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

Percentage Accurate: 85.6% → 91.0%

Time: 26.8s

Alternatives: 30

Speedup: 0.8×

• 51.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (-
  (-
   (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c))
   (* (* x 4.0) i))
  (* (* j 27.0) k)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	return (((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    code = (((((((x * 18.0d0) * y) * z) * t) - ((a * 4.0d0) * t)) + (b * c)) - ((x * 4.0d0) * i)) - ((j * 27.0d0) * k)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	return (((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k);
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	return (((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k)

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	return Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 18.0) * y) * z) * t) - Float64(Float64(a * 4.0) * t)) + Float64(b * c)) - Float64(Float64(x * 4.0) * i)) - Float64(Float64(j * 27.0) * k))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j, k)
	tmp = (((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := N[(N[(N[(N[(N[(N[(N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision] - N[(N[(a * 4.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]

Initial Program: 85.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (-
  (-
   (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c))
   (* (* x 4.0) i))
  (* (* j 27.0) k)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	return (((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    code = (((((((x * 18.0d0) * y) * z) * t) - ((a * 4.0d0) * t)) + (b * c)) - ((x * 4.0d0) * i)) - ((j * 27.0d0) * k)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	return (((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k);
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	return (((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k)

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	return Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 18.0) * y) * z) * t) - Float64(Float64(a * 4.0) * t)) + Float64(b * c)) - Float64(Float64(x * 4.0) * i)) - Float64(Float64(j * 27.0) * k))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j, k)
	tmp = (((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := N[(N[(N[(N[(N[(N[(N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision] - N[(N[(a * 4.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]

Alternative 1: 91.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -7.6 \cdot 10^{-83} \lor \neg \left(t \leq 1.55 \cdot 10^{-209}\right):\\ \;\;\;\;\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(-4 \cdot i\right)\right)\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(y \cdot \left(\left(x \cdot 18\right) \cdot \left(t \cdot z\right)\right) - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - i \cdot \left(x \cdot 4\right)\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= t -7.6e-83) (not (<= t 1.55e-209)))
   (+
    (fma t (fma x (* 18.0 (* y z)) (* a -4.0)) (fma b c (* x (* -4.0 i))))
    (* j (* k -27.0)))
   (-
    (-
     (+ (- (* y (* (* x 18.0) (* t z))) (* t (* a 4.0))) (* b c))
     (* i (* x 4.0)))
    (* k (* j 27.0)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((t <= -7.6e-83) || !(t <= 1.55e-209)) {
		tmp = fma(t, fma(x, (18.0 * (y * z)), (a * -4.0)), fma(b, c, (x * (-4.0 * i)))) + (j * (k * -27.0));
	} else {
		tmp = ((((y * ((x * 18.0) * (t * z))) - (t * (a * 4.0))) + (b * c)) - (i * (x * 4.0))) - (k * (j * 27.0));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((t <= -7.6e-83) || !(t <= 1.55e-209))
		tmp = Float64(fma(t, fma(x, Float64(18.0 * Float64(y * z)), Float64(a * -4.0)), fma(b, c, Float64(x * Float64(-4.0 * i)))) + Float64(j * Float64(k * -27.0)));
	else
		tmp = Float64(Float64(Float64(Float64(Float64(y * Float64(Float64(x * 18.0) * Float64(t * z))) - Float64(t * Float64(a * 4.0))) + Float64(b * c)) - Float64(i * Float64(x * 4.0))) - Float64(k * Float64(j * 27.0)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[t, -7.6e-83], N[Not[LessEqual[t, 1.55e-209]], $MachinePrecision]], N[(N[(t * N[(x * N[(18.0 * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + N[(b * c + N[(x * N[(-4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(y * N[(N[(x * 18.0), $MachinePrecision] * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - N[(i * N[(x * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -7.59999999999999953e-83 or 1.55e-209 < t

   1. Initial program 89.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 94.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]
   4. Add Preprocessing

   if -7.59999999999999953e-83 < t < 1.55e-209

   1. Initial program 80.6%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. pow1 80.6%

         \[\leadsto \left(\left(\left(\color{blue}{{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t\right)}^{1}} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      2. associate-*l* 84.3%

         \[\leadsto \left(\left(\left({\color{blue}{\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot \left(z \cdot t\right)\right)}}^{1} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      3. *-commutative 84.3%

         \[\leadsto \left(\left(\left({\left(\color{blue}{\left(y \cdot \left(x \cdot 18\right)\right)} \cdot \left(z \cdot t\right)\right)}^{1} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   4. Applied egg-rr 84.3%

      \[\leadsto \left(\left(\left(\color{blue}{{\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right)\right)}^{1}} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   5. Step-by-step derivation

      1. unpow1 84.3%

         \[\leadsto \left(\left(\left(\color{blue}{\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right)} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      2. associate-*l* 94.6%

         \[\leadsto \left(\left(\left(\color{blue}{y \cdot \left(\left(x \cdot 18\right) \cdot \left(z \cdot t\right)\right)} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      3. *-commutative 94.6%

         \[\leadsto \left(\left(\left(y \cdot \left(\left(x \cdot 18\right) \cdot \color{blue}{\left(t \cdot z\right)}\right) - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   6. Simplified 94.6%

      \[\leadsto \left(\left(\left(\color{blue}{y \cdot \left(\left(x \cdot 18\right) \cdot \left(t \cdot z\right)\right)} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
3. Recombined 2 regimes into one program.

4. Final simplification 94.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.6 \cdot 10^{-83} \lor \neg \left(t \leq 1.55 \cdot 10^{-209}\right):\\ \;\;\;\;\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(-4 \cdot i\right)\right)\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(y \cdot \left(\left(x \cdot 18\right) \cdot \left(t \cdot z\right)\right) - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - i \cdot \left(x \cdot 4\right)\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 59.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := t\_1 + b \cdot c\\ t_3 := b \cdot c - x \cdot \left(i \cdot 4\right)\\ t_4 := t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{if}\;t \leq -2.15 \cdot 10^{+41}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t \leq -4.2 \cdot 10^{-102}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-177}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-78}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq 7.6 \cdot 10^{-28}:\\ \;\;\;\;-18 \cdot \left(t \cdot \left(z \cdot \left(-x \cdot y\right)\right)\right)\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-7}:\\ \;\;\;\;t\_1 + i \cdot \left(x \cdot -4\right)\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{+41} \lor \neg \left(t \leq 5.5 \cdot 10^{+79}\right):\\ \;\;\;\;t\_4\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0)))
        (t_2 (+ t_1 (* b c)))
        (t_3 (- (* b c) (* x (* i 4.0))))
        (t_4 (* t (- (* 18.0 (* x (* y z))) (* a 4.0)))))
   (if (<= t -2.15e+41)
     t_4
     (if (<= t -4.2e-102)
       t_3
       (if (<= t 7.5e-177)
         t_2
         (if (<= t 2.5e-78)
           t_3
           (if (<= t 7.6e-28)
             (* -18.0 (* t (* z (- (* x y)))))
             (if (<= t 7e-7)
               (+ t_1 (* i (* x -4.0)))
               (if (or (<= t 4.8e+41) (not (<= t 5.5e+79))) t_4 t_2)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = t_1 + (b * c);
	double t_3 = (b * c) - (x * (i * 4.0));
	double t_4 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	double tmp;
	if (t <= -2.15e+41) {
		tmp = t_4;
	} else if (t <= -4.2e-102) {
		tmp = t_3;
	} else if (t <= 7.5e-177) {
		tmp = t_2;
	} else if (t <= 2.5e-78) {
		tmp = t_3;
	} else if (t <= 7.6e-28) {
		tmp = -18.0 * (t * (z * -(x * y)));
	} else if (t <= 7e-7) {
		tmp = t_1 + (i * (x * -4.0));
	} else if ((t <= 4.8e+41) || !(t <= 5.5e+79)) {
		tmp = t_4;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = j * (k * (-27.0d0))
    t_2 = t_1 + (b * c)
    t_3 = (b * c) - (x * (i * 4.0d0))
    t_4 = t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0))
    if (t <= (-2.15d+41)) then
        tmp = t_4
    else if (t <= (-4.2d-102)) then
        tmp = t_3
    else if (t <= 7.5d-177) then
        tmp = t_2
    else if (t <= 2.5d-78) then
        tmp = t_3
    else if (t <= 7.6d-28) then
        tmp = (-18.0d0) * (t * (z * -(x * y)))
    else if (t <= 7d-7) then
        tmp = t_1 + (i * (x * (-4.0d0)))
    else if ((t <= 4.8d+41) .or. (.not. (t <= 5.5d+79))) then
        tmp = t_4
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = t_1 + (b * c);
	double t_3 = (b * c) - (x * (i * 4.0));
	double t_4 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	double tmp;
	if (t <= -2.15e+41) {
		tmp = t_4;
	} else if (t <= -4.2e-102) {
		tmp = t_3;
	} else if (t <= 7.5e-177) {
		tmp = t_2;
	} else if (t <= 2.5e-78) {
		tmp = t_3;
	} else if (t <= 7.6e-28) {
		tmp = -18.0 * (t * (z * -(x * y)));
	} else if (t <= 7e-7) {
		tmp = t_1 + (i * (x * -4.0));
	} else if ((t <= 4.8e+41) || !(t <= 5.5e+79)) {
		tmp = t_4;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	t_2 = t_1 + (b * c)
	t_3 = (b * c) - (x * (i * 4.0))
	t_4 = t * ((18.0 * (x * (y * z))) - (a * 4.0))
	tmp = 0
	if t <= -2.15e+41:
		tmp = t_4
	elif t <= -4.2e-102:
		tmp = t_3
	elif t <= 7.5e-177:
		tmp = t_2
	elif t <= 2.5e-78:
		tmp = t_3
	elif t <= 7.6e-28:
		tmp = -18.0 * (t * (z * -(x * y)))
	elif t <= 7e-7:
		tmp = t_1 + (i * (x * -4.0))
	elif (t <= 4.8e+41) or not (t <= 5.5e+79):
		tmp = t_4
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * -27.0))
	t_2 = Float64(t_1 + Float64(b * c))
	t_3 = Float64(Float64(b * c) - Float64(x * Float64(i * 4.0)))
	t_4 = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)))
	tmp = 0.0
	if (t <= -2.15e+41)
		tmp = t_4;
	elseif (t <= -4.2e-102)
		tmp = t_3;
	elseif (t <= 7.5e-177)
		tmp = t_2;
	elseif (t <= 2.5e-78)
		tmp = t_3;
	elseif (t <= 7.6e-28)
		tmp = Float64(-18.0 * Float64(t * Float64(z * Float64(-Float64(x * y)))));
	elseif (t <= 7e-7)
		tmp = Float64(t_1 + Float64(i * Float64(x * -4.0)));
	elseif ((t <= 4.8e+41) || !(t <= 5.5e+79))
		tmp = t_4;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * -27.0);
	t_2 = t_1 + (b * c);
	t_3 = (b * c) - (x * (i * 4.0));
	t_4 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	tmp = 0.0;
	if (t <= -2.15e+41)
		tmp = t_4;
	elseif (t <= -4.2e-102)
		tmp = t_3;
	elseif (t <= 7.5e-177)
		tmp = t_2;
	elseif (t <= 2.5e-78)
		tmp = t_3;
	elseif (t <= 7.6e-28)
		tmp = -18.0 * (t * (z * -(x * y)));
	elseif (t <= 7e-7)
		tmp = t_1 + (i * (x * -4.0));
	elseif ((t <= 4.8e+41) || ~((t <= 5.5e+79)))
		tmp = t_4;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(b * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(b * c), $MachinePrecision] - N[(x * N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.15e+41], t$95$4, If[LessEqual[t, -4.2e-102], t$95$3, If[LessEqual[t, 7.5e-177], t$95$2, If[LessEqual[t, 2.5e-78], t$95$3, If[LessEqual[t, 7.6e-28], N[(-18.0 * N[(t * N[(z * (-N[(x * y), $MachinePrecision])), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7e-7], N[(t$95$1 + N[(i * N[(x * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, 4.8e+41], N[Not[LessEqual[t, 5.5e+79]], $MachinePrecision]], t$95$4, t$95$2]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -2.15000000000000012e41 or 6.99999999999999968e-7 < t < 4.8000000000000003e41 or 5.50000000000000007e79 < t

   1. Initial program 88.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 92.7%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-*r* 93.5%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot z} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. distribute-rgt-out-- 89.0%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. associate-*l* 81.8%

         \[\leadsto \left(\left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot \left(z \cdot t\right)} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      4. *-commutative 81.8%

         \[\leadsto \left(\left(\color{blue}{\left(y \cdot \left(x \cdot 18\right)\right)} \cdot \left(z \cdot t\right) - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      5. *-commutative 81.8%

         \[\leadsto \left(\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) - \color{blue}{t \cdot \left(a \cdot 4\right)}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   6. Applied egg-rr 81.8%

      \[\leadsto \left(\color{blue}{\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) - t \cdot \left(a \cdot 4\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   7. Taylor expanded in t around inf 74.0%

      \[\leadsto \color{blue}{t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)} \]

   if -2.15000000000000012e41 < t < -4.2e-102 or 7.5e-177 < t < 2.4999999999999998e-78

   1. Initial program 88.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 86.9%

      \[\leadsto \color{blue}{\left(b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   4. Taylor expanded in j around 0 73.7%

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)} \]

   5. Taylor expanded in a around 0 61.5%

      \[\leadsto b \cdot c - \color{blue}{4 \cdot \left(i \cdot x\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 61.5%

         \[\leadsto b \cdot c - \color{blue}{\left(4 \cdot i\right) \cdot x} \]

   7. Simplified 61.5%

      \[\leadsto b \cdot c - \color{blue}{\left(4 \cdot i\right) \cdot x} \]

   if -4.2e-102 < t < 7.5e-177 or 4.8000000000000003e41 < t < 5.50000000000000007e79

   1. Initial program 81.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 78.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 66.2%

      \[\leadsto \color{blue}{b \cdot c} + j \cdot \left(k \cdot -27\right) \]

   if 2.4999999999999998e-78 < t < 7.60000000000000018e-28

   1. Initial program 86.2%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-*r* 86.2%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot z} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. distribute-rgt-out-- 86.2%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. sub-neg 86.2%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(a \cdot 4\right) \cdot t\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      4. associate-*l* 86.2%

         \[\leadsto \left(\left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot \left(z \cdot t\right)} + \left(-\left(a \cdot 4\right) \cdot t\right)\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      5. *-commutative 86.2%

         \[\leadsto \left(\left(\color{blue}{\left(y \cdot \left(x \cdot 18\right)\right)} \cdot \left(z \cdot t\right) + \left(-\left(a \cdot 4\right) \cdot t\right)\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      6. *-commutative 86.2%

         \[\leadsto \left(\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) + \left(-\color{blue}{t \cdot \left(a \cdot 4\right)}\right)\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   6. Applied egg-rr 86.2%

      \[\leadsto \left(\color{blue}{\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) + \left(-t \cdot \left(a \cdot 4\right)\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
   7. Step-by-step derivation

      1. distribute-lft-neg-in 86.2%

         \[\leadsto \left(\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) + \color{blue}{\left(-t\right) \cdot \left(a \cdot 4\right)}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. *-commutative 86.2%

         \[\leadsto \left(\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) + \left(-t\right) \cdot \color{blue}{\left(4 \cdot a\right)}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. cancel-sign-sub-inv 86.2%

         \[\leadsto \left(\color{blue}{\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) - t \cdot \left(4 \cdot a\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      4. *-commutative 86.2%

         \[\leadsto \left(\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) - \color{blue}{\left(4 \cdot a\right) \cdot t}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      5. associate-*r* 86.2%

         \[\leadsto \left(\left(\color{blue}{\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot z\right) \cdot t} - \left(4 \cdot a\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      6. distribute-rgt-out-- 86.2%

         \[\leadsto \left(\color{blue}{t \cdot \left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot z - 4 \cdot a\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      7. associate-*r* 86.2%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(\left(y \cdot x\right) \cdot 18\right)} \cdot z - 4 \cdot a\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      8. *-commutative 86.2%

         \[\leadsto \left(t \cdot \left(\left(\color{blue}{\left(x \cdot y\right)} \cdot 18\right) \cdot z - 4 \cdot a\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      9. *-commutative 86.2%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(18 \cdot \left(x \cdot y\right)\right)} \cdot z - 4 \cdot a\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      10. *-commutative 86.2%

          \[\leadsto \left(t \cdot \left(\left(18 \cdot \left(x \cdot y\right)\right) \cdot z - \color{blue}{a \cdot 4}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   8. Simplified 86.2%

      \[\leadsto \left(\color{blue}{t \cdot \left(\left(18 \cdot \left(x \cdot y\right)\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   9. Taylor expanded in x around -inf 72.4%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - -4 \cdot i\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 72.4%

          \[\leadsto \color{blue}{-x \cdot \left(-18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - -4 \cdot i\right)} \]

       2. cancel-sign-sub-inv 72.4%

          \[\leadsto -x \cdot \color{blue}{\left(-18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \left(--4\right) \cdot i\right)} \]

       3. associate-*r* 72.4%

          \[\leadsto -x \cdot \left(\color{blue}{\left(-18 \cdot t\right) \cdot \left(y \cdot z\right)} + \left(--4\right) \cdot i\right) \]

       4. metadata-eval 72.4%

          \[\leadsto -x \cdot \left(\left(-18 \cdot t\right) \cdot \left(y \cdot z\right) + \color{blue}{4} \cdot i\right) \]

   11. Simplified 72.4%

       \[\leadsto \color{blue}{-x \cdot \left(\left(-18 \cdot t\right) \cdot \left(y \cdot z\right) + 4 \cdot i\right)} \]

   12. Taylor expanded in t around inf 72.1%

       \[\leadsto -\color{blue}{-18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]
   13. Step-by-step derivation

       1. *-commutative 72.1%

          \[\leadsto -\color{blue}{\left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) \cdot -18} \]

       2. associate-*r* 58.7%

          \[\leadsto -\left(t \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot z\right)}\right) \cdot -18 \]

   14. Simplified 58.7%

       \[\leadsto -\color{blue}{\left(t \cdot \left(\left(x \cdot y\right) \cdot z\right)\right) \cdot -18} \]

   if 7.60000000000000018e-28 < t < 6.99999999999999968e-7

   1. Initial program 87.5%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 87.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around inf 87.6%

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right)} + j \cdot \left(k \cdot -27\right) \]
   6. Step-by-step derivation

      1. associate-*r* 87.6%

         \[\leadsto \color{blue}{\left(-4 \cdot i\right) \cdot x} + j \cdot \left(k \cdot -27\right) \]

      2. *-commutative 87.6%

         \[\leadsto \color{blue}{x \cdot \left(-4 \cdot i\right)} + j \cdot \left(k \cdot -27\right) \]

      3. associate-*r* 87.6%

         \[\leadsto \color{blue}{\left(x \cdot -4\right) \cdot i} + j \cdot \left(k \cdot -27\right) \]

      4. *-commutative 87.6%

         \[\leadsto \color{blue}{\left(-4 \cdot x\right)} \cdot i + j \cdot \left(k \cdot -27\right) \]

      5. *-commutative 87.6%

         \[\leadsto \color{blue}{i \cdot \left(-4 \cdot x\right)} + j \cdot \left(k \cdot -27\right) \]

   7. Simplified 87.6%

      \[\leadsto \color{blue}{i \cdot \left(-4 \cdot x\right)} + j \cdot \left(k \cdot -27\right) \]
3. Recombined 5 regimes into one program.

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.15 \cdot 10^{+41}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq -4.2 \cdot 10^{-102}:\\ \;\;\;\;b \cdot c - x \cdot \left(i \cdot 4\right)\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-177}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-78}:\\ \;\;\;\;b \cdot c - x \cdot \left(i \cdot 4\right)\\ \mathbf{elif}\;t \leq 7.6 \cdot 10^{-28}:\\ \;\;\;\;-18 \cdot \left(t \cdot \left(z \cdot \left(-x \cdot y\right)\right)\right)\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-7}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + i \cdot \left(x \cdot -4\right)\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{+41} \lor \neg \left(t \leq 5.5 \cdot 10^{+79}\right):\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 46.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := y \cdot \left(\left(t \cdot x\right) \cdot \left(-z \cdot -18\right)\right)\\ t_2 := j \cdot \left(k \cdot -27\right)\\ t_3 := t\_2 + b \cdot c\\ \mathbf{if}\;x \leq -5.2 \cdot 10^{+250}:\\ \;\;\;\;b \cdot c - x \cdot \left(i \cdot 4\right)\\ \mathbf{elif}\;x \leq -3 \cdot 10^{+143}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{+109}:\\ \;\;\;\;b \cdot c - t \cdot \left(a \cdot 4\right)\\ \mathbf{elif}\;x \leq -2.4 \cdot 10^{-127}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{-212}:\\ \;\;\;\;t\_2 + t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{-118}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq 9.8 \cdot 10^{+23}:\\ \;\;\;\;k \cdot \left(j \cdot -27 + -4 \cdot \frac{t \cdot a}{k}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* y (* (* t x) (- (* z -18.0)))))
        (t_2 (* j (* k -27.0)))
        (t_3 (+ t_2 (* b c))))
   (if (<= x -5.2e+250)
     (- (* b c) (* x (* i 4.0)))
     (if (<= x -3e+143)
       t_1
       (if (<= x -5.8e+109)
         (- (* b c) (* t (* a 4.0)))
         (if (<= x -2.4e-127)
           t_3
           (if (<= x 5.6e-212)
             (+ t_2 (* t (* a -4.0)))
             (if (<= x 2.9e-118)
               t_3
               (if (<= x 9.8e+23)
                 (* k (+ (* j -27.0) (* -4.0 (/ (* t a) k))))
                 t_1)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = y * ((t * x) * -(z * -18.0));
	double t_2 = j * (k * -27.0);
	double t_3 = t_2 + (b * c);
	double tmp;
	if (x <= -5.2e+250) {
		tmp = (b * c) - (x * (i * 4.0));
	} else if (x <= -3e+143) {
		tmp = t_1;
	} else if (x <= -5.8e+109) {
		tmp = (b * c) - (t * (a * 4.0));
	} else if (x <= -2.4e-127) {
		tmp = t_3;
	} else if (x <= 5.6e-212) {
		tmp = t_2 + (t * (a * -4.0));
	} else if (x <= 2.9e-118) {
		tmp = t_3;
	} else if (x <= 9.8e+23) {
		tmp = k * ((j * -27.0) + (-4.0 * ((t * a) / k)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = y * ((t * x) * -(z * (-18.0d0)))
    t_2 = j * (k * (-27.0d0))
    t_3 = t_2 + (b * c)
    if (x <= (-5.2d+250)) then
        tmp = (b * c) - (x * (i * 4.0d0))
    else if (x <= (-3d+143)) then
        tmp = t_1
    else if (x <= (-5.8d+109)) then
        tmp = (b * c) - (t * (a * 4.0d0))
    else if (x <= (-2.4d-127)) then
        tmp = t_3
    else if (x <= 5.6d-212) then
        tmp = t_2 + (t * (a * (-4.0d0)))
    else if (x <= 2.9d-118) then
        tmp = t_3
    else if (x <= 9.8d+23) then
        tmp = k * ((j * (-27.0d0)) + ((-4.0d0) * ((t * a) / k)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = y * ((t * x) * -(z * -18.0));
	double t_2 = j * (k * -27.0);
	double t_3 = t_2 + (b * c);
	double tmp;
	if (x <= -5.2e+250) {
		tmp = (b * c) - (x * (i * 4.0));
	} else if (x <= -3e+143) {
		tmp = t_1;
	} else if (x <= -5.8e+109) {
		tmp = (b * c) - (t * (a * 4.0));
	} else if (x <= -2.4e-127) {
		tmp = t_3;
	} else if (x <= 5.6e-212) {
		tmp = t_2 + (t * (a * -4.0));
	} else if (x <= 2.9e-118) {
		tmp = t_3;
	} else if (x <= 9.8e+23) {
		tmp = k * ((j * -27.0) + (-4.0 * ((t * a) / k)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = y * ((t * x) * -(z * -18.0))
	t_2 = j * (k * -27.0)
	t_3 = t_2 + (b * c)
	tmp = 0
	if x <= -5.2e+250:
		tmp = (b * c) - (x * (i * 4.0))
	elif x <= -3e+143:
		tmp = t_1
	elif x <= -5.8e+109:
		tmp = (b * c) - (t * (a * 4.0))
	elif x <= -2.4e-127:
		tmp = t_3
	elif x <= 5.6e-212:
		tmp = t_2 + (t * (a * -4.0))
	elif x <= 2.9e-118:
		tmp = t_3
	elif x <= 9.8e+23:
		tmp = k * ((j * -27.0) + (-4.0 * ((t * a) / k)))
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(y * Float64(Float64(t * x) * Float64(-Float64(z * -18.0))))
	t_2 = Float64(j * Float64(k * -27.0))
	t_3 = Float64(t_2 + Float64(b * c))
	tmp = 0.0
	if (x <= -5.2e+250)
		tmp = Float64(Float64(b * c) - Float64(x * Float64(i * 4.0)));
	elseif (x <= -3e+143)
		tmp = t_1;
	elseif (x <= -5.8e+109)
		tmp = Float64(Float64(b * c) - Float64(t * Float64(a * 4.0)));
	elseif (x <= -2.4e-127)
		tmp = t_3;
	elseif (x <= 5.6e-212)
		tmp = Float64(t_2 + Float64(t * Float64(a * -4.0)));
	elseif (x <= 2.9e-118)
		tmp = t_3;
	elseif (x <= 9.8e+23)
		tmp = Float64(k * Float64(Float64(j * -27.0) + Float64(-4.0 * Float64(Float64(t * a) / k))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = y * ((t * x) * -(z * -18.0));
	t_2 = j * (k * -27.0);
	t_3 = t_2 + (b * c);
	tmp = 0.0;
	if (x <= -5.2e+250)
		tmp = (b * c) - (x * (i * 4.0));
	elseif (x <= -3e+143)
		tmp = t_1;
	elseif (x <= -5.8e+109)
		tmp = (b * c) - (t * (a * 4.0));
	elseif (x <= -2.4e-127)
		tmp = t_3;
	elseif (x <= 5.6e-212)
		tmp = t_2 + (t * (a * -4.0));
	elseif (x <= 2.9e-118)
		tmp = t_3;
	elseif (x <= 9.8e+23)
		tmp = k * ((j * -27.0) + (-4.0 * ((t * a) / k)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(y * N[(N[(t * x), $MachinePrecision] * (-N[(z * -18.0), $MachinePrecision])), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 + N[(b * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5.2e+250], N[(N[(b * c), $MachinePrecision] - N[(x * N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3e+143], t$95$1, If[LessEqual[x, -5.8e+109], N[(N[(b * c), $MachinePrecision] - N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.4e-127], t$95$3, If[LessEqual[x, 5.6e-212], N[(t$95$2 + N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.9e-118], t$95$3, If[LessEqual[x, 9.8e+23], N[(k * N[(N[(j * -27.0), $MachinePrecision] + N[(-4.0 * N[(N[(t * a), $MachinePrecision] / k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -5.20000000000000023e250

   1. Initial program 74.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 81.6%

      \[\leadsto \color{blue}{\left(b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   4. Taylor expanded in j around 0 75.1%

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)} \]

   5. Taylor expanded in a around 0 68.1%

      \[\leadsto b \cdot c - \color{blue}{4 \cdot \left(i \cdot x\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 68.1%

         \[\leadsto b \cdot c - \color{blue}{\left(4 \cdot i\right) \cdot x} \]

   7. Simplified 68.1%

      \[\leadsto b \cdot c - \color{blue}{\left(4 \cdot i\right) \cdot x} \]

   if -5.20000000000000023e250 < x < -3.0000000000000001e143 or 9.8000000000000006e23 < x

   1. Initial program 72.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 81.5%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-*r* 77.2%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot z} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. distribute-rgt-out-- 72.8%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. sub-neg 72.8%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(a \cdot 4\right) \cdot t\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      4. associate-*l* 74.1%

         \[\leadsto \left(\left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot \left(z \cdot t\right)} + \left(-\left(a \cdot 4\right) \cdot t\right)\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      5. *-commutative 74.1%

         \[\leadsto \left(\left(\color{blue}{\left(y \cdot \left(x \cdot 18\right)\right)} \cdot \left(z \cdot t\right) + \left(-\left(a \cdot 4\right) \cdot t\right)\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      6. *-commutative 74.1%

         \[\leadsto \left(\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) + \left(-\color{blue}{t \cdot \left(a \cdot 4\right)}\right)\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   6. Applied egg-rr 74.1%

      \[\leadsto \left(\color{blue}{\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) + \left(-t \cdot \left(a \cdot 4\right)\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
   7. Step-by-step derivation

      1. distribute-lft-neg-in 74.1%

         \[\leadsto \left(\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) + \color{blue}{\left(-t\right) \cdot \left(a \cdot 4\right)}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. *-commutative 74.1%

         \[\leadsto \left(\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) + \left(-t\right) \cdot \color{blue}{\left(4 \cdot a\right)}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. cancel-sign-sub-inv 74.1%

         \[\leadsto \left(\color{blue}{\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) - t \cdot \left(4 \cdot a\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      4. *-commutative 74.1%

         \[\leadsto \left(\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) - \color{blue}{\left(4 \cdot a\right) \cdot t}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      5. associate-*r* 72.8%

         \[\leadsto \left(\left(\color{blue}{\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot z\right) \cdot t} - \left(4 \cdot a\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      6. distribute-rgt-out-- 77.2%

         \[\leadsto \left(\color{blue}{t \cdot \left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot z - 4 \cdot a\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      7. associate-*r* 77.2%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(\left(y \cdot x\right) \cdot 18\right)} \cdot z - 4 \cdot a\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      8. *-commutative 77.2%

         \[\leadsto \left(t \cdot \left(\left(\color{blue}{\left(x \cdot y\right)} \cdot 18\right) \cdot z - 4 \cdot a\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      9. *-commutative 77.2%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(18 \cdot \left(x \cdot y\right)\right)} \cdot z - 4 \cdot a\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      10. *-commutative 77.2%

          \[\leadsto \left(t \cdot \left(\left(18 \cdot \left(x \cdot y\right)\right) \cdot z - \color{blue}{a \cdot 4}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   8. Simplified 77.2%

      \[\leadsto \left(\color{blue}{t \cdot \left(\left(18 \cdot \left(x \cdot y\right)\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   9. Taylor expanded in x around -inf 74.7%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - -4 \cdot i\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 74.7%

          \[\leadsto \color{blue}{-x \cdot \left(-18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - -4 \cdot i\right)} \]

       2. cancel-sign-sub-inv 74.7%

          \[\leadsto -x \cdot \color{blue}{\left(-18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \left(--4\right) \cdot i\right)} \]

       3. associate-*r* 74.7%

          \[\leadsto -x \cdot \left(\color{blue}{\left(-18 \cdot t\right) \cdot \left(y \cdot z\right)} + \left(--4\right) \cdot i\right) \]

       4. metadata-eval 74.7%

          \[\leadsto -x \cdot \left(\left(-18 \cdot t\right) \cdot \left(y \cdot z\right) + \color{blue}{4} \cdot i\right) \]

   11. Simplified 74.7%

       \[\leadsto \color{blue}{-x \cdot \left(\left(-18 \cdot t\right) \cdot \left(y \cdot z\right) + 4 \cdot i\right)} \]

   12. Taylor expanded in t around inf 50.1%

       \[\leadsto -\color{blue}{-18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]
   13. Step-by-step derivation

       1. associate-*r* 53.7%

          \[\leadsto --18 \cdot \color{blue}{\left(\left(t \cdot x\right) \cdot \left(y \cdot z\right)\right)} \]

       2. *-commutative 53.7%

          \[\leadsto --18 \cdot \left(\left(t \cdot x\right) \cdot \color{blue}{\left(z \cdot y\right)}\right) \]

       3. associate-*r* 62.0%

          \[\leadsto --18 \cdot \color{blue}{\left(\left(\left(t \cdot x\right) \cdot z\right) \cdot y\right)} \]

       4. associate-*r* 60.6%

          \[\leadsto --18 \cdot \left(\color{blue}{\left(t \cdot \left(x \cdot z\right)\right)} \cdot y\right) \]

       5. associate-*l* 60.6%

          \[\leadsto -\color{blue}{\left(-18 \cdot \left(t \cdot \left(x \cdot z\right)\right)\right) \cdot y} \]

       6. *-commutative 60.6%

          \[\leadsto -\color{blue}{\left(\left(t \cdot \left(x \cdot z\right)\right) \cdot -18\right)} \cdot y \]

       7. associate-*r* 62.0%

          \[\leadsto -\left(\color{blue}{\left(\left(t \cdot x\right) \cdot z\right)} \cdot -18\right) \cdot y \]

       8. associate-*l* 61.9%

          \[\leadsto -\color{blue}{\left(\left(t \cdot x\right) \cdot \left(z \cdot -18\right)\right)} \cdot y \]

   14. Simplified 61.9%

       \[\leadsto -\color{blue}{\left(\left(t \cdot x\right) \cdot \left(z \cdot -18\right)\right) \cdot y} \]

   if -3.0000000000000001e143 < x < -5.8e109

   1. Initial program 88.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 88.9%

      \[\leadsto \color{blue}{\left(b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   4. Taylor expanded in j around 0 88.9%

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)} \]

   5. Taylor expanded in a around inf 67.0%

      \[\leadsto b \cdot c - \color{blue}{4 \cdot \left(a \cdot t\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 67.0%

         \[\leadsto b \cdot c - \color{blue}{\left(4 \cdot a\right) \cdot t} \]

      2. *-commutative 67.0%

         \[\leadsto b \cdot c - \color{blue}{t \cdot \left(4 \cdot a\right)} \]

   7. Simplified 67.0%

      \[\leadsto b \cdot c - \color{blue}{t \cdot \left(4 \cdot a\right)} \]

   if -5.8e109 < x < -2.39999999999999982e-127 or 5.60000000000000027e-212 < x < 2.8999999999999998e-118

   1. Initial program 95.6%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 95.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 57.5%

      \[\leadsto \color{blue}{b \cdot c} + j \cdot \left(k \cdot -27\right) \]

   if -2.39999999999999982e-127 < x < 5.60000000000000027e-212

   1. Initial program 96.6%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 90.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 71.7%

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t\right)} + j \cdot \left(k \cdot -27\right) \]
   6. Step-by-step derivation

      1. associate-*r* 71.7%

         \[\leadsto \color{blue}{\left(-4 \cdot a\right) \cdot t} + j \cdot \left(k \cdot -27\right) \]

      2. *-commutative 71.7%

         \[\leadsto \color{blue}{t \cdot \left(-4 \cdot a\right)} + j \cdot \left(k \cdot -27\right) \]

   7. Simplified 71.7%

      \[\leadsto \color{blue}{t \cdot \left(-4 \cdot a\right)} + j \cdot \left(k \cdot -27\right) \]

   if 2.8999999999999998e-118 < x < 9.8000000000000006e23

   1. Initial program 81.2%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 84.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 52.3%

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t\right)} + j \cdot \left(k \cdot -27\right) \]
   6. Step-by-step derivation

      1. associate-*r* 52.3%

         \[\leadsto \color{blue}{\left(-4 \cdot a\right) \cdot t} + j \cdot \left(k \cdot -27\right) \]

      2. *-commutative 52.3%

         \[\leadsto \color{blue}{t \cdot \left(-4 \cdot a\right)} + j \cdot \left(k \cdot -27\right) \]

   7. Simplified 52.3%

      \[\leadsto \color{blue}{t \cdot \left(-4 \cdot a\right)} + j \cdot \left(k \cdot -27\right) \]

   8. Taylor expanded in k around inf 54.9%

      \[\leadsto \color{blue}{k \cdot \left(-27 \cdot j + -4 \cdot \frac{a \cdot t}{k}\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 62.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{+250}:\\ \;\;\;\;b \cdot c - x \cdot \left(i \cdot 4\right)\\ \mathbf{elif}\;x \leq -3 \cdot 10^{+143}:\\ \;\;\;\;y \cdot \left(\left(t \cdot x\right) \cdot \left(-z \cdot -18\right)\right)\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{+109}:\\ \;\;\;\;b \cdot c - t \cdot \left(a \cdot 4\right)\\ \mathbf{elif}\;x \leq -2.4 \cdot 10^{-127}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{-212}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{-118}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \mathbf{elif}\;x \leq 9.8 \cdot 10^{+23}:\\ \;\;\;\;k \cdot \left(j \cdot -27 + -4 \cdot \frac{t \cdot a}{k}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\left(t \cdot x\right) \cdot \left(-z \cdot -18\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 88.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot 27\right) + x \cdot \left(i \cdot 4\right)\\ t_2 := \left(b \cdot c + x \cdot \left(z \cdot \left(y \cdot \left(t \cdot 18\right)\right)\right)\right) - t\_1\\ \mathbf{if}\;x \leq -2 \cdot 10^{+135}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 10^{-163}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(z \cdot \left(18 \cdot \left(x \cdot y\right)\right) - a \cdot 4\right)\right) - t\_1\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{+77}:\\ \;\;\;\;\left(b \cdot c + \left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(t \cdot z\right) - t \cdot \left(a \cdot 4\right)\right)\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (+ (* j (* k 27.0)) (* x (* i 4.0))))
        (t_2 (- (+ (* b c) (* x (* z (* y (* t 18.0))))) t_1)))
   (if (<= x -2e+135)
     t_2
     (if (<= x 1e-163)
       (- (+ (* b c) (* t (- (* z (* 18.0 (* x y))) (* a 4.0)))) t_1)
       (if (<= x 1.65e+77)
         (- (+ (* b c) (- (* (* y (* x 18.0)) (* t z)) (* t (* a 4.0)))) t_1)
         t_2)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * (k * 27.0)) + (x * (i * 4.0));
	double t_2 = ((b * c) + (x * (z * (y * (t * 18.0))))) - t_1;
	double tmp;
	if (x <= -2e+135) {
		tmp = t_2;
	} else if (x <= 1e-163) {
		tmp = ((b * c) + (t * ((z * (18.0 * (x * y))) - (a * 4.0)))) - t_1;
	} else if (x <= 1.65e+77) {
		tmp = ((b * c) + (((y * (x * 18.0)) * (t * z)) - (t * (a * 4.0)))) - t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (j * (k * 27.0d0)) + (x * (i * 4.0d0))
    t_2 = ((b * c) + (x * (z * (y * (t * 18.0d0))))) - t_1
    if (x <= (-2d+135)) then
        tmp = t_2
    else if (x <= 1d-163) then
        tmp = ((b * c) + (t * ((z * (18.0d0 * (x * y))) - (a * 4.0d0)))) - t_1
    else if (x <= 1.65d+77) then
        tmp = ((b * c) + (((y * (x * 18.0d0)) * (t * z)) - (t * (a * 4.0d0)))) - t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * (k * 27.0)) + (x * (i * 4.0));
	double t_2 = ((b * c) + (x * (z * (y * (t * 18.0))))) - t_1;
	double tmp;
	if (x <= -2e+135) {
		tmp = t_2;
	} else if (x <= 1e-163) {
		tmp = ((b * c) + (t * ((z * (18.0 * (x * y))) - (a * 4.0)))) - t_1;
	} else if (x <= 1.65e+77) {
		tmp = ((b * c) + (((y * (x * 18.0)) * (t * z)) - (t * (a * 4.0)))) - t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * (k * 27.0)) + (x * (i * 4.0))
	t_2 = ((b * c) + (x * (z * (y * (t * 18.0))))) - t_1
	tmp = 0
	if x <= -2e+135:
		tmp = t_2
	elif x <= 1e-163:
		tmp = ((b * c) + (t * ((z * (18.0 * (x * y))) - (a * 4.0)))) - t_1
	elif x <= 1.65e+77:
		tmp = ((b * c) + (((y * (x * 18.0)) * (t * z)) - (t * (a * 4.0)))) - t_1
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * Float64(k * 27.0)) + Float64(x * Float64(i * 4.0)))
	t_2 = Float64(Float64(Float64(b * c) + Float64(x * Float64(z * Float64(y * Float64(t * 18.0))))) - t_1)
	tmp = 0.0
	if (x <= -2e+135)
		tmp = t_2;
	elseif (x <= 1e-163)
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(z * Float64(18.0 * Float64(x * y))) - Float64(a * 4.0)))) - t_1);
	elseif (x <= 1.65e+77)
		tmp = Float64(Float64(Float64(b * c) + Float64(Float64(Float64(y * Float64(x * 18.0)) * Float64(t * z)) - Float64(t * Float64(a * 4.0)))) - t_1);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * (k * 27.0)) + (x * (i * 4.0));
	t_2 = ((b * c) + (x * (z * (y * (t * 18.0))))) - t_1;
	tmp = 0.0;
	if (x <= -2e+135)
		tmp = t_2;
	elseif (x <= 1e-163)
		tmp = ((b * c) + (t * ((z * (18.0 * (x * y))) - (a * 4.0)))) - t_1;
	elseif (x <= 1.65e+77)
		tmp = ((b * c) + (((y * (x * 18.0)) * (t * z)) - (t * (a * 4.0)))) - t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * N[(k * 27.0), $MachinePrecision]), $MachinePrecision] + N[(x * N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(b * c), $MachinePrecision] + N[(x * N[(z * N[(y * N[(t * 18.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]}, If[LessEqual[x, -2e+135], t$95$2, If[LessEqual[x, 1e-163], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(z * N[(18.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[x, 1.65e+77], N[(N[(N[(b * c), $MachinePrecision] + N[(N[(N[(y * N[(x * 18.0), $MachinePrecision]), $MachinePrecision] * N[(t * z), $MachinePrecision]), $MachinePrecision] - N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.99999999999999992e135 or 1.6499999999999999e77 < x

   1. Initial program 69.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 80.9%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-*r* 74.2%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot z} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. distribute-rgt-out-- 69.9%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. sub-neg 69.9%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(a \cdot 4\right) \cdot t\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      4. associate-*l* 71.0%

         \[\leadsto \left(\left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot \left(z \cdot t\right)} + \left(-\left(a \cdot 4\right) \cdot t\right)\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      5. *-commutative 71.0%

         \[\leadsto \left(\left(\color{blue}{\left(y \cdot \left(x \cdot 18\right)\right)} \cdot \left(z \cdot t\right) + \left(-\left(a \cdot 4\right) \cdot t\right)\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      6. *-commutative 71.0%

         \[\leadsto \left(\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) + \left(-\color{blue}{t \cdot \left(a \cdot 4\right)}\right)\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   6. Applied egg-rr 71.0%

      \[\leadsto \left(\color{blue}{\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) + \left(-t \cdot \left(a \cdot 4\right)\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
   7. Step-by-step derivation

      1. distribute-lft-neg-in 71.0%

         \[\leadsto \left(\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) + \color{blue}{\left(-t\right) \cdot \left(a \cdot 4\right)}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. *-commutative 71.0%

         \[\leadsto \left(\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) + \left(-t\right) \cdot \color{blue}{\left(4 \cdot a\right)}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. cancel-sign-sub-inv 71.0%

         \[\leadsto \left(\color{blue}{\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) - t \cdot \left(4 \cdot a\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      4. *-commutative 71.0%

         \[\leadsto \left(\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) - \color{blue}{\left(4 \cdot a\right) \cdot t}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      5. associate-*r* 69.9%

         \[\leadsto \left(\left(\color{blue}{\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot z\right) \cdot t} - \left(4 \cdot a\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      6. distribute-rgt-out-- 74.2%

         \[\leadsto \left(\color{blue}{t \cdot \left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot z - 4 \cdot a\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      7. associate-*r* 74.2%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(\left(y \cdot x\right) \cdot 18\right)} \cdot z - 4 \cdot a\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      8. *-commutative 74.2%

         \[\leadsto \left(t \cdot \left(\left(\color{blue}{\left(x \cdot y\right)} \cdot 18\right) \cdot z - 4 \cdot a\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      9. *-commutative 74.2%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(18 \cdot \left(x \cdot y\right)\right)} \cdot z - 4 \cdot a\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      10. *-commutative 74.2%

          \[\leadsto \left(t \cdot \left(\left(18 \cdot \left(x \cdot y\right)\right) \cdot z - \color{blue}{a \cdot 4}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   8. Simplified 74.2%

      \[\leadsto \left(\color{blue}{t \cdot \left(\left(18 \cdot \left(x \cdot y\right)\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   9. Taylor expanded in x around 0 80.9%

      \[\leadsto \left(t \cdot \left(\color{blue}{18 \cdot \left(x \cdot \left(y \cdot z\right)\right)} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
   10. Step-by-step derivation

       1. associate-*r* 74.2%

          \[\leadsto \left(t \cdot \left(18 \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot z\right)} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   11. Simplified 74.2%

       \[\leadsto \left(t \cdot \left(\color{blue}{18 \cdot \left(\left(x \cdot y\right) \cdot z\right)} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   12. Taylor expanded in x around inf 80.8%

       \[\leadsto \left(\color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
   13. Step-by-step derivation

       1. *-commutative 80.8%

          \[\leadsto \left(\color{blue}{\left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) \cdot 18} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

       2. *-commutative 80.8%

          \[\leadsto \left(\color{blue}{\left(\left(x \cdot \left(y \cdot z\right)\right) \cdot t\right)} \cdot 18 + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

       3. associate-*l* 90.2%

          \[\leadsto \left(\color{blue}{\left(x \cdot \left(\left(y \cdot z\right) \cdot t\right)\right)} \cdot 18 + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

       4. *-commutative 90.2%

          \[\leadsto \left(\left(x \cdot \color{blue}{\left(t \cdot \left(y \cdot z\right)\right)}\right) \cdot 18 + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

       5. associate-*r* 90.2%

          \[\leadsto \left(\color{blue}{x \cdot \left(\left(t \cdot \left(y \cdot z\right)\right) \cdot 18\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

       6. *-commutative 90.2%

          \[\leadsto \left(x \cdot \color{blue}{\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

       7. associate-*r* 90.2%

          \[\leadsto \left(x \cdot \color{blue}{\left(\left(18 \cdot t\right) \cdot \left(y \cdot z\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

       8. associate-*r* 90.2%

          \[\leadsto \left(x \cdot \color{blue}{\left(\left(\left(18 \cdot t\right) \cdot y\right) \cdot z\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   14. Simplified 90.2%

       \[\leadsto \left(\color{blue}{x \cdot \left(\left(\left(18 \cdot t\right) \cdot y\right) \cdot z\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   if -1.99999999999999992e135 < x < 9.99999999999999923e-164

   1. Initial program 96.1%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 93.3%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-*r* 97.6%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot z} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. distribute-rgt-out-- 96.1%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. sub-neg 96.1%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(a \cdot 4\right) \cdot t\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      4. associate-*l* 90.1%

         \[\leadsto \left(\left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot \left(z \cdot t\right)} + \left(-\left(a \cdot 4\right) \cdot t\right)\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      5. *-commutative 90.1%

         \[\leadsto \left(\left(\color{blue}{\left(y \cdot \left(x \cdot 18\right)\right)} \cdot \left(z \cdot t\right) + \left(-\left(a \cdot 4\right) \cdot t\right)\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      6. *-commutative 90.1%

         \[\leadsto \left(\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) + \left(-\color{blue}{t \cdot \left(a \cdot 4\right)}\right)\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   6. Applied egg-rr 90.1%

      \[\leadsto \left(\color{blue}{\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) + \left(-t \cdot \left(a \cdot 4\right)\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
   7. Step-by-step derivation

      1. distribute-lft-neg-in 90.1%

         \[\leadsto \left(\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) + \color{blue}{\left(-t\right) \cdot \left(a \cdot 4\right)}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. *-commutative 90.1%

         \[\leadsto \left(\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) + \left(-t\right) \cdot \color{blue}{\left(4 \cdot a\right)}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. cancel-sign-sub-inv 90.1%

         \[\leadsto \left(\color{blue}{\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) - t \cdot \left(4 \cdot a\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      4. *-commutative 90.1%

         \[\leadsto \left(\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) - \color{blue}{\left(4 \cdot a\right) \cdot t}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      5. associate-*r* 96.1%

         \[\leadsto \left(\left(\color{blue}{\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot z\right) \cdot t} - \left(4 \cdot a\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      6. distribute-rgt-out-- 97.6%

         \[\leadsto \left(\color{blue}{t \cdot \left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot z - 4 \cdot a\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      7. associate-*r* 97.6%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(\left(y \cdot x\right) \cdot 18\right)} \cdot z - 4 \cdot a\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      8. *-commutative 97.6%

         \[\leadsto \left(t \cdot \left(\left(\color{blue}{\left(x \cdot y\right)} \cdot 18\right) \cdot z - 4 \cdot a\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      9. *-commutative 97.6%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(18 \cdot \left(x \cdot y\right)\right)} \cdot z - 4 \cdot a\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      10. *-commutative 97.6%

          \[\leadsto \left(t \cdot \left(\left(18 \cdot \left(x \cdot y\right)\right) \cdot z - \color{blue}{a \cdot 4}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   8. Simplified 97.6%

      \[\leadsto \left(\color{blue}{t \cdot \left(\left(18 \cdot \left(x \cdot y\right)\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   if 9.99999999999999923e-164 < x < 1.6499999999999999e77

   1. Initial program 85.1%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 85.1%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-*r* 85.1%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot z} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. distribute-rgt-out-- 85.1%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. associate-*l* 90.4%

         \[\leadsto \left(\left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot \left(z \cdot t\right)} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      4. *-commutative 90.4%

         \[\leadsto \left(\left(\color{blue}{\left(y \cdot \left(x \cdot 18\right)\right)} \cdot \left(z \cdot t\right) - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      5. *-commutative 90.4%

         \[\leadsto \left(\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) - \color{blue}{t \cdot \left(a \cdot 4\right)}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   6. Applied egg-rr 90.4%

      \[\leadsto \left(\color{blue}{\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) - t \cdot \left(a \cdot 4\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 94.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{+135}:\\ \;\;\;\;\left(b \cdot c + x \cdot \left(z \cdot \left(y \cdot \left(t \cdot 18\right)\right)\right)\right) - \left(j \cdot \left(k \cdot 27\right) + x \cdot \left(i \cdot 4\right)\right)\\ \mathbf{elif}\;x \leq 10^{-163}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(z \cdot \left(18 \cdot \left(x \cdot y\right)\right) - a \cdot 4\right)\right) - \left(j \cdot \left(k \cdot 27\right) + x \cdot \left(i \cdot 4\right)\right)\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{+77}:\\ \;\;\;\;\left(b \cdot c + \left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(t \cdot z\right) - t \cdot \left(a \cdot 4\right)\right)\right) - \left(j \cdot \left(k \cdot 27\right) + x \cdot \left(i \cdot 4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + x \cdot \left(z \cdot \left(y \cdot \left(t \cdot 18\right)\right)\right)\right) - \left(j \cdot \left(k \cdot 27\right) + x \cdot \left(i \cdot 4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 67.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := k \cdot \left(j \cdot 27\right)\\ t_2 := z \cdot \left(x \cdot y\right)\\ t_3 := \left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - t\_1\\ t_4 := t \cdot \left(a \cdot \left(-4\right) - t\_2 \cdot -18\right)\\ \mathbf{if}\;t \leq -3.7 \cdot 10^{+126}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t \leq -1.45 \cdot 10^{-100}:\\ \;\;\;\;t \cdot \left(\frac{b \cdot c}{t} - 4 \cdot \left(a + i \cdot \frac{x}{t}\right)\right)\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-249}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-78}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - t\_1\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{+42}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + 18 \cdot \left(t \cdot t\_2\right)\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+219}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* k (* j 27.0)))
        (t_2 (* z (* x y)))
        (t_3 (- (- (* b c) (* 4.0 (* t a))) t_1))
        (t_4 (* t (- (* a (- 4.0)) (* t_2 -18.0)))))
   (if (<= t -3.7e+126)
     t_4
     (if (<= t -1.45e-100)
       (* t (- (/ (* b c) t) (* 4.0 (+ a (* i (/ x t))))))
       (if (<= t -5e-249)
         t_3
         (if (<= t 2.5e-78)
           (- (- (* b c) (* 4.0 (* x i))) t_1)
           (if (<= t 1.95e+42)
             (+ (* j (* k -27.0)) (* 18.0 (* t t_2)))
             (if (<= t 9.5e+219) t_3 t_4))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = k * (j * 27.0);
	double t_2 = z * (x * y);
	double t_3 = ((b * c) - (4.0 * (t * a))) - t_1;
	double t_4 = t * ((a * -4.0) - (t_2 * -18.0));
	double tmp;
	if (t <= -3.7e+126) {
		tmp = t_4;
	} else if (t <= -1.45e-100) {
		tmp = t * (((b * c) / t) - (4.0 * (a + (i * (x / t)))));
	} else if (t <= -5e-249) {
		tmp = t_3;
	} else if (t <= 2.5e-78) {
		tmp = ((b * c) - (4.0 * (x * i))) - t_1;
	} else if (t <= 1.95e+42) {
		tmp = (j * (k * -27.0)) + (18.0 * (t * t_2));
	} else if (t <= 9.5e+219) {
		tmp = t_3;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = k * (j * 27.0d0)
    t_2 = z * (x * y)
    t_3 = ((b * c) - (4.0d0 * (t * a))) - t_1
    t_4 = t * ((a * -4.0d0) - (t_2 * (-18.0d0)))
    if (t <= (-3.7d+126)) then
        tmp = t_4
    else if (t <= (-1.45d-100)) then
        tmp = t * (((b * c) / t) - (4.0d0 * (a + (i * (x / t)))))
    else if (t <= (-5d-249)) then
        tmp = t_3
    else if (t <= 2.5d-78) then
        tmp = ((b * c) - (4.0d0 * (x * i))) - t_1
    else if (t <= 1.95d+42) then
        tmp = (j * (k * (-27.0d0))) + (18.0d0 * (t * t_2))
    else if (t <= 9.5d+219) then
        tmp = t_3
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = k * (j * 27.0);
	double t_2 = z * (x * y);
	double t_3 = ((b * c) - (4.0 * (t * a))) - t_1;
	double t_4 = t * ((a * -4.0) - (t_2 * -18.0));
	double tmp;
	if (t <= -3.7e+126) {
		tmp = t_4;
	} else if (t <= -1.45e-100) {
		tmp = t * (((b * c) / t) - (4.0 * (a + (i * (x / t)))));
	} else if (t <= -5e-249) {
		tmp = t_3;
	} else if (t <= 2.5e-78) {
		tmp = ((b * c) - (4.0 * (x * i))) - t_1;
	} else if (t <= 1.95e+42) {
		tmp = (j * (k * -27.0)) + (18.0 * (t * t_2));
	} else if (t <= 9.5e+219) {
		tmp = t_3;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = k * (j * 27.0)
	t_2 = z * (x * y)
	t_3 = ((b * c) - (4.0 * (t * a))) - t_1
	t_4 = t * ((a * -4.0) - (t_2 * -18.0))
	tmp = 0
	if t <= -3.7e+126:
		tmp = t_4
	elif t <= -1.45e-100:
		tmp = t * (((b * c) / t) - (4.0 * (a + (i * (x / t)))))
	elif t <= -5e-249:
		tmp = t_3
	elif t <= 2.5e-78:
		tmp = ((b * c) - (4.0 * (x * i))) - t_1
	elif t <= 1.95e+42:
		tmp = (j * (k * -27.0)) + (18.0 * (t * t_2))
	elif t <= 9.5e+219:
		tmp = t_3
	else:
		tmp = t_4
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(k * Float64(j * 27.0))
	t_2 = Float64(z * Float64(x * y))
	t_3 = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(t * a))) - t_1)
	t_4 = Float64(t * Float64(Float64(a * Float64(-4.0)) - Float64(t_2 * -18.0)))
	tmp = 0.0
	if (t <= -3.7e+126)
		tmp = t_4;
	elseif (t <= -1.45e-100)
		tmp = Float64(t * Float64(Float64(Float64(b * c) / t) - Float64(4.0 * Float64(a + Float64(i * Float64(x / t))))));
	elseif (t <= -5e-249)
		tmp = t_3;
	elseif (t <= 2.5e-78)
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(x * i))) - t_1);
	elseif (t <= 1.95e+42)
		tmp = Float64(Float64(j * Float64(k * -27.0)) + Float64(18.0 * Float64(t * t_2)));
	elseif (t <= 9.5e+219)
		tmp = t_3;
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = k * (j * 27.0);
	t_2 = z * (x * y);
	t_3 = ((b * c) - (4.0 * (t * a))) - t_1;
	t_4 = t * ((a * -4.0) - (t_2 * -18.0));
	tmp = 0.0;
	if (t <= -3.7e+126)
		tmp = t_4;
	elseif (t <= -1.45e-100)
		tmp = t * (((b * c) / t) - (4.0 * (a + (i * (x / t)))));
	elseif (t <= -5e-249)
		tmp = t_3;
	elseif (t <= 2.5e-78)
		tmp = ((b * c) - (4.0 * (x * i))) - t_1;
	elseif (t <= 1.95e+42)
		tmp = (j * (k * -27.0)) + (18.0 * (t * t_2));
	elseif (t <= 9.5e+219)
		tmp = t_3;
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]}, Block[{t$95$4 = N[(t * N[(N[(a * (-4.0)), $MachinePrecision] - N[(t$95$2 * -18.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.7e+126], t$95$4, If[LessEqual[t, -1.45e-100], N[(t * N[(N[(N[(b * c), $MachinePrecision] / t), $MachinePrecision] - N[(4.0 * N[(a + N[(i * N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -5e-249], t$95$3, If[LessEqual[t, 2.5e-78], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[t, 1.95e+42], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(18.0 * N[(t * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.5e+219], t$95$3, t$95$4]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -3.6999999999999998e126 or 9.49999999999999959e219 < t

   1. Initial program 83.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 89.7%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-*r* 89.8%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot z} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. distribute-rgt-out-- 83.0%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. associate-*l* 76.2%

         \[\leadsto \left(\left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot \left(z \cdot t\right)} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      4. *-commutative 76.2%

         \[\leadsto \left(\left(\color{blue}{\left(y \cdot \left(x \cdot 18\right)\right)} \cdot \left(z \cdot t\right) - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      5. *-commutative 76.2%

         \[\leadsto \left(\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) - \color{blue}{t \cdot \left(a \cdot 4\right)}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   6. Applied egg-rr 76.2%

      \[\leadsto \left(\color{blue}{\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) - t \cdot \left(a \cdot 4\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   7. Taylor expanded in t around -inf 86.9%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 86.9%

         \[\leadsto \color{blue}{\left(-1 \cdot t\right) \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right)} \]

      2. neg-mul-1 86.9%

         \[\leadsto \color{blue}{\left(-t\right)} \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right) \]

      3. cancel-sign-sub-inv 86.9%

         \[\leadsto \left(-t\right) \cdot \color{blue}{\left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + \left(--4\right) \cdot a\right)} \]

      4. metadata-eval 86.9%

         \[\leadsto \left(-t\right) \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + \color{blue}{4} \cdot a\right) \]

      5. *-commutative 86.9%

         \[\leadsto \left(-t\right) \cdot \left(\color{blue}{\left(x \cdot \left(y \cdot z\right)\right) \cdot -18} + 4 \cdot a\right) \]

      6. associate-*r* 87.0%

         \[\leadsto \left(-t\right) \cdot \left(\color{blue}{\left(\left(x \cdot y\right) \cdot z\right)} \cdot -18 + 4 \cdot a\right) \]

   9. Simplified 87.0%

      \[\leadsto \color{blue}{\left(-t\right) \cdot \left(\left(\left(x \cdot y\right) \cdot z\right) \cdot -18 + 4 \cdot a\right)} \]

   if -3.6999999999999998e126 < t < -1.44999999999999988e-100

   1. Initial program 85.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 83.3%

      \[\leadsto \color{blue}{\left(b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   4. Taylor expanded in j around 0 68.8%

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)} \]

   5. Taylor expanded in t around inf 64.2%

      \[\leadsto \color{blue}{t \cdot \left(\frac{b \cdot c}{t} - \left(4 \cdot a + 4 \cdot \frac{i \cdot x}{t}\right)\right)} \]
   6. Step-by-step derivation

      1. distribute-lft-out 64.2%

         \[\leadsto t \cdot \left(\frac{b \cdot c}{t} - \color{blue}{4 \cdot \left(a + \frac{i \cdot x}{t}\right)}\right) \]

      2. associate-/l* 69.0%

         \[\leadsto t \cdot \left(\frac{b \cdot c}{t} - 4 \cdot \left(a + \color{blue}{i \cdot \frac{x}{t}}\right)\right) \]

   7. Simplified 69.0%

      \[\leadsto \color{blue}{t \cdot \left(\frac{b \cdot c}{t} - 4 \cdot \left(a + i \cdot \frac{x}{t}\right)\right)} \]

   if -1.44999999999999988e-100 < t < -4.9999999999999999e-249 or 1.94999999999999985e42 < t < 9.49999999999999959e219

   1. Initial program 91.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 79.6%

      \[\leadsto \color{blue}{\left(b \cdot c - 4 \cdot \left(a \cdot t\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   if -4.9999999999999999e-249 < t < 2.4999999999999998e-78

   1. Initial program 88.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 81.6%

      \[\leadsto \color{blue}{\left(b \cdot c - 4 \cdot \left(i \cdot x\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   if 2.4999999999999998e-78 < t < 1.94999999999999985e42

   1. Initial program 80.1%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 88.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 72.7%

      \[\leadsto \color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} + j \cdot \left(k \cdot -27\right) \]
   6. Step-by-step derivation

      1. pow1 72.7%

         \[\leadsto 18 \cdot \left(t \cdot \color{blue}{{\left(x \cdot \left(y \cdot z\right)\right)}^{1}}\right) + j \cdot \left(k \cdot -27\right) \]

   7. Applied egg-rr 72.7%

      \[\leadsto 18 \cdot \left(t \cdot \color{blue}{{\left(x \cdot \left(y \cdot z\right)\right)}^{1}}\right) + j \cdot \left(k \cdot -27\right) \]
   8. Step-by-step derivation

      1. unpow1 72.7%

         \[\leadsto 18 \cdot \left(t \cdot \color{blue}{\left(x \cdot \left(y \cdot z\right)\right)}\right) + j \cdot \left(k \cdot -27\right) \]

      2. associate-*r* 72.7%

         \[\leadsto 18 \cdot \left(t \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot z\right)}\right) + j \cdot \left(k \cdot -27\right) \]

   9. Simplified 72.7%

      \[\leadsto 18 \cdot \left(t \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot z\right)}\right) + j \cdot \left(k \cdot -27\right) \]
3. Recombined 5 regimes into one program.

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.7 \cdot 10^{+126}:\\ \;\;\;\;t \cdot \left(a \cdot \left(-4\right) - \left(z \cdot \left(x \cdot y\right)\right) \cdot -18\right)\\ \mathbf{elif}\;t \leq -1.45 \cdot 10^{-100}:\\ \;\;\;\;t \cdot \left(\frac{b \cdot c}{t} - 4 \cdot \left(a + i \cdot \frac{x}{t}\right)\right)\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-249}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-78}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{+42}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + 18 \cdot \left(t \cdot \left(z \cdot \left(x \cdot y\right)\right)\right)\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+219}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot \left(-4\right) - \left(z \cdot \left(x \cdot y\right)\right) \cdot -18\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 68.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y\right)\\ t_2 := k \cdot \left(j \cdot 27\right)\\ t_3 := \left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - t\_2\\ t_4 := t \cdot \left(a \cdot \left(-4\right) - t\_1 \cdot -18\right)\\ \mathbf{if}\;t \leq -4.3 \cdot 10^{+129}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t \leq -1.08 \cdot 10^{-100}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\\ \mathbf{elif}\;t \leq -6.4 \cdot 10^{-249}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-78}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - t\_2\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{+42}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + 18 \cdot \left(t \cdot t\_1\right)\\ \mathbf{elif}\;t \leq 10^{+220}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* z (* x y)))
        (t_2 (* k (* j 27.0)))
        (t_3 (- (- (* b c) (* 4.0 (* t a))) t_2))
        (t_4 (* t (- (* a (- 4.0)) (* t_1 -18.0)))))
   (if (<= t -4.3e+129)
     t_4
     (if (<= t -1.08e-100)
       (- (* b c) (* 4.0 (+ (* x i) (* t a))))
       (if (<= t -6.4e-249)
         t_3
         (if (<= t 2.5e-78)
           (- (- (* b c) (* 4.0 (* x i))) t_2)
           (if (<= t 1.95e+42)
             (+ (* j (* k -27.0)) (* 18.0 (* t t_1)))
             (if (<= t 1e+220) t_3 t_4))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = z * (x * y);
	double t_2 = k * (j * 27.0);
	double t_3 = ((b * c) - (4.0 * (t * a))) - t_2;
	double t_4 = t * ((a * -4.0) - (t_1 * -18.0));
	double tmp;
	if (t <= -4.3e+129) {
		tmp = t_4;
	} else if (t <= -1.08e-100) {
		tmp = (b * c) - (4.0 * ((x * i) + (t * a)));
	} else if (t <= -6.4e-249) {
		tmp = t_3;
	} else if (t <= 2.5e-78) {
		tmp = ((b * c) - (4.0 * (x * i))) - t_2;
	} else if (t <= 1.95e+42) {
		tmp = (j * (k * -27.0)) + (18.0 * (t * t_1));
	} else if (t <= 1e+220) {
		tmp = t_3;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = z * (x * y)
    t_2 = k * (j * 27.0d0)
    t_3 = ((b * c) - (4.0d0 * (t * a))) - t_2
    t_4 = t * ((a * -4.0d0) - (t_1 * (-18.0d0)))
    if (t <= (-4.3d+129)) then
        tmp = t_4
    else if (t <= (-1.08d-100)) then
        tmp = (b * c) - (4.0d0 * ((x * i) + (t * a)))
    else if (t <= (-6.4d-249)) then
        tmp = t_3
    else if (t <= 2.5d-78) then
        tmp = ((b * c) - (4.0d0 * (x * i))) - t_2
    else if (t <= 1.95d+42) then
        tmp = (j * (k * (-27.0d0))) + (18.0d0 * (t * t_1))
    else if (t <= 1d+220) then
        tmp = t_3
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = z * (x * y);
	double t_2 = k * (j * 27.0);
	double t_3 = ((b * c) - (4.0 * (t * a))) - t_2;
	double t_4 = t * ((a * -4.0) - (t_1 * -18.0));
	double tmp;
	if (t <= -4.3e+129) {
		tmp = t_4;
	} else if (t <= -1.08e-100) {
		tmp = (b * c) - (4.0 * ((x * i) + (t * a)));
	} else if (t <= -6.4e-249) {
		tmp = t_3;
	} else if (t <= 2.5e-78) {
		tmp = ((b * c) - (4.0 * (x * i))) - t_2;
	} else if (t <= 1.95e+42) {
		tmp = (j * (k * -27.0)) + (18.0 * (t * t_1));
	} else if (t <= 1e+220) {
		tmp = t_3;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = z * (x * y)
	t_2 = k * (j * 27.0)
	t_3 = ((b * c) - (4.0 * (t * a))) - t_2
	t_4 = t * ((a * -4.0) - (t_1 * -18.0))
	tmp = 0
	if t <= -4.3e+129:
		tmp = t_4
	elif t <= -1.08e-100:
		tmp = (b * c) - (4.0 * ((x * i) + (t * a)))
	elif t <= -6.4e-249:
		tmp = t_3
	elif t <= 2.5e-78:
		tmp = ((b * c) - (4.0 * (x * i))) - t_2
	elif t <= 1.95e+42:
		tmp = (j * (k * -27.0)) + (18.0 * (t * t_1))
	elif t <= 1e+220:
		tmp = t_3
	else:
		tmp = t_4
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(z * Float64(x * y))
	t_2 = Float64(k * Float64(j * 27.0))
	t_3 = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(t * a))) - t_2)
	t_4 = Float64(t * Float64(Float64(a * Float64(-4.0)) - Float64(t_1 * -18.0)))
	tmp = 0.0
	if (t <= -4.3e+129)
		tmp = t_4;
	elseif (t <= -1.08e-100)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(Float64(x * i) + Float64(t * a))));
	elseif (t <= -6.4e-249)
		tmp = t_3;
	elseif (t <= 2.5e-78)
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(x * i))) - t_2);
	elseif (t <= 1.95e+42)
		tmp = Float64(Float64(j * Float64(k * -27.0)) + Float64(18.0 * Float64(t * t_1)));
	elseif (t <= 1e+220)
		tmp = t_3;
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = z * (x * y);
	t_2 = k * (j * 27.0);
	t_3 = ((b * c) - (4.0 * (t * a))) - t_2;
	t_4 = t * ((a * -4.0) - (t_1 * -18.0));
	tmp = 0.0;
	if (t <= -4.3e+129)
		tmp = t_4;
	elseif (t <= -1.08e-100)
		tmp = (b * c) - (4.0 * ((x * i) + (t * a)));
	elseif (t <= -6.4e-249)
		tmp = t_3;
	elseif (t <= 2.5e-78)
		tmp = ((b * c) - (4.0 * (x * i))) - t_2;
	elseif (t <= 1.95e+42)
		tmp = (j * (k * -27.0)) + (18.0 * (t * t_1));
	elseif (t <= 1e+220)
		tmp = t_3;
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(t * N[(N[(a * (-4.0)), $MachinePrecision] - N[(t$95$1 * -18.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.3e+129], t$95$4, If[LessEqual[t, -1.08e-100], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(N[(x * i), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -6.4e-249], t$95$3, If[LessEqual[t, 2.5e-78], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], If[LessEqual[t, 1.95e+42], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(18.0 * N[(t * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1e+220], t$95$3, t$95$4]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -4.30000000000000021e129 or 1e220 < t

   1. Initial program 83.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 89.7%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-*r* 89.8%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot z} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. distribute-rgt-out-- 83.0%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. associate-*l* 76.2%

         \[\leadsto \left(\left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot \left(z \cdot t\right)} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      4. *-commutative 76.2%

         \[\leadsto \left(\left(\color{blue}{\left(y \cdot \left(x \cdot 18\right)\right)} \cdot \left(z \cdot t\right) - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      5. *-commutative 76.2%

         \[\leadsto \left(\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) - \color{blue}{t \cdot \left(a \cdot 4\right)}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   6. Applied egg-rr 76.2%

      \[\leadsto \left(\color{blue}{\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) - t \cdot \left(a \cdot 4\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   7. Taylor expanded in t around -inf 86.9%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 86.9%

         \[\leadsto \color{blue}{\left(-1 \cdot t\right) \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right)} \]

      2. neg-mul-1 86.9%

         \[\leadsto \color{blue}{\left(-t\right)} \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right) \]

      3. cancel-sign-sub-inv 86.9%

         \[\leadsto \left(-t\right) \cdot \color{blue}{\left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + \left(--4\right) \cdot a\right)} \]

      4. metadata-eval 86.9%

         \[\leadsto \left(-t\right) \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + \color{blue}{4} \cdot a\right) \]

      5. *-commutative 86.9%

         \[\leadsto \left(-t\right) \cdot \left(\color{blue}{\left(x \cdot \left(y \cdot z\right)\right) \cdot -18} + 4 \cdot a\right) \]

      6. associate-*r* 87.0%

         \[\leadsto \left(-t\right) \cdot \left(\color{blue}{\left(\left(x \cdot y\right) \cdot z\right)} \cdot -18 + 4 \cdot a\right) \]

   9. Simplified 87.0%

      \[\leadsto \color{blue}{\left(-t\right) \cdot \left(\left(\left(x \cdot y\right) \cdot z\right) \cdot -18 + 4 \cdot a\right)} \]

   if -4.30000000000000021e129 < t < -1.0800000000000001e-100

   1. Initial program 85.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 83.3%

      \[\leadsto \color{blue}{\left(b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   4. Taylor expanded in j around 0 68.8%

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 68.8%

         \[\leadsto b \cdot c - \color{blue}{\left(4 \cdot \left(i \cdot x\right) + 4 \cdot \left(a \cdot t\right)\right)} \]

      2. associate-*r* 68.8%

         \[\leadsto b \cdot c - \left(\color{blue}{\left(4 \cdot i\right) \cdot x} + 4 \cdot \left(a \cdot t\right)\right) \]

      3. *-commutative 68.8%

         \[\leadsto b \cdot c - \left(\color{blue}{x \cdot \left(4 \cdot i\right)} + 4 \cdot \left(a \cdot t\right)\right) \]

      4. fma-define 68.8%

         \[\leadsto b \cdot c - \color{blue}{\mathsf{fma}\left(x, 4 \cdot i, 4 \cdot \left(a \cdot t\right)\right)} \]

      5. associate-*r* 68.8%

         \[\leadsto b \cdot c - \mathsf{fma}\left(x, 4 \cdot i, \color{blue}{\left(4 \cdot a\right) \cdot t}\right) \]

      6. *-commutative 68.8%

         \[\leadsto b \cdot c - \mathsf{fma}\left(x, 4 \cdot i, \color{blue}{\left(a \cdot 4\right)} \cdot t\right) \]

   6. Applied egg-rr 68.8%

      \[\leadsto b \cdot c - \color{blue}{\mathsf{fma}\left(x, 4 \cdot i, \left(a \cdot 4\right) \cdot t\right)} \]
   7. Step-by-step derivation

      1. fma-undefine 68.8%

         \[\leadsto b \cdot c - \color{blue}{\left(x \cdot \left(4 \cdot i\right) + \left(a \cdot 4\right) \cdot t\right)} \]

      2. *-commutative 68.8%

         \[\leadsto b \cdot c - \left(x \cdot \color{blue}{\left(i \cdot 4\right)} + \left(a \cdot 4\right) \cdot t\right) \]

      3. associate-*r* 68.8%

         \[\leadsto b \cdot c - \left(\color{blue}{\left(x \cdot i\right) \cdot 4} + \left(a \cdot 4\right) \cdot t\right) \]

      4. *-commutative 68.8%

         \[\leadsto b \cdot c - \left(\color{blue}{\left(i \cdot x\right)} \cdot 4 + \left(a \cdot 4\right) \cdot t\right) \]

      5. *-commutative 68.8%

         \[\leadsto b \cdot c - \left(\color{blue}{4 \cdot \left(i \cdot x\right)} + \left(a \cdot 4\right) \cdot t\right) \]

      6. *-commutative 68.8%

         \[\leadsto b \cdot c - \left(4 \cdot \left(i \cdot x\right) + \color{blue}{\left(4 \cdot a\right)} \cdot t\right) \]

      7. associate-*r* 68.8%

         \[\leadsto b \cdot c - \left(4 \cdot \left(i \cdot x\right) + \color{blue}{4 \cdot \left(a \cdot t\right)}\right) \]

      8. distribute-lft-out 68.8%

         \[\leadsto b \cdot c - \color{blue}{4 \cdot \left(i \cdot x + a \cdot t\right)} \]

      9. *-commutative 68.8%

         \[\leadsto b \cdot c - 4 \cdot \left(\color{blue}{x \cdot i} + a \cdot t\right) \]

      10. *-commutative 68.8%

          \[\leadsto b \cdot c - 4 \cdot \left(x \cdot i + \color{blue}{t \cdot a}\right) \]

   8. Simplified 68.8%

      \[\leadsto b \cdot c - \color{blue}{4 \cdot \left(x \cdot i + t \cdot a\right)} \]

   if -1.0800000000000001e-100 < t < -6.4000000000000003e-249 or 1.94999999999999985e42 < t < 1e220

   1. Initial program 91.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 79.6%

      \[\leadsto \color{blue}{\left(b \cdot c - 4 \cdot \left(a \cdot t\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   if -6.4000000000000003e-249 < t < 2.4999999999999998e-78

   1. Initial program 88.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 81.6%

      \[\leadsto \color{blue}{\left(b \cdot c - 4 \cdot \left(i \cdot x\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   if 2.4999999999999998e-78 < t < 1.94999999999999985e42

   1. Initial program 80.1%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 88.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 72.7%

      \[\leadsto \color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} + j \cdot \left(k \cdot -27\right) \]
   6. Step-by-step derivation

      1. pow1 72.7%

         \[\leadsto 18 \cdot \left(t \cdot \color{blue}{{\left(x \cdot \left(y \cdot z\right)\right)}^{1}}\right) + j \cdot \left(k \cdot -27\right) \]

   7. Applied egg-rr 72.7%

      \[\leadsto 18 \cdot \left(t \cdot \color{blue}{{\left(x \cdot \left(y \cdot z\right)\right)}^{1}}\right) + j \cdot \left(k \cdot -27\right) \]
   8. Step-by-step derivation

      1. unpow1 72.7%

         \[\leadsto 18 \cdot \left(t \cdot \color{blue}{\left(x \cdot \left(y \cdot z\right)\right)}\right) + j \cdot \left(k \cdot -27\right) \]

      2. associate-*r* 72.7%

         \[\leadsto 18 \cdot \left(t \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot z\right)}\right) + j \cdot \left(k \cdot -27\right) \]

   9. Simplified 72.7%

      \[\leadsto 18 \cdot \left(t \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot z\right)}\right) + j \cdot \left(k \cdot -27\right) \]
3. Recombined 5 regimes into one program.

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.3 \cdot 10^{+129}:\\ \;\;\;\;t \cdot \left(a \cdot \left(-4\right) - \left(z \cdot \left(x \cdot y\right)\right) \cdot -18\right)\\ \mathbf{elif}\;t \leq -1.08 \cdot 10^{-100}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\\ \mathbf{elif}\;t \leq -6.4 \cdot 10^{-249}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-78}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{+42}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + 18 \cdot \left(t \cdot \left(z \cdot \left(x \cdot y\right)\right)\right)\\ \mathbf{elif}\;t \leq 10^{+220}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot \left(-4\right) - \left(z \cdot \left(x \cdot y\right)\right) \cdot -18\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 59.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right) + b \cdot c\\ t_2 := t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{if}\;t \leq -2.9 \cdot 10^{+74}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -5.4 \cdot 10^{-105}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - i \cdot 4\right)\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-177}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{-145}:\\ \;\;\;\;b \cdot c - x \cdot \left(i \cdot 4\right)\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-104}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{+71}:\\ \;\;\;\;x \cdot \left(-4 \cdot i + 18 \cdot \left(z \cdot \left(t \cdot y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (+ (* j (* k -27.0)) (* b c)))
        (t_2 (* t (- (* 18.0 (* x (* y z))) (* a 4.0)))))
   (if (<= t -2.9e+74)
     t_2
     (if (<= t -5.4e-105)
       (* x (- (* 18.0 (* t (* y z))) (* i 4.0)))
       (if (<= t 9.5e-177)
         t_1
         (if (<= t 2.25e-145)
           (- (* b c) (* x (* i 4.0)))
           (if (<= t 6e-104)
             t_1
             (if (<= t 1.95e+71)
               (* x (+ (* -4.0 i) (* 18.0 (* z (* t y)))))
               t_2))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * (k * -27.0)) + (b * c);
	double t_2 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	double tmp;
	if (t <= -2.9e+74) {
		tmp = t_2;
	} else if (t <= -5.4e-105) {
		tmp = x * ((18.0 * (t * (y * z))) - (i * 4.0));
	} else if (t <= 9.5e-177) {
		tmp = t_1;
	} else if (t <= 2.25e-145) {
		tmp = (b * c) - (x * (i * 4.0));
	} else if (t <= 6e-104) {
		tmp = t_1;
	} else if (t <= 1.95e+71) {
		tmp = x * ((-4.0 * i) + (18.0 * (z * (t * y))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (j * (k * (-27.0d0))) + (b * c)
    t_2 = t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0))
    if (t <= (-2.9d+74)) then
        tmp = t_2
    else if (t <= (-5.4d-105)) then
        tmp = x * ((18.0d0 * (t * (y * z))) - (i * 4.0d0))
    else if (t <= 9.5d-177) then
        tmp = t_1
    else if (t <= 2.25d-145) then
        tmp = (b * c) - (x * (i * 4.0d0))
    else if (t <= 6d-104) then
        tmp = t_1
    else if (t <= 1.95d+71) then
        tmp = x * (((-4.0d0) * i) + (18.0d0 * (z * (t * y))))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * (k * -27.0)) + (b * c);
	double t_2 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	double tmp;
	if (t <= -2.9e+74) {
		tmp = t_2;
	} else if (t <= -5.4e-105) {
		tmp = x * ((18.0 * (t * (y * z))) - (i * 4.0));
	} else if (t <= 9.5e-177) {
		tmp = t_1;
	} else if (t <= 2.25e-145) {
		tmp = (b * c) - (x * (i * 4.0));
	} else if (t <= 6e-104) {
		tmp = t_1;
	} else if (t <= 1.95e+71) {
		tmp = x * ((-4.0 * i) + (18.0 * (z * (t * y))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * (k * -27.0)) + (b * c)
	t_2 = t * ((18.0 * (x * (y * z))) - (a * 4.0))
	tmp = 0
	if t <= -2.9e+74:
		tmp = t_2
	elif t <= -5.4e-105:
		tmp = x * ((18.0 * (t * (y * z))) - (i * 4.0))
	elif t <= 9.5e-177:
		tmp = t_1
	elif t <= 2.25e-145:
		tmp = (b * c) - (x * (i * 4.0))
	elif t <= 6e-104:
		tmp = t_1
	elif t <= 1.95e+71:
		tmp = x * ((-4.0 * i) + (18.0 * (z * (t * y))))
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * Float64(k * -27.0)) + Float64(b * c))
	t_2 = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)))
	tmp = 0.0
	if (t <= -2.9e+74)
		tmp = t_2;
	elseif (t <= -5.4e-105)
		tmp = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(i * 4.0)));
	elseif (t <= 9.5e-177)
		tmp = t_1;
	elseif (t <= 2.25e-145)
		tmp = Float64(Float64(b * c) - Float64(x * Float64(i * 4.0)));
	elseif (t <= 6e-104)
		tmp = t_1;
	elseif (t <= 1.95e+71)
		tmp = Float64(x * Float64(Float64(-4.0 * i) + Float64(18.0 * Float64(z * Float64(t * y)))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * (k * -27.0)) + (b * c);
	t_2 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	tmp = 0.0;
	if (t <= -2.9e+74)
		tmp = t_2;
	elseif (t <= -5.4e-105)
		tmp = x * ((18.0 * (t * (y * z))) - (i * 4.0));
	elseif (t <= 9.5e-177)
		tmp = t_1;
	elseif (t <= 2.25e-145)
		tmp = (b * c) - (x * (i * 4.0));
	elseif (t <= 6e-104)
		tmp = t_1;
	elseif (t <= 1.95e+71)
		tmp = x * ((-4.0 * i) + (18.0 * (z * (t * y))));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.9e+74], t$95$2, If[LessEqual[t, -5.4e-105], N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.5e-177], t$95$1, If[LessEqual[t, 2.25e-145], N[(N[(b * c), $MachinePrecision] - N[(x * N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6e-104], t$95$1, If[LessEqual[t, 1.95e+71], N[(x * N[(N[(-4.0 * i), $MachinePrecision] + N[(18.0 * N[(z * N[(t * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -2.9000000000000002e74 or 1.9500000000000001e71 < t

   1. Initial program 89.5%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 93.7%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-*r* 93.7%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot z} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. distribute-rgt-out-- 89.6%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. associate-*l* 81.4%

         \[\leadsto \left(\left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot \left(z \cdot t\right)} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      4. *-commutative 81.4%

         \[\leadsto \left(\left(\color{blue}{\left(y \cdot \left(x \cdot 18\right)\right)} \cdot \left(z \cdot t\right) - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      5. *-commutative 81.4%

         \[\leadsto \left(\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) - \color{blue}{t \cdot \left(a \cdot 4\right)}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   6. Applied egg-rr 81.4%

      \[\leadsto \left(\color{blue}{\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) - t \cdot \left(a \cdot 4\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   7. Taylor expanded in t around inf 75.5%

      \[\leadsto \color{blue}{t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)} \]

   if -2.9000000000000002e74 < t < -5.39999999999999985e-105

   1. Initial program 81.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 91.9%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 55.8%

      \[\leadsto \color{blue}{x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)} \]

   if -5.39999999999999985e-105 < t < 9.50000000000000031e-177 or 2.25e-145 < t < 6.0000000000000005e-104

   1. Initial program 84.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 78.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 65.6%

      \[\leadsto \color{blue}{b \cdot c} + j \cdot \left(k \cdot -27\right) \]

   if 9.50000000000000031e-177 < t < 2.25e-145

   1. Initial program 100.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 100.0%

      \[\leadsto \color{blue}{\left(b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   4. Taylor expanded in j around 0 91.3%

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)} \]

   5. Taylor expanded in a around 0 72.5%

      \[\leadsto b \cdot c - \color{blue}{4 \cdot \left(i \cdot x\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 72.5%

         \[\leadsto b \cdot c - \color{blue}{\left(4 \cdot i\right) \cdot x} \]

   7. Simplified 72.5%

      \[\leadsto b \cdot c - \color{blue}{\left(4 \cdot i\right) \cdot x} \]

   if 6.0000000000000005e-104 < t < 1.9500000000000001e71

   1. Initial program 84.5%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 87.7%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-*r* 87.6%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot z} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. distribute-rgt-out-- 84.5%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. associate-*l* 84.5%

         \[\leadsto \left(\left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot \left(z \cdot t\right)} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      4. *-commutative 84.5%

         \[\leadsto \left(\left(\color{blue}{\left(y \cdot \left(x \cdot 18\right)\right)} \cdot \left(z \cdot t\right) - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      5. *-commutative 84.5%

         \[\leadsto \left(\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) - \color{blue}{t \cdot \left(a \cdot 4\right)}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   6. Applied egg-rr 84.5%

      \[\leadsto \left(\color{blue}{\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) - t \cdot \left(a \cdot 4\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   7. Taylor expanded in x around inf 57.8%

      \[\leadsto \color{blue}{x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)} \]
   8. Step-by-step derivation

      1. cancel-sign-sub-inv 57.8%

         \[\leadsto x \cdot \color{blue}{\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \left(-4\right) \cdot i\right)} \]

      2. associate-*r* 57.7%

         \[\leadsto x \cdot \left(18 \cdot \color{blue}{\left(\left(t \cdot y\right) \cdot z\right)} + \left(-4\right) \cdot i\right) \]

      3. metadata-eval 57.7%

         \[\leadsto x \cdot \left(18 \cdot \left(\left(t \cdot y\right) \cdot z\right) + \color{blue}{-4} \cdot i\right) \]

      4. *-commutative 57.7%

         \[\leadsto x \cdot \left(18 \cdot \left(\left(t \cdot y\right) \cdot z\right) + \color{blue}{i \cdot -4}\right) \]

   9. Simplified 57.7%

      \[\leadsto \color{blue}{x \cdot \left(18 \cdot \left(\left(t \cdot y\right) \cdot z\right) + i \cdot -4\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{+74}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq -5.4 \cdot 10^{-105}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - i \cdot 4\right)\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-177}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{-145}:\\ \;\;\;\;b \cdot c - x \cdot \left(i \cdot 4\right)\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-104}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{+71}:\\ \;\;\;\;x \cdot \left(-4 \cdot i + 18 \cdot \left(z \cdot \left(t \cdot y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 59.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right) + b \cdot c\\ t_2 := x \cdot \left(-4 \cdot i + 18 \cdot \left(z \cdot \left(t \cdot y\right)\right)\right)\\ t_3 := t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{if}\;t \leq -6 \cdot 10^{+73}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-106}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 7.6 \cdot 10^{-177}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 7.6 \cdot 10^{-146}:\\ \;\;\;\;b \cdot c - x \cdot \left(i \cdot 4\right)\\ \mathbf{elif}\;t \leq 9.8 \cdot 10^{-104}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+71}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (+ (* j (* k -27.0)) (* b c)))
        (t_2 (* x (+ (* -4.0 i) (* 18.0 (* z (* t y))))))
        (t_3 (* t (- (* 18.0 (* x (* y z))) (* a 4.0)))))
   (if (<= t -6e+73)
     t_3
     (if (<= t -1e-106)
       t_2
       (if (<= t 7.6e-177)
         t_1
         (if (<= t 7.6e-146)
           (- (* b c) (* x (* i 4.0)))
           (if (<= t 9.8e-104) t_1 (if (<= t 3.4e+71) t_2 t_3))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * (k * -27.0)) + (b * c);
	double t_2 = x * ((-4.0 * i) + (18.0 * (z * (t * y))));
	double t_3 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	double tmp;
	if (t <= -6e+73) {
		tmp = t_3;
	} else if (t <= -1e-106) {
		tmp = t_2;
	} else if (t <= 7.6e-177) {
		tmp = t_1;
	} else if (t <= 7.6e-146) {
		tmp = (b * c) - (x * (i * 4.0));
	} else if (t <= 9.8e-104) {
		tmp = t_1;
	} else if (t <= 3.4e+71) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (j * (k * (-27.0d0))) + (b * c)
    t_2 = x * (((-4.0d0) * i) + (18.0d0 * (z * (t * y))))
    t_3 = t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0))
    if (t <= (-6d+73)) then
        tmp = t_3
    else if (t <= (-1d-106)) then
        tmp = t_2
    else if (t <= 7.6d-177) then
        tmp = t_1
    else if (t <= 7.6d-146) then
        tmp = (b * c) - (x * (i * 4.0d0))
    else if (t <= 9.8d-104) then
        tmp = t_1
    else if (t <= 3.4d+71) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * (k * -27.0)) + (b * c);
	double t_2 = x * ((-4.0 * i) + (18.0 * (z * (t * y))));
	double t_3 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	double tmp;
	if (t <= -6e+73) {
		tmp = t_3;
	} else if (t <= -1e-106) {
		tmp = t_2;
	} else if (t <= 7.6e-177) {
		tmp = t_1;
	} else if (t <= 7.6e-146) {
		tmp = (b * c) - (x * (i * 4.0));
	} else if (t <= 9.8e-104) {
		tmp = t_1;
	} else if (t <= 3.4e+71) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * (k * -27.0)) + (b * c)
	t_2 = x * ((-4.0 * i) + (18.0 * (z * (t * y))))
	t_3 = t * ((18.0 * (x * (y * z))) - (a * 4.0))
	tmp = 0
	if t <= -6e+73:
		tmp = t_3
	elif t <= -1e-106:
		tmp = t_2
	elif t <= 7.6e-177:
		tmp = t_1
	elif t <= 7.6e-146:
		tmp = (b * c) - (x * (i * 4.0))
	elif t <= 9.8e-104:
		tmp = t_1
	elif t <= 3.4e+71:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * Float64(k * -27.0)) + Float64(b * c))
	t_2 = Float64(x * Float64(Float64(-4.0 * i) + Float64(18.0 * Float64(z * Float64(t * y)))))
	t_3 = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)))
	tmp = 0.0
	if (t <= -6e+73)
		tmp = t_3;
	elseif (t <= -1e-106)
		tmp = t_2;
	elseif (t <= 7.6e-177)
		tmp = t_1;
	elseif (t <= 7.6e-146)
		tmp = Float64(Float64(b * c) - Float64(x * Float64(i * 4.0)));
	elseif (t <= 9.8e-104)
		tmp = t_1;
	elseif (t <= 3.4e+71)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * (k * -27.0)) + (b * c);
	t_2 = x * ((-4.0 * i) + (18.0 * (z * (t * y))));
	t_3 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	tmp = 0.0;
	if (t <= -6e+73)
		tmp = t_3;
	elseif (t <= -1e-106)
		tmp = t_2;
	elseif (t <= 7.6e-177)
		tmp = t_1;
	elseif (t <= 7.6e-146)
		tmp = (b * c) - (x * (i * 4.0));
	elseif (t <= 9.8e-104)
		tmp = t_1;
	elseif (t <= 3.4e+71)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(-4.0 * i), $MachinePrecision] + N[(18.0 * N[(z * N[(t * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6e+73], t$95$3, If[LessEqual[t, -1e-106], t$95$2, If[LessEqual[t, 7.6e-177], t$95$1, If[LessEqual[t, 7.6e-146], N[(N[(b * c), $MachinePrecision] - N[(x * N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.8e-104], t$95$1, If[LessEqual[t, 3.4e+71], t$95$2, t$95$3]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -6.00000000000000021e73 or 3.3999999999999998e71 < t

   1. Initial program 89.5%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 93.7%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-*r* 93.7%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot z} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. distribute-rgt-out-- 89.6%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. associate-*l* 81.4%

         \[\leadsto \left(\left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot \left(z \cdot t\right)} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      4. *-commutative 81.4%

         \[\leadsto \left(\left(\color{blue}{\left(y \cdot \left(x \cdot 18\right)\right)} \cdot \left(z \cdot t\right) - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      5. *-commutative 81.4%

         \[\leadsto \left(\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) - \color{blue}{t \cdot \left(a \cdot 4\right)}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   6. Applied egg-rr 81.4%

      \[\leadsto \left(\color{blue}{\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) - t \cdot \left(a \cdot 4\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   7. Taylor expanded in t around inf 75.5%

      \[\leadsto \color{blue}{t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)} \]

   if -6.00000000000000021e73 < t < -9.99999999999999941e-107 or 9.8000000000000006e-104 < t < 3.3999999999999998e71

   1. Initial program 82.6%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 89.9%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-*r* 84.1%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot z} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. distribute-rgt-out-- 82.6%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. associate-*l* 82.4%

         \[\leadsto \left(\left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot \left(z \cdot t\right)} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      4. *-commutative 82.4%

         \[\leadsto \left(\left(\color{blue}{\left(y \cdot \left(x \cdot 18\right)\right)} \cdot \left(z \cdot t\right) - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      5. *-commutative 82.4%

         \[\leadsto \left(\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) - \color{blue}{t \cdot \left(a \cdot 4\right)}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   6. Applied egg-rr 82.4%

      \[\leadsto \left(\color{blue}{\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) - t \cdot \left(a \cdot 4\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   7. Taylor expanded in x around inf 56.7%

      \[\leadsto \color{blue}{x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)} \]
   8. Step-by-step derivation

      1. cancel-sign-sub-inv 56.7%

         \[\leadsto x \cdot \color{blue}{\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \left(-4\right) \cdot i\right)} \]

      2. associate-*r* 56.7%

         \[\leadsto x \cdot \left(18 \cdot \color{blue}{\left(\left(t \cdot y\right) \cdot z\right)} + \left(-4\right) \cdot i\right) \]

      3. metadata-eval 56.7%

         \[\leadsto x \cdot \left(18 \cdot \left(\left(t \cdot y\right) \cdot z\right) + \color{blue}{-4} \cdot i\right) \]

      4. *-commutative 56.7%

         \[\leadsto x \cdot \left(18 \cdot \left(\left(t \cdot y\right) \cdot z\right) + \color{blue}{i \cdot -4}\right) \]

   9. Simplified 56.7%

      \[\leadsto \color{blue}{x \cdot \left(18 \cdot \left(\left(t \cdot y\right) \cdot z\right) + i \cdot -4\right)} \]

   if -9.99999999999999941e-107 < t < 7.60000000000000007e-177 or 7.59999999999999989e-146 < t < 9.8000000000000006e-104

   1. Initial program 84.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 78.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 65.6%

      \[\leadsto \color{blue}{b \cdot c} + j \cdot \left(k \cdot -27\right) \]

   if 7.60000000000000007e-177 < t < 7.59999999999999989e-146

   1. Initial program 100.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 100.0%

      \[\leadsto \color{blue}{\left(b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   4. Taylor expanded in j around 0 91.3%

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)} \]

   5. Taylor expanded in a around 0 72.5%

      \[\leadsto b \cdot c - \color{blue}{4 \cdot \left(i \cdot x\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 72.5%

         \[\leadsto b \cdot c - \color{blue}{\left(4 \cdot i\right) \cdot x} \]

   7. Simplified 72.5%

      \[\leadsto b \cdot c - \color{blue}{\left(4 \cdot i\right) \cdot x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{+73}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-106}:\\ \;\;\;\;x \cdot \left(-4 \cdot i + 18 \cdot \left(z \cdot \left(t \cdot y\right)\right)\right)\\ \mathbf{elif}\;t \leq 7.6 \cdot 10^{-177}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \mathbf{elif}\;t \leq 7.6 \cdot 10^{-146}:\\ \;\;\;\;b \cdot c - x \cdot \left(i \cdot 4\right)\\ \mathbf{elif}\;t \leq 9.8 \cdot 10^{-104}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+71}:\\ \;\;\;\;x \cdot \left(-4 \cdot i + 18 \cdot \left(z \cdot \left(t \cdot y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 90.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := k \cdot \left(j \cdot 27\right)\\ \mathbf{if}\;t \leq -8 \cdot 10^{-83}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot 18\right) - a \cdot 4\right)\right) - \left(j \cdot \left(k \cdot 27\right) + x \cdot \left(i \cdot 4\right)\right)\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{-98}:\\ \;\;\;\;\left(\left(\left(y \cdot \left(\left(x \cdot 18\right) \cdot \left(t \cdot z\right)\right) - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - i \cdot \left(x \cdot 4\right)\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + \frac{b \cdot c}{t}\right) - \left(a \cdot 4 + 4 \cdot \frac{x \cdot i}{t}\right)\right) - t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* k (* j 27.0))))
   (if (<= t -8e-83)
     (-
      (+ (* b c) (* t (- (* (* y z) (* x 18.0)) (* a 4.0))))
      (+ (* j (* k 27.0)) (* x (* i 4.0))))
     (if (<= t 4.3e-98)
       (-
        (-
         (+ (- (* y (* (* x 18.0) (* t z))) (* t (* a 4.0))) (* b c))
         (* i (* x 4.0)))
        t_1)
       (-
        (*
         t
         (-
          (+ (* 18.0 (* x (* y z))) (/ (* b c) t))
          (+ (* a 4.0) (* 4.0 (/ (* x i) t)))))
        t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = k * (j * 27.0);
	double tmp;
	if (t <= -8e-83) {
		tmp = ((b * c) + (t * (((y * z) * (x * 18.0)) - (a * 4.0)))) - ((j * (k * 27.0)) + (x * (i * 4.0)));
	} else if (t <= 4.3e-98) {
		tmp = ((((y * ((x * 18.0) * (t * z))) - (t * (a * 4.0))) + (b * c)) - (i * (x * 4.0))) - t_1;
	} else {
		tmp = (t * (((18.0 * (x * (y * z))) + ((b * c) / t)) - ((a * 4.0) + (4.0 * ((x * i) / t))))) - t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = k * (j * 27.0d0)
    if (t <= (-8d-83)) then
        tmp = ((b * c) + (t * (((y * z) * (x * 18.0d0)) - (a * 4.0d0)))) - ((j * (k * 27.0d0)) + (x * (i * 4.0d0)))
    else if (t <= 4.3d-98) then
        tmp = ((((y * ((x * 18.0d0) * (t * z))) - (t * (a * 4.0d0))) + (b * c)) - (i * (x * 4.0d0))) - t_1
    else
        tmp = (t * (((18.0d0 * (x * (y * z))) + ((b * c) / t)) - ((a * 4.0d0) + (4.0d0 * ((x * i) / t))))) - t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = k * (j * 27.0);
	double tmp;
	if (t <= -8e-83) {
		tmp = ((b * c) + (t * (((y * z) * (x * 18.0)) - (a * 4.0)))) - ((j * (k * 27.0)) + (x * (i * 4.0)));
	} else if (t <= 4.3e-98) {
		tmp = ((((y * ((x * 18.0) * (t * z))) - (t * (a * 4.0))) + (b * c)) - (i * (x * 4.0))) - t_1;
	} else {
		tmp = (t * (((18.0 * (x * (y * z))) + ((b * c) / t)) - ((a * 4.0) + (4.0 * ((x * i) / t))))) - t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = k * (j * 27.0)
	tmp = 0
	if t <= -8e-83:
		tmp = ((b * c) + (t * (((y * z) * (x * 18.0)) - (a * 4.0)))) - ((j * (k * 27.0)) + (x * (i * 4.0)))
	elif t <= 4.3e-98:
		tmp = ((((y * ((x * 18.0) * (t * z))) - (t * (a * 4.0))) + (b * c)) - (i * (x * 4.0))) - t_1
	else:
		tmp = (t * (((18.0 * (x * (y * z))) + ((b * c) / t)) - ((a * 4.0) + (4.0 * ((x * i) / t))))) - t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(k * Float64(j * 27.0))
	tmp = 0.0
	if (t <= -8e-83)
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(Float64(y * z) * Float64(x * 18.0)) - Float64(a * 4.0)))) - Float64(Float64(j * Float64(k * 27.0)) + Float64(x * Float64(i * 4.0))));
	elseif (t <= 4.3e-98)
		tmp = Float64(Float64(Float64(Float64(Float64(y * Float64(Float64(x * 18.0) * Float64(t * z))) - Float64(t * Float64(a * 4.0))) + Float64(b * c)) - Float64(i * Float64(x * 4.0))) - t_1);
	else
		tmp = Float64(Float64(t * Float64(Float64(Float64(18.0 * Float64(x * Float64(y * z))) + Float64(Float64(b * c) / t)) - Float64(Float64(a * 4.0) + Float64(4.0 * Float64(Float64(x * i) / t))))) - t_1);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = k * (j * 27.0);
	tmp = 0.0;
	if (t <= -8e-83)
		tmp = ((b * c) + (t * (((y * z) * (x * 18.0)) - (a * 4.0)))) - ((j * (k * 27.0)) + (x * (i * 4.0)));
	elseif (t <= 4.3e-98)
		tmp = ((((y * ((x * 18.0) * (t * z))) - (t * (a * 4.0))) + (b * c)) - (i * (x * 4.0))) - t_1;
	else
		tmp = (t * (((18.0 * (x * (y * z))) + ((b * c) / t)) - ((a * 4.0) + (4.0 * ((x * i) / t))))) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8e-83], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(N[(y * z), $MachinePrecision] * N[(x * 18.0), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * N[(k * 27.0), $MachinePrecision]), $MachinePrecision] + N[(x * N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.3e-98], N[(N[(N[(N[(N[(y * N[(N[(x * 18.0), $MachinePrecision] * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - N[(i * N[(x * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(t * N[(N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(b * c), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] - N[(N[(a * 4.0), $MachinePrecision] + N[(4.0 * N[(N[(x * i), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.0000000000000003e-83

   1. Initial program 88.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 95.8%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing

   if -8.0000000000000003e-83 < t < 4.29999999999999988e-98

   1. Initial program 85.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. pow1 85.7%

         \[\leadsto \left(\left(\left(\color{blue}{{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t\right)}^{1}} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      2. associate-*l* 88.5%

         \[\leadsto \left(\left(\left({\color{blue}{\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot \left(z \cdot t\right)\right)}}^{1} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      3. *-commutative 88.5%

         \[\leadsto \left(\left(\left({\left(\color{blue}{\left(y \cdot \left(x \cdot 18\right)\right)} \cdot \left(z \cdot t\right)\right)}^{1} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   4. Applied egg-rr 88.5%

      \[\leadsto \left(\left(\left(\color{blue}{{\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right)\right)}^{1}} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   5. Step-by-step derivation

      1. unpow1 88.5%

         \[\leadsto \left(\left(\left(\color{blue}{\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right)} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      2. associate-*l* 96.0%

         \[\leadsto \left(\left(\left(\color{blue}{y \cdot \left(\left(x \cdot 18\right) \cdot \left(z \cdot t\right)\right)} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      3. *-commutative 96.0%

         \[\leadsto \left(\left(\left(y \cdot \left(\left(x \cdot 18\right) \cdot \color{blue}{\left(t \cdot z\right)}\right) - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   6. Simplified 96.0%

      \[\leadsto \left(\left(\left(\color{blue}{y \cdot \left(\left(x \cdot 18\right) \cdot \left(t \cdot z\right)\right)} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   if 4.29999999999999988e-98 < t

   1. Initial program 85.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 90.4%

      \[\leadsto \color{blue}{t \cdot \left(\left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + \frac{b \cdot c}{t}\right) - \left(4 \cdot a + 4 \cdot \frac{i \cdot x}{t}\right)\right)} - \left(j \cdot 27\right) \cdot k \]
3. Recombined 3 regimes into one program.

4. Final simplification 94.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{-83}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot 18\right) - a \cdot 4\right)\right) - \left(j \cdot \left(k \cdot 27\right) + x \cdot \left(i \cdot 4\right)\right)\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{-98}:\\ \;\;\;\;\left(\left(\left(y \cdot \left(\left(x \cdot 18\right) \cdot \left(t \cdot z\right)\right) - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - i \cdot \left(x \cdot 4\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + \frac{b \cdot c}{t}\right) - \left(a \cdot 4 + 4 \cdot \frac{x \cdot i}{t}\right)\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 90.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -7.8 \cdot 10^{-83} \lor \neg \left(t \leq 2 \cdot 10^{-210}\right):\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot 18\right) - a \cdot 4\right)\right) - \left(j \cdot \left(k \cdot 27\right) + x \cdot \left(i \cdot 4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(y \cdot \left(\left(x \cdot 18\right) \cdot \left(t \cdot z\right)\right) - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - i \cdot \left(x \cdot 4\right)\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= t -7.8e-83) (not (<= t 2e-210)))
   (-
    (+ (* b c) (* t (- (* (* y z) (* x 18.0)) (* a 4.0))))
    (+ (* j (* k 27.0)) (* x (* i 4.0))))
   (-
    (-
     (+ (- (* y (* (* x 18.0) (* t z))) (* t (* a 4.0))) (* b c))
     (* i (* x 4.0)))
    (* k (* j 27.0)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((t <= -7.8e-83) || !(t <= 2e-210)) {
		tmp = ((b * c) + (t * (((y * z) * (x * 18.0)) - (a * 4.0)))) - ((j * (k * 27.0)) + (x * (i * 4.0)));
	} else {
		tmp = ((((y * ((x * 18.0) * (t * z))) - (t * (a * 4.0))) + (b * c)) - (i * (x * 4.0))) - (k * (j * 27.0));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((t <= (-7.8d-83)) .or. (.not. (t <= 2d-210))) then
        tmp = ((b * c) + (t * (((y * z) * (x * 18.0d0)) - (a * 4.0d0)))) - ((j * (k * 27.0d0)) + (x * (i * 4.0d0)))
    else
        tmp = ((((y * ((x * 18.0d0) * (t * z))) - (t * (a * 4.0d0))) + (b * c)) - (i * (x * 4.0d0))) - (k * (j * 27.0d0))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((t <= -7.8e-83) || !(t <= 2e-210)) {
		tmp = ((b * c) + (t * (((y * z) * (x * 18.0)) - (a * 4.0)))) - ((j * (k * 27.0)) + (x * (i * 4.0)));
	} else {
		tmp = ((((y * ((x * 18.0) * (t * z))) - (t * (a * 4.0))) + (b * c)) - (i * (x * 4.0))) - (k * (j * 27.0));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (t <= -7.8e-83) or not (t <= 2e-210):
		tmp = ((b * c) + (t * (((y * z) * (x * 18.0)) - (a * 4.0)))) - ((j * (k * 27.0)) + (x * (i * 4.0)))
	else:
		tmp = ((((y * ((x * 18.0) * (t * z))) - (t * (a * 4.0))) + (b * c)) - (i * (x * 4.0))) - (k * (j * 27.0))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((t <= -7.8e-83) || !(t <= 2e-210))
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(Float64(y * z) * Float64(x * 18.0)) - Float64(a * 4.0)))) - Float64(Float64(j * Float64(k * 27.0)) + Float64(x * Float64(i * 4.0))));
	else
		tmp = Float64(Float64(Float64(Float64(Float64(y * Float64(Float64(x * 18.0) * Float64(t * z))) - Float64(t * Float64(a * 4.0))) + Float64(b * c)) - Float64(i * Float64(x * 4.0))) - Float64(k * Float64(j * 27.0)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((t <= -7.8e-83) || ~((t <= 2e-210)))
		tmp = ((b * c) + (t * (((y * z) * (x * 18.0)) - (a * 4.0)))) - ((j * (k * 27.0)) + (x * (i * 4.0)));
	else
		tmp = ((((y * ((x * 18.0) * (t * z))) - (t * (a * 4.0))) + (b * c)) - (i * (x * 4.0))) - (k * (j * 27.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[t, -7.8e-83], N[Not[LessEqual[t, 2e-210]], $MachinePrecision]], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(N[(y * z), $MachinePrecision] * N[(x * 18.0), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * N[(k * 27.0), $MachinePrecision]), $MachinePrecision] + N[(x * N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(y * N[(N[(x * 18.0), $MachinePrecision] * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - N[(i * N[(x * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -7.800000000000001e-83 or 2.0000000000000001e-210 < t

   1. Initial program 89.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 93.4%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing

   if -7.800000000000001e-83 < t < 2.0000000000000001e-210

   1. Initial program 80.6%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. pow1 80.6%

         \[\leadsto \left(\left(\left(\color{blue}{{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t\right)}^{1}} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      2. associate-*l* 84.3%

         \[\leadsto \left(\left(\left({\color{blue}{\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot \left(z \cdot t\right)\right)}}^{1} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      3. *-commutative 84.3%

         \[\leadsto \left(\left(\left({\left(\color{blue}{\left(y \cdot \left(x \cdot 18\right)\right)} \cdot \left(z \cdot t\right)\right)}^{1} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   4. Applied egg-rr 84.3%

      \[\leadsto \left(\left(\left(\color{blue}{{\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right)\right)}^{1}} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   5. Step-by-step derivation

      1. unpow1 84.3%

         \[\leadsto \left(\left(\left(\color{blue}{\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right)} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      2. associate-*l* 94.6%

         \[\leadsto \left(\left(\left(\color{blue}{y \cdot \left(\left(x \cdot 18\right) \cdot \left(z \cdot t\right)\right)} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      3. *-commutative 94.6%

         \[\leadsto \left(\left(\left(y \cdot \left(\left(x \cdot 18\right) \cdot \color{blue}{\left(t \cdot z\right)}\right) - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   6. Simplified 94.6%

      \[\leadsto \left(\left(\left(\color{blue}{y \cdot \left(\left(x \cdot 18\right) \cdot \left(t \cdot z\right)\right)} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
3. Recombined 2 regimes into one program.

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.8 \cdot 10^{-83} \lor \neg \left(t \leq 2 \cdot 10^{-210}\right):\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot 18\right) - a \cdot 4\right)\right) - \left(j \cdot \left(k \cdot 27\right) + x \cdot \left(i \cdot 4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(y \cdot \left(\left(x \cdot 18\right) \cdot \left(t \cdot z\right)\right) - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - i \cdot \left(x \cdot 4\right)\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 81.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := k \cdot \left(j \cdot 27\right)\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+215}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+131}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(z \cdot \left(x \cdot y\right)\right) - a \cdot 4\right)\right) - x \cdot \left(i \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - \left(4 \cdot \left(t \cdot a\right) + 4 \cdot \left(x \cdot i\right)\right)\right) - t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* k (* j 27.0))))
   (if (<= t_1 -2e+215)
     (+ (* j (* k -27.0)) (* t (+ (* 18.0 (* x (* y z))) (* a -4.0))))
     (if (<= t_1 5e+131)
       (-
        (+ (* b c) (* t (- (* 18.0 (* z (* x y))) (* a 4.0))))
        (* x (* i 4.0)))
       (- (- (* b c) (+ (* 4.0 (* t a)) (* 4.0 (* x i)))) t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = k * (j * 27.0);
	double tmp;
	if (t_1 <= -2e+215) {
		tmp = (j * (k * -27.0)) + (t * ((18.0 * (x * (y * z))) + (a * -4.0)));
	} else if (t_1 <= 5e+131) {
		tmp = ((b * c) + (t * ((18.0 * (z * (x * y))) - (a * 4.0)))) - (x * (i * 4.0));
	} else {
		tmp = ((b * c) - ((4.0 * (t * a)) + (4.0 * (x * i)))) - t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = k * (j * 27.0d0)
    if (t_1 <= (-2d+215)) then
        tmp = (j * (k * (-27.0d0))) + (t * ((18.0d0 * (x * (y * z))) + (a * (-4.0d0))))
    else if (t_1 <= 5d+131) then
        tmp = ((b * c) + (t * ((18.0d0 * (z * (x * y))) - (a * 4.0d0)))) - (x * (i * 4.0d0))
    else
        tmp = ((b * c) - ((4.0d0 * (t * a)) + (4.0d0 * (x * i)))) - t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = k * (j * 27.0);
	double tmp;
	if (t_1 <= -2e+215) {
		tmp = (j * (k * -27.0)) + (t * ((18.0 * (x * (y * z))) + (a * -4.0)));
	} else if (t_1 <= 5e+131) {
		tmp = ((b * c) + (t * ((18.0 * (z * (x * y))) - (a * 4.0)))) - (x * (i * 4.0));
	} else {
		tmp = ((b * c) - ((4.0 * (t * a)) + (4.0 * (x * i)))) - t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = k * (j * 27.0)
	tmp = 0
	if t_1 <= -2e+215:
		tmp = (j * (k * -27.0)) + (t * ((18.0 * (x * (y * z))) + (a * -4.0)))
	elif t_1 <= 5e+131:
		tmp = ((b * c) + (t * ((18.0 * (z * (x * y))) - (a * 4.0)))) - (x * (i * 4.0))
	else:
		tmp = ((b * c) - ((4.0 * (t * a)) + (4.0 * (x * i)))) - t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(k * Float64(j * 27.0))
	tmp = 0.0
	if (t_1 <= -2e+215)
		tmp = Float64(Float64(j * Float64(k * -27.0)) + Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) + Float64(a * -4.0))));
	elseif (t_1 <= 5e+131)
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(18.0 * Float64(z * Float64(x * y))) - Float64(a * 4.0)))) - Float64(x * Float64(i * 4.0)));
	else
		tmp = Float64(Float64(Float64(b * c) - Float64(Float64(4.0 * Float64(t * a)) + Float64(4.0 * Float64(x * i)))) - t_1);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = k * (j * 27.0);
	tmp = 0.0;
	if (t_1 <= -2e+215)
		tmp = (j * (k * -27.0)) + (t * ((18.0 * (x * (y * z))) + (a * -4.0)));
	elseif (t_1 <= 5e+131)
		tmp = ((b * c) + (t * ((18.0 * (z * (x * y))) - (a * 4.0)))) - (x * (i * 4.0));
	else
		tmp = ((b * c) - ((4.0 * (t * a)) + (4.0 * (x * i)))) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+215], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+131], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(18.0 * N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] - N[(N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -1.99999999999999981e215

   1. Initial program 89.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 92.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 99.9%

      \[\leadsto \color{blue}{t \cdot \left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} + j \cdot \left(k \cdot -27\right) \]

   if -1.99999999999999981e215 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 4.99999999999999995e131

   1. Initial program 87.2%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 87.7%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-*r* 88.8%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot z} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. distribute-rgt-out-- 87.2%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. sub-neg 87.2%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(a \cdot 4\right) \cdot t\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      4. associate-*l* 86.0%

         \[\leadsto \left(\left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot \left(z \cdot t\right)} + \left(-\left(a \cdot 4\right) \cdot t\right)\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      5. *-commutative 86.0%

         \[\leadsto \left(\left(\color{blue}{\left(y \cdot \left(x \cdot 18\right)\right)} \cdot \left(z \cdot t\right) + \left(-\left(a \cdot 4\right) \cdot t\right)\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      6. *-commutative 86.0%

         \[\leadsto \left(\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) + \left(-\color{blue}{t \cdot \left(a \cdot 4\right)}\right)\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   6. Applied egg-rr 86.0%

      \[\leadsto \left(\color{blue}{\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) + \left(-t \cdot \left(a \cdot 4\right)\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
   7. Step-by-step derivation

      1. distribute-lft-neg-in 86.0%

         \[\leadsto \left(\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) + \color{blue}{\left(-t\right) \cdot \left(a \cdot 4\right)}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. *-commutative 86.0%

         \[\leadsto \left(\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) + \left(-t\right) \cdot \color{blue}{\left(4 \cdot a\right)}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. cancel-sign-sub-inv 86.0%

         \[\leadsto \left(\color{blue}{\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) - t \cdot \left(4 \cdot a\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      4. *-commutative 86.0%

         \[\leadsto \left(\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) - \color{blue}{\left(4 \cdot a\right) \cdot t}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      5. associate-*r* 87.2%

         \[\leadsto \left(\left(\color{blue}{\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot z\right) \cdot t} - \left(4 \cdot a\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      6. distribute-rgt-out-- 88.8%

         \[\leadsto \left(\color{blue}{t \cdot \left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot z - 4 \cdot a\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      7. associate-*r* 88.7%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(\left(y \cdot x\right) \cdot 18\right)} \cdot z - 4 \cdot a\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      8. *-commutative 88.7%

         \[\leadsto \left(t \cdot \left(\left(\color{blue}{\left(x \cdot y\right)} \cdot 18\right) \cdot z - 4 \cdot a\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      9. *-commutative 88.7%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(18 \cdot \left(x \cdot y\right)\right)} \cdot z - 4 \cdot a\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      10. *-commutative 88.7%

          \[\leadsto \left(t \cdot \left(\left(18 \cdot \left(x \cdot y\right)\right) \cdot z - \color{blue}{a \cdot 4}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   8. Simplified 88.7%

      \[\leadsto \left(\color{blue}{t \cdot \left(\left(18 \cdot \left(x \cdot y\right)\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   9. Taylor expanded in x around 0 87.7%

      \[\leadsto \left(t \cdot \left(\color{blue}{18 \cdot \left(x \cdot \left(y \cdot z\right)\right)} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
   10. Step-by-step derivation

       1. associate-*r* 88.8%

          \[\leadsto \left(t \cdot \left(18 \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot z\right)} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   11. Simplified 88.8%

       \[\leadsto \left(t \cdot \left(\color{blue}{18 \cdot \left(\left(x \cdot y\right) \cdot z\right)} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   12. Taylor expanded in x around inf 82.6%

       \[\leadsto \left(t \cdot \left(18 \cdot \left(\left(x \cdot y\right) \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \color{blue}{4 \cdot \left(i \cdot x\right)} \]
   13. Step-by-step derivation

       1. associate-*r* 82.6%

          \[\leadsto \left(t \cdot \left(18 \cdot \left(\left(x \cdot y\right) \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \color{blue}{\left(4 \cdot i\right) \cdot x} \]

       2. *-commutative 82.6%

          \[\leadsto \left(t \cdot \left(18 \cdot \left(\left(x \cdot y\right) \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \color{blue}{\left(i \cdot 4\right)} \cdot x \]

   14. Simplified 82.6%

       \[\leadsto \left(t \cdot \left(18 \cdot \left(\left(x \cdot y\right) \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \color{blue}{\left(i \cdot 4\right) \cdot x} \]

   if 4.99999999999999995e131 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 82.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 79.6%

      \[\leadsto \color{blue}{\left(b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]
3. Recombined 3 regimes into one program.

4. Final simplification 84.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \cdot \left(j \cdot 27\right) \leq -2 \cdot 10^{+215}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 5 \cdot 10^{+131}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(z \cdot \left(x \cdot y\right)\right) - a \cdot 4\right)\right) - x \cdot \left(i \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - \left(4 \cdot \left(t \cdot a\right) + 4 \cdot \left(x \cdot i\right)\right)\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 35.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ \mathbf{if}\;b \cdot c \leq -3.4 \cdot 10^{+16}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -1.2 \cdot 10^{-237}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq 5.5 \cdot 10^{-251}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 7.8 \cdot 10^{-79}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq 9.5 \cdot 10^{+102}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* t (* a -4.0))))
   (if (<= (* b c) -3.4e+16)
     (* b c)
     (if (<= (* b c) -1.2e-237)
       t_1
       (if (<= (* b c) 5.5e-251)
         (* j (* k -27.0))
         (if (<= (* b c) 7.8e-79)
           t_1
           (if (<= (* b c) 9.5e+102) (* -27.0 (* j k)) (* b c))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * (a * -4.0);
	double tmp;
	if ((b * c) <= -3.4e+16) {
		tmp = b * c;
	} else if ((b * c) <= -1.2e-237) {
		tmp = t_1;
	} else if ((b * c) <= 5.5e-251) {
		tmp = j * (k * -27.0);
	} else if ((b * c) <= 7.8e-79) {
		tmp = t_1;
	} else if ((b * c) <= 9.5e+102) {
		tmp = -27.0 * (j * k);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (a * (-4.0d0))
    if ((b * c) <= (-3.4d+16)) then
        tmp = b * c
    else if ((b * c) <= (-1.2d-237)) then
        tmp = t_1
    else if ((b * c) <= 5.5d-251) then
        tmp = j * (k * (-27.0d0))
    else if ((b * c) <= 7.8d-79) then
        tmp = t_1
    else if ((b * c) <= 9.5d+102) then
        tmp = (-27.0d0) * (j * k)
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * (a * -4.0);
	double tmp;
	if ((b * c) <= -3.4e+16) {
		tmp = b * c;
	} else if ((b * c) <= -1.2e-237) {
		tmp = t_1;
	} else if ((b * c) <= 5.5e-251) {
		tmp = j * (k * -27.0);
	} else if ((b * c) <= 7.8e-79) {
		tmp = t_1;
	} else if ((b * c) <= 9.5e+102) {
		tmp = -27.0 * (j * k);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = t * (a * -4.0)
	tmp = 0
	if (b * c) <= -3.4e+16:
		tmp = b * c
	elif (b * c) <= -1.2e-237:
		tmp = t_1
	elif (b * c) <= 5.5e-251:
		tmp = j * (k * -27.0)
	elif (b * c) <= 7.8e-79:
		tmp = t_1
	elif (b * c) <= 9.5e+102:
		tmp = -27.0 * (j * k)
	else:
		tmp = b * c
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(t * Float64(a * -4.0))
	tmp = 0.0
	if (Float64(b * c) <= -3.4e+16)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -1.2e-237)
		tmp = t_1;
	elseif (Float64(b * c) <= 5.5e-251)
		tmp = Float64(j * Float64(k * -27.0));
	elseif (Float64(b * c) <= 7.8e-79)
		tmp = t_1;
	elseif (Float64(b * c) <= 9.5e+102)
		tmp = Float64(-27.0 * Float64(j * k));
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = t * (a * -4.0);
	tmp = 0.0;
	if ((b * c) <= -3.4e+16)
		tmp = b * c;
	elseif ((b * c) <= -1.2e-237)
		tmp = t_1;
	elseif ((b * c) <= 5.5e-251)
		tmp = j * (k * -27.0);
	elseif ((b * c) <= 7.8e-79)
		tmp = t_1;
	elseif ((b * c) <= 9.5e+102)
		tmp = -27.0 * (j * k);
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -3.4e+16], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -1.2e-237], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 5.5e-251], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 7.8e-79], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 9.5e+102], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 b c) < -3.4e16 or 9.4999999999999992e102 < (*.f64 b c)

   1. Initial program 82.2%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 80.2%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-*r* 84.1%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot z} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. distribute-rgt-out-- 82.2%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. sub-neg 82.2%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(a \cdot 4\right) \cdot t\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      4. associate-*l* 81.9%

         \[\leadsto \left(\left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot \left(z \cdot t\right)} + \left(-\left(a \cdot 4\right) \cdot t\right)\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      5. *-commutative 81.9%

         \[\leadsto \left(\left(\color{blue}{\left(y \cdot \left(x \cdot 18\right)\right)} \cdot \left(z \cdot t\right) + \left(-\left(a \cdot 4\right) \cdot t\right)\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      6. *-commutative 81.9%

         \[\leadsto \left(\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) + \left(-\color{blue}{t \cdot \left(a \cdot 4\right)}\right)\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   6. Applied egg-rr 81.9%

      \[\leadsto \left(\color{blue}{\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) + \left(-t \cdot \left(a \cdot 4\right)\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
   7. Step-by-step derivation

      1. distribute-lft-neg-in 81.9%

         \[\leadsto \left(\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) + \color{blue}{\left(-t\right) \cdot \left(a \cdot 4\right)}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. *-commutative 81.9%

         \[\leadsto \left(\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) + \left(-t\right) \cdot \color{blue}{\left(4 \cdot a\right)}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. cancel-sign-sub-inv 81.9%

         \[\leadsto \left(\color{blue}{\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) - t \cdot \left(4 \cdot a\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      4. *-commutative 81.9%

         \[\leadsto \left(\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) - \color{blue}{\left(4 \cdot a\right) \cdot t}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      5. associate-*r* 82.2%

         \[\leadsto \left(\left(\color{blue}{\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot z\right) \cdot t} - \left(4 \cdot a\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      6. distribute-rgt-out-- 84.1%

         \[\leadsto \left(\color{blue}{t \cdot \left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot z - 4 \cdot a\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      7. associate-*r* 84.0%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(\left(y \cdot x\right) \cdot 18\right)} \cdot z - 4 \cdot a\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      8. *-commutative 84.0%

         \[\leadsto \left(t \cdot \left(\left(\color{blue}{\left(x \cdot y\right)} \cdot 18\right) \cdot z - 4 \cdot a\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      9. *-commutative 84.0%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(18 \cdot \left(x \cdot y\right)\right)} \cdot z - 4 \cdot a\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      10. *-commutative 84.0%

          \[\leadsto \left(t \cdot \left(\left(18 \cdot \left(x \cdot y\right)\right) \cdot z - \color{blue}{a \cdot 4}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   8. Simplified 84.0%

      \[\leadsto \left(\color{blue}{t \cdot \left(\left(18 \cdot \left(x \cdot y\right)\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   9. Taylor expanded in b around inf 47.5%

      \[\leadsto \color{blue}{b \cdot c} \]

   if -3.4e16 < (*.f64 b c) < -1.2e-237 or 5.5e-251 < (*.f64 b c) < 7.80000000000000011e-79

   1. Initial program 91.1%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 92.6%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-*r* 92.6%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot z} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. distribute-rgt-out-- 91.1%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. associate-*l* 92.3%

         \[\leadsto \left(\left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot \left(z \cdot t\right)} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      4. *-commutative 92.3%

         \[\leadsto \left(\left(\color{blue}{\left(y \cdot \left(x \cdot 18\right)\right)} \cdot \left(z \cdot t\right) - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      5. *-commutative 92.3%

         \[\leadsto \left(\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) - \color{blue}{t \cdot \left(a \cdot 4\right)}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   6. Applied egg-rr 92.3%

      \[\leadsto \left(\color{blue}{\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) - t \cdot \left(a \cdot 4\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   7. Taylor expanded in a around inf 38.8%

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t\right)} \]
   8. Step-by-step derivation

      1. *-commutative 38.8%

         \[\leadsto \color{blue}{\left(a \cdot t\right) \cdot -4} \]

      2. *-commutative 38.8%

         \[\leadsto \color{blue}{\left(t \cdot a\right)} \cdot -4 \]

      3. associate-*r* 38.8%

         \[\leadsto \color{blue}{t \cdot \left(a \cdot -4\right)} \]

   9. Simplified 38.8%

      \[\leadsto \color{blue}{t \cdot \left(a \cdot -4\right)} \]

   if -1.2e-237 < (*.f64 b c) < 5.5e-251

   1. Initial program 91.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 95.8%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-*r* 93.6%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot z} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. distribute-rgt-out-- 91.4%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. sub-neg 91.4%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(a \cdot 4\right) \cdot t\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      4. associate-*l* 82.8%

         \[\leadsto \left(\left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot \left(z \cdot t\right)} + \left(-\left(a \cdot 4\right) \cdot t\right)\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      5. *-commutative 82.8%

         \[\leadsto \left(\left(\color{blue}{\left(y \cdot \left(x \cdot 18\right)\right)} \cdot \left(z \cdot t\right) + \left(-\left(a \cdot 4\right) \cdot t\right)\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      6. *-commutative 82.8%

         \[\leadsto \left(\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) + \left(-\color{blue}{t \cdot \left(a \cdot 4\right)}\right)\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   6. Applied egg-rr 82.8%

      \[\leadsto \left(\color{blue}{\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) + \left(-t \cdot \left(a \cdot 4\right)\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
   7. Step-by-step derivation

      1. distribute-lft-neg-in 82.8%

         \[\leadsto \left(\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) + \color{blue}{\left(-t\right) \cdot \left(a \cdot 4\right)}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. *-commutative 82.8%

         \[\leadsto \left(\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) + \left(-t\right) \cdot \color{blue}{\left(4 \cdot a\right)}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. cancel-sign-sub-inv 82.8%

         \[\leadsto \left(\color{blue}{\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) - t \cdot \left(4 \cdot a\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      4. *-commutative 82.8%

         \[\leadsto \left(\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) - \color{blue}{\left(4 \cdot a\right) \cdot t}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      5. associate-*r* 91.4%

         \[\leadsto \left(\left(\color{blue}{\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot z\right) \cdot t} - \left(4 \cdot a\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      6. distribute-rgt-out-- 93.6%

         \[\leadsto \left(\color{blue}{t \cdot \left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot z - 4 \cdot a\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      7. associate-*r* 93.6%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(\left(y \cdot x\right) \cdot 18\right)} \cdot z - 4 \cdot a\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      8. *-commutative 93.6%

         \[\leadsto \left(t \cdot \left(\left(\color{blue}{\left(x \cdot y\right)} \cdot 18\right) \cdot z - 4 \cdot a\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      9. *-commutative 93.6%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(18 \cdot \left(x \cdot y\right)\right)} \cdot z - 4 \cdot a\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      10. *-commutative 93.6%

          \[\leadsto \left(t \cdot \left(\left(18 \cdot \left(x \cdot y\right)\right) \cdot z - \color{blue}{a \cdot 4}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   8. Simplified 93.6%

      \[\leadsto \left(\color{blue}{t \cdot \left(\left(18 \cdot \left(x \cdot y\right)\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   9. Taylor expanded in j around inf 42.7%

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

       1. metadata-eval 42.7%

          \[\leadsto \color{blue}{\left(-27\right)} \cdot \left(j \cdot k\right) \]

       2. distribute-lft-neg-in 42.7%

          \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]

       3. associate-*r* 42.6%

          \[\leadsto -\color{blue}{\left(27 \cdot j\right) \cdot k} \]

       4. *-commutative 42.6%

          \[\leadsto -\color{blue}{\left(j \cdot 27\right)} \cdot k \]

       5. associate-*r* 42.7%

          \[\leadsto -\color{blue}{j \cdot \left(27 \cdot k\right)} \]

       6. distribute-rgt-neg-in 42.7%

          \[\leadsto \color{blue}{j \cdot \left(-27 \cdot k\right)} \]

       7. distribute-lft-neg-in 42.7%

          \[\leadsto j \cdot \color{blue}{\left(\left(-27\right) \cdot k\right)} \]

       8. metadata-eval 42.7%

          \[\leadsto j \cdot \left(\color{blue}{-27} \cdot k\right) \]

       9. *-commutative 42.7%

          \[\leadsto j \cdot \color{blue}{\left(k \cdot -27\right)} \]

   11. Simplified 42.7%

       \[\leadsto \color{blue}{j \cdot \left(k \cdot -27\right)} \]

   if 7.80000000000000011e-79 < (*.f64 b c) < 9.4999999999999992e102

   1. Initial program 85.5%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 92.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in j around inf 33.4%

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 13: 81.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right) + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{if}\;t \leq -6.5 \cdot 10^{+126}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.55 \cdot 10^{+34}:\\ \;\;\;\;a \cdot \left(b \cdot \frac{c}{a} - 4 \cdot \left(t + \frac{x \cdot i}{a}\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;t \leq 10000:\\ \;\;\;\;\left(b \cdot c + x \cdot \left(z \cdot \left(y \cdot \left(t \cdot 18\right)\right)\right)\right) - \left(j \cdot \left(k \cdot 27\right) + x \cdot \left(i \cdot 4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1
         (+ (* j (* k -27.0)) (* t (+ (* 18.0 (* x (* y z))) (* a -4.0))))))
   (if (<= t -6.5e+126)
     t_1
     (if (<= t -1.55e+34)
       (- (* a (- (* b (/ c a)) (* 4.0 (+ t (/ (* x i) a))))) (* k (* j 27.0)))
       (if (<= t 10000.0)
         (-
          (+ (* b c) (* x (* z (* y (* t 18.0)))))
          (+ (* j (* k 27.0)) (* x (* i 4.0))))
         t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * (k * -27.0)) + (t * ((18.0 * (x * (y * z))) + (a * -4.0)));
	double tmp;
	if (t <= -6.5e+126) {
		tmp = t_1;
	} else if (t <= -1.55e+34) {
		tmp = (a * ((b * (c / a)) - (4.0 * (t + ((x * i) / a))))) - (k * (j * 27.0));
	} else if (t <= 10000.0) {
		tmp = ((b * c) + (x * (z * (y * (t * 18.0))))) - ((j * (k * 27.0)) + (x * (i * 4.0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (j * (k * (-27.0d0))) + (t * ((18.0d0 * (x * (y * z))) + (a * (-4.0d0))))
    if (t <= (-6.5d+126)) then
        tmp = t_1
    else if (t <= (-1.55d+34)) then
        tmp = (a * ((b * (c / a)) - (4.0d0 * (t + ((x * i) / a))))) - (k * (j * 27.0d0))
    else if (t <= 10000.0d0) then
        tmp = ((b * c) + (x * (z * (y * (t * 18.0d0))))) - ((j * (k * 27.0d0)) + (x * (i * 4.0d0)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * (k * -27.0)) + (t * ((18.0 * (x * (y * z))) + (a * -4.0)));
	double tmp;
	if (t <= -6.5e+126) {
		tmp = t_1;
	} else if (t <= -1.55e+34) {
		tmp = (a * ((b * (c / a)) - (4.0 * (t + ((x * i) / a))))) - (k * (j * 27.0));
	} else if (t <= 10000.0) {
		tmp = ((b * c) + (x * (z * (y * (t * 18.0))))) - ((j * (k * 27.0)) + (x * (i * 4.0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * (k * -27.0)) + (t * ((18.0 * (x * (y * z))) + (a * -4.0)))
	tmp = 0
	if t <= -6.5e+126:
		tmp = t_1
	elif t <= -1.55e+34:
		tmp = (a * ((b * (c / a)) - (4.0 * (t + ((x * i) / a))))) - (k * (j * 27.0))
	elif t <= 10000.0:
		tmp = ((b * c) + (x * (z * (y * (t * 18.0))))) - ((j * (k * 27.0)) + (x * (i * 4.0)))
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * Float64(k * -27.0)) + Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) + Float64(a * -4.0))))
	tmp = 0.0
	if (t <= -6.5e+126)
		tmp = t_1;
	elseif (t <= -1.55e+34)
		tmp = Float64(Float64(a * Float64(Float64(b * Float64(c / a)) - Float64(4.0 * Float64(t + Float64(Float64(x * i) / a))))) - Float64(k * Float64(j * 27.0)));
	elseif (t <= 10000.0)
		tmp = Float64(Float64(Float64(b * c) + Float64(x * Float64(z * Float64(y * Float64(t * 18.0))))) - Float64(Float64(j * Float64(k * 27.0)) + Float64(x * Float64(i * 4.0))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * (k * -27.0)) + (t * ((18.0 * (x * (y * z))) + (a * -4.0)));
	tmp = 0.0;
	if (t <= -6.5e+126)
		tmp = t_1;
	elseif (t <= -1.55e+34)
		tmp = (a * ((b * (c / a)) - (4.0 * (t + ((x * i) / a))))) - (k * (j * 27.0));
	elseif (t <= 10000.0)
		tmp = ((b * c) + (x * (z * (y * (t * 18.0))))) - ((j * (k * 27.0)) + (x * (i * 4.0)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.5e+126], t$95$1, If[LessEqual[t, -1.55e+34], N[(N[(a * N[(N[(b * N[(c / a), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(t + N[(N[(x * i), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 10000.0], N[(N[(N[(b * c), $MachinePrecision] + N[(x * N[(z * N[(y * N[(t * 18.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * N[(k * 27.0), $MachinePrecision]), $MachinePrecision] + N[(x * N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.5000000000000005e126 or 1e4 < t

   1. Initial program 87.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 92.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 87.6%

      \[\leadsto \color{blue}{t \cdot \left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} + j \cdot \left(k \cdot -27\right) \]

   if -6.5000000000000005e126 < t < -1.54999999999999989e34

   1. Initial program 99.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 93.8%

      \[\leadsto \color{blue}{\left(b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   4. Taylor expanded in a around inf 99.8%

      \[\leadsto \color{blue}{a \cdot \left(\frac{b \cdot c}{a} - \left(4 \cdot t + 4 \cdot \frac{i \cdot x}{a}\right)\right)} - \left(j \cdot 27\right) \cdot k \]
   5. Step-by-step derivation

      1. associate-/l* 99.8%

         \[\leadsto a \cdot \left(\color{blue}{b \cdot \frac{c}{a}} - \left(4 \cdot t + 4 \cdot \frac{i \cdot x}{a}\right)\right) - \left(j \cdot 27\right) \cdot k \]

      2. distribute-lft-out 99.8%

         \[\leadsto a \cdot \left(b \cdot \frac{c}{a} - \color{blue}{4 \cdot \left(t + \frac{i \cdot x}{a}\right)}\right) - \left(j \cdot 27\right) \cdot k \]

      3. *-commutative 99.8%

         \[\leadsto a \cdot \left(b \cdot \frac{c}{a} - 4 \cdot \left(t + \frac{\color{blue}{x \cdot i}}{a}\right)\right) - \left(j \cdot 27\right) \cdot k \]

   6. Simplified 99.8%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \frac{c}{a} - 4 \cdot \left(t + \frac{x \cdot i}{a}\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   if -1.54999999999999989e34 < t < 1e4

   1. Initial program 84.5%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 84.4%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-*r* 84.5%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot z} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. distribute-rgt-out-- 84.5%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. sub-neg 84.5%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(a \cdot 4\right) \cdot t\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      4. associate-*l* 87.8%

         \[\leadsto \left(\left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot \left(z \cdot t\right)} + \left(-\left(a \cdot 4\right) \cdot t\right)\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      5. *-commutative 87.8%

         \[\leadsto \left(\left(\color{blue}{\left(y \cdot \left(x \cdot 18\right)\right)} \cdot \left(z \cdot t\right) + \left(-\left(a \cdot 4\right) \cdot t\right)\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      6. *-commutative 87.8%

         \[\leadsto \left(\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) + \left(-\color{blue}{t \cdot \left(a \cdot 4\right)}\right)\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   6. Applied egg-rr 87.8%

      \[\leadsto \left(\color{blue}{\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) + \left(-t \cdot \left(a \cdot 4\right)\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
   7. Step-by-step derivation

      1. distribute-lft-neg-in 87.8%

         \[\leadsto \left(\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) + \color{blue}{\left(-t\right) \cdot \left(a \cdot 4\right)}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. *-commutative 87.8%

         \[\leadsto \left(\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) + \left(-t\right) \cdot \color{blue}{\left(4 \cdot a\right)}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. cancel-sign-sub-inv 87.8%

         \[\leadsto \left(\color{blue}{\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) - t \cdot \left(4 \cdot a\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      4. *-commutative 87.8%

         \[\leadsto \left(\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) - \color{blue}{\left(4 \cdot a\right) \cdot t}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      5. associate-*r* 84.5%

         \[\leadsto \left(\left(\color{blue}{\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot z\right) \cdot t} - \left(4 \cdot a\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      6. distribute-rgt-out-- 84.5%

         \[\leadsto \left(\color{blue}{t \cdot \left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot z - 4 \cdot a\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      7. associate-*r* 84.5%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(\left(y \cdot x\right) \cdot 18\right)} \cdot z - 4 \cdot a\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      8. *-commutative 84.5%

         \[\leadsto \left(t \cdot \left(\left(\color{blue}{\left(x \cdot y\right)} \cdot 18\right) \cdot z - 4 \cdot a\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      9. *-commutative 84.5%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(18 \cdot \left(x \cdot y\right)\right)} \cdot z - 4 \cdot a\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      10. *-commutative 84.5%

          \[\leadsto \left(t \cdot \left(\left(18 \cdot \left(x \cdot y\right)\right) \cdot z - \color{blue}{a \cdot 4}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   8. Simplified 84.5%

      \[\leadsto \left(\color{blue}{t \cdot \left(\left(18 \cdot \left(x \cdot y\right)\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   9. Taylor expanded in x around 0 84.4%

      \[\leadsto \left(t \cdot \left(\color{blue}{18 \cdot \left(x \cdot \left(y \cdot z\right)\right)} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
   10. Step-by-step derivation

       1. associate-*r* 84.5%

          \[\leadsto \left(t \cdot \left(18 \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot z\right)} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   11. Simplified 84.5%

       \[\leadsto \left(t \cdot \left(\color{blue}{18 \cdot \left(\left(x \cdot y\right) \cdot z\right)} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   12. Taylor expanded in x around inf 76.7%

       \[\leadsto \left(\color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
   13. Step-by-step derivation

       1. *-commutative 76.7%

          \[\leadsto \left(\color{blue}{\left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) \cdot 18} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

       2. *-commutative 76.7%

          \[\leadsto \left(\color{blue}{\left(\left(x \cdot \left(y \cdot z\right)\right) \cdot t\right)} \cdot 18 + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

       3. associate-*l* 81.6%

          \[\leadsto \left(\color{blue}{\left(x \cdot \left(\left(y \cdot z\right) \cdot t\right)\right)} \cdot 18 + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

       4. *-commutative 81.6%

          \[\leadsto \left(\left(x \cdot \color{blue}{\left(t \cdot \left(y \cdot z\right)\right)}\right) \cdot 18 + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

       5. associate-*r* 81.6%

          \[\leadsto \left(\color{blue}{x \cdot \left(\left(t \cdot \left(y \cdot z\right)\right) \cdot 18\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

       6. *-commutative 81.6%

          \[\leadsto \left(x \cdot \color{blue}{\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

       7. associate-*r* 81.6%

          \[\leadsto \left(x \cdot \color{blue}{\left(\left(18 \cdot t\right) \cdot \left(y \cdot z\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

       8. associate-*r* 87.9%

          \[\leadsto \left(x \cdot \color{blue}{\left(\left(\left(18 \cdot t\right) \cdot y\right) \cdot z\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   14. Simplified 87.9%

       \[\leadsto \left(\color{blue}{x \cdot \left(\left(\left(18 \cdot t\right) \cdot y\right) \cdot z\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{+126}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{elif}\;t \leq -1.55 \cdot 10^{+34}:\\ \;\;\;\;a \cdot \left(b \cdot \frac{c}{a} - 4 \cdot \left(t + \frac{x \cdot i}{a}\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;t \leq 10000:\\ \;\;\;\;\left(b \cdot c + x \cdot \left(z \cdot \left(y \cdot \left(t \cdot 18\right)\right)\right)\right) - \left(j \cdot \left(k \cdot 27\right) + x \cdot \left(i \cdot 4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 72.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := k \cdot \left(j \cdot 27\right)\\ t_2 := j \cdot \left(k \cdot -27\right) + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{if}\;t \leq -2.1 \cdot 10^{+126}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.45 \cdot 10^{-100}:\\ \;\;\;\;t \cdot \left(\frac{b \cdot c}{t} - 4 \cdot \left(a + i \cdot \frac{x}{t}\right)\right)\\ \mathbf{elif}\;t \leq -4.1 \cdot 10^{-249}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - t\_1\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-79}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* k (* j 27.0)))
        (t_2
         (+ (* j (* k -27.0)) (* t (+ (* 18.0 (* x (* y z))) (* a -4.0))))))
   (if (<= t -2.1e+126)
     t_2
     (if (<= t -1.45e-100)
       (* t (- (/ (* b c) t) (* 4.0 (+ a (* i (/ x t))))))
       (if (<= t -4.1e-249)
         (- (- (* b c) (* 4.0 (* t a))) t_1)
         (if (<= t 2.5e-79) (- (- (* b c) (* 4.0 (* x i))) t_1) t_2))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = k * (j * 27.0);
	double t_2 = (j * (k * -27.0)) + (t * ((18.0 * (x * (y * z))) + (a * -4.0)));
	double tmp;
	if (t <= -2.1e+126) {
		tmp = t_2;
	} else if (t <= -1.45e-100) {
		tmp = t * (((b * c) / t) - (4.0 * (a + (i * (x / t)))));
	} else if (t <= -4.1e-249) {
		tmp = ((b * c) - (4.0 * (t * a))) - t_1;
	} else if (t <= 2.5e-79) {
		tmp = ((b * c) - (4.0 * (x * i))) - t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = k * (j * 27.0d0)
    t_2 = (j * (k * (-27.0d0))) + (t * ((18.0d0 * (x * (y * z))) + (a * (-4.0d0))))
    if (t <= (-2.1d+126)) then
        tmp = t_2
    else if (t <= (-1.45d-100)) then
        tmp = t * (((b * c) / t) - (4.0d0 * (a + (i * (x / t)))))
    else if (t <= (-4.1d-249)) then
        tmp = ((b * c) - (4.0d0 * (t * a))) - t_1
    else if (t <= 2.5d-79) then
        tmp = ((b * c) - (4.0d0 * (x * i))) - t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = k * (j * 27.0);
	double t_2 = (j * (k * -27.0)) + (t * ((18.0 * (x * (y * z))) + (a * -4.0)));
	double tmp;
	if (t <= -2.1e+126) {
		tmp = t_2;
	} else if (t <= -1.45e-100) {
		tmp = t * (((b * c) / t) - (4.0 * (a + (i * (x / t)))));
	} else if (t <= -4.1e-249) {
		tmp = ((b * c) - (4.0 * (t * a))) - t_1;
	} else if (t <= 2.5e-79) {
		tmp = ((b * c) - (4.0 * (x * i))) - t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = k * (j * 27.0)
	t_2 = (j * (k * -27.0)) + (t * ((18.0 * (x * (y * z))) + (a * -4.0)))
	tmp = 0
	if t <= -2.1e+126:
		tmp = t_2
	elif t <= -1.45e-100:
		tmp = t * (((b * c) / t) - (4.0 * (a + (i * (x / t)))))
	elif t <= -4.1e-249:
		tmp = ((b * c) - (4.0 * (t * a))) - t_1
	elif t <= 2.5e-79:
		tmp = ((b * c) - (4.0 * (x * i))) - t_1
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(k * Float64(j * 27.0))
	t_2 = Float64(Float64(j * Float64(k * -27.0)) + Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) + Float64(a * -4.0))))
	tmp = 0.0
	if (t <= -2.1e+126)
		tmp = t_2;
	elseif (t <= -1.45e-100)
		tmp = Float64(t * Float64(Float64(Float64(b * c) / t) - Float64(4.0 * Float64(a + Float64(i * Float64(x / t))))));
	elseif (t <= -4.1e-249)
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(t * a))) - t_1);
	elseif (t <= 2.5e-79)
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(x * i))) - t_1);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = k * (j * 27.0);
	t_2 = (j * (k * -27.0)) + (t * ((18.0 * (x * (y * z))) + (a * -4.0)));
	tmp = 0.0;
	if (t <= -2.1e+126)
		tmp = t_2;
	elseif (t <= -1.45e-100)
		tmp = t * (((b * c) / t) - (4.0 * (a + (i * (x / t)))));
	elseif (t <= -4.1e-249)
		tmp = ((b * c) - (4.0 * (t * a))) - t_1;
	elseif (t <= 2.5e-79)
		tmp = ((b * c) - (4.0 * (x * i))) - t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.1e+126], t$95$2, If[LessEqual[t, -1.45e-100], N[(t * N[(N[(N[(b * c), $MachinePrecision] / t), $MachinePrecision] - N[(4.0 * N[(a + N[(i * N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -4.1e-249], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[t, 2.5e-79], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.0999999999999999e126 or 2.5e-79 < t

   1. Initial program 87.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 92.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 86.7%

      \[\leadsto \color{blue}{t \cdot \left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} + j \cdot \left(k \cdot -27\right) \]

   if -2.0999999999999999e126 < t < -1.44999999999999988e-100

   1. Initial program 85.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 83.3%

      \[\leadsto \color{blue}{\left(b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   4. Taylor expanded in j around 0 68.8%

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)} \]

   5. Taylor expanded in t around inf 64.2%

      \[\leadsto \color{blue}{t \cdot \left(\frac{b \cdot c}{t} - \left(4 \cdot a + 4 \cdot \frac{i \cdot x}{t}\right)\right)} \]
   6. Step-by-step derivation

      1. distribute-lft-out 64.2%

         \[\leadsto t \cdot \left(\frac{b \cdot c}{t} - \color{blue}{4 \cdot \left(a + \frac{i \cdot x}{t}\right)}\right) \]

      2. associate-/l* 69.0%

         \[\leadsto t \cdot \left(\frac{b \cdot c}{t} - 4 \cdot \left(a + \color{blue}{i \cdot \frac{x}{t}}\right)\right) \]

   7. Simplified 69.0%

      \[\leadsto \color{blue}{t \cdot \left(\frac{b \cdot c}{t} - 4 \cdot \left(a + i \cdot \frac{x}{t}\right)\right)} \]

   if -1.44999999999999988e-100 < t < -4.10000000000000004e-249

   1. Initial program 82.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 79.1%

      \[\leadsto \color{blue}{\left(b \cdot c - 4 \cdot \left(a \cdot t\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   if -4.10000000000000004e-249 < t < 2.5e-79

   1. Initial program 88.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 81.6%

      \[\leadsto \color{blue}{\left(b \cdot c - 4 \cdot \left(i \cdot x\right)\right)} - \left(j \cdot 27\right) \cdot k \]
3. Recombined 4 regimes into one program.

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{+126}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{elif}\;t \leq -1.45 \cdot 10^{-100}:\\ \;\;\;\;t \cdot \left(\frac{b \cdot c}{t} - 4 \cdot \left(a + i \cdot \frac{x}{t}\right)\right)\\ \mathbf{elif}\;t \leq -4.1 \cdot 10^{-249}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-79}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 88.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot 27\right) + x \cdot \left(i \cdot 4\right)\\ \mathbf{if}\;x \leq -6.8 \cdot 10^{+135}:\\ \;\;\;\;\left(b \cdot c + x \cdot \left(z \cdot \left(y \cdot \left(t \cdot 18\right)\right)\right)\right) - t\_1\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+145}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(z \cdot \left(x \cdot y\right)\right) - a \cdot 4\right)\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - i \cdot 4\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (+ (* j (* k 27.0)) (* x (* i 4.0)))))
   (if (<= x -6.8e+135)
     (- (+ (* b c) (* x (* z (* y (* t 18.0))))) t_1)
     (if (<= x 1.7e+145)
       (- (+ (* b c) (* t (- (* 18.0 (* z (* x y))) (* a 4.0)))) t_1)
       (* x (- (* 18.0 (* t (* y z))) (* i 4.0)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * (k * 27.0)) + (x * (i * 4.0));
	double tmp;
	if (x <= -6.8e+135) {
		tmp = ((b * c) + (x * (z * (y * (t * 18.0))))) - t_1;
	} else if (x <= 1.7e+145) {
		tmp = ((b * c) + (t * ((18.0 * (z * (x * y))) - (a * 4.0)))) - t_1;
	} else {
		tmp = x * ((18.0 * (t * (y * z))) - (i * 4.0));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (j * (k * 27.0d0)) + (x * (i * 4.0d0))
    if (x <= (-6.8d+135)) then
        tmp = ((b * c) + (x * (z * (y * (t * 18.0d0))))) - t_1
    else if (x <= 1.7d+145) then
        tmp = ((b * c) + (t * ((18.0d0 * (z * (x * y))) - (a * 4.0d0)))) - t_1
    else
        tmp = x * ((18.0d0 * (t * (y * z))) - (i * 4.0d0))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * (k * 27.0)) + (x * (i * 4.0));
	double tmp;
	if (x <= -6.8e+135) {
		tmp = ((b * c) + (x * (z * (y * (t * 18.0))))) - t_1;
	} else if (x <= 1.7e+145) {
		tmp = ((b * c) + (t * ((18.0 * (z * (x * y))) - (a * 4.0)))) - t_1;
	} else {
		tmp = x * ((18.0 * (t * (y * z))) - (i * 4.0));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * (k * 27.0)) + (x * (i * 4.0))
	tmp = 0
	if x <= -6.8e+135:
		tmp = ((b * c) + (x * (z * (y * (t * 18.0))))) - t_1
	elif x <= 1.7e+145:
		tmp = ((b * c) + (t * ((18.0 * (z * (x * y))) - (a * 4.0)))) - t_1
	else:
		tmp = x * ((18.0 * (t * (y * z))) - (i * 4.0))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * Float64(k * 27.0)) + Float64(x * Float64(i * 4.0)))
	tmp = 0.0
	if (x <= -6.8e+135)
		tmp = Float64(Float64(Float64(b * c) + Float64(x * Float64(z * Float64(y * Float64(t * 18.0))))) - t_1);
	elseif (x <= 1.7e+145)
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(18.0 * Float64(z * Float64(x * y))) - Float64(a * 4.0)))) - t_1);
	else
		tmp = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(i * 4.0)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * (k * 27.0)) + (x * (i * 4.0));
	tmp = 0.0;
	if (x <= -6.8e+135)
		tmp = ((b * c) + (x * (z * (y * (t * 18.0))))) - t_1;
	elseif (x <= 1.7e+145)
		tmp = ((b * c) + (t * ((18.0 * (z * (x * y))) - (a * 4.0)))) - t_1;
	else
		tmp = x * ((18.0 * (t * (y * z))) - (i * 4.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * N[(k * 27.0), $MachinePrecision]), $MachinePrecision] + N[(x * N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6.8e+135], N[(N[(N[(b * c), $MachinePrecision] + N[(x * N[(z * N[(y * N[(t * 18.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[x, 1.7e+145], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(18.0 * N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.80000000000000019e135

   1. Initial program 70.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 83.3%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-*r* 70.1%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot z} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. distribute-rgt-out-- 70.1%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. sub-neg 70.1%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(a \cdot 4\right) \cdot t\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      4. associate-*l* 73.0%

         \[\leadsto \left(\left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot \left(z \cdot t\right)} + \left(-\left(a \cdot 4\right) \cdot t\right)\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      5. *-commutative 73.0%

         \[\leadsto \left(\left(\color{blue}{\left(y \cdot \left(x \cdot 18\right)\right)} \cdot \left(z \cdot t\right) + \left(-\left(a \cdot 4\right) \cdot t\right)\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      6. *-commutative 73.0%

         \[\leadsto \left(\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) + \left(-\color{blue}{t \cdot \left(a \cdot 4\right)}\right)\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   6. Applied egg-rr 73.0%

      \[\leadsto \left(\color{blue}{\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) + \left(-t \cdot \left(a \cdot 4\right)\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
   7. Step-by-step derivation

      1. distribute-lft-neg-in 73.0%

         \[\leadsto \left(\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) + \color{blue}{\left(-t\right) \cdot \left(a \cdot 4\right)}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. *-commutative 73.0%

         \[\leadsto \left(\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) + \left(-t\right) \cdot \color{blue}{\left(4 \cdot a\right)}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. cancel-sign-sub-inv 73.0%

         \[\leadsto \left(\color{blue}{\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) - t \cdot \left(4 \cdot a\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      4. *-commutative 73.0%

         \[\leadsto \left(\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) - \color{blue}{\left(4 \cdot a\right) \cdot t}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      5. associate-*r* 70.1%

         \[\leadsto \left(\left(\color{blue}{\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot z\right) \cdot t} - \left(4 \cdot a\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      6. distribute-rgt-out-- 70.1%

         \[\leadsto \left(\color{blue}{t \cdot \left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot z - 4 \cdot a\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      7. associate-*r* 70.1%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(\left(y \cdot x\right) \cdot 18\right)} \cdot z - 4 \cdot a\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      8. *-commutative 70.1%

         \[\leadsto \left(t \cdot \left(\left(\color{blue}{\left(x \cdot y\right)} \cdot 18\right) \cdot z - 4 \cdot a\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      9. *-commutative 70.1%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(18 \cdot \left(x \cdot y\right)\right)} \cdot z - 4 \cdot a\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      10. *-commutative 70.1%

          \[\leadsto \left(t \cdot \left(\left(18 \cdot \left(x \cdot y\right)\right) \cdot z - \color{blue}{a \cdot 4}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   8. Simplified 70.1%

      \[\leadsto \left(\color{blue}{t \cdot \left(\left(18 \cdot \left(x \cdot y\right)\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   9. Taylor expanded in x around 0 83.3%

      \[\leadsto \left(t \cdot \left(\color{blue}{18 \cdot \left(x \cdot \left(y \cdot z\right)\right)} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
   10. Step-by-step derivation

       1. associate-*r* 70.1%

          \[\leadsto \left(t \cdot \left(18 \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot z\right)} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   11. Simplified 70.1%

       \[\leadsto \left(t \cdot \left(\color{blue}{18 \cdot \left(\left(x \cdot y\right) \cdot z\right)} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   12. Taylor expanded in x around inf 83.2%

       \[\leadsto \left(\color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
   13. Step-by-step derivation

       1. *-commutative 83.2%

          \[\leadsto \left(\color{blue}{\left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) \cdot 18} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

       2. *-commutative 83.2%

          \[\leadsto \left(\color{blue}{\left(\left(x \cdot \left(y \cdot z\right)\right) \cdot t\right)} \cdot 18 + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

       3. associate-*l* 93.0%

          \[\leadsto \left(\color{blue}{\left(x \cdot \left(\left(y \cdot z\right) \cdot t\right)\right)} \cdot 18 + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

       4. *-commutative 93.0%

          \[\leadsto \left(\left(x \cdot \color{blue}{\left(t \cdot \left(y \cdot z\right)\right)}\right) \cdot 18 + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

       5. associate-*r* 93.0%

          \[\leadsto \left(\color{blue}{x \cdot \left(\left(t \cdot \left(y \cdot z\right)\right) \cdot 18\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

       6. *-commutative 93.0%

          \[\leadsto \left(x \cdot \color{blue}{\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

       7. associate-*r* 93.0%

          \[\leadsto \left(x \cdot \color{blue}{\left(\left(18 \cdot t\right) \cdot \left(y \cdot z\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

       8. associate-*r* 93.0%

          \[\leadsto \left(x \cdot \color{blue}{\left(\left(\left(18 \cdot t\right) \cdot y\right) \cdot z\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   14. Simplified 93.0%

       \[\leadsto \left(\color{blue}{x \cdot \left(\left(\left(18 \cdot t\right) \cdot y\right) \cdot z\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   if -6.80000000000000019e135 < x < 1.7e145

   1. Initial program 92.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 91.4%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-*r* 94.0%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot z} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. distribute-rgt-out-- 92.9%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. sub-neg 92.9%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(a \cdot 4\right) \cdot t\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      4. associate-*l* 90.3%

         \[\leadsto \left(\left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot \left(z \cdot t\right)} + \left(-\left(a \cdot 4\right) \cdot t\right)\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      5. *-commutative 90.3%

         \[\leadsto \left(\left(\color{blue}{\left(y \cdot \left(x \cdot 18\right)\right)} \cdot \left(z \cdot t\right) + \left(-\left(a \cdot 4\right) \cdot t\right)\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      6. *-commutative 90.3%

         \[\leadsto \left(\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) + \left(-\color{blue}{t \cdot \left(a \cdot 4\right)}\right)\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   6. Applied egg-rr 90.3%

      \[\leadsto \left(\color{blue}{\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) + \left(-t \cdot \left(a \cdot 4\right)\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
   7. Step-by-step derivation

      1. distribute-lft-neg-in 90.3%

         \[\leadsto \left(\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) + \color{blue}{\left(-t\right) \cdot \left(a \cdot 4\right)}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. *-commutative 90.3%

         \[\leadsto \left(\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) + \left(-t\right) \cdot \color{blue}{\left(4 \cdot a\right)}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. cancel-sign-sub-inv 90.3%

         \[\leadsto \left(\color{blue}{\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) - t \cdot \left(4 \cdot a\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      4. *-commutative 90.3%

         \[\leadsto \left(\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) - \color{blue}{\left(4 \cdot a\right) \cdot t}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      5. associate-*r* 92.9%

         \[\leadsto \left(\left(\color{blue}{\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot z\right) \cdot t} - \left(4 \cdot a\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      6. distribute-rgt-out-- 94.0%

         \[\leadsto \left(\color{blue}{t \cdot \left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot z - 4 \cdot a\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      7. associate-*r* 93.9%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(\left(y \cdot x\right) \cdot 18\right)} \cdot z - 4 \cdot a\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      8. *-commutative 93.9%

         \[\leadsto \left(t \cdot \left(\left(\color{blue}{\left(x \cdot y\right)} \cdot 18\right) \cdot z - 4 \cdot a\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      9. *-commutative 93.9%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(18 \cdot \left(x \cdot y\right)\right)} \cdot z - 4 \cdot a\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      10. *-commutative 93.9%

          \[\leadsto \left(t \cdot \left(\left(18 \cdot \left(x \cdot y\right)\right) \cdot z - \color{blue}{a \cdot 4}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   8. Simplified 93.9%

      \[\leadsto \left(\color{blue}{t \cdot \left(\left(18 \cdot \left(x \cdot y\right)\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   9. Taylor expanded in x around 0 91.4%

      \[\leadsto \left(t \cdot \left(\color{blue}{18 \cdot \left(x \cdot \left(y \cdot z\right)\right)} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
   10. Step-by-step derivation

       1. associate-*r* 93.9%

          \[\leadsto \left(t \cdot \left(18 \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot z\right)} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   11. Simplified 93.9%

       \[\leadsto \left(t \cdot \left(\color{blue}{18 \cdot \left(\left(x \cdot y\right) \cdot z\right)} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   if 1.7e145 < x

   1. Initial program 62.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 71.9%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 84.4%

      \[\leadsto \color{blue}{x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{+135}:\\ \;\;\;\;\left(b \cdot c + x \cdot \left(z \cdot \left(y \cdot \left(t \cdot 18\right)\right)\right)\right) - \left(j \cdot \left(k \cdot 27\right) + x \cdot \left(i \cdot 4\right)\right)\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+145}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(z \cdot \left(x \cdot y\right)\right) - a \cdot 4\right)\right) - \left(j \cdot \left(k \cdot 27\right) + x \cdot \left(i \cdot 4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - i \cdot 4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 59.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right) + b \cdot c\\ \mathbf{if}\;j \leq -1.95 \cdot 10^{+261}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;j \leq -7.8 \cdot 10^{+202}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -1.1 \cdot 10^{+193}:\\ \;\;\;\;-18 \cdot \left(t \cdot \left(z \cdot \left(-x \cdot y\right)\right)\right)\\ \mathbf{elif}\;j \leq -2.9 \cdot 10^{+157} \lor \neg \left(j \leq 5.8 \cdot 10^{-127}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (+ (* j (* k -27.0)) (* b c))))
   (if (<= j -1.95e+261)
     (* t (- (* 18.0 (* x (* y z))) (* a 4.0)))
     (if (<= j -7.8e+202)
       t_1
       (if (<= j -1.1e+193)
         (* -18.0 (* t (* z (- (* x y)))))
         (if (or (<= j -2.9e+157) (not (<= j 5.8e-127)))
           t_1
           (- (* b c) (* 4.0 (+ (* x i) (* t a))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * (k * -27.0)) + (b * c);
	double tmp;
	if (j <= -1.95e+261) {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	} else if (j <= -7.8e+202) {
		tmp = t_1;
	} else if (j <= -1.1e+193) {
		tmp = -18.0 * (t * (z * -(x * y)));
	} else if ((j <= -2.9e+157) || !(j <= 5.8e-127)) {
		tmp = t_1;
	} else {
		tmp = (b * c) - (4.0 * ((x * i) + (t * a)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (j * (k * (-27.0d0))) + (b * c)
    if (j <= (-1.95d+261)) then
        tmp = t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0))
    else if (j <= (-7.8d+202)) then
        tmp = t_1
    else if (j <= (-1.1d+193)) then
        tmp = (-18.0d0) * (t * (z * -(x * y)))
    else if ((j <= (-2.9d+157)) .or. (.not. (j <= 5.8d-127))) then
        tmp = t_1
    else
        tmp = (b * c) - (4.0d0 * ((x * i) + (t * a)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * (k * -27.0)) + (b * c);
	double tmp;
	if (j <= -1.95e+261) {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	} else if (j <= -7.8e+202) {
		tmp = t_1;
	} else if (j <= -1.1e+193) {
		tmp = -18.0 * (t * (z * -(x * y)));
	} else if ((j <= -2.9e+157) || !(j <= 5.8e-127)) {
		tmp = t_1;
	} else {
		tmp = (b * c) - (4.0 * ((x * i) + (t * a)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * (k * -27.0)) + (b * c)
	tmp = 0
	if j <= -1.95e+261:
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0))
	elif j <= -7.8e+202:
		tmp = t_1
	elif j <= -1.1e+193:
		tmp = -18.0 * (t * (z * -(x * y)))
	elif (j <= -2.9e+157) or not (j <= 5.8e-127):
		tmp = t_1
	else:
		tmp = (b * c) - (4.0 * ((x * i) + (t * a)))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * Float64(k * -27.0)) + Float64(b * c))
	tmp = 0.0
	if (j <= -1.95e+261)
		tmp = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)));
	elseif (j <= -7.8e+202)
		tmp = t_1;
	elseif (j <= -1.1e+193)
		tmp = Float64(-18.0 * Float64(t * Float64(z * Float64(-Float64(x * y)))));
	elseif ((j <= -2.9e+157) || !(j <= 5.8e-127))
		tmp = t_1;
	else
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(Float64(x * i) + Float64(t * a))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * (k * -27.0)) + (b * c);
	tmp = 0.0;
	if (j <= -1.95e+261)
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	elseif (j <= -7.8e+202)
		tmp = t_1;
	elseif (j <= -1.1e+193)
		tmp = -18.0 * (t * (z * -(x * y)));
	elseif ((j <= -2.9e+157) || ~((j <= 5.8e-127)))
		tmp = t_1;
	else
		tmp = (b * c) - (4.0 * ((x * i) + (t * a)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.95e+261], N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -7.8e+202], t$95$1, If[LessEqual[j, -1.1e+193], N[(-18.0 * N[(t * N[(z * (-N[(x * y), $MachinePrecision])), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[j, -2.9e+157], N[Not[LessEqual[j, 5.8e-127]], $MachinePrecision]], t$95$1, N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(N[(x * i), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -1.94999999999999997e261

   1. Initial program 71.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 71.6%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-*r* 71.5%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot z} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. distribute-rgt-out-- 71.5%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. associate-*l* 79.8%

         \[\leadsto \left(\left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot \left(z \cdot t\right)} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      4. *-commutative 79.8%

         \[\leadsto \left(\left(\color{blue}{\left(y \cdot \left(x \cdot 18\right)\right)} \cdot \left(z \cdot t\right) - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      5. *-commutative 79.8%

         \[\leadsto \left(\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) - \color{blue}{t \cdot \left(a \cdot 4\right)}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   6. Applied egg-rr 79.8%

      \[\leadsto \left(\color{blue}{\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) - t \cdot \left(a \cdot 4\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   7. Taylor expanded in t around inf 62.7%

      \[\leadsto \color{blue}{t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)} \]

   if -1.94999999999999997e261 < j < -7.79999999999999967e202 or -1.09999999999999993e193 < j < -2.89999999999999988e157 or 5.8000000000000001e-127 < j

   1. Initial program 88.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 91.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 55.1%

      \[\leadsto \color{blue}{b \cdot c} + j \cdot \left(k \cdot -27\right) \]

   if -7.79999999999999967e202 < j < -1.09999999999999993e193

   1. Initial program 100.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 53.7%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-*r* 100.0%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot z} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. distribute-rgt-out-- 100.0%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. sub-neg 100.0%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(a \cdot 4\right) \cdot t\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      4. associate-*l* 100.0%

         \[\leadsto \left(\left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot \left(z \cdot t\right)} + \left(-\left(a \cdot 4\right) \cdot t\right)\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      5. *-commutative 100.0%

         \[\leadsto \left(\left(\color{blue}{\left(y \cdot \left(x \cdot 18\right)\right)} \cdot \left(z \cdot t\right) + \left(-\left(a \cdot 4\right) \cdot t\right)\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      6. *-commutative 100.0%

         \[\leadsto \left(\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) + \left(-\color{blue}{t \cdot \left(a \cdot 4\right)}\right)\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   6. Applied egg-rr 100.0%

      \[\leadsto \left(\color{blue}{\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) + \left(-t \cdot \left(a \cdot 4\right)\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
   7. Step-by-step derivation

      1. distribute-lft-neg-in 100.0%

         \[\leadsto \left(\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) + \color{blue}{\left(-t\right) \cdot \left(a \cdot 4\right)}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. *-commutative 100.0%

         \[\leadsto \left(\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) + \left(-t\right) \cdot \color{blue}{\left(4 \cdot a\right)}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. cancel-sign-sub-inv 100.0%

         \[\leadsto \left(\color{blue}{\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) - t \cdot \left(4 \cdot a\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      4. *-commutative 100.0%

         \[\leadsto \left(\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) - \color{blue}{\left(4 \cdot a\right) \cdot t}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      5. associate-*r* 100.0%

         \[\leadsto \left(\left(\color{blue}{\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot z\right) \cdot t} - \left(4 \cdot a\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      6. distribute-rgt-out-- 100.0%

         \[\leadsto \left(\color{blue}{t \cdot \left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot z - 4 \cdot a\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      7. associate-*r* 100.0%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(\left(y \cdot x\right) \cdot 18\right)} \cdot z - 4 \cdot a\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      8. *-commutative 100.0%

         \[\leadsto \left(t \cdot \left(\left(\color{blue}{\left(x \cdot y\right)} \cdot 18\right) \cdot z - 4 \cdot a\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      9. *-commutative 100.0%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(18 \cdot \left(x \cdot y\right)\right)} \cdot z - 4 \cdot a\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      10. *-commutative 100.0%

          \[\leadsto \left(t \cdot \left(\left(18 \cdot \left(x \cdot y\right)\right) \cdot z - \color{blue}{a \cdot 4}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   8. Simplified 100.0%

      \[\leadsto \left(\color{blue}{t \cdot \left(\left(18 \cdot \left(x \cdot y\right)\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   9. Taylor expanded in x around -inf 53.7%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - -4 \cdot i\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 53.7%

          \[\leadsto \color{blue}{-x \cdot \left(-18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - -4 \cdot i\right)} \]

       2. cancel-sign-sub-inv 53.7%

          \[\leadsto -x \cdot \color{blue}{\left(-18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \left(--4\right) \cdot i\right)} \]

       3. associate-*r* 53.7%

          \[\leadsto -x \cdot \left(\color{blue}{\left(-18 \cdot t\right) \cdot \left(y \cdot z\right)} + \left(--4\right) \cdot i\right) \]

       4. metadata-eval 53.7%

          \[\leadsto -x \cdot \left(\left(-18 \cdot t\right) \cdot \left(y \cdot z\right) + \color{blue}{4} \cdot i\right) \]

   11. Simplified 53.7%

       \[\leadsto \color{blue}{-x \cdot \left(\left(-18 \cdot t\right) \cdot \left(y \cdot z\right) + 4 \cdot i\right)} \]

   12. Taylor expanded in t around inf 53.7%

       \[\leadsto -\color{blue}{-18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]
   13. Step-by-step derivation

       1. *-commutative 53.7%

          \[\leadsto -\color{blue}{\left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) \cdot -18} \]

       2. associate-*r* 100.0%

          \[\leadsto -\left(t \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot z\right)}\right) \cdot -18 \]

   14. Simplified 100.0%

       \[\leadsto -\color{blue}{\left(t \cdot \left(\left(x \cdot y\right) \cdot z\right)\right) \cdot -18} \]

   if -2.89999999999999988e157 < j < 5.8000000000000001e-127

   1. Initial program 86.1%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 72.2%

      \[\leadsto \color{blue}{\left(b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   4. Taylor expanded in j around 0 59.9%

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 59.9%

         \[\leadsto b \cdot c - \color{blue}{\left(4 \cdot \left(i \cdot x\right) + 4 \cdot \left(a \cdot t\right)\right)} \]

      2. associate-*r* 59.9%

         \[\leadsto b \cdot c - \left(\color{blue}{\left(4 \cdot i\right) \cdot x} + 4 \cdot \left(a \cdot t\right)\right) \]

      3. *-commutative 59.9%

         \[\leadsto b \cdot c - \left(\color{blue}{x \cdot \left(4 \cdot i\right)} + 4 \cdot \left(a \cdot t\right)\right) \]

      4. fma-define 59.9%

         \[\leadsto b \cdot c - \color{blue}{\mathsf{fma}\left(x, 4 \cdot i, 4 \cdot \left(a \cdot t\right)\right)} \]

      5. associate-*r* 59.9%

         \[\leadsto b \cdot c - \mathsf{fma}\left(x, 4 \cdot i, \color{blue}{\left(4 \cdot a\right) \cdot t}\right) \]

      6. *-commutative 59.9%

         \[\leadsto b \cdot c - \mathsf{fma}\left(x, 4 \cdot i, \color{blue}{\left(a \cdot 4\right)} \cdot t\right) \]

   6. Applied egg-rr 59.9%

      \[\leadsto b \cdot c - \color{blue}{\mathsf{fma}\left(x, 4 \cdot i, \left(a \cdot 4\right) \cdot t\right)} \]
   7. Step-by-step derivation

      1. fma-undefine 59.9%

         \[\leadsto b \cdot c - \color{blue}{\left(x \cdot \left(4 \cdot i\right) + \left(a \cdot 4\right) \cdot t\right)} \]

      2. *-commutative 59.9%

         \[\leadsto b \cdot c - \left(x \cdot \color{blue}{\left(i \cdot 4\right)} + \left(a \cdot 4\right) \cdot t\right) \]

      3. associate-*r* 59.9%

         \[\leadsto b \cdot c - \left(\color{blue}{\left(x \cdot i\right) \cdot 4} + \left(a \cdot 4\right) \cdot t\right) \]

      4. *-commutative 59.9%

         \[\leadsto b \cdot c - \left(\color{blue}{\left(i \cdot x\right)} \cdot 4 + \left(a \cdot 4\right) \cdot t\right) \]

      5. *-commutative 59.9%

         \[\leadsto b \cdot c - \left(\color{blue}{4 \cdot \left(i \cdot x\right)} + \left(a \cdot 4\right) \cdot t\right) \]

      6. *-commutative 59.9%

         \[\leadsto b \cdot c - \left(4 \cdot \left(i \cdot x\right) + \color{blue}{\left(4 \cdot a\right)} \cdot t\right) \]

      7. associate-*r* 59.9%

         \[\leadsto b \cdot c - \left(4 \cdot \left(i \cdot x\right) + \color{blue}{4 \cdot \left(a \cdot t\right)}\right) \]

      8. distribute-lft-out 59.9%

         \[\leadsto b \cdot c - \color{blue}{4 \cdot \left(i \cdot x + a \cdot t\right)} \]

      9. *-commutative 59.9%

         \[\leadsto b \cdot c - 4 \cdot \left(\color{blue}{x \cdot i} + a \cdot t\right) \]

      10. *-commutative 59.9%

          \[\leadsto b \cdot c - 4 \cdot \left(x \cdot i + \color{blue}{t \cdot a}\right) \]

   8. Simplified 59.9%

      \[\leadsto b \cdot c - \color{blue}{4 \cdot \left(x \cdot i + t \cdot a\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 58.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.95 \cdot 10^{+261}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;j \leq -7.8 \cdot 10^{+202}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \mathbf{elif}\;j \leq -1.1 \cdot 10^{+193}:\\ \;\;\;\;-18 \cdot \left(t \cdot \left(z \cdot \left(-x \cdot y\right)\right)\right)\\ \mathbf{elif}\;j \leq -2.9 \cdot 10^{+157} \lor \neg \left(j \leq 5.8 \cdot 10^{-127}\right):\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 47.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := y \cdot \left(\left(t \cdot x\right) \cdot \left(-z \cdot -18\right)\right)\\ t_2 := j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;x \leq -4 \cdot 10^{+250}:\\ \;\;\;\;b \cdot c - x \cdot \left(i \cdot 4\right)\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{+143}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -5.5 \cdot 10^{+109}:\\ \;\;\;\;b \cdot c - t \cdot \left(a \cdot 4\right)\\ \mathbf{elif}\;x \leq -1.35 \cdot 10^{-126}:\\ \;\;\;\;t\_2 + b \cdot c\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{+23}:\\ \;\;\;\;t\_2 + t \cdot \left(a \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* y (* (* t x) (- (* z -18.0))))) (t_2 (* j (* k -27.0))))
   (if (<= x -4e+250)
     (- (* b c) (* x (* i 4.0)))
     (if (<= x -1.2e+143)
       t_1
       (if (<= x -5.5e+109)
         (- (* b c) (* t (* a 4.0)))
         (if (<= x -1.35e-126)
           (+ t_2 (* b c))
           (if (<= x 8.5e+23) (+ t_2 (* t (* a -4.0))) t_1)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = y * ((t * x) * -(z * -18.0));
	double t_2 = j * (k * -27.0);
	double tmp;
	if (x <= -4e+250) {
		tmp = (b * c) - (x * (i * 4.0));
	} else if (x <= -1.2e+143) {
		tmp = t_1;
	} else if (x <= -5.5e+109) {
		tmp = (b * c) - (t * (a * 4.0));
	} else if (x <= -1.35e-126) {
		tmp = t_2 + (b * c);
	} else if (x <= 8.5e+23) {
		tmp = t_2 + (t * (a * -4.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * ((t * x) * -(z * (-18.0d0)))
    t_2 = j * (k * (-27.0d0))
    if (x <= (-4d+250)) then
        tmp = (b * c) - (x * (i * 4.0d0))
    else if (x <= (-1.2d+143)) then
        tmp = t_1
    else if (x <= (-5.5d+109)) then
        tmp = (b * c) - (t * (a * 4.0d0))
    else if (x <= (-1.35d-126)) then
        tmp = t_2 + (b * c)
    else if (x <= 8.5d+23) then
        tmp = t_2 + (t * (a * (-4.0d0)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = y * ((t * x) * -(z * -18.0));
	double t_2 = j * (k * -27.0);
	double tmp;
	if (x <= -4e+250) {
		tmp = (b * c) - (x * (i * 4.0));
	} else if (x <= -1.2e+143) {
		tmp = t_1;
	} else if (x <= -5.5e+109) {
		tmp = (b * c) - (t * (a * 4.0));
	} else if (x <= -1.35e-126) {
		tmp = t_2 + (b * c);
	} else if (x <= 8.5e+23) {
		tmp = t_2 + (t * (a * -4.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = y * ((t * x) * -(z * -18.0))
	t_2 = j * (k * -27.0)
	tmp = 0
	if x <= -4e+250:
		tmp = (b * c) - (x * (i * 4.0))
	elif x <= -1.2e+143:
		tmp = t_1
	elif x <= -5.5e+109:
		tmp = (b * c) - (t * (a * 4.0))
	elif x <= -1.35e-126:
		tmp = t_2 + (b * c)
	elif x <= 8.5e+23:
		tmp = t_2 + (t * (a * -4.0))
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(y * Float64(Float64(t * x) * Float64(-Float64(z * -18.0))))
	t_2 = Float64(j * Float64(k * -27.0))
	tmp = 0.0
	if (x <= -4e+250)
		tmp = Float64(Float64(b * c) - Float64(x * Float64(i * 4.0)));
	elseif (x <= -1.2e+143)
		tmp = t_1;
	elseif (x <= -5.5e+109)
		tmp = Float64(Float64(b * c) - Float64(t * Float64(a * 4.0)));
	elseif (x <= -1.35e-126)
		tmp = Float64(t_2 + Float64(b * c));
	elseif (x <= 8.5e+23)
		tmp = Float64(t_2 + Float64(t * Float64(a * -4.0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = y * ((t * x) * -(z * -18.0));
	t_2 = j * (k * -27.0);
	tmp = 0.0;
	if (x <= -4e+250)
		tmp = (b * c) - (x * (i * 4.0));
	elseif (x <= -1.2e+143)
		tmp = t_1;
	elseif (x <= -5.5e+109)
		tmp = (b * c) - (t * (a * 4.0));
	elseif (x <= -1.35e-126)
		tmp = t_2 + (b * c);
	elseif (x <= 8.5e+23)
		tmp = t_2 + (t * (a * -4.0));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(y * N[(N[(t * x), $MachinePrecision] * (-N[(z * -18.0), $MachinePrecision])), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4e+250], N[(N[(b * c), $MachinePrecision] - N[(x * N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.2e+143], t$95$1, If[LessEqual[x, -5.5e+109], N[(N[(b * c), $MachinePrecision] - N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.35e-126], N[(t$95$2 + N[(b * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8.5e+23], N[(t$95$2 + N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -3.9999999999999997e250

   1. Initial program 74.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 81.6%

      \[\leadsto \color{blue}{\left(b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   4. Taylor expanded in j around 0 75.1%

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)} \]

   5. Taylor expanded in a around 0 68.1%

      \[\leadsto b \cdot c - \color{blue}{4 \cdot \left(i \cdot x\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 68.1%

         \[\leadsto b \cdot c - \color{blue}{\left(4 \cdot i\right) \cdot x} \]

   7. Simplified 68.1%

      \[\leadsto b \cdot c - \color{blue}{\left(4 \cdot i\right) \cdot x} \]

   if -3.9999999999999997e250 < x < -1.1999999999999999e143 or 8.5000000000000001e23 < x

   1. Initial program 72.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 81.5%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-*r* 77.2%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot z} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. distribute-rgt-out-- 72.8%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. sub-neg 72.8%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(a \cdot 4\right) \cdot t\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      4. associate-*l* 74.1%

         \[\leadsto \left(\left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot \left(z \cdot t\right)} + \left(-\left(a \cdot 4\right) \cdot t\right)\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      5. *-commutative 74.1%

         \[\leadsto \left(\left(\color{blue}{\left(y \cdot \left(x \cdot 18\right)\right)} \cdot \left(z \cdot t\right) + \left(-\left(a \cdot 4\right) \cdot t\right)\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      6. *-commutative 74.1%

         \[\leadsto \left(\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) + \left(-\color{blue}{t \cdot \left(a \cdot 4\right)}\right)\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   6. Applied egg-rr 74.1%

      \[\leadsto \left(\color{blue}{\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) + \left(-t \cdot \left(a \cdot 4\right)\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
   7. Step-by-step derivation

      1. distribute-lft-neg-in 74.1%

         \[\leadsto \left(\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) + \color{blue}{\left(-t\right) \cdot \left(a \cdot 4\right)}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. *-commutative 74.1%

         \[\leadsto \left(\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) + \left(-t\right) \cdot \color{blue}{\left(4 \cdot a\right)}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. cancel-sign-sub-inv 74.1%

         \[\leadsto \left(\color{blue}{\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) - t \cdot \left(4 \cdot a\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      4. *-commutative 74.1%

         \[\leadsto \left(\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) - \color{blue}{\left(4 \cdot a\right) \cdot t}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      5. associate-*r* 72.8%

         \[\leadsto \left(\left(\color{blue}{\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot z\right) \cdot t} - \left(4 \cdot a\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      6. distribute-rgt-out-- 77.2%

         \[\leadsto \left(\color{blue}{t \cdot \left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot z - 4 \cdot a\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      7. associate-*r* 77.2%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(\left(y \cdot x\right) \cdot 18\right)} \cdot z - 4 \cdot a\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      8. *-commutative 77.2%

         \[\leadsto \left(t \cdot \left(\left(\color{blue}{\left(x \cdot y\right)} \cdot 18\right) \cdot z - 4 \cdot a\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      9. *-commutative 77.2%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(18 \cdot \left(x \cdot y\right)\right)} \cdot z - 4 \cdot a\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      10. *-commutative 77.2%

          \[\leadsto \left(t \cdot \left(\left(18 \cdot \left(x \cdot y\right)\right) \cdot z - \color{blue}{a \cdot 4}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   8. Simplified 77.2%

      \[\leadsto \left(\color{blue}{t \cdot \left(\left(18 \cdot \left(x \cdot y\right)\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   9. Taylor expanded in x around -inf 74.7%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - -4 \cdot i\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 74.7%

          \[\leadsto \color{blue}{-x \cdot \left(-18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - -4 \cdot i\right)} \]

       2. cancel-sign-sub-inv 74.7%

          \[\leadsto -x \cdot \color{blue}{\left(-18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \left(--4\right) \cdot i\right)} \]

       3. associate-*r* 74.7%

          \[\leadsto -x \cdot \left(\color{blue}{\left(-18 \cdot t\right) \cdot \left(y \cdot z\right)} + \left(--4\right) \cdot i\right) \]

       4. metadata-eval 74.7%

          \[\leadsto -x \cdot \left(\left(-18 \cdot t\right) \cdot \left(y \cdot z\right) + \color{blue}{4} \cdot i\right) \]

   11. Simplified 74.7%

       \[\leadsto \color{blue}{-x \cdot \left(\left(-18 \cdot t\right) \cdot \left(y \cdot z\right) + 4 \cdot i\right)} \]

   12. Taylor expanded in t around inf 50.1%

       \[\leadsto -\color{blue}{-18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]
   13. Step-by-step derivation

       1. associate-*r* 53.7%

          \[\leadsto --18 \cdot \color{blue}{\left(\left(t \cdot x\right) \cdot \left(y \cdot z\right)\right)} \]

       2. *-commutative 53.7%

          \[\leadsto --18 \cdot \left(\left(t \cdot x\right) \cdot \color{blue}{\left(z \cdot y\right)}\right) \]

       3. associate-*r* 62.0%

          \[\leadsto --18 \cdot \color{blue}{\left(\left(\left(t \cdot x\right) \cdot z\right) \cdot y\right)} \]

       4. associate-*r* 60.6%

          \[\leadsto --18 \cdot \left(\color{blue}{\left(t \cdot \left(x \cdot z\right)\right)} \cdot y\right) \]

       5. associate-*l* 60.6%

          \[\leadsto -\color{blue}{\left(-18 \cdot \left(t \cdot \left(x \cdot z\right)\right)\right) \cdot y} \]

       6. *-commutative 60.6%

          \[\leadsto -\color{blue}{\left(\left(t \cdot \left(x \cdot z\right)\right) \cdot -18\right)} \cdot y \]

       7. associate-*r* 62.0%

          \[\leadsto -\left(\color{blue}{\left(\left(t \cdot x\right) \cdot z\right)} \cdot -18\right) \cdot y \]

       8. associate-*l* 61.9%

          \[\leadsto -\color{blue}{\left(\left(t \cdot x\right) \cdot \left(z \cdot -18\right)\right)} \cdot y \]

   14. Simplified 61.9%

       \[\leadsto -\color{blue}{\left(\left(t \cdot x\right) \cdot \left(z \cdot -18\right)\right) \cdot y} \]

   if -1.1999999999999999e143 < x < -5.4999999999999998e109

   1. Initial program 88.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 88.9%

      \[\leadsto \color{blue}{\left(b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   4. Taylor expanded in j around 0 88.9%

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)} \]

   5. Taylor expanded in a around inf 67.0%

      \[\leadsto b \cdot c - \color{blue}{4 \cdot \left(a \cdot t\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 67.0%

         \[\leadsto b \cdot c - \color{blue}{\left(4 \cdot a\right) \cdot t} \]

      2. *-commutative 67.0%

         \[\leadsto b \cdot c - \color{blue}{t \cdot \left(4 \cdot a\right)} \]

   7. Simplified 67.0%

      \[\leadsto b \cdot c - \color{blue}{t \cdot \left(4 \cdot a\right)} \]

   if -5.4999999999999998e109 < x < -1.34999999999999998e-126

   1. Initial program 96.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 96.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 53.9%

      \[\leadsto \color{blue}{b \cdot c} + j \cdot \left(k \cdot -27\right) \]

   if -1.34999999999999998e-126 < x < 8.5000000000000001e23

   1. Initial program 91.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 89.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 60.5%

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t\right)} + j \cdot \left(k \cdot -27\right) \]
   6. Step-by-step derivation

      1. associate-*r* 60.5%

         \[\leadsto \color{blue}{\left(-4 \cdot a\right) \cdot t} + j \cdot \left(k \cdot -27\right) \]

      2. *-commutative 60.5%

         \[\leadsto \color{blue}{t \cdot \left(-4 \cdot a\right)} + j \cdot \left(k \cdot -27\right) \]

   7. Simplified 60.5%

      \[\leadsto \color{blue}{t \cdot \left(-4 \cdot a\right)} + j \cdot \left(k \cdot -27\right) \]
3. Recombined 5 regimes into one program.

4. Final simplification 60.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+250}:\\ \;\;\;\;b \cdot c - x \cdot \left(i \cdot 4\right)\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{+143}:\\ \;\;\;\;y \cdot \left(\left(t \cdot x\right) \cdot \left(-z \cdot -18\right)\right)\\ \mathbf{elif}\;x \leq -5.5 \cdot 10^{+109}:\\ \;\;\;\;b \cdot c - t \cdot \left(a \cdot 4\right)\\ \mathbf{elif}\;x \leq -1.35 \cdot 10^{-126}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{+23}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(a \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\left(t \cdot x\right) \cdot \left(-z \cdot -18\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 47.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c - t \cdot \left(a \cdot 4\right)\\ t_2 := y \cdot \left(\left(t \cdot x\right) \cdot \left(-z \cdot -18\right)\right)\\ \mathbf{if}\;x \leq -4.2 \cdot 10^{+250}:\\ \;\;\;\;b \cdot c - x \cdot \left(i \cdot 4\right)\\ \mathbf{elif}\;x \leq -9.2 \cdot 10^{+142}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -7.4 \cdot 10^{+109}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{-131}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \mathbf{elif}\;x \leq 7 \cdot 10^{+25}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (- (* b c) (* t (* a 4.0))))
        (t_2 (* y (* (* t x) (- (* z -18.0))))))
   (if (<= x -4.2e+250)
     (- (* b c) (* x (* i 4.0)))
     (if (<= x -9.2e+142)
       t_2
       (if (<= x -7.4e+109)
         t_1
         (if (<= x 1.65e-131)
           (+ (* j (* k -27.0)) (* b c))
           (if (<= x 7e+25) t_1 t_2)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) - (t * (a * 4.0));
	double t_2 = y * ((t * x) * -(z * -18.0));
	double tmp;
	if (x <= -4.2e+250) {
		tmp = (b * c) - (x * (i * 4.0));
	} else if (x <= -9.2e+142) {
		tmp = t_2;
	} else if (x <= -7.4e+109) {
		tmp = t_1;
	} else if (x <= 1.65e-131) {
		tmp = (j * (k * -27.0)) + (b * c);
	} else if (x <= 7e+25) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (b * c) - (t * (a * 4.0d0))
    t_2 = y * ((t * x) * -(z * (-18.0d0)))
    if (x <= (-4.2d+250)) then
        tmp = (b * c) - (x * (i * 4.0d0))
    else if (x <= (-9.2d+142)) then
        tmp = t_2
    else if (x <= (-7.4d+109)) then
        tmp = t_1
    else if (x <= 1.65d-131) then
        tmp = (j * (k * (-27.0d0))) + (b * c)
    else if (x <= 7d+25) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) - (t * (a * 4.0));
	double t_2 = y * ((t * x) * -(z * -18.0));
	double tmp;
	if (x <= -4.2e+250) {
		tmp = (b * c) - (x * (i * 4.0));
	} else if (x <= -9.2e+142) {
		tmp = t_2;
	} else if (x <= -7.4e+109) {
		tmp = t_1;
	} else if (x <= 1.65e-131) {
		tmp = (j * (k * -27.0)) + (b * c);
	} else if (x <= 7e+25) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) - (t * (a * 4.0))
	t_2 = y * ((t * x) * -(z * -18.0))
	tmp = 0
	if x <= -4.2e+250:
		tmp = (b * c) - (x * (i * 4.0))
	elif x <= -9.2e+142:
		tmp = t_2
	elif x <= -7.4e+109:
		tmp = t_1
	elif x <= 1.65e-131:
		tmp = (j * (k * -27.0)) + (b * c)
	elif x <= 7e+25:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) - Float64(t * Float64(a * 4.0)))
	t_2 = Float64(y * Float64(Float64(t * x) * Float64(-Float64(z * -18.0))))
	tmp = 0.0
	if (x <= -4.2e+250)
		tmp = Float64(Float64(b * c) - Float64(x * Float64(i * 4.0)));
	elseif (x <= -9.2e+142)
		tmp = t_2;
	elseif (x <= -7.4e+109)
		tmp = t_1;
	elseif (x <= 1.65e-131)
		tmp = Float64(Float64(j * Float64(k * -27.0)) + Float64(b * c));
	elseif (x <= 7e+25)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) - (t * (a * 4.0));
	t_2 = y * ((t * x) * -(z * -18.0));
	tmp = 0.0;
	if (x <= -4.2e+250)
		tmp = (b * c) - (x * (i * 4.0));
	elseif (x <= -9.2e+142)
		tmp = t_2;
	elseif (x <= -7.4e+109)
		tmp = t_1;
	elseif (x <= 1.65e-131)
		tmp = (j * (k * -27.0)) + (b * c);
	elseif (x <= 7e+25)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] - N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(t * x), $MachinePrecision] * (-N[(z * -18.0), $MachinePrecision])), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.2e+250], N[(N[(b * c), $MachinePrecision] - N[(x * N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -9.2e+142], t$95$2, If[LessEqual[x, -7.4e+109], t$95$1, If[LessEqual[x, 1.65e-131], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7e+25], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -4.2000000000000003e250

   1. Initial program 74.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 81.6%

      \[\leadsto \color{blue}{\left(b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   4. Taylor expanded in j around 0 75.1%

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)} \]

   5. Taylor expanded in a around 0 68.1%

      \[\leadsto b \cdot c - \color{blue}{4 \cdot \left(i \cdot x\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 68.1%

         \[\leadsto b \cdot c - \color{blue}{\left(4 \cdot i\right) \cdot x} \]

   7. Simplified 68.1%

      \[\leadsto b \cdot c - \color{blue}{\left(4 \cdot i\right) \cdot x} \]

   if -4.2000000000000003e250 < x < -9.20000000000000009e142 or 6.99999999999999999e25 < x

   1. Initial program 72.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 81.2%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-*r* 76.9%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot z} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. distribute-rgt-out-- 72.4%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. sub-neg 72.4%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(a \cdot 4\right) \cdot t\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      4. associate-*l* 73.7%

         \[\leadsto \left(\left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot \left(z \cdot t\right)} + \left(-\left(a \cdot 4\right) \cdot t\right)\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      5. *-commutative 73.7%

         \[\leadsto \left(\left(\color{blue}{\left(y \cdot \left(x \cdot 18\right)\right)} \cdot \left(z \cdot t\right) + \left(-\left(a \cdot 4\right) \cdot t\right)\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      6. *-commutative 73.7%

         \[\leadsto \left(\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) + \left(-\color{blue}{t \cdot \left(a \cdot 4\right)}\right)\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   6. Applied egg-rr 73.7%

      \[\leadsto \left(\color{blue}{\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) + \left(-t \cdot \left(a \cdot 4\right)\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
   7. Step-by-step derivation

      1. distribute-lft-neg-in 73.7%

         \[\leadsto \left(\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) + \color{blue}{\left(-t\right) \cdot \left(a \cdot 4\right)}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. *-commutative 73.7%

         \[\leadsto \left(\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) + \left(-t\right) \cdot \color{blue}{\left(4 \cdot a\right)}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. cancel-sign-sub-inv 73.7%

         \[\leadsto \left(\color{blue}{\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) - t \cdot \left(4 \cdot a\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      4. *-commutative 73.7%

         \[\leadsto \left(\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) - \color{blue}{\left(4 \cdot a\right) \cdot t}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      5. associate-*r* 72.4%

         \[\leadsto \left(\left(\color{blue}{\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot z\right) \cdot t} - \left(4 \cdot a\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      6. distribute-rgt-out-- 76.9%

         \[\leadsto \left(\color{blue}{t \cdot \left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot z - 4 \cdot a\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      7. associate-*r* 76.9%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(\left(y \cdot x\right) \cdot 18\right)} \cdot z - 4 \cdot a\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      8. *-commutative 76.9%

         \[\leadsto \left(t \cdot \left(\left(\color{blue}{\left(x \cdot y\right)} \cdot 18\right) \cdot z - 4 \cdot a\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      9. *-commutative 76.9%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(18 \cdot \left(x \cdot y\right)\right)} \cdot z - 4 \cdot a\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      10. *-commutative 76.9%

          \[\leadsto \left(t \cdot \left(\left(18 \cdot \left(x \cdot y\right)\right) \cdot z - \color{blue}{a \cdot 4}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   8. Simplified 76.9%

      \[\leadsto \left(\color{blue}{t \cdot \left(\left(18 \cdot \left(x \cdot y\right)\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   9. Taylor expanded in x around -inf 75.8%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - -4 \cdot i\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 75.8%

          \[\leadsto \color{blue}{-x \cdot \left(-18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - -4 \cdot i\right)} \]

       2. cancel-sign-sub-inv 75.8%

          \[\leadsto -x \cdot \color{blue}{\left(-18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \left(--4\right) \cdot i\right)} \]

       3. associate-*r* 75.7%

          \[\leadsto -x \cdot \left(\color{blue}{\left(-18 \cdot t\right) \cdot \left(y \cdot z\right)} + \left(--4\right) \cdot i\right) \]

       4. metadata-eval 75.7%

          \[\leadsto -x \cdot \left(\left(-18 \cdot t\right) \cdot \left(y \cdot z\right) + \color{blue}{4} \cdot i\right) \]

   11. Simplified 75.7%

       \[\leadsto \color{blue}{-x \cdot \left(\left(-18 \cdot t\right) \cdot \left(y \cdot z\right) + 4 \cdot i\right)} \]

   12. Taylor expanded in t around inf 50.9%

       \[\leadsto -\color{blue}{-18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]
   13. Step-by-step derivation

       1. associate-*r* 54.5%

          \[\leadsto --18 \cdot \color{blue}{\left(\left(t \cdot x\right) \cdot \left(y \cdot z\right)\right)} \]

       2. *-commutative 54.5%

          \[\leadsto --18 \cdot \left(\left(t \cdot x\right) \cdot \color{blue}{\left(z \cdot y\right)}\right) \]

       3. associate-*r* 62.9%

          \[\leadsto --18 \cdot \color{blue}{\left(\left(\left(t \cdot x\right) \cdot z\right) \cdot y\right)} \]

       4. associate-*r* 61.5%

          \[\leadsto --18 \cdot \left(\color{blue}{\left(t \cdot \left(x \cdot z\right)\right)} \cdot y\right) \]

       5. associate-*l* 61.5%

          \[\leadsto -\color{blue}{\left(-18 \cdot \left(t \cdot \left(x \cdot z\right)\right)\right) \cdot y} \]

       6. *-commutative 61.5%

          \[\leadsto -\color{blue}{\left(\left(t \cdot \left(x \cdot z\right)\right) \cdot -18\right)} \cdot y \]

       7. associate-*r* 62.9%

          \[\leadsto -\left(\color{blue}{\left(\left(t \cdot x\right) \cdot z\right)} \cdot -18\right) \cdot y \]

       8. associate-*l* 62.8%

          \[\leadsto -\color{blue}{\left(\left(t \cdot x\right) \cdot \left(z \cdot -18\right)\right)} \cdot y \]

   14. Simplified 62.8%

       \[\leadsto -\color{blue}{\left(\left(t \cdot x\right) \cdot \left(z \cdot -18\right)\right) \cdot y} \]

   if -9.20000000000000009e142 < x < -7.40000000000000041e109 or 1.6500000000000001e-131 < x < 6.99999999999999999e25

   1. Initial program 83.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 76.9%

      \[\leadsto \color{blue}{\left(b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   4. Taylor expanded in j around 0 67.7%

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)} \]

   5. Taylor expanded in a around inf 51.9%

      \[\leadsto b \cdot c - \color{blue}{4 \cdot \left(a \cdot t\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 51.9%

         \[\leadsto b \cdot c - \color{blue}{\left(4 \cdot a\right) \cdot t} \]

      2. *-commutative 51.9%

         \[\leadsto b \cdot c - \color{blue}{t \cdot \left(4 \cdot a\right)} \]

   7. Simplified 51.9%

      \[\leadsto b \cdot c - \color{blue}{t \cdot \left(4 \cdot a\right)} \]

   if -7.40000000000000041e109 < x < 1.6500000000000001e-131

   1. Initial program 96.1%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 93.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 57.0%

      \[\leadsto \color{blue}{b \cdot c} + j \cdot \left(k \cdot -27\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 58.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{+250}:\\ \;\;\;\;b \cdot c - x \cdot \left(i \cdot 4\right)\\ \mathbf{elif}\;x \leq -9.2 \cdot 10^{+142}:\\ \;\;\;\;y \cdot \left(\left(t \cdot x\right) \cdot \left(-z \cdot -18\right)\right)\\ \mathbf{elif}\;x \leq -7.4 \cdot 10^{+109}:\\ \;\;\;\;b \cdot c - t \cdot \left(a \cdot 4\right)\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{-131}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \mathbf{elif}\;x \leq 7 \cdot 10^{+25}:\\ \;\;\;\;b \cdot c - t \cdot \left(a \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\left(t \cdot x\right) \cdot \left(-z \cdot -18\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 71.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{if}\;x \leq -2.7 \cdot 10^{+126}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - i \cdot 4\right)\\ \mathbf{elif}\;x \leq -8.5 \cdot 10^{+100}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -5 \cdot 10^{+27}:\\ \;\;\;\;x \cdot \left(4 \cdot \left(-i\right) - \left(y \cdot z\right) \cdot \left(t \cdot -18\right)\right)\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+29}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-4 \cdot i + 18 \cdot \left(z \cdot \left(t \cdot y\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (- (- (* b c) (* 4.0 (* t a))) (* k (* j 27.0)))))
   (if (<= x -2.7e+126)
     (* x (- (* 18.0 (* t (* y z))) (* i 4.0)))
     (if (<= x -8.5e+100)
       t_1
       (if (<= x -5e+27)
         (* x (- (* 4.0 (- i)) (* (* y z) (* t -18.0))))
         (if (<= x 7.5e+29)
           t_1
           (* x (+ (* -4.0 i) (* 18.0 (* z (* t y)))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((b * c) - (4.0 * (t * a))) - (k * (j * 27.0));
	double tmp;
	if (x <= -2.7e+126) {
		tmp = x * ((18.0 * (t * (y * z))) - (i * 4.0));
	} else if (x <= -8.5e+100) {
		tmp = t_1;
	} else if (x <= -5e+27) {
		tmp = x * ((4.0 * -i) - ((y * z) * (t * -18.0)));
	} else if (x <= 7.5e+29) {
		tmp = t_1;
	} else {
		tmp = x * ((-4.0 * i) + (18.0 * (z * (t * y))));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((b * c) - (4.0d0 * (t * a))) - (k * (j * 27.0d0))
    if (x <= (-2.7d+126)) then
        tmp = x * ((18.0d0 * (t * (y * z))) - (i * 4.0d0))
    else if (x <= (-8.5d+100)) then
        tmp = t_1
    else if (x <= (-5d+27)) then
        tmp = x * ((4.0d0 * -i) - ((y * z) * (t * (-18.0d0))))
    else if (x <= 7.5d+29) then
        tmp = t_1
    else
        tmp = x * (((-4.0d0) * i) + (18.0d0 * (z * (t * y))))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((b * c) - (4.0 * (t * a))) - (k * (j * 27.0));
	double tmp;
	if (x <= -2.7e+126) {
		tmp = x * ((18.0 * (t * (y * z))) - (i * 4.0));
	} else if (x <= -8.5e+100) {
		tmp = t_1;
	} else if (x <= -5e+27) {
		tmp = x * ((4.0 * -i) - ((y * z) * (t * -18.0)));
	} else if (x <= 7.5e+29) {
		tmp = t_1;
	} else {
		tmp = x * ((-4.0 * i) + (18.0 * (z * (t * y))));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = ((b * c) - (4.0 * (t * a))) - (k * (j * 27.0))
	tmp = 0
	if x <= -2.7e+126:
		tmp = x * ((18.0 * (t * (y * z))) - (i * 4.0))
	elif x <= -8.5e+100:
		tmp = t_1
	elif x <= -5e+27:
		tmp = x * ((4.0 * -i) - ((y * z) * (t * -18.0)))
	elif x <= 7.5e+29:
		tmp = t_1
	else:
		tmp = x * ((-4.0 * i) + (18.0 * (z * (t * y))))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(t * a))) - Float64(k * Float64(j * 27.0)))
	tmp = 0.0
	if (x <= -2.7e+126)
		tmp = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(i * 4.0)));
	elseif (x <= -8.5e+100)
		tmp = t_1;
	elseif (x <= -5e+27)
		tmp = Float64(x * Float64(Float64(4.0 * Float64(-i)) - Float64(Float64(y * z) * Float64(t * -18.0))));
	elseif (x <= 7.5e+29)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(Float64(-4.0 * i) + Float64(18.0 * Float64(z * Float64(t * y)))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = ((b * c) - (4.0 * (t * a))) - (k * (j * 27.0));
	tmp = 0.0;
	if (x <= -2.7e+126)
		tmp = x * ((18.0 * (t * (y * z))) - (i * 4.0));
	elseif (x <= -8.5e+100)
		tmp = t_1;
	elseif (x <= -5e+27)
		tmp = x * ((4.0 * -i) - ((y * z) * (t * -18.0)));
	elseif (x <= 7.5e+29)
		tmp = t_1;
	else
		tmp = x * ((-4.0 * i) + (18.0 * (z * (t * y))));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.7e+126], N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -8.5e+100], t$95$1, If[LessEqual[x, -5e+27], N[(x * N[(N[(4.0 * (-i)), $MachinePrecision] - N[(N[(y * z), $MachinePrecision] * N[(t * -18.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.5e+29], t$95$1, N[(x * N[(N[(-4.0 * i), $MachinePrecision] + N[(18.0 * N[(z * N[(t * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.70000000000000002e126

   1. Initial program 71.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 83.8%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 70.8%

      \[\leadsto \color{blue}{x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)} \]

   if -2.70000000000000002e126 < x < -8.50000000000000043e100 or -4.99999999999999979e27 < x < 7.49999999999999945e29

   1. Initial program 93.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 77.6%

      \[\leadsto \color{blue}{\left(b \cdot c - 4 \cdot \left(a \cdot t\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   if -8.50000000000000043e100 < x < -4.99999999999999979e27

   1. Initial program 100.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-*r* 100.0%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot z} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. distribute-rgt-out-- 100.0%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. sub-neg 100.0%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(a \cdot 4\right) \cdot t\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      4. associate-*l* 93.2%

         \[\leadsto \left(\left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot \left(z \cdot t\right)} + \left(-\left(a \cdot 4\right) \cdot t\right)\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      5. *-commutative 93.2%

         \[\leadsto \left(\left(\color{blue}{\left(y \cdot \left(x \cdot 18\right)\right)} \cdot \left(z \cdot t\right) + \left(-\left(a \cdot 4\right) \cdot t\right)\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      6. *-commutative 93.2%

         \[\leadsto \left(\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) + \left(-\color{blue}{t \cdot \left(a \cdot 4\right)}\right)\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   6. Applied egg-rr 93.2%

      \[\leadsto \left(\color{blue}{\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) + \left(-t \cdot \left(a \cdot 4\right)\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
   7. Step-by-step derivation

      1. distribute-lft-neg-in 93.2%

         \[\leadsto \left(\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) + \color{blue}{\left(-t\right) \cdot \left(a \cdot 4\right)}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. *-commutative 93.2%

         \[\leadsto \left(\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) + \left(-t\right) \cdot \color{blue}{\left(4 \cdot a\right)}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. cancel-sign-sub-inv 93.2%

         \[\leadsto \left(\color{blue}{\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) - t \cdot \left(4 \cdot a\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      4. *-commutative 93.2%

         \[\leadsto \left(\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) - \color{blue}{\left(4 \cdot a\right) \cdot t}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      5. associate-*r* 100.0%

         \[\leadsto \left(\left(\color{blue}{\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot z\right) \cdot t} - \left(4 \cdot a\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      6. distribute-rgt-out-- 100.0%

         \[\leadsto \left(\color{blue}{t \cdot \left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot z - 4 \cdot a\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      7. associate-*r* 100.0%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(\left(y \cdot x\right) \cdot 18\right)} \cdot z - 4 \cdot a\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      8. *-commutative 100.0%

         \[\leadsto \left(t \cdot \left(\left(\color{blue}{\left(x \cdot y\right)} \cdot 18\right) \cdot z - 4 \cdot a\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      9. *-commutative 100.0%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(18 \cdot \left(x \cdot y\right)\right)} \cdot z - 4 \cdot a\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      10. *-commutative 100.0%

          \[\leadsto \left(t \cdot \left(\left(18 \cdot \left(x \cdot y\right)\right) \cdot z - \color{blue}{a \cdot 4}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   8. Simplified 100.0%

      \[\leadsto \left(\color{blue}{t \cdot \left(\left(18 \cdot \left(x \cdot y\right)\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   9. Taylor expanded in x around -inf 78.5%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - -4 \cdot i\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 78.5%

          \[\leadsto \color{blue}{-x \cdot \left(-18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - -4 \cdot i\right)} \]

       2. cancel-sign-sub-inv 78.5%

          \[\leadsto -x \cdot \color{blue}{\left(-18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \left(--4\right) \cdot i\right)} \]

       3. associate-*r* 78.6%

          \[\leadsto -x \cdot \left(\color{blue}{\left(-18 \cdot t\right) \cdot \left(y \cdot z\right)} + \left(--4\right) \cdot i\right) \]

       4. metadata-eval 78.6%

          \[\leadsto -x \cdot \left(\left(-18 \cdot t\right) \cdot \left(y \cdot z\right) + \color{blue}{4} \cdot i\right) \]

   11. Simplified 78.6%

       \[\leadsto \color{blue}{-x \cdot \left(\left(-18 \cdot t\right) \cdot \left(y \cdot z\right) + 4 \cdot i\right)} \]

   if 7.49999999999999945e29 < x

   1. Initial program 73.5%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 80.6%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-*r* 78.9%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot z} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. distribute-rgt-out-- 73.5%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. associate-*l* 75.1%

         \[\leadsto \left(\left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot \left(z \cdot t\right)} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      4. *-commutative 75.1%

         \[\leadsto \left(\left(\color{blue}{\left(y \cdot \left(x \cdot 18\right)\right)} \cdot \left(z \cdot t\right) - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      5. *-commutative 75.1%

         \[\leadsto \left(\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) - \color{blue}{t \cdot \left(a \cdot 4\right)}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   6. Applied egg-rr 75.1%

      \[\leadsto \left(\color{blue}{\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) - t \cdot \left(a \cdot 4\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   7. Taylor expanded in x around inf 77.7%

      \[\leadsto \color{blue}{x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)} \]
   8. Step-by-step derivation

      1. cancel-sign-sub-inv 77.7%

         \[\leadsto x \cdot \color{blue}{\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \left(-4\right) \cdot i\right)} \]

      2. associate-*r* 79.3%

         \[\leadsto x \cdot \left(18 \cdot \color{blue}{\left(\left(t \cdot y\right) \cdot z\right)} + \left(-4\right) \cdot i\right) \]

      3. metadata-eval 79.3%

         \[\leadsto x \cdot \left(18 \cdot \left(\left(t \cdot y\right) \cdot z\right) + \color{blue}{-4} \cdot i\right) \]

      4. *-commutative 79.3%

         \[\leadsto x \cdot \left(18 \cdot \left(\left(t \cdot y\right) \cdot z\right) + \color{blue}{i \cdot -4}\right) \]

   9. Simplified 79.3%

      \[\leadsto \color{blue}{x \cdot \left(18 \cdot \left(\left(t \cdot y\right) \cdot z\right) + i \cdot -4\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{+126}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - i \cdot 4\right)\\ \mathbf{elif}\;x \leq -8.5 \cdot 10^{+100}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;x \leq -5 \cdot 10^{+27}:\\ \;\;\;\;x \cdot \left(4 \cdot \left(-i\right) - \left(y \cdot z\right) \cdot \left(t \cdot -18\right)\right)\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+29}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-4 \cdot i + 18 \cdot \left(z \cdot \left(t \cdot y\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 51.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right) + b \cdot c\\ t_2 := b \cdot c - x \cdot \left(i \cdot 4\right)\\ t_3 := b \cdot c - t \cdot \left(a \cdot 4\right)\\ \mathbf{if}\;a \leq -2.25 \cdot 10^{+95}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{+44}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -2.25 \cdot 10^{-135}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -4.25 \cdot 10^{-215}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{+16}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (+ (* j (* k -27.0)) (* b c)))
        (t_2 (- (* b c) (* x (* i 4.0))))
        (t_3 (- (* b c) (* t (* a 4.0)))))
   (if (<= a -2.25e+95)
     t_3
     (if (<= a -6.8e+44)
       t_2
       (if (<= a -2.25e-135)
         t_1
         (if (<= a -4.25e-215) t_2 (if (<= a 3.9e+16) t_1 t_3)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * (k * -27.0)) + (b * c);
	double t_2 = (b * c) - (x * (i * 4.0));
	double t_3 = (b * c) - (t * (a * 4.0));
	double tmp;
	if (a <= -2.25e+95) {
		tmp = t_3;
	} else if (a <= -6.8e+44) {
		tmp = t_2;
	} else if (a <= -2.25e-135) {
		tmp = t_1;
	} else if (a <= -4.25e-215) {
		tmp = t_2;
	} else if (a <= 3.9e+16) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (j * (k * (-27.0d0))) + (b * c)
    t_2 = (b * c) - (x * (i * 4.0d0))
    t_3 = (b * c) - (t * (a * 4.0d0))
    if (a <= (-2.25d+95)) then
        tmp = t_3
    else if (a <= (-6.8d+44)) then
        tmp = t_2
    else if (a <= (-2.25d-135)) then
        tmp = t_1
    else if (a <= (-4.25d-215)) then
        tmp = t_2
    else if (a <= 3.9d+16) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * (k * -27.0)) + (b * c);
	double t_2 = (b * c) - (x * (i * 4.0));
	double t_3 = (b * c) - (t * (a * 4.0));
	double tmp;
	if (a <= -2.25e+95) {
		tmp = t_3;
	} else if (a <= -6.8e+44) {
		tmp = t_2;
	} else if (a <= -2.25e-135) {
		tmp = t_1;
	} else if (a <= -4.25e-215) {
		tmp = t_2;
	} else if (a <= 3.9e+16) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * (k * -27.0)) + (b * c)
	t_2 = (b * c) - (x * (i * 4.0))
	t_3 = (b * c) - (t * (a * 4.0))
	tmp = 0
	if a <= -2.25e+95:
		tmp = t_3
	elif a <= -6.8e+44:
		tmp = t_2
	elif a <= -2.25e-135:
		tmp = t_1
	elif a <= -4.25e-215:
		tmp = t_2
	elif a <= 3.9e+16:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * Float64(k * -27.0)) + Float64(b * c))
	t_2 = Float64(Float64(b * c) - Float64(x * Float64(i * 4.0)))
	t_3 = Float64(Float64(b * c) - Float64(t * Float64(a * 4.0)))
	tmp = 0.0
	if (a <= -2.25e+95)
		tmp = t_3;
	elseif (a <= -6.8e+44)
		tmp = t_2;
	elseif (a <= -2.25e-135)
		tmp = t_1;
	elseif (a <= -4.25e-215)
		tmp = t_2;
	elseif (a <= 3.9e+16)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * (k * -27.0)) + (b * c);
	t_2 = (b * c) - (x * (i * 4.0));
	t_3 = (b * c) - (t * (a * 4.0));
	tmp = 0.0;
	if (a <= -2.25e+95)
		tmp = t_3;
	elseif (a <= -6.8e+44)
		tmp = t_2;
	elseif (a <= -2.25e-135)
		tmp = t_1;
	elseif (a <= -4.25e-215)
		tmp = t_2;
	elseif (a <= 3.9e+16)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] - N[(x * N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(b * c), $MachinePrecision] - N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.25e+95], t$95$3, If[LessEqual[a, -6.8e+44], t$95$2, If[LessEqual[a, -2.25e-135], t$95$1, If[LessEqual[a, -4.25e-215], t$95$2, If[LessEqual[a, 3.9e+16], t$95$1, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.25000000000000008e95 or 3.9e16 < a

   1. Initial program 85.1%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 80.2%

      \[\leadsto \color{blue}{\left(b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   4. Taylor expanded in j around 0 69.8%

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)} \]

   5. Taylor expanded in a around inf 60.2%

      \[\leadsto b \cdot c - \color{blue}{4 \cdot \left(a \cdot t\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 60.2%

         \[\leadsto b \cdot c - \color{blue}{\left(4 \cdot a\right) \cdot t} \]

      2. *-commutative 60.2%

         \[\leadsto b \cdot c - \color{blue}{t \cdot \left(4 \cdot a\right)} \]

   7. Simplified 60.2%

      \[\leadsto b \cdot c - \color{blue}{t \cdot \left(4 \cdot a\right)} \]

   if -2.25000000000000008e95 < a < -6.8e44 or -2.24999999999999994e-135 < a < -4.2499999999999999e-215

   1. Initial program 85.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 83.3%

      \[\leadsto \color{blue}{\left(b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   4. Taylor expanded in j around 0 75.3%

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)} \]

   5. Taylor expanded in a around 0 71.1%

      \[\leadsto b \cdot c - \color{blue}{4 \cdot \left(i \cdot x\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 71.1%

         \[\leadsto b \cdot c - \color{blue}{\left(4 \cdot i\right) \cdot x} \]

   7. Simplified 71.1%

      \[\leadsto b \cdot c - \color{blue}{\left(4 \cdot i\right) \cdot x} \]

   if -6.8e44 < a < -2.24999999999999994e-135 or -4.2499999999999999e-215 < a < 3.9e16

   1. Initial program 88.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 88.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 52.3%

      \[\leadsto \color{blue}{b \cdot c} + j \cdot \left(k \cdot -27\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.25 \cdot 10^{+95}:\\ \;\;\;\;b \cdot c - t \cdot \left(a \cdot 4\right)\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{+44}:\\ \;\;\;\;b \cdot c - x \cdot \left(i \cdot 4\right)\\ \mathbf{elif}\;a \leq -2.25 \cdot 10^{-135}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \mathbf{elif}\;a \leq -4.25 \cdot 10^{-215}:\\ \;\;\;\;b \cdot c - x \cdot \left(i \cdot 4\right)\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{+16}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - t \cdot \left(a \cdot 4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 61.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\\ \mathbf{if}\;j \leq -3.2 \cdot 10^{+154}:\\ \;\;\;\;t\_1 + 18 \cdot \left(t \cdot \left(z \cdot \left(x \cdot y\right)\right)\right)\\ \mathbf{elif}\;j \leq -1.8 \cdot 10^{+77}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -0.00036:\\ \;\;\;\;t\_1 + 18 \cdot \left(\left(y \cdot z\right) \cdot \left(t \cdot x\right)\right)\\ \mathbf{elif}\;j \leq 5.8 \cdot 10^{-127}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1 + b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0))) (t_2 (- (* b c) (* 4.0 (+ (* x i) (* t a))))))
   (if (<= j -3.2e+154)
     (+ t_1 (* 18.0 (* t (* z (* x y)))))
     (if (<= j -1.8e+77)
       t_2
       (if (<= j -0.00036)
         (+ t_1 (* 18.0 (* (* y z) (* t x))))
         (if (<= j 5.8e-127) t_2 (+ t_1 (* b c))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = (b * c) - (4.0 * ((x * i) + (t * a)));
	double tmp;
	if (j <= -3.2e+154) {
		tmp = t_1 + (18.0 * (t * (z * (x * y))));
	} else if (j <= -1.8e+77) {
		tmp = t_2;
	} else if (j <= -0.00036) {
		tmp = t_1 + (18.0 * ((y * z) * (t * x)));
	} else if (j <= 5.8e-127) {
		tmp = t_2;
	} else {
		tmp = t_1 + (b * c);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * (k * (-27.0d0))
    t_2 = (b * c) - (4.0d0 * ((x * i) + (t * a)))
    if (j <= (-3.2d+154)) then
        tmp = t_1 + (18.0d0 * (t * (z * (x * y))))
    else if (j <= (-1.8d+77)) then
        tmp = t_2
    else if (j <= (-0.00036d0)) then
        tmp = t_1 + (18.0d0 * ((y * z) * (t * x)))
    else if (j <= 5.8d-127) then
        tmp = t_2
    else
        tmp = t_1 + (b * c)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = (b * c) - (4.0 * ((x * i) + (t * a)));
	double tmp;
	if (j <= -3.2e+154) {
		tmp = t_1 + (18.0 * (t * (z * (x * y))));
	} else if (j <= -1.8e+77) {
		tmp = t_2;
	} else if (j <= -0.00036) {
		tmp = t_1 + (18.0 * ((y * z) * (t * x)));
	} else if (j <= 5.8e-127) {
		tmp = t_2;
	} else {
		tmp = t_1 + (b * c);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	t_2 = (b * c) - (4.0 * ((x * i) + (t * a)))
	tmp = 0
	if j <= -3.2e+154:
		tmp = t_1 + (18.0 * (t * (z * (x * y))))
	elif j <= -1.8e+77:
		tmp = t_2
	elif j <= -0.00036:
		tmp = t_1 + (18.0 * ((y * z) * (t * x)))
	elif j <= 5.8e-127:
		tmp = t_2
	else:
		tmp = t_1 + (b * c)
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * -27.0))
	t_2 = Float64(Float64(b * c) - Float64(4.0 * Float64(Float64(x * i) + Float64(t * a))))
	tmp = 0.0
	if (j <= -3.2e+154)
		tmp = Float64(t_1 + Float64(18.0 * Float64(t * Float64(z * Float64(x * y)))));
	elseif (j <= -1.8e+77)
		tmp = t_2;
	elseif (j <= -0.00036)
		tmp = Float64(t_1 + Float64(18.0 * Float64(Float64(y * z) * Float64(t * x))));
	elseif (j <= 5.8e-127)
		tmp = t_2;
	else
		tmp = Float64(t_1 + Float64(b * c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * -27.0);
	t_2 = (b * c) - (4.0 * ((x * i) + (t * a)));
	tmp = 0.0;
	if (j <= -3.2e+154)
		tmp = t_1 + (18.0 * (t * (z * (x * y))));
	elseif (j <= -1.8e+77)
		tmp = t_2;
	elseif (j <= -0.00036)
		tmp = t_1 + (18.0 * ((y * z) * (t * x)));
	elseif (j <= 5.8e-127)
		tmp = t_2;
	else
		tmp = t_1 + (b * c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(N[(x * i), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -3.2e+154], N[(t$95$1 + N[(18.0 * N[(t * N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.8e+77], t$95$2, If[LessEqual[j, -0.00036], N[(t$95$1 + N[(18.0 * N[(N[(y * z), $MachinePrecision] * N[(t * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 5.8e-127], t$95$2, N[(t$95$1 + N[(b * c), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -3.2e154

   1. Initial program 90.6%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 87.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 62.4%

      \[\leadsto \color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} + j \cdot \left(k \cdot -27\right) \]
   6. Step-by-step derivation

      1. pow1 62.4%

         \[\leadsto 18 \cdot \left(t \cdot \color{blue}{{\left(x \cdot \left(y \cdot z\right)\right)}^{1}}\right) + j \cdot \left(k \cdot -27\right) \]

   7. Applied egg-rr 62.4%

      \[\leadsto 18 \cdot \left(t \cdot \color{blue}{{\left(x \cdot \left(y \cdot z\right)\right)}^{1}}\right) + j \cdot \left(k \cdot -27\right) \]
   8. Step-by-step derivation

      1. unpow1 62.4%

         \[\leadsto 18 \cdot \left(t \cdot \color{blue}{\left(x \cdot \left(y \cdot z\right)\right)}\right) + j \cdot \left(k \cdot -27\right) \]

      2. associate-*r* 65.4%

         \[\leadsto 18 \cdot \left(t \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot z\right)}\right) + j \cdot \left(k \cdot -27\right) \]

   9. Simplified 65.4%

      \[\leadsto 18 \cdot \left(t \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot z\right)}\right) + j \cdot \left(k \cdot -27\right) \]

   if -3.2e154 < j < -1.7999999999999999e77 or -3.60000000000000023e-4 < j < 5.8000000000000001e-127

   1. Initial program 85.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 72.4%

      \[\leadsto \color{blue}{\left(b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   4. Taylor expanded in j around 0 63.6%

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 63.6%

         \[\leadsto b \cdot c - \color{blue}{\left(4 \cdot \left(i \cdot x\right) + 4 \cdot \left(a \cdot t\right)\right)} \]

      2. associate-*r* 63.6%

         \[\leadsto b \cdot c - \left(\color{blue}{\left(4 \cdot i\right) \cdot x} + 4 \cdot \left(a \cdot t\right)\right) \]

      3. *-commutative 63.6%

         \[\leadsto b \cdot c - \left(\color{blue}{x \cdot \left(4 \cdot i\right)} + 4 \cdot \left(a \cdot t\right)\right) \]

      4. fma-define 63.6%

         \[\leadsto b \cdot c - \color{blue}{\mathsf{fma}\left(x, 4 \cdot i, 4 \cdot \left(a \cdot t\right)\right)} \]

      5. associate-*r* 63.6%

         \[\leadsto b \cdot c - \mathsf{fma}\left(x, 4 \cdot i, \color{blue}{\left(4 \cdot a\right) \cdot t}\right) \]

      6. *-commutative 63.6%

         \[\leadsto b \cdot c - \mathsf{fma}\left(x, 4 \cdot i, \color{blue}{\left(a \cdot 4\right)} \cdot t\right) \]

   6. Applied egg-rr 63.6%

      \[\leadsto b \cdot c - \color{blue}{\mathsf{fma}\left(x, 4 \cdot i, \left(a \cdot 4\right) \cdot t\right)} \]
   7. Step-by-step derivation

      1. fma-undefine 63.6%

         \[\leadsto b \cdot c - \color{blue}{\left(x \cdot \left(4 \cdot i\right) + \left(a \cdot 4\right) \cdot t\right)} \]

      2. *-commutative 63.6%

         \[\leadsto b \cdot c - \left(x \cdot \color{blue}{\left(i \cdot 4\right)} + \left(a \cdot 4\right) \cdot t\right) \]

      3. associate-*r* 63.6%

         \[\leadsto b \cdot c - \left(\color{blue}{\left(x \cdot i\right) \cdot 4} + \left(a \cdot 4\right) \cdot t\right) \]

      4. *-commutative 63.6%

         \[\leadsto b \cdot c - \left(\color{blue}{\left(i \cdot x\right)} \cdot 4 + \left(a \cdot 4\right) \cdot t\right) \]

      5. *-commutative 63.6%

         \[\leadsto b \cdot c - \left(\color{blue}{4 \cdot \left(i \cdot x\right)} + \left(a \cdot 4\right) \cdot t\right) \]

      6. *-commutative 63.6%

         \[\leadsto b \cdot c - \left(4 \cdot \left(i \cdot x\right) + \color{blue}{\left(4 \cdot a\right)} \cdot t\right) \]

      7. associate-*r* 63.6%

         \[\leadsto b \cdot c - \left(4 \cdot \left(i \cdot x\right) + \color{blue}{4 \cdot \left(a \cdot t\right)}\right) \]

      8. distribute-lft-out 63.6%

         \[\leadsto b \cdot c - \color{blue}{4 \cdot \left(i \cdot x + a \cdot t\right)} \]

      9. *-commutative 63.6%

         \[\leadsto b \cdot c - 4 \cdot \left(\color{blue}{x \cdot i} + a \cdot t\right) \]

      10. *-commutative 63.6%

          \[\leadsto b \cdot c - 4 \cdot \left(x \cdot i + \color{blue}{t \cdot a}\right) \]

   8. Simplified 63.6%

      \[\leadsto b \cdot c - \color{blue}{4 \cdot \left(x \cdot i + t \cdot a\right)} \]

   if -1.7999999999999999e77 < j < -3.60000000000000023e-4

   1. Initial program 92.5%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 92.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 75.9%

      \[\leadsto \color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} + j \cdot \left(k \cdot -27\right) \]
   6. Step-by-step derivation

      1. associate-*r* 83.1%

         \[\leadsto 18 \cdot \color{blue}{\left(\left(t \cdot x\right) \cdot \left(y \cdot z\right)\right)} + j \cdot \left(k \cdot -27\right) \]

   7. Simplified 83.1%

      \[\leadsto \color{blue}{18 \cdot \left(\left(t \cdot x\right) \cdot \left(y \cdot z\right)\right)} + j \cdot \left(k \cdot -27\right) \]

   if 5.8000000000000001e-127 < j

   1. Initial program 86.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 89.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 51.4%

      \[\leadsto \color{blue}{b \cdot c} + j \cdot \left(k \cdot -27\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 60.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -3.2 \cdot 10^{+154}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + 18 \cdot \left(t \cdot \left(z \cdot \left(x \cdot y\right)\right)\right)\\ \mathbf{elif}\;j \leq -1.8 \cdot 10^{+77}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\\ \mathbf{elif}\;j \leq -0.00036:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + 18 \cdot \left(\left(y \cdot z\right) \cdot \left(t \cdot x\right)\right)\\ \mathbf{elif}\;j \leq 5.8 \cdot 10^{-127}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 62.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y\right)\\ t_2 := j \cdot \left(k \cdot -27\right)\\ t_3 := b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\\ \mathbf{if}\;j \leq -5 \cdot 10^{+155}:\\ \;\;\;\;t\_2 + 18 \cdot \left(t \cdot t\_1\right)\\ \mathbf{elif}\;j \leq -5.5 \cdot 10^{+61}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;j \leq -1800000:\\ \;\;\;\;t \cdot \left(a \cdot \left(-4\right) - t\_1 \cdot -18\right)\\ \mathbf{elif}\;j \leq 5.8 \cdot 10^{-127}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2 + b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* z (* x y)))
        (t_2 (* j (* k -27.0)))
        (t_3 (- (* b c) (* 4.0 (+ (* x i) (* t a))))))
   (if (<= j -5e+155)
     (+ t_2 (* 18.0 (* t t_1)))
     (if (<= j -5.5e+61)
       t_3
       (if (<= j -1800000.0)
         (* t (- (* a (- 4.0)) (* t_1 -18.0)))
         (if (<= j 5.8e-127) t_3 (+ t_2 (* b c))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = z * (x * y);
	double t_2 = j * (k * -27.0);
	double t_3 = (b * c) - (4.0 * ((x * i) + (t * a)));
	double tmp;
	if (j <= -5e+155) {
		tmp = t_2 + (18.0 * (t * t_1));
	} else if (j <= -5.5e+61) {
		tmp = t_3;
	} else if (j <= -1800000.0) {
		tmp = t * ((a * -4.0) - (t_1 * -18.0));
	} else if (j <= 5.8e-127) {
		tmp = t_3;
	} else {
		tmp = t_2 + (b * c);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = z * (x * y)
    t_2 = j * (k * (-27.0d0))
    t_3 = (b * c) - (4.0d0 * ((x * i) + (t * a)))
    if (j <= (-5d+155)) then
        tmp = t_2 + (18.0d0 * (t * t_1))
    else if (j <= (-5.5d+61)) then
        tmp = t_3
    else if (j <= (-1800000.0d0)) then
        tmp = t * ((a * -4.0d0) - (t_1 * (-18.0d0)))
    else if (j <= 5.8d-127) then
        tmp = t_3
    else
        tmp = t_2 + (b * c)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = z * (x * y);
	double t_2 = j * (k * -27.0);
	double t_3 = (b * c) - (4.0 * ((x * i) + (t * a)));
	double tmp;
	if (j <= -5e+155) {
		tmp = t_2 + (18.0 * (t * t_1));
	} else if (j <= -5.5e+61) {
		tmp = t_3;
	} else if (j <= -1800000.0) {
		tmp = t * ((a * -4.0) - (t_1 * -18.0));
	} else if (j <= 5.8e-127) {
		tmp = t_3;
	} else {
		tmp = t_2 + (b * c);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = z * (x * y)
	t_2 = j * (k * -27.0)
	t_3 = (b * c) - (4.0 * ((x * i) + (t * a)))
	tmp = 0
	if j <= -5e+155:
		tmp = t_2 + (18.0 * (t * t_1))
	elif j <= -5.5e+61:
		tmp = t_3
	elif j <= -1800000.0:
		tmp = t * ((a * -4.0) - (t_1 * -18.0))
	elif j <= 5.8e-127:
		tmp = t_3
	else:
		tmp = t_2 + (b * c)
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(z * Float64(x * y))
	t_2 = Float64(j * Float64(k * -27.0))
	t_3 = Float64(Float64(b * c) - Float64(4.0 * Float64(Float64(x * i) + Float64(t * a))))
	tmp = 0.0
	if (j <= -5e+155)
		tmp = Float64(t_2 + Float64(18.0 * Float64(t * t_1)));
	elseif (j <= -5.5e+61)
		tmp = t_3;
	elseif (j <= -1800000.0)
		tmp = Float64(t * Float64(Float64(a * Float64(-4.0)) - Float64(t_1 * -18.0)));
	elseif (j <= 5.8e-127)
		tmp = t_3;
	else
		tmp = Float64(t_2 + Float64(b * c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = z * (x * y);
	t_2 = j * (k * -27.0);
	t_3 = (b * c) - (4.0 * ((x * i) + (t * a)));
	tmp = 0.0;
	if (j <= -5e+155)
		tmp = t_2 + (18.0 * (t * t_1));
	elseif (j <= -5.5e+61)
		tmp = t_3;
	elseif (j <= -1800000.0)
		tmp = t * ((a * -4.0) - (t_1 * -18.0));
	elseif (j <= 5.8e-127)
		tmp = t_3;
	else
		tmp = t_2 + (b * c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(N[(x * i), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -5e+155], N[(t$95$2 + N[(18.0 * N[(t * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -5.5e+61], t$95$3, If[LessEqual[j, -1800000.0], N[(t * N[(N[(a * (-4.0)), $MachinePrecision] - N[(t$95$1 * -18.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 5.8e-127], t$95$3, N[(t$95$2 + N[(b * c), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -4.9999999999999999e155

   1. Initial program 90.6%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 87.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 62.4%

      \[\leadsto \color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} + j \cdot \left(k \cdot -27\right) \]
   6. Step-by-step derivation

      1. pow1 62.4%

         \[\leadsto 18 \cdot \left(t \cdot \color{blue}{{\left(x \cdot \left(y \cdot z\right)\right)}^{1}}\right) + j \cdot \left(k \cdot -27\right) \]

   7. Applied egg-rr 62.4%

      \[\leadsto 18 \cdot \left(t \cdot \color{blue}{{\left(x \cdot \left(y \cdot z\right)\right)}^{1}}\right) + j \cdot \left(k \cdot -27\right) \]
   8. Step-by-step derivation

      1. unpow1 62.4%

         \[\leadsto 18 \cdot \left(t \cdot \color{blue}{\left(x \cdot \left(y \cdot z\right)\right)}\right) + j \cdot \left(k \cdot -27\right) \]

      2. associate-*r* 65.4%

         \[\leadsto 18 \cdot \left(t \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot z\right)}\right) + j \cdot \left(k \cdot -27\right) \]

   9. Simplified 65.4%

      \[\leadsto 18 \cdot \left(t \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot z\right)}\right) + j \cdot \left(k \cdot -27\right) \]

   if -4.9999999999999999e155 < j < -5.50000000000000036e61 or -1.8e6 < j < 5.8000000000000001e-127

   1. Initial program 86.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 72.8%

      \[\leadsto \color{blue}{\left(b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   4. Taylor expanded in j around 0 62.0%

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 62.0%

         \[\leadsto b \cdot c - \color{blue}{\left(4 \cdot \left(i \cdot x\right) + 4 \cdot \left(a \cdot t\right)\right)} \]

      2. associate-*r* 62.0%

         \[\leadsto b \cdot c - \left(\color{blue}{\left(4 \cdot i\right) \cdot x} + 4 \cdot \left(a \cdot t\right)\right) \]

      3. *-commutative 62.0%

         \[\leadsto b \cdot c - \left(\color{blue}{x \cdot \left(4 \cdot i\right)} + 4 \cdot \left(a \cdot t\right)\right) \]

      4. fma-define 62.0%

         \[\leadsto b \cdot c - \color{blue}{\mathsf{fma}\left(x, 4 \cdot i, 4 \cdot \left(a \cdot t\right)\right)} \]

      5. associate-*r* 62.0%

         \[\leadsto b \cdot c - \mathsf{fma}\left(x, 4 \cdot i, \color{blue}{\left(4 \cdot a\right) \cdot t}\right) \]

      6. *-commutative 62.0%

         \[\leadsto b \cdot c - \mathsf{fma}\left(x, 4 \cdot i, \color{blue}{\left(a \cdot 4\right)} \cdot t\right) \]

   6. Applied egg-rr 62.0%

      \[\leadsto b \cdot c - \color{blue}{\mathsf{fma}\left(x, 4 \cdot i, \left(a \cdot 4\right) \cdot t\right)} \]
   7. Step-by-step derivation

      1. fma-undefine 62.0%

         \[\leadsto b \cdot c - \color{blue}{\left(x \cdot \left(4 \cdot i\right) + \left(a \cdot 4\right) \cdot t\right)} \]

      2. *-commutative 62.0%

         \[\leadsto b \cdot c - \left(x \cdot \color{blue}{\left(i \cdot 4\right)} + \left(a \cdot 4\right) \cdot t\right) \]

      3. associate-*r* 62.0%

         \[\leadsto b \cdot c - \left(\color{blue}{\left(x \cdot i\right) \cdot 4} + \left(a \cdot 4\right) \cdot t\right) \]

      4. *-commutative 62.0%

         \[\leadsto b \cdot c - \left(\color{blue}{\left(i \cdot x\right)} \cdot 4 + \left(a \cdot 4\right) \cdot t\right) \]

      5. *-commutative 62.0%

         \[\leadsto b \cdot c - \left(\color{blue}{4 \cdot \left(i \cdot x\right)} + \left(a \cdot 4\right) \cdot t\right) \]

      6. *-commutative 62.0%

         \[\leadsto b \cdot c - \left(4 \cdot \left(i \cdot x\right) + \color{blue}{\left(4 \cdot a\right)} \cdot t\right) \]

      7. associate-*r* 62.0%

         \[\leadsto b \cdot c - \left(4 \cdot \left(i \cdot x\right) + \color{blue}{4 \cdot \left(a \cdot t\right)}\right) \]

      8. distribute-lft-out 62.0%

         \[\leadsto b \cdot c - \color{blue}{4 \cdot \left(i \cdot x + a \cdot t\right)} \]

      9. *-commutative 62.0%

         \[\leadsto b \cdot c - 4 \cdot \left(\color{blue}{x \cdot i} + a \cdot t\right) \]

      10. *-commutative 62.0%

          \[\leadsto b \cdot c - 4 \cdot \left(x \cdot i + \color{blue}{t \cdot a}\right) \]

   8. Simplified 62.0%

      \[\leadsto b \cdot c - \color{blue}{4 \cdot \left(x \cdot i + t \cdot a\right)} \]

   if -5.50000000000000036e61 < j < -1.8e6

   1. Initial program 88.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 88.2%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-*r* 88.2%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot z} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. distribute-rgt-out-- 88.2%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. associate-*l* 88.0%

         \[\leadsto \left(\left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot \left(z \cdot t\right)} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      4. *-commutative 88.0%

         \[\leadsto \left(\left(\color{blue}{\left(y \cdot \left(x \cdot 18\right)\right)} \cdot \left(z \cdot t\right) - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      5. *-commutative 88.0%

         \[\leadsto \left(\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) - \color{blue}{t \cdot \left(a \cdot 4\right)}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   6. Applied egg-rr 88.0%

      \[\leadsto \left(\color{blue}{\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) - t \cdot \left(a \cdot 4\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   7. Taylor expanded in t around -inf 51.1%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 51.1%

         \[\leadsto \color{blue}{\left(-1 \cdot t\right) \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right)} \]

      2. neg-mul-1 51.1%

         \[\leadsto \color{blue}{\left(-t\right)} \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right) \]

      3. cancel-sign-sub-inv 51.1%

         \[\leadsto \left(-t\right) \cdot \color{blue}{\left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + \left(--4\right) \cdot a\right)} \]

      4. metadata-eval 51.1%

         \[\leadsto \left(-t\right) \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + \color{blue}{4} \cdot a\right) \]

      5. *-commutative 51.1%

         \[\leadsto \left(-t\right) \cdot \left(\color{blue}{\left(x \cdot \left(y \cdot z\right)\right) \cdot -18} + 4 \cdot a\right) \]

      6. associate-*r* 51.3%

         \[\leadsto \left(-t\right) \cdot \left(\color{blue}{\left(\left(x \cdot y\right) \cdot z\right)} \cdot -18 + 4 \cdot a\right) \]

   9. Simplified 51.3%

      \[\leadsto \color{blue}{\left(-t\right) \cdot \left(\left(\left(x \cdot y\right) \cdot z\right) \cdot -18 + 4 \cdot a\right)} \]

   if 5.8000000000000001e-127 < j

   1. Initial program 86.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 89.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 51.4%

      \[\leadsto \color{blue}{b \cdot c} + j \cdot \left(k \cdot -27\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 58.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -5 \cdot 10^{+155}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + 18 \cdot \left(t \cdot \left(z \cdot \left(x \cdot y\right)\right)\right)\\ \mathbf{elif}\;j \leq -5.5 \cdot 10^{+61}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\\ \mathbf{elif}\;j \leq -1800000:\\ \;\;\;\;t \cdot \left(a \cdot \left(-4\right) - \left(z \cdot \left(x \cdot y\right)\right) \cdot -18\right)\\ \mathbf{elif}\;j \leq 5.8 \cdot 10^{-127}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 61.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\\ \mathbf{if}\;j \leq -3 \cdot 10^{+155}:\\ \;\;\;\;t\_1 + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;j \leq -2.75 \cdot 10^{+54}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -6000:\\ \;\;\;\;t \cdot \left(a \cdot \left(-4\right) - \left(z \cdot \left(x \cdot y\right)\right) \cdot -18\right)\\ \mathbf{elif}\;j \leq 5.8 \cdot 10^{-127}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1 + b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0))) (t_2 (- (* b c) (* 4.0 (+ (* x i) (* t a))))))
   (if (<= j -3e+155)
     (+ t_1 (* 18.0 (* t (* x (* y z)))))
     (if (<= j -2.75e+54)
       t_2
       (if (<= j -6000.0)
         (* t (- (* a (- 4.0)) (* (* z (* x y)) -18.0)))
         (if (<= j 5.8e-127) t_2 (+ t_1 (* b c))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = (b * c) - (4.0 * ((x * i) + (t * a)));
	double tmp;
	if (j <= -3e+155) {
		tmp = t_1 + (18.0 * (t * (x * (y * z))));
	} else if (j <= -2.75e+54) {
		tmp = t_2;
	} else if (j <= -6000.0) {
		tmp = t * ((a * -4.0) - ((z * (x * y)) * -18.0));
	} else if (j <= 5.8e-127) {
		tmp = t_2;
	} else {
		tmp = t_1 + (b * c);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * (k * (-27.0d0))
    t_2 = (b * c) - (4.0d0 * ((x * i) + (t * a)))
    if (j <= (-3d+155)) then
        tmp = t_1 + (18.0d0 * (t * (x * (y * z))))
    else if (j <= (-2.75d+54)) then
        tmp = t_2
    else if (j <= (-6000.0d0)) then
        tmp = t * ((a * -4.0d0) - ((z * (x * y)) * (-18.0d0)))
    else if (j <= 5.8d-127) then
        tmp = t_2
    else
        tmp = t_1 + (b * c)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = (b * c) - (4.0 * ((x * i) + (t * a)));
	double tmp;
	if (j <= -3e+155) {
		tmp = t_1 + (18.0 * (t * (x * (y * z))));
	} else if (j <= -2.75e+54) {
		tmp = t_2;
	} else if (j <= -6000.0) {
		tmp = t * ((a * -4.0) - ((z * (x * y)) * -18.0));
	} else if (j <= 5.8e-127) {
		tmp = t_2;
	} else {
		tmp = t_1 + (b * c);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	t_2 = (b * c) - (4.0 * ((x * i) + (t * a)))
	tmp = 0
	if j <= -3e+155:
		tmp = t_1 + (18.0 * (t * (x * (y * z))))
	elif j <= -2.75e+54:
		tmp = t_2
	elif j <= -6000.0:
		tmp = t * ((a * -4.0) - ((z * (x * y)) * -18.0))
	elif j <= 5.8e-127:
		tmp = t_2
	else:
		tmp = t_1 + (b * c)
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * -27.0))
	t_2 = Float64(Float64(b * c) - Float64(4.0 * Float64(Float64(x * i) + Float64(t * a))))
	tmp = 0.0
	if (j <= -3e+155)
		tmp = Float64(t_1 + Float64(18.0 * Float64(t * Float64(x * Float64(y * z)))));
	elseif (j <= -2.75e+54)
		tmp = t_2;
	elseif (j <= -6000.0)
		tmp = Float64(t * Float64(Float64(a * Float64(-4.0)) - Float64(Float64(z * Float64(x * y)) * -18.0)));
	elseif (j <= 5.8e-127)
		tmp = t_2;
	else
		tmp = Float64(t_1 + Float64(b * c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * -27.0);
	t_2 = (b * c) - (4.0 * ((x * i) + (t * a)));
	tmp = 0.0;
	if (j <= -3e+155)
		tmp = t_1 + (18.0 * (t * (x * (y * z))));
	elseif (j <= -2.75e+54)
		tmp = t_2;
	elseif (j <= -6000.0)
		tmp = t * ((a * -4.0) - ((z * (x * y)) * -18.0));
	elseif (j <= 5.8e-127)
		tmp = t_2;
	else
		tmp = t_1 + (b * c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(N[(x * i), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -3e+155], N[(t$95$1 + N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -2.75e+54], t$95$2, If[LessEqual[j, -6000.0], N[(t * N[(N[(a * (-4.0)), $MachinePrecision] - N[(N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision] * -18.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 5.8e-127], t$95$2, N[(t$95$1 + N[(b * c), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -3.0000000000000001e155

   1. Initial program 90.6%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 87.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 62.4%

      \[\leadsto \color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} + j \cdot \left(k \cdot -27\right) \]

   if -3.0000000000000001e155 < j < -2.75000000000000013e54 or -6e3 < j < 5.8000000000000001e-127

   1. Initial program 86.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 72.8%

      \[\leadsto \color{blue}{\left(b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   4. Taylor expanded in j around 0 62.0%

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 62.0%

         \[\leadsto b \cdot c - \color{blue}{\left(4 \cdot \left(i \cdot x\right) + 4 \cdot \left(a \cdot t\right)\right)} \]

      2. associate-*r* 62.0%

         \[\leadsto b \cdot c - \left(\color{blue}{\left(4 \cdot i\right) \cdot x} + 4 \cdot \left(a \cdot t\right)\right) \]

      3. *-commutative 62.0%

         \[\leadsto b \cdot c - \left(\color{blue}{x \cdot \left(4 \cdot i\right)} + 4 \cdot \left(a \cdot t\right)\right) \]

      4. fma-define 62.0%

         \[\leadsto b \cdot c - \color{blue}{\mathsf{fma}\left(x, 4 \cdot i, 4 \cdot \left(a \cdot t\right)\right)} \]

      5. associate-*r* 62.0%

         \[\leadsto b \cdot c - \mathsf{fma}\left(x, 4 \cdot i, \color{blue}{\left(4 \cdot a\right) \cdot t}\right) \]

      6. *-commutative 62.0%

         \[\leadsto b \cdot c - \mathsf{fma}\left(x, 4 \cdot i, \color{blue}{\left(a \cdot 4\right)} \cdot t\right) \]

   6. Applied egg-rr 62.0%

      \[\leadsto b \cdot c - \color{blue}{\mathsf{fma}\left(x, 4 \cdot i, \left(a \cdot 4\right) \cdot t\right)} \]
   7. Step-by-step derivation

      1. fma-undefine 62.0%

         \[\leadsto b \cdot c - \color{blue}{\left(x \cdot \left(4 \cdot i\right) + \left(a \cdot 4\right) \cdot t\right)} \]

      2. *-commutative 62.0%

         \[\leadsto b \cdot c - \left(x \cdot \color{blue}{\left(i \cdot 4\right)} + \left(a \cdot 4\right) \cdot t\right) \]

      3. associate-*r* 62.0%

         \[\leadsto b \cdot c - \left(\color{blue}{\left(x \cdot i\right) \cdot 4} + \left(a \cdot 4\right) \cdot t\right) \]

      4. *-commutative 62.0%

         \[\leadsto b \cdot c - \left(\color{blue}{\left(i \cdot x\right)} \cdot 4 + \left(a \cdot 4\right) \cdot t\right) \]

      5. *-commutative 62.0%

         \[\leadsto b \cdot c - \left(\color{blue}{4 \cdot \left(i \cdot x\right)} + \left(a \cdot 4\right) \cdot t\right) \]

      6. *-commutative 62.0%

         \[\leadsto b \cdot c - \left(4 \cdot \left(i \cdot x\right) + \color{blue}{\left(4 \cdot a\right)} \cdot t\right) \]

      7. associate-*r* 62.0%

         \[\leadsto b \cdot c - \left(4 \cdot \left(i \cdot x\right) + \color{blue}{4 \cdot \left(a \cdot t\right)}\right) \]

      8. distribute-lft-out 62.0%

         \[\leadsto b \cdot c - \color{blue}{4 \cdot \left(i \cdot x + a \cdot t\right)} \]

      9. *-commutative 62.0%

         \[\leadsto b \cdot c - 4 \cdot \left(\color{blue}{x \cdot i} + a \cdot t\right) \]

      10. *-commutative 62.0%

          \[\leadsto b \cdot c - 4 \cdot \left(x \cdot i + \color{blue}{t \cdot a}\right) \]

   8. Simplified 62.0%

      \[\leadsto b \cdot c - \color{blue}{4 \cdot \left(x \cdot i + t \cdot a\right)} \]

   if -2.75000000000000013e54 < j < -6e3

   1. Initial program 88.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 88.2%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-*r* 88.2%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot z} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. distribute-rgt-out-- 88.2%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. associate-*l* 88.0%

         \[\leadsto \left(\left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot \left(z \cdot t\right)} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      4. *-commutative 88.0%

         \[\leadsto \left(\left(\color{blue}{\left(y \cdot \left(x \cdot 18\right)\right)} \cdot \left(z \cdot t\right) - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      5. *-commutative 88.0%

         \[\leadsto \left(\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) - \color{blue}{t \cdot \left(a \cdot 4\right)}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   6. Applied egg-rr 88.0%

      \[\leadsto \left(\color{blue}{\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) - t \cdot \left(a \cdot 4\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   7. Taylor expanded in t around -inf 51.1%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 51.1%

         \[\leadsto \color{blue}{\left(-1 \cdot t\right) \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right)} \]

      2. neg-mul-1 51.1%

         \[\leadsto \color{blue}{\left(-t\right)} \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right) \]

      3. cancel-sign-sub-inv 51.1%

         \[\leadsto \left(-t\right) \cdot \color{blue}{\left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + \left(--4\right) \cdot a\right)} \]

      4. metadata-eval 51.1%

         \[\leadsto \left(-t\right) \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + \color{blue}{4} \cdot a\right) \]

      5. *-commutative 51.1%

         \[\leadsto \left(-t\right) \cdot \left(\color{blue}{\left(x \cdot \left(y \cdot z\right)\right) \cdot -18} + 4 \cdot a\right) \]

      6. associate-*r* 51.3%

         \[\leadsto \left(-t\right) \cdot \left(\color{blue}{\left(\left(x \cdot y\right) \cdot z\right)} \cdot -18 + 4 \cdot a\right) \]

   9. Simplified 51.3%

      \[\leadsto \color{blue}{\left(-t\right) \cdot \left(\left(\left(x \cdot y\right) \cdot z\right) \cdot -18 + 4 \cdot a\right)} \]

   if 5.8000000000000001e-127 < j

   1. Initial program 86.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 89.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 51.4%

      \[\leadsto \color{blue}{b \cdot c} + j \cdot \left(k \cdot -27\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -3 \cdot 10^{+155}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;j \leq -2.75 \cdot 10^{+54}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\\ \mathbf{elif}\;j \leq -6000:\\ \;\;\;\;t \cdot \left(a \cdot \left(-4\right) - \left(z \cdot \left(x \cdot y\right)\right) \cdot -18\right)\\ \mathbf{elif}\;j \leq 5.8 \cdot 10^{-127}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 52.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -0.085:\\ \;\;\;\;b \cdot c - x \cdot \left(i \cdot 4\right)\\ \mathbf{elif}\;b \cdot c \leq -4.2 \cdot 10^{-126} \lor \neg \left(b \cdot c \leq 8 \cdot 10^{+96}\right):\\ \;\;\;\;b \cdot c - t \cdot \left(a \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + i \cdot \left(x \cdot -4\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= (* b c) -0.085)
   (- (* b c) (* x (* i 4.0)))
   (if (or (<= (* b c) -4.2e-126) (not (<= (* b c) 8e+96)))
     (- (* b c) (* t (* a 4.0)))
     (+ (* j (* k -27.0)) (* i (* x -4.0))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b * c) <= -0.085) {
		tmp = (b * c) - (x * (i * 4.0));
	} else if (((b * c) <= -4.2e-126) || !((b * c) <= 8e+96)) {
		tmp = (b * c) - (t * (a * 4.0));
	} else {
		tmp = (j * (k * -27.0)) + (i * (x * -4.0));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((b * c) <= (-0.085d0)) then
        tmp = (b * c) - (x * (i * 4.0d0))
    else if (((b * c) <= (-4.2d-126)) .or. (.not. ((b * c) <= 8d+96))) then
        tmp = (b * c) - (t * (a * 4.0d0))
    else
        tmp = (j * (k * (-27.0d0))) + (i * (x * (-4.0d0)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b * c) <= -0.085) {
		tmp = (b * c) - (x * (i * 4.0));
	} else if (((b * c) <= -4.2e-126) || !((b * c) <= 8e+96)) {
		tmp = (b * c) - (t * (a * 4.0));
	} else {
		tmp = (j * (k * -27.0)) + (i * (x * -4.0));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (b * c) <= -0.085:
		tmp = (b * c) - (x * (i * 4.0))
	elif ((b * c) <= -4.2e-126) or not ((b * c) <= 8e+96):
		tmp = (b * c) - (t * (a * 4.0))
	else:
		tmp = (j * (k * -27.0)) + (i * (x * -4.0))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (Float64(b * c) <= -0.085)
		tmp = Float64(Float64(b * c) - Float64(x * Float64(i * 4.0)));
	elseif ((Float64(b * c) <= -4.2e-126) || !(Float64(b * c) <= 8e+96))
		tmp = Float64(Float64(b * c) - Float64(t * Float64(a * 4.0)));
	else
		tmp = Float64(Float64(j * Float64(k * -27.0)) + Float64(i * Float64(x * -4.0)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((b * c) <= -0.085)
		tmp = (b * c) - (x * (i * 4.0));
	elseif (((b * c) <= -4.2e-126) || ~(((b * c) <= 8e+96)))
		tmp = (b * c) - (t * (a * 4.0));
	else
		tmp = (j * (k * -27.0)) + (i * (x * -4.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[N[(b * c), $MachinePrecision], -0.085], N[(N[(b * c), $MachinePrecision] - N[(x * N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[N[(b * c), $MachinePrecision], -4.2e-126], N[Not[LessEqual[N[(b * c), $MachinePrecision], 8e+96]], $MachinePrecision]], N[(N[(b * c), $MachinePrecision] - N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(i * N[(x * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -0.0850000000000000061

   1. Initial program 82.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 74.3%

      \[\leadsto \color{blue}{\left(b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   4. Taylor expanded in j around 0 66.8%

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)} \]

   5. Taylor expanded in a around 0 59.6%

      \[\leadsto b \cdot c - \color{blue}{4 \cdot \left(i \cdot x\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 59.6%

         \[\leadsto b \cdot c - \color{blue}{\left(4 \cdot i\right) \cdot x} \]

   7. Simplified 59.6%

      \[\leadsto b \cdot c - \color{blue}{\left(4 \cdot i\right) \cdot x} \]

   if -0.0850000000000000061 < (*.f64 b c) < -4.1999999999999997e-126 or 8.0000000000000004e96 < (*.f64 b c)

   1. Initial program 84.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 68.3%

      \[\leadsto \color{blue}{\left(b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   4. Taylor expanded in j around 0 60.6%

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)} \]

   5. Taylor expanded in a around inf 53.3%

      \[\leadsto b \cdot c - \color{blue}{4 \cdot \left(a \cdot t\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 53.3%

         \[\leadsto b \cdot c - \color{blue}{\left(4 \cdot a\right) \cdot t} \]

      2. *-commutative 53.3%

         \[\leadsto b \cdot c - \color{blue}{t \cdot \left(4 \cdot a\right)} \]

   7. Simplified 53.3%

      \[\leadsto b \cdot c - \color{blue}{t \cdot \left(4 \cdot a\right)} \]

   if -4.1999999999999997e-126 < (*.f64 b c) < 8.0000000000000004e96

   1. Initial program 89.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 93.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around inf 54.5%

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right)} + j \cdot \left(k \cdot -27\right) \]
   6. Step-by-step derivation

      1. associate-*r* 54.5%

         \[\leadsto \color{blue}{\left(-4 \cdot i\right) \cdot x} + j \cdot \left(k \cdot -27\right) \]

      2. *-commutative 54.5%

         \[\leadsto \color{blue}{x \cdot \left(-4 \cdot i\right)} + j \cdot \left(k \cdot -27\right) \]

      3. associate-*r* 54.5%

         \[\leadsto \color{blue}{\left(x \cdot -4\right) \cdot i} + j \cdot \left(k \cdot -27\right) \]

      4. *-commutative 54.5%

         \[\leadsto \color{blue}{\left(-4 \cdot x\right)} \cdot i + j \cdot \left(k \cdot -27\right) \]

      5. *-commutative 54.5%

         \[\leadsto \color{blue}{i \cdot \left(-4 \cdot x\right)} + j \cdot \left(k \cdot -27\right) \]

   7. Simplified 54.5%

      \[\leadsto \color{blue}{i \cdot \left(-4 \cdot x\right)} + j \cdot \left(k \cdot -27\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 55.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -0.085:\\ \;\;\;\;b \cdot c - x \cdot \left(i \cdot 4\right)\\ \mathbf{elif}\;b \cdot c \leq -4.2 \cdot 10^{-126} \lor \neg \left(b \cdot c \leq 8 \cdot 10^{+96}\right):\\ \;\;\;\;b \cdot c - t \cdot \left(a \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + i \cdot \left(x \cdot -4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 79.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -3.7 \cdot 10^{+126} \lor \neg \left(t \leq 4.3 \cdot 10^{-79}\right):\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - \left(4 \cdot \left(t \cdot a\right) + 4 \cdot \left(x \cdot i\right)\right)\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= t -3.7e+126) (not (<= t 4.3e-79)))
   (+ (* j (* k -27.0)) (* t (+ (* 18.0 (* x (* y z))) (* a -4.0))))
   (- (- (* b c) (+ (* 4.0 (* t a)) (* 4.0 (* x i)))) (* k (* j 27.0)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((t <= -3.7e+126) || !(t <= 4.3e-79)) {
		tmp = (j * (k * -27.0)) + (t * ((18.0 * (x * (y * z))) + (a * -4.0)));
	} else {
		tmp = ((b * c) - ((4.0 * (t * a)) + (4.0 * (x * i)))) - (k * (j * 27.0));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((t <= (-3.7d+126)) .or. (.not. (t <= 4.3d-79))) then
        tmp = (j * (k * (-27.0d0))) + (t * ((18.0d0 * (x * (y * z))) + (a * (-4.0d0))))
    else
        tmp = ((b * c) - ((4.0d0 * (t * a)) + (4.0d0 * (x * i)))) - (k * (j * 27.0d0))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((t <= -3.7e+126) || !(t <= 4.3e-79)) {
		tmp = (j * (k * -27.0)) + (t * ((18.0 * (x * (y * z))) + (a * -4.0)));
	} else {
		tmp = ((b * c) - ((4.0 * (t * a)) + (4.0 * (x * i)))) - (k * (j * 27.0));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (t <= -3.7e+126) or not (t <= 4.3e-79):
		tmp = (j * (k * -27.0)) + (t * ((18.0 * (x * (y * z))) + (a * -4.0)))
	else:
		tmp = ((b * c) - ((4.0 * (t * a)) + (4.0 * (x * i)))) - (k * (j * 27.0))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((t <= -3.7e+126) || !(t <= 4.3e-79))
		tmp = Float64(Float64(j * Float64(k * -27.0)) + Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) + Float64(a * -4.0))));
	else
		tmp = Float64(Float64(Float64(b * c) - Float64(Float64(4.0 * Float64(t * a)) + Float64(4.0 * Float64(x * i)))) - Float64(k * Float64(j * 27.0)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((t <= -3.7e+126) || ~((t <= 4.3e-79)))
		tmp = (j * (k * -27.0)) + (t * ((18.0 * (x * (y * z))) + (a * -4.0)));
	else
		tmp = ((b * c) - ((4.0 * (t * a)) + (4.0 * (x * i)))) - (k * (j * 27.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[t, -3.7e+126], N[Not[LessEqual[t, 4.3e-79]], $MachinePrecision]], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] - N[(N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.6999999999999998e126 or 4.29999999999999982e-79 < t

   1. Initial program 87.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 92.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 86.7%

      \[\leadsto \color{blue}{t \cdot \left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} + j \cdot \left(k \cdot -27\right) \]

   if -3.6999999999999998e126 < t < 4.29999999999999982e-79

   1. Initial program 86.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 85.1%

      \[\leadsto \color{blue}{\left(b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]
3. Recombined 2 regimes into one program.

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.7 \cdot 10^{+126} \lor \neg \left(t \leq 4.3 \cdot 10^{-79}\right):\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - \left(4 \cdot \left(t \cdot a\right) + 4 \cdot \left(x \cdot i\right)\right)\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 50.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c - t \cdot \left(a \cdot 4\right)\\ \mathbf{if}\;a \leq -2.2 \cdot 10^{+95}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -5.2 \cdot 10^{+46}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{+17}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (- (* b c) (* t (* a 4.0)))))
   (if (<= a -2.2e+95)
     t_1
     (if (<= a -5.2e+46)
       (* -4.0 (* x i))
       (if (<= a 3.3e+17) (+ (* j (* k -27.0)) (* b c)) t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) - (t * (a * 4.0));
	double tmp;
	if (a <= -2.2e+95) {
		tmp = t_1;
	} else if (a <= -5.2e+46) {
		tmp = -4.0 * (x * i);
	} else if (a <= 3.3e+17) {
		tmp = (j * (k * -27.0)) + (b * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b * c) - (t * (a * 4.0d0))
    if (a <= (-2.2d+95)) then
        tmp = t_1
    else if (a <= (-5.2d+46)) then
        tmp = (-4.0d0) * (x * i)
    else if (a <= 3.3d+17) then
        tmp = (j * (k * (-27.0d0))) + (b * c)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) - (t * (a * 4.0));
	double tmp;
	if (a <= -2.2e+95) {
		tmp = t_1;
	} else if (a <= -5.2e+46) {
		tmp = -4.0 * (x * i);
	} else if (a <= 3.3e+17) {
		tmp = (j * (k * -27.0)) + (b * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) - (t * (a * 4.0))
	tmp = 0
	if a <= -2.2e+95:
		tmp = t_1
	elif a <= -5.2e+46:
		tmp = -4.0 * (x * i)
	elif a <= 3.3e+17:
		tmp = (j * (k * -27.0)) + (b * c)
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) - Float64(t * Float64(a * 4.0)))
	tmp = 0.0
	if (a <= -2.2e+95)
		tmp = t_1;
	elseif (a <= -5.2e+46)
		tmp = Float64(-4.0 * Float64(x * i));
	elseif (a <= 3.3e+17)
		tmp = Float64(Float64(j * Float64(k * -27.0)) + Float64(b * c));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) - (t * (a * 4.0));
	tmp = 0.0;
	if (a <= -2.2e+95)
		tmp = t_1;
	elseif (a <= -5.2e+46)
		tmp = -4.0 * (x * i);
	elseif (a <= 3.3e+17)
		tmp = (j * (k * -27.0)) + (b * c);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] - N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.2e+95], t$95$1, If[LessEqual[a, -5.2e+46], N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.3e+17], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.1999999999999999e95 or 3.3e17 < a

   1. Initial program 85.1%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 80.2%

      \[\leadsto \color{blue}{\left(b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   4. Taylor expanded in j around 0 69.8%

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)} \]

   5. Taylor expanded in a around inf 60.2%

      \[\leadsto b \cdot c - \color{blue}{4 \cdot \left(a \cdot t\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 60.2%

         \[\leadsto b \cdot c - \color{blue}{\left(4 \cdot a\right) \cdot t} \]

      2. *-commutative 60.2%

         \[\leadsto b \cdot c - \color{blue}{t \cdot \left(4 \cdot a\right)} \]

   7. Simplified 60.2%

      \[\leadsto b \cdot c - \color{blue}{t \cdot \left(4 \cdot a\right)} \]

   if -2.1999999999999999e95 < a < -5.20000000000000027e46

   1. Initial program 82.1%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 82.1%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-*r* 82.1%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot z} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. distribute-rgt-out-- 82.1%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. sub-neg 82.1%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(a \cdot 4\right) \cdot t\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      4. associate-*l* 90.8%

         \[\leadsto \left(\left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot \left(z \cdot t\right)} + \left(-\left(a \cdot 4\right) \cdot t\right)\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      5. *-commutative 90.8%

         \[\leadsto \left(\left(\color{blue}{\left(y \cdot \left(x \cdot 18\right)\right)} \cdot \left(z \cdot t\right) + \left(-\left(a \cdot 4\right) \cdot t\right)\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      6. *-commutative 90.8%

         \[\leadsto \left(\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) + \left(-\color{blue}{t \cdot \left(a \cdot 4\right)}\right)\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   6. Applied egg-rr 90.8%

      \[\leadsto \left(\color{blue}{\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) + \left(-t \cdot \left(a \cdot 4\right)\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
   7. Step-by-step derivation

      1. distribute-lft-neg-in 90.8%

         \[\leadsto \left(\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) + \color{blue}{\left(-t\right) \cdot \left(a \cdot 4\right)}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. *-commutative 90.8%

         \[\leadsto \left(\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) + \left(-t\right) \cdot \color{blue}{\left(4 \cdot a\right)}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. cancel-sign-sub-inv 90.8%

         \[\leadsto \left(\color{blue}{\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) - t \cdot \left(4 \cdot a\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      4. *-commutative 90.8%

         \[\leadsto \left(\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) - \color{blue}{\left(4 \cdot a\right) \cdot t}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      5. associate-*r* 82.1%

         \[\leadsto \left(\left(\color{blue}{\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot z\right) \cdot t} - \left(4 \cdot a\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      6. distribute-rgt-out-- 82.1%

         \[\leadsto \left(\color{blue}{t \cdot \left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot z - 4 \cdot a\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      7. associate-*r* 82.1%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(\left(y \cdot x\right) \cdot 18\right)} \cdot z - 4 \cdot a\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      8. *-commutative 82.1%

         \[\leadsto \left(t \cdot \left(\left(\color{blue}{\left(x \cdot y\right)} \cdot 18\right) \cdot z - 4 \cdot a\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      9. *-commutative 82.1%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(18 \cdot \left(x \cdot y\right)\right)} \cdot z - 4 \cdot a\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      10. *-commutative 82.1%

          \[\leadsto \left(t \cdot \left(\left(18 \cdot \left(x \cdot y\right)\right) \cdot z - \color{blue}{a \cdot 4}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   8. Simplified 82.1%

      \[\leadsto \left(\color{blue}{t \cdot \left(\left(18 \cdot \left(x \cdot y\right)\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   9. Taylor expanded in i around inf 63.0%

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right)} \]
   10. Step-by-step derivation

       1. *-commutative 63.0%

          \[\leadsto -4 \cdot \color{blue}{\left(x \cdot i\right)} \]

   11. Simplified 63.0%

       \[\leadsto \color{blue}{-4 \cdot \left(x \cdot i\right)} \]

   if -5.20000000000000027e46 < a < 3.3e17

   1. Initial program 87.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 88.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 49.9%

      \[\leadsto \color{blue}{b \cdot c} + j \cdot \left(k \cdot -27\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 54.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.2 \cdot 10^{+95}:\\ \;\;\;\;b \cdot c - t \cdot \left(a \cdot 4\right)\\ \mathbf{elif}\;a \leq -5.2 \cdot 10^{+46}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{+17}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - t \cdot \left(a \cdot 4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 47.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -5.8 \cdot 10^{+118} \lor \neg \left(a \leq 1.7 \cdot 10^{+122}\right):\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= a -5.8e+118) (not (<= a 1.7e+122)))
   (* t (* a -4.0))
   (+ (* j (* k -27.0)) (* b c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((a <= -5.8e+118) || !(a <= 1.7e+122)) {
		tmp = t * (a * -4.0);
	} else {
		tmp = (j * (k * -27.0)) + (b * c);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((a <= (-5.8d+118)) .or. (.not. (a <= 1.7d+122))) then
        tmp = t * (a * (-4.0d0))
    else
        tmp = (j * (k * (-27.0d0))) + (b * c)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((a <= -5.8e+118) || !(a <= 1.7e+122)) {
		tmp = t * (a * -4.0);
	} else {
		tmp = (j * (k * -27.0)) + (b * c);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (a <= -5.8e+118) or not (a <= 1.7e+122):
		tmp = t * (a * -4.0)
	else:
		tmp = (j * (k * -27.0)) + (b * c)
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((a <= -5.8e+118) || !(a <= 1.7e+122))
		tmp = Float64(t * Float64(a * -4.0));
	else
		tmp = Float64(Float64(j * Float64(k * -27.0)) + Float64(b * c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((a <= -5.8e+118) || ~((a <= 1.7e+122)))
		tmp = t * (a * -4.0);
	else
		tmp = (j * (k * -27.0)) + (b * c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[a, -5.8e+118], N[Not[LessEqual[a, 1.7e+122]], $MachinePrecision]], N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -5.80000000000000032e118 or 1.7e122 < a

   1. Initial program 83.6%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 87.3%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-*r* 88.8%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot z} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. distribute-rgt-out-- 83.6%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. associate-*l* 83.3%

         \[\leadsto \left(\left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot \left(z \cdot t\right)} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      4. *-commutative 83.3%

         \[\leadsto \left(\left(\color{blue}{\left(y \cdot \left(x \cdot 18\right)\right)} \cdot \left(z \cdot t\right) - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      5. *-commutative 83.3%

         \[\leadsto \left(\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) - \color{blue}{t \cdot \left(a \cdot 4\right)}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   6. Applied egg-rr 83.3%

      \[\leadsto \left(\color{blue}{\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) - t \cdot \left(a \cdot 4\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   7. Taylor expanded in a around inf 54.4%

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t\right)} \]
   8. Step-by-step derivation

      1. *-commutative 54.4%

         \[\leadsto \color{blue}{\left(a \cdot t\right) \cdot -4} \]

      2. *-commutative 54.4%

         \[\leadsto \color{blue}{\left(t \cdot a\right)} \cdot -4 \]

      3. associate-*r* 54.4%

         \[\leadsto \color{blue}{t \cdot \left(a \cdot -4\right)} \]

   9. Simplified 54.4%

      \[\leadsto \color{blue}{t \cdot \left(a \cdot -4\right)} \]

   if -5.80000000000000032e118 < a < 1.7e122

   1. Initial program 87.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 88.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 47.0%

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

4. Final simplification 49.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.8 \cdot 10^{+118} \lor \neg \left(a \leq 1.7 \cdot 10^{+122}\right):\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 28: 36.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -0.0235 \lor \neg \left(b \cdot c \leq 1.8 \cdot 10^{+103}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= (* b c) -0.0235) (not (<= (* b c) 1.8e+103)))
   (* b c)
   (* j (* k -27.0))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (((b * c) <= -0.0235) || !((b * c) <= 1.8e+103)) {
		tmp = b * c;
	} else {
		tmp = j * (k * -27.0);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (((b * c) <= (-0.0235d0)) .or. (.not. ((b * c) <= 1.8d+103))) then
        tmp = b * c
    else
        tmp = j * (k * (-27.0d0))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (((b * c) <= -0.0235) || !((b * c) <= 1.8e+103)) {
		tmp = b * c;
	} else {
		tmp = j * (k * -27.0);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if ((b * c) <= -0.0235) or not ((b * c) <= 1.8e+103):
		tmp = b * c
	else:
		tmp = j * (k * -27.0)
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((Float64(b * c) <= -0.0235) || !(Float64(b * c) <= 1.8e+103))
		tmp = Float64(b * c);
	else
		tmp = Float64(j * Float64(k * -27.0));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (((b * c) <= -0.0235) || ~(((b * c) <= 1.8e+103)))
		tmp = b * c;
	else
		tmp = j * (k * -27.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[N[(b * c), $MachinePrecision], -0.0235], N[Not[LessEqual[N[(b * c), $MachinePrecision], 1.8e+103]], $MachinePrecision]], N[(b * c), $MachinePrecision], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -0.0235 or 1.80000000000000008e103 < (*.f64 b c)

   1. Initial program 81.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 81.0%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-*r* 84.6%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot z} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. distribute-rgt-out-- 81.9%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. sub-neg 81.9%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(a \cdot 4\right) \cdot t\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      4. associate-*l* 81.6%

         \[\leadsto \left(\left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot \left(z \cdot t\right)} + \left(-\left(a \cdot 4\right) \cdot t\right)\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      5. *-commutative 81.6%

         \[\leadsto \left(\left(\color{blue}{\left(y \cdot \left(x \cdot 18\right)\right)} \cdot \left(z \cdot t\right) + \left(-\left(a \cdot 4\right) \cdot t\right)\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      6. *-commutative 81.6%

         \[\leadsto \left(\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) + \left(-\color{blue}{t \cdot \left(a \cdot 4\right)}\right)\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   6. Applied egg-rr 81.6%

      \[\leadsto \left(\color{blue}{\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) + \left(-t \cdot \left(a \cdot 4\right)\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
   7. Step-by-step derivation

      1. distribute-lft-neg-in 81.6%

         \[\leadsto \left(\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) + \color{blue}{\left(-t\right) \cdot \left(a \cdot 4\right)}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. *-commutative 81.6%

         \[\leadsto \left(\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) + \left(-t\right) \cdot \color{blue}{\left(4 \cdot a\right)}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. cancel-sign-sub-inv 81.6%

         \[\leadsto \left(\color{blue}{\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) - t \cdot \left(4 \cdot a\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      4. *-commutative 81.6%

         \[\leadsto \left(\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) - \color{blue}{\left(4 \cdot a\right) \cdot t}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      5. associate-*r* 81.9%

         \[\leadsto \left(\left(\color{blue}{\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot z\right) \cdot t} - \left(4 \cdot a\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      6. distribute-rgt-out-- 84.6%

         \[\leadsto \left(\color{blue}{t \cdot \left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot z - 4 \cdot a\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      7. associate-*r* 84.6%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(\left(y \cdot x\right) \cdot 18\right)} \cdot z - 4 \cdot a\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      8. *-commutative 84.6%

         \[\leadsto \left(t \cdot \left(\left(\color{blue}{\left(x \cdot y\right)} \cdot 18\right) \cdot z - 4 \cdot a\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      9. *-commutative 84.6%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(18 \cdot \left(x \cdot y\right)\right)} \cdot z - 4 \cdot a\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      10. *-commutative 84.6%

          \[\leadsto \left(t \cdot \left(\left(18 \cdot \left(x \cdot y\right)\right) \cdot z - \color{blue}{a \cdot 4}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   8. Simplified 84.6%

      \[\leadsto \left(\color{blue}{t \cdot \left(\left(18 \cdot \left(x \cdot y\right)\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   9. Taylor expanded in b around inf 45.8%

      \[\leadsto \color{blue}{b \cdot c} \]

   if -0.0235 < (*.f64 b c) < 1.80000000000000008e103

   1. Initial program 90.1%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 93.4%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-*r* 91.5%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot z} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. distribute-rgt-out-- 90.1%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. sub-neg 90.1%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(a \cdot 4\right) \cdot t\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      4. associate-*l* 87.3%

         \[\leadsto \left(\left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot \left(z \cdot t\right)} + \left(-\left(a \cdot 4\right) \cdot t\right)\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      5. *-commutative 87.3%

         \[\leadsto \left(\left(\color{blue}{\left(y \cdot \left(x \cdot 18\right)\right)} \cdot \left(z \cdot t\right) + \left(-\left(a \cdot 4\right) \cdot t\right)\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      6. *-commutative 87.3%

         \[\leadsto \left(\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) + \left(-\color{blue}{t \cdot \left(a \cdot 4\right)}\right)\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   6. Applied egg-rr 87.3%

      \[\leadsto \left(\color{blue}{\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) + \left(-t \cdot \left(a \cdot 4\right)\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
   7. Step-by-step derivation

      1. distribute-lft-neg-in 87.3%

         \[\leadsto \left(\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) + \color{blue}{\left(-t\right) \cdot \left(a \cdot 4\right)}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. *-commutative 87.3%

         \[\leadsto \left(\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) + \left(-t\right) \cdot \color{blue}{\left(4 \cdot a\right)}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. cancel-sign-sub-inv 87.3%

         \[\leadsto \left(\color{blue}{\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) - t \cdot \left(4 \cdot a\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      4. *-commutative 87.3%

         \[\leadsto \left(\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) - \color{blue}{\left(4 \cdot a\right) \cdot t}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      5. associate-*r* 90.1%

         \[\leadsto \left(\left(\color{blue}{\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot z\right) \cdot t} - \left(4 \cdot a\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      6. distribute-rgt-out-- 91.5%

         \[\leadsto \left(\color{blue}{t \cdot \left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot z - 4 \cdot a\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      7. associate-*r* 91.5%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(\left(y \cdot x\right) \cdot 18\right)} \cdot z - 4 \cdot a\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      8. *-commutative 91.5%

         \[\leadsto \left(t \cdot \left(\left(\color{blue}{\left(x \cdot y\right)} \cdot 18\right) \cdot z - 4 \cdot a\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      9. *-commutative 91.5%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(18 \cdot \left(x \cdot y\right)\right)} \cdot z - 4 \cdot a\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      10. *-commutative 91.5%

          \[\leadsto \left(t \cdot \left(\left(18 \cdot \left(x \cdot y\right)\right) \cdot z - \color{blue}{a \cdot 4}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   8. Simplified 91.5%

      \[\leadsto \left(\color{blue}{t \cdot \left(\left(18 \cdot \left(x \cdot y\right)\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   9. Taylor expanded in j around inf 32.0%

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

       1. metadata-eval 32.0%

          \[\leadsto \color{blue}{\left(-27\right)} \cdot \left(j \cdot k\right) \]

       2. distribute-lft-neg-in 32.0%

          \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]

       3. associate-*r* 32.0%

          \[\leadsto -\color{blue}{\left(27 \cdot j\right) \cdot k} \]

       4. *-commutative 32.0%

          \[\leadsto -\color{blue}{\left(j \cdot 27\right)} \cdot k \]

       5. associate-*r* 32.0%

          \[\leadsto -\color{blue}{j \cdot \left(27 \cdot k\right)} \]

       6. distribute-rgt-neg-in 32.0%

          \[\leadsto \color{blue}{j \cdot \left(-27 \cdot k\right)} \]

       7. distribute-lft-neg-in 32.0%

          \[\leadsto j \cdot \color{blue}{\left(\left(-27\right) \cdot k\right)} \]

       8. metadata-eval 32.0%

          \[\leadsto j \cdot \left(\color{blue}{-27} \cdot k\right) \]

       9. *-commutative 32.0%

          \[\leadsto j \cdot \color{blue}{\left(k \cdot -27\right)} \]

   11. Simplified 32.0%

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

4. Final simplification 37.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -0.0235 \lor \neg \left(b \cdot c \leq 1.8 \cdot 10^{+103}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 29: 36.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -0.0235 \lor \neg \left(b \cdot c \leq 5.9 \cdot 10^{+102}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= (* b c) -0.0235) (not (<= (* b c) 5.9e+102)))
   (* b c)
   (* -27.0 (* j k))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (((b * c) <= -0.0235) || !((b * c) <= 5.9e+102)) {
		tmp = b * c;
	} else {
		tmp = -27.0 * (j * k);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (((b * c) <= (-0.0235d0)) .or. (.not. ((b * c) <= 5.9d+102))) then
        tmp = b * c
    else
        tmp = (-27.0d0) * (j * k)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (((b * c) <= -0.0235) || !((b * c) <= 5.9e+102)) {
		tmp = b * c;
	} else {
		tmp = -27.0 * (j * k);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if ((b * c) <= -0.0235) or not ((b * c) <= 5.9e+102):
		tmp = b * c
	else:
		tmp = -27.0 * (j * k)
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((Float64(b * c) <= -0.0235) || !(Float64(b * c) <= 5.9e+102))
		tmp = Float64(b * c);
	else
		tmp = Float64(-27.0 * Float64(j * k));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (((b * c) <= -0.0235) || ~(((b * c) <= 5.9e+102)))
		tmp = b * c;
	else
		tmp = -27.0 * (j * k);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[N[(b * c), $MachinePrecision], -0.0235], N[Not[LessEqual[N[(b * c), $MachinePrecision], 5.9e+102]], $MachinePrecision]], N[(b * c), $MachinePrecision], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -0.0235 or 5.90000000000000005e102 < (*.f64 b c)

   1. Initial program 81.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 81.0%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-*r* 84.6%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot z} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. distribute-rgt-out-- 81.9%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. sub-neg 81.9%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(a \cdot 4\right) \cdot t\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      4. associate-*l* 81.6%

         \[\leadsto \left(\left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot \left(z \cdot t\right)} + \left(-\left(a \cdot 4\right) \cdot t\right)\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      5. *-commutative 81.6%

         \[\leadsto \left(\left(\color{blue}{\left(y \cdot \left(x \cdot 18\right)\right)} \cdot \left(z \cdot t\right) + \left(-\left(a \cdot 4\right) \cdot t\right)\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      6. *-commutative 81.6%

         \[\leadsto \left(\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) + \left(-\color{blue}{t \cdot \left(a \cdot 4\right)}\right)\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   6. Applied egg-rr 81.6%

      \[\leadsto \left(\color{blue}{\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) + \left(-t \cdot \left(a \cdot 4\right)\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
   7. Step-by-step derivation

      1. distribute-lft-neg-in 81.6%

         \[\leadsto \left(\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) + \color{blue}{\left(-t\right) \cdot \left(a \cdot 4\right)}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. *-commutative 81.6%

         \[\leadsto \left(\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) + \left(-t\right) \cdot \color{blue}{\left(4 \cdot a\right)}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. cancel-sign-sub-inv 81.6%

         \[\leadsto \left(\color{blue}{\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) - t \cdot \left(4 \cdot a\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      4. *-commutative 81.6%

         \[\leadsto \left(\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) - \color{blue}{\left(4 \cdot a\right) \cdot t}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      5. associate-*r* 81.9%

         \[\leadsto \left(\left(\color{blue}{\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot z\right) \cdot t} - \left(4 \cdot a\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      6. distribute-rgt-out-- 84.6%

         \[\leadsto \left(\color{blue}{t \cdot \left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot z - 4 \cdot a\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      7. associate-*r* 84.6%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(\left(y \cdot x\right) \cdot 18\right)} \cdot z - 4 \cdot a\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      8. *-commutative 84.6%

         \[\leadsto \left(t \cdot \left(\left(\color{blue}{\left(x \cdot y\right)} \cdot 18\right) \cdot z - 4 \cdot a\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      9. *-commutative 84.6%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(18 \cdot \left(x \cdot y\right)\right)} \cdot z - 4 \cdot a\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      10. *-commutative 84.6%

          \[\leadsto \left(t \cdot \left(\left(18 \cdot \left(x \cdot y\right)\right) \cdot z - \color{blue}{a \cdot 4}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   8. Simplified 84.6%

      \[\leadsto \left(\color{blue}{t \cdot \left(\left(18 \cdot \left(x \cdot y\right)\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   9. Taylor expanded in b around inf 45.8%

      \[\leadsto \color{blue}{b \cdot c} \]

   if -0.0235 < (*.f64 b c) < 5.90000000000000005e102

   1. Initial program 90.1%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 93.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in j around inf 32.0%

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

4. Final simplification 37.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -0.0235 \lor \neg \left(b \cdot c \leq 5.9 \cdot 10^{+102}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 30: 23.9% accurate, 10.3× speedup

Math

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

FPCore

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

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	return b * c;
}

Fortran

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

Java

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

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	return b * c

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	return Float64(b * c)
end

MATLAB

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

Wolfram

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

Derivation

1. Initial program 86.6%

   \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

3. Simplified 88.2%

   \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
4. Add Preprocessing
5. Step-by-step derivation

   1. associate-*r* 88.6%

      \[\leadsto \left(t \cdot \left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot z} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   2. distribute-rgt-out-- 86.6%

      \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   3. sub-neg 86.6%

      \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(a \cdot 4\right) \cdot t\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   4. associate-*l* 84.9%

      \[\leadsto \left(\left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot \left(z \cdot t\right)} + \left(-\left(a \cdot 4\right) \cdot t\right)\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   5. *-commutative 84.9%

      \[\leadsto \left(\left(\color{blue}{\left(y \cdot \left(x \cdot 18\right)\right)} \cdot \left(z \cdot t\right) + \left(-\left(a \cdot 4\right) \cdot t\right)\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   6. *-commutative 84.9%

      \[\leadsto \left(\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) + \left(-\color{blue}{t \cdot \left(a \cdot 4\right)}\right)\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

6. Applied egg-rr 84.9%

   \[\leadsto \left(\color{blue}{\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) + \left(-t \cdot \left(a \cdot 4\right)\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
7. Step-by-step derivation

   1. distribute-lft-neg-in 84.9%

      \[\leadsto \left(\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) + \color{blue}{\left(-t\right) \cdot \left(a \cdot 4\right)}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   2. *-commutative 84.9%

      \[\leadsto \left(\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) + \left(-t\right) \cdot \color{blue}{\left(4 \cdot a\right)}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   3. cancel-sign-sub-inv 84.9%

      \[\leadsto \left(\color{blue}{\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) - t \cdot \left(4 \cdot a\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   4. *-commutative 84.9%

      \[\leadsto \left(\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right) - \color{blue}{\left(4 \cdot a\right) \cdot t}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   5. associate-*r* 86.6%

      \[\leadsto \left(\left(\color{blue}{\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot z\right) \cdot t} - \left(4 \cdot a\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   6. distribute-rgt-out-- 88.6%

      \[\leadsto \left(\color{blue}{t \cdot \left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot z - 4 \cdot a\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   7. associate-*r* 88.6%

      \[\leadsto \left(t \cdot \left(\color{blue}{\left(\left(y \cdot x\right) \cdot 18\right)} \cdot z - 4 \cdot a\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   8. *-commutative 88.6%

      \[\leadsto \left(t \cdot \left(\left(\color{blue}{\left(x \cdot y\right)} \cdot 18\right) \cdot z - 4 \cdot a\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   9. *-commutative 88.6%

      \[\leadsto \left(t \cdot \left(\color{blue}{\left(18 \cdot \left(x \cdot y\right)\right)} \cdot z - 4 \cdot a\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   10. *-commutative 88.6%

       \[\leadsto \left(t \cdot \left(\left(18 \cdot \left(x \cdot y\right)\right) \cdot z - \color{blue}{a \cdot 4}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

8. Simplified 88.6%

   \[\leadsto \left(\color{blue}{t \cdot \left(\left(18 \cdot \left(x \cdot y\right)\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

9. Taylor expanded in b around inf 21.1%

   \[\leadsto \color{blue}{b \cdot c} \]
10. Add Preprocessing

Developer target: 89.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a \cdot t + i \cdot x\right) \cdot 4\\ t_2 := \left(\left(18 \cdot t\right) \cdot \left(\left(x \cdot y\right) \cdot z\right) - t\_1\right) - \left(\left(k \cdot j\right) \cdot 27 - c \cdot b\right)\\ \mathbf{if}\;t < -1.6210815397541398 \cdot 10^{-69}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t < 165.68027943805222:\\ \;\;\;\;\left(\left(18 \cdot y\right) \cdot \left(x \cdot \left(z \cdot t\right)\right) - t\_1\right) + \left(c \cdot b - 27 \cdot \left(k \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (+ (* a t) (* i x)) 4.0))
        (t_2
         (-
          (- (* (* 18.0 t) (* (* x y) z)) t_1)
          (- (* (* k j) 27.0) (* c b)))))
   (if (< t -1.6210815397541398e-69)
     t_2
     (if (< t 165.68027943805222)
       (+ (- (* (* 18.0 y) (* x (* z t))) t_1) (- (* c b) (* 27.0 (* k j))))
       t_2))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((a * t) + (i * x)) * 4.0;
	double t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b));
	double tmp;
	if (t < -1.6210815397541398e-69) {
		tmp = t_2;
	} else if (t < 165.68027943805222) {
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((a * t) + (i * x)) * 4.0d0
    t_2 = (((18.0d0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0d0) - (c * b))
    if (t < (-1.6210815397541398d-69)) then
        tmp = t_2
    else if (t < 165.68027943805222d0) then
        tmp = (((18.0d0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0d0 * (k * j)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((a * t) + (i * x)) * 4.0;
	double t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b));
	double tmp;
	if (t < -1.6210815397541398e-69) {
		tmp = t_2;
	} else if (t < 165.68027943805222) {
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = ((a * t) + (i * x)) * 4.0
	t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b))
	tmp = 0
	if t < -1.6210815397541398e-69:
		tmp = t_2
	elif t < 165.68027943805222:
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(Float64(a * t) + Float64(i * x)) * 4.0)
	t_2 = Float64(Float64(Float64(Float64(18.0 * t) * Float64(Float64(x * y) * z)) - t_1) - Float64(Float64(Float64(k * j) * 27.0) - Float64(c * b)))
	tmp = 0.0
	if (t < -1.6210815397541398e-69)
		tmp = t_2;
	elseif (t < 165.68027943805222)
		tmp = Float64(Float64(Float64(Float64(18.0 * y) * Float64(x * Float64(z * t))) - t_1) + Float64(Float64(c * b) - Float64(27.0 * Float64(k * j))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = ((a * t) + (i * x)) * 4.0;
	t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b));
	tmp = 0.0;
	if (t < -1.6210815397541398e-69)
		tmp = t_2;
	elseif (t < 165.68027943805222)
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(N[(a * t), $MachinePrecision] + N[(i * x), $MachinePrecision]), $MachinePrecision] * 4.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(18.0 * t), $MachinePrecision] * N[(N[(x * y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] - N[(N[(N[(k * j), $MachinePrecision] * 27.0), $MachinePrecision] - N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -1.6210815397541398e-69], t$95$2, If[Less[t, 165.68027943805222], N[(N[(N[(N[(18.0 * y), $MachinePrecision] * N[(x * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] + N[(N[(c * b), $MachinePrecision] - N[(27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2024092 
(FPCore (x y z t a b c i j k)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, E"
  :precision binary64

  :alt
  (if (< t -1.6210815397541398e-69) (- (- (* (* 18.0 t) (* (* x y) z)) (* (+ (* a t) (* i x)) 4.0)) (- (* (* k j) 27.0) (* c b))) (if (< t 165.68027943805222) (+ (- (* (* 18.0 y) (* x (* z t))) (* (+ (* a t) (* i x)) 4.0)) (- (* c b) (* 27.0 (* k j)))) (- (- (* (* 18.0 t) (* (* x y) z)) (* (+ (* a t) (* i x)) 4.0)) (- (* (* k j) 27.0) (* c b)))))

  (- (- (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i)) (* (* j 27.0) k)))