), fma(x, 2.0, Float64(y * Float64(Float64(-9.0 * z) * t))));
	else
		tmp = Float64(Float64(Float64(x * 2.0) - Float64(Float64(y * t) * Float64(9.0 * z))) + Float64(a * Float64(27.0 * b)));
	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[N[(y * 9.0), $MachinePrecision], -200.0], N[(a * N[(27.0 * b), $MachinePrecision] + N[(x * 2.0 + N[(y * N[(N[(-9.0 * z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * 2.0), $MachinePrecision] - N[(N[(y * t), $MachinePrecision] * N[(9.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y 9) < -200

   1. Initial program 88.1%

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

      1. +-commutative 88.1%

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

      2. associate-+r- 88.1%

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

      3. *-commutative 88.1%

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

      4. cancel-sign-sub-inv 88.1%

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

      5. associate-*r* 92.3%

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

      6. distribute-lft-neg-in 92.3%

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

      7. *-commutative 92.3%

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

      8. cancel-sign-sub-inv 92.3%

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

      9. associate-+r- 92.3%

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

      10. associate-*l* 92.3%

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

      11. fma-define 93.9%

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

      12. sub-neg 93.9%

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

      13. fma-define 93.9%

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

      14. *-commutative 93.9%

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

      15. distribute-lft-neg-in 93.9%

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

      16. associate-*l* 89.6%

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

      17. *-commutative 89.6%

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

   3. Simplified 99.7%

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

   if -200 < (*.f64 y 9)

   1. Initial program 95.3%

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

      1. sub-neg 95.3%

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

      2. sub-neg 95.3%

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

      3. associate-*l* 95.8%

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

      4. associate-*l* 95.8%

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

   3. Simplified 95.8%

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

   5. Taylor expanded in y around 0 95.3%

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

      1. *-commutative 95.3%

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

      2. associate-*r* 95.7%

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

      3. *-commutative 95.7%

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

      4. associate-*r* 95.3%

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

      5. *-commutative 95.3%

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

      6. associate-*r* 96.7%

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

      7. associate-*l* 96.8%

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

      8. *-commutative 96.8%

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

   7. Simplified 96.8%

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

4. Final simplification 97.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot 9 \leq -200:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, y \cdot \left(\left(-9 \cdot z\right) \cdot t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - \left(y \cdot t\right) \cdot \left(9 \cdot z\right)\right) + a \cdot \left(27 \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 47.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := t \cdot \left(z \cdot \left(y \cdot -9\right)\right)\\ \mathbf{if}\;a \cdot 27 \leq -5 \cdot 10^{+120}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \mathbf{elif}\;a \cdot 27 \leq -2 \cdot 10^{+29}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-9 \cdot t\right)\right)\\ \mathbf{elif}\;a \cdot 27 \leq -5000000:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;a \cdot 27 \leq -4 \cdot 10^{-82}:\\ \;\;\;\;z \cdot \left(y \cdot \left(-9 \cdot t\right)\right)\\ \mathbf{elif}\;a \cdot 27 \leq -2 \cdot 10^{-106}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;a \cdot 27 \leq -1 \cdot 10^{-277}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot 27 \leq 5 \cdot 10^{-199}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;a \cdot 27 \leq 10^{+20}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (* z (* y -9.0)))))
   (if (<= (* a 27.0) -5e+120)
     (* b (* a 27.0))
     (if (<= (* a 27.0) -2e+29)
       (* y (* z (* -9.0 t)))
       (if (<= (* a 27.0) -5000000.0)
         (* x 2.0)
         (if (<= (* a 27.0) -4e-82)
           (* z (* y (* -9.0 t)))
           (if (<= (* a 27.0) -2e-106)
             (* x 2.0)
             (if (<= (* a 27.0) -1e-277)
               t_1
               (if (<= (* a 27.0) 5e-199)
                 (* x 2.0)
                 (if (<= (* a 27.0) 1e+20) t_1 (* 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 t_1 = t * (z * (y * -9.0));
	double tmp;
	if ((a * 27.0) <= -5e+120) {
		tmp = b * (a * 27.0);
	} else if ((a * 27.0) <= -2e+29) {
		tmp = y * (z * (-9.0 * t));
	} else if ((a * 27.0) <= -5000000.0) {
		tmp = x * 2.0;
	} else if ((a * 27.0) <= -4e-82) {
		tmp = z * (y * (-9.0 * t));
	} else if ((a * 27.0) <= -2e-106) {
		tmp = x * 2.0;
	} else if ((a * 27.0) <= -1e-277) {
		tmp = t_1;
	} else if ((a * 27.0) <= 5e-199) {
		tmp = x * 2.0;
	} else if ((a * 27.0) <= 1e+20) {
		tmp = t_1;
	} else {
		tmp = 27.0 * (a * b);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (z * (y * (-9.0d0)))
    if ((a * 27.0d0) <= (-5d+120)) then
        tmp = b * (a * 27.0d0)
    else if ((a * 27.0d0) <= (-2d+29)) then
        tmp = y * (z * ((-9.0d0) * t))
    else if ((a * 27.0d0) <= (-5000000.0d0)) then
        tmp = x * 2.0d0
    else if ((a * 27.0d0) <= (-4d-82)) then
        tmp = z * (y * ((-9.0d0) * t))
    else if ((a * 27.0d0) <= (-2d-106)) then
        tmp = x * 2.0d0
    else if ((a * 27.0d0) <= (-1d-277)) then
        tmp = t_1
    else if ((a * 27.0d0) <= 5d-199) then
        tmp = x * 2.0d0
    else if ((a * 27.0d0) <= 1d+20) then
        tmp = t_1
    else
        tmp = 27.0d0 * (a * b)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (z * (y * -9.0));
	double tmp;
	if ((a * 27.0) <= -5e+120) {
		tmp = b * (a * 27.0);
	} else if ((a * 27.0) <= -2e+29) {
		tmp = y * (z * (-9.0 * t));
	} else if ((a * 27.0) <= -5000000.0) {
		tmp = x * 2.0;
	} else if ((a * 27.0) <= -4e-82) {
		tmp = z * (y * (-9.0 * t));
	} else if ((a * 27.0) <= -2e-106) {
		tmp = x * 2.0;
	} else if ((a * 27.0) <= -1e-277) {
		tmp = t_1;
	} else if ((a * 27.0) <= 5e-199) {
		tmp = x * 2.0;
	} else if ((a * 27.0) <= 1e+20) {
		tmp = t_1;
	} else {
		tmp = 27.0 * (a * b);
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = t * (z * (y * -9.0))
	tmp = 0
	if (a * 27.0) <= -5e+120:
		tmp = b * (a * 27.0)
	elif (a * 27.0) <= -2e+29:
		tmp = y * (z * (-9.0 * t))
	elif (a * 27.0) <= -5000000.0:
		tmp = x * 2.0
	elif (a * 27.0) <= -4e-82:
		tmp = z * (y * (-9.0 * t))
	elif (a * 27.0) <= -2e-106:
		tmp = x * 2.0
	elif (a * 27.0) <= -1e-277:
		tmp = t_1
	elif (a * 27.0) <= 5e-199:
		tmp = x * 2.0
	elif (a * 27.0) <= 1e+20:
		tmp = t_1
	else:
		tmp = 27.0 * (a * b)
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(z * Float64(y * -9.0)))
	tmp = 0.0
	if (Float64(a * 27.0) <= -5e+120)
		tmp = Float64(b * Float64(a * 27.0));
	elseif (Float64(a * 27.0) <= -2e+29)
		tmp = Float64(y * Float64(z * Float64(-9.0 * t)));
	elseif (Float64(a * 27.0) <= -5000000.0)
		tmp = Float64(x * 2.0);
	elseif (Float64(a * 27.0) <= -4e-82)
		tmp = Float64(z * Float64(y * Float64(-9.0 * t)));
	elseif (Float64(a * 27.0) <= -2e-106)
		tmp = Float64(x * 2.0);
	elseif (Float64(a * 27.0) <= -1e-277)
		tmp = t_1;
	elseif (Float64(a * 27.0) <= 5e-199)
		tmp = Float64(x * 2.0);
	elseif (Float64(a * 27.0) <= 1e+20)
		tmp = t_1;
	else
		tmp = Float64(27.0 * Float64(a * b));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (z * (y * -9.0));
	tmp = 0.0;
	if ((a * 27.0) <= -5e+120)
		tmp = b * (a * 27.0);
	elseif ((a * 27.0) <= -2e+29)
		tmp = y * (z * (-9.0 * t));
	elseif ((a * 27.0) <= -5000000.0)
		tmp = x * 2.0;
	elseif ((a * 27.0) <= -4e-82)
		tmp = z * (y * (-9.0 * t));
	elseif ((a * 27.0) <= -2e-106)
		tmp = x * 2.0;
	elseif ((a * 27.0) <= -1e-277)
		tmp = t_1;
	elseif ((a * 27.0) <= 5e-199)
		tmp = x * 2.0;
	elseif ((a * 27.0) <= 1e+20)
		tmp = t_1;
	else
		tmp = 27.0 * (a * b);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(z * N[(y * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * 27.0), $MachinePrecision], -5e+120], N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 27.0), $MachinePrecision], -2e+29], N[(y * N[(z * N[(-9.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 27.0), $MachinePrecision], -5000000.0], N[(x * 2.0), $MachinePrecision], If[LessEqual[N[(a * 27.0), $MachinePrecision], -4e-82], N[(z * N[(y * N[(-9.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 27.0), $MachinePrecision], -2e-106], N[(x * 2.0), $MachinePrecision], If[LessEqual[N[(a * 27.0), $MachinePrecision], -1e-277], t$95$1, If[LessEqual[N[(a * 27.0), $MachinePrecision], 5e-199], N[(x * 2.0), $MachinePrecision], If[LessEqual[N[(a * 27.0), $MachinePrecision], 1e+20], t$95$1, N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if (*.f64 a 27) < -5.00000000000000019e120

   1. Initial program 97.5%

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

      1. sub-neg 97.5%

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

      2. sub-neg 97.5%

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

      3. associate-*l* 97.6%

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

      4. associate-*l* 97.6%

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

   3. Simplified 97.6%

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

   5. Taylor expanded in a around inf 78.8%

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

      1. associate-*r* 78.9%

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

      2. *-commutative 78.9%

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

      3. associate-*r* 78.9%

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

   7. Simplified 78.9%

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

      1. add-cbrt-cube 56.5%

         \[\leadsto \color{blue}{\sqrt[3]{\left(\left(a \cdot \left(27 \cdot b\right)\right) \cdot \left(a \cdot \left(27 \cdot b\right)\right)\right) \cdot \left(a \cdot \left(27 \cdot b\right)\right)}} \]

      2. pow3 56.5%

         \[\leadsto \sqrt[3]{\color{blue}{{\left(a \cdot \left(27 \cdot b\right)\right)}^{3}}} \]

   9. Applied egg-rr 56.5%

      \[\leadsto \color{blue}{\sqrt[3]{{\left(a \cdot \left(27 \cdot b\right)\right)}^{3}}} \]
   10. Step-by-step derivation

       1. rem-cbrt-cube 78.9%

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

       2. associate-*r* 78.9%

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

   11. Applied egg-rr 78.9%

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

   if -5.00000000000000019e120 < (*.f64 a 27) < -1.99999999999999983e29

   1. Initial program 90.7%

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

      1. sub-neg 90.7%

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

      2. sub-neg 90.7%

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

      3. associate-*l* 85.9%

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

      4. associate-*l* 85.7%

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

   3. Simplified 85.7%

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

   5. Taylor expanded in y around 0 90.4%

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

      1. *-commutative 90.4%

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

      2. associate-*r* 85.7%

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

      3. *-commutative 85.7%

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

      4. associate-*r* 90.4%

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

      5. *-commutative 90.4%

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

      6. associate-*r* 86.2%

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

      7. associate-*l* 86.3%

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

      8. *-commutative 86.3%

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

   7. Simplified 86.3%

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

   8. Taylor expanded in t around inf 53.7%

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

      1. associate-*r* 53.7%

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

      2. *-commutative 53.7%

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

      3. associate-*l* 53.9%

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

      4. *-commutative 53.9%

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

   10. Simplified 53.9%

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

   if -1.99999999999999983e29 < (*.f64 a 27) < -5e6 or -4e-82 < (*.f64 a 27) < -1.99999999999999988e-106 or -9.99999999999999969e-278 < (*.f64 a 27) < 4.9999999999999996e-199

   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. sub-neg 94.2%

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

      2. sub-neg 94.2%

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

      3. associate-*l* 99.7%

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

      4. associate-*l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 53.1%

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

   if -5e6 < (*.f64 a 27) < -4e-82

   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. sub-neg 92.8%

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

      2. sub-neg 92.8%

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

      3. associate-*l* 99.7%

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

      4. associate-*l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around 0 92.7%

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

      1. *-commutative 92.7%

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

      2. associate-*r* 99.7%

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

      3. *-commutative 99.7%

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

      4. associate-*r* 92.7%

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

      5. *-commutative 92.7%

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

      6. associate-*r* 99.6%

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

      7. associate-*l* 99.6%

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

      8. *-commutative 99.6%

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

   7. Simplified 99.6%

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

   8. Taylor expanded in t around inf 48.7%

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

      1. associate-*r* 48.8%

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

      2. associate-*r* 54.4%

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

      3. *-commutative 54.4%

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

   10. Simplified 54.4%

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

   if -1.99999999999999988e-106 < (*.f64 a 27) < -9.99999999999999969e-278 or 4.9999999999999996e-199 < (*.f64 a 27) < 1e20

   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. sub-neg 92.8%

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

      2. sub-neg 92.8%

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

      3. associate-*l* 96.3%

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

      4. associate-*l* 96.3%

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

   3. Simplified 96.3%

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

   5. Taylor expanded in x around 0 56.0%

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

      1. pow1 56.0%

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

   7. Applied egg-rr 56.0%

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

      1. unpow1 56.0%

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

      2. associate-*r* 60.6%

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

      3. *-commutative 60.6%

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

   9. Simplified 60.6%

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

   10. Taylor expanded in a around 0 45.8%

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

       1. associate-*r* 45.8%

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

       2. *-commutative 45.8%

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

       3. associate-*l* 45.8%

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

       4. associate-*l* 45.8%

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

       5. *-commutative 45.8%

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

       6. *-commutative 45.8%

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

   12. Simplified 45.8%

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

   if 1e20 < (*.f64 a 27)

   1. Initial program 92.3%

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

      1. sub-neg 92.3%

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

      2. sub-neg 92.3%

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

      3. associate-*l* 96.8%

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

      4. associate-*l* 96.9%

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

   3. Simplified 96.9%

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

   5. Taylor expanded in a around inf 52.7%

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 55.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 27 \leq -5 \cdot 10^{+120}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \mathbf{elif}\;a \cdot 27 \leq -2 \cdot 10^{+29}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-9 \cdot t\right)\right)\\ \mathbf{elif}\;a \cdot 27 \leq -5000000:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;a \cdot 27 \leq -4 \cdot 10^{-82}:\\ \;\;\;\;z \cdot \left(y \cdot \left(-9 \cdot t\right)\right)\\ \mathbf{elif}\;a \cdot 27 \leq -2 \cdot 10^{-106}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;a \cdot 27 \leq -1 \cdot 10^{-277}:\\ \;\;\;\;t \cdot \left(z \cdot \left(y \cdot -9\right)\right)\\ \mathbf{elif}\;a \cdot 27 \leq 5 \cdot 10^{-199}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;a \cdot 27 \leq 10^{+20}:\\ \;\;\;\;t \cdot \left(z \cdot \left(y \cdot -9\right)\right)\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 47.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := t \cdot \left(z \cdot \left(y \cdot -9\right)\right)\\ \mathbf{if}\;a \cdot 27 \leq -5 \cdot 10^{+120}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \mathbf{elif}\;a \cdot 27 \leq -2 \cdot 10^{+29}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-9 \cdot t\right)\right)\\ \mathbf{elif}\;a \cdot 27 \leq -5000000:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;a \cdot 27 \leq -4 \cdot 10^{-82}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(9 \cdot \left(-z\right)\right)\\ \mathbf{elif}\;a \cdot 27 \leq -2 \cdot 10^{-106}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;a \cdot 27 \leq -1 \cdot 10^{-277}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot 27 \leq 5 \cdot 10^{-199}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;a \cdot 27 \leq 10^{+20}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (* z (* y -9.0)))))
   (if (<= (* a 27.0) -5e+120)
     (* b (* a 27.0))
     (if (<= (* a 27.0) -2e+29)
       (* y (* z (* -9.0 t)))
       (if (<= (* a 27.0) -5000000.0)
         (* x 2.0)
         (if (<= (* a 27.0) -4e-82)
           (* (* y t) (* 9.0 (- z)))
           (if (<= (* a 27.0) -2e-106)
             (* x 2.0)
             (if (<= (* a 27.0) -1e-277)
               t_1
               (if (<= (* a 27.0) 5e-199)
                 (* x 2.0)
                 (if (<= (* a 27.0) 1e+20) t_1 (* 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 t_1 = t * (z * (y * -9.0));
	double tmp;
	if ((a * 27.0) <= -5e+120) {
		tmp = b * (a * 27.0);
	} else if ((a * 27.0) <= -2e+29) {
		tmp = y * (z * (-9.0 * t));
	} else if ((a * 27.0) <= -5000000.0) {
		tmp = x * 2.0;
	} else if ((a * 27.0) <= -4e-82) {
		tmp = (y * t) * (9.0 * -z);
	} else if ((a * 27.0) <= -2e-106) {
		tmp = x * 2.0;
	} else if ((a * 27.0) <= -1e-277) {
		tmp = t_1;
	} else if ((a * 27.0) <= 5e-199) {
		tmp = x * 2.0;
	} else if ((a * 27.0) <= 1e+20) {
		tmp = t_1;
	} else {
		tmp = 27.0 * (a * b);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (z * (y * (-9.0d0)))
    if ((a * 27.0d0) <= (-5d+120)) then
        tmp = b * (a * 27.0d0)
    else if ((a * 27.0d0) <= (-2d+29)) then
        tmp = y * (z * ((-9.0d0) * t))
    else if ((a * 27.0d0) <= (-5000000.0d0)) then
        tmp = x * 2.0d0
    else if ((a * 27.0d0) <= (-4d-82)) then
        tmp = (y * t) * (9.0d0 * -z)
    else if ((a * 27.0d0) <= (-2d-106)) then
        tmp = x * 2.0d0
    else if ((a * 27.0d0) <= (-1d-277)) then
        tmp = t_1
    else if ((a * 27.0d0) <= 5d-199) then
        tmp = x * 2.0d0
    else if ((a * 27.0d0) <= 1d+20) then
        tmp = t_1
    else
        tmp = 27.0d0 * (a * b)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (z * (y * -9.0));
	double tmp;
	if ((a * 27.0) <= -5e+120) {
		tmp = b * (a * 27.0);
	} else if ((a * 27.0) <= -2e+29) {
		tmp = y * (z * (-9.0 * t));
	} else if ((a * 27.0) <= -5000000.0) {
		tmp = x * 2.0;
	} else if ((a * 27.0) <= -4e-82) {
		tmp = (y * t) * (9.0 * -z);
	} else if ((a * 27.0) <= -2e-106) {
		tmp = x * 2.0;
	} else if ((a * 27.0) <= -1e-277) {
		tmp = t_1;
	} else if ((a * 27.0) <= 5e-199) {
		tmp = x * 2.0;
	} else if ((a * 27.0) <= 1e+20) {
		tmp = t_1;
	} else {
		tmp = 27.0 * (a * b);
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = t * (z * (y * -9.0))
	tmp = 0
	if (a * 27.0) <= -5e+120:
		tmp = b * (a * 27.0)
	elif (a * 27.0) <= -2e+29:
		tmp = y * (z * (-9.0 * t))
	elif (a * 27.0) <= -5000000.0:
		tmp = x * 2.0
	elif (a * 27.0) <= -4e-82:
		tmp = (y * t) * (9.0 * -z)
	elif (a * 27.0) <= -2e-106:
		tmp = x * 2.0
	elif (a * 27.0) <= -1e-277:
		tmp = t_1
	elif (a * 27.0) <= 5e-199:
		tmp = x * 2.0
	elif (a * 27.0) <= 1e+20:
		tmp = t_1
	else:
		tmp = 27.0 * (a * b)
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(z * Float64(y * -9.0)))
	tmp = 0.0
	if (Float64(a * 27.0) <= -5e+120)
		tmp = Float64(b * Float64(a * 27.0));
	elseif (Float64(a * 27.0) <= -2e+29)
		tmp = Float64(y * Float64(z * Float64(-9.0 * t)));
	elseif (Float64(a * 27.0) <= -5000000.0)
		tmp = Float64(x * 2.0);
	elseif (Float64(a * 27.0) <= -4e-82)
		tmp = Float64(Float64(y * t) * Float64(9.0 * Float64(-z)));
	elseif (Float64(a * 27.0) <= -2e-106)
		tmp = Float64(x * 2.0);
	elseif (Float64(a * 27.0) <= -1e-277)
		tmp = t_1;
	elseif (Float64(a * 27.0) <= 5e-199)
		tmp = Float64(x * 2.0);
	elseif (Float64(a * 27.0) <= 1e+20)
		tmp = t_1;
	else
		tmp = Float64(27.0 * Float64(a * b));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (z * (y * -9.0));
	tmp = 0.0;
	if ((a * 27.0) <= -5e+120)
		tmp = b * (a * 27.0);
	elseif ((a * 27.0) <= -2e+29)
		tmp = y * (z * (-9.0 * t));
	elseif ((a * 27.0) <= -5000000.0)
		tmp = x * 2.0;
	elseif ((a * 27.0) <= -4e-82)
		tmp = (y * t) * (9.0 * -z);
	elseif ((a * 27.0) <= -2e-106)
		tmp = x * 2.0;
	elseif ((a * 27.0) <= -1e-277)
		tmp = t_1;
	elseif ((a * 27.0) <= 5e-199)
		tmp = x * 2.0;
	elseif ((a * 27.0) <= 1e+20)
		tmp = t_1;
	else
		tmp = 27.0 * (a * b);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(z * N[(y * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * 27.0), $MachinePrecision], -5e+120], N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 27.0), $MachinePrecision], -2e+29], N[(y * N[(z * N[(-9.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 27.0), $MachinePrecision], -5000000.0], N[(x * 2.0), $MachinePrecision], If[LessEqual[N[(a * 27.0), $MachinePrecision], -4e-82], N[(N[(y * t), $MachinePrecision] * N[(9.0 * (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 27.0), $MachinePrecision], -2e-106], N[(x * 2.0), $MachinePrecision], If[LessEqual[N[(a * 27.0), $MachinePrecision], -1e-277], t$95$1, If[LessEqual[N[(a * 27.0), $MachinePrecision], 5e-199], N[(x * 2.0), $MachinePrecision], If[LessEqual[N[(a * 27.0), $MachinePrecision], 1e+20], t$95$1, N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if (*.f64 a 27) < -5.00000000000000019e120

   1. Initial program 97.5%

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

      1. sub-neg 97.5%

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

      2. sub-neg 97.5%

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

      3. associate-*l* 97.6%

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

      4. associate-*l* 97.6%

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

   3. Simplified 97.6%

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

   5. Taylor expanded in a around inf 78.8%

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

      1. associate-*r* 78.9%

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

      2. *-commutative 78.9%

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

      3. associate-*r* 78.9%

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

   7. Simplified 78.9%

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

      1. add-cbrt-cube 56.5%

         \[\leadsto \color{blue}{\sqrt[3]{\left(\left(a \cdot \left(27 \cdot b\right)\right) \cdot \left(a \cdot \left(27 \cdot b\right)\right)\right) \cdot \left(a \cdot \left(27 \cdot b\right)\right)}} \]

      2. pow3 56.5%

         \[\leadsto \sqrt[3]{\color{blue}{{\left(a \cdot \left(27 \cdot b\right)\right)}^{3}}} \]

   9. Applied egg-rr 56.5%

      \[\leadsto \color{blue}{\sqrt[3]{{\left(a \cdot \left(27 \cdot b\right)\right)}^{3}}} \]
   10. Step-by-step derivation

       1. rem-cbrt-cube 78.9%

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

       2. associate-*r* 78.9%

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

   11. Applied egg-rr 78.9%

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

   if -5.00000000000000019e120 < (*.f64 a 27) < -1.99999999999999983e29

   1. Initial program 90.7%

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

      1. sub-neg 90.7%

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

      2. sub-neg 90.7%

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

      3. associate-*l* 85.9%

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

      4. associate-*l* 85.7%

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

   3. Simplified 85.7%

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

   5. Taylor expanded in y around 0 90.4%

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

      1. *-commutative 90.4%

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

      2. associate-*r* 85.7%

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

      3. *-commutative 85.7%

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

      4. associate-*r* 90.4%

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

      5. *-commutative 90.4%

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

      6. associate-*r* 86.2%

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

      7. associate-*l* 86.3%

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

      8. *-commutative 86.3%

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

   7. Simplified 86.3%

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

   8. Taylor expanded in t around inf 53.7%

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

      1. associate-*r* 53.7%

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

      2. *-commutative 53.7%

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

      3. associate-*l* 53.9%

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

      4. *-commutative 53.9%

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

   10. Simplified 53.9%

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

   if -1.99999999999999983e29 < (*.f64 a 27) < -5e6 or -4e-82 < (*.f64 a 27) < -1.99999999999999988e-106 or -9.99999999999999969e-278 < (*.f64 a 27) < 4.9999999999999996e-199

   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. sub-neg 94.2%

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

      2. sub-neg 94.2%

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

      3. associate-*l* 99.7%

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

      4. associate-*l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 53.1%

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

   if -5e6 < (*.f64 a 27) < -4e-82

   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. sub-neg 92.8%

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

      2. sub-neg 92.8%

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

      3. associate-*l* 99.7%

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

      4. associate-*l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around 0 92.7%

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

      1. *-commutative 92.7%

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

      2. associate-*r* 99.7%

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

      3. *-commutative 99.7%

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

      4. associate-*r* 92.7%

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

      5. *-commutative 92.7%

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

      6. associate-*r* 99.6%

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

      7. associate-*l* 99.6%

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

      8. *-commutative 99.6%

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

   7. Simplified 99.6%

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

   8. Taylor expanded in t around inf 48.7%

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

      1. associate-*r* 48.8%

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

      2. *-commutative 48.8%

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

      3. associate-*l* 54.6%

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

      4. *-commutative 54.6%

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

   10. Simplified 54.6%

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

   11. Taylor expanded in z around 0 54.6%

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

       1. *-commutative 54.6%

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

       2. associate-*r* 54.5%

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

       3. metadata-eval 54.5%

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

       4. *-commutative 54.5%

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

       5. associate-*r* 54.3%

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

       6. distribute-lft-neg-in 54.3%

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

       7. *-commutative 54.3%

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

       8. *-commutative 54.3%

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

       9. associate-*l* 54.4%

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

   13. Applied egg-rr 54.4%

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

   if -1.99999999999999988e-106 < (*.f64 a 27) < -9.99999999999999969e-278 or 4.9999999999999996e-199 < (*.f64 a 27) < 1e20

   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. sub-neg 92.8%

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

      2. sub-neg 92.8%

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

      3. associate-*l* 96.3%

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

      4. associate-*l* 96.3%

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

   3. Simplified 96.3%

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

   5. Taylor expanded in x around 0 56.0%

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

      1. pow1 56.0%

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

   7. Applied egg-rr 56.0%

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

      1. unpow1 56.0%

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

      2. associate-*r* 60.6%

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

      3. *-commutative 60.6%

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

   9. Simplified 60.6%

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

   10. Taylor expanded in a around 0 45.8%

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

       1. associate-*r* 45.8%

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

       2. *-commutative 45.8%

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

       3. associate-*l* 45.8%

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

       4. associate-*l* 45.8%

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

       5. *-commutative 45.8%

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

       6. *-commutative 45.8%

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

   12. Simplified 45.8%

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

   if 1e20 < (*.f64 a 27)

   1. Initial program 92.3%

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

      1. sub-neg 92.3%

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

      2. sub-neg 92.3%

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

      3. associate-*l* 96.8%

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

      4. associate-*l* 96.9%

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

   3. Simplified 96.9%

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

   5. Taylor expanded in a around inf 52.7%

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 55.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 27 \leq -5 \cdot 10^{+120}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \mathbf{elif}\;a \cdot 27 \leq -2 \cdot 10^{+29}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-9 \cdot t\right)\right)\\ \mathbf{elif}\;a \cdot 27 \leq -5000000:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;a \cdot 27 \leq -4 \cdot 10^{-82}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(9 \cdot \left(-z\right)\right)\\ \mathbf{elif}\;a \cdot 27 \leq -2 \cdot 10^{-106}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;a \cdot 27 \leq -1 \cdot 10^{-277}:\\ \;\;\;\;t \cdot \left(z \cdot \left(y \cdot -9\right)\right)\\ \mathbf{elif}\;a \cdot 27 \leq 5 \cdot 10^{-199}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;a \cdot 27 \leq 10^{+20}:\\ \;\;\;\;t \cdot \left(z \cdot \left(y \cdot -9\right)\right)\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 53.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot 27\right)\\ t_2 := 27 \cdot \left(a \cdot b\right)\\ t_3 := y \cdot \left(-9 \cdot \left(z \cdot t\right)\right)\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{+41}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq -2 \cdot 10^{+23}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;t_1 \leq -400:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+69}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+129}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq 4 \cdot 10^{+160}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (* a 27.0)))
        (t_2 (* 27.0 (* a b)))
        (t_3 (* y (* -9.0 (* z t)))))
   (if (<= t_1 -2e+41)
     t_2
     (if (<= t_1 -2e+23)
       (* x 2.0)
       (if (<= t_1 -400.0)
         (* a (* 27.0 b))
         (if (<= t_1 2e+69)
           t_3
           (if (<= t_1 2e+129) t_2 (if (<= t_1 4e+160) t_3 t_1))))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a * 27.0);
	double t_2 = 27.0 * (a * b);
	double t_3 = y * (-9.0 * (z * t));
	double tmp;
	if (t_1 <= -2e+41) {
		tmp = t_2;
	} else if (t_1 <= -2e+23) {
		tmp = x * 2.0;
	} else if (t_1 <= -400.0) {
		tmp = a * (27.0 * b);
	} else if (t_1 <= 2e+69) {
		tmp = t_3;
	} else if (t_1 <= 2e+129) {
		tmp = t_2;
	} else if (t_1 <= 4e+160) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = b * (a * 27.0d0)
    t_2 = 27.0d0 * (a * b)
    t_3 = y * ((-9.0d0) * (z * t))
    if (t_1 <= (-2d+41)) then
        tmp = t_2
    else if (t_1 <= (-2d+23)) then
        tmp = x * 2.0d0
    else if (t_1 <= (-400.0d0)) then
        tmp = a * (27.0d0 * b)
    else if (t_1 <= 2d+69) then
        tmp = t_3
    else if (t_1 <= 2d+129) then
        tmp = t_2
    else if (t_1 <= 4d+160) then
        tmp = t_3
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a * 27.0);
	double t_2 = 27.0 * (a * b);
	double t_3 = y * (-9.0 * (z * t));
	double tmp;
	if (t_1 <= -2e+41) {
		tmp = t_2;
	} else if (t_1 <= -2e+23) {
		tmp = x * 2.0;
	} else if (t_1 <= -400.0) {
		tmp = a * (27.0 * b);
	} else if (t_1 <= 2e+69) {
		tmp = t_3;
	} else if (t_1 <= 2e+129) {
		tmp = t_2;
	} else if (t_1 <= 4e+160) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = b * (a * 27.0)
	t_2 = 27.0 * (a * b)
	t_3 = y * (-9.0 * (z * t))
	tmp = 0
	if t_1 <= -2e+41:
		tmp = t_2
	elif t_1 <= -2e+23:
		tmp = x * 2.0
	elif t_1 <= -400.0:
		tmp = a * (27.0 * b)
	elif t_1 <= 2e+69:
		tmp = t_3
	elif t_1 <= 2e+129:
		tmp = t_2
	elif t_1 <= 4e+160:
		tmp = t_3
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a * 27.0))
	t_2 = Float64(27.0 * Float64(a * b))
	t_3 = Float64(y * Float64(-9.0 * Float64(z * t)))
	tmp = 0.0
	if (t_1 <= -2e+41)
		tmp = t_2;
	elseif (t_1 <= -2e+23)
		tmp = Float64(x * 2.0);
	elseif (t_1 <= -400.0)
		tmp = Float64(a * Float64(27.0 * b));
	elseif (t_1 <= 2e+69)
		tmp = t_3;
	elseif (t_1 <= 2e+129)
		tmp = t_2;
	elseif (t_1 <= 4e+160)
		tmp = t_3;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (a * 27.0);
	t_2 = 27.0 * (a * b);
	t_3 = y * (-9.0 * (z * t));
	tmp = 0.0;
	if (t_1 <= -2e+41)
		tmp = t_2;
	elseif (t_1 <= -2e+23)
		tmp = x * 2.0;
	elseif (t_1 <= -400.0)
		tmp = a * (27.0 * b);
	elseif (t_1 <= 2e+69)
		tmp = t_3;
	elseif (t_1 <= 2e+129)
		tmp = t_2;
	elseif (t_1 <= 4e+160)
		tmp = t_3;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y * N[(-9.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+41], t$95$2, If[LessEqual[t$95$1, -2e+23], N[(x * 2.0), $MachinePrecision], If[LessEqual[t$95$1, -400.0], N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+69], t$95$3, If[LessEqual[t$95$1, 2e+129], t$95$2, If[LessEqual[t$95$1, 4e+160], t$95$3, t$95$1]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 (*.f64 a 27) b) < -2.00000000000000001e41 or 2.0000000000000001e69 < (*.f64 (*.f64 a 27) b) < 2e129

   1. Initial program 93.9%

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

      1. sub-neg 93.9%

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

      2. sub-neg 93.9%

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

      3. associate-*l* 96.7%

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

      4. associate-*l* 96.7%

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

   3. Simplified 96.7%

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

   5. Taylor expanded in a around inf 71.4%

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

   if -2.00000000000000001e41 < (*.f64 (*.f64 a 27) b) < -1.9999999999999998e23

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. sub-neg 100.0%

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

      3. associate-*l* 100.0%

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

      4. associate-*l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 76.1%

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

   if -1.9999999999999998e23 < (*.f64 (*.f64 a 27) b) < -400

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. sub-neg 100.0%

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

      3. associate-*l* 100.0%

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

      4. associate-*l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in a around inf 67.7%

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

      1. associate-*r* 68.7%

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

      2. *-commutative 68.7%

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

      3. associate-*r* 68.7%

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

   7. Simplified 68.7%

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

   if -400 < (*.f64 (*.f64 a 27) b) < 2.0000000000000001e69 or 2e129 < (*.f64 (*.f64 a 27) b) < 4.00000000000000003e160

   1. Initial program 93.0%

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

      1. sub-neg 93.0%

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

      2. sub-neg 93.0%

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

      3. associate-*l* 96.1%

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

      4. associate-*l* 96.0%

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

   3. Simplified 96.0%

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

   5. Taylor expanded in y around 0 93.0%

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

      1. *-commutative 93.0%

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

      2. associate-*r* 96.0%

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

      3. *-commutative 96.0%

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

      4. associate-*r* 93.0%

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

      5. *-commutative 93.0%

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

      6. associate-*r* 96.7%

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

      7. associate-*l* 96.8%

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

      8. *-commutative 96.8%

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

   7. Simplified 96.8%

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

   8. Taylor expanded in t around inf 50.0%

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

      1. associate-*r* 50.0%

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

      2. *-commutative 50.0%

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

      3. associate-*l* 52.4%

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

      4. *-commutative 52.4%

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

   10. Simplified 52.4%

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

   11. Taylor expanded in z around 0 52.4%

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

   if 4.00000000000000003e160 < (*.f64 (*.f64 a 27) b)

   1. Initial program 93.0%

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

      1. sub-neg 93.0%

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

      2. sub-neg 93.0%

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

      3. associate-*l* 96.5%

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

      4. associate-*l* 96.4%

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

   3. Simplified 96.4%

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

   5. Taylor expanded in a around inf 92.8%

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

      1. associate-*r* 93.1%

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

      2. *-commutative 93.1%

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

      3. associate-*r* 93.0%

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

   7. Simplified 93.0%

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

      1. add-cbrt-cube 57.6%

         \[\leadsto \color{blue}{\sqrt[3]{\left(\left(a \cdot \left(27 \cdot b\right)\right) \cdot \left(a \cdot \left(27 \cdot b\right)\right)\right) \cdot \left(a \cdot \left(27 \cdot b\right)\right)}} \]

      2. pow3 57.6%

         \[\leadsto \sqrt[3]{\color{blue}{{\left(a \cdot \left(27 \cdot b\right)\right)}^{3}}} \]

   9. Applied egg-rr 57.6%

      \[\leadsto \color{blue}{\sqrt[3]{{\left(a \cdot \left(27 \cdot b\right)\right)}^{3}}} \]
   10. Step-by-step derivation

       1. rem-cbrt-cube 93.0%

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

       2. associate-*r* 93.1%

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

   11. Applied egg-rr 93.1%

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

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a \cdot 27\right) \leq -2 \cdot 10^{+41}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;b \cdot \left(a \cdot 27\right) \leq -2 \cdot 10^{+23}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;b \cdot \left(a \cdot 27\right) \leq -400:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;b \cdot \left(a \cdot 27\right) \leq 2 \cdot 10^{+69}:\\ \;\;\;\;y \cdot \left(-9 \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;b \cdot \left(a \cdot 27\right) \leq 2 \cdot 10^{+129}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;b \cdot \left(a \cdot 27\right) \leq 4 \cdot 10^{+160}:\\ \;\;\;\;y \cdot \left(-9 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 53.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot 27\right)\\ t_2 := 27 \cdot \left(a \cdot b\right)\\ t_3 := y \cdot \left(z \cdot \left(-9 \cdot t\right)\right)\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{+41}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq -2 \cdot 10^{+23}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;t_1 \leq -400:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+69}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+129}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq 4 \cdot 10^{+160}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (* a 27.0)))
        (t_2 (* 27.0 (* a b)))
        (t_3 (* y (* z (* -9.0 t)))))
   (if (<= t_1 -2e+41)
     t_2
     (if (<= t_1 -2e+23)
       (* x 2.0)
       (if (<= t_1 -400.0)
         (* a (* 27.0 b))
         (if (<= t_1 2e+69)
           t_3
           (if (<= t_1 2e+129) t_2 (if (<= t_1 4e+160) t_3 t_1))))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a * 27.0);
	double t_2 = 27.0 * (a * b);
	double t_3 = y * (z * (-9.0 * t));
	double tmp;
	if (t_1 <= -2e+41) {
		tmp = t_2;
	} else if (t_1 <= -2e+23) {
		tmp = x * 2.0;
	} else if (t_1 <= -400.0) {
		tmp = a * (27.0 * b);
	} else if (t_1 <= 2e+69) {
		tmp = t_3;
	} else if (t_1 <= 2e+129) {
		tmp = t_2;
	} else if (t_1 <= 4e+160) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = b * (a * 27.0d0)
    t_2 = 27.0d0 * (a * b)
    t_3 = y * (z * ((-9.0d0) * t))
    if (t_1 <= (-2d+41)) then
        tmp = t_2
    else if (t_1 <= (-2d+23)) then
        tmp = x * 2.0d0
    else if (t_1 <= (-400.0d0)) then
        tmp = a * (27.0d0 * b)
    else if (t_1 <= 2d+69) then
        tmp = t_3
    else if (t_1 <= 2d+129) then
        tmp = t_2
    else if (t_1 <= 4d+160) then
        tmp = t_3
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a * 27.0);
	double t_2 = 27.0 * (a * b);
	double t_3 = y * (z * (-9.0 * t));
	double tmp;
	if (t_1 <= -2e+41) {
		tmp = t_2;
	} else if (t_1 <= -2e+23) {
		tmp = x * 2.0;
	} else if (t_1 <= -400.0) {
		tmp = a * (27.0 * b);
	} else if (t_1 <= 2e+69) {
		tmp = t_3;
	} else if (t_1 <= 2e+129) {
		tmp = t_2;
	} else if (t_1 <= 4e+160) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = b * (a * 27.0)
	t_2 = 27.0 * (a * b)
	t_3 = y * (z * (-9.0 * t))
	tmp = 0
	if t_1 <= -2e+41:
		tmp = t_2
	elif t_1 <= -2e+23:
		tmp = x * 2.0
	elif t_1 <= -400.0:
		tmp = a * (27.0 * b)
	elif t_1 <= 2e+69:
		tmp = t_3
	elif t_1 <= 2e+129:
		tmp = t_2
	elif t_1 <= 4e+160:
		tmp = t_3
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a * 27.0))
	t_2 = Float64(27.0 * Float64(a * b))
	t_3 = Float64(y * Float64(z * Float64(-9.0 * t)))
	tmp = 0.0
	if (t_1 <= -2e+41)
		tmp = t_2;
	elseif (t_1 <= -2e+23)
		tmp = Float64(x * 2.0);
	elseif (t_1 <= -400.0)
		tmp = Float64(a * Float64(27.0 * b));
	elseif (t_1 <= 2e+69)
		tmp = t_3;
	elseif (t_1 <= 2e+129)
		tmp = t_2;
	elseif (t_1 <= 4e+160)
		tmp = t_3;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (a * 27.0);
	t_2 = 27.0 * (a * b);
	t_3 = y * (z * (-9.0 * t));
	tmp = 0.0;
	if (t_1 <= -2e+41)
		tmp = t_2;
	elseif (t_1 <= -2e+23)
		tmp = x * 2.0;
	elseif (t_1 <= -400.0)
		tmp = a * (27.0 * b);
	elseif (t_1 <= 2e+69)
		tmp = t_3;
	elseif (t_1 <= 2e+129)
		tmp = t_2;
	elseif (t_1 <= 4e+160)
		tmp = t_3;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y * N[(z * N[(-9.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+41], t$95$2, If[LessEqual[t$95$1, -2e+23], N[(x * 2.0), $MachinePrecision], If[LessEqual[t$95$1, -400.0], N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+69], t$95$3, If[LessEqual[t$95$1, 2e+129], t$95$2, If[LessEqual[t$95$1, 4e+160], t$95$3, t$95$1]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 (*.f64 a 27) b) < -2.00000000000000001e41 or 2.0000000000000001e69 < (*.f64 (*.f64 a 27) b) < 2e129

   1. Initial program 93.9%

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

      1. sub-neg 93.9%

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

      2. sub-neg 93.9%

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

      3. associate-*l* 96.7%

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

      4. associate-*l* 96.7%

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

   3. Simplified 96.7%

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

   5. Taylor expanded in a around inf 71.4%

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

   if -2.00000000000000001e41 < (*.f64 (*.f64 a 27) b) < -1.9999999999999998e23

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. sub-neg 100.0%

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

      3. associate-*l* 100.0%

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

      4. associate-*l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 76.1%

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

   if -1.9999999999999998e23 < (*.f64 (*.f64 a 27) b) < -400

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. sub-neg 100.0%

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

      3. associate-*l* 100.0%

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

      4. associate-*l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in a around inf 67.7%

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

      1. associate-*r* 68.7%

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

      2. *-commutative 68.7%

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

      3. associate-*r* 68.7%

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

   7. Simplified 68.7%

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

   if -400 < (*.f64 (*.f64 a 27) b) < 2.0000000000000001e69 or 2e129 < (*.f64 (*.f64 a 27) b) < 4.00000000000000003e160

   1. Initial program 93.0%

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

      1. sub-neg 93.0%

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

      2. sub-neg 93.0%

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

      3. associate-*l* 96.1%

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

      4. associate-*l* 96.0%

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

   3. Simplified 96.0%

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

   5. Taylor expanded in y around 0 93.0%

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

      1. *-commutative 93.0%

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

      2. associate-*r* 96.0%

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

      3. *-commutative 96.0%

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

      4. associate-*r* 93.0%

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

      5. *-commutative 93.0%

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

      6. associate-*r* 96.7%

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

      7. associate-*l* 96.8%

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

      8. *-commutative 96.8%

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

   7. Simplified 96.8%

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

   8. Taylor expanded in t around inf 50.0%

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

      1. associate-*r* 50.0%

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

      2. *-commutative 50.0%

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

      3. associate-*l* 52.4%

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

      4. *-commutative 52.4%

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

   10. Simplified 52.4%

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

   if 4.00000000000000003e160 < (*.f64 (*.f64 a 27) b)

   1. Initial program 93.0%

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

      1. sub-neg 93.0%

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

      2. sub-neg 93.0%

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

      3. associate-*l* 96.5%

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

      4. associate-*l* 96.4%

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

   3. Simplified 96.4%

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

   5. Taylor expanded in a around inf 92.8%

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

      1. associate-*r* 93.1%

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

      2. *-commutative 93.1%

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

      3. associate-*r* 93.0%

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

   7. Simplified 93.0%

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

      1. add-cbrt-cube 57.6%

         \[\leadsto \color{blue}{\sqrt[3]{\left(\left(a \cdot \left(27 \cdot b\right)\right) \cdot \left(a \cdot \left(27 \cdot b\right)\right)\right) \cdot \left(a \cdot \left(27 \cdot b\right)\right)}} \]

      2. pow3 57.6%

         \[\leadsto \sqrt[3]{\color{blue}{{\left(a \cdot \left(27 \cdot b\right)\right)}^{3}}} \]

   9. Applied egg-rr 57.6%

      \[\leadsto \color{blue}{\sqrt[3]{{\left(a \cdot \left(27 \cdot b\right)\right)}^{3}}} \]
   10. Step-by-step derivation

       1. rem-cbrt-cube 93.0%

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

       2. associate-*r* 93.1%

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

   11. Applied egg-rr 93.1%

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

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a \cdot 27\right) \leq -2 \cdot 10^{+41}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;b \cdot \left(a \cdot 27\right) \leq -2 \cdot 10^{+23}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;b \cdot \left(a \cdot 27\right) \leq -400:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;b \cdot \left(a \cdot 27\right) \leq 2 \cdot 10^{+69}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-9 \cdot t\right)\right)\\ \mathbf{elif}\;b \cdot \left(a \cdot 27\right) \leq 2 \cdot 10^{+129}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;b \cdot \left(a \cdot 27\right) \leq 4 \cdot 10^{+160}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-9 \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 81.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot 27\right)\\ \mathbf{if}\;t_1 \leq -400 \lor \neg \left(t_1 \leq 10^{+82}\right) \land \left(t_1 \leq 5 \cdot 10^{+134} \lor \neg \left(t_1 \leq 4 \cdot 10^{+160}\right)\right):\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + -9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (* a 27.0))))
   (if (or (<= t_1 -400.0)
           (and (not (<= t_1 1e+82))
                (or (<= t_1 5e+134) (not (<= t_1 4e+160)))))
     (+ (* x 2.0) (* 27.0 (* a b)))
     (+ (* x 2.0) (* -9.0 (* t (* y z)))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a * 27.0);
	double tmp;
	if ((t_1 <= -400.0) || (!(t_1 <= 1e+82) && ((t_1 <= 5e+134) || !(t_1 <= 4e+160)))) {
		tmp = (x * 2.0) + (27.0 * (a * b));
	} else {
		tmp = (x * 2.0) + (-9.0 * (t * (y * z)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (a * 27.0d0)
    if ((t_1 <= (-400.0d0)) .or. (.not. (t_1 <= 1d+82)) .and. (t_1 <= 5d+134) .or. (.not. (t_1 <= 4d+160))) then
        tmp = (x * 2.0d0) + (27.0d0 * (a * b))
    else
        tmp = (x * 2.0d0) + ((-9.0d0) * (t * (y * z)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a * 27.0);
	double tmp;
	if ((t_1 <= -400.0) || (!(t_1 <= 1e+82) && ((t_1 <= 5e+134) || !(t_1 <= 4e+160)))) {
		tmp = (x * 2.0) + (27.0 * (a * b));
	} else {
		tmp = (x * 2.0) + (-9.0 * (t * (y * z)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = b * (a * 27.0)
	tmp = 0
	if (t_1 <= -400.0) or (not (t_1 <= 1e+82) and ((t_1 <= 5e+134) or not (t_1 <= 4e+160))):
		tmp = (x * 2.0) + (27.0 * (a * b))
	else:
		tmp = (x * 2.0) + (-9.0 * (t * (y * z)))
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a * 27.0))
	tmp = 0.0
	if ((t_1 <= -400.0) || (!(t_1 <= 1e+82) && ((t_1 <= 5e+134) || !(t_1 <= 4e+160))))
		tmp = Float64(Float64(x * 2.0) + Float64(27.0 * Float64(a * b)));
	else
		tmp = Float64(Float64(x * 2.0) + Float64(-9.0 * Float64(t * Float64(y * z))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (a * 27.0);
	tmp = 0.0;
	if ((t_1 <= -400.0) || (~((t_1 <= 1e+82)) && ((t_1 <= 5e+134) || ~((t_1 <= 4e+160)))))
		tmp = (x * 2.0) + (27.0 * (a * b));
	else
		tmp = (x * 2.0) + (-9.0 * (t * (y * z)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -400.0], And[N[Not[LessEqual[t$95$1, 1e+82]], $MachinePrecision], Or[LessEqual[t$95$1, 5e+134], N[Not[LessEqual[t$95$1, 4e+160]], $MachinePrecision]]]], N[(N[(x * 2.0), $MachinePrecision] + N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] + N[(-9.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 a 27) b) < -400 or 9.9999999999999996e81 < (*.f64 (*.f64 a 27) b) < 4.99999999999999981e134 or 4.00000000000000003e160 < (*.f64 (*.f64 a 27) b)

   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. sub-neg 94.2%

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

      2. sub-neg 94.2%

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

      3. associate-*l* 96.9%

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

      4. associate-*l* 96.9%

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

   3. Simplified 96.9%

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

   5. Taylor expanded in y around 0 87.8%

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

   if -400 < (*.f64 (*.f64 a 27) b) < 9.9999999999999996e81 or 4.99999999999999981e134 < (*.f64 (*.f64 a 27) b) < 4.00000000000000003e160

   1. Initial program 93.0%

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

      1. sub-neg 93.0%

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

      2. sub-neg 93.0%

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

      3. associate-*l* 96.1%

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

      4. associate-*l* 96.1%

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

   3. Simplified 96.1%

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

   5. Taylor expanded in a around 0 83.6%

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

      1. cancel-sign-sub-inv 83.6%

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

      2. metadata-eval 83.6%

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

      3. associate-*l* 83.6%

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

      4. +-commutative 83.6%

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

      5. *-commutative 83.6%

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

      6. *-commutative 83.6%

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

      7. associate-*r* 86.8%

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

      8. *-commutative 86.8%

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

      9. associate-*r* 86.7%

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

      10. associate-*l* 86.7%

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

      11. *-commutative 86.7%

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

   7. Applied egg-rr 86.7%

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

   8. Taylor expanded in t around 0 83.6%

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

4. Final simplification 85.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a \cdot 27\right) \leq -400 \lor \neg \left(b \cdot \left(a \cdot 27\right) \leq 10^{+82}\right) \land \left(b \cdot \left(a \cdot 27\right) \leq 5 \cdot 10^{+134} \lor \neg \left(b \cdot \left(a \cdot 27\right) \leq 4 \cdot 10^{+160}\right)\right):\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + -9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 81.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot 27\right)\\ \mathbf{if}\;t_1 \leq -400 \lor \neg \left(t_1 \leq 10^{+82}\right) \land \left(t_1 \leq 5 \cdot 10^{+134} \lor \neg \left(t_1 \leq 4 \cdot 10^{+160}\right)\right):\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + \left(z \cdot t\right) \cdot \left(y \cdot -9\right)\\ \end{array} \end{array} \]

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 (* a 27.0))))
   (if (or (<= t_1 -400.0)
           (and (not (<= t_1 1e+82))
                (or (<= t_1 5e+134) (not (<= t_1 4e+160)))))
     (+ (* x 2.0) (* 27.0 (* a b)))
     (+ (* x 2.0) (* (* z t) (* y -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 t_1 = b * (a * 27.0);
	double tmp;
	if ((t_1 <= -400.0) || (!(t_1 <= 1e+82) && ((t_1 <= 5e+134) || !(t_1 <= 4e+160)))) {
		tmp = (x * 2.0) + (27.0 * (a * b));
	} else {
		tmp = (x * 2.0) + ((z * t) * (y * -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) :: t_1
    real(8) :: tmp
    t_1 = b * (a * 27.0d0)
    if ((t_1 <= (-400.0d0)) .or. (.not. (t_1 <= 1d+82)) .and. (t_1 <= 5d+134) .or. (.not. (t_1 <= 4d+160))) then
        tmp = (x * 2.0d0) + (27.0d0 * (a * b))
    else
        tmp = (x * 2.0d0) + ((z * t) * (y * (-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 t_1 = b * (a * 27.0);
	double tmp;
	if ((t_1 <= -400.0) || (!(t_1 <= 1e+82) && ((t_1 <= 5e+134) || !(t_1 <= 4e+160)))) {
		tmp = (x * 2.0) + (27.0 * (a * b));
	} else {
		tmp = (x * 2.0) + ((z * t) * (y * -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):
	t_1 = b * (a * 27.0)
	tmp = 0
	if (t_1 <= -400.0) or (not (t_1 <= 1e+82) and ((t_1 <= 5e+134) or not (t_1 <= 4e+160))):
		tmp = (x * 2.0) + (27.0 * (a * b))
	else:
		tmp = (x * 2.0) + ((z * t) * (y * -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)
	t_1 = Float64(b * Float64(a * 27.0))
	tmp = 0.0
	if ((t_1 <= -400.0) || (!(t_1 <= 1e+82) && ((t_1 <= 5e+134) || !(t_1 <= 4e+160))))
		tmp = Float64(Float64(x * 2.0) + Float64(27.0 * Float64(a * b)));
	else
		tmp = Float64(Float64(x * 2.0) + Float64(Float64(z * t) * Float64(y * -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)
	t_1 = b * (a * 27.0);
	tmp = 0.0;
	if ((t_1 <= -400.0) || (~((t_1 <= 1e+82)) && ((t_1 <= 5e+134) || ~((t_1 <= 4e+160)))))
		tmp = (x * 2.0) + (27.0 * (a * b));
	else
		tmp = (x * 2.0) + ((z * t) * (y * -9.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -400.0], And[N[Not[LessEqual[t$95$1, 1e+82]], $MachinePrecision], Or[LessEqual[t$95$1, 5e+134], N[Not[LessEqual[t$95$1, 4e+160]], $MachinePrecision]]]], N[(N[(x * 2.0), $MachinePrecision] + N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] * N[(y * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 a 27) b) < -400 or 9.9999999999999996e81 < (*.f64 (*.f64 a 27) b) < 4.99999999999999981e134 or 4.00000000000000003e160 < (*.f64 (*.f64 a 27) b)

   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. sub-neg 94.2%

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

      2. sub-neg 94.2%

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

      3. associate-*l* 96.9%

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

      4. associate-*l* 96.9%

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

   3. Simplified 96.9%

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

   5. Taylor expanded in y around 0 87.8%

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

   if -400 < (*.f64 (*.f64 a 27) b) < 9.9999999999999996e81 or 4.99999999999999981e134 < (*.f64 (*.f64 a 27) b) < 4.00000000000000003e160

   1. Initial program 93.0%

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

      1. sub-neg 93.0%

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

      2. sub-neg 93.0%

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

      3. associate-*l* 96.1%

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

      4. associate-*l* 96.1%

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

   3. Simplified 96.1%

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

   5. Taylor expanded in a around 0 83.6%

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

      1. cancel-sign-sub-inv 83.6%

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

      2. metadata-eval 83.6%

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

      3. associate-*l* 83.6%

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

      4. +-commutative 83.6%

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

      5. *-commutative 83.6%

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

      6. *-commutative 83.6%

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

      7. associate-*r* 86.8%

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

      8. *-commutative 86.8%

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

      9. associate-*r* 86.7%

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

      10. associate-*l* 86.7%

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

      11. *-commutative 86.7%

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

   7. Applied egg-rr 86.7%

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

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a \cdot 27\right) \leq -400 \lor \neg \left(b \cdot \left(a \cdot 27\right) \leq 10^{+82}\right) \land \left(b \cdot \left(a \cdot 27\right) \leq 5 \cdot 10^{+134} \lor \neg \left(b \cdot \left(a \cdot 27\right) \leq 4 \cdot 10^{+160}\right)\right):\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + \left(z \cdot t\right) \cdot \left(y \cdot -9\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 83.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot 27\right)\\ \mathbf{if}\;t_1 \leq -400:\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{-15}:\\ \;\;\;\;x \cdot 2 + \left(z \cdot t\right) \cdot \left(y \cdot -9\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right) + \left(y \cdot z\right) \cdot \left(-9 \cdot t\right)\\ \end{array} \end{array} \]

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
 (let* ((t_1 (* b (* a 27.0))))
   (if (<= t_1 -400.0)
     (+ (* x 2.0) (* 27.0 (* a b)))
     (if (<= t_1 5e-15)
       (+ (* x 2.0) (* (* z t) (* y -9.0)))
       (+ (* a (* 27.0 b)) (* (* y z) (* -9.0 t)))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a * 27.0);
	double tmp;
	if (t_1 <= -400.0) {
		tmp = (x * 2.0) + (27.0 * (a * b));
	} else if (t_1 <= 5e-15) {
		tmp = (x * 2.0) + ((z * t) * (y * -9.0));
	} else {
		tmp = (a * (27.0 * b)) + ((y * z) * (-9.0 * t));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (a * 27.0d0)
    if (t_1 <= (-400.0d0)) then
        tmp = (x * 2.0d0) + (27.0d0 * (a * b))
    else if (t_1 <= 5d-15) then
        tmp = (x * 2.0d0) + ((z * t) * (y * (-9.0d0)))
    else
        tmp = (a * (27.0d0 * b)) + ((y * z) * ((-9.0d0) * t))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a * 27.0);
	double tmp;
	if (t_1 <= -400.0) {
		tmp = (x * 2.0) + (27.0 * (a * b));
	} else if (t_1 <= 5e-15) {
		tmp = (x * 2.0) + ((z * t) * (y * -9.0));
	} else {
		tmp = (a * (27.0 * b)) + ((y * z) * (-9.0 * t));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = b * (a * 27.0)
	tmp = 0
	if t_1 <= -400.0:
		tmp = (x * 2.0) + (27.0 * (a * b))
	elif t_1 <= 5e-15:
		tmp = (x * 2.0) + ((z * t) * (y * -9.0))
	else:
		tmp = (a * (27.0 * b)) + ((y * z) * (-9.0 * t))
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a * 27.0))
	tmp = 0.0
	if (t_1 <= -400.0)
		tmp = Float64(Float64(x * 2.0) + Float64(27.0 * Float64(a * b)));
	elseif (t_1 <= 5e-15)
		tmp = Float64(Float64(x * 2.0) + Float64(Float64(z * t) * Float64(y * -9.0)));
	else
		tmp = Float64(Float64(a * Float64(27.0 * b)) + Float64(Float64(y * z) * Float64(-9.0 * t)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (a * 27.0);
	tmp = 0.0;
	if (t_1 <= -400.0)
		tmp = (x * 2.0) + (27.0 * (a * b));
	elseif (t_1 <= 5e-15)
		tmp = (x * 2.0) + ((z * t) * (y * -9.0));
	else
		tmp = (a * (27.0 * b)) + ((y * z) * (-9.0 * t));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -400.0], N[(N[(x * 2.0), $MachinePrecision] + N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e-15], N[(N[(x * 2.0), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] * N[(y * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision] + N[(N[(y * z), $MachinePrecision] * N[(-9.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 a 27) b) < -400

   1. Initial program 93.4%

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

      1. sub-neg 93.4%

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

      2. sub-neg 93.4%

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

      3. associate-*l* 96.5%

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

      4. associate-*l* 96.5%

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

   3. Simplified 96.5%

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

   5. Taylor expanded in y around 0 85.6%

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

   if -400 < (*.f64 (*.f64 a 27) b) < 4.99999999999999999e-15

   1. Initial program 92.2%

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

      1. sub-neg 92.2%

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

      2. sub-neg 92.2%

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

      3. associate-*l* 96.0%

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

      4. associate-*l* 96.0%

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

   3. Simplified 96.0%

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

   5. Taylor expanded in a around 0 86.3%

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

      1. cancel-sign-sub-inv 86.3%

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

      2. metadata-eval 86.3%

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

      3. associate-*l* 86.3%

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

      4. +-commutative 86.3%

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

      5. *-commutative 86.3%

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

      6. *-commutative 86.3%

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

      7. associate-*r* 90.1%

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

      8. *-commutative 90.1%

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

      9. associate-*r* 90.1%

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

      10. associate-*l* 90.1%

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

      11. *-commutative 90.1%

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

   7. Applied egg-rr 90.1%

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

   if 4.99999999999999999e-15 < (*.f64 (*.f64 a 27) b)

   1. Initial program 95.6%

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

      1. sub-neg 95.6%

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

      2. sub-neg 95.6%

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

      3. associate-*l* 97.0%

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

      4. associate-*l* 97.0%

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

   3. Simplified 97.0%

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

   5. Taylor expanded in x around 0 84.4%

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

      1. sub-neg 84.4%

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

      2. +-commutative 84.4%

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

      3. distribute-lft-neg-in 84.4%

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

      4. associate-*r* 84.4%

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

      5. metadata-eval 84.4%

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

      6. *-commutative 84.4%

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

      7. associate-*r* 84.5%

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

      8. *-commutative 84.5%

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

   7. Applied egg-rr 84.5%

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

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a \cdot 27\right) \leq -400:\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;b \cdot \left(a \cdot 27\right) \leq 5 \cdot 10^{-15}:\\ \;\;\;\;x \cdot 2 + \left(z \cdot t\right) \cdot \left(y \cdot -9\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right) + \left(y \cdot z\right) \cdot \left(-9 \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 48.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := -9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \mathbf{if}\;z \leq -245:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-158}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-236}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-129}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* -9.0 (* t (* y z)))))
   (if (<= z -245.0)
     t_1
     (if (<= z -5.8e-158)
       (* a (* 27.0 b))
       (if (<= z -5.2e-236)
         (* x 2.0)
         (if (<= z 9e-129) (* 27.0 (* a b)) t_1))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -9.0 * (t * (y * z));
	double tmp;
	if (z <= -245.0) {
		tmp = t_1;
	} else if (z <= -5.8e-158) {
		tmp = a * (27.0 * b);
	} else if (z <= -5.2e-236) {
		tmp = x * 2.0;
	} else if (z <= 9e-129) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-9.0d0) * (t * (y * z))
    if (z <= (-245.0d0)) then
        tmp = t_1
    else if (z <= (-5.8d-158)) then
        tmp = a * (27.0d0 * b)
    else if (z <= (-5.2d-236)) then
        tmp = x * 2.0d0
    else if (z <= 9d-129) then
        tmp = 27.0d0 * (a * b)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -9.0 * (t * (y * z));
	double tmp;
	if (z <= -245.0) {
		tmp = t_1;
	} else if (z <= -5.8e-158) {
		tmp = a * (27.0 * b);
	} else if (z <= -5.2e-236) {
		tmp = x * 2.0;
	} else if (z <= 9e-129) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = -9.0 * (t * (y * z))
	tmp = 0
	if z <= -245.0:
		tmp = t_1
	elif z <= -5.8e-158:
		tmp = a * (27.0 * b)
	elif z <= -5.2e-236:
		tmp = x * 2.0
	elif z <= 9e-129:
		tmp = 27.0 * (a * b)
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(-9.0 * Float64(t * Float64(y * z)))
	tmp = 0.0
	if (z <= -245.0)
		tmp = t_1;
	elseif (z <= -5.8e-158)
		tmp = Float64(a * Float64(27.0 * b));
	elseif (z <= -5.2e-236)
		tmp = Float64(x * 2.0);
	elseif (z <= 9e-129)
		tmp = Float64(27.0 * Float64(a * b));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = -9.0 * (t * (y * z));
	tmp = 0.0;
	if (z <= -245.0)
		tmp = t_1;
	elseif (z <= -5.8e-158)
		tmp = a * (27.0 * b);
	elseif (z <= -5.2e-236)
		tmp = x * 2.0;
	elseif (z <= 9e-129)
		tmp = 27.0 * (a * b);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(-9.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -245.0], t$95$1, If[LessEqual[z, -5.8e-158], N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5.2e-236], N[(x * 2.0), $MachinePrecision], If[LessEqual[z, 9e-129], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -245 or 9.00000000000000061e-129 < z

   1. Initial program 88.8%

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

      1. sub-neg 88.8%

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

      2. sub-neg 88.8%

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

      3. associate-*l* 94.6%

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

      4. associate-*l* 94.6%

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

   3. Simplified 94.6%

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

   5. Taylor expanded in y around inf 48.6%

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

   if -245 < z < -5.79999999999999961e-158

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. sub-neg 99.9%

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

      3. associate-*l* 99.8%

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

      4. associate-*l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in a around inf 41.3%

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

      1. associate-*r* 41.3%

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

      2. *-commutative 41.3%

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

      3. associate-*r* 41.3%

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

   7. Simplified 41.3%

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

   if -5.79999999999999961e-158 < z < -5.2000000000000001e-236

   1. Initial program 99.5%

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

      1. sub-neg 99.5%

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

      2. sub-neg 99.5%

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

      3. associate-*l* 99.8%

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

      4. associate-*l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 40.9%

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

   if -5.2000000000000001e-236 < z < 9.00000000000000061e-129

   1. Initial program 99.8%

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

      1. sub-neg 99.8%

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

      2. sub-neg 99.8%

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

      3. associate-*l* 98.1%

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

      4. associate-*l* 98.0%

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

   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 52.4%

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

4. Final simplification 47.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -245:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-158}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-236}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-129}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 48.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := t \cdot \left(z \cdot \left(y \cdot -9\right)\right)\\ \mathbf{if}\;z \leq -90:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-158}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-237}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-129}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (* z (* y -9.0)))))
   (if (<= z -90.0)
     t_1
     (if (<= z -5e-158)
       (* a (* 27.0 b))
       (if (<= z -5e-237)
         (* x 2.0)
         (if (<= z 1.8e-129) (* 27.0 (* a b)) t_1))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (z * (y * -9.0));
	double tmp;
	if (z <= -90.0) {
		tmp = t_1;
	} else if (z <= -5e-158) {
		tmp = a * (27.0 * b);
	} else if (z <= -5e-237) {
		tmp = x * 2.0;
	} else if (z <= 1.8e-129) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (z * (y * (-9.0d0)))
    if (z <= (-90.0d0)) then
        tmp = t_1
    else if (z <= (-5d-158)) then
        tmp = a * (27.0d0 * b)
    else if (z <= (-5d-237)) then
        tmp = x * 2.0d0
    else if (z <= 1.8d-129) then
        tmp = 27.0d0 * (a * b)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (z * (y * -9.0));
	double tmp;
	if (z <= -90.0) {
		tmp = t_1;
	} else if (z <= -5e-158) {
		tmp = a * (27.0 * b);
	} else if (z <= -5e-237) {
		tmp = x * 2.0;
	} else if (z <= 1.8e-129) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = t * (z * (y * -9.0))
	tmp = 0
	if z <= -90.0:
		tmp = t_1
	elif z <= -5e-158:
		tmp = a * (27.0 * b)
	elif z <= -5e-237:
		tmp = x * 2.0
	elif z <= 1.8e-129:
		tmp = 27.0 * (a * b)
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(z * Float64(y * -9.0)))
	tmp = 0.0
	if (z <= -90.0)
		tmp = t_1;
	elseif (z <= -5e-158)
		tmp = Float64(a * Float64(27.0 * b));
	elseif (z <= -5e-237)
		tmp = Float64(x * 2.0);
	elseif (z <= 1.8e-129)
		tmp = Float64(27.0 * Float64(a * b));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (z * (y * -9.0));
	tmp = 0.0;
	if (z <= -90.0)
		tmp = t_1;
	elseif (z <= -5e-158)
		tmp = a * (27.0 * b);
	elseif (z <= -5e-237)
		tmp = x * 2.0;
	elseif (z <= 1.8e-129)
		tmp = 27.0 * (a * b);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(z * N[(y * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -90.0], t$95$1, If[LessEqual[z, -5e-158], N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5e-237], N[(x * 2.0), $MachinePrecision], If[LessEqual[z, 1.8e-129], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -90 or 1.8e-129 < z

   1. Initial program 88.8%

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

      1. sub-neg 88.8%

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

      2. sub-neg 88.8%

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

      3. associate-*l* 94.6%

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

      4. associate-*l* 94.6%

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

   3. Simplified 94.6%

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

   5. Taylor expanded in x around 0 68.9%

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

      1. pow1 68.9%

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

   7. Applied egg-rr 68.9%

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

      1. unpow1 68.9%

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

      2. associate-*r* 76.4%

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

      3. *-commutative 76.4%

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

   9. Simplified 76.4%

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

   10. Taylor expanded in a around 0 48.6%

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

       1. associate-*r* 48.6%

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

       2. *-commutative 48.6%

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

       3. associate-*l* 48.6%

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

       4. associate-*l* 48.5%

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

       5. *-commutative 48.5%

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

       6. *-commutative 48.5%

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

   12. Simplified 48.5%

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

   if -90 < z < -4.99999999999999972e-158

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. sub-neg 99.9%

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

      3. associate-*l* 99.8%

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

      4. associate-*l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in a around inf 41.3%

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

      1. associate-*r* 41.3%

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

      2. *-commutative 41.3%

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

      3. associate-*r* 41.3%

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

   7. Simplified 41.3%

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

   if -4.99999999999999972e-158 < z < -5.0000000000000002e-237

   1. Initial program 99.5%

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

      1. sub-neg 99.5%

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

      2. sub-neg 99.5%

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

      3. associate-*l* 99.8%

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

      4. associate-*l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 40.9%

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

   if -5.0000000000000002e-237 < z < 1.8e-129

   1. Initial program 99.8%

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

      1. sub-neg 99.8%

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

      2. sub-neg 99.8%

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

      3. associate-*l* 98.1%

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

      4. associate-*l* 98.0%

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

   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 52.4%

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

4. Final simplification 47.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -90:\\ \;\;\;\;t \cdot \left(z \cdot \left(y \cdot -9\right)\right)\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-158}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-237}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-129}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(z \cdot \left(y \cdot -9\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 97.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := a \cdot \left(27 \cdot b\right)\\ \mathbf{if}\;y \cdot 9 \leq -2 \cdot 10^{+51}:\\ \;\;\;\;t_1 + \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - \left(y \cdot t\right) \cdot \left(9 \cdot z\right)\right) + t_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (* 27.0 b))))
   (if (<= (* y 9.0) -2e+51)
     (+ t_1 (- (* x 2.0) (* (* y 9.0) (* z t))))
     (+ (- (* x 2.0) (* (* y t) (* 9.0 z))) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (27.0 * b);
	double tmp;
	if ((y * 9.0) <= -2e+51) {
		tmp = t_1 + ((x * 2.0) - ((y * 9.0) * (z * t)));
	} else {
		tmp = ((x * 2.0) - ((y * t) * (9.0 * z))) + t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (27.0d0 * b)
    if ((y * 9.0d0) <= (-2d+51)) then
        tmp = t_1 + ((x * 2.0d0) - ((y * 9.0d0) * (z * t)))
    else
        tmp = ((x * 2.0d0) - ((y * t) * (9.0d0 * z))) + t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (27.0 * b);
	double tmp;
	if ((y * 9.0) <= -2e+51) {
		tmp = t_1 + ((x * 2.0) - ((y * 9.0) * (z * t)));
	} else {
		tmp = ((x * 2.0) - ((y * t) * (9.0 * z))) + t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = a * (27.0 * b)
	tmp = 0
	if (y * 9.0) <= -2e+51:
		tmp = t_1 + ((x * 2.0) - ((y * 9.0) * (z * t)))
	else:
		tmp = ((x * 2.0) - ((y * t) * (9.0 * z))) + t_1
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(27.0 * b))
	tmp = 0.0
	if (Float64(y * 9.0) <= -2e+51)
		tmp = Float64(t_1 + Float64(Float64(x * 2.0) - Float64(Float64(y * 9.0) * Float64(z * t))));
	else
		tmp = Float64(Float64(Float64(x * 2.0) - Float64(Float64(y * t) * Float64(9.0 * z))) + t_1);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (27.0 * b);
	tmp = 0.0;
	if ((y * 9.0) <= -2e+51)
		tmp = t_1 + ((x * 2.0) - ((y * 9.0) * (z * t)));
	else
		tmp = ((x * 2.0) - ((y * t) * (9.0 * z))) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(y * 9.0), $MachinePrecision], -2e+51], N[(t$95$1 + N[(N[(x * 2.0), $MachinePrecision] - N[(N[(y * 9.0), $MachinePrecision] * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * 2.0), $MachinePrecision] - N[(N[(y * t), $MachinePrecision] * N[(9.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y 9) < -2e51

   1. Initial program 85.8%

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

      1. sub-neg 85.8%

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

      2. sub-neg 85.8%

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

      3. associate-*l* 97.9%

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

      4. associate-*l* 97.9%

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

   3. Simplified 97.9%

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

   if -2e51 < (*.f64 y 9)

   1. Initial program 95.5%

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

      1. sub-neg 95.5%

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

      2. sub-neg 95.5%

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

      3. associate-*l* 96.0%

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

      4. associate-*l* 96.0%

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

   3. Simplified 96.0%

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

   5. Taylor expanded in y around 0 95.5%

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

      1. *-commutative 95.5%

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

      2. associate-*r* 96.0%

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

      3. *-commutative 96.0%

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

      4. associate-*r* 95.5%

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

      5. *-commutative 95.5%

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

      6. associate-*r* 96.9%

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

      7. associate-*l* 96.9%

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

      8. *-commutative 96.9%

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

   7. Simplified 96.9%

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

4. Final simplification 97.1%

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

Alternative 12: 52.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot 27\right)\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{+41}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t_1 \leq 0.0004:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (* a 27.0))))
   (if (<= t_1 -2e+41)
     (* 27.0 (* a b))
     (if (<= t_1 0.0004) (* x 2.0) (* a (* 27.0 b))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a * 27.0);
	double tmp;
	if (t_1 <= -2e+41) {
		tmp = 27.0 * (a * b);
	} else if (t_1 <= 0.0004) {
		tmp = x * 2.0;
	} else {
		tmp = a * (27.0 * b);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (a * 27.0d0)
    if (t_1 <= (-2d+41)) then
        tmp = 27.0d0 * (a * b)
    else if (t_1 <= 0.0004d0) then
        tmp = x * 2.0d0
    else
        tmp = a * (27.0d0 * b)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a * 27.0);
	double tmp;
	if (t_1 <= -2e+41) {
		tmp = 27.0 * (a * b);
	} else if (t_1 <= 0.0004) {
		tmp = x * 2.0;
	} else {
		tmp = a * (27.0 * b);
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = b * (a * 27.0)
	tmp = 0
	if t_1 <= -2e+41:
		tmp = 27.0 * (a * b)
	elif t_1 <= 0.0004:
		tmp = x * 2.0
	else:
		tmp = a * (27.0 * b)
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a * 27.0))
	tmp = 0.0
	if (t_1 <= -2e+41)
		tmp = Float64(27.0 * Float64(a * b));
	elseif (t_1 <= 0.0004)
		tmp = Float64(x * 2.0);
	else
		tmp = Float64(a * Float64(27.0 * b));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (a * 27.0);
	tmp = 0.0;
	if (t_1 <= -2e+41)
		tmp = 27.0 * (a * b);
	elseif (t_1 <= 0.0004)
		tmp = x * 2.0;
	else
		tmp = a * (27.0 * b);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+41], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.0004], N[(x * 2.0), $MachinePrecision], N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 a 27) b) < -2.00000000000000001e41

   1. Initial program 92.2%

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

      1. sub-neg 92.2%

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

      2. sub-neg 92.2%

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

      3. associate-*l* 95.8%

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

      4. associate-*l* 95.8%

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

   3. Simplified 95.8%

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

   5. Taylor expanded in a around inf 74.9%

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

   if -2.00000000000000001e41 < (*.f64 (*.f64 a 27) b) < 4.00000000000000019e-4

   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. sub-neg 92.8%

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

      2. sub-neg 92.8%

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

      3. associate-*l* 96.3%

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

      4. associate-*l* 96.3%

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

   3. Simplified 96.3%

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

   5. Taylor expanded in x around inf 42.5%

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

   if 4.00000000000000019e-4 < (*.f64 (*.f64 a 27) b)

   1. Initial program 95.6%

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

      1. sub-neg 95.6%

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

      2. sub-neg 95.6%

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

      3. associate-*l* 97.0%

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

      4. associate-*l* 96.9%

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

   3. Simplified 96.9%

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

   5. Taylor expanded in a around inf 61.3%

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

      1. associate-*r* 61.4%

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

      2. *-commutative 61.4%

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

      3. associate-*r* 61.3%

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

   7. Simplified 61.3%

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

4. Final simplification 54.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a \cdot 27\right) \leq -2 \cdot 10^{+41}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;b \cdot \left(a \cdot 27\right) \leq 0.0004:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 76.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -85000:\\ \;\;\;\;y \cdot \left(z \cdot \left(-9 \cdot t\right)\right)\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-26}:\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(9 \cdot \left(-z\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -85000.0)
   (* y (* z (* -9.0 t)))
   (if (<= z 2e-26) (+ (* x 2.0) (* 27.0 (* a b))) (* (* y t) (* 9.0 (- z))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -85000.0) {
		tmp = y * (z * (-9.0 * t));
	} else if (z <= 2e-26) {
		tmp = (x * 2.0) + (27.0 * (a * b));
	} else {
		tmp = (y * t) * (9.0 * -z);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-85000.0d0)) then
        tmp = y * (z * ((-9.0d0) * t))
    else if (z <= 2d-26) then
        tmp = (x * 2.0d0) + (27.0d0 * (a * b))
    else
        tmp = (y * t) * (9.0d0 * -z)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -85000.0) {
		tmp = y * (z * (-9.0 * t));
	} else if (z <= 2e-26) {
		tmp = (x * 2.0) + (27.0 * (a * b));
	} else {
		tmp = (y * t) * (9.0 * -z);
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -85000.0:
		tmp = y * (z * (-9.0 * t))
	elif z <= 2e-26:
		tmp = (x * 2.0) + (27.0 * (a * b))
	else:
		tmp = (y * t) * (9.0 * -z)
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -85000.0)
		tmp = Float64(y * Float64(z * Float64(-9.0 * t)));
	elseif (z <= 2e-26)
		tmp = Float64(Float64(x * 2.0) + Float64(27.0 * Float64(a * b)));
	else
		tmp = Float64(Float64(y * t) * Float64(9.0 * Float64(-z)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -85000.0)
		tmp = y * (z * (-9.0 * t));
	elseif (z <= 2e-26)
		tmp = (x * 2.0) + (27.0 * (a * b));
	else
		tmp = (y * t) * (9.0 * -z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -85000.0], N[(y * N[(z * N[(-9.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2e-26], N[(N[(x * 2.0), $MachinePrecision] + N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * t), $MachinePrecision] * N[(9.0 * (-z)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -85000

   1. Initial program 74.5%

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

      1. sub-neg 74.5%

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

      2. sub-neg 74.5%

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

      3. associate-*l* 90.2%

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

      4. associate-*l* 90.2%

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

   3. Simplified 90.2%

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

   5. Taylor expanded in y around 0 74.6%

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

      1. *-commutative 74.6%

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

      2. associate-*r* 90.3%

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

      3. *-commutative 90.3%

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

      4. associate-*r* 74.6%

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

      5. *-commutative 74.6%

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

      6. associate-*r* 95.0%

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

      7. associate-*l* 95.0%

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

      8. *-commutative 95.0%

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

   7. Simplified 95.0%

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

   8. Taylor expanded in t around inf 45.3%

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

      1. associate-*r* 45.2%

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

      2. *-commutative 45.2%

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

      3. associate-*l* 58.7%

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

      4. *-commutative 58.7%

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

   10. Simplified 58.7%

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

   if -85000 < z < 2.0000000000000001e-26

   1. Initial program 99.7%

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

      1. sub-neg 99.7%

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

      2. sub-neg 99.7%

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

      3. associate-*l* 99.0%

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

      4. associate-*l* 99.0%

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

   3. Simplified 99.0%

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

   5. Taylor expanded in y around 0 78.4%

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

   if 2.0000000000000001e-26 < z

   1. Initial program 92.9%

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

      1. sub-neg 92.9%

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

      2. sub-neg 92.9%

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

      3. associate-*l* 95.3%

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

      4. associate-*l* 95.3%

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

   3. Simplified 95.3%

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

   5. Taylor expanded in y around 0 92.9%

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

      1. *-commutative 92.9%

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

      2. associate-*r* 95.3%

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

      3. *-commutative 95.3%

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

      4. associate-*r* 92.9%

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

      5. *-commutative 92.9%

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

      6. associate-*r* 98.6%

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

      7. associate-*l* 98.7%

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

      8. *-commutative 98.7%

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

   7. Simplified 98.7%

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

   8. Taylor expanded in t around inf 52.4%

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

      1. associate-*r* 52.4%

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

      2. *-commutative 52.4%

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

      3. associate-*l* 52.4%

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

      4. *-commutative 52.4%

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

   10. Simplified 52.4%

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

   11. Taylor expanded in z around 0 52.4%

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

       1. *-commutative 52.4%

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

       2. associate-*r* 52.4%

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

       3. metadata-eval 52.4%

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

       4. *-commutative 52.4%

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

       5. associate-*r* 54.5%

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

       6. distribute-lft-neg-in 54.5%

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

       7. *-commutative 54.5%

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

       8. *-commutative 54.5%

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

       9. associate-*l* 54.6%

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

   13. Applied egg-rr 54.6%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -85000:\\ \;\;\;\;y \cdot \left(z \cdot \left(-9 \cdot t\right)\right)\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-26}:\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(9 \cdot \left(-z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 93.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.4%

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

   1. sub-neg 93.4%

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

   2. sub-neg 93.4%

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

   3. associate-*l* 96.4%

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

   4. associate-*l* 96.4%

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

3. Simplified 96.4%

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

5. Taylor expanded in y around 0 93.4%

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

   1. *-commutative 93.4%

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

   2. associate-*r* 96.4%

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

   3. *-commutative 96.4%

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

   4. associate-*r* 93.4%

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

   5. *-commutative 93.4%

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

   6. associate-*r* 95.6%

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

   7. associate-*l* 95.7%

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

   8. *-commutative 95.7%

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

7. Simplified 95.7%

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

8. Final simplification 95.7%

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

Alternative 15: 45.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -1.08 \cdot 10^{+39} \lor \neg \left(a \leq 1.05 \cdot 10^{-144}\right):\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -1.08e+39) (not (<= a 1.05e-144))) (* 27.0 (* a b)) (* x 2.0)))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -1.08e+39) || !(a <= 1.05e-144)) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((a <= (-1.08d+39)) .or. (.not. (a <= 1.05d-144))) then
        tmp = 27.0d0 * (a * b)
    else
        tmp = x * 2.0d0
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -1.08e+39) || !(a <= 1.05e-144)) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -1.08e+39) or not (a <= 1.05e-144):
		tmp = 27.0 * (a * b)
	else:
		tmp = x * 2.0
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -1.08e+39) || !(a <= 1.05e-144))
		tmp = Float64(27.0 * Float64(a * b));
	else
		tmp = Float64(x * 2.0);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -1.08e+39) || ~((a <= 1.05e-144)))
		tmp = 27.0 * (a * b);
	else
		tmp = x * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -1.08e+39], N[Not[LessEqual[a, 1.05e-144]], $MachinePrecision]], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], N[(x * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.07999999999999998e39 or 1.0500000000000001e-144 < a

   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. sub-neg 94.0%

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

      2. sub-neg 94.0%

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

      3. associate-*l* 95.4%

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

      4. associate-*l* 95.4%

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

   3. Simplified 95.4%

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

   5. Taylor expanded in a around inf 52.8%

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

   if -1.07999999999999998e39 < a < 1.0500000000000001e-144

   1. Initial program 92.6%

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

      1. sub-neg 92.6%

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

      2. sub-neg 92.6%

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

      3. associate-*l* 97.9%

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

      4. associate-*l* 97.9%

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

   3. Simplified 97.9%

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

   5. Taylor expanded in x around inf 40.9%

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

4. Final simplification 47.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.08 \cdot 10^{+39} \lor \neg \left(a \leq 1.05 \cdot 10^{-144}\right):\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 30.1% accurate, 5.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.4%

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

   1. sub-neg 93.4%

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

   2. sub-neg 93.4%

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

   3. associate-*l* 96.4%

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

   4. associate-*l* 96.4%

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

3. Simplified 96.4%

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

5. Taylor expanded in x around inf 28.4%

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

6. Final simplification 28.4%

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

Developer target: 94.7% 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 2024026 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, A"
  :precision binary64

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

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