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

Percentage Accurate: 85.8% → 91.4%

Time: 22.3s

Alternatives: 22

Speedup: 0.9×

• 50.6% 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: 85.8% 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: 91.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{+267}:\\ \;\;\;\;t \cdot \left(a \cdot -4 + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq -2 \cdot 10^{+68} \lor \neg \left(t \leq 2 \cdot 10^{-28}\right):\\ \;\;\;\;\left(b \cdot c + t \cdot \left(y \cdot \left(x \cdot \left(18 \cdot z\right)\right) - a \cdot 4\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b \cdot c + \left(y \cdot \left(\left(x \cdot 18\right) \cdot \left(z \cdot t\right)\right) - t \cdot \left(a \cdot 4\right)\right)\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= t -3.5e+267)
   (* t (+ (* a -4.0) (* 18.0 (* x (* y z)))))
   (if (or (<= t -2e+68) (not (<= t 2e-28)))
     (-
      (+ (* b c) (* t (- (* y (* x (* 18.0 z))) (* a 4.0))))
      (+ (* x (* 4.0 i)) (* j (* 27.0 k))))
     (-
      (-
       (+ (* b c) (- (* y (* (* x 18.0) (* z t))) (* t (* a 4.0))))
       (* (* x 4.0) i))
      (* (* j 27.0) k)))))

C

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 <= -3.5e+267) {
		tmp = t * ((a * -4.0) + (18.0 * (x * (y * z))));
	} else if ((t <= -2e+68) || !(t <= 2e-28)) {
		tmp = ((b * c) + (t * ((y * (x * (18.0 * z))) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	} else {
		tmp = (((b * c) + ((y * ((x * 18.0) * (z * t))) - (t * (a * 4.0)))) - ((x * 4.0) * i)) - ((j * 27.0) * 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.
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 <= (-3.5d+267)) then
        tmp = t * ((a * (-4.0d0)) + (18.0d0 * (x * (y * z))))
    else if ((t <= (-2d+68)) .or. (.not. (t <= 2d-28))) then
        tmp = ((b * c) + (t * ((y * (x * (18.0d0 * z))) - (a * 4.0d0)))) - ((x * (4.0d0 * i)) + (j * (27.0d0 * k)))
    else
        tmp = (((b * c) + ((y * ((x * 18.0d0) * (z * t))) - (t * (a * 4.0d0)))) - ((x * 4.0d0) * i)) - ((j * 27.0d0) * 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;
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 <= -3.5e+267) {
		tmp = t * ((a * -4.0) + (18.0 * (x * (y * z))));
	} else if ((t <= -2e+68) || !(t <= 2e-28)) {
		tmp = ((b * c) + (t * ((y * (x * (18.0 * z))) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	} else {
		tmp = (((b * c) + ((y * ((x * 18.0) * (z * t))) - (t * (a * 4.0)))) - ((x * 4.0) * i)) - ((j * 27.0) * 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])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if t <= -3.5e+267:
		tmp = t * ((a * -4.0) + (18.0 * (x * (y * z))))
	elif (t <= -2e+68) or not (t <= 2e-28):
		tmp = ((b * c) + (t * ((y * (x * (18.0 * z))) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)))
	else:
		tmp = (((b * c) + ((y * ((x * 18.0) * (z * t))) - (t * (a * 4.0)))) - ((x * 4.0) * i)) - ((j * 27.0) * 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])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (t <= -3.5e+267)
		tmp = Float64(t * Float64(Float64(a * -4.0) + Float64(18.0 * Float64(x * Float64(y * z)))));
	elseif ((t <= -2e+68) || !(t <= 2e-28))
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(y * Float64(x * Float64(18.0 * z))) - Float64(a * 4.0)))) - Float64(Float64(x * Float64(4.0 * i)) + Float64(j * Float64(27.0 * k))));
	else
		tmp = Float64(Float64(Float64(Float64(b * c) + Float64(Float64(y * Float64(Float64(x * 18.0) * Float64(z * t))) - Float64(t * Float64(a * 4.0)))) - Float64(Float64(x * 4.0) * i)) - Float64(Float64(j * 27.0) * 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])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (t <= -3.5e+267)
		tmp = t * ((a * -4.0) + (18.0 * (x * (y * z))));
	elseif ((t <= -2e+68) || ~((t <= 2e-28)))
		tmp = ((b * c) + (t * ((y * (x * (18.0 * z))) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	else
		tmp = (((b * c) + ((y * ((x * 18.0) * (z * t))) - (t * (a * 4.0)))) - ((x * 4.0) * i)) - ((j * 27.0) * 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.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[t, -3.5e+267], N[(t * N[(N[(a * -4.0), $MachinePrecision] + N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, -2e+68], N[Not[LessEqual[t, 2e-28]], $MachinePrecision]], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(y * N[(x * N[(18.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision] + N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(b * c), $MachinePrecision] + N[(N[(y * N[(N[(x * 18.0), $MachinePrecision] * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.4999999999999999e267

   1. Initial program 45.5%

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

   3. Simplified 54.5%

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

   5. Taylor expanded in t around inf 81.8%

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

   6. Taylor expanded in t around inf 100.0%

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

   if -3.4999999999999999e267 < t < -1.99999999999999991e68 or 1.99999999999999994e-28 < t

   1. Initial program 82.9%

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

   3. Simplified 87.6%

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

      1. pow1 87.6%

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

      2. associate-*l* 87.6%

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

      3. associate-*r* 87.6%

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

   6. Applied egg-rr 87.6%

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

      1. unpow1 87.6%

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

      2. *-commutative 87.6%

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

   8. Simplified 87.6%

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

      1. pow1 87.6%

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

      2. associate-*r* 87.6%

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

   10. Applied egg-rr 87.6%

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

       1. unpow1 87.6%

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

       2. associate-*r* 93.6%

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

       3. *-commutative 93.6%

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

   12. Simplified 93.6%

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

   if -1.99999999999999991e68 < t < 1.99999999999999994e-28

   1. Initial program 85.5%

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

      1. pow1 85.5%

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

      2. associate-*l* 88.9%

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

      3. *-commutative 88.9%

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

   4. Applied egg-rr 88.9%

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

      1. unpow1 88.9%

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

      2. associate-*l* 96.3%

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

      3. *-commutative 96.3%

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

   6. Simplified 96.3%

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

4. Final simplification 95.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{+267}:\\ \;\;\;\;t \cdot \left(a \cdot -4 + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq -2 \cdot 10^{+68} \lor \neg \left(t \leq 2 \cdot 10^{-28}\right):\\ \;\;\;\;\left(b \cdot c + t \cdot \left(y \cdot \left(x \cdot \left(18 \cdot z\right)\right) - a \cdot 4\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b \cdot c + \left(y \cdot \left(\left(x \cdot 18\right) \cdot \left(z \cdot t\right)\right) - t \cdot \left(a \cdot 4\right)\right)\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 92.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(x \cdot 4\right) \cdot i\\ t_2 := \left(j \cdot 27\right) \cdot k\\ t_3 := t \cdot \left(a \cdot 4\right)\\ t_4 := \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - t\_3\right) + b \cdot c\right) - t\_1\right) - t\_2\\ \mathbf{if}\;t\_4 \leq 2 \cdot 10^{+304}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t\_4 \leq \infty:\\ \;\;\;\;\left(\left(b \cdot c + \left(y \cdot \left(\left(x \cdot 18\right) \cdot \left(z \cdot t\right)\right) - t\_3\right)\right) - t\_1\right) - t\_2\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* x 4.0) i))
        (t_2 (* (* j 27.0) k))
        (t_3 (* t (* a 4.0)))
        (t_4 (- (- (+ (- (* (* (* (* x 18.0) y) z) t) t_3) (* b c)) t_1) t_2)))
   (if (<= t_4 2e+304)
     t_4
     (if (<= t_4 INFINITY)
       (- (- (+ (* b c) (- (* y (* (* x 18.0) (* z t))) t_3)) t_1) t_2)
       (* x (- (* 18.0 (* t (* y z))) (* 4.0 i)))))))

C

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 = (x * 4.0) * i;
	double t_2 = (j * 27.0) * k;
	double t_3 = t * (a * 4.0);
	double t_4 = (((((((x * 18.0) * y) * z) * t) - t_3) + (b * c)) - t_1) - t_2;
	double tmp;
	if (t_4 <= 2e+304) {
		tmp = t_4;
	} else if (t_4 <= ((double) INFINITY)) {
		tmp = (((b * c) + ((y * ((x * 18.0) * (z * t))) - t_3)) - t_1) - t_2;
	} else {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	}
	return tmp;
}

Java

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 = (x * 4.0) * i;
	double t_2 = (j * 27.0) * k;
	double t_3 = t * (a * 4.0);
	double t_4 = (((((((x * 18.0) * y) * z) * t) - t_3) + (b * c)) - t_1) - t_2;
	double tmp;
	if (t_4 <= 2e+304) {
		tmp = t_4;
	} else if (t_4 <= Double.POSITIVE_INFINITY) {
		tmp = (((b * c) + ((y * ((x * 18.0) * (z * t))) - t_3)) - t_1) - t_2;
	} else {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	}
	return tmp;
}

Python

[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 = (x * 4.0) * i
	t_2 = (j * 27.0) * k
	t_3 = t * (a * 4.0)
	t_4 = (((((((x * 18.0) * y) * z) * t) - t_3) + (b * c)) - t_1) - t_2
	tmp = 0
	if t_4 <= 2e+304:
		tmp = t_4
	elif t_4 <= math.inf:
		tmp = (((b * c) + ((y * ((x * 18.0) * (z * t))) - t_3)) - t_1) - t_2
	else:
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i))
	return tmp

Julia

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(x * 4.0) * i)
	t_2 = Float64(Float64(j * 27.0) * k)
	t_3 = Float64(t * Float64(a * 4.0))
	t_4 = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 18.0) * y) * z) * t) - t_3) + Float64(b * c)) - t_1) - t_2)
	tmp = 0.0
	if (t_4 <= 2e+304)
		tmp = t_4;
	elseif (t_4 <= Inf)
		tmp = Float64(Float64(Float64(Float64(b * c) + Float64(Float64(y * Float64(Float64(x * 18.0) * Float64(z * t))) - t_3)) - t_1) - t_2);
	else
		tmp = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)));
	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])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (x * 4.0) * i;
	t_2 = (j * 27.0) * k;
	t_3 = t * (a * 4.0);
	t_4 = (((((((x * 18.0) * y) * z) * t) - t_3) + (b * c)) - t_1) - t_2;
	tmp = 0.0;
	if (t_4 <= 2e+304)
		tmp = t_4;
	elseif (t_4 <= Inf)
		tmp = (((b * c) + ((y * ((x * 18.0) * (z * t))) - t_3)) - t_1) - t_2;
	else
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	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.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(N[(N[(N[(N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision] - t$95$3), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision]}, If[LessEqual[t$95$4, 2e+304], t$95$4, If[LessEqual[t$95$4, Infinity], N[(N[(N[(N[(b * c), $MachinePrecision] + N[(N[(y * N[(N[(x * 18.0), $MachinePrecision] * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$3), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision], N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x #s(literal 18 binary64)) y) z) t) (*.f64 (*.f64 a #s(literal 4 binary64)) t)) (*.f64 b c)) (*.f64 (*.f64 x #s(literal 4 binary64)) i)) (*.f64 (*.f64 j #s(literal 27 binary64)) k)) < 1.9999999999999999e304

   1. Initial program 94.5%

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

   if 1.9999999999999999e304 < (-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x #s(literal 18 binary64)) y) z) t) (*.f64 (*.f64 a #s(literal 4 binary64)) t)) (*.f64 b c)) (*.f64 (*.f64 x #s(literal 4 binary64)) i)) (*.f64 (*.f64 j #s(literal 27 binary64)) k)) < +inf.0

   1. Initial program 90.3%

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

      1. pow1 90.3%

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

      2. associate-*l* 88.0%

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

      3. *-commutative 88.0%

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

   4. Applied egg-rr 88.0%

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

      1. unpow1 88.0%

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

      2. associate-*l* 95.9%

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

      3. *-commutative 95.9%

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

   6. Simplified 95.9%

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

   if +inf.0 < (-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x #s(literal 18 binary64)) y) z) t) (*.f64 (*.f64 a #s(literal 4 binary64)) t)) (*.f64 b c)) (*.f64 (*.f64 x #s(literal 4 binary64)) i)) (*.f64 (*.f64 j #s(literal 27 binary64)) k))

   1. Initial program 0.0%

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

   3. Simplified 26.7%

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

   5. Taylor expanded in x around inf 76.7%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \leq 2 \cdot 10^{+304}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \leq \infty:\\ \;\;\;\;\left(\left(b \cdot c + \left(y \cdot \left(\left(x \cdot 18\right) \cdot \left(z \cdot t\right)\right) - t \cdot \left(a \cdot 4\right)\right)\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 53.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(z \cdot t\right) \cdot \left(18 \cdot \left(x \cdot y\right)\right)\\ t_2 := j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\\ \mathbf{if}\;b \cdot c \leq -5 \cdot 10^{+135}:\\ \;\;\;\;b \cdot \left(c + -27 \cdot \left(j \cdot \frac{k}{b}\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 5 \cdot 10^{-223}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \cdot c \leq 2 \cdot 10^{-172}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq 0.004:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \cdot c \leq 5 \cdot 10^{+97}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(b + -27 \cdot \frac{j \cdot k}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* z t) (* 18.0 (* x y))))
        (t_2 (+ (* j (* k -27.0)) (* -4.0 (* t a)))))
   (if (<= (* b c) -5e+135)
     (* b (+ c (* -27.0 (* j (/ k b)))))
     (if (<= (* b c) 5e-223)
       t_2
       (if (<= (* b c) 2e-172)
         t_1
         (if (<= (* b c) 0.004)
           t_2
           (if (<= (* b c) 5e+97)
             t_1
             (* c (+ b (* -27.0 (/ (* j k) c)))))))))))

C

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 * t) * (18.0 * (x * y));
	double t_2 = (j * (k * -27.0)) + (-4.0 * (t * a));
	double tmp;
	if ((b * c) <= -5e+135) {
		tmp = b * (c + (-27.0 * (j * (k / b))));
	} else if ((b * c) <= 5e-223) {
		tmp = t_2;
	} else if ((b * c) <= 2e-172) {
		tmp = t_1;
	} else if ((b * c) <= 0.004) {
		tmp = t_2;
	} else if ((b * c) <= 5e+97) {
		tmp = t_1;
	} else {
		tmp = c * (b + (-27.0 * ((j * k) / 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.
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 = (z * t) * (18.0d0 * (x * y))
    t_2 = (j * (k * (-27.0d0))) + ((-4.0d0) * (t * a))
    if ((b * c) <= (-5d+135)) then
        tmp = b * (c + ((-27.0d0) * (j * (k / b))))
    else if ((b * c) <= 5d-223) then
        tmp = t_2
    else if ((b * c) <= 2d-172) then
        tmp = t_1
    else if ((b * c) <= 0.004d0) then
        tmp = t_2
    else if ((b * c) <= 5d+97) then
        tmp = t_1
    else
        tmp = c * (b + ((-27.0d0) * ((j * k) / 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;
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 * t) * (18.0 * (x * y));
	double t_2 = (j * (k * -27.0)) + (-4.0 * (t * a));
	double tmp;
	if ((b * c) <= -5e+135) {
		tmp = b * (c + (-27.0 * (j * (k / b))));
	} else if ((b * c) <= 5e-223) {
		tmp = t_2;
	} else if ((b * c) <= 2e-172) {
		tmp = t_1;
	} else if ((b * c) <= 0.004) {
		tmp = t_2;
	} else if ((b * c) <= 5e+97) {
		tmp = t_1;
	} else {
		tmp = c * (b + (-27.0 * ((j * k) / 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])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (z * t) * (18.0 * (x * y))
	t_2 = (j * (k * -27.0)) + (-4.0 * (t * a))
	tmp = 0
	if (b * c) <= -5e+135:
		tmp = b * (c + (-27.0 * (j * (k / b))))
	elif (b * c) <= 5e-223:
		tmp = t_2
	elif (b * c) <= 2e-172:
		tmp = t_1
	elif (b * c) <= 0.004:
		tmp = t_2
	elif (b * c) <= 5e+97:
		tmp = t_1
	else:
		tmp = c * (b + (-27.0 * ((j * k) / 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])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(z * t) * Float64(18.0 * Float64(x * y)))
	t_2 = Float64(Float64(j * Float64(k * -27.0)) + Float64(-4.0 * Float64(t * a)))
	tmp = 0.0
	if (Float64(b * c) <= -5e+135)
		tmp = Float64(b * Float64(c + Float64(-27.0 * Float64(j * Float64(k / b)))));
	elseif (Float64(b * c) <= 5e-223)
		tmp = t_2;
	elseif (Float64(b * c) <= 2e-172)
		tmp = t_1;
	elseif (Float64(b * c) <= 0.004)
		tmp = t_2;
	elseif (Float64(b * c) <= 5e+97)
		tmp = t_1;
	else
		tmp = Float64(c * Float64(b + Float64(-27.0 * Float64(Float64(j * k) / 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])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (z * t) * (18.0 * (x * y));
	t_2 = (j * (k * -27.0)) + (-4.0 * (t * a));
	tmp = 0.0;
	if ((b * c) <= -5e+135)
		tmp = b * (c + (-27.0 * (j * (k / b))));
	elseif ((b * c) <= 5e-223)
		tmp = t_2;
	elseif ((b * c) <= 2e-172)
		tmp = t_1;
	elseif ((b * c) <= 0.004)
		tmp = t_2;
	elseif ((b * c) <= 5e+97)
		tmp = t_1;
	else
		tmp = c * (b + (-27.0 * ((j * k) / 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.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(z * t), $MachinePrecision] * N[(18.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -5e+135], N[(b * N[(c + N[(-27.0 * N[(j * N[(k / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 5e-223], t$95$2, If[LessEqual[N[(b * c), $MachinePrecision], 2e-172], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 0.004], t$95$2, If[LessEqual[N[(b * c), $MachinePrecision], 5e+97], t$95$1, N[(c * N[(b + N[(-27.0 * N[(N[(j * k), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 b c) < -5.00000000000000029e135

   1. Initial program 75.2%

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

      1. pow1 75.2%

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

      2. associate-*l* 75.2%

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

      3. *-commutative 75.2%

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

   4. Applied egg-rr 75.2%

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

      1. unpow1 75.2%

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

      2. associate-*l* 74.9%

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

      3. *-commutative 74.9%

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

   6. Simplified 74.9%

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

   7. Taylor expanded in b around inf 63.9%

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

   8. Taylor expanded in b around inf 66.4%

      \[\leadsto \color{blue}{b \cdot \left(c + -27 \cdot \frac{j \cdot k}{b}\right)} \]
   9. Step-by-step derivation

      1. *-commutative 66.4%

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

      2. associate-/l* 66.4%

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

   10. Simplified 66.4%

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

   if -5.00000000000000029e135 < (*.f64 b c) < 5.00000000000000024e-223 or 2.0000000000000001e-172 < (*.f64 b c) < 0.0040000000000000001

   1. Initial program 83.5%

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

   3. Simplified 87.4%

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

   5. Taylor expanded in a around inf 54.5%

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

      1. *-commutative 54.5%

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

   7. Simplified 54.5%

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

   if 5.00000000000000024e-223 < (*.f64 b c) < 2.0000000000000001e-172 or 0.0040000000000000001 < (*.f64 b c) < 4.99999999999999999e97

   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 76.6%

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

   5. Taylor expanded in y around inf 50.1%

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

      1. associate-*r* 49.8%

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

   7. Simplified 49.8%

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

   8. Taylor expanded in t around 0 50.1%

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

      1. associate-*r* 61.5%

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

      2. *-commutative 61.5%

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

   10. Simplified 61.5%

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

   11. Taylor expanded in t around inf 47.3%

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

       1. *-commutative 47.3%

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

       2. associate-*r* 55.7%

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

       3. *-commutative 55.7%

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

       4. associate-*l* 55.6%

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

       5. associate-*l* 55.5%

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

   13. Simplified 55.5%

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

   if 4.99999999999999999e97 < (*.f64 b c)

   1. Initial program 85.3%

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

      1. pow1 85.3%

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

      2. associate-*l* 82.5%

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

      3. *-commutative 82.5%

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

   4. Applied egg-rr 82.5%

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

      1. unpow1 82.5%

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

      2. associate-*l* 79.9%

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

      3. *-commutative 79.9%

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

   6. Simplified 79.9%

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

   7. Taylor expanded in b around inf 82.8%

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

   8. Taylor expanded in c around inf 85.6%

      \[\leadsto \color{blue}{c \cdot \left(b + -27 \cdot \frac{j \cdot k}{c}\right)} \]
   9. Step-by-step derivation

      1. *-commutative 85.6%

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

   10. Simplified 85.6%

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

4. Final simplification 60.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -5 \cdot 10^{+135}:\\ \;\;\;\;b \cdot \left(c + -27 \cdot \left(j \cdot \frac{k}{b}\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 5 \cdot 10^{-223}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;b \cdot c \leq 2 \cdot 10^{-172}:\\ \;\;\;\;\left(z \cdot t\right) \cdot \left(18 \cdot \left(x \cdot y\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 0.004:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;b \cdot c \leq 5 \cdot 10^{+97}:\\ \;\;\;\;\left(z \cdot t\right) \cdot \left(18 \cdot \left(x \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(b + -27 \cdot \frac{j \cdot k}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 50.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c - 27 \cdot \left(j \cdot k\right)\\ t_2 := j \cdot \left(k \cdot -27\right)\\ t_3 := t\_2 + i \cdot \left(x \cdot -4\right)\\ \mathbf{if}\;t \leq -3.6 \cdot 10^{+198}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq -2.2 \cdot 10^{-23}:\\ \;\;\;\;t\_2 + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-278}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-186}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-5}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+138}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(t \cdot a\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (- (* b c) (* 27.0 (* j k))))
        (t_2 (* j (* k -27.0)))
        (t_3 (+ t_2 (* i (* x -4.0)))))
   (if (<= t -3.6e+198)
     (* 18.0 (* t (* x (* y z))))
     (if (<= t -2.2e-23)
       (+ t_2 (* -4.0 (* t a)))
       (if (<= t -5e-278)
         t_1
         (if (<= t 8e-186)
           t_3
           (if (<= t 3.5e-5)
             t_1
             (if (<= t 1.2e+138) t_3 (- (* b c) (* 4.0 (* t a)))))))))))

C

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) - (27.0 * (j * k));
	double t_2 = j * (k * -27.0);
	double t_3 = t_2 + (i * (x * -4.0));
	double tmp;
	if (t <= -3.6e+198) {
		tmp = 18.0 * (t * (x * (y * z)));
	} else if (t <= -2.2e-23) {
		tmp = t_2 + (-4.0 * (t * a));
	} else if (t <= -5e-278) {
		tmp = t_1;
	} else if (t <= 8e-186) {
		tmp = t_3;
	} else if (t <= 3.5e-5) {
		tmp = t_1;
	} else if (t <= 1.2e+138) {
		tmp = t_3;
	} else {
		tmp = (b * c) - (4.0 * (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.
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 = (b * c) - (27.0d0 * (j * k))
    t_2 = j * (k * (-27.0d0))
    t_3 = t_2 + (i * (x * (-4.0d0)))
    if (t <= (-3.6d+198)) then
        tmp = 18.0d0 * (t * (x * (y * z)))
    else if (t <= (-2.2d-23)) then
        tmp = t_2 + ((-4.0d0) * (t * a))
    else if (t <= (-5d-278)) then
        tmp = t_1
    else if (t <= 8d-186) then
        tmp = t_3
    else if (t <= 3.5d-5) then
        tmp = t_1
    else if (t <= 1.2d+138) then
        tmp = t_3
    else
        tmp = (b * c) - (4.0d0 * (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;
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) - (27.0 * (j * k));
	double t_2 = j * (k * -27.0);
	double t_3 = t_2 + (i * (x * -4.0));
	double tmp;
	if (t <= -3.6e+198) {
		tmp = 18.0 * (t * (x * (y * z)));
	} else if (t <= -2.2e-23) {
		tmp = t_2 + (-4.0 * (t * a));
	} else if (t <= -5e-278) {
		tmp = t_1;
	} else if (t <= 8e-186) {
		tmp = t_3;
	} else if (t <= 3.5e-5) {
		tmp = t_1;
	} else if (t <= 1.2e+138) {
		tmp = t_3;
	} else {
		tmp = (b * c) - (4.0 * (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])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) - (27.0 * (j * k))
	t_2 = j * (k * -27.0)
	t_3 = t_2 + (i * (x * -4.0))
	tmp = 0
	if t <= -3.6e+198:
		tmp = 18.0 * (t * (x * (y * z)))
	elif t <= -2.2e-23:
		tmp = t_2 + (-4.0 * (t * a))
	elif t <= -5e-278:
		tmp = t_1
	elif t <= 8e-186:
		tmp = t_3
	elif t <= 3.5e-5:
		tmp = t_1
	elif t <= 1.2e+138:
		tmp = t_3
	else:
		tmp = (b * c) - (4.0 * (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])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) - Float64(27.0 * Float64(j * k)))
	t_2 = Float64(j * Float64(k * -27.0))
	t_3 = Float64(t_2 + Float64(i * Float64(x * -4.0)))
	tmp = 0.0
	if (t <= -3.6e+198)
		tmp = Float64(18.0 * Float64(t * Float64(x * Float64(y * z))));
	elseif (t <= -2.2e-23)
		tmp = Float64(t_2 + Float64(-4.0 * Float64(t * a)));
	elseif (t <= -5e-278)
		tmp = t_1;
	elseif (t <= 8e-186)
		tmp = t_3;
	elseif (t <= 3.5e-5)
		tmp = t_1;
	elseif (t <= 1.2e+138)
		tmp = t_3;
	else
		tmp = Float64(Float64(b * c) - Float64(4.0 * 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])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) - (27.0 * (j * k));
	t_2 = j * (k * -27.0);
	t_3 = t_2 + (i * (x * -4.0));
	tmp = 0.0;
	if (t <= -3.6e+198)
		tmp = 18.0 * (t * (x * (y * z)));
	elseif (t <= -2.2e-23)
		tmp = t_2 + (-4.0 * (t * a));
	elseif (t <= -5e-278)
		tmp = t_1;
	elseif (t <= 8e-186)
		tmp = t_3;
	elseif (t <= 3.5e-5)
		tmp = t_1;
	elseif (t <= 1.2e+138)
		tmp = t_3;
	else
		tmp = (b * c) - (4.0 * (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.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 + N[(i * N[(x * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.6e+198], N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.2e-23], N[(t$95$2 + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -5e-278], t$95$1, If[LessEqual[t, 8e-186], t$95$3, If[LessEqual[t, 3.5e-5], t$95$1, If[LessEqual[t, 1.2e+138], t$95$3, N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -3.6000000000000002e198

   1. Initial program 69.6%

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

   3. Simplified 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 y around inf 70.4%

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

      1. associate-*r* 70.1%

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

   7. Simplified 70.1%

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

   8. Taylor expanded in t around 0 70.4%

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

      1. associate-*r* 70.4%

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

      2. *-commutative 70.4%

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

   10. Simplified 70.4%

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

   11. Taylor expanded in t around inf 66.6%

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

   if -3.6000000000000002e198 < t < -2.1999999999999999e-23

   1. Initial program 74.5%

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

   3. Simplified 77.2%

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

   5. Taylor expanded in a around inf 54.5%

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

      1. *-commutative 54.5%

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

   7. Simplified 54.5%

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

   if -2.1999999999999999e-23 < t < -4.99999999999999985e-278 or 7.9999999999999993e-186 < t < 3.4999999999999997e-5

   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 t around 0 81.6%

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

   4. Taylor expanded in i around 0 65.7%

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

   if -4.99999999999999985e-278 < t < 7.9999999999999993e-186 or 3.4999999999999997e-5 < t < 1.2e138

   1. Initial program 84.6%

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

   3. Simplified 91.4%

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

   5. Taylor expanded in i around inf 66.4%

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

      1. associate-*r* 66.4%

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

      2. *-commutative 66.4%

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

      3. associate-*r* 66.4%

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

      4. *-commutative 66.4%

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

      5. *-commutative 66.4%

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

   7. Simplified 66.4%

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

   if 1.2e138 < t

   1. Initial program 81.5%

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

   3. Taylor expanded in x around 0 65.8%

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

   4. Taylor expanded in j around 0 65.8%

      \[\leadsto \color{blue}{b \cdot c - 4 \cdot \left(a \cdot t\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{+198}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq -2.2 \cdot 10^{-23}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-278}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-186}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + i \cdot \left(x \cdot -4\right)\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-5}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+138}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + i \cdot \left(x \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 58.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\\ \mathbf{if}\;x \leq -4.6 \cdot 10^{+77}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;x \leq -5.5 \cdot 10^{-56}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq -5 \cdot 10^{-201}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{-297}:\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{+52}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(i \cdot -4 + 18 \cdot \left(z \cdot \left(y \cdot t\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (+ (* j (* k -27.0)) (* -4.0 (* t a)))))
   (if (<= x -4.6e+77)
     (* x (- (* 18.0 (* t (* y z))) (* 4.0 i)))
     (if (<= x -5.5e-56)
       (- (* b c) (* 4.0 (* t a)))
       (if (<= x -5e-201)
         t_1
         (if (<= x 1.7e-297)
           (- (* b c) (* (* j 27.0) k))
           (if (<= x 1.1e+52)
             t_1
             (* x (+ (* i -4.0) (* 18.0 (* z (* y t))))))))))))

C

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)) + (-4.0 * (t * a));
	double tmp;
	if (x <= -4.6e+77) {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	} else if (x <= -5.5e-56) {
		tmp = (b * c) - (4.0 * (t * a));
	} else if (x <= -5e-201) {
		tmp = t_1;
	} else if (x <= 1.7e-297) {
		tmp = (b * c) - ((j * 27.0) * k);
	} else if (x <= 1.1e+52) {
		tmp = t_1;
	} else {
		tmp = x * ((i * -4.0) + (18.0 * (z * (y * t))));
	}
	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.
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))) + ((-4.0d0) * (t * a))
    if (x <= (-4.6d+77)) then
        tmp = x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i))
    else if (x <= (-5.5d-56)) then
        tmp = (b * c) - (4.0d0 * (t * a))
    else if (x <= (-5d-201)) then
        tmp = t_1
    else if (x <= 1.7d-297) then
        tmp = (b * c) - ((j * 27.0d0) * k)
    else if (x <= 1.1d+52) then
        tmp = t_1
    else
        tmp = x * ((i * (-4.0d0)) + (18.0d0 * (z * (y * t))))
    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;
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)) + (-4.0 * (t * a));
	double tmp;
	if (x <= -4.6e+77) {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	} else if (x <= -5.5e-56) {
		tmp = (b * c) - (4.0 * (t * a));
	} else if (x <= -5e-201) {
		tmp = t_1;
	} else if (x <= 1.7e-297) {
		tmp = (b * c) - ((j * 27.0) * k);
	} else if (x <= 1.1e+52) {
		tmp = t_1;
	} else {
		tmp = x * ((i * -4.0) + (18.0 * (z * (y * t))));
	}
	return tmp;
}

Python

[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)) + (-4.0 * (t * a))
	tmp = 0
	if x <= -4.6e+77:
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i))
	elif x <= -5.5e-56:
		tmp = (b * c) - (4.0 * (t * a))
	elif x <= -5e-201:
		tmp = t_1
	elif x <= 1.7e-297:
		tmp = (b * c) - ((j * 27.0) * k)
	elif x <= 1.1e+52:
		tmp = t_1
	else:
		tmp = x * ((i * -4.0) + (18.0 * (z * (y * t))))
	return tmp

Julia

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(-4.0 * Float64(t * a)))
	tmp = 0.0
	if (x <= -4.6e+77)
		tmp = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)));
	elseif (x <= -5.5e-56)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(t * a)));
	elseif (x <= -5e-201)
		tmp = t_1;
	elseif (x <= 1.7e-297)
		tmp = Float64(Float64(b * c) - Float64(Float64(j * 27.0) * k));
	elseif (x <= 1.1e+52)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(Float64(i * -4.0) + Float64(18.0 * Float64(z * Float64(y * t)))));
	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])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * (k * -27.0)) + (-4.0 * (t * a));
	tmp = 0.0;
	if (x <= -4.6e+77)
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	elseif (x <= -5.5e-56)
		tmp = (b * c) - (4.0 * (t * a));
	elseif (x <= -5e-201)
		tmp = t_1;
	elseif (x <= 1.7e-297)
		tmp = (b * c) - ((j * 27.0) * k);
	elseif (x <= 1.1e+52)
		tmp = t_1;
	else
		tmp = x * ((i * -4.0) + (18.0 * (z * (y * t))));
	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.
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[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.6e+77], N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -5.5e-56], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -5e-201], t$95$1, If[LessEqual[x, 1.7e-297], N[(N[(b * c), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.1e+52], t$95$1, N[(x * N[(N[(i * -4.0), $MachinePrecision] + N[(18.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -4.5999999999999999e77

   1. Initial program 70.5%

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

   3. Simplified 83.9%

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

   5. Taylor expanded in x around inf 75.0%

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

   if -4.5999999999999999e77 < x < -5.4999999999999999e-56

   1. Initial program 86.6%

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

   3. Taylor expanded in x around 0 67.5%

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

   4. Taylor expanded in j around 0 61.4%

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

   if -5.4999999999999999e-56 < x < -4.9999999999999999e-201 or 1.69999999999999991e-297 < x < 1.1e52

   1. Initial program 92.7%

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

   3. Simplified 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 a around inf 65.1%

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

      1. *-commutative 65.1%

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

   7. Simplified 65.1%

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

   if -4.9999999999999999e-201 < x < 1.69999999999999991e-297

   1. Initial program 95.1%

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

      1. pow1 95.1%

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

      2. associate-*l* 81.1%

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

      3. *-commutative 81.1%

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

   4. Applied egg-rr 81.1%

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

      1. unpow1 81.1%

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

      2. associate-*l* 81.5%

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

      3. *-commutative 81.5%

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

   6. Simplified 81.5%

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

   7. Taylor expanded in b around inf 74.6%

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

   if 1.1e52 < x

   1. Initial program 63.0%

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

   3. Simplified 70.7%

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

      1. pow1 70.7%

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

      2. associate-*l* 70.7%

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

      3. associate-*r* 70.7%

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

   6. Applied egg-rr 70.7%

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

      1. unpow1 70.7%

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

      2. *-commutative 70.7%

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

   8. Simplified 70.7%

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

      1. pow1 70.7%

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

      2. associate-*r* 70.7%

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

   10. Applied egg-rr 70.7%

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

       1. unpow1 70.7%

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

       2. associate-*r* 68.8%

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

       3. *-commutative 68.8%

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

   12. Simplified 68.8%

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

   13. Taylor expanded in x around inf 68.3%

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

       1. cancel-sign-sub-inv 68.3%

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

       2. metadata-eval 68.3%

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

       3. associate-*r* 72.0%

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

   15. Simplified 72.0%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{+77}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;x \leq -5.5 \cdot 10^{-56}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq -5 \cdot 10^{-201}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{-297}:\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{+52}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(i \cdot -4 + 18 \cdot \left(z \cdot \left(y \cdot t\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 58.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\\ t_2 := x \cdot \left(i \cdot -4 + 18 \cdot \left(z \cdot \left(y \cdot t\right)\right)\right)\\ \mathbf{if}\;x \leq -4.6 \cdot 10^{+76}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -2.1 \cdot 10^{-58}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq -2.7 \cdot 10^{-201}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-297}:\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{+53}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (+ (* j (* k -27.0)) (* -4.0 (* t a))))
        (t_2 (* x (+ (* i -4.0) (* 18.0 (* z (* y t)))))))
   (if (<= x -4.6e+76)
     t_2
     (if (<= x -2.1e-58)
       (- (* b c) (* 4.0 (* t a)))
       (if (<= x -2.7e-201)
         t_1
         (if (<= x 7e-297)
           (- (* b c) (* (* j 27.0) k))
           (if (<= x 2.2e+53) t_1 t_2)))))))

C

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)) + (-4.0 * (t * a));
	double t_2 = x * ((i * -4.0) + (18.0 * (z * (y * t))));
	double tmp;
	if (x <= -4.6e+76) {
		tmp = t_2;
	} else if (x <= -2.1e-58) {
		tmp = (b * c) - (4.0 * (t * a));
	} else if (x <= -2.7e-201) {
		tmp = t_1;
	} else if (x <= 7e-297) {
		tmp = (b * c) - ((j * 27.0) * k);
	} else if (x <= 2.2e+53) {
		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.
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))) + ((-4.0d0) * (t * a))
    t_2 = x * ((i * (-4.0d0)) + (18.0d0 * (z * (y * t))))
    if (x <= (-4.6d+76)) then
        tmp = t_2
    else if (x <= (-2.1d-58)) then
        tmp = (b * c) - (4.0d0 * (t * a))
    else if (x <= (-2.7d-201)) then
        tmp = t_1
    else if (x <= 7d-297) then
        tmp = (b * c) - ((j * 27.0d0) * k)
    else if (x <= 2.2d+53) 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;
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)) + (-4.0 * (t * a));
	double t_2 = x * ((i * -4.0) + (18.0 * (z * (y * t))));
	double tmp;
	if (x <= -4.6e+76) {
		tmp = t_2;
	} else if (x <= -2.1e-58) {
		tmp = (b * c) - (4.0 * (t * a));
	} else if (x <= -2.7e-201) {
		tmp = t_1;
	} else if (x <= 7e-297) {
		tmp = (b * c) - ((j * 27.0) * k);
	} else if (x <= 2.2e+53) {
		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])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * (k * -27.0)) + (-4.0 * (t * a))
	t_2 = x * ((i * -4.0) + (18.0 * (z * (y * t))))
	tmp = 0
	if x <= -4.6e+76:
		tmp = t_2
	elif x <= -2.1e-58:
		tmp = (b * c) - (4.0 * (t * a))
	elif x <= -2.7e-201:
		tmp = t_1
	elif x <= 7e-297:
		tmp = (b * c) - ((j * 27.0) * k)
	elif x <= 2.2e+53:
		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])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * Float64(k * -27.0)) + Float64(-4.0 * Float64(t * a)))
	t_2 = Float64(x * Float64(Float64(i * -4.0) + Float64(18.0 * Float64(z * Float64(y * t)))))
	tmp = 0.0
	if (x <= -4.6e+76)
		tmp = t_2;
	elseif (x <= -2.1e-58)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(t * a)));
	elseif (x <= -2.7e-201)
		tmp = t_1;
	elseif (x <= 7e-297)
		tmp = Float64(Float64(b * c) - Float64(Float64(j * 27.0) * k));
	elseif (x <= 2.2e+53)
		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])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * (k * -27.0)) + (-4.0 * (t * a));
	t_2 = x * ((i * -4.0) + (18.0 * (z * (y * t))));
	tmp = 0.0;
	if (x <= -4.6e+76)
		tmp = t_2;
	elseif (x <= -2.1e-58)
		tmp = (b * c) - (4.0 * (t * a));
	elseif (x <= -2.7e-201)
		tmp = t_1;
	elseif (x <= 7e-297)
		tmp = (b * c) - ((j * 27.0) * k);
	elseif (x <= 2.2e+53)
		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.
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[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(i * -4.0), $MachinePrecision] + N[(18.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.6e+76], t$95$2, If[LessEqual[x, -2.1e-58], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.7e-201], t$95$1, If[LessEqual[x, 7e-297], N[(N[(b * c), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.2e+53], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -4.60000000000000002e76 or 2.19999999999999999e53 < x

   1. Initial program 66.5%

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

   3. Simplified 76.8%

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

      1. pow1 76.8%

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

      2. associate-*l* 76.8%

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

      3. associate-*r* 76.8%

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

   6. Applied egg-rr 76.8%

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

      1. unpow1 76.8%

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

      2. *-commutative 76.8%

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

   8. Simplified 76.8%

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

      1. pow1 76.8%

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

      2. associate-*r* 76.8%

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

   10. Applied egg-rr 76.8%

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

       1. unpow1 76.8%

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

       2. associate-*r* 73.8%

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

       3. *-commutative 73.8%

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

   12. Simplified 73.8%

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

   13. Taylor expanded in x around inf 71.4%

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

       1. cancel-sign-sub-inv 71.4%

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

       2. metadata-eval 71.4%

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

       3. associate-*r* 72.0%

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

   15. Simplified 72.0%

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

   if -4.60000000000000002e76 < x < -2.09999999999999988e-58

   1. Initial program 86.6%

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

   3. Taylor expanded in x around 0 67.5%

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

   4. Taylor expanded in j around 0 61.4%

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

   if -2.09999999999999988e-58 < x < -2.70000000000000005e-201 or 6.9999999999999998e-297 < x < 2.19999999999999999e53

   1. Initial program 92.7%

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

   3. Simplified 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 a around inf 65.1%

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

      1. *-commutative 65.1%

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

   7. Simplified 65.1%

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

   if -2.70000000000000005e-201 < x < 6.9999999999999998e-297

   1. Initial program 95.1%

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

      1. pow1 95.1%

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

      2. associate-*l* 81.1%

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

      3. *-commutative 81.1%

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

   4. Applied egg-rr 81.1%

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

      1. unpow1 81.1%

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

      2. associate-*l* 81.5%

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

      3. *-commutative 81.5%

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

   6. Simplified 81.5%

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

   7. Taylor expanded in b around inf 74.6%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{+76}:\\ \;\;\;\;x \cdot \left(i \cdot -4 + 18 \cdot \left(z \cdot \left(y \cdot t\right)\right)\right)\\ \mathbf{elif}\;x \leq -2.1 \cdot 10^{-58}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq -2.7 \cdot 10^{-201}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-297}:\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{+53}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(i \cdot -4 + 18 \cdot \left(z \cdot \left(y \cdot t\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 49.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c - 4 \cdot \left(t \cdot a\right)\\ \mathbf{if}\;t \leq -6 \cdot 10^{+200}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{+100}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{-21}:\\ \;\;\;\;\left(z \cdot t\right) \cdot \left(18 \cdot \left(x \cdot y\right)\right)\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{+23}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+56}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (- (* b c) (* 4.0 (* t a)))))
   (if (<= t -6e+200)
     (* 18.0 (* t (* x (* y z))))
     (if (<= t -5.5e+100)
       t_1
       (if (<= t -2.4e-21)
         (* (* z t) (* 18.0 (* x y)))
         (if (<= t 1.85e+23)
           (- (* b c) (* 27.0 (* j k)))
           (if (<= t 1.05e+56) (* -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);
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));
	double tmp;
	if (t <= -6e+200) {
		tmp = 18.0 * (t * (x * (y * z)));
	} else if (t <= -5.5e+100) {
		tmp = t_1;
	} else if (t <= -2.4e-21) {
		tmp = (z * t) * (18.0 * (x * y));
	} else if (t <= 1.85e+23) {
		tmp = (b * c) - (27.0 * (j * k));
	} else if (t <= 1.05e+56) {
		tmp = -4.0 * (x * i);
	} 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.
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))
    if (t <= (-6d+200)) then
        tmp = 18.0d0 * (t * (x * (y * z)))
    else if (t <= (-5.5d+100)) then
        tmp = t_1
    else if (t <= (-2.4d-21)) then
        tmp = (z * t) * (18.0d0 * (x * y))
    else if (t <= 1.85d+23) then
        tmp = (b * c) - (27.0d0 * (j * k))
    else if (t <= 1.05d+56) then
        tmp = (-4.0d0) * (x * i)
    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;
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));
	double tmp;
	if (t <= -6e+200) {
		tmp = 18.0 * (t * (x * (y * z)));
	} else if (t <= -5.5e+100) {
		tmp = t_1;
	} else if (t <= -2.4e-21) {
		tmp = (z * t) * (18.0 * (x * y));
	} else if (t <= 1.85e+23) {
		tmp = (b * c) - (27.0 * (j * k));
	} else if (t <= 1.05e+56) {
		tmp = -4.0 * (x * i);
	} 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])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) - (4.0 * (t * a))
	tmp = 0
	if t <= -6e+200:
		tmp = 18.0 * (t * (x * (y * z)))
	elif t <= -5.5e+100:
		tmp = t_1
	elif t <= -2.4e-21:
		tmp = (z * t) * (18.0 * (x * y))
	elif t <= 1.85e+23:
		tmp = (b * c) - (27.0 * (j * k))
	elif t <= 1.05e+56:
		tmp = -4.0 * (x * i)
	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])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) - Float64(4.0 * Float64(t * a)))
	tmp = 0.0
	if (t <= -6e+200)
		tmp = Float64(18.0 * Float64(t * Float64(x * Float64(y * z))));
	elseif (t <= -5.5e+100)
		tmp = t_1;
	elseif (t <= -2.4e-21)
		tmp = Float64(Float64(z * t) * Float64(18.0 * Float64(x * y)));
	elseif (t <= 1.85e+23)
		tmp = Float64(Float64(b * c) - Float64(27.0 * Float64(j * k)));
	elseif (t <= 1.05e+56)
		tmp = Float64(-4.0 * Float64(x * i));
	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])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) - (4.0 * (t * a));
	tmp = 0.0;
	if (t <= -6e+200)
		tmp = 18.0 * (t * (x * (y * z)));
	elseif (t <= -5.5e+100)
		tmp = t_1;
	elseif (t <= -2.4e-21)
		tmp = (z * t) * (18.0 * (x * y));
	elseif (t <= 1.85e+23)
		tmp = (b * c) - (27.0 * (j * k));
	elseif (t <= 1.05e+56)
		tmp = -4.0 * (x * i);
	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.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6e+200], N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -5.5e+100], t$95$1, If[LessEqual[t, -2.4e-21], N[(N[(z * t), $MachinePrecision] * N[(18.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.85e+23], N[(N[(b * c), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.05e+56], N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -5.99999999999999982e200

   1. Initial program 69.6%

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

   3. Simplified 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 y around inf 70.4%

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

      1. associate-*r* 70.1%

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

   7. Simplified 70.1%

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

   8. Taylor expanded in t around 0 70.4%

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

      1. associate-*r* 70.4%

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

      2. *-commutative 70.4%

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

   10. Simplified 70.4%

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

   11. Taylor expanded in t around inf 66.6%

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

   if -5.99999999999999982e200 < t < -5.5000000000000002e100 or 1.05000000000000009e56 < t

   1. Initial program 81.5%

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

   3. Taylor expanded in x around 0 66.4%

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

   4. Taylor expanded in j around 0 56.3%

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

   if -5.5000000000000002e100 < t < -2.3999999999999999e-21

   1. Initial program 70.4%

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

   3. Simplified 65.8%

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

   5. Taylor expanded in y around inf 61.3%

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

      1. associate-*r* 65.7%

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

   7. Simplified 65.7%

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

   8. Taylor expanded in t around 0 61.3%

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

      1. associate-*r* 66.0%

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

      2. *-commutative 66.0%

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

   10. Simplified 66.0%

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

   11. Taylor expanded in t around inf 42.1%

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

       1. *-commutative 42.1%

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

       2. associate-*r* 46.8%

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

       3. *-commutative 46.8%

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

       4. associate-*l* 46.6%

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

       5. associate-*l* 46.5%

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

   13. Simplified 46.5%

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

   if -2.3999999999999999e-21 < t < 1.85000000000000006e23

   1. Initial program 87.7%

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

   3. Taylor expanded in t around 0 82.1%

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

   4. Taylor expanded in i around 0 62.6%

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

   if 1.85000000000000006e23 < t < 1.05000000000000009e56

   1. Initial program 80.0%

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

   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. pow1 100.0%

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

      2. associate-*l* 100.0%

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

      3. associate-*r* 100.0%

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

   6. Applied egg-rr 100.0%

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

      1. unpow1 100.0%

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

      2. *-commutative 100.0%

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

   8. Simplified 100.0%

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

      1. pow1 100.0%

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

      2. associate-*r* 100.0%

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

   10. Applied egg-rr 100.0%

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

       1. unpow1 100.0%

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

       2. associate-*r* 100.0%

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

       3. *-commutative 100.0%

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

   12. Simplified 100.0%

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

   13. Taylor expanded in i around inf 100.0%

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

       1. *-commutative 100.0%

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

   15. Simplified 100.0%

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

4. Final simplification 60.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{+200}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{+100}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{-21}:\\ \;\;\;\;\left(z \cdot t\right) \cdot \left(18 \cdot \left(x \cdot y\right)\right)\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{+23}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+56}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 49.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c - 4 \cdot \left(t \cdot a\right)\\ \mathbf{if}\;t \leq -6.5 \cdot 10^{+198}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq -9 \cdot 10^{+101}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{-23}:\\ \;\;\;\;\left(z \cdot t\right) \cdot \left(18 \cdot \left(x \cdot y\right)\right)\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+23}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+55}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (- (* b c) (* 4.0 (* t a)))))
   (if (<= t -6.5e+198)
     (* 18.0 (* t (* x (* y z))))
     (if (<= t -9e+101)
       t_1
       (if (<= t -2.9e-23)
         (* (* z t) (* 18.0 (* x y)))
         (if (<= t 1.6e+23)
           (+ (* b c) (* j (* k -27.0)))
           (if (<= t 6.2e+55) (* -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);
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));
	double tmp;
	if (t <= -6.5e+198) {
		tmp = 18.0 * (t * (x * (y * z)));
	} else if (t <= -9e+101) {
		tmp = t_1;
	} else if (t <= -2.9e-23) {
		tmp = (z * t) * (18.0 * (x * y));
	} else if (t <= 1.6e+23) {
		tmp = (b * c) + (j * (k * -27.0));
	} else if (t <= 6.2e+55) {
		tmp = -4.0 * (x * i);
	} 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.
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))
    if (t <= (-6.5d+198)) then
        tmp = 18.0d0 * (t * (x * (y * z)))
    else if (t <= (-9d+101)) then
        tmp = t_1
    else if (t <= (-2.9d-23)) then
        tmp = (z * t) * (18.0d0 * (x * y))
    else if (t <= 1.6d+23) then
        tmp = (b * c) + (j * (k * (-27.0d0)))
    else if (t <= 6.2d+55) then
        tmp = (-4.0d0) * (x * i)
    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;
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));
	double tmp;
	if (t <= -6.5e+198) {
		tmp = 18.0 * (t * (x * (y * z)));
	} else if (t <= -9e+101) {
		tmp = t_1;
	} else if (t <= -2.9e-23) {
		tmp = (z * t) * (18.0 * (x * y));
	} else if (t <= 1.6e+23) {
		tmp = (b * c) + (j * (k * -27.0));
	} else if (t <= 6.2e+55) {
		tmp = -4.0 * (x * i);
	} 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])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) - (4.0 * (t * a))
	tmp = 0
	if t <= -6.5e+198:
		tmp = 18.0 * (t * (x * (y * z)))
	elif t <= -9e+101:
		tmp = t_1
	elif t <= -2.9e-23:
		tmp = (z * t) * (18.0 * (x * y))
	elif t <= 1.6e+23:
		tmp = (b * c) + (j * (k * -27.0))
	elif t <= 6.2e+55:
		tmp = -4.0 * (x * i)
	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])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) - Float64(4.0 * Float64(t * a)))
	tmp = 0.0
	if (t <= -6.5e+198)
		tmp = Float64(18.0 * Float64(t * Float64(x * Float64(y * z))));
	elseif (t <= -9e+101)
		tmp = t_1;
	elseif (t <= -2.9e-23)
		tmp = Float64(Float64(z * t) * Float64(18.0 * Float64(x * y)));
	elseif (t <= 1.6e+23)
		tmp = Float64(Float64(b * c) + Float64(j * Float64(k * -27.0)));
	elseif (t <= 6.2e+55)
		tmp = Float64(-4.0 * Float64(x * i));
	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])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) - (4.0 * (t * a));
	tmp = 0.0;
	if (t <= -6.5e+198)
		tmp = 18.0 * (t * (x * (y * z)));
	elseif (t <= -9e+101)
		tmp = t_1;
	elseif (t <= -2.9e-23)
		tmp = (z * t) * (18.0 * (x * y));
	elseif (t <= 1.6e+23)
		tmp = (b * c) + (j * (k * -27.0));
	elseif (t <= 6.2e+55)
		tmp = -4.0 * (x * i);
	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.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.5e+198], N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -9e+101], t$95$1, If[LessEqual[t, -2.9e-23], N[(N[(z * t), $MachinePrecision] * N[(18.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.6e+23], N[(N[(b * c), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.2e+55], N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -6.5000000000000003e198

   1. Initial program 69.6%

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

   3. Simplified 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 y around inf 70.4%

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

      1. associate-*r* 70.1%

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

   7. Simplified 70.1%

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

   8. Taylor expanded in t around 0 70.4%

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

      1. associate-*r* 70.4%

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

      2. *-commutative 70.4%

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

   10. Simplified 70.4%

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

   11. Taylor expanded in t around inf 66.6%

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

   if -6.5000000000000003e198 < t < -9.0000000000000004e101 or 6.19999999999999987e55 < t

   1. Initial program 81.5%

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

   3. Taylor expanded in x around 0 66.4%

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

   4. Taylor expanded in j around 0 56.3%

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

   if -9.0000000000000004e101 < t < -2.9000000000000002e-23

   1. Initial program 70.4%

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

   3. Simplified 65.8%

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

   5. Taylor expanded in y around inf 61.3%

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

      1. associate-*r* 65.7%

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

   7. Simplified 65.7%

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

   8. Taylor expanded in t around 0 61.3%

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

      1. associate-*r* 66.0%

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

      2. *-commutative 66.0%

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

   10. Simplified 66.0%

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

   11. Taylor expanded in t around inf 42.1%

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

       1. *-commutative 42.1%

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

       2. associate-*r* 46.8%

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

       3. *-commutative 46.8%

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

       4. associate-*l* 46.6%

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

       5. associate-*l* 46.5%

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

   13. Simplified 46.5%

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

   if -2.9000000000000002e-23 < t < 1.6e23

   1. Initial program 87.7%

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

   3. Simplified 87.7%

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

   5. Taylor expanded in b around inf 62.6%

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

   if 1.6e23 < t < 6.19999999999999987e55

   1. Initial program 80.0%

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

   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. pow1 100.0%

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

      2. associate-*l* 100.0%

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

      3. associate-*r* 100.0%

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

   6. Applied egg-rr 100.0%

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

      1. unpow1 100.0%

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

      2. *-commutative 100.0%

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

   8. Simplified 100.0%

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

      1. pow1 100.0%

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

      2. associate-*r* 100.0%

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

   10. Applied egg-rr 100.0%

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

       1. unpow1 100.0%

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

       2. associate-*r* 100.0%

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

       3. *-commutative 100.0%

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

   12. Simplified 100.0%

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

   13. Taylor expanded in i around inf 100.0%

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

       1. *-commutative 100.0%

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

   15. Simplified 100.0%

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

4. Final simplification 60.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{+198}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq -9 \cdot 10^{+101}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{-23}:\\ \;\;\;\;\left(z \cdot t\right) \cdot \left(18 \cdot \left(x \cdot y\right)\right)\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+23}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+55}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 88.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq 1.02 \cdot 10^{+173}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(y \cdot \left(x \cdot \left(18 \cdot z\right)\right) - a \cdot 4\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + i \cdot -4\right) + j \cdot \left(k \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= x 1.02e+173)
   (-
    (+ (* b c) (* t (- (* y (* x (* 18.0 z))) (* a 4.0))))
    (+ (* x (* 4.0 i)) (* j (* 27.0 k))))
   (+ (* x (+ (* 18.0 (* t (* y z))) (* i -4.0))) (* j (* k -27.0)))))

C

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 (x <= 1.02e+173) {
		tmp = ((b * c) + (t * ((y * (x * (18.0 * z))) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	} else {
		tmp = (x * ((18.0 * (t * (y * z))) + (i * -4.0))) + (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.
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 (x <= 1.02d+173) then
        tmp = ((b * c) + (t * ((y * (x * (18.0d0 * z))) - (a * 4.0d0)))) - ((x * (4.0d0 * i)) + (j * (27.0d0 * k)))
    else
        tmp = (x * ((18.0d0 * (t * (y * z))) + (i * (-4.0d0)))) + (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;
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 (x <= 1.02e+173) {
		tmp = ((b * c) + (t * ((y * (x * (18.0 * z))) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	} else {
		tmp = (x * ((18.0 * (t * (y * z))) + (i * -4.0))) + (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])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if x <= 1.02e+173:
		tmp = ((b * c) + (t * ((y * (x * (18.0 * z))) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)))
	else:
		tmp = (x * ((18.0 * (t * (y * z))) + (i * -4.0))) + (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])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (x <= 1.02e+173)
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(y * Float64(x * Float64(18.0 * z))) - Float64(a * 4.0)))) - Float64(Float64(x * Float64(4.0 * i)) + Float64(j * Float64(27.0 * k))));
	else
		tmp = Float64(Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) + Float64(i * -4.0))) + 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])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (x <= 1.02e+173)
		tmp = ((b * c) + (t * ((y * (x * (18.0 * z))) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	else
		tmp = (x * ((18.0 * (t * (y * z))) + (i * -4.0))) + (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.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[x, 1.02e+173], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(y * N[(x * N[(18.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision] + N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1.02e173

   1. Initial program 86.9%

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

   3. Simplified 88.7%

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

      1. pow1 88.7%

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

      2. associate-*l* 88.7%

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

      3. associate-*r* 88.3%

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

   6. Applied egg-rr 88.3%

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

      1. unpow1 88.3%

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

      2. *-commutative 88.3%

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

   8. Simplified 88.3%

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

      1. pow1 88.3%

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

      2. associate-*r* 88.7%

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

   10. Applied egg-rr 88.7%

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

       1. unpow1 88.7%

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

       2. associate-*r* 91.2%

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

       3. *-commutative 91.2%

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

   12. Simplified 91.2%

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

   if 1.02e173 < x

   1. Initial program 49.4%

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

   3. Simplified 66.1%

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

   5. Taylor expanded in x around inf 83.5%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.02 \cdot 10^{+173}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(y \cdot \left(x \cdot \left(18 \cdot z\right)\right) - a \cdot 4\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + i \cdot -4\right) + j \cdot \left(k \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 87.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq 9.5 \cdot 10^{+174}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + i \cdot -4\right) + j \cdot \left(k \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= x 9.5e+174)
   (-
    (+ (* b c) (* t (- (* (* x 18.0) (* y z)) (* a 4.0))))
    (+ (* x (* 4.0 i)) (* j (* 27.0 k))))
   (+ (* x (+ (* 18.0 (* t (* y z))) (* i -4.0))) (* j (* k -27.0)))))

C

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 (x <= 9.5e+174) {
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	} else {
		tmp = (x * ((18.0 * (t * (y * z))) + (i * -4.0))) + (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.
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 (x <= 9.5d+174) then
        tmp = ((b * c) + (t * (((x * 18.0d0) * (y * z)) - (a * 4.0d0)))) - ((x * (4.0d0 * i)) + (j * (27.0d0 * k)))
    else
        tmp = (x * ((18.0d0 * (t * (y * z))) + (i * (-4.0d0)))) + (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;
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 (x <= 9.5e+174) {
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	} else {
		tmp = (x * ((18.0 * (t * (y * z))) + (i * -4.0))) + (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])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if x <= 9.5e+174:
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)))
	else:
		tmp = (x * ((18.0 * (t * (y * z))) + (i * -4.0))) + (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])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (x <= 9.5e+174)
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(Float64(x * 18.0) * Float64(y * z)) - Float64(a * 4.0)))) - Float64(Float64(x * Float64(4.0 * i)) + Float64(j * Float64(27.0 * k))));
	else
		tmp = Float64(Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) + Float64(i * -4.0))) + 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])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (x <= 9.5e+174)
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	else
		tmp = (x * ((18.0 * (t * (y * z))) + (i * -4.0))) + (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.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[x, 9.5e+174], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(N[(x * 18.0), $MachinePrecision] * N[(y * z), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision] + N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 9.4999999999999992e174

   1. Initial program 86.9%

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

   3. Simplified 88.7%

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

   if 9.4999999999999992e174 < x

   1. Initial program 49.4%

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

   3. Simplified 66.1%

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

   5. Taylor expanded in x around inf 83.5%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 9.5 \cdot 10^{+174}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + i \cdot -4\right) + j \cdot \left(k \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 87.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq 4.7 \cdot 10^{+176}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(x \cdot \left(z \cdot \left(18 \cdot y\right)\right) - a \cdot 4\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + i \cdot -4\right) + j \cdot \left(k \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= x 4.7e+176)
   (-
    (+ (* b c) (* t (- (* x (* z (* 18.0 y))) (* a 4.0))))
    (+ (* x (* 4.0 i)) (* j (* 27.0 k))))
   (+ (* x (+ (* 18.0 (* t (* y z))) (* i -4.0))) (* j (* k -27.0)))))

C

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 (x <= 4.7e+176) {
		tmp = ((b * c) + (t * ((x * (z * (18.0 * y))) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	} else {
		tmp = (x * ((18.0 * (t * (y * z))) + (i * -4.0))) + (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.
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 (x <= 4.7d+176) then
        tmp = ((b * c) + (t * ((x * (z * (18.0d0 * y))) - (a * 4.0d0)))) - ((x * (4.0d0 * i)) + (j * (27.0d0 * k)))
    else
        tmp = (x * ((18.0d0 * (t * (y * z))) + (i * (-4.0d0)))) + (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;
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 (x <= 4.7e+176) {
		tmp = ((b * c) + (t * ((x * (z * (18.0 * y))) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	} else {
		tmp = (x * ((18.0 * (t * (y * z))) + (i * -4.0))) + (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])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if x <= 4.7e+176:
		tmp = ((b * c) + (t * ((x * (z * (18.0 * y))) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)))
	else:
		tmp = (x * ((18.0 * (t * (y * z))) + (i * -4.0))) + (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])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (x <= 4.7e+176)
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(x * Float64(z * Float64(18.0 * y))) - Float64(a * 4.0)))) - Float64(Float64(x * Float64(4.0 * i)) + Float64(j * Float64(27.0 * k))));
	else
		tmp = Float64(Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) + Float64(i * -4.0))) + 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])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (x <= 4.7e+176)
		tmp = ((b * c) + (t * ((x * (z * (18.0 * y))) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	else
		tmp = (x * ((18.0 * (t * (y * z))) + (i * -4.0))) + (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.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[x, 4.7e+176], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(x * N[(z * N[(18.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision] + N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 4.69999999999999981e176

   1. Initial program 86.9%

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

   3. Simplified 88.7%

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

      1. pow1 88.7%

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

      2. associate-*l* 88.7%

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

      3. associate-*r* 88.3%

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

   6. Applied egg-rr 88.3%

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

      1. unpow1 88.3%

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

      2. *-commutative 88.3%

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

   8. Simplified 88.3%

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

   if 4.69999999999999981e176 < x

   1. Initial program 49.4%

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

   3. Simplified 66.1%

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

   5. Taylor expanded in x around inf 83.5%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 4.7 \cdot 10^{+176}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(x \cdot \left(z \cdot \left(18 \cdot y\right)\right) - a \cdot 4\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + i \cdot -4\right) + j \cdot \left(k \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 60.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c - 27 \cdot \left(j \cdot k\right)\\ t_2 := t \cdot \left(a \cdot -4 + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{if}\;t \leq -6.2 \cdot 10^{-22}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-280}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{-185}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + i \cdot \left(x \cdot -4\right)\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+23}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (- (* b c) (* 27.0 (* j k))))
        (t_2 (* t (+ (* a -4.0) (* 18.0 (* x (* y z)))))))
   (if (<= t -6.2e-22)
     t_2
     (if (<= t -3e-280)
       t_1
       (if (<= t 1.6e-185)
         (+ (* j (* k -27.0)) (* i (* x -4.0)))
         (if (<= t 1.15e+23) t_1 t_2))))))

C

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) - (27.0 * (j * k));
	double t_2 = t * ((a * -4.0) + (18.0 * (x * (y * z))));
	double tmp;
	if (t <= -6.2e-22) {
		tmp = t_2;
	} else if (t <= -3e-280) {
		tmp = t_1;
	} else if (t <= 1.6e-185) {
		tmp = (j * (k * -27.0)) + (i * (x * -4.0));
	} else if (t <= 1.15e+23) {
		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.
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) - (27.0d0 * (j * k))
    t_2 = t * ((a * (-4.0d0)) + (18.0d0 * (x * (y * z))))
    if (t <= (-6.2d-22)) then
        tmp = t_2
    else if (t <= (-3d-280)) then
        tmp = t_1
    else if (t <= 1.6d-185) then
        tmp = (j * (k * (-27.0d0))) + (i * (x * (-4.0d0)))
    else if (t <= 1.15d+23) 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;
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) - (27.0 * (j * k));
	double t_2 = t * ((a * -4.0) + (18.0 * (x * (y * z))));
	double tmp;
	if (t <= -6.2e-22) {
		tmp = t_2;
	} else if (t <= -3e-280) {
		tmp = t_1;
	} else if (t <= 1.6e-185) {
		tmp = (j * (k * -27.0)) + (i * (x * -4.0));
	} else if (t <= 1.15e+23) {
		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])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) - (27.0 * (j * k))
	t_2 = t * ((a * -4.0) + (18.0 * (x * (y * z))))
	tmp = 0
	if t <= -6.2e-22:
		tmp = t_2
	elif t <= -3e-280:
		tmp = t_1
	elif t <= 1.6e-185:
		tmp = (j * (k * -27.0)) + (i * (x * -4.0))
	elif t <= 1.15e+23:
		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])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) - Float64(27.0 * Float64(j * k)))
	t_2 = Float64(t * Float64(Float64(a * -4.0) + Float64(18.0 * Float64(x * Float64(y * z)))))
	tmp = 0.0
	if (t <= -6.2e-22)
		tmp = t_2;
	elseif (t <= -3e-280)
		tmp = t_1;
	elseif (t <= 1.6e-185)
		tmp = Float64(Float64(j * Float64(k * -27.0)) + Float64(i * Float64(x * -4.0)));
	elseif (t <= 1.15e+23)
		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])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) - (27.0 * (j * k));
	t_2 = t * ((a * -4.0) + (18.0 * (x * (y * z))));
	tmp = 0.0;
	if (t <= -6.2e-22)
		tmp = t_2;
	elseif (t <= -3e-280)
		tmp = t_1;
	elseif (t <= 1.6e-185)
		tmp = (j * (k * -27.0)) + (i * (x * -4.0));
	elseif (t <= 1.15e+23)
		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.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(a * -4.0), $MachinePrecision] + N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.2e-22], t$95$2, If[LessEqual[t, -3e-280], t$95$1, If[LessEqual[t, 1.6e-185], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(i * N[(x * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.15e+23], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.20000000000000025e-22 or 1.15e23 < t

   1. Initial program 77.6%

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

   3. Simplified 86.2%

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

   5. Taylor expanded in t around inf 74.3%

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

   6. Taylor expanded in t around inf 66.2%

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

   if -6.20000000000000025e-22 < t < -2.99999999999999987e-280 or 1.5999999999999999e-185 < t < 1.15e23

   1. Initial program 89.2%

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

   3. Taylor expanded in t around 0 81.4%

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

   4. Taylor expanded in i around 0 65.1%

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

   if -2.99999999999999987e-280 < t < 1.5999999999999999e-185

   1. Initial program 82.5%

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

   3. Simplified 82.5%

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

   5. Taylor expanded in i around inf 72.1%

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

      1. associate-*r* 72.1%

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

      2. *-commutative 72.1%

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

      3. associate-*r* 72.1%

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

      4. *-commutative 72.1%

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

      5. *-commutative 72.1%

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

   7. Simplified 72.1%

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

4. Final simplification 66.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{-22}:\\ \;\;\;\;t \cdot \left(a \cdot -4 + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-280}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{-185}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + i \cdot \left(x \cdot -4\right)\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+23}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot -4 + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 78.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\\ t_2 := 4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;t \leq -8.2 \cdot 10^{-23}:\\ \;\;\;\;t \cdot \left(a \cdot -4 + t\_1\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-42}:\\ \;\;\;\;\left(b \cdot c - t\_2\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(t\_1 - a \cdot 4\right)\right) - t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* 18.0 (* x (* y z)))) (t_2 (* 4.0 (* x i))))
   (if (<= t -8.2e-23)
     (+ (* t (+ (* a -4.0) t_1)) (* j (* k -27.0)))
     (if (<= t 1.05e-42)
       (- (- (* b c) t_2) (* (* j 27.0) k))
       (- (+ (* b c) (* t (- t_1 (* a 4.0)))) t_2)))))

C

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 = 18.0 * (x * (y * z));
	double t_2 = 4.0 * (x * i);
	double tmp;
	if (t <= -8.2e-23) {
		tmp = (t * ((a * -4.0) + t_1)) + (j * (k * -27.0));
	} else if (t <= 1.05e-42) {
		tmp = ((b * c) - t_2) - ((j * 27.0) * k);
	} else {
		tmp = ((b * c) + (t * (t_1 - (a * 4.0)))) - 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.
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 = 18.0d0 * (x * (y * z))
    t_2 = 4.0d0 * (x * i)
    if (t <= (-8.2d-23)) then
        tmp = (t * ((a * (-4.0d0)) + t_1)) + (j * (k * (-27.0d0)))
    else if (t <= 1.05d-42) then
        tmp = ((b * c) - t_2) - ((j * 27.0d0) * k)
    else
        tmp = ((b * c) + (t * (t_1 - (a * 4.0d0)))) - 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;
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 = 18.0 * (x * (y * z));
	double t_2 = 4.0 * (x * i);
	double tmp;
	if (t <= -8.2e-23) {
		tmp = (t * ((a * -4.0) + t_1)) + (j * (k * -27.0));
	} else if (t <= 1.05e-42) {
		tmp = ((b * c) - t_2) - ((j * 27.0) * k);
	} else {
		tmp = ((b * c) + (t * (t_1 - (a * 4.0)))) - 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])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = 18.0 * (x * (y * z))
	t_2 = 4.0 * (x * i)
	tmp = 0
	if t <= -8.2e-23:
		tmp = (t * ((a * -4.0) + t_1)) + (j * (k * -27.0))
	elif t <= 1.05e-42:
		tmp = ((b * c) - t_2) - ((j * 27.0) * k)
	else:
		tmp = ((b * c) + (t * (t_1 - (a * 4.0)))) - 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])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(18.0 * Float64(x * Float64(y * z)))
	t_2 = Float64(4.0 * Float64(x * i))
	tmp = 0.0
	if (t <= -8.2e-23)
		tmp = Float64(Float64(t * Float64(Float64(a * -4.0) + t_1)) + Float64(j * Float64(k * -27.0)));
	elseif (t <= 1.05e-42)
		tmp = Float64(Float64(Float64(b * c) - t_2) - Float64(Float64(j * 27.0) * k));
	else
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(t_1 - Float64(a * 4.0)))) - 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])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = 18.0 * (x * (y * z));
	t_2 = 4.0 * (x * i);
	tmp = 0.0;
	if (t <= -8.2e-23)
		tmp = (t * ((a * -4.0) + t_1)) + (j * (k * -27.0));
	elseif (t <= 1.05e-42)
		tmp = ((b * c) - t_2) - ((j * 27.0) * k);
	else
		tmp = ((b * c) + (t * (t_1 - (a * 4.0)))) - 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.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8.2e-23], N[(N[(t * N[(N[(a * -4.0), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.05e-42], N[(N[(N[(b * c), $MachinePrecision] - t$95$2), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(t$95$1 - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.20000000000000059e-23

   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 77.6%

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

   5. Taylor expanded in t around inf 73.5%

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

   if -8.20000000000000059e-23 < t < 1.05000000000000003e-42

   1. Initial program 87.6%

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

   3. Taylor expanded in t around 0 84.0%

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

   if 1.05000000000000003e-42 < t

   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 93.2%

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

   5. Taylor expanded in j around 0 85.5%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.2 \cdot 10^{-23}:\\ \;\;\;\;t \cdot \left(a \cdot -4 + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-42}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 76.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{-25} \lor \neg \left(t \leq 2.05 \cdot 10^{+55}\right):\\ \;\;\;\;t \cdot \left(a \cdot -4 + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= t -9e-25) (not (<= t 2.05e+55)))
   (+ (* t (+ (* a -4.0) (* 18.0 (* x (* y z))))) (* j (* k -27.0)))
   (- (- (* b c) (* 4.0 (* x i))) (* (* j 27.0) k))))

C

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 <= -9e-25) || !(t <= 2.05e+55)) {
		tmp = (t * ((a * -4.0) + (18.0 * (x * (y * z))))) + (j * (k * -27.0));
	} else {
		tmp = ((b * c) - (4.0 * (x * i))) - ((j * 27.0) * 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.
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 <= (-9d-25)) .or. (.not. (t <= 2.05d+55))) then
        tmp = (t * ((a * (-4.0d0)) + (18.0d0 * (x * (y * z))))) + (j * (k * (-27.0d0)))
    else
        tmp = ((b * c) - (4.0d0 * (x * i))) - ((j * 27.0d0) * 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;
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 <= -9e-25) || !(t <= 2.05e+55)) {
		tmp = (t * ((a * -4.0) + (18.0 * (x * (y * z))))) + (j * (k * -27.0));
	} else {
		tmp = ((b * c) - (4.0 * (x * i))) - ((j * 27.0) * 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])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (t <= -9e-25) or not (t <= 2.05e+55):
		tmp = (t * ((a * -4.0) + (18.0 * (x * (y * z))))) + (j * (k * -27.0))
	else:
		tmp = ((b * c) - (4.0 * (x * i))) - ((j * 27.0) * 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])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((t <= -9e-25) || !(t <= 2.05e+55))
		tmp = Float64(Float64(t * Float64(Float64(a * -4.0) + Float64(18.0 * Float64(x * Float64(y * z))))) + Float64(j * Float64(k * -27.0)));
	else
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(x * i))) - Float64(Float64(j * 27.0) * 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])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((t <= -9e-25) || ~((t <= 2.05e+55)))
		tmp = (t * ((a * -4.0) + (18.0 * (x * (y * z))))) + (j * (k * -27.0));
	else
		tmp = ((b * c) - (4.0 * (x * i))) - ((j * 27.0) * 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.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[t, -9e-25], N[Not[LessEqual[t, 2.05e+55]], $MachinePrecision]], N[(N[(t * N[(N[(a * -4.0), $MachinePrecision] + N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -9.0000000000000002e-25 or 2.04999999999999991e55 < t

   1. Initial program 76.9%

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

   3. Simplified 85.7%

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

   5. Taylor expanded in t around inf 75.8%

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

   if -9.0000000000000002e-25 < t < 2.04999999999999991e55

   1. Initial program 88.1%

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

   3. Taylor expanded in t around 0 82.6%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{-25} \lor \neg \left(t \leq 2.05 \cdot 10^{+55}\right):\\ \;\;\;\;t \cdot \left(a \cdot -4 + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 71.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{+34}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{+80}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(i \cdot -4 + 18 \cdot \left(z \cdot \left(y \cdot t\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= x -1.4e+34)
   (* x (- (* 18.0 (* t (* y z))) (* 4.0 i)))
   (if (<= x 3.8e+80)
     (- (- (* b c) (* 4.0 (* t a))) (* (* j 27.0) k))
     (* x (+ (* i -4.0) (* 18.0 (* z (* y t))))))))

C

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 (x <= -1.4e+34) {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	} else if (x <= 3.8e+80) {
		tmp = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k);
	} else {
		tmp = x * ((i * -4.0) + (18.0 * (z * (y * t))));
	}
	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.
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 (x <= (-1.4d+34)) then
        tmp = x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i))
    else if (x <= 3.8d+80) then
        tmp = ((b * c) - (4.0d0 * (t * a))) - ((j * 27.0d0) * k)
    else
        tmp = x * ((i * (-4.0d0)) + (18.0d0 * (z * (y * t))))
    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;
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 (x <= -1.4e+34) {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	} else if (x <= 3.8e+80) {
		tmp = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k);
	} else {
		tmp = x * ((i * -4.0) + (18.0 * (z * (y * t))));
	}
	return tmp;
}

Python

[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 x <= -1.4e+34:
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i))
	elif x <= 3.8e+80:
		tmp = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k)
	else:
		tmp = x * ((i * -4.0) + (18.0 * (z * (y * t))))
	return tmp

Julia

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 (x <= -1.4e+34)
		tmp = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)));
	elseif (x <= 3.8e+80)
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(t * a))) - Float64(Float64(j * 27.0) * k));
	else
		tmp = Float64(x * Float64(Float64(i * -4.0) + Float64(18.0 * Float64(z * Float64(y * t)))));
	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])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (x <= -1.4e+34)
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	elseif (x <= 3.8e+80)
		tmp = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k);
	else
		tmp = x * ((i * -4.0) + (18.0 * (z * (y * t))));
	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.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[x, -1.4e+34], N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.8e+80], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(i * -4.0), $MachinePrecision] + N[(18.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.40000000000000004e34

   1. Initial program 70.2%

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

   3. Simplified 82.3%

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

   5. Taylor expanded in x around inf 70.4%

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

   if -1.40000000000000004e34 < x < 3.79999999999999997e80

   1. Initial program 94.1%

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

   3. Taylor expanded in x around 0 76.9%

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

   if 3.79999999999999997e80 < x

   1. Initial program 58.0%

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

   3. Simplified 66.7%

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

      1. pow1 66.7%

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

      2. associate-*l* 66.7%

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

      3. associate-*r* 66.7%

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

   6. Applied egg-rr 66.7%

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

      1. unpow1 66.7%

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

      2. *-commutative 66.7%

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

   8. Simplified 66.7%

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

      1. pow1 66.7%

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

      2. associate-*r* 66.7%

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

   10. Applied egg-rr 66.7%

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

       1. unpow1 66.7%

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

       2. associate-*r* 64.5%

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

       3. *-commutative 64.5%

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

   12. Simplified 64.5%

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

   13. Taylor expanded in x around inf 70.7%

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

       1. cancel-sign-sub-inv 70.7%

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

       2. metadata-eval 70.7%

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

       3. associate-*r* 74.9%

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

   15. Simplified 74.9%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{+34}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{+80}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(i \cdot -4 + 18 \cdot \left(z \cdot \left(y \cdot t\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 33.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -3.9 \cdot 10^{-14}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;x \leq -3.9 \cdot 10^{-56}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{+51}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot t\right) \cdot \left(18 \cdot \left(x \cdot y\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= x -3.9e-14)
   (* 18.0 (* t (* x (* y z))))
   (if (<= x -3.9e-56)
     (* b c)
     (if (<= x 1.35e+51) (* -27.0 (* j k)) (* (* z t) (* 18.0 (* x y)))))))

C

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 (x <= -3.9e-14) {
		tmp = 18.0 * (t * (x * (y * z)));
	} else if (x <= -3.9e-56) {
		tmp = b * c;
	} else if (x <= 1.35e+51) {
		tmp = -27.0 * (j * k);
	} else {
		tmp = (z * t) * (18.0 * (x * 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.
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 (x <= (-3.9d-14)) then
        tmp = 18.0d0 * (t * (x * (y * z)))
    else if (x <= (-3.9d-56)) then
        tmp = b * c
    else if (x <= 1.35d+51) then
        tmp = (-27.0d0) * (j * k)
    else
        tmp = (z * t) * (18.0d0 * (x * 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;
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 (x <= -3.9e-14) {
		tmp = 18.0 * (t * (x * (y * z)));
	} else if (x <= -3.9e-56) {
		tmp = b * c;
	} else if (x <= 1.35e+51) {
		tmp = -27.0 * (j * k);
	} else {
		tmp = (z * t) * (18.0 * (x * 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])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if x <= -3.9e-14:
		tmp = 18.0 * (t * (x * (y * z)))
	elif x <= -3.9e-56:
		tmp = b * c
	elif x <= 1.35e+51:
		tmp = -27.0 * (j * k)
	else:
		tmp = (z * t) * (18.0 * (x * 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])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (x <= -3.9e-14)
		tmp = Float64(18.0 * Float64(t * Float64(x * Float64(y * z))));
	elseif (x <= -3.9e-56)
		tmp = Float64(b * c);
	elseif (x <= 1.35e+51)
		tmp = Float64(-27.0 * Float64(j * k));
	else
		tmp = Float64(Float64(z * t) * Float64(18.0 * Float64(x * 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])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (x <= -3.9e-14)
		tmp = 18.0 * (t * (x * (y * z)));
	elseif (x <= -3.9e-56)
		tmp = b * c;
	elseif (x <= 1.35e+51)
		tmp = -27.0 * (j * k);
	else
		tmp = (z * t) * (18.0 * (x * 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.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[x, -3.9e-14], N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3.9e-56], N[(b * c), $MachinePrecision], If[LessEqual[x, 1.35e+51], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], N[(N[(z * t), $MachinePrecision] * N[(18.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -3.8999999999999998e-14

   1. Initial program 74.7%

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

   3. Simplified 86.5%

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

   5. Taylor expanded in y around inf 52.8%

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

      1. associate-*r* 54.2%

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

   7. Simplified 54.2%

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

   8. Taylor expanded in t around 0 52.8%

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

      1. associate-*r* 51.5%

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

      2. *-commutative 51.5%

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

   10. Simplified 51.5%

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

   11. Taylor expanded in t around inf 42.4%

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

   if -3.8999999999999998e-14 < x < -3.9e-56

   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. pow1 100.0%

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

      2. associate-*l* 100.0%

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

      3. associate-*r* 100.0%

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

   6. Applied egg-rr 100.0%

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

      1. unpow1 100.0%

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

      2. *-commutative 100.0%

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

   8. Simplified 100.0%

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

      1. pow1 100.0%

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

      2. associate-*r* 100.0%

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

   10. Applied egg-rr 100.0%

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

       1. unpow1 100.0%

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

       2. associate-*r* 100.0%

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

       3. *-commutative 100.0%

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

   12. Simplified 100.0%

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

   13. Taylor expanded in b around inf 71.7%

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

   if -3.9e-56 < x < 1.34999999999999996e51

   1. Initial program 93.1%

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

   3. Simplified 91.8%

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

   5. Taylor expanded in j around inf 39.2%

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

   if 1.34999999999999996e51 < x

   1. Initial program 63.0%

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

   3. Simplified 72.7%

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

   5. Taylor expanded in y around inf 45.5%

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

      1. associate-*r* 51.1%

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

   7. Simplified 51.1%

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

   8. Taylor expanded in t around 0 45.5%

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

      1. associate-*r* 47.6%

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

      2. *-commutative 47.6%

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

   10. Simplified 47.6%

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

   11. Taylor expanded in t around inf 39.9%

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

       1. *-commutative 39.9%

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

       2. associate-*r* 41.9%

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

       3. *-commutative 41.9%

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

       4. associate-*l* 48.7%

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

       5. associate-*l* 48.7%

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

   13. Simplified 48.7%

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

4. Final simplification 42.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.9 \cdot 10^{-14}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;x \leq -3.9 \cdot 10^{-56}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{+51}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot t\right) \cdot \left(18 \cdot \left(x \cdot y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 33.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{if}\;x \leq -2.35 \cdot 10^{-14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -1.85 \cdot 10^{-56}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{+53}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* 18.0 (* t (* x (* y z))))))
   (if (<= x -2.35e-14)
     t_1
     (if (<= x -1.85e-56) (* b c) (if (<= x 1.5e+53) (* -27.0 (* j k)) t_1)))))

C

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 = 18.0 * (t * (x * (y * z)));
	double tmp;
	if (x <= -2.35e-14) {
		tmp = t_1;
	} else if (x <= -1.85e-56) {
		tmp = b * c;
	} else if (x <= 1.5e+53) {
		tmp = -27.0 * (j * 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.
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 = 18.0d0 * (t * (x * (y * z)))
    if (x <= (-2.35d-14)) then
        tmp = t_1
    else if (x <= (-1.85d-56)) then
        tmp = b * c
    else if (x <= 1.5d+53) then
        tmp = (-27.0d0) * (j * 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;
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 = 18.0 * (t * (x * (y * z)));
	double tmp;
	if (x <= -2.35e-14) {
		tmp = t_1;
	} else if (x <= -1.85e-56) {
		tmp = b * c;
	} else if (x <= 1.5e+53) {
		tmp = -27.0 * (j * 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])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = 18.0 * (t * (x * (y * z)))
	tmp = 0
	if x <= -2.35e-14:
		tmp = t_1
	elif x <= -1.85e-56:
		tmp = b * c
	elif x <= 1.5e+53:
		tmp = -27.0 * (j * 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])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(18.0 * Float64(t * Float64(x * Float64(y * z))))
	tmp = 0.0
	if (x <= -2.35e-14)
		tmp = t_1;
	elseif (x <= -1.85e-56)
		tmp = Float64(b * c);
	elseif (x <= 1.5e+53)
		tmp = Float64(-27.0 * Float64(j * 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])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = 18.0 * (t * (x * (y * z)));
	tmp = 0.0;
	if (x <= -2.35e-14)
		tmp = t_1;
	elseif (x <= -1.85e-56)
		tmp = b * c;
	elseif (x <= 1.5e+53)
		tmp = -27.0 * (j * 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.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.35e-14], t$95$1, If[LessEqual[x, -1.85e-56], N[(b * c), $MachinePrecision], If[LessEqual[x, 1.5e+53], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.3500000000000001e-14 or 1.49999999999999999e53 < x

   1. Initial program 69.6%

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

   3. Simplified 80.5%

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

   5. Taylor expanded in y around inf 49.7%

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

      1. associate-*r* 52.9%

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

   7. Simplified 52.9%

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

   8. Taylor expanded in t around 0 49.7%

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

      1. associate-*r* 49.8%

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

      2. *-commutative 49.8%

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

   10. Simplified 49.8%

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

   11. Taylor expanded in t around inf 41.3%

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

   if -2.3500000000000001e-14 < x < -1.8500000000000001e-56

   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. pow1 100.0%

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

      2. associate-*l* 100.0%

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

      3. associate-*r* 100.0%

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

   6. Applied egg-rr 100.0%

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

      1. unpow1 100.0%

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

      2. *-commutative 100.0%

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

   8. Simplified 100.0%

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

      1. pow1 100.0%

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

      2. associate-*r* 100.0%

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

   10. Applied egg-rr 100.0%

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

       1. unpow1 100.0%

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

       2. associate-*r* 100.0%

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

       3. *-commutative 100.0%

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

   12. Simplified 100.0%

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

   13. Taylor expanded in b around inf 71.7%

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

   if -1.8500000000000001e-56 < x < 1.49999999999999999e53

   1. Initial program 93.1%

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

   3. Simplified 91.8%

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

   5. Taylor expanded in j around inf 39.2%

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

Alternative 18: 31.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ \mathbf{if}\;a \leq -1.35 \cdot 10^{+81}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -5.9 \cdot 10^{-192}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{+192}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* t (* a -4.0))))
   (if (<= a -1.35e+81)
     t_1
     (if (<= a -5.9e-192)
       (* b c)
       (if (<= a 1.15e+192) (* -27.0 (* j k)) t_1)))))

C

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 (a <= -1.35e+81) {
		tmp = t_1;
	} else if (a <= -5.9e-192) {
		tmp = b * c;
	} else if (a <= 1.15e+192) {
		tmp = -27.0 * (j * 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.
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 (a <= (-1.35d+81)) then
        tmp = t_1
    else if (a <= (-5.9d-192)) then
        tmp = b * c
    else if (a <= 1.15d+192) then
        tmp = (-27.0d0) * (j * 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;
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 (a <= -1.35e+81) {
		tmp = t_1;
	} else if (a <= -5.9e-192) {
		tmp = b * c;
	} else if (a <= 1.15e+192) {
		tmp = -27.0 * (j * 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])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = t * (a * -4.0)
	tmp = 0
	if a <= -1.35e+81:
		tmp = t_1
	elif a <= -5.9e-192:
		tmp = b * c
	elif a <= 1.15e+192:
		tmp = -27.0 * (j * 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])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(t * Float64(a * -4.0))
	tmp = 0.0
	if (a <= -1.35e+81)
		tmp = t_1;
	elseif (a <= -5.9e-192)
		tmp = Float64(b * c);
	elseif (a <= 1.15e+192)
		tmp = Float64(-27.0 * Float64(j * 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])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = t * (a * -4.0);
	tmp = 0.0;
	if (a <= -1.35e+81)
		tmp = t_1;
	elseif (a <= -5.9e-192)
		tmp = b * c;
	elseif (a <= 1.15e+192)
		tmp = -27.0 * (j * 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.
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[a, -1.35e+81], t$95$1, If[LessEqual[a, -5.9e-192], N[(b * c), $MachinePrecision], If[LessEqual[a, 1.15e+192], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.35e81 or 1.15e192 < a

   1. Initial program 71.6%

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

   3. Taylor expanded in x around 0 68.6%

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

   4. Taylor expanded in a around inf 48.9%

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

      1. metadata-eval 48.9%

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

      2. distribute-lft-neg-in 48.9%

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

      3. associate-*r* 48.9%

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

      4. *-commutative 48.9%

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

      5. distribute-rgt-neg-in 48.9%

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

      6. distribute-lft-neg-in 48.9%

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

      7. metadata-eval 48.9%

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

      8. *-commutative 48.9%

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

   6. Simplified 48.9%

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

   if -1.35e81 < a < -5.8999999999999997e-192

   1. Initial program 83.5%

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

   3. Simplified 83.6%

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

      1. pow1 83.6%

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

      2. associate-*l* 83.6%

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

      3. associate-*r* 83.6%

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

   6. Applied egg-rr 83.6%

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

      1. unpow1 83.6%

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

      2. *-commutative 83.6%

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

   8. Simplified 83.6%

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

      1. pow1 83.6%

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

      2. associate-*r* 83.6%

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

   10. Applied egg-rr 83.6%

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

       1. unpow1 83.6%

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

       2. associate-*r* 83.6%

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

       3. *-commutative 83.6%

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

   12. Simplified 83.6%

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

   13. Taylor expanded in b around inf 34.6%

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

   if -5.8999999999999997e-192 < a < 1.15e192

   1. Initial program 88.2%

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

   3. Simplified 88.3%

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

   5. Taylor expanded in j around inf 36.4%

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

Alternative 19: 31.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := -4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;x \leq -1.15 \cdot 10^{+116}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -3 \cdot 10^{-56}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{+115}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* -4.0 (* x i))))
   (if (<= x -1.15e+116)
     t_1
     (if (<= x -3e-56) (* b c) (if (<= x 1.2e+115) (* -27.0 (* j k)) t_1)))))

C

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 = -4.0 * (x * i);
	double tmp;
	if (x <= -1.15e+116) {
		tmp = t_1;
	} else if (x <= -3e-56) {
		tmp = b * c;
	} else if (x <= 1.2e+115) {
		tmp = -27.0 * (j * 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.
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 = (-4.0d0) * (x * i)
    if (x <= (-1.15d+116)) then
        tmp = t_1
    else if (x <= (-3d-56)) then
        tmp = b * c
    else if (x <= 1.2d+115) then
        tmp = (-27.0d0) * (j * 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;
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 = -4.0 * (x * i);
	double tmp;
	if (x <= -1.15e+116) {
		tmp = t_1;
	} else if (x <= -3e-56) {
		tmp = b * c;
	} else if (x <= 1.2e+115) {
		tmp = -27.0 * (j * 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])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = -4.0 * (x * i)
	tmp = 0
	if x <= -1.15e+116:
		tmp = t_1
	elif x <= -3e-56:
		tmp = b * c
	elif x <= 1.2e+115:
		tmp = -27.0 * (j * 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])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(-4.0 * Float64(x * i))
	tmp = 0.0
	if (x <= -1.15e+116)
		tmp = t_1;
	elseif (x <= -3e-56)
		tmp = Float64(b * c);
	elseif (x <= 1.2e+115)
		tmp = Float64(-27.0 * Float64(j * 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])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = -4.0 * (x * i);
	tmp = 0.0;
	if (x <= -1.15e+116)
		tmp = t_1;
	elseif (x <= -3e-56)
		tmp = b * c;
	elseif (x <= 1.2e+115)
		tmp = -27.0 * (j * 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.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.15e+116], t$95$1, If[LessEqual[x, -3e-56], N[(b * c), $MachinePrecision], If[LessEqual[x, 1.2e+115], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.14999999999999997e116 or 1.2e115 < x

   1. Initial program 62.7%

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

   3. Simplified 75.4%

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

      1. pow1 75.4%

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

      2. associate-*l* 75.3%

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

      3. associate-*r* 75.4%

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

   6. Applied egg-rr 75.4%

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

      1. unpow1 75.4%

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

      2. *-commutative 75.4%

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

   8. Simplified 75.4%

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

      1. pow1 75.4%

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

      2. associate-*r* 75.4%

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

   10. Applied egg-rr 75.4%

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

       1. unpow1 75.4%

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

       2. associate-*r* 71.6%

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

       3. *-commutative 71.6%

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

   12. Simplified 71.6%

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

   13. Taylor expanded in i around inf 43.3%

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

       1. *-commutative 43.3%

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

   15. Simplified 43.3%

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

   if -1.14999999999999997e116 < x < -2.99999999999999989e-56

   1. Initial program 86.4%

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

   3. Simplified 89.1%

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

      1. pow1 89.1%

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

      2. associate-*l* 89.1%

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

      3. associate-*r* 89.1%

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

   6. Applied egg-rr 89.1%

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

      1. unpow1 89.1%

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

      2. *-commutative 89.1%

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

   8. Simplified 89.1%

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

      1. pow1 89.1%

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

      2. associate-*r* 89.1%

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

   10. Applied egg-rr 89.1%

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

       1. unpow1 89.1%

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

       2. associate-*r* 89.1%

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

       3. *-commutative 89.1%

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

   12. Simplified 89.1%

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

   13. Taylor expanded in b around inf 31.9%

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

   if -2.99999999999999989e-56 < x < 1.2e115

   1. Initial program 92.3%

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

   3. Simplified 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 j around inf 38.0%

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

Alternative 20: 48.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+142}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-15}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot t\right) \cdot \left(18 \cdot \left(x \cdot y\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= y -4.2e+142)
   (* 18.0 (* t (* x (* y z))))
   (if (<= y 1.55e-15)
     (+ (* b c) (* j (* k -27.0)))
     (* (* z t) (* 18.0 (* x y))))))

C

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 (y <= -4.2e+142) {
		tmp = 18.0 * (t * (x * (y * z)));
	} else if (y <= 1.55e-15) {
		tmp = (b * c) + (j * (k * -27.0));
	} else {
		tmp = (z * t) * (18.0 * (x * 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.
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 (y <= (-4.2d+142)) then
        tmp = 18.0d0 * (t * (x * (y * z)))
    else if (y <= 1.55d-15) then
        tmp = (b * c) + (j * (k * (-27.0d0)))
    else
        tmp = (z * t) * (18.0d0 * (x * 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;
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 (y <= -4.2e+142) {
		tmp = 18.0 * (t * (x * (y * z)));
	} else if (y <= 1.55e-15) {
		tmp = (b * c) + (j * (k * -27.0));
	} else {
		tmp = (z * t) * (18.0 * (x * 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])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if y <= -4.2e+142:
		tmp = 18.0 * (t * (x * (y * z)))
	elif y <= 1.55e-15:
		tmp = (b * c) + (j * (k * -27.0))
	else:
		tmp = (z * t) * (18.0 * (x * 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])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (y <= -4.2e+142)
		tmp = Float64(18.0 * Float64(t * Float64(x * Float64(y * z))));
	elseif (y <= 1.55e-15)
		tmp = Float64(Float64(b * c) + Float64(j * Float64(k * -27.0)));
	else
		tmp = Float64(Float64(z * t) * Float64(18.0 * Float64(x * 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])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (y <= -4.2e+142)
		tmp = 18.0 * (t * (x * (y * z)));
	elseif (y <= 1.55e-15)
		tmp = (b * c) + (j * (k * -27.0));
	else
		tmp = (z * t) * (18.0 * (x * 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.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[y, -4.2e+142], N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.55e-15], N[(N[(b * c), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z * t), $MachinePrecision] * N[(18.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.2e142

   1. Initial program 62.9%

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

   3. Simplified 72.6%

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

   5. Taylor expanded in y around inf 55.6%

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

      1. associate-*r* 58.1%

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

   7. Simplified 58.1%

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

   8. Taylor expanded in t around 0 55.6%

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

      1. associate-*r* 50.9%

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

      2. *-commutative 50.9%

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

   10. Simplified 50.9%

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

   11. Taylor expanded in t around inf 48.6%

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

   if -4.2e142 < y < 1.5499999999999999e-15

   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 94.6%

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

   5. Taylor expanded in b around inf 53.6%

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

   if 1.5499999999999999e-15 < y

   1. Initial program 74.6%

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

   3. Simplified 77.8%

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

   5. Taylor expanded in y around inf 43.5%

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

      1. associate-*r* 46.3%

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

   7. Simplified 46.3%

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

   8. Taylor expanded in t around 0 43.5%

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

      1. associate-*r* 52.4%

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

      2. *-commutative 52.4%

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

   10. Simplified 52.4%

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

   11. Taylor expanded in t around inf 31.2%

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

       1. *-commutative 31.2%

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

       2. associate-*r* 38.6%

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

       3. *-commutative 38.6%

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

       4. associate-*l* 39.3%

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

       5. associate-*l* 39.3%

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

   13. Simplified 39.3%

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

4. Final simplification 49.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+142}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-15}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot t\right) \cdot \left(18 \cdot \left(x \cdot y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 32.9% accurate, 2.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;k \leq -7.5 \cdot 10^{-17} \lor \neg \left(k \leq 1.85 \cdot 10^{+126}\right):\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= k -7.5e-17) (not (<= k 1.85e+126))) (* -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);
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 ((k <= -7.5e-17) || !(k <= 1.85e+126)) {
		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.
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 ((k <= (-7.5d-17)) .or. (.not. (k <= 1.85d+126))) 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;
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 ((k <= -7.5e-17) || !(k <= 1.85e+126)) {
		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])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (k <= -7.5e-17) or not (k <= 1.85e+126):
		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])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((k <= -7.5e-17) || !(k <= 1.85e+126))
		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])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((k <= -7.5e-17) || ~((k <= 1.85e+126)))
		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.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[k, -7.5e-17], N[Not[LessEqual[k, 1.85e+126]], $MachinePrecision]], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if k < -7.49999999999999984e-17 or 1.8499999999999999e126 < k

   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 87.1%

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

   5. Taylor expanded in j around inf 42.8%

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

   if -7.49999999999999984e-17 < k < 1.8499999999999999e126

   1. Initial program 81.1%

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

   3. Simplified 86.1%

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

      1. pow1 86.1%

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

      2. associate-*l* 86.1%

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

      3. associate-*r* 86.1%

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

   6. Applied egg-rr 86.1%

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

      1. unpow1 86.1%

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

      2. *-commutative 86.1%

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

   8. Simplified 86.1%

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

      1. pow1 86.1%

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

      2. associate-*r* 86.1%

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

   10. Applied egg-rr 86.1%

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

       1. unpow1 86.1%

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

       2. associate-*r* 88.1%

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

       3. *-commutative 88.1%

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

   12. Simplified 88.1%

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

   13. Taylor expanded in b around inf 27.0%

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

4. Final simplification 34.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -7.5 \cdot 10^{-17} \lor \neg \left(k \leq 1.85 \cdot 10^{+126}\right):\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 23.7% accurate, 10.3× speedup

Math

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

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(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);
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.
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;
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])
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])
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])){:}
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.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := N[(b * c), $MachinePrecision]

Derivation

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 85.8%

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

   1. pow1 85.8%

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

   2. associate-*l* 85.7%

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

   3. associate-*r* 85.4%

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

6. Applied egg-rr 85.4%

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

   1. unpow1 85.4%

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

   2. *-commutative 85.4%

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

8. Simplified 85.4%

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

   1. pow1 85.4%

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

   2. associate-*r* 85.8%

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

10. Applied egg-rr 85.8%

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

    1. unpow1 85.8%

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

    2. associate-*r* 87.6%

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

    3. *-commutative 87.6%

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

12. Simplified 87.6%

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

13. Taylor expanded in b around inf 21.0%

    \[\leadsto \color{blue}{b \cdot c} \]
14. Add Preprocessing

Developer target: 89.4% 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 2024106 
(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)))