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

Percentage Accurate: 85.2% → 91.3%

Time: 28.4s

Alternatives: 26

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: 85.2% 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: 91.3% accurate, 0.5× speedup

Math

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

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
         (-
          (-
           (+ (- (* (* (* (* x 18.0) y) z) t) (* t (* a 4.0))) (* b c))
           (* (* x 4.0) i))
          (* (* j 27.0) k))))
   (if (<= t_1 INFINITY)
     t_1
     (* c (+ b (/ (* t (+ (* a -4.0) (* 18.0 (* z (* x y))))) 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 = (((((((x * 18.0) * y) * z) * t) - (t * (a * 4.0))) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = c * (b + ((t * ((a * -4.0) + (18.0 * (z * (x * y))))) / c));
	}
	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 * 18.0) * y) * z) * t) - (t * (a * 4.0))) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = c * (b + ((t * ((a * -4.0) + (18.0 * (z * (x * y))))) / 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 = (((((((x * 18.0) * y) * z) * t) - (t * (a * 4.0))) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k)
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = c * (b + ((t * ((a * -4.0) + (18.0 * (z * (x * y))))) / 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(Float64(Float64(Float64(Float64(Float64(Float64(x * 18.0) * y) * z) * t) - Float64(t * Float64(a * 4.0))) + Float64(b * c)) - Float64(Float64(x * 4.0) * i)) - Float64(Float64(j * 27.0) * k))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(c * Float64(b + Float64(Float64(t * Float64(Float64(a * -4.0) + Float64(18.0 * Float64(z * Float64(x * y))))) / 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 = (((((((x * 18.0) * y) * z) * t) - (t * (a * 4.0))) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = c * (b + ((t * ((a * -4.0) + (18.0 * (z * (x * y))))) / 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[(N[(N[(N[(N[(N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision] - N[(t * N[(a * 4.0), $MachinePrecision]), $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]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(c * N[(b + N[(N[(t * N[(N[(a * -4.0), $MachinePrecision] + N[(18.0 * N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 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)) < +inf.0

   1. Initial program 95.4%

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

   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%

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

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 0.0%

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

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \color{blue}{\left(b \cdot c\right)}\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 32.3%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \mathsf{*.f64}\left(b, \color{blue}{c}\right)\right) \]

   7. Simplified 32.3%

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

   8. Taylor expanded in c around inf

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

   10. Simplified 57.3%

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

4. Final simplification 91.2%

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

Alternative 2: 53.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c + x \cdot \left(i \cdot -4\right)\\ t_2 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+20}:\\ \;\;\;\;b \cdot c - t\_2\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{-216}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{-290}:\\ \;\;\;\;b \cdot c + t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+150}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right) - t\_2\\ \end{array} \end{array} \]

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 (+ (* b c) (* x (* i -4.0)))) (t_2 (* (* j 27.0) k)))
   (if (<= t_2 -2e+20)
     (- (* b c) t_2)
     (if (<= t_2 -1e-216)
       t_1
       (if (<= t_2 2e-290)
         (+ (* b c) (* t (* a -4.0)))
         (if (<= t_2 2e+150) t_1 (- (* -4.0 (* t a)) 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) + (x * (i * -4.0));
	double t_2 = (j * 27.0) * k;
	double tmp;
	if (t_2 <= -2e+20) {
		tmp = (b * c) - t_2;
	} else if (t_2 <= -1e-216) {
		tmp = t_1;
	} else if (t_2 <= 2e-290) {
		tmp = (b * c) + (t * (a * -4.0));
	} else if (t_2 <= 2e+150) {
		tmp = t_1;
	} else {
		tmp = (-4.0 * (t * a)) - 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) + (x * (i * (-4.0d0)))
    t_2 = (j * 27.0d0) * k
    if (t_2 <= (-2d+20)) then
        tmp = (b * c) - t_2
    else if (t_2 <= (-1d-216)) then
        tmp = t_1
    else if (t_2 <= 2d-290) then
        tmp = (b * c) + (t * (a * (-4.0d0)))
    else if (t_2 <= 2d+150) then
        tmp = t_1
    else
        tmp = ((-4.0d0) * (t * a)) - 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) + (x * (i * -4.0));
	double t_2 = (j * 27.0) * k;
	double tmp;
	if (t_2 <= -2e+20) {
		tmp = (b * c) - t_2;
	} else if (t_2 <= -1e-216) {
		tmp = t_1;
	} else if (t_2 <= 2e-290) {
		tmp = (b * c) + (t * (a * -4.0));
	} else if (t_2 <= 2e+150) {
		tmp = t_1;
	} else {
		tmp = (-4.0 * (t * a)) - 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) + (x * (i * -4.0))
	t_2 = (j * 27.0) * k
	tmp = 0
	if t_2 <= -2e+20:
		tmp = (b * c) - t_2
	elif t_2 <= -1e-216:
		tmp = t_1
	elif t_2 <= 2e-290:
		tmp = (b * c) + (t * (a * -4.0))
	elif t_2 <= 2e+150:
		tmp = t_1
	else:
		tmp = (-4.0 * (t * a)) - 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(x * Float64(i * -4.0)))
	t_2 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_2 <= -2e+20)
		tmp = Float64(Float64(b * c) - t_2);
	elseif (t_2 <= -1e-216)
		tmp = t_1;
	elseif (t_2 <= 2e-290)
		tmp = Float64(Float64(b * c) + Float64(t * Float64(a * -4.0)));
	elseif (t_2 <= 2e+150)
		tmp = t_1;
	else
		tmp = Float64(Float64(-4.0 * Float64(t * a)) - 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) + (x * (i * -4.0));
	t_2 = (j * 27.0) * k;
	tmp = 0.0;
	if (t_2 <= -2e+20)
		tmp = (b * c) - t_2;
	elseif (t_2 <= -1e-216)
		tmp = t_1;
	elseif (t_2 <= 2e-290)
		tmp = (b * c) + (t * (a * -4.0));
	elseif (t_2 <= 2e+150)
		tmp = t_1;
	else
		tmp = (-4.0 * (t * a)) - 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[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+20], N[(N[(b * c), $MachinePrecision] - t$95$2), $MachinePrecision], If[LessEqual[t$95$2, -1e-216], t$95$1, If[LessEqual[t$95$2, 2e-290], N[(N[(b * c), $MachinePrecision] + N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+150], t$95$1, N[(N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -2e20

   1. Initial program 78.9%

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

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(b \cdot c\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 61.4%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

   5. Simplified 61.4%

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

   if -2e20 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -1e-216 or 2.0000000000000001e-290 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 1.99999999999999996e150

   1. Initial program 86.5%

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

   3. Taylor expanded in t around 0

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\color{blue}{\left(b \cdot c\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 63.3%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

   5. Simplified 63.3%

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

   6. Taylor expanded in j around 0

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

      1. cancel-sign-sub-inv N/A

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

      2. metadata-eval N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(b \cdot c\right), \color{blue}{\left(-4 \cdot \left(i \cdot x\right)\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\color{blue}{-4} \cdot \left(i \cdot x\right)\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\left(-4 \cdot i\right) \cdot \color{blue}{x}\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(x \cdot \color{blue}{\left(-4 \cdot i\right)}\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \color{blue}{\left(-4 \cdot i\right)}\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \left(i \cdot \color{blue}{-4}\right)\right)\right) \]

      9. *-lowering-*.f64 58.0%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, \color{blue}{-4}\right)\right)\right) \]

   8. Simplified 58.0%

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

   if -1e-216 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 2.0000000000000001e-290

   1. Initial program 95.9%

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

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 95.9%

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

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \color{blue}{\left(b \cdot c\right)}\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 84.5%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \mathsf{*.f64}\left(b, \color{blue}{c}\right)\right) \]

   7. Simplified 84.5%

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

   8. Taylor expanded in x around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \color{blue}{\left(-4 \cdot a\right)}\right), \mathsf{*.f64}\left(b, c\right)\right) \]
   9. Step-by-step derivation

      1. *-lowering-*.f64 64.9%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(-4, a\right)\right), \mathsf{*.f64}\left(b, c\right)\right) \]

   10. Simplified 64.9%

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

   if 1.99999999999999996e150 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 74.9%

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

   3. Taylor expanded in a around inf

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(-4 \cdot \left(a \cdot t\right)\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(-4, \left(a \cdot t\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(-4, \left(t \cdot a\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, \color{blue}{27}\right), k\right)\right) \]

      3. *-lowering-*.f64 78.2%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(-4, \mathsf{*.f64}\left(t, a\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, \color{blue}{27}\right), k\right)\right) \]

   5. Simplified 78.2%

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

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \leq -2 \cdot 10^{+20}:\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq -1 \cdot 10^{-216}:\\ \;\;\;\;b \cdot c + x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 2 \cdot 10^{-290}:\\ \;\;\;\;b \cdot c + t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 2 \cdot 10^{+150}:\\ \;\;\;\;b \cdot c + x \cdot \left(i \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 53.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c + x \cdot \left(i \cdot -4\right)\\ t_2 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+20}:\\ \;\;\;\;b \cdot c - t\_2\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{-216}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{-290}:\\ \;\;\;\;b \cdot c + t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+150}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(b + -27 \cdot \frac{j \cdot k}{c}\right)\\ \end{array} \end{array} \]

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 (+ (* b c) (* x (* i -4.0)))) (t_2 (* (* j 27.0) k)))
   (if (<= t_2 -2e+20)
     (- (* b c) t_2)
     (if (<= t_2 -1e-216)
       t_1
       (if (<= t_2 2e-290)
         (+ (* b c) (* t (* a -4.0)))
         (if (<= t_2 2e+150) 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 = (b * c) + (x * (i * -4.0));
	double t_2 = (j * 27.0) * k;
	double tmp;
	if (t_2 <= -2e+20) {
		tmp = (b * c) - t_2;
	} else if (t_2 <= -1e-216) {
		tmp = t_1;
	} else if (t_2 <= 2e-290) {
		tmp = (b * c) + (t * (a * -4.0));
	} else if (t_2 <= 2e+150) {
		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 = (b * c) + (x * (i * (-4.0d0)))
    t_2 = (j * 27.0d0) * k
    if (t_2 <= (-2d+20)) then
        tmp = (b * c) - t_2
    else if (t_2 <= (-1d-216)) then
        tmp = t_1
    else if (t_2 <= 2d-290) then
        tmp = (b * c) + (t * (a * (-4.0d0)))
    else if (t_2 <= 2d+150) 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 = (b * c) + (x * (i * -4.0));
	double t_2 = (j * 27.0) * k;
	double tmp;
	if (t_2 <= -2e+20) {
		tmp = (b * c) - t_2;
	} else if (t_2 <= -1e-216) {
		tmp = t_1;
	} else if (t_2 <= 2e-290) {
		tmp = (b * c) + (t * (a * -4.0));
	} else if (t_2 <= 2e+150) {
		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 = (b * c) + (x * (i * -4.0))
	t_2 = (j * 27.0) * k
	tmp = 0
	if t_2 <= -2e+20:
		tmp = (b * c) - t_2
	elif t_2 <= -1e-216:
		tmp = t_1
	elif t_2 <= 2e-290:
		tmp = (b * c) + (t * (a * -4.0))
	elif t_2 <= 2e+150:
		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(b * c) + Float64(x * Float64(i * -4.0)))
	t_2 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_2 <= -2e+20)
		tmp = Float64(Float64(b * c) - t_2);
	elseif (t_2 <= -1e-216)
		tmp = t_1;
	elseif (t_2 <= 2e-290)
		tmp = Float64(Float64(b * c) + Float64(t * Float64(a * -4.0)));
	elseif (t_2 <= 2e+150)
		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 = (b * c) + (x * (i * -4.0));
	t_2 = (j * 27.0) * k;
	tmp = 0.0;
	if (t_2 <= -2e+20)
		tmp = (b * c) - t_2;
	elseif (t_2 <= -1e-216)
		tmp = t_1;
	elseif (t_2 <= 2e-290)
		tmp = (b * c) + (t * (a * -4.0));
	elseif (t_2 <= 2e+150)
		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[(b * c), $MachinePrecision] + N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+20], N[(N[(b * c), $MachinePrecision] - t$95$2), $MachinePrecision], If[LessEqual[t$95$2, -1e-216], t$95$1, If[LessEqual[t$95$2, 2e-290], N[(N[(b * c), $MachinePrecision] + N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+150], 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 (*.f64 j #s(literal 27 binary64)) k) < -2e20

   1. Initial program 78.9%

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

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(b \cdot c\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 61.4%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

   5. Simplified 61.4%

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

   if -2e20 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -1e-216 or 2.0000000000000001e-290 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 1.99999999999999996e150

   1. Initial program 86.5%

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

   3. Taylor expanded in t around 0

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\color{blue}{\left(b \cdot c\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 63.3%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

   5. Simplified 63.3%

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

   6. Taylor expanded in j around 0

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

      1. cancel-sign-sub-inv N/A

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

      2. metadata-eval N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(b \cdot c\right), \color{blue}{\left(-4 \cdot \left(i \cdot x\right)\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\color{blue}{-4} \cdot \left(i \cdot x\right)\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\left(-4 \cdot i\right) \cdot \color{blue}{x}\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(x \cdot \color{blue}{\left(-4 \cdot i\right)}\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \color{blue}{\left(-4 \cdot i\right)}\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \left(i \cdot \color{blue}{-4}\right)\right)\right) \]

      9. *-lowering-*.f64 58.0%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, \color{blue}{-4}\right)\right)\right) \]

   8. Simplified 58.0%

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

   if -1e-216 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 2.0000000000000001e-290

   1. Initial program 95.9%

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

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 95.9%

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

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \color{blue}{\left(b \cdot c\right)}\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 84.5%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \mathsf{*.f64}\left(b, \color{blue}{c}\right)\right) \]

   7. Simplified 84.5%

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

   8. Taylor expanded in x around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \color{blue}{\left(-4 \cdot a\right)}\right), \mathsf{*.f64}\left(b, c\right)\right) \]
   9. Step-by-step derivation

      1. *-lowering-*.f64 64.9%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(-4, a\right)\right), \mathsf{*.f64}\left(b, c\right)\right) \]

   10. Simplified 64.9%

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

   if 1.99999999999999996e150 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 74.9%

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

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(b \cdot c\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 65.8%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

   5. Simplified 65.8%

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

   6. Taylor expanded in c around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(b + -27 \cdot \frac{j \cdot k}{c}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(b, \color{blue}{\left(-27 \cdot \frac{j \cdot k}{c}\right)}\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(b, \left(\frac{j \cdot k}{c} \cdot \color{blue}{-27}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(b, \mathsf{*.f64}\left(\left(\frac{j \cdot k}{c}\right), \color{blue}{-27}\right)\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(b, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(j \cdot k\right), c\right), -27\right)\right)\right) \]

      6. *-lowering-*.f64 74.0%

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(b, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(j, k\right), c\right), -27\right)\right)\right) \]

   8. Simplified 74.0%

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

4. Final simplification 62.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \leq -2 \cdot 10^{+20}:\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq -1 \cdot 10^{-216}:\\ \;\;\;\;b \cdot c + x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 2 \cdot 10^{-290}:\\ \;\;\;\;b \cdot c + t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 2 \cdot 10^{+150}:\\ \;\;\;\;b \cdot c + x \cdot \left(i \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(b + -27 \cdot \frac{j \cdot k}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 52.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c + x \cdot \left(i \cdot -4\right)\\ t_2 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+20}:\\ \;\;\;\;b \cdot c - t\_2\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{-216}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{-290}:\\ \;\;\;\;b \cdot c + t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+150}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (+ (* b c) (* x (* i -4.0)))) (t_2 (* (* j 27.0) k)))
   (if (<= t_2 -2e+20)
     (- (* b c) t_2)
     (if (<= t_2 -1e-216)
       t_1
       (if (<= t_2 2e-290)
         (+ (* b c) (* t (* a -4.0)))
         (if (<= t_2 2e+150) t_1 (* k (* j -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 t_1 = (b * c) + (x * (i * -4.0));
	double t_2 = (j * 27.0) * k;
	double tmp;
	if (t_2 <= -2e+20) {
		tmp = (b * c) - t_2;
	} else if (t_2 <= -1e-216) {
		tmp = t_1;
	} else if (t_2 <= 2e-290) {
		tmp = (b * c) + (t * (a * -4.0));
	} else if (t_2 <= 2e+150) {
		tmp = t_1;
	} else {
		tmp = k * (j * -27.0);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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) + (x * (i * (-4.0d0)))
    t_2 = (j * 27.0d0) * k
    if (t_2 <= (-2d+20)) then
        tmp = (b * c) - t_2
    else if (t_2 <= (-1d-216)) then
        tmp = t_1
    else if (t_2 <= 2d-290) then
        tmp = (b * c) + (t * (a * (-4.0d0)))
    else if (t_2 <= 2d+150) then
        tmp = t_1
    else
        tmp = k * (j * (-27.0d0))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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) + (x * (i * -4.0));
	double t_2 = (j * 27.0) * k;
	double tmp;
	if (t_2 <= -2e+20) {
		tmp = (b * c) - t_2;
	} else if (t_2 <= -1e-216) {
		tmp = t_1;
	} else if (t_2 <= 2e-290) {
		tmp = (b * c) + (t * (a * -4.0));
	} else if (t_2 <= 2e+150) {
		tmp = t_1;
	} else {
		tmp = k * (j * -27.0);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) + (x * (i * -4.0))
	t_2 = (j * 27.0) * k
	tmp = 0
	if t_2 <= -2e+20:
		tmp = (b * c) - t_2
	elif t_2 <= -1e-216:
		tmp = t_1
	elif t_2 <= 2e-290:
		tmp = (b * c) + (t * (a * -4.0))
	elif t_2 <= 2e+150:
		tmp = t_1
	else:
		tmp = k * (j * -27.0)
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) + Float64(x * Float64(i * -4.0)))
	t_2 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_2 <= -2e+20)
		tmp = Float64(Float64(b * c) - t_2);
	elseif (t_2 <= -1e-216)
		tmp = t_1;
	elseif (t_2 <= 2e-290)
		tmp = Float64(Float64(b * c) + Float64(t * Float64(a * -4.0)));
	elseif (t_2 <= 2e+150)
		tmp = t_1;
	else
		tmp = Float64(k * Float64(j * -27.0));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) + (x * (i * -4.0));
	t_2 = (j * 27.0) * k;
	tmp = 0.0;
	if (t_2 <= -2e+20)
		tmp = (b * c) - t_2;
	elseif (t_2 <= -1e-216)
		tmp = t_1;
	elseif (t_2 <= 2e-290)
		tmp = (b * c) + (t * (a * -4.0));
	elseif (t_2 <= 2e+150)
		tmp = t_1;
	else
		tmp = k * (j * -27.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] + N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+20], N[(N[(b * c), $MachinePrecision] - t$95$2), $MachinePrecision], If[LessEqual[t$95$2, -1e-216], t$95$1, If[LessEqual[t$95$2, 2e-290], N[(N[(b * c), $MachinePrecision] + N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+150], t$95$1, N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -2e20

   1. Initial program 78.9%

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

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(b \cdot c\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 61.4%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

   5. Simplified 61.4%

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

   if -2e20 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -1e-216 or 2.0000000000000001e-290 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 1.99999999999999996e150

   1. Initial program 86.5%

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

   3. Taylor expanded in t around 0

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\color{blue}{\left(b \cdot c\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 63.3%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

   5. Simplified 63.3%

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

   6. Taylor expanded in j around 0

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

      1. cancel-sign-sub-inv N/A

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

      2. metadata-eval N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(b \cdot c\right), \color{blue}{\left(-4 \cdot \left(i \cdot x\right)\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\color{blue}{-4} \cdot \left(i \cdot x\right)\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\left(-4 \cdot i\right) \cdot \color{blue}{x}\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(x \cdot \color{blue}{\left(-4 \cdot i\right)}\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \color{blue}{\left(-4 \cdot i\right)}\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \left(i \cdot \color{blue}{-4}\right)\right)\right) \]

      9. *-lowering-*.f64 58.0%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, \color{blue}{-4}\right)\right)\right) \]

   8. Simplified 58.0%

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

   if -1e-216 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 2.0000000000000001e-290

   1. Initial program 95.9%

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

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 95.9%

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

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \color{blue}{\left(b \cdot c\right)}\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 84.5%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \mathsf{*.f64}\left(b, \color{blue}{c}\right)\right) \]

   7. Simplified 84.5%

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

   8. Taylor expanded in x around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \color{blue}{\left(-4 \cdot a\right)}\right), \mathsf{*.f64}\left(b, c\right)\right) \]
   9. Step-by-step derivation

      1. *-lowering-*.f64 64.9%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(-4, a\right)\right), \mathsf{*.f64}\left(b, c\right)\right) \]

   10. Simplified 64.9%

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

   if 1.99999999999999996e150 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 74.9%

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

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 74.8%

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

   5. Taylor expanded in j around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-27, \color{blue}{\left(j \cdot k\right)}\right) \]

      2. *-lowering-*.f64 68.6%

         \[\leadsto \mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, \color{blue}{k}\right)\right) \]

   7. Simplified 68.6%

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

      1. associate-*r* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-27 \cdot j\right), \color{blue}{k}\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\left(j \cdot -27\right), k\right) \]

      4. *-lowering-*.f64 68.7%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, -27\right), k\right) \]

   9. Applied egg-rr 68.7%

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

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \leq -2 \cdot 10^{+20}:\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq -1 \cdot 10^{-216}:\\ \;\;\;\;b \cdot c + x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 2 \cdot 10^{-290}:\\ \;\;\;\;b \cdot c + t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 2 \cdot 10^{+150}:\\ \;\;\;\;b \cdot c + x \cdot \left(i \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 31.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;k \leq -1.7 \cdot 10^{-93}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;k \leq -9.5 \cdot 10^{-272}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;k \leq 9.5 \cdot 10^{-271}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 5.2 \cdot 10^{-138}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;k \leq 3.6 \cdot 10^{-86}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 5.6 \cdot 10^{+82}:\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(\left(x \cdot 18\right) \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= k -1.7e-93)
   (* j (* k -27.0))
   (if (<= k -9.5e-272)
     (* -4.0 (* x i))
     (if (<= k 9.5e-271)
       (* b c)
       (if (<= k 5.2e-138)
         (* -4.0 (* t a))
         (if (<= k 3.6e-86)
           (* b c)
           (if (<= k 5.6e+82)
             (* (* y z) (* (* x 18.0) t))
             (* k (* j -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 (k <= -1.7e-93) {
		tmp = j * (k * -27.0);
	} else if (k <= -9.5e-272) {
		tmp = -4.0 * (x * i);
	} else if (k <= 9.5e-271) {
		tmp = b * c;
	} else if (k <= 5.2e-138) {
		tmp = -4.0 * (t * a);
	} else if (k <= 3.6e-86) {
		tmp = b * c;
	} else if (k <= 5.6e+82) {
		tmp = (y * z) * ((x * 18.0) * t);
	} else {
		tmp = k * (j * -27.0);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 <= (-1.7d-93)) then
        tmp = j * (k * (-27.0d0))
    else if (k <= (-9.5d-272)) then
        tmp = (-4.0d0) * (x * i)
    else if (k <= 9.5d-271) then
        tmp = b * c
    else if (k <= 5.2d-138) then
        tmp = (-4.0d0) * (t * a)
    else if (k <= 3.6d-86) then
        tmp = b * c
    else if (k <= 5.6d+82) then
        tmp = (y * z) * ((x * 18.0d0) * t)
    else
        tmp = k * (j * (-27.0d0))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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 <= -1.7e-93) {
		tmp = j * (k * -27.0);
	} else if (k <= -9.5e-272) {
		tmp = -4.0 * (x * i);
	} else if (k <= 9.5e-271) {
		tmp = b * c;
	} else if (k <= 5.2e-138) {
		tmp = -4.0 * (t * a);
	} else if (k <= 3.6e-86) {
		tmp = b * c;
	} else if (k <= 5.6e+82) {
		tmp = (y * z) * ((x * 18.0) * t);
	} else {
		tmp = k * (j * -27.0);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if k <= -1.7e-93:
		tmp = j * (k * -27.0)
	elif k <= -9.5e-272:
		tmp = -4.0 * (x * i)
	elif k <= 9.5e-271:
		tmp = b * c
	elif k <= 5.2e-138:
		tmp = -4.0 * (t * a)
	elif k <= 3.6e-86:
		tmp = b * c
	elif k <= 5.6e+82:
		tmp = (y * z) * ((x * 18.0) * t)
	else:
		tmp = k * (j * -27.0)
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (k <= -1.7e-93)
		tmp = Float64(j * Float64(k * -27.0));
	elseif (k <= -9.5e-272)
		tmp = Float64(-4.0 * Float64(x * i));
	elseif (k <= 9.5e-271)
		tmp = Float64(b * c);
	elseif (k <= 5.2e-138)
		tmp = Float64(-4.0 * Float64(t * a));
	elseif (k <= 3.6e-86)
		tmp = Float64(b * c);
	elseif (k <= 5.6e+82)
		tmp = Float64(Float64(y * z) * Float64(Float64(x * 18.0) * t));
	else
		tmp = Float64(k * Float64(j * -27.0));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (k <= -1.7e-93)
		tmp = j * (k * -27.0);
	elseif (k <= -9.5e-272)
		tmp = -4.0 * (x * i);
	elseif (k <= 9.5e-271)
		tmp = b * c;
	elseif (k <= 5.2e-138)
		tmp = -4.0 * (t * a);
	elseif (k <= 3.6e-86)
		tmp = b * c;
	elseif (k <= 5.6e+82)
		tmp = (y * z) * ((x * 18.0) * t);
	else
		tmp = k * (j * -27.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[k, -1.7e-93], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -9.5e-272], N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 9.5e-271], N[(b * c), $MachinePrecision], If[LessEqual[k, 5.2e-138], N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 3.6e-86], N[(b * c), $MachinePrecision], If[LessEqual[k, 5.6e+82], N[(N[(y * z), $MachinePrecision] * N[(N[(x * 18.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 6 regimes

2. if k < -1.70000000000000001e-93

   1. Initial program 80.8%

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

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 80.8%

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

   5. Taylor expanded in j around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-27, \color{blue}{\left(j \cdot k\right)}\right) \]

      2. *-lowering-*.f64 36.0%

         \[\leadsto \mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, \color{blue}{k}\right)\right) \]

   7. Simplified 36.0%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-27 \cdot k\right), \color{blue}{j}\right) \]

      4. *-lowering-*.f64 35.9%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-27, k\right), j\right) \]

   9. Applied egg-rr 35.9%

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

   if -1.70000000000000001e-93 < k < -9.50000000000000024e-272

   1. Initial program 93.4%

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

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 93.4%

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

   5. Taylor expanded in i around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-4, \color{blue}{\left(i \cdot x\right)}\right) \]

      2. *-lowering-*.f64 31.8%

         \[\leadsto \mathsf{*.f64}\left(-4, \mathsf{*.f64}\left(i, \color{blue}{x}\right)\right) \]

   7. Simplified 31.8%

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

   if -9.50000000000000024e-272 < k < 9.50000000000000103e-271 or 5.2e-138 < k < 3.59999999999999966e-86

   1. Initial program 94.9%

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

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 94.9%

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

   5. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot c} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 56.7%

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{c}\right) \]

   7. Simplified 56.7%

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

   if 9.50000000000000103e-271 < k < 5.2e-138

   1. Initial program 96.2%

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

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 92.5%

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

   5. Taylor expanded in a around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-4, \color{blue}{\left(a \cdot t\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(-4, \left(t \cdot \color{blue}{a}\right)\right) \]

      3. *-lowering-*.f64 43.9%

         \[\leadsto \mathsf{*.f64}\left(-4, \mathsf{*.f64}\left(t, \color{blue}{a}\right)\right) \]

   7. Simplified 43.9%

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

   if 3.59999999999999966e-86 < k < 5.6000000000000001e82

   1. Initial program 77.4%

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

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 77.4%

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

   5. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. associate-*r* N/A

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

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(t \cdot \left(18 \cdot x\right)\right), \color{blue}{\left(y \cdot z\right)}\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \left(18 \cdot x\right)\right), \left(\color{blue}{y} \cdot z\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(18, x\right)\right), \left(y \cdot z\right)\right) \]

      9. *-lowering-*.f64 38.8%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(18, x\right)\right), \mathsf{*.f64}\left(y, \color{blue}{z}\right)\right) \]

   7. Simplified 38.8%

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

   if 5.6000000000000001e82 < k

   1. Initial program 79.7%

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

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 79.6%

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

   5. Taylor expanded in j around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-27, \color{blue}{\left(j \cdot k\right)}\right) \]

      2. *-lowering-*.f64 54.5%

         \[\leadsto \mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, \color{blue}{k}\right)\right) \]

   7. Simplified 54.5%

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

      1. associate-*r* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-27 \cdot j\right), \color{blue}{k}\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\left(j \cdot -27\right), k\right) \]

      4. *-lowering-*.f64 54.7%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, -27\right), k\right) \]

   9. Applied egg-rr 54.7%

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

4. Final simplification 41.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -1.7 \cdot 10^{-93}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;k \leq -9.5 \cdot 10^{-272}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;k \leq 9.5 \cdot 10^{-271}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 5.2 \cdot 10^{-138}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;k \leq 3.6 \cdot 10^{-86}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 5.6 \cdot 10^{+82}:\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(\left(x \cdot 18\right) \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 31.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;k \leq -1.75 \cdot 10^{-93}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;k \leq -3.7 \cdot 10^{-272}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;k \leq 1.4 \cdot 10^{-269}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 4.8 \cdot 10^{-134}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;k \leq 2.3 \cdot 10^{-84}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 5.3 \cdot 10^{+82}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= k -1.75e-93)
   (* j (* k -27.0))
   (if (<= k -3.7e-272)
     (* -4.0 (* x i))
     (if (<= k 1.4e-269)
       (* b c)
       (if (<= k 4.8e-134)
         (* -4.0 (* t a))
         (if (<= k 2.3e-84)
           (* b c)
           (if (<= k 5.3e+82)
             (* t (* 18.0 (* x (* y z))))
             (* k (* j -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 (k <= -1.75e-93) {
		tmp = j * (k * -27.0);
	} else if (k <= -3.7e-272) {
		tmp = -4.0 * (x * i);
	} else if (k <= 1.4e-269) {
		tmp = b * c;
	} else if (k <= 4.8e-134) {
		tmp = -4.0 * (t * a);
	} else if (k <= 2.3e-84) {
		tmp = b * c;
	} else if (k <= 5.3e+82) {
		tmp = t * (18.0 * (x * (y * z)));
	} else {
		tmp = k * (j * -27.0);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 <= (-1.75d-93)) then
        tmp = j * (k * (-27.0d0))
    else if (k <= (-3.7d-272)) then
        tmp = (-4.0d0) * (x * i)
    else if (k <= 1.4d-269) then
        tmp = b * c
    else if (k <= 4.8d-134) then
        tmp = (-4.0d0) * (t * a)
    else if (k <= 2.3d-84) then
        tmp = b * c
    else if (k <= 5.3d+82) then
        tmp = t * (18.0d0 * (x * (y * z)))
    else
        tmp = k * (j * (-27.0d0))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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 <= -1.75e-93) {
		tmp = j * (k * -27.0);
	} else if (k <= -3.7e-272) {
		tmp = -4.0 * (x * i);
	} else if (k <= 1.4e-269) {
		tmp = b * c;
	} else if (k <= 4.8e-134) {
		tmp = -4.0 * (t * a);
	} else if (k <= 2.3e-84) {
		tmp = b * c;
	} else if (k <= 5.3e+82) {
		tmp = t * (18.0 * (x * (y * z)));
	} else {
		tmp = k * (j * -27.0);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if k <= -1.75e-93:
		tmp = j * (k * -27.0)
	elif k <= -3.7e-272:
		tmp = -4.0 * (x * i)
	elif k <= 1.4e-269:
		tmp = b * c
	elif k <= 4.8e-134:
		tmp = -4.0 * (t * a)
	elif k <= 2.3e-84:
		tmp = b * c
	elif k <= 5.3e+82:
		tmp = t * (18.0 * (x * (y * z)))
	else:
		tmp = k * (j * -27.0)
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (k <= -1.75e-93)
		tmp = Float64(j * Float64(k * -27.0));
	elseif (k <= -3.7e-272)
		tmp = Float64(-4.0 * Float64(x * i));
	elseif (k <= 1.4e-269)
		tmp = Float64(b * c);
	elseif (k <= 4.8e-134)
		tmp = Float64(-4.0 * Float64(t * a));
	elseif (k <= 2.3e-84)
		tmp = Float64(b * c);
	elseif (k <= 5.3e+82)
		tmp = Float64(t * Float64(18.0 * Float64(x * Float64(y * z))));
	else
		tmp = Float64(k * Float64(j * -27.0));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (k <= -1.75e-93)
		tmp = j * (k * -27.0);
	elseif (k <= -3.7e-272)
		tmp = -4.0 * (x * i);
	elseif (k <= 1.4e-269)
		tmp = b * c;
	elseif (k <= 4.8e-134)
		tmp = -4.0 * (t * a);
	elseif (k <= 2.3e-84)
		tmp = b * c;
	elseif (k <= 5.3e+82)
		tmp = t * (18.0 * (x * (y * z)));
	else
		tmp = k * (j * -27.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[k, -1.75e-93], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -3.7e-272], N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 1.4e-269], N[(b * c), $MachinePrecision], If[LessEqual[k, 4.8e-134], N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 2.3e-84], N[(b * c), $MachinePrecision], If[LessEqual[k, 5.3e+82], N[(t * N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 6 regimes

2. if k < -1.75e-93

   1. Initial program 80.8%

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

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 80.8%

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

   5. Taylor expanded in j around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-27, \color{blue}{\left(j \cdot k\right)}\right) \]

      2. *-lowering-*.f64 36.0%

         \[\leadsto \mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, \color{blue}{k}\right)\right) \]

   7. Simplified 36.0%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-27 \cdot k\right), \color{blue}{j}\right) \]

      4. *-lowering-*.f64 35.9%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-27, k\right), j\right) \]

   9. Applied egg-rr 35.9%

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

   if -1.75e-93 < k < -3.6999999999999997e-272

   1. Initial program 93.4%

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

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 93.4%

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

   5. Taylor expanded in i around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-4, \color{blue}{\left(i \cdot x\right)}\right) \]

      2. *-lowering-*.f64 31.8%

         \[\leadsto \mathsf{*.f64}\left(-4, \mathsf{*.f64}\left(i, \color{blue}{x}\right)\right) \]

   7. Simplified 31.8%

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

   if -3.6999999999999997e-272 < k < 1.39999999999999997e-269 or 4.80000000000000019e-134 < k < 2.29999999999999981e-84

   1. Initial program 94.9%

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

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 94.9%

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

   5. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot c} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 56.7%

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{c}\right) \]

   7. Simplified 56.7%

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

   if 1.39999999999999997e-269 < k < 4.80000000000000019e-134

   1. Initial program 96.2%

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

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 92.5%

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

   5. Taylor expanded in a around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-4, \color{blue}{\left(a \cdot t\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(-4, \left(t \cdot \color{blue}{a}\right)\right) \]

      3. *-lowering-*.f64 43.9%

         \[\leadsto \mathsf{*.f64}\left(-4, \mathsf{*.f64}\left(t, \color{blue}{a}\right)\right) \]

   7. Simplified 43.9%

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

   if 2.29999999999999981e-84 < k < 5.29999999999999977e82

   1. Initial program 77.4%

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

      1. +-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

      2. associate-+r- N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\left(\left(b \cdot c + \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t\right) - \left(a \cdot 4\right) \cdot t\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t\right), \left(\left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(b \cdot c\right), \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t\right)\right), \left(\left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t\right)\right), \left(\left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      6. associate-*l* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot \left(z \cdot t\right)\right)\right), \left(\left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      7. associate-*l* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\left(x \cdot 18\right) \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\right), \left(\left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\left(x \cdot 18\right), \left(y \cdot \left(z \cdot t\right)\right)\right)\right), \left(\left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), \left(y \cdot \left(z \cdot t\right)\right)\right)\right), \left(\left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), \mathsf{*.f64}\left(y, \left(z \cdot t\right)\right)\right)\right), \left(\left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), \mathsf{*.f64}\left(y, \left(t \cdot z\right)\right)\right)\right), \left(\left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, z\right)\right)\right)\right), \left(\left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      13. associate-*l* N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, z\right)\right)\right)\right), \left(a \cdot \left(4 \cdot t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, z\right)\right)\right)\right), \mathsf{*.f64}\left(a, \left(4 \cdot t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      15. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, z\right)\right)\right)\right), \mathsf{*.f64}\left(a, \left(t \cdot 4\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      16. *-lowering-*.f64 77.6%

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, z\right)\right)\right)\right), \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(t, 4\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

   4. Applied egg-rr 77.6%

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

   5. Taylor expanded in x around inf

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(x \cdot \left(\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \frac{b \cdot c}{x}\right) - \left(4 \cdot i + 4 \cdot \frac{a \cdot t}{x}\right)\right)\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   6. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(x \cdot \left(\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \frac{b \cdot c}{x}\right) + \left(\mathsf{neg}\left(\left(4 \cdot i + 4 \cdot \frac{a \cdot t}{x}\right)\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, \color{blue}{27}\right), k\right)\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(x \cdot \left(\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \frac{b \cdot c}{x}\right) + \left(\mathsf{neg}\left(\left(4 \cdot \frac{a \cdot t}{x} + 4 \cdot i\right)\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      3. distribute-neg-in N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(x \cdot \left(\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \frac{b \cdot c}{x}\right) + \left(\left(\mathsf{neg}\left(4 \cdot \frac{a \cdot t}{x}\right)\right) + \left(\mathsf{neg}\left(4 \cdot i\right)\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      4. distribute-lft-neg-in N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(x \cdot \left(\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \frac{b \cdot c}{x}\right) + \left(\left(\mathsf{neg}\left(4\right)\right) \cdot \frac{a \cdot t}{x} + \left(\mathsf{neg}\left(4 \cdot i\right)\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(x \cdot \left(\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \frac{b \cdot c}{x}\right) + \left(-4 \cdot \frac{a \cdot t}{x} + \left(\mathsf{neg}\left(4 \cdot i\right)\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      6. distribute-lft-neg-in N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(x \cdot \left(\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \frac{b \cdot c}{x}\right) + \left(-4 \cdot \frac{a \cdot t}{x} + \left(\mathsf{neg}\left(4\right)\right) \cdot i\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(x \cdot \left(\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \frac{b \cdot c}{x}\right) + \left(-4 \cdot \frac{a \cdot t}{x} + -4 \cdot i\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      8. associate-+l+ N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(x \cdot \left(\left(\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \frac{b \cdot c}{x}\right) + -4 \cdot \frac{a \cdot t}{x}\right) + -4 \cdot i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, \color{blue}{27}\right), k\right)\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(x \cdot \left(\left(-4 \cdot \frac{a \cdot t}{x} + \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \frac{b \cdot c}{x}\right)\right) + -4 \cdot i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(\left(x \cdot \left(-4 \cdot i + \left(-4 \cdot \frac{a \cdot t}{x} + \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \frac{b \cdot c}{x}\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, \color{blue}{27}\right), k\right)\right) \]

   7. Simplified 75.5%

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

   8. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(x \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right)}\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(x \cdot \left(\left(y \cdot z\right) \cdot \color{blue}{18}\right)\right)\right) \]

      7. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(\left(x \cdot \left(y \cdot z\right)\right) \cdot \color{blue}{18}\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(18 \cdot \color{blue}{\left(x \cdot \left(y \cdot z\right)\right)}\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(18, \color{blue}{\left(x \cdot \left(y \cdot z\right)\right)}\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(x, \color{blue}{\left(y \cdot z\right)}\right)\right)\right) \]

      11. *-lowering-*.f64 38.7%

          \[\leadsto \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{z}\right)\right)\right)\right) \]

   10. Simplified 38.7%

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

   if 5.29999999999999977e82 < k

   1. Initial program 79.7%

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

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 79.6%

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

   5. Taylor expanded in j around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-27, \color{blue}{\left(j \cdot k\right)}\right) \]

      2. *-lowering-*.f64 54.5%

         \[\leadsto \mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, \color{blue}{k}\right)\right) \]

   7. Simplified 54.5%

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

      1. associate-*r* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-27 \cdot j\right), \color{blue}{k}\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\left(j \cdot -27\right), k\right) \]

      4. *-lowering-*.f64 54.7%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, -27\right), k\right) \]

   9. Applied egg-rr 54.7%

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

4. Final simplification 41.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -1.75 \cdot 10^{-93}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;k \leq -3.7 \cdot 10^{-272}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;k \leq 1.4 \cdot 10^{-269}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 4.8 \cdot 10^{-134}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;k \leq 2.3 \cdot 10^{-84}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 5.3 \cdot 10^{+82}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 90.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ t_2 := y \cdot \left(z \cdot \left(18 \cdot t\right)\right)\\ \mathbf{if}\;x \leq -7.2 \cdot 10^{+105}:\\ \;\;\;\;x \cdot \left(i \cdot -4 + \left(t\_2 + \frac{b \cdot c + -4 \cdot \left(t \cdot a\right)}{x}\right)\right) - t\_1\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+34}:\\ \;\;\;\;t \cdot \left(a \cdot -4 + y \cdot \left(\left(x \cdot 18\right) \cdot z\right)\right) + \left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + x \cdot \left(i \cdot -4 + t\_2\right)\right) - t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)) (t_2 (* y (* z (* 18.0 t)))))
   (if (<= x -7.2e+105)
     (- (* x (+ (* i -4.0) (+ t_2 (/ (+ (* b c) (* -4.0 (* t a))) x)))) t_1)
     (if (<= x 9.5e+34)
       (+
        (* t (+ (* a -4.0) (* y (* (* x 18.0) z))))
        (+ (* -27.0 (* j k)) (+ (* b c) (* x (* i -4.0)))))
       (- (+ (* b c) (* x (+ (* i -4.0) t_2))) 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 = (j * 27.0) * k;
	double t_2 = y * (z * (18.0 * t));
	double tmp;
	if (x <= -7.2e+105) {
		tmp = (x * ((i * -4.0) + (t_2 + (((b * c) + (-4.0 * (t * a))) / x)))) - t_1;
	} else if (x <= 9.5e+34) {
		tmp = (t * ((a * -4.0) + (y * ((x * 18.0) * z)))) + ((-27.0 * (j * k)) + ((b * c) + (x * (i * -4.0))));
	} else {
		tmp = ((b * c) + (x * ((i * -4.0) + t_2))) - 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) :: t_2
    real(8) :: tmp
    t_1 = (j * 27.0d0) * k
    t_2 = y * (z * (18.0d0 * t))
    if (x <= (-7.2d+105)) then
        tmp = (x * ((i * (-4.0d0)) + (t_2 + (((b * c) + ((-4.0d0) * (t * a))) / x)))) - t_1
    else if (x <= 9.5d+34) then
        tmp = (t * ((a * (-4.0d0)) + (y * ((x * 18.0d0) * z)))) + (((-27.0d0) * (j * k)) + ((b * c) + (x * (i * (-4.0d0)))))
    else
        tmp = ((b * c) + (x * ((i * (-4.0d0)) + t_2))) - 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 = (j * 27.0) * k;
	double t_2 = y * (z * (18.0 * t));
	double tmp;
	if (x <= -7.2e+105) {
		tmp = (x * ((i * -4.0) + (t_2 + (((b * c) + (-4.0 * (t * a))) / x)))) - t_1;
	} else if (x <= 9.5e+34) {
		tmp = (t * ((a * -4.0) + (y * ((x * 18.0) * z)))) + ((-27.0 * (j * k)) + ((b * c) + (x * (i * -4.0))));
	} else {
		tmp = ((b * c) + (x * ((i * -4.0) + t_2))) - 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 = (j * 27.0) * k
	t_2 = y * (z * (18.0 * t))
	tmp = 0
	if x <= -7.2e+105:
		tmp = (x * ((i * -4.0) + (t_2 + (((b * c) + (-4.0 * (t * a))) / x)))) - t_1
	elif x <= 9.5e+34:
		tmp = (t * ((a * -4.0) + (y * ((x * 18.0) * z)))) + ((-27.0 * (j * k)) + ((b * c) + (x * (i * -4.0))))
	else:
		tmp = ((b * c) + (x * ((i * -4.0) + t_2))) - 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(j * 27.0) * k)
	t_2 = Float64(y * Float64(z * Float64(18.0 * t)))
	tmp = 0.0
	if (x <= -7.2e+105)
		tmp = Float64(Float64(x * Float64(Float64(i * -4.0) + Float64(t_2 + Float64(Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a))) / x)))) - t_1);
	elseif (x <= 9.5e+34)
		tmp = Float64(Float64(t * Float64(Float64(a * -4.0) + Float64(y * Float64(Float64(x * 18.0) * z)))) + Float64(Float64(-27.0 * Float64(j * k)) + Float64(Float64(b * c) + Float64(x * Float64(i * -4.0)))));
	else
		tmp = Float64(Float64(Float64(b * c) + Float64(x * Float64(Float64(i * -4.0) + t_2))) - 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 = (j * 27.0) * k;
	t_2 = y * (z * (18.0 * t));
	tmp = 0.0;
	if (x <= -7.2e+105)
		tmp = (x * ((i * -4.0) + (t_2 + (((b * c) + (-4.0 * (t * a))) / x)))) - t_1;
	elseif (x <= 9.5e+34)
		tmp = (t * ((a * -4.0) + (y * ((x * 18.0) * z)))) + ((-27.0 * (j * k)) + ((b * c) + (x * (i * -4.0))));
	else
		tmp = ((b * c) + (x * ((i * -4.0) + t_2))) - 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[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(z * N[(18.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -7.2e+105], N[(N[(x * N[(N[(i * -4.0), $MachinePrecision] + N[(t$95$2 + N[(N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[x, 9.5e+34], N[(N[(t * N[(N[(a * -4.0), $MachinePrecision] + N[(y * N[(N[(x * 18.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision] + N[(N[(b * c), $MachinePrecision] + N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] + N[(x * N[(N[(i * -4.0), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.1999999999999998e105

   1. Initial program 60.9%

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

      1. +-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

      2. associate-+r- N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\left(\left(b \cdot c + \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t\right) - \left(a \cdot 4\right) \cdot t\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t\right), \left(\left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(b \cdot c\right), \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t\right)\right), \left(\left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t\right)\right), \left(\left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      6. associate-*l* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot \left(z \cdot t\right)\right)\right), \left(\left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      7. associate-*l* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\left(x \cdot 18\right) \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\right), \left(\left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\left(x \cdot 18\right), \left(y \cdot \left(z \cdot t\right)\right)\right)\right), \left(\left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), \left(y \cdot \left(z \cdot t\right)\right)\right)\right), \left(\left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), \mathsf{*.f64}\left(y, \left(z \cdot t\right)\right)\right)\right), \left(\left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), \mathsf{*.f64}\left(y, \left(t \cdot z\right)\right)\right)\right), \left(\left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, z\right)\right)\right)\right), \left(\left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      13. associate-*l* N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, z\right)\right)\right)\right), \left(a \cdot \left(4 \cdot t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, z\right)\right)\right)\right), \mathsf{*.f64}\left(a, \left(4 \cdot t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      15. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, z\right)\right)\right)\right), \mathsf{*.f64}\left(a, \left(t \cdot 4\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      16. *-lowering-*.f64 77.4%

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, z\right)\right)\right)\right), \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(t, 4\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

   4. Applied egg-rr 77.4%

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

   5. Taylor expanded in x around inf

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(x \cdot \left(\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \frac{b \cdot c}{x}\right) - \left(4 \cdot i + 4 \cdot \frac{a \cdot t}{x}\right)\right)\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   6. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(x \cdot \left(\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \frac{b \cdot c}{x}\right) + \left(\mathsf{neg}\left(\left(4 \cdot i + 4 \cdot \frac{a \cdot t}{x}\right)\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, \color{blue}{27}\right), k\right)\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(x \cdot \left(\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \frac{b \cdot c}{x}\right) + \left(\mathsf{neg}\left(\left(4 \cdot \frac{a \cdot t}{x} + 4 \cdot i\right)\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      3. distribute-neg-in N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(x \cdot \left(\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \frac{b \cdot c}{x}\right) + \left(\left(\mathsf{neg}\left(4 \cdot \frac{a \cdot t}{x}\right)\right) + \left(\mathsf{neg}\left(4 \cdot i\right)\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      4. distribute-lft-neg-in N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(x \cdot \left(\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \frac{b \cdot c}{x}\right) + \left(\left(\mathsf{neg}\left(4\right)\right) \cdot \frac{a \cdot t}{x} + \left(\mathsf{neg}\left(4 \cdot i\right)\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(x \cdot \left(\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \frac{b \cdot c}{x}\right) + \left(-4 \cdot \frac{a \cdot t}{x} + \left(\mathsf{neg}\left(4 \cdot i\right)\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      6. distribute-lft-neg-in N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(x \cdot \left(\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \frac{b \cdot c}{x}\right) + \left(-4 \cdot \frac{a \cdot t}{x} + \left(\mathsf{neg}\left(4\right)\right) \cdot i\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(x \cdot \left(\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \frac{b \cdot c}{x}\right) + \left(-4 \cdot \frac{a \cdot t}{x} + -4 \cdot i\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      8. associate-+l+ N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(x \cdot \left(\left(\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \frac{b \cdot c}{x}\right) + -4 \cdot \frac{a \cdot t}{x}\right) + -4 \cdot i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, \color{blue}{27}\right), k\right)\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(x \cdot \left(\left(-4 \cdot \frac{a \cdot t}{x} + \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \frac{b \cdot c}{x}\right)\right) + -4 \cdot i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(\left(x \cdot \left(-4 \cdot i + \left(-4 \cdot \frac{a \cdot t}{x} + \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \frac{b \cdot c}{x}\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, \color{blue}{27}\right), k\right)\right) \]

   7. Simplified 79.8%

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

   if -7.1999999999999998e105 < x < 9.4999999999999999e34

   1. Initial program 95.3%

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

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 94.6%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(z \cdot \left(\left(x \cdot 18\right) \cdot y\right)\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(\color{blue}{j}, k\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

      2. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(z \cdot \left(x \cdot 18\right)\right) \cdot y\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(\color{blue}{j}, k\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(z \cdot \left(x \cdot 18\right)\right), y\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(\color{blue}{j}, k\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(z, \left(x \cdot 18\right)\right), y\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, k\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 95.2%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(x, 18\right)\right), y\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, k\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

   6. Applied egg-rr 95.2%

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

   if 9.4999999999999999e34 < x

   1. Initial program 75.3%

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

      1. +-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

      2. associate-+r- N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\left(\left(b \cdot c + \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t\right) - \left(a \cdot 4\right) \cdot t\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t\right), \left(\left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(b \cdot c\right), \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t\right)\right), \left(\left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t\right)\right), \left(\left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      6. associate-*l* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot \left(z \cdot t\right)\right)\right), \left(\left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      7. associate-*l* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\left(x \cdot 18\right) \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\right), \left(\left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\left(x \cdot 18\right), \left(y \cdot \left(z \cdot t\right)\right)\right)\right), \left(\left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), \left(y \cdot \left(z \cdot t\right)\right)\right)\right), \left(\left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), \mathsf{*.f64}\left(y, \left(z \cdot t\right)\right)\right)\right), \left(\left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), \mathsf{*.f64}\left(y, \left(t \cdot z\right)\right)\right)\right), \left(\left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, z\right)\right)\right)\right), \left(\left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      13. associate-*l* N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, z\right)\right)\right)\right), \left(a \cdot \left(4 \cdot t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, z\right)\right)\right)\right), \mathsf{*.f64}\left(a, \left(4 \cdot t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      15. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, z\right)\right)\right)\right), \mathsf{*.f64}\left(a, \left(t \cdot 4\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      16. *-lowering-*.f64 87.4%

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, z\right)\right)\right)\right), \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(t, 4\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

   4. Applied egg-rr 87.4%

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

   5. Taylor expanded in a around 0

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(i \cdot x\right)\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   6. Step-by-step derivation

      1. cancel-sign-sub-inv N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(i \cdot x\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + -4 \cdot \left(i \cdot x\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\left(b \cdot c + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) + -4 \cdot \left(i \cdot x\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

      4. associate-+l+ N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + -4 \cdot \left(i \cdot x\right)\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(18 \cdot t\right) \cdot \left(x \cdot \left(y \cdot z\right)\right) + -4 \cdot \left(i \cdot x\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(18 \cdot t\right) \cdot \left(\left(y \cdot z\right) \cdot x\right) + -4 \cdot \left(i \cdot x\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      7. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(\left(18 \cdot t\right) \cdot \left(y \cdot z\right)\right) \cdot x + -4 \cdot \left(i \cdot x\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      8. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right) \cdot x + -4 \cdot \left(i \cdot x\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      9. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right) \cdot x + \left(-4 \cdot i\right) \cdot x\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      10. distribute-rgt-in N/A

          \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + -4 \cdot i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, \color{blue}{27}\right), k\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      12. cancel-sign-sub-inv N/A

          \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      13. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(b \cdot c\right), \left(x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

   7. Simplified 92.2%

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

4. Final simplification 92.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{+105}:\\ \;\;\;\;x \cdot \left(i \cdot -4 + \left(y \cdot \left(z \cdot \left(18 \cdot t\right)\right) + \frac{b \cdot c + -4 \cdot \left(t \cdot a\right)}{x}\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+34}:\\ \;\;\;\;t \cdot \left(a \cdot -4 + y \cdot \left(\left(x \cdot 18\right) \cdot z\right)\right) + \left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + x \cdot \left(i \cdot -4 + y \cdot \left(z \cdot \left(18 \cdot t\right)\right)\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 57.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;x \leq -9.2 \cdot 10^{+46}:\\ \;\;\;\;x \cdot \left(i \cdot -4 + y \cdot \left(z \cdot \left(18 \cdot t\right)\right)\right)\\ \mathbf{elif}\;x \leq -7.8 \cdot 10^{-222}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right) - t\_1\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-135}:\\ \;\;\;\;b \cdot c + t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{-9}:\\ \;\;\;\;b \cdot c - t\_1\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{+168}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right) - j \cdot \left(27 \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(i \cdot -4 + 18 \cdot \left(z \cdot \left(y \cdot t\right)\right)\right)\\ \end{array} \end{array} \]

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 27.0) k)))
   (if (<= x -9.2e+46)
     (* x (+ (* i -4.0) (* y (* z (* 18.0 t)))))
     (if (<= x -7.8e-222)
       (- (* -4.0 (* t a)) t_1)
       (if (<= x 1.8e-135)
         (+ (* b c) (* t (* a -4.0)))
         (if (<= x 3.8e-9)
           (- (* b c) t_1)
           (if (<= x 3.3e+168)
             (- (* x (* i -4.0)) (* 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 t_1 = (j * 27.0) * k;
	double tmp;
	if (x <= -9.2e+46) {
		tmp = x * ((i * -4.0) + (y * (z * (18.0 * t))));
	} else if (x <= -7.8e-222) {
		tmp = (-4.0 * (t * a)) - t_1;
	} else if (x <= 1.8e-135) {
		tmp = (b * c) + (t * (a * -4.0));
	} else if (x <= 3.8e-9) {
		tmp = (b * c) - t_1;
	} else if (x <= 3.3e+168) {
		tmp = (x * (i * -4.0)) - (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) :: t_1
    real(8) :: tmp
    t_1 = (j * 27.0d0) * k
    if (x <= (-9.2d+46)) then
        tmp = x * ((i * (-4.0d0)) + (y * (z * (18.0d0 * t))))
    else if (x <= (-7.8d-222)) then
        tmp = ((-4.0d0) * (t * a)) - t_1
    else if (x <= 1.8d-135) then
        tmp = (b * c) + (t * (a * (-4.0d0)))
    else if (x <= 3.8d-9) then
        tmp = (b * c) - t_1
    else if (x <= 3.3d+168) then
        tmp = (x * (i * (-4.0d0))) - (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 t_1 = (j * 27.0) * k;
	double tmp;
	if (x <= -9.2e+46) {
		tmp = x * ((i * -4.0) + (y * (z * (18.0 * t))));
	} else if (x <= -7.8e-222) {
		tmp = (-4.0 * (t * a)) - t_1;
	} else if (x <= 1.8e-135) {
		tmp = (b * c) + (t * (a * -4.0));
	} else if (x <= 3.8e-9) {
		tmp = (b * c) - t_1;
	} else if (x <= 3.3e+168) {
		tmp = (x * (i * -4.0)) - (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):
	t_1 = (j * 27.0) * k
	tmp = 0
	if x <= -9.2e+46:
		tmp = x * ((i * -4.0) + (y * (z * (18.0 * t))))
	elif x <= -7.8e-222:
		tmp = (-4.0 * (t * a)) - t_1
	elif x <= 1.8e-135:
		tmp = (b * c) + (t * (a * -4.0))
	elif x <= 3.8e-9:
		tmp = (b * c) - t_1
	elif x <= 3.3e+168:
		tmp = (x * (i * -4.0)) - (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)
	t_1 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (x <= -9.2e+46)
		tmp = Float64(x * Float64(Float64(i * -4.0) + Float64(y * Float64(z * Float64(18.0 * t)))));
	elseif (x <= -7.8e-222)
		tmp = Float64(Float64(-4.0 * Float64(t * a)) - t_1);
	elseif (x <= 1.8e-135)
		tmp = Float64(Float64(b * c) + Float64(t * Float64(a * -4.0)));
	elseif (x <= 3.8e-9)
		tmp = Float64(Float64(b * c) - t_1);
	elseif (x <= 3.3e+168)
		tmp = Float64(Float64(x * Float64(i * -4.0)) - Float64(j * Float64(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)
	t_1 = (j * 27.0) * k;
	tmp = 0.0;
	if (x <= -9.2e+46)
		tmp = x * ((i * -4.0) + (y * (z * (18.0 * t))));
	elseif (x <= -7.8e-222)
		tmp = (-4.0 * (t * a)) - t_1;
	elseif (x <= 1.8e-135)
		tmp = (b * c) + (t * (a * -4.0));
	elseif (x <= 3.8e-9)
		tmp = (b * c) - t_1;
	elseif (x <= 3.3e+168)
		tmp = (x * (i * -4.0)) - (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_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[x, -9.2e+46], N[(x * N[(N[(i * -4.0), $MachinePrecision] + N[(y * N[(z * N[(18.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -7.8e-222], N[(N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[x, 1.8e-135], N[(N[(b * c), $MachinePrecision] + N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.8e-9], N[(N[(b * c), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[x, 3.3e+168], N[(N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision] - N[(j * N[(27.0 * k), $MachinePrecision]), $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 6 regimes

2. if x < -9.2000000000000002e46

   1. Initial program 66.1%

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

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 66.1%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(z \cdot \left(\left(x \cdot 18\right) \cdot y\right)\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(\color{blue}{j}, k\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

      2. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(z \cdot \left(x \cdot 18\right)\right) \cdot y\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(\color{blue}{j}, k\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(z \cdot \left(x \cdot 18\right)\right), y\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(\color{blue}{j}, k\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(z, \left(x \cdot 18\right)\right), y\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, k\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 69.5%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(x, 18\right)\right), y\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, k\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

   6. Applied egg-rr 69.5%

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

   7. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(-4 \cdot i\right), \color{blue}{\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \left(\color{blue}{18} \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \left(\left(18 \cdot t\right) \cdot \color{blue}{\left(y \cdot z\right)}\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \left(\left(18 \cdot t\right) \cdot \left(z \cdot \color{blue}{y}\right)\right)\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \left(\left(\left(18 \cdot t\right) \cdot z\right) \cdot \color{blue}{y}\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \mathsf{*.f64}\left(\left(\left(18 \cdot t\right) \cdot z\right), \color{blue}{y}\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(18 \cdot t\right), z\right), y\right)\right)\right) \]

      9. *-lowering-*.f64 56.7%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(18, t\right), z\right), y\right)\right)\right) \]

   9. Simplified 56.7%

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

   if -9.2000000000000002e46 < x < -7.8000000000000002e-222

   1. Initial program 97.8%

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

   3. Taylor expanded in a around inf

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(-4 \cdot \left(a \cdot t\right)\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(-4, \left(a \cdot t\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(-4, \left(t \cdot a\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, \color{blue}{27}\right), k\right)\right) \]

      3. *-lowering-*.f64 60.9%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(-4, \mathsf{*.f64}\left(t, a\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, \color{blue}{27}\right), k\right)\right) \]

   5. Simplified 60.9%

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

   if -7.8000000000000002e-222 < x < 1.79999999999999989e-135

   1. Initial program 96.0%

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

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 94.1%

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

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \color{blue}{\left(b \cdot c\right)}\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 70.2%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \mathsf{*.f64}\left(b, \color{blue}{c}\right)\right) \]

   7. Simplified 70.2%

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

   8. Taylor expanded in x around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \color{blue}{\left(-4 \cdot a\right)}\right), \mathsf{*.f64}\left(b, c\right)\right) \]
   9. Step-by-step derivation

      1. *-lowering-*.f64 69.9%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(-4, a\right)\right), \mathsf{*.f64}\left(b, c\right)\right) \]

   10. Simplified 69.9%

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

   if 1.79999999999999989e-135 < x < 3.80000000000000011e-9

   1. Initial program 96.2%

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

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(b \cdot c\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 74.9%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

   5. Simplified 74.9%

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

   if 3.80000000000000011e-9 < x < 3.2999999999999999e168

   1. Initial program 76.0%

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

   3. Taylor expanded in i around inf

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(-4 \cdot \left(i \cdot x\right)\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(-4, \left(i \cdot x\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

      2. *-lowering-*.f64 61.4%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(-4, \mathsf{*.f64}\left(i, x\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, \color{blue}{27}\right), k\right)\right) \]

   5. Simplified 61.4%

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(x \cdot \left(i \cdot -4\right)\right), \color{blue}{\left(\left(j \cdot 27\right) \cdot k\right)}\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \left(i \cdot -4\right)\right), \left(\color{blue}{\left(j \cdot 27\right)} \cdot k\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \left(-4 \cdot i\right)\right), \left(\left(j \cdot \color{blue}{27}\right) \cdot k\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(-4, i\right)\right), \left(\left(j \cdot \color{blue}{27}\right) \cdot k\right)\right) \]

      8. associate-*l* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(-4, i\right)\right), \left(j \cdot \color{blue}{\left(27 \cdot k\right)}\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(-4, i\right)\right), \mathsf{*.f64}\left(j, \color{blue}{\left(27 \cdot k\right)}\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(-4, i\right)\right), \mathsf{*.f64}\left(j, \left(k \cdot \color{blue}{27}\right)\right)\right) \]

      11. *-lowering-*.f64 61.4%

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(-4, i\right)\right), \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(k, \color{blue}{27}\right)\right)\right) \]

   7. Applied egg-rr 61.4%

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

   if 3.2999999999999999e168 < x

   1. Initial program 80.7%

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

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 80.6%

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

   5. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(-4 \cdot i\right), \color{blue}{\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \left(\color{blue}{18} \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \mathsf{*.f64}\left(18, \color{blue}{\left(t \cdot \left(y \cdot z\right)\right)}\right)\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \mathsf{*.f64}\left(18, \left(\left(t \cdot y\right) \cdot \color{blue}{z}\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(\left(t \cdot y\right), \color{blue}{z}\right)\right)\right)\right) \]

      7. *-lowering-*.f64 91.7%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, y\right), z\right)\right)\right)\right) \]

   7. Simplified 91.7%

      \[\leadsto \color{blue}{x \cdot \left(-4 \cdot i + 18 \cdot \left(\left(t \cdot y\right) \cdot z\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.2 \cdot 10^{+46}:\\ \;\;\;\;x \cdot \left(i \cdot -4 + y \cdot \left(z \cdot \left(18 \cdot t\right)\right)\right)\\ \mathbf{elif}\;x \leq -7.8 \cdot 10^{-222}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-135}:\\ \;\;\;\;b \cdot c + t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{-9}:\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{+168}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right) - j \cdot \left(27 \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(i \cdot -4 + 18 \cdot \left(z \cdot \left(y \cdot t\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 57.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ t_2 := x \cdot \left(i \cdot -4 + 18 \cdot \left(z \cdot \left(y \cdot t\right)\right)\right)\\ \mathbf{if}\;x \leq -1.06 \cdot 10^{+49}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -7.4 \cdot 10^{-222}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right) - t\_1\\ \mathbf{elif}\;x \leq 5.3 \cdot 10^{-135}:\\ \;\;\;\;b \cdot c + t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{-16}:\\ \;\;\;\;b \cdot c - t\_1\\ \mathbf{elif}\;x \leq 3.15 \cdot 10^{+168}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right) - j \cdot \left(27 \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k))
        (t_2 (* x (+ (* i -4.0) (* 18.0 (* z (* y t)))))))
   (if (<= x -1.06e+49)
     t_2
     (if (<= x -7.4e-222)
       (- (* -4.0 (* t a)) t_1)
       (if (<= x 5.3e-135)
         (+ (* b c) (* t (* a -4.0)))
         (if (<= x 3.9e-16)
           (- (* b c) t_1)
           (if (<= x 3.15e+168)
             (- (* x (* i -4.0)) (* j (* 27.0 k)))
             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 * 27.0) * k;
	double t_2 = x * ((i * -4.0) + (18.0 * (z * (y * t))));
	double tmp;
	if (x <= -1.06e+49) {
		tmp = t_2;
	} else if (x <= -7.4e-222) {
		tmp = (-4.0 * (t * a)) - t_1;
	} else if (x <= 5.3e-135) {
		tmp = (b * c) + (t * (a * -4.0));
	} else if (x <= 3.9e-16) {
		tmp = (b * c) - t_1;
	} else if (x <= 3.15e+168) {
		tmp = (x * (i * -4.0)) - (j * (27.0 * k));
	} 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 * 27.0d0) * k
    t_2 = x * ((i * (-4.0d0)) + (18.0d0 * (z * (y * t))))
    if (x <= (-1.06d+49)) then
        tmp = t_2
    else if (x <= (-7.4d-222)) then
        tmp = ((-4.0d0) * (t * a)) - t_1
    else if (x <= 5.3d-135) then
        tmp = (b * c) + (t * (a * (-4.0d0)))
    else if (x <= 3.9d-16) then
        tmp = (b * c) - t_1
    else if (x <= 3.15d+168) then
        tmp = (x * (i * (-4.0d0))) - (j * (27.0d0 * k))
    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 * 27.0) * k;
	double t_2 = x * ((i * -4.0) + (18.0 * (z * (y * t))));
	double tmp;
	if (x <= -1.06e+49) {
		tmp = t_2;
	} else if (x <= -7.4e-222) {
		tmp = (-4.0 * (t * a)) - t_1;
	} else if (x <= 5.3e-135) {
		tmp = (b * c) + (t * (a * -4.0));
	} else if (x <= 3.9e-16) {
		tmp = (b * c) - t_1;
	} else if (x <= 3.15e+168) {
		tmp = (x * (i * -4.0)) - (j * (27.0 * k));
	} 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 * 27.0) * k
	t_2 = x * ((i * -4.0) + (18.0 * (z * (y * t))))
	tmp = 0
	if x <= -1.06e+49:
		tmp = t_2
	elif x <= -7.4e-222:
		tmp = (-4.0 * (t * a)) - t_1
	elif x <= 5.3e-135:
		tmp = (b * c) + (t * (a * -4.0))
	elif x <= 3.9e-16:
		tmp = (b * c) - t_1
	elif x <= 3.15e+168:
		tmp = (x * (i * -4.0)) - (j * (27.0 * k))
	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 * 27.0) * k)
	t_2 = Float64(x * Float64(Float64(i * -4.0) + Float64(18.0 * Float64(z * Float64(y * t)))))
	tmp = 0.0
	if (x <= -1.06e+49)
		tmp = t_2;
	elseif (x <= -7.4e-222)
		tmp = Float64(Float64(-4.0 * Float64(t * a)) - t_1);
	elseif (x <= 5.3e-135)
		tmp = Float64(Float64(b * c) + Float64(t * Float64(a * -4.0)));
	elseif (x <= 3.9e-16)
		tmp = Float64(Float64(b * c) - t_1);
	elseif (x <= 3.15e+168)
		tmp = Float64(Float64(x * Float64(i * -4.0)) - Float64(j * Float64(27.0 * k)));
	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 * 27.0) * k;
	t_2 = x * ((i * -4.0) + (18.0 * (z * (y * t))));
	tmp = 0.0;
	if (x <= -1.06e+49)
		tmp = t_2;
	elseif (x <= -7.4e-222)
		tmp = (-4.0 * (t * a)) - t_1;
	elseif (x <= 5.3e-135)
		tmp = (b * c) + (t * (a * -4.0));
	elseif (x <= 3.9e-16)
		tmp = (b * c) - t_1;
	elseif (x <= 3.15e+168)
		tmp = (x * (i * -4.0)) - (j * (27.0 * k));
	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 * 27.0), $MachinePrecision] * k), $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, -1.06e+49], t$95$2, If[LessEqual[x, -7.4e-222], N[(N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[x, 5.3e-135], N[(N[(b * c), $MachinePrecision] + N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.9e-16], N[(N[(b * c), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[x, 3.15e+168], N[(N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision] - N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -1.06e49 or 3.1499999999999998e168 < x

   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. Step-by-step derivation

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 71.6%

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

   5. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(-4 \cdot i\right), \color{blue}{\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \left(\color{blue}{18} \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \mathsf{*.f64}\left(18, \color{blue}{\left(t \cdot \left(y \cdot z\right)\right)}\right)\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \mathsf{*.f64}\left(18, \left(\left(t \cdot y\right) \cdot \color{blue}{z}\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(\left(t \cdot y\right), \color{blue}{z}\right)\right)\right)\right) \]

      7. *-lowering-*.f64 71.5%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, y\right), z\right)\right)\right)\right) \]

   7. Simplified 71.5%

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

   if -1.06e49 < x < -7.3999999999999997e-222

   1. Initial program 97.9%

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

   3. Taylor expanded in a around inf

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(-4 \cdot \left(a \cdot t\right)\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(-4, \left(a \cdot t\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(-4, \left(t \cdot a\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, \color{blue}{27}\right), k\right)\right) \]

      3. *-lowering-*.f64 59.7%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(-4, \mathsf{*.f64}\left(t, a\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, \color{blue}{27}\right), k\right)\right) \]

   5. Simplified 59.7%

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

   if -7.3999999999999997e-222 < x < 5.3e-135

   1. Initial program 96.0%

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

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 94.1%

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

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \color{blue}{\left(b \cdot c\right)}\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 70.2%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \mathsf{*.f64}\left(b, \color{blue}{c}\right)\right) \]

   7. Simplified 70.2%

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

   8. Taylor expanded in x around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \color{blue}{\left(-4 \cdot a\right)}\right), \mathsf{*.f64}\left(b, c\right)\right) \]
   9. Step-by-step derivation

      1. *-lowering-*.f64 69.9%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(-4, a\right)\right), \mathsf{*.f64}\left(b, c\right)\right) \]

   10. Simplified 69.9%

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

   if 5.3e-135 < x < 3.89999999999999977e-16

   1. Initial program 96.2%

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

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(b \cdot c\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 74.9%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

   5. Simplified 74.9%

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

   if 3.89999999999999977e-16 < x < 3.1499999999999998e168

   1. Initial program 76.0%

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

   3. Taylor expanded in i around inf

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(-4 \cdot \left(i \cdot x\right)\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(-4, \left(i \cdot x\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

      2. *-lowering-*.f64 61.4%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(-4, \mathsf{*.f64}\left(i, x\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, \color{blue}{27}\right), k\right)\right) \]

   5. Simplified 61.4%

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(x \cdot \left(i \cdot -4\right)\right), \color{blue}{\left(\left(j \cdot 27\right) \cdot k\right)}\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \left(i \cdot -4\right)\right), \left(\color{blue}{\left(j \cdot 27\right)} \cdot k\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \left(-4 \cdot i\right)\right), \left(\left(j \cdot \color{blue}{27}\right) \cdot k\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(-4, i\right)\right), \left(\left(j \cdot \color{blue}{27}\right) \cdot k\right)\right) \]

      8. associate-*l* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(-4, i\right)\right), \left(j \cdot \color{blue}{\left(27 \cdot k\right)}\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(-4, i\right)\right), \mathsf{*.f64}\left(j, \color{blue}{\left(27 \cdot k\right)}\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(-4, i\right)\right), \mathsf{*.f64}\left(j, \left(k \cdot \color{blue}{27}\right)\right)\right) \]

      11. *-lowering-*.f64 61.4%

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(-4, i\right)\right), \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(k, \color{blue}{27}\right)\right)\right) \]

   7. Applied egg-rr 61.4%

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

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.06 \cdot 10^{+49}:\\ \;\;\;\;x \cdot \left(i \cdot -4 + 18 \cdot \left(z \cdot \left(y \cdot t\right)\right)\right)\\ \mathbf{elif}\;x \leq -7.4 \cdot 10^{-222}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;x \leq 5.3 \cdot 10^{-135}:\\ \;\;\;\;b \cdot c + t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{-16}:\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;x \leq 3.15 \cdot 10^{+168}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right) - j \cdot \left(27 \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(i \cdot -4 + 18 \cdot \left(z \cdot \left(y \cdot t\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 80.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;x \leq -9.5 \cdot 10^{+253}:\\ \;\;\;\;t \cdot \left(a \cdot -4 + x \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;x \leq -2.2 \cdot 10^{-21}:\\ \;\;\;\;\left(b \cdot c + x \cdot \left(i \cdot -4 + y \cdot \left(z \cdot \left(18 \cdot t\right)\right)\right)\right) - t\_1\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-37}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + x \cdot \left(i \cdot -4 + 18 \cdot \left(z \cdot \left(y \cdot t\right)\right)\right)\right) - t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)))
   (if (<= x -9.5e+253)
     (* t (+ (* a -4.0) (* x (* 18.0 (* y z)))))
     (if (<= x -2.2e-21)
       (- (+ (* b c) (* x (+ (* i -4.0) (* y (* z (* 18.0 t)))))) t_1)
       (if (<= x 6e-37)
         (- (+ (* b c) (* -4.0 (* t a))) t_1)
         (- (+ (* b c) (* x (+ (* i -4.0) (* 18.0 (* z (* y t)))))) 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 = (j * 27.0) * k;
	double tmp;
	if (x <= -9.5e+253) {
		tmp = t * ((a * -4.0) + (x * (18.0 * (y * z))));
	} else if (x <= -2.2e-21) {
		tmp = ((b * c) + (x * ((i * -4.0) + (y * (z * (18.0 * t)))))) - t_1;
	} else if (x <= 6e-37) {
		tmp = ((b * c) + (-4.0 * (t * a))) - t_1;
	} else {
		tmp = ((b * c) + (x * ((i * -4.0) + (18.0 * (z * (y * t)))))) - t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 * 27.0d0) * k
    if (x <= (-9.5d+253)) then
        tmp = t * ((a * (-4.0d0)) + (x * (18.0d0 * (y * z))))
    else if (x <= (-2.2d-21)) then
        tmp = ((b * c) + (x * ((i * (-4.0d0)) + (y * (z * (18.0d0 * t)))))) - t_1
    else if (x <= 6d-37) then
        tmp = ((b * c) + ((-4.0d0) * (t * a))) - t_1
    else
        tmp = ((b * c) + (x * ((i * (-4.0d0)) + (18.0d0 * (z * (y * t)))))) - t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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 * 27.0) * k;
	double tmp;
	if (x <= -9.5e+253) {
		tmp = t * ((a * -4.0) + (x * (18.0 * (y * z))));
	} else if (x <= -2.2e-21) {
		tmp = ((b * c) + (x * ((i * -4.0) + (y * (z * (18.0 * t)))))) - t_1;
	} else if (x <= 6e-37) {
		tmp = ((b * c) + (-4.0 * (t * a))) - t_1;
	} else {
		tmp = ((b * c) + (x * ((i * -4.0) + (18.0 * (z * (y * t)))))) - t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	tmp = 0
	if x <= -9.5e+253:
		tmp = t * ((a * -4.0) + (x * (18.0 * (y * z))))
	elif x <= -2.2e-21:
		tmp = ((b * c) + (x * ((i * -4.0) + (y * (z * (18.0 * t)))))) - t_1
	elif x <= 6e-37:
		tmp = ((b * c) + (-4.0 * (t * a))) - t_1
	else:
		tmp = ((b * c) + (x * ((i * -4.0) + (18.0 * (z * (y * t)))))) - t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (x <= -9.5e+253)
		tmp = Float64(t * Float64(Float64(a * -4.0) + Float64(x * Float64(18.0 * Float64(y * z)))));
	elseif (x <= -2.2e-21)
		tmp = Float64(Float64(Float64(b * c) + Float64(x * Float64(Float64(i * -4.0) + Float64(y * Float64(z * Float64(18.0 * t)))))) - t_1);
	elseif (x <= 6e-37)
		tmp = Float64(Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a))) - t_1);
	else
		tmp = Float64(Float64(Float64(b * c) + Float64(x * Float64(Float64(i * -4.0) + Float64(18.0 * Float64(z * Float64(y * t)))))) - t_1);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * 27.0) * k;
	tmp = 0.0;
	if (x <= -9.5e+253)
		tmp = t * ((a * -4.0) + (x * (18.0 * (y * z))));
	elseif (x <= -2.2e-21)
		tmp = ((b * c) + (x * ((i * -4.0) + (y * (z * (18.0 * t)))))) - t_1;
	elseif (x <= 6e-37)
		tmp = ((b * c) + (-4.0 * (t * a))) - t_1;
	else
		tmp = ((b * c) + (x * ((i * -4.0) + (18.0 * (z * (y * t)))))) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[x, -9.5e+253], N[(t * N[(N[(a * -4.0), $MachinePrecision] + N[(x * N[(18.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.2e-21], N[(N[(N[(b * c), $MachinePrecision] + N[(x * N[(N[(i * -4.0), $MachinePrecision] + N[(y * N[(z * N[(18.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[x, 6e-37], N[(N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] + N[(x * N[(N[(i * -4.0), $MachinePrecision] + N[(18.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -9.50000000000000005e253

   1. Initial program 51.2%

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

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 51.2%

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

   5. Taylor expanded in t around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(-4 \cdot a\right), \color{blue}{\left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \left(\color{blue}{18} \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \left(\left(x \cdot \left(y \cdot z\right)\right) \cdot \color{blue}{18}\right)\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \left(x \cdot \color{blue}{\left(\left(y \cdot z\right) \cdot 18\right)}\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \left(x \cdot \left(18 \cdot \color{blue}{\left(y \cdot z\right)}\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \mathsf{*.f64}\left(x, \color{blue}{\left(18 \cdot \left(y \cdot z\right)\right)}\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(18, \color{blue}{\left(y \cdot z\right)}\right)\right)\right)\right) \]

      9. *-lowering-*.f64 90.8%

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(y, \color{blue}{z}\right)\right)\right)\right)\right) \]

   7. Simplified 90.8%

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

   if -9.50000000000000005e253 < x < -2.2000000000000001e-21

   1. Initial program 72.1%

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

      1. +-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

      2. associate-+r- N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\left(\left(b \cdot c + \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t\right) - \left(a \cdot 4\right) \cdot t\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t\right), \left(\left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(b \cdot c\right), \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t\right)\right), \left(\left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t\right)\right), \left(\left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      6. associate-*l* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot \left(z \cdot t\right)\right)\right), \left(\left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      7. associate-*l* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\left(x \cdot 18\right) \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\right), \left(\left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\left(x \cdot 18\right), \left(y \cdot \left(z \cdot t\right)\right)\right)\right), \left(\left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), \left(y \cdot \left(z \cdot t\right)\right)\right)\right), \left(\left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), \mathsf{*.f64}\left(y, \left(z \cdot t\right)\right)\right)\right), \left(\left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), \mathsf{*.f64}\left(y, \left(t \cdot z\right)\right)\right)\right), \left(\left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, z\right)\right)\right)\right), \left(\left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      13. associate-*l* N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, z\right)\right)\right)\right), \left(a \cdot \left(4 \cdot t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, z\right)\right)\right)\right), \mathsf{*.f64}\left(a, \left(4 \cdot t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      15. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, z\right)\right)\right)\right), \mathsf{*.f64}\left(a, \left(t \cdot 4\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      16. *-lowering-*.f64 82.9%

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, z\right)\right)\right)\right), \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(t, 4\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

   4. Applied egg-rr 82.9%

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

   5. Taylor expanded in a around 0

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(i \cdot x\right)\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   6. Step-by-step derivation

      1. cancel-sign-sub-inv N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(i \cdot x\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + -4 \cdot \left(i \cdot x\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\left(b \cdot c + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) + -4 \cdot \left(i \cdot x\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

      4. associate-+l+ N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + -4 \cdot \left(i \cdot x\right)\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(18 \cdot t\right) \cdot \left(x \cdot \left(y \cdot z\right)\right) + -4 \cdot \left(i \cdot x\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(18 \cdot t\right) \cdot \left(\left(y \cdot z\right) \cdot x\right) + -4 \cdot \left(i \cdot x\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      7. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(\left(18 \cdot t\right) \cdot \left(y \cdot z\right)\right) \cdot x + -4 \cdot \left(i \cdot x\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      8. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right) \cdot x + -4 \cdot \left(i \cdot x\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      9. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right) \cdot x + \left(-4 \cdot i\right) \cdot x\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      10. distribute-rgt-in N/A

          \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + -4 \cdot i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, \color{blue}{27}\right), k\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      12. cancel-sign-sub-inv N/A

          \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      13. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(b \cdot c\right), \left(x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

   7. Simplified 74.4%

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

   if -2.2000000000000001e-21 < x < 6e-37

   1. Initial program 97.3%

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

   3. Taylor expanded in x around 0

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(b \cdot c - 4 \cdot \left(a \cdot t\right)\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   4. Step-by-step derivation

      1. cancel-sign-sub-inv N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(a \cdot t\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + -4 \cdot \left(a \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(b \cdot c\right), \left(-4 \cdot \left(a \cdot t\right)\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(-4 \cdot \left(a \cdot t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(-4, \left(a \cdot t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, \color{blue}{27}\right), k\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(-4, \left(t \cdot a\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      7. *-lowering-*.f64 85.8%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(-4, \mathsf{*.f64}\left(t, a\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

   5. Simplified 85.8%

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

   if 6e-37 < x

   1. Initial program 79.4%

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

   3. Taylor expanded in a around 0

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(i \cdot x\right)\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   4. Step-by-step derivation

      1. cancel-sign-sub-inv N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(i \cdot x\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + -4 \cdot \left(i \cdot x\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\left(b \cdot c + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) + -4 \cdot \left(i \cdot x\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

      4. associate-+l+ N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + -4 \cdot \left(i \cdot x\right)\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(18 \cdot t\right) \cdot \left(x \cdot \left(y \cdot z\right)\right) + -4 \cdot \left(i \cdot x\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(18 \cdot t\right) \cdot \left(\left(y \cdot z\right) \cdot x\right) + -4 \cdot \left(i \cdot x\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      7. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(\left(18 \cdot t\right) \cdot \left(y \cdot z\right)\right) \cdot x + -4 \cdot \left(i \cdot x\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      8. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right) \cdot x + -4 \cdot \left(i \cdot x\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      9. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right) \cdot x + \left(-4 \cdot i\right) \cdot x\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      10. distribute-rgt-in N/A

          \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + -4 \cdot i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, \color{blue}{27}\right), k\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      12. cancel-sign-sub-inv N/A

          \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      13. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(b \cdot c\right), \left(x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

   5. Simplified 89.7%

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

4. Final simplification 84.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+253}:\\ \;\;\;\;t \cdot \left(a \cdot -4 + x \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;x \leq -2.2 \cdot 10^{-21}:\\ \;\;\;\;\left(b \cdot c + x \cdot \left(i \cdot -4 + y \cdot \left(z \cdot \left(18 \cdot t\right)\right)\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-37}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + x \cdot \left(i \cdot -4 + 18 \cdot \left(z \cdot \left(y \cdot t\right)\right)\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 80.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ t_2 := \left(b \cdot c + x \cdot \left(i \cdot -4 + 18 \cdot \left(z \cdot \left(y \cdot t\right)\right)\right)\right) - t\_1\\ \mathbf{if}\;x \leq -9.5 \cdot 10^{+253}:\\ \;\;\;\;t \cdot \left(a \cdot -4 + x \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{-19}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{-36}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k))
        (t_2 (- (+ (* b c) (* x (+ (* i -4.0) (* 18.0 (* z (* y t)))))) t_1)))
   (if (<= x -9.5e+253)
     (* t (+ (* a -4.0) (* x (* 18.0 (* y z)))))
     (if (<= x -2.5e-19)
       t_2
       (if (<= x 2.7e-36) (- (+ (* b c) (* -4.0 (* t a))) 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 * 27.0) * k;
	double t_2 = ((b * c) + (x * ((i * -4.0) + (18.0 * (z * (y * t)))))) - t_1;
	double tmp;
	if (x <= -9.5e+253) {
		tmp = t * ((a * -4.0) + (x * (18.0 * (y * z))));
	} else if (x <= -2.5e-19) {
		tmp = t_2;
	} else if (x <= 2.7e-36) {
		tmp = ((b * c) + (-4.0 * (t * a))) - 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 * 27.0d0) * k
    t_2 = ((b * c) + (x * ((i * (-4.0d0)) + (18.0d0 * (z * (y * t)))))) - t_1
    if (x <= (-9.5d+253)) then
        tmp = t * ((a * (-4.0d0)) + (x * (18.0d0 * (y * z))))
    else if (x <= (-2.5d-19)) then
        tmp = t_2
    else if (x <= 2.7d-36) then
        tmp = ((b * c) + ((-4.0d0) * (t * a))) - 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 * 27.0) * k;
	double t_2 = ((b * c) + (x * ((i * -4.0) + (18.0 * (z * (y * t)))))) - t_1;
	double tmp;
	if (x <= -9.5e+253) {
		tmp = t * ((a * -4.0) + (x * (18.0 * (y * z))));
	} else if (x <= -2.5e-19) {
		tmp = t_2;
	} else if (x <= 2.7e-36) {
		tmp = ((b * c) + (-4.0 * (t * a))) - 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 * 27.0) * k
	t_2 = ((b * c) + (x * ((i * -4.0) + (18.0 * (z * (y * t)))))) - t_1
	tmp = 0
	if x <= -9.5e+253:
		tmp = t * ((a * -4.0) + (x * (18.0 * (y * z))))
	elif x <= -2.5e-19:
		tmp = t_2
	elif x <= 2.7e-36:
		tmp = ((b * c) + (-4.0 * (t * a))) - 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 * 27.0) * k)
	t_2 = Float64(Float64(Float64(b * c) + Float64(x * Float64(Float64(i * -4.0) + Float64(18.0 * Float64(z * Float64(y * t)))))) - t_1)
	tmp = 0.0
	if (x <= -9.5e+253)
		tmp = Float64(t * Float64(Float64(a * -4.0) + Float64(x * Float64(18.0 * Float64(y * z)))));
	elseif (x <= -2.5e-19)
		tmp = t_2;
	elseif (x <= 2.7e-36)
		tmp = Float64(Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a))) - 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 * 27.0) * k;
	t_2 = ((b * c) + (x * ((i * -4.0) + (18.0 * (z * (y * t)))))) - t_1;
	tmp = 0.0;
	if (x <= -9.5e+253)
		tmp = t * ((a * -4.0) + (x * (18.0 * (y * z))));
	elseif (x <= -2.5e-19)
		tmp = t_2;
	elseif (x <= 2.7e-36)
		tmp = ((b * c) + (-4.0 * (t * a))) - 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 * 27.0), $MachinePrecision] * k), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(b * c), $MachinePrecision] + N[(x * N[(N[(i * -4.0), $MachinePrecision] + N[(18.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]}, If[LessEqual[x, -9.5e+253], N[(t * N[(N[(a * -4.0), $MachinePrecision] + N[(x * N[(18.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.5e-19], t$95$2, If[LessEqual[x, 2.7e-36], N[(N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -9.50000000000000005e253

   1. Initial program 51.2%

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

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 51.2%

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

   5. Taylor expanded in t around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(-4 \cdot a\right), \color{blue}{\left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \left(\color{blue}{18} \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \left(\left(x \cdot \left(y \cdot z\right)\right) \cdot \color{blue}{18}\right)\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \left(x \cdot \color{blue}{\left(\left(y \cdot z\right) \cdot 18\right)}\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \left(x \cdot \left(18 \cdot \color{blue}{\left(y \cdot z\right)}\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \mathsf{*.f64}\left(x, \color{blue}{\left(18 \cdot \left(y \cdot z\right)\right)}\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(18, \color{blue}{\left(y \cdot z\right)}\right)\right)\right)\right) \]

      9. *-lowering-*.f64 90.8%

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(y, \color{blue}{z}\right)\right)\right)\right)\right) \]

   7. Simplified 90.8%

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

   if -9.50000000000000005e253 < x < -2.5000000000000002e-19 or 2.70000000000000007e-36 < x

   1. Initial program 76.5%

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

   3. Taylor expanded in a around 0

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(i \cdot x\right)\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   4. Step-by-step derivation

      1. cancel-sign-sub-inv N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(i \cdot x\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + -4 \cdot \left(i \cdot x\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\left(b \cdot c + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) + -4 \cdot \left(i \cdot x\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

      4. associate-+l+ N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + -4 \cdot \left(i \cdot x\right)\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(18 \cdot t\right) \cdot \left(x \cdot \left(y \cdot z\right)\right) + -4 \cdot \left(i \cdot x\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(18 \cdot t\right) \cdot \left(\left(y \cdot z\right) \cdot x\right) + -4 \cdot \left(i \cdot x\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      7. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(\left(18 \cdot t\right) \cdot \left(y \cdot z\right)\right) \cdot x + -4 \cdot \left(i \cdot x\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      8. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right) \cdot x + -4 \cdot \left(i \cdot x\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      9. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right) \cdot x + \left(-4 \cdot i\right) \cdot x\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      10. distribute-rgt-in N/A

          \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + -4 \cdot i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, \color{blue}{27}\right), k\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      12. cancel-sign-sub-inv N/A

          \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      13. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(b \cdot c\right), \left(x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

   5. Simplified 84.3%

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

   if -2.5000000000000002e-19 < x < 2.70000000000000007e-36

   1. Initial program 97.3%

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

   3. Taylor expanded in x around 0

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(b \cdot c - 4 \cdot \left(a \cdot t\right)\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   4. Step-by-step derivation

      1. cancel-sign-sub-inv N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(a \cdot t\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + -4 \cdot \left(a \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(b \cdot c\right), \left(-4 \cdot \left(a \cdot t\right)\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(-4 \cdot \left(a \cdot t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(-4, \left(a \cdot t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, \color{blue}{27}\right), k\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(-4, \left(t \cdot a\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      7. *-lowering-*.f64 85.8%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(-4, \mathsf{*.f64}\left(t, a\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

   5. Simplified 85.8%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+253}:\\ \;\;\;\;t \cdot \left(a \cdot -4 + x \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{-19}:\\ \;\;\;\;\left(b \cdot c + x \cdot \left(i \cdot -4 + 18 \cdot \left(z \cdot \left(y \cdot t\right)\right)\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{-36}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + x \cdot \left(i \cdot -4 + 18 \cdot \left(z \cdot \left(y \cdot t\right)\right)\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 31.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := -4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;k \leq -1.7 \cdot 10^{-93}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;k \leq -2.35 \cdot 10^{-271}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;k \leq 4.3 \cdot 10^{-270}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 4.3 \cdot 10^{-138}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;k \leq 3.7 \cdot 10^{+55}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 4.5 \cdot 10^{+84}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* -4.0 (* x i))))
   (if (<= k -1.7e-93)
     (* j (* k -27.0))
     (if (<= k -2.35e-271)
       t_1
       (if (<= k 4.3e-270)
         (* b c)
         (if (<= k 4.3e-138)
           (* -4.0 (* t a))
           (if (<= k 3.7e+55)
             (* b c)
             (if (<= k 4.5e+84) t_1 (* k (* j -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 t_1 = -4.0 * (x * i);
	double tmp;
	if (k <= -1.7e-93) {
		tmp = j * (k * -27.0);
	} else if (k <= -2.35e-271) {
		tmp = t_1;
	} else if (k <= 4.3e-270) {
		tmp = b * c;
	} else if (k <= 4.3e-138) {
		tmp = -4.0 * (t * a);
	} else if (k <= 3.7e+55) {
		tmp = b * c;
	} else if (k <= 4.5e+84) {
		tmp = t_1;
	} else {
		tmp = k * (j * -27.0);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 (k <= (-1.7d-93)) then
        tmp = j * (k * (-27.0d0))
    else if (k <= (-2.35d-271)) then
        tmp = t_1
    else if (k <= 4.3d-270) then
        tmp = b * c
    else if (k <= 4.3d-138) then
        tmp = (-4.0d0) * (t * a)
    else if (k <= 3.7d+55) then
        tmp = b * c
    else if (k <= 4.5d+84) then
        tmp = t_1
    else
        tmp = k * (j * (-27.0d0))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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 (k <= -1.7e-93) {
		tmp = j * (k * -27.0);
	} else if (k <= -2.35e-271) {
		tmp = t_1;
	} else if (k <= 4.3e-270) {
		tmp = b * c;
	} else if (k <= 4.3e-138) {
		tmp = -4.0 * (t * a);
	} else if (k <= 3.7e+55) {
		tmp = b * c;
	} else if (k <= 4.5e+84) {
		tmp = t_1;
	} else {
		tmp = k * (j * -27.0);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = -4.0 * (x * i)
	tmp = 0
	if k <= -1.7e-93:
		tmp = j * (k * -27.0)
	elif k <= -2.35e-271:
		tmp = t_1
	elif k <= 4.3e-270:
		tmp = b * c
	elif k <= 4.3e-138:
		tmp = -4.0 * (t * a)
	elif k <= 3.7e+55:
		tmp = b * c
	elif k <= 4.5e+84:
		tmp = t_1
	else:
		tmp = k * (j * -27.0)
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(-4.0 * Float64(x * i))
	tmp = 0.0
	if (k <= -1.7e-93)
		tmp = Float64(j * Float64(k * -27.0));
	elseif (k <= -2.35e-271)
		tmp = t_1;
	elseif (k <= 4.3e-270)
		tmp = Float64(b * c);
	elseif (k <= 4.3e-138)
		tmp = Float64(-4.0 * Float64(t * a));
	elseif (k <= 3.7e+55)
		tmp = Float64(b * c);
	elseif (k <= 4.5e+84)
		tmp = t_1;
	else
		tmp = Float64(k * Float64(j * -27.0));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = -4.0 * (x * i);
	tmp = 0.0;
	if (k <= -1.7e-93)
		tmp = j * (k * -27.0);
	elseif (k <= -2.35e-271)
		tmp = t_1;
	elseif (k <= 4.3e-270)
		tmp = b * c;
	elseif (k <= 4.3e-138)
		tmp = -4.0 * (t * a);
	elseif (k <= 3.7e+55)
		tmp = b * c;
	elseif (k <= 4.5e+84)
		tmp = t_1;
	else
		tmp = k * (j * -27.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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[k, -1.7e-93], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -2.35e-271], t$95$1, If[LessEqual[k, 4.3e-270], N[(b * c), $MachinePrecision], If[LessEqual[k, 4.3e-138], N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 3.7e+55], N[(b * c), $MachinePrecision], If[LessEqual[k, 4.5e+84], t$95$1, N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if k < -1.70000000000000001e-93

   1. Initial program 80.8%

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

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 80.8%

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

   5. Taylor expanded in j around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-27, \color{blue}{\left(j \cdot k\right)}\right) \]

      2. *-lowering-*.f64 36.0%

         \[\leadsto \mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, \color{blue}{k}\right)\right) \]

   7. Simplified 36.0%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-27 \cdot k\right), \color{blue}{j}\right) \]

      4. *-lowering-*.f64 35.9%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-27, k\right), j\right) \]

   9. Applied egg-rr 35.9%

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

   if -1.70000000000000001e-93 < k < -2.35000000000000002e-271 or 3.7000000000000002e55 < k < 4.4999999999999997e84

   1. Initial program 92.5%

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

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 92.5%

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

   5. Taylor expanded in i around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-4, \color{blue}{\left(i \cdot x\right)}\right) \]

      2. *-lowering-*.f64 32.9%

         \[\leadsto \mathsf{*.f64}\left(-4, \mathsf{*.f64}\left(i, \color{blue}{x}\right)\right) \]

   7. Simplified 32.9%

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

   if -2.35000000000000002e-271 < k < 4.3000000000000002e-270 or 4.3e-138 < k < 3.7000000000000002e55

   1. Initial program 82.9%

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

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 82.9%

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

   5. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot c} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 36.8%

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{c}\right) \]

   7. Simplified 36.8%

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

   if 4.3000000000000002e-270 < k < 4.3e-138

   1. Initial program 96.2%

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

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 92.5%

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

   5. Taylor expanded in a around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-4, \color{blue}{\left(a \cdot t\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(-4, \left(t \cdot \color{blue}{a}\right)\right) \]

      3. *-lowering-*.f64 43.9%

         \[\leadsto \mathsf{*.f64}\left(-4, \mathsf{*.f64}\left(t, \color{blue}{a}\right)\right) \]

   7. Simplified 43.9%

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

   if 4.4999999999999997e84 < k

   1. Initial program 79.7%

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

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 79.6%

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

   5. Taylor expanded in j around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-27, \color{blue}{\left(j \cdot k\right)}\right) \]

      2. *-lowering-*.f64 54.5%

         \[\leadsto \mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, \color{blue}{k}\right)\right) \]

   7. Simplified 54.5%

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

      1. associate-*r* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-27 \cdot j\right), \color{blue}{k}\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\left(j \cdot -27\right), k\right) \]

      4. *-lowering-*.f64 54.7%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, -27\right), k\right) \]

   9. Applied egg-rr 54.7%

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

4. Final simplification 39.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -1.7 \cdot 10^{-93}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;k \leq -2.35 \cdot 10^{-271}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;k \leq 4.3 \cdot 10^{-270}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 4.3 \cdot 10^{-138}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;k \leq 3.7 \cdot 10^{+55}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 4.5 \cdot 10^{+84}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 31.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := -4 \cdot \left(x \cdot i\right)\\ t_2 := j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;k \leq -6.8 \cdot 10^{-94}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;k \leq -2.15 \cdot 10^{-271}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;k \leq 1.12 \cdot 10^{-269}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 2.65 \cdot 10^{-135}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;k \leq 3.8 \cdot 10^{+55}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 2.3 \cdot 10^{+84}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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 (* -4.0 (* x i))) (t_2 (* j (* k -27.0))))
   (if (<= k -6.8e-94)
     t_2
     (if (<= k -2.15e-271)
       t_1
       (if (<= k 1.12e-269)
         (* b c)
         (if (<= k 2.65e-135)
           (* -4.0 (* t a))
           (if (<= k 3.8e+55) (* b c) (if (<= k 2.3e+84) 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 = -4.0 * (x * i);
	double t_2 = j * (k * -27.0);
	double tmp;
	if (k <= -6.8e-94) {
		tmp = t_2;
	} else if (k <= -2.15e-271) {
		tmp = t_1;
	} else if (k <= 1.12e-269) {
		tmp = b * c;
	} else if (k <= 2.65e-135) {
		tmp = -4.0 * (t * a);
	} else if (k <= 3.8e+55) {
		tmp = b * c;
	} else if (k <= 2.3e+84) {
		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 = (-4.0d0) * (x * i)
    t_2 = j * (k * (-27.0d0))
    if (k <= (-6.8d-94)) then
        tmp = t_2
    else if (k <= (-2.15d-271)) then
        tmp = t_1
    else if (k <= 1.12d-269) then
        tmp = b * c
    else if (k <= 2.65d-135) then
        tmp = (-4.0d0) * (t * a)
    else if (k <= 3.8d+55) then
        tmp = b * c
    else if (k <= 2.3d+84) 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 = -4.0 * (x * i);
	double t_2 = j * (k * -27.0);
	double tmp;
	if (k <= -6.8e-94) {
		tmp = t_2;
	} else if (k <= -2.15e-271) {
		tmp = t_1;
	} else if (k <= 1.12e-269) {
		tmp = b * c;
	} else if (k <= 2.65e-135) {
		tmp = -4.0 * (t * a);
	} else if (k <= 3.8e+55) {
		tmp = b * c;
	} else if (k <= 2.3e+84) {
		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 = -4.0 * (x * i)
	t_2 = j * (k * -27.0)
	tmp = 0
	if k <= -6.8e-94:
		tmp = t_2
	elif k <= -2.15e-271:
		tmp = t_1
	elif k <= 1.12e-269:
		tmp = b * c
	elif k <= 2.65e-135:
		tmp = -4.0 * (t * a)
	elif k <= 3.8e+55:
		tmp = b * c
	elif k <= 2.3e+84:
		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(-4.0 * Float64(x * i))
	t_2 = Float64(j * Float64(k * -27.0))
	tmp = 0.0
	if (k <= -6.8e-94)
		tmp = t_2;
	elseif (k <= -2.15e-271)
		tmp = t_1;
	elseif (k <= 1.12e-269)
		tmp = Float64(b * c);
	elseif (k <= 2.65e-135)
		tmp = Float64(-4.0 * Float64(t * a));
	elseif (k <= 3.8e+55)
		tmp = Float64(b * c);
	elseif (k <= 2.3e+84)
		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 = -4.0 * (x * i);
	t_2 = j * (k * -27.0);
	tmp = 0.0;
	if (k <= -6.8e-94)
		tmp = t_2;
	elseif (k <= -2.15e-271)
		tmp = t_1;
	elseif (k <= 1.12e-269)
		tmp = b * c;
	elseif (k <= 2.65e-135)
		tmp = -4.0 * (t * a);
	elseif (k <= 3.8e+55)
		tmp = b * c;
	elseif (k <= 2.3e+84)
		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[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[k, -6.8e-94], t$95$2, If[LessEqual[k, -2.15e-271], t$95$1, If[LessEqual[k, 1.12e-269], N[(b * c), $MachinePrecision], If[LessEqual[k, 2.65e-135], N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 3.8e+55], N[(b * c), $MachinePrecision], If[LessEqual[k, 2.3e+84], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if k < -6.7999999999999996e-94 or 2.2999999999999999e84 < k

   1. Initial program 80.4%

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

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 80.3%

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

   5. Taylor expanded in j around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-27, \color{blue}{\left(j \cdot k\right)}\right) \]

      2. *-lowering-*.f64 43.2%

         \[\leadsto \mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, \color{blue}{k}\right)\right) \]

   7. Simplified 43.2%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-27 \cdot k\right), \color{blue}{j}\right) \]

      4. *-lowering-*.f64 43.2%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-27, k\right), j\right) \]

   9. Applied egg-rr 43.2%

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

   if -6.7999999999999996e-94 < k < -2.15e-271 or 3.8e55 < k < 2.2999999999999999e84

   1. Initial program 92.5%

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

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 92.5%

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

   5. Taylor expanded in i around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-4, \color{blue}{\left(i \cdot x\right)}\right) \]

      2. *-lowering-*.f64 32.9%

         \[\leadsto \mathsf{*.f64}\left(-4, \mathsf{*.f64}\left(i, \color{blue}{x}\right)\right) \]

   7. Simplified 32.9%

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

   if -2.15e-271 < k < 1.12e-269 or 2.65e-135 < k < 3.8e55

   1. Initial program 82.9%

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

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 82.9%

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

   5. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot c} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 36.8%

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{c}\right) \]

   7. Simplified 36.8%

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

   if 1.12e-269 < k < 2.65e-135

   1. Initial program 96.2%

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

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 92.5%

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

   5. Taylor expanded in a around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-4, \color{blue}{\left(a \cdot t\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(-4, \left(t \cdot \color{blue}{a}\right)\right) \]

      3. *-lowering-*.f64 43.9%

         \[\leadsto \mathsf{*.f64}\left(-4, \mathsf{*.f64}\left(t, \color{blue}{a}\right)\right) \]

   7. Simplified 43.9%

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

4. Final simplification 39.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -6.8 \cdot 10^{-94}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;k \leq -2.15 \cdot 10^{-271}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;k \leq 1.12 \cdot 10^{-269}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 2.65 \cdot 10^{-135}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;k \leq 3.8 \cdot 10^{+55}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 2.3 \cdot 10^{+84}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 31.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := -4 \cdot \left(x \cdot i\right)\\ t_2 := -27 \cdot \left(j \cdot k\right)\\ \mathbf{if}\;k \leq -3.2 \cdot 10^{-100}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;k \leq -1.9 \cdot 10^{-270}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;k \leq 3.3 \cdot 10^{-270}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 2.9 \cdot 10^{-135}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;k \leq 3.8 \cdot 10^{+55}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 3.1 \cdot 10^{+84}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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 (* -4.0 (* x i))) (t_2 (* -27.0 (* j k))))
   (if (<= k -3.2e-100)
     t_2
     (if (<= k -1.9e-270)
       t_1
       (if (<= k 3.3e-270)
         (* b c)
         (if (<= k 2.9e-135)
           (* -4.0 (* t a))
           (if (<= k 3.8e+55) (* b c) (if (<= k 3.1e+84) 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 = -4.0 * (x * i);
	double t_2 = -27.0 * (j * k);
	double tmp;
	if (k <= -3.2e-100) {
		tmp = t_2;
	} else if (k <= -1.9e-270) {
		tmp = t_1;
	} else if (k <= 3.3e-270) {
		tmp = b * c;
	} else if (k <= 2.9e-135) {
		tmp = -4.0 * (t * a);
	} else if (k <= 3.8e+55) {
		tmp = b * c;
	} else if (k <= 3.1e+84) {
		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 = (-4.0d0) * (x * i)
    t_2 = (-27.0d0) * (j * k)
    if (k <= (-3.2d-100)) then
        tmp = t_2
    else if (k <= (-1.9d-270)) then
        tmp = t_1
    else if (k <= 3.3d-270) then
        tmp = b * c
    else if (k <= 2.9d-135) then
        tmp = (-4.0d0) * (t * a)
    else if (k <= 3.8d+55) then
        tmp = b * c
    else if (k <= 3.1d+84) 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 = -4.0 * (x * i);
	double t_2 = -27.0 * (j * k);
	double tmp;
	if (k <= -3.2e-100) {
		tmp = t_2;
	} else if (k <= -1.9e-270) {
		tmp = t_1;
	} else if (k <= 3.3e-270) {
		tmp = b * c;
	} else if (k <= 2.9e-135) {
		tmp = -4.0 * (t * a);
	} else if (k <= 3.8e+55) {
		tmp = b * c;
	} else if (k <= 3.1e+84) {
		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 = -4.0 * (x * i)
	t_2 = -27.0 * (j * k)
	tmp = 0
	if k <= -3.2e-100:
		tmp = t_2
	elif k <= -1.9e-270:
		tmp = t_1
	elif k <= 3.3e-270:
		tmp = b * c
	elif k <= 2.9e-135:
		tmp = -4.0 * (t * a)
	elif k <= 3.8e+55:
		tmp = b * c
	elif k <= 3.1e+84:
		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(-4.0 * Float64(x * i))
	t_2 = Float64(-27.0 * Float64(j * k))
	tmp = 0.0
	if (k <= -3.2e-100)
		tmp = t_2;
	elseif (k <= -1.9e-270)
		tmp = t_1;
	elseif (k <= 3.3e-270)
		tmp = Float64(b * c);
	elseif (k <= 2.9e-135)
		tmp = Float64(-4.0 * Float64(t * a));
	elseif (k <= 3.8e+55)
		tmp = Float64(b * c);
	elseif (k <= 3.1e+84)
		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 = -4.0 * (x * i);
	t_2 = -27.0 * (j * k);
	tmp = 0.0;
	if (k <= -3.2e-100)
		tmp = t_2;
	elseif (k <= -1.9e-270)
		tmp = t_1;
	elseif (k <= 3.3e-270)
		tmp = b * c;
	elseif (k <= 2.9e-135)
		tmp = -4.0 * (t * a);
	elseif (k <= 3.8e+55)
		tmp = b * c;
	elseif (k <= 3.1e+84)
		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[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[k, -3.2e-100], t$95$2, If[LessEqual[k, -1.9e-270], t$95$1, If[LessEqual[k, 3.3e-270], N[(b * c), $MachinePrecision], If[LessEqual[k, 2.9e-135], N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 3.8e+55], N[(b * c), $MachinePrecision], If[LessEqual[k, 3.1e+84], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if k < -3.20000000000000017e-100 or 3.10000000000000003e84 < k

   1. Initial program 80.4%

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

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 80.3%

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

   5. Taylor expanded in j around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-27, \color{blue}{\left(j \cdot k\right)}\right) \]

      2. *-lowering-*.f64 43.2%

         \[\leadsto \mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, \color{blue}{k}\right)\right) \]

   7. Simplified 43.2%

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

   if -3.20000000000000017e-100 < k < -1.90000000000000021e-270 or 3.8e55 < k < 3.10000000000000003e84

   1. Initial program 92.5%

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

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 92.5%

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

   5. Taylor expanded in i around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-4, \color{blue}{\left(i \cdot x\right)}\right) \]

      2. *-lowering-*.f64 32.9%

         \[\leadsto \mathsf{*.f64}\left(-4, \mathsf{*.f64}\left(i, \color{blue}{x}\right)\right) \]

   7. Simplified 32.9%

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

   if -1.90000000000000021e-270 < k < 3.30000000000000018e-270 or 2.9000000000000002e-135 < k < 3.8e55

   1. Initial program 82.9%

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

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 82.9%

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

   5. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot c} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 36.8%

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{c}\right) \]

   7. Simplified 36.8%

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

   if 3.30000000000000018e-270 < k < 2.9000000000000002e-135

   1. Initial program 96.2%

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

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 92.5%

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

   5. Taylor expanded in a around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-4, \color{blue}{\left(a \cdot t\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(-4, \left(t \cdot \color{blue}{a}\right)\right) \]

      3. *-lowering-*.f64 43.9%

         \[\leadsto \mathsf{*.f64}\left(-4, \mathsf{*.f64}\left(t, \color{blue}{a}\right)\right) \]

   7. Simplified 43.9%

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

4. Final simplification 39.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -3.2 \cdot 10^{-100}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;k \leq -1.9 \cdot 10^{-270}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;k \leq 3.3 \cdot 10^{-270}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 2.9 \cdot 10^{-135}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;k \leq 3.8 \cdot 10^{+55}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 3.1 \cdot 10^{+84}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 71.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;x \leq -1.9 \cdot 10^{+191}:\\ \;\;\;\;c \cdot \left(b + \frac{t \cdot \left(a \cdot -4 + 18 \cdot \left(z \cdot \left(x \cdot y\right)\right)\right)}{c}\right)\\ \mathbf{elif}\;x \leq -2.1 \cdot 10^{+47}:\\ \;\;\;\;t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right) + -4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{-47}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - t\_1\\ \mathbf{elif}\;x \leq 4.7 \cdot 10^{+168}:\\ \;\;\;\;\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(i \cdot -4 + t \cdot \left(z \cdot \left(18 \cdot y\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)))
   (if (<= x -1.9e+191)
     (* c (+ b (/ (* t (+ (* a -4.0) (* 18.0 (* z (* x y))))) c)))
     (if (<= x -2.1e+47)
       (+ (* t (+ (* (* (* x 18.0) y) z) (* a -4.0))) (* -4.0 (* x i)))
       (if (<= x 3.8e-47)
         (- (+ (* b c) (* -4.0 (* t a))) t_1)
         (if (<= x 4.7e+168)
           (- (- (* b c) (* (* x 4.0) i)) t_1)
           (* x (+ (* i -4.0) (* t (* z (* 18.0 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 t_1 = (j * 27.0) * k;
	double tmp;
	if (x <= -1.9e+191) {
		tmp = c * (b + ((t * ((a * -4.0) + (18.0 * (z * (x * y))))) / c));
	} else if (x <= -2.1e+47) {
		tmp = (t * ((((x * 18.0) * y) * z) + (a * -4.0))) + (-4.0 * (x * i));
	} else if (x <= 3.8e-47) {
		tmp = ((b * c) + (-4.0 * (t * a))) - t_1;
	} else if (x <= 4.7e+168) {
		tmp = ((b * c) - ((x * 4.0) * i)) - t_1;
	} else {
		tmp = x * ((i * -4.0) + (t * (z * (18.0 * 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) :: t_1
    real(8) :: tmp
    t_1 = (j * 27.0d0) * k
    if (x <= (-1.9d+191)) then
        tmp = c * (b + ((t * ((a * (-4.0d0)) + (18.0d0 * (z * (x * y))))) / c))
    else if (x <= (-2.1d+47)) then
        tmp = (t * ((((x * 18.0d0) * y) * z) + (a * (-4.0d0)))) + ((-4.0d0) * (x * i))
    else if (x <= 3.8d-47) then
        tmp = ((b * c) + ((-4.0d0) * (t * a))) - t_1
    else if (x <= 4.7d+168) then
        tmp = ((b * c) - ((x * 4.0d0) * i)) - t_1
    else
        tmp = x * ((i * (-4.0d0)) + (t * (z * (18.0d0 * 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 t_1 = (j * 27.0) * k;
	double tmp;
	if (x <= -1.9e+191) {
		tmp = c * (b + ((t * ((a * -4.0) + (18.0 * (z * (x * y))))) / c));
	} else if (x <= -2.1e+47) {
		tmp = (t * ((((x * 18.0) * y) * z) + (a * -4.0))) + (-4.0 * (x * i));
	} else if (x <= 3.8e-47) {
		tmp = ((b * c) + (-4.0 * (t * a))) - t_1;
	} else if (x <= 4.7e+168) {
		tmp = ((b * c) - ((x * 4.0) * i)) - t_1;
	} else {
		tmp = x * ((i * -4.0) + (t * (z * (18.0 * 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):
	t_1 = (j * 27.0) * k
	tmp = 0
	if x <= -1.9e+191:
		tmp = c * (b + ((t * ((a * -4.0) + (18.0 * (z * (x * y))))) / c))
	elif x <= -2.1e+47:
		tmp = (t * ((((x * 18.0) * y) * z) + (a * -4.0))) + (-4.0 * (x * i))
	elif x <= 3.8e-47:
		tmp = ((b * c) + (-4.0 * (t * a))) - t_1
	elif x <= 4.7e+168:
		tmp = ((b * c) - ((x * 4.0) * i)) - t_1
	else:
		tmp = x * ((i * -4.0) + (t * (z * (18.0 * 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)
	t_1 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (x <= -1.9e+191)
		tmp = Float64(c * Float64(b + Float64(Float64(t * Float64(Float64(a * -4.0) + Float64(18.0 * Float64(z * Float64(x * y))))) / c)));
	elseif (x <= -2.1e+47)
		tmp = Float64(Float64(t * Float64(Float64(Float64(Float64(x * 18.0) * y) * z) + Float64(a * -4.0))) + Float64(-4.0 * Float64(x * i)));
	elseif (x <= 3.8e-47)
		tmp = Float64(Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a))) - t_1);
	elseif (x <= 4.7e+168)
		tmp = Float64(Float64(Float64(b * c) - Float64(Float64(x * 4.0) * i)) - t_1);
	else
		tmp = Float64(x * Float64(Float64(i * -4.0) + Float64(t * Float64(z * Float64(18.0 * 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)
	t_1 = (j * 27.0) * k;
	tmp = 0.0;
	if (x <= -1.9e+191)
		tmp = c * (b + ((t * ((a * -4.0) + (18.0 * (z * (x * y))))) / c));
	elseif (x <= -2.1e+47)
		tmp = (t * ((((x * 18.0) * y) * z) + (a * -4.0))) + (-4.0 * (x * i));
	elseif (x <= 3.8e-47)
		tmp = ((b * c) + (-4.0 * (t * a))) - t_1;
	elseif (x <= 4.7e+168)
		tmp = ((b * c) - ((x * 4.0) * i)) - t_1;
	else
		tmp = x * ((i * -4.0) + (t * (z * (18.0 * 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_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[x, -1.9e+191], N[(c * N[(b + N[(N[(t * N[(N[(a * -4.0), $MachinePrecision] + N[(18.0 * N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.1e+47], N[(N[(t * N[(N[(N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.8e-47], N[(N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[x, 4.7e+168], N[(N[(N[(b * c), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(x * N[(N[(i * -4.0), $MachinePrecision] + N[(t * N[(z * N[(18.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -1.8999999999999999e191

   1. Initial program 51.1%

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

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 51.1%

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

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \color{blue}{\left(b \cdot c\right)}\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 68.0%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \mathsf{*.f64}\left(b, \color{blue}{c}\right)\right) \]

   7. Simplified 68.0%

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

   8. Taylor expanded in c around inf

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

   10. Simplified 79.0%

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

   if -1.8999999999999999e191 < x < -2.1e47

   1. Initial program 73.4%

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

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 73.4%

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

   5. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \color{blue}{\left(-4 \cdot \left(i \cdot x\right)\right)}\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \mathsf{*.f64}\left(-4, \color{blue}{\left(i \cdot x\right)}\right)\right) \]

      2. *-lowering-*.f64 63.9%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \mathsf{*.f64}\left(-4, \mathsf{*.f64}\left(i, \color{blue}{x}\right)\right)\right) \]

   7. Simplified 63.9%

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

   if -2.1e47 < x < 3.80000000000000015e-47

   1. Initial program 96.6%

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

   3. Taylor expanded in x around 0

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(b \cdot c - 4 \cdot \left(a \cdot t\right)\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   4. Step-by-step derivation

      1. cancel-sign-sub-inv N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(a \cdot t\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + -4 \cdot \left(a \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(b \cdot c\right), \left(-4 \cdot \left(a \cdot t\right)\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(-4 \cdot \left(a \cdot t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(-4, \left(a \cdot t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, \color{blue}{27}\right), k\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(-4, \left(t \cdot a\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      7. *-lowering-*.f64 83.9%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(-4, \mathsf{*.f64}\left(t, a\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

   5. Simplified 83.9%

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

   if 3.80000000000000015e-47 < x < 4.69999999999999961e168

   1. Initial program 79.8%

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

   3. Taylor expanded in t around 0

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\color{blue}{\left(b \cdot c\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 79.2%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

   5. Simplified 79.2%

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

   if 4.69999999999999961e168 < x

   1. Initial program 80.7%

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

      1. +-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

      2. associate-+r- N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\left(\left(b \cdot c + \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t\right) - \left(a \cdot 4\right) \cdot t\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t\right), \left(\left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(b \cdot c\right), \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t\right)\right), \left(\left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t\right)\right), \left(\left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      6. associate-*l* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot \left(z \cdot t\right)\right)\right), \left(\left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      7. associate-*l* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\left(x \cdot 18\right) \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\right), \left(\left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\left(x \cdot 18\right), \left(y \cdot \left(z \cdot t\right)\right)\right)\right), \left(\left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), \left(y \cdot \left(z \cdot t\right)\right)\right)\right), \left(\left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), \mathsf{*.f64}\left(y, \left(z \cdot t\right)\right)\right)\right), \left(\left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), \mathsf{*.f64}\left(y, \left(t \cdot z\right)\right)\right)\right), \left(\left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, z\right)\right)\right)\right), \left(\left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      13. associate-*l* N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, z\right)\right)\right)\right), \left(a \cdot \left(4 \cdot t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, z\right)\right)\right)\right), \mathsf{*.f64}\left(a, \left(4 \cdot t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      15. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, z\right)\right)\right)\right), \mathsf{*.f64}\left(a, \left(t \cdot 4\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      16. *-lowering-*.f64 88.8%

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, z\right)\right)\right)\right), \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(t, 4\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

   4. Applied egg-rr 88.8%

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

   5. Taylor expanded in y around inf

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\color{blue}{\left(y \cdot \left(18 \cdot \left(t \cdot \left(x \cdot z\right)\right) + \frac{b \cdot c}{y}\right)\right)}, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(t, 4\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \left(18 \cdot \left(t \cdot \left(x \cdot z\right)\right) + \frac{b \cdot c}{y}\right)\right), \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(t, 4\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\left(18 \cdot \left(t \cdot \left(x \cdot z\right)\right)\right), \left(\frac{b \cdot c}{y}\right)\right)\right), \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(t, 4\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\left(\left(18 \cdot t\right) \cdot \left(x \cdot z\right)\right), \left(\frac{b \cdot c}{y}\right)\right)\right), \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(t, 4\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(18 \cdot t\right), \left(x \cdot z\right)\right), \left(\frac{b \cdot c}{y}\right)\right)\right), \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(t, 4\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(18, t\right), \left(x \cdot z\right)\right), \left(\frac{b \cdot c}{y}\right)\right)\right), \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(t, 4\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(18, t\right), \mathsf{*.f64}\left(x, z\right)\right), \left(\frac{b \cdot c}{y}\right)\right)\right), \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(t, 4\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      7. associate-/l* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(18, t\right), \mathsf{*.f64}\left(x, z\right)\right), \left(b \cdot \frac{c}{y}\right)\right)\right), \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(t, 4\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(18, t\right), \mathsf{*.f64}\left(x, z\right)\right), \mathsf{*.f64}\left(b, \left(\frac{c}{y}\right)\right)\right)\right), \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(t, 4\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      9. /-lowering-/.f64 72.5%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(18, t\right), \mathsf{*.f64}\left(x, z\right)\right), \mathsf{*.f64}\left(b, \mathsf{/.f64}\left(c, y\right)\right)\right)\right), \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(t, 4\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

   7. Simplified 72.5%

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

   8. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)}\right) \]

      2. cancel-sign-sub-inv N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \color{blue}{\left(\mathsf{neg}\left(4\right)\right) \cdot i}\right)\right) \]

      3. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + -4 \cdot i\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right), \color{blue}{\left(-4 \cdot i\right)}\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(t \cdot \left(y \cdot z\right)\right) \cdot 18\right), \left(\color{blue}{-4} \cdot i\right)\right)\right) \]

      6. associate-*l* N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(t \cdot \left(\left(y \cdot z\right) \cdot 18\right)\right), \left(\color{blue}{-4} \cdot i\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(t \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right), \left(-4 \cdot i\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(18 \cdot \left(y \cdot z\right)\right)\right), \left(\color{blue}{-4} \cdot i\right)\right)\right) \]

      9. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(18 \cdot y\right) \cdot z\right)\right), \left(-4 \cdot i\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(z \cdot \left(18 \cdot y\right)\right)\right), \left(-4 \cdot i\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(z, \left(18 \cdot y\right)\right)\right), \left(-4 \cdot i\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(18, y\right)\right)\right), \left(-4 \cdot i\right)\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(18, y\right)\right)\right), \left(i \cdot \color{blue}{-4}\right)\right)\right) \]

      14. *-lowering-*.f64 91.8%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(18, y\right)\right)\right), \mathsf{*.f64}\left(i, \color{blue}{-4}\right)\right)\right) \]

   10. Simplified 91.8%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{+191}:\\ \;\;\;\;c \cdot \left(b + \frac{t \cdot \left(a \cdot -4 + 18 \cdot \left(z \cdot \left(x \cdot y\right)\right)\right)}{c}\right)\\ \mathbf{elif}\;x \leq -2.1 \cdot 10^{+47}:\\ \;\;\;\;t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right) + -4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{-47}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;x \leq 4.7 \cdot 10^{+168}:\\ \;\;\;\;\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(i \cdot -4 + t \cdot \left(z \cdot \left(18 \cdot y\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 81.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := t \cdot \left(a \cdot -4 + x \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right) - \left(\left(x \cdot 4\right) \cdot i + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{if}\;t \leq -2.8 \cdot 10^{-93}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.26 \cdot 10^{-84}:\\ \;\;\;\;\left(b \cdot c + x \cdot \left(i \cdot -4 + 18 \cdot \left(z \cdot \left(y \cdot t\right)\right)\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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) (* x (* 18.0 (* y z)))))
          (+ (* (* x 4.0) i) (* j (* 27.0 k))))))
   (if (<= t -2.8e-93)
     t_1
     (if (<= t 1.26e-84)
       (-
        (+ (* b c) (* x (+ (* i -4.0) (* 18.0 (* z (* y t))))))
        (* (* j 27.0) 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) + (x * (18.0 * (y * z))))) - (((x * 4.0) * i) + (j * (27.0 * k)));
	double tmp;
	if (t <= -2.8e-93) {
		tmp = t_1;
	} else if (t <= 1.26e-84) {
		tmp = ((b * c) + (x * ((i * -4.0) + (18.0 * (z * (y * t)))))) - ((j * 27.0) * 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)) + (x * (18.0d0 * (y * z))))) - (((x * 4.0d0) * i) + (j * (27.0d0 * k)))
    if (t <= (-2.8d-93)) then
        tmp = t_1
    else if (t <= 1.26d-84) then
        tmp = ((b * c) + (x * ((i * (-4.0d0)) + (18.0d0 * (z * (y * t)))))) - ((j * 27.0d0) * 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) + (x * (18.0 * (y * z))))) - (((x * 4.0) * i) + (j * (27.0 * k)));
	double tmp;
	if (t <= -2.8e-93) {
		tmp = t_1;
	} else if (t <= 1.26e-84) {
		tmp = ((b * c) + (x * ((i * -4.0) + (18.0 * (z * (y * t)))))) - ((j * 27.0) * 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) + (x * (18.0 * (y * z))))) - (((x * 4.0) * i) + (j * (27.0 * k)))
	tmp = 0
	if t <= -2.8e-93:
		tmp = t_1
	elif t <= 1.26e-84:
		tmp = ((b * c) + (x * ((i * -4.0) + (18.0 * (z * (y * t)))))) - ((j * 27.0) * 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(Float64(t * Float64(Float64(a * -4.0) + Float64(x * Float64(18.0 * Float64(y * z))))) - Float64(Float64(Float64(x * 4.0) * i) + Float64(j * Float64(27.0 * k))))
	tmp = 0.0
	if (t <= -2.8e-93)
		tmp = t_1;
	elseif (t <= 1.26e-84)
		tmp = Float64(Float64(Float64(b * c) + Float64(x * Float64(Float64(i * -4.0) + Float64(18.0 * Float64(z * Float64(y * t)))))) - Float64(Float64(j * 27.0) * 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) + (x * (18.0 * (y * z))))) - (((x * 4.0) * i) + (j * (27.0 * k)));
	tmp = 0.0;
	if (t <= -2.8e-93)
		tmp = t_1;
	elseif (t <= 1.26e-84)
		tmp = ((b * c) + (x * ((i * -4.0) + (18.0 * (z * (y * t)))))) - ((j * 27.0) * 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[(N[(t * N[(N[(a * -4.0), $MachinePrecision] + N[(x * N[(18.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision] + N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.8e-93], t$95$1, If[LessEqual[t, 1.26e-84], N[(N[(N[(b * c), $MachinePrecision] + N[(x * N[(N[(i * -4.0), $MachinePrecision] + N[(18.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -2.79999999999999998e-93 or 1.26e-84 < t

   1. Initial program 85.9%

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

   3. Taylor expanded in b around 0

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

      1. associate--r+ N/A

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

      2. cancel-sign-sub-inv N/A

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

      5. associate--l+ N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. associate--l+ N/A

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

   5. Simplified 81.3%

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

   if -2.79999999999999998e-93 < t < 1.26e-84

   1. Initial program 83.1%

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

   3. Taylor expanded in a around 0

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(i \cdot x\right)\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   4. Step-by-step derivation

      1. cancel-sign-sub-inv N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(i \cdot x\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + -4 \cdot \left(i \cdot x\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\left(b \cdot c + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) + -4 \cdot \left(i \cdot x\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

      4. associate-+l+ N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + -4 \cdot \left(i \cdot x\right)\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(18 \cdot t\right) \cdot \left(x \cdot \left(y \cdot z\right)\right) + -4 \cdot \left(i \cdot x\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(18 \cdot t\right) \cdot \left(\left(y \cdot z\right) \cdot x\right) + -4 \cdot \left(i \cdot x\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      7. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(\left(18 \cdot t\right) \cdot \left(y \cdot z\right)\right) \cdot x + -4 \cdot \left(i \cdot x\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      8. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right) \cdot x + -4 \cdot \left(i \cdot x\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      9. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right) \cdot x + \left(-4 \cdot i\right) \cdot x\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      10. distribute-rgt-in N/A

          \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + -4 \cdot i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, \color{blue}{27}\right), k\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      12. cancel-sign-sub-inv N/A

          \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      13. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(b \cdot c\right), \left(x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

   5. Simplified 91.7%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{-93}:\\ \;\;\;\;t \cdot \left(a \cdot -4 + x \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right) - \left(\left(x \cdot 4\right) \cdot i + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{elif}\;t \leq 1.26 \cdot 10^{-84}:\\ \;\;\;\;\left(b \cdot c + x \cdot \left(i \cdot -4 + 18 \cdot \left(z \cdot \left(y \cdot t\right)\right)\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot -4 + x \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right) - \left(\left(x \cdot 4\right) \cdot i + j \cdot \left(27 \cdot k\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 88.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq 2.9 \cdot 10^{+34}:\\ \;\;\;\;t \cdot \left(a \cdot -4 + y \cdot \left(\left(x \cdot 18\right) \cdot z\right)\right) + \left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + x \cdot \left(i \cdot -4 + y \cdot \left(z \cdot \left(18 \cdot t\right)\right)\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \end{array} \]

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 (<= x 2.9e+34)
   (+
    (* t (+ (* a -4.0) (* y (* (* x 18.0) z))))
    (+ (* -27.0 (* j k)) (+ (* b c) (* x (* i -4.0)))))
   (-
    (+ (* b c) (* x (+ (* i -4.0) (* y (* z (* 18.0 t))))))
    (* (* 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 (x <= 2.9e+34) {
		tmp = (t * ((a * -4.0) + (y * ((x * 18.0) * z)))) + ((-27.0 * (j * k)) + ((b * c) + (x * (i * -4.0))));
	} else {
		tmp = ((b * c) + (x * ((i * -4.0) + (y * (z * (18.0 * t)))))) - ((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 (x <= 2.9d+34) then
        tmp = (t * ((a * (-4.0d0)) + (y * ((x * 18.0d0) * z)))) + (((-27.0d0) * (j * k)) + ((b * c) + (x * (i * (-4.0d0)))))
    else
        tmp = ((b * c) + (x * ((i * (-4.0d0)) + (y * (z * (18.0d0 * t)))))) - ((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 (x <= 2.9e+34) {
		tmp = (t * ((a * -4.0) + (y * ((x * 18.0) * z)))) + ((-27.0 * (j * k)) + ((b * c) + (x * (i * -4.0))));
	} else {
		tmp = ((b * c) + (x * ((i * -4.0) + (y * (z * (18.0 * t)))))) - ((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 x <= 2.9e+34:
		tmp = (t * ((a * -4.0) + (y * ((x * 18.0) * z)))) + ((-27.0 * (j * k)) + ((b * c) + (x * (i * -4.0))))
	else:
		tmp = ((b * c) + (x * ((i * -4.0) + (y * (z * (18.0 * t)))))) - ((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 (x <= 2.9e+34)
		tmp = Float64(Float64(t * Float64(Float64(a * -4.0) + Float64(y * Float64(Float64(x * 18.0) * z)))) + Float64(Float64(-27.0 * Float64(j * k)) + Float64(Float64(b * c) + Float64(x * Float64(i * -4.0)))));
	else
		tmp = Float64(Float64(Float64(b * c) + Float64(x * Float64(Float64(i * -4.0) + Float64(y * Float64(z * Float64(18.0 * t)))))) - 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 (x <= 2.9e+34)
		tmp = (t * ((a * -4.0) + (y * ((x * 18.0) * z)))) + ((-27.0 * (j * k)) + ((b * c) + (x * (i * -4.0))));
	else
		tmp = ((b * c) + (x * ((i * -4.0) + (y * (z * (18.0 * t)))))) - ((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[x, 2.9e+34], N[(N[(t * N[(N[(a * -4.0), $MachinePrecision] + N[(y * N[(N[(x * 18.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision] + N[(N[(b * c), $MachinePrecision] + N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] + N[(x * N[(N[(i * -4.0), $MachinePrecision] + N[(y * N[(z * N[(18.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 2.9000000000000001e34

   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. Step-by-step derivation

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 87.6%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(z \cdot \left(\left(x \cdot 18\right) \cdot y\right)\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(\color{blue}{j}, k\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

      2. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(z \cdot \left(x \cdot 18\right)\right) \cdot y\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(\color{blue}{j}, k\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(z \cdot \left(x \cdot 18\right)\right), y\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(\color{blue}{j}, k\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(z, \left(x \cdot 18\right)\right), y\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, k\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 88.5%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(x, 18\right)\right), y\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, k\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

   6. Applied egg-rr 88.5%

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

   if 2.9000000000000001e34 < x

   1. Initial program 75.3%

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

      1. +-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

      2. associate-+r- N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\left(\left(b \cdot c + \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t\right) - \left(a \cdot 4\right) \cdot t\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t\right), \left(\left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(b \cdot c\right), \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t\right)\right), \left(\left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t\right)\right), \left(\left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      6. associate-*l* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot \left(z \cdot t\right)\right)\right), \left(\left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      7. associate-*l* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\left(x \cdot 18\right) \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\right), \left(\left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\left(x \cdot 18\right), \left(y \cdot \left(z \cdot t\right)\right)\right)\right), \left(\left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), \left(y \cdot \left(z \cdot t\right)\right)\right)\right), \left(\left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), \mathsf{*.f64}\left(y, \left(z \cdot t\right)\right)\right)\right), \left(\left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), \mathsf{*.f64}\left(y, \left(t \cdot z\right)\right)\right)\right), \left(\left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, z\right)\right)\right)\right), \left(\left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      13. associate-*l* N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, z\right)\right)\right)\right), \left(a \cdot \left(4 \cdot t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, z\right)\right)\right)\right), \mathsf{*.f64}\left(a, \left(4 \cdot t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      15. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, z\right)\right)\right)\right), \mathsf{*.f64}\left(a, \left(t \cdot 4\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      16. *-lowering-*.f64 87.4%

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, z\right)\right)\right)\right), \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(t, 4\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

   4. Applied egg-rr 87.4%

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

   5. Taylor expanded in a around 0

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(i \cdot x\right)\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   6. Step-by-step derivation

      1. cancel-sign-sub-inv N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(i \cdot x\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + -4 \cdot \left(i \cdot x\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\left(b \cdot c + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) + -4 \cdot \left(i \cdot x\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

      4. associate-+l+ N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + -4 \cdot \left(i \cdot x\right)\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(18 \cdot t\right) \cdot \left(x \cdot \left(y \cdot z\right)\right) + -4 \cdot \left(i \cdot x\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(18 \cdot t\right) \cdot \left(\left(y \cdot z\right) \cdot x\right) + -4 \cdot \left(i \cdot x\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      7. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(\left(18 \cdot t\right) \cdot \left(y \cdot z\right)\right) \cdot x + -4 \cdot \left(i \cdot x\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      8. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right) \cdot x + -4 \cdot \left(i \cdot x\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      9. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right) \cdot x + \left(-4 \cdot i\right) \cdot x\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      10. distribute-rgt-in N/A

          \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + -4 \cdot i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, \color{blue}{27}\right), k\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      12. cancel-sign-sub-inv N/A

          \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      13. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(b \cdot c\right), \left(x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

   7. Simplified 92.2%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 2.9 \cdot 10^{+34}:\\ \;\;\;\;t \cdot \left(a \cdot -4 + y \cdot \left(\left(x \cdot 18\right) \cdot z\right)\right) + \left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + x \cdot \left(i \cdot -4 + y \cdot \left(z \cdot \left(18 \cdot t\right)\right)\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 58.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ t_2 := x \cdot \left(i \cdot -4 + t \cdot \left(z \cdot \left(18 \cdot y\right)\right)\right)\\ \mathbf{if}\;x \leq -1.6 \cdot 10^{+47}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{-215}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right) - t\_1\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{-136}:\\ \;\;\;\;b \cdot c + t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-20}:\\ \;\;\;\;b \cdot c - t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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 27.0) k))
        (t_2 (* x (+ (* i -4.0) (* t (* z (* 18.0 y)))))))
   (if (<= x -1.6e+47)
     t_2
     (if (<= x -1.3e-215)
       (- (* -4.0 (* t a)) t_1)
       (if (<= x 6.2e-136)
         (+ (* b c) (* t (* a -4.0)))
         (if (<= x 4.2e-20) (- (* b c) 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 * 27.0) * k;
	double t_2 = x * ((i * -4.0) + (t * (z * (18.0 * y))));
	double tmp;
	if (x <= -1.6e+47) {
		tmp = t_2;
	} else if (x <= -1.3e-215) {
		tmp = (-4.0 * (t * a)) - t_1;
	} else if (x <= 6.2e-136) {
		tmp = (b * c) + (t * (a * -4.0));
	} else if (x <= 4.2e-20) {
		tmp = (b * c) - 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 * 27.0d0) * k
    t_2 = x * ((i * (-4.0d0)) + (t * (z * (18.0d0 * y))))
    if (x <= (-1.6d+47)) then
        tmp = t_2
    else if (x <= (-1.3d-215)) then
        tmp = ((-4.0d0) * (t * a)) - t_1
    else if (x <= 6.2d-136) then
        tmp = (b * c) + (t * (a * (-4.0d0)))
    else if (x <= 4.2d-20) then
        tmp = (b * c) - 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 * 27.0) * k;
	double t_2 = x * ((i * -4.0) + (t * (z * (18.0 * y))));
	double tmp;
	if (x <= -1.6e+47) {
		tmp = t_2;
	} else if (x <= -1.3e-215) {
		tmp = (-4.0 * (t * a)) - t_1;
	} else if (x <= 6.2e-136) {
		tmp = (b * c) + (t * (a * -4.0));
	} else if (x <= 4.2e-20) {
		tmp = (b * c) - 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 * 27.0) * k
	t_2 = x * ((i * -4.0) + (t * (z * (18.0 * y))))
	tmp = 0
	if x <= -1.6e+47:
		tmp = t_2
	elif x <= -1.3e-215:
		tmp = (-4.0 * (t * a)) - t_1
	elif x <= 6.2e-136:
		tmp = (b * c) + (t * (a * -4.0))
	elif x <= 4.2e-20:
		tmp = (b * c) - 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 * 27.0) * k)
	t_2 = Float64(x * Float64(Float64(i * -4.0) + Float64(t * Float64(z * Float64(18.0 * y)))))
	tmp = 0.0
	if (x <= -1.6e+47)
		tmp = t_2;
	elseif (x <= -1.3e-215)
		tmp = Float64(Float64(-4.0 * Float64(t * a)) - t_1);
	elseif (x <= 6.2e-136)
		tmp = Float64(Float64(b * c) + Float64(t * Float64(a * -4.0)));
	elseif (x <= 4.2e-20)
		tmp = Float64(Float64(b * c) - 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 * 27.0) * k;
	t_2 = x * ((i * -4.0) + (t * (z * (18.0 * y))));
	tmp = 0.0;
	if (x <= -1.6e+47)
		tmp = t_2;
	elseif (x <= -1.3e-215)
		tmp = (-4.0 * (t * a)) - t_1;
	elseif (x <= 6.2e-136)
		tmp = (b * c) + (t * (a * -4.0));
	elseif (x <= 4.2e-20)
		tmp = (b * c) - 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 * 27.0), $MachinePrecision] * k), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(i * -4.0), $MachinePrecision] + N[(t * N[(z * N[(18.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.6e+47], t$95$2, If[LessEqual[x, -1.3e-215], N[(N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[x, 6.2e-136], N[(N[(b * c), $MachinePrecision] + N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.2e-20], N[(N[(b * c), $MachinePrecision] - t$95$1), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.6e47 or 4.1999999999999998e-20 < x

   1. Initial program 73.1%

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

      1. +-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

      2. associate-+r- N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\left(\left(b \cdot c + \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t\right) - \left(a \cdot 4\right) \cdot t\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t\right), \left(\left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(b \cdot c\right), \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t\right)\right), \left(\left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t\right)\right), \left(\left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      6. associate-*l* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot \left(z \cdot t\right)\right)\right), \left(\left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      7. associate-*l* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\left(x \cdot 18\right) \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\right), \left(\left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\left(x \cdot 18\right), \left(y \cdot \left(z \cdot t\right)\right)\right)\right), \left(\left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), \left(y \cdot \left(z \cdot t\right)\right)\right)\right), \left(\left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), \mathsf{*.f64}\left(y, \left(z \cdot t\right)\right)\right)\right), \left(\left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), \mathsf{*.f64}\left(y, \left(t \cdot z\right)\right)\right)\right), \left(\left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, z\right)\right)\right)\right), \left(\left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      13. associate-*l* N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, z\right)\right)\right)\right), \left(a \cdot \left(4 \cdot t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, z\right)\right)\right)\right), \mathsf{*.f64}\left(a, \left(4 \cdot t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      15. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, z\right)\right)\right)\right), \mathsf{*.f64}\left(a, \left(t \cdot 4\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      16. *-lowering-*.f64 83.5%

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, z\right)\right)\right)\right), \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(t, 4\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

   4. Applied egg-rr 83.5%

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

   5. Taylor expanded in y around inf

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\color{blue}{\left(y \cdot \left(18 \cdot \left(t \cdot \left(x \cdot z\right)\right) + \frac{b \cdot c}{y}\right)\right)}, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(t, 4\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \left(18 \cdot \left(t \cdot \left(x \cdot z\right)\right) + \frac{b \cdot c}{y}\right)\right), \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(t, 4\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\left(18 \cdot \left(t \cdot \left(x \cdot z\right)\right)\right), \left(\frac{b \cdot c}{y}\right)\right)\right), \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(t, 4\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\left(\left(18 \cdot t\right) \cdot \left(x \cdot z\right)\right), \left(\frac{b \cdot c}{y}\right)\right)\right), \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(t, 4\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(18 \cdot t\right), \left(x \cdot z\right)\right), \left(\frac{b \cdot c}{y}\right)\right)\right), \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(t, 4\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(18, t\right), \left(x \cdot z\right)\right), \left(\frac{b \cdot c}{y}\right)\right)\right), \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(t, 4\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(18, t\right), \mathsf{*.f64}\left(x, z\right)\right), \left(\frac{b \cdot c}{y}\right)\right)\right), \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(t, 4\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      7. associate-/l* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(18, t\right), \mathsf{*.f64}\left(x, z\right)\right), \left(b \cdot \frac{c}{y}\right)\right)\right), \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(t, 4\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(18, t\right), \mathsf{*.f64}\left(x, z\right)\right), \mathsf{*.f64}\left(b, \left(\frac{c}{y}\right)\right)\right)\right), \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(t, 4\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      9. /-lowering-/.f64 70.6%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(18, t\right), \mathsf{*.f64}\left(x, z\right)\right), \mathsf{*.f64}\left(b, \mathsf{/.f64}\left(c, y\right)\right)\right)\right), \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(t, 4\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

   7. Simplified 70.6%

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

   8. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)}\right) \]

      2. cancel-sign-sub-inv N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \color{blue}{\left(\mathsf{neg}\left(4\right)\right) \cdot i}\right)\right) \]

      3. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + -4 \cdot i\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right), \color{blue}{\left(-4 \cdot i\right)}\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(t \cdot \left(y \cdot z\right)\right) \cdot 18\right), \left(\color{blue}{-4} \cdot i\right)\right)\right) \]

      6. associate-*l* N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(t \cdot \left(\left(y \cdot z\right) \cdot 18\right)\right), \left(\color{blue}{-4} \cdot i\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(t \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right), \left(-4 \cdot i\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(18 \cdot \left(y \cdot z\right)\right)\right), \left(\color{blue}{-4} \cdot i\right)\right)\right) \]

      9. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(18 \cdot y\right) \cdot z\right)\right), \left(-4 \cdot i\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(z \cdot \left(18 \cdot y\right)\right)\right), \left(-4 \cdot i\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(z, \left(18 \cdot y\right)\right)\right), \left(-4 \cdot i\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(18, y\right)\right)\right), \left(-4 \cdot i\right)\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(18, y\right)\right)\right), \left(i \cdot \color{blue}{-4}\right)\right)\right) \]

      14. *-lowering-*.f64 67.0%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(18, y\right)\right)\right), \mathsf{*.f64}\left(i, \color{blue}{-4}\right)\right)\right) \]

   10. Simplified 67.0%

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

   if -1.6e47 < x < -1.3e-215

   1. Initial program 97.8%

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

   3. Taylor expanded in a around inf

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(-4 \cdot \left(a \cdot t\right)\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(-4, \left(a \cdot t\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(-4, \left(t \cdot a\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, \color{blue}{27}\right), k\right)\right) \]

      3. *-lowering-*.f64 60.9%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(-4, \mathsf{*.f64}\left(t, a\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, \color{blue}{27}\right), k\right)\right) \]

   5. Simplified 60.9%

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

   if -1.3e-215 < x < 6.2e-136

   1. Initial program 96.0%

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

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 94.1%

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

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \color{blue}{\left(b \cdot c\right)}\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 70.2%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \mathsf{*.f64}\left(b, \color{blue}{c}\right)\right) \]

   7. Simplified 70.2%

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

   8. Taylor expanded in x around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \color{blue}{\left(-4 \cdot a\right)}\right), \mathsf{*.f64}\left(b, c\right)\right) \]
   9. Step-by-step derivation

      1. *-lowering-*.f64 69.9%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(-4, a\right)\right), \mathsf{*.f64}\left(b, c\right)\right) \]

   10. Simplified 69.9%

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

   if 6.2e-136 < x < 4.1999999999999998e-20

   1. Initial program 96.2%

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

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(b \cdot c\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 74.9%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

   5. Simplified 74.9%

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

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{+47}:\\ \;\;\;\;x \cdot \left(i \cdot -4 + t \cdot \left(z \cdot \left(18 \cdot y\right)\right)\right)\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{-215}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{-136}:\\ \;\;\;\;b \cdot c + t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-20}:\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(i \cdot -4 + t \cdot \left(z \cdot \left(18 \cdot y\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 49.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := x \cdot \left(i \cdot -4\right)\\ t_2 := t \cdot \left(a \cdot -4 + x \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{if}\;x \leq -4.2 \cdot 10^{+253}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -1.1 \cdot 10^{+88}:\\ \;\;\;\;b \cdot c + t\_1\\ \mathbf{elif}\;x \leq -3.1 \cdot 10^{-159}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-27}:\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;t\_1 - j \cdot \left(27 \cdot k\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* x (* i -4.0)))
        (t_2 (* t (+ (* a -4.0) (* x (* 18.0 (* y z)))))))
   (if (<= x -4.2e+253)
     t_2
     (if (<= x -1.1e+88)
       (+ (* b c) t_1)
       (if (<= x -3.1e-159)
         t_2
         (if (<= x 5.8e-27)
           (- (* b c) (* (* j 27.0) k))
           (- t_1 (* 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 t_1 = x * (i * -4.0);
	double t_2 = t * ((a * -4.0) + (x * (18.0 * (y * z))));
	double tmp;
	if (x <= -4.2e+253) {
		tmp = t_2;
	} else if (x <= -1.1e+88) {
		tmp = (b * c) + t_1;
	} else if (x <= -3.1e-159) {
		tmp = t_2;
	} else if (x <= 5.8e-27) {
		tmp = (b * c) - ((j * 27.0) * k);
	} else {
		tmp = t_1 - (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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (i * (-4.0d0))
    t_2 = t * ((a * (-4.0d0)) + (x * (18.0d0 * (y * z))))
    if (x <= (-4.2d+253)) then
        tmp = t_2
    else if (x <= (-1.1d+88)) then
        tmp = (b * c) + t_1
    else if (x <= (-3.1d-159)) then
        tmp = t_2
    else if (x <= 5.8d-27) then
        tmp = (b * c) - ((j * 27.0d0) * k)
    else
        tmp = t_1 - (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 t_1 = x * (i * -4.0);
	double t_2 = t * ((a * -4.0) + (x * (18.0 * (y * z))));
	double tmp;
	if (x <= -4.2e+253) {
		tmp = t_2;
	} else if (x <= -1.1e+88) {
		tmp = (b * c) + t_1;
	} else if (x <= -3.1e-159) {
		tmp = t_2;
	} else if (x <= 5.8e-27) {
		tmp = (b * c) - ((j * 27.0) * k);
	} else {
		tmp = t_1 - (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):
	t_1 = x * (i * -4.0)
	t_2 = t * ((a * -4.0) + (x * (18.0 * (y * z))))
	tmp = 0
	if x <= -4.2e+253:
		tmp = t_2
	elif x <= -1.1e+88:
		tmp = (b * c) + t_1
	elif x <= -3.1e-159:
		tmp = t_2
	elif x <= 5.8e-27:
		tmp = (b * c) - ((j * 27.0) * k)
	else:
		tmp = t_1 - (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)
	t_1 = Float64(x * Float64(i * -4.0))
	t_2 = Float64(t * Float64(Float64(a * -4.0) + Float64(x * Float64(18.0 * Float64(y * z)))))
	tmp = 0.0
	if (x <= -4.2e+253)
		tmp = t_2;
	elseif (x <= -1.1e+88)
		tmp = Float64(Float64(b * c) + t_1);
	elseif (x <= -3.1e-159)
		tmp = t_2;
	elseif (x <= 5.8e-27)
		tmp = Float64(Float64(b * c) - Float64(Float64(j * 27.0) * k));
	else
		tmp = Float64(t_1 - Float64(j * Float64(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)
	t_1 = x * (i * -4.0);
	t_2 = t * ((a * -4.0) + (x * (18.0 * (y * z))));
	tmp = 0.0;
	if (x <= -4.2e+253)
		tmp = t_2;
	elseif (x <= -1.1e+88)
		tmp = (b * c) + t_1;
	elseif (x <= -3.1e-159)
		tmp = t_2;
	elseif (x <= 5.8e-27)
		tmp = (b * c) - ((j * 27.0) * k);
	else
		tmp = t_1 - (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_] := Block[{t$95$1 = N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(a * -4.0), $MachinePrecision] + N[(x * N[(18.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.2e+253], t$95$2, If[LessEqual[x, -1.1e+88], N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[x, -3.1e-159], t$95$2, If[LessEqual[x, 5.8e-27], N[(N[(b * c), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], N[(t$95$1 - N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -4.2000000000000003e253 or -1.10000000000000004e88 < x < -3.1e-159

   1. Initial program 86.3%

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

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 86.3%

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

   5. Taylor expanded in t around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(-4 \cdot a\right), \color{blue}{\left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \left(\color{blue}{18} \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \left(\left(x \cdot \left(y \cdot z\right)\right) \cdot \color{blue}{18}\right)\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \left(x \cdot \color{blue}{\left(\left(y \cdot z\right) \cdot 18\right)}\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \left(x \cdot \left(18 \cdot \color{blue}{\left(y \cdot z\right)}\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \mathsf{*.f64}\left(x, \color{blue}{\left(18 \cdot \left(y \cdot z\right)\right)}\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(18, \color{blue}{\left(y \cdot z\right)}\right)\right)\right)\right) \]

      9. *-lowering-*.f64 63.6%

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(y, \color{blue}{z}\right)\right)\right)\right)\right) \]

   7. Simplified 63.6%

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

   if -4.2000000000000003e253 < x < -1.10000000000000004e88

   1. Initial program 65.4%

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

   3. Taylor expanded in t around 0

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\color{blue}{\left(b \cdot c\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 56.6%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

   5. Simplified 56.6%

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

   6. Taylor expanded in j around 0

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

      1. cancel-sign-sub-inv N/A

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

      2. metadata-eval N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(b \cdot c\right), \color{blue}{\left(-4 \cdot \left(i \cdot x\right)\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\color{blue}{-4} \cdot \left(i \cdot x\right)\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\left(-4 \cdot i\right) \cdot \color{blue}{x}\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(x \cdot \color{blue}{\left(-4 \cdot i\right)}\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \color{blue}{\left(-4 \cdot i\right)}\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \left(i \cdot \color{blue}{-4}\right)\right)\right) \]

      9. *-lowering-*.f64 55.0%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, \color{blue}{-4}\right)\right)\right) \]

   8. Simplified 55.0%

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

   if -3.1e-159 < x < 5.80000000000000008e-27

   1. Initial program 96.6%

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

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(b \cdot c\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 64.7%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

   5. Simplified 64.7%

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

   if 5.80000000000000008e-27 < x

   1. Initial program 78.3%

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

   3. Taylor expanded in i around inf

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(-4 \cdot \left(i \cdot x\right)\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(-4, \left(i \cdot x\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

      2. *-lowering-*.f64 65.7%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(-4, \mathsf{*.f64}\left(i, x\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, \color{blue}{27}\right), k\right)\right) \]

   5. Simplified 65.7%

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(x \cdot \left(i \cdot -4\right)\right), \color{blue}{\left(\left(j \cdot 27\right) \cdot k\right)}\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \left(i \cdot -4\right)\right), \left(\color{blue}{\left(j \cdot 27\right)} \cdot k\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \left(-4 \cdot i\right)\right), \left(\left(j \cdot \color{blue}{27}\right) \cdot k\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(-4, i\right)\right), \left(\left(j \cdot \color{blue}{27}\right) \cdot k\right)\right) \]

      8. associate-*l* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(-4, i\right)\right), \left(j \cdot \color{blue}{\left(27 \cdot k\right)}\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(-4, i\right)\right), \mathsf{*.f64}\left(j, \color{blue}{\left(27 \cdot k\right)}\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(-4, i\right)\right), \mathsf{*.f64}\left(j, \left(k \cdot \color{blue}{27}\right)\right)\right) \]

      11. *-lowering-*.f64 65.7%

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(-4, i\right)\right), \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(k, \color{blue}{27}\right)\right)\right) \]

   7. Applied egg-rr 65.7%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{+253}:\\ \;\;\;\;t \cdot \left(a \cdot -4 + x \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;x \leq -1.1 \cdot 10^{+88}:\\ \;\;\;\;b \cdot c + x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;x \leq -3.1 \cdot 10^{-159}:\\ \;\;\;\;t \cdot \left(a \cdot -4 + x \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-27}:\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right) - j \cdot \left(27 \cdot k\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 72.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ t_2 := x \cdot \left(i \cdot -4 + t \cdot \left(z \cdot \left(18 \cdot y\right)\right)\right)\\ \mathbf{if}\;x \leq -4.8 \cdot 10^{+46}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{-47}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - t\_1\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+168}:\\ \;\;\;\;\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k))
        (t_2 (* x (+ (* i -4.0) (* t (* z (* 18.0 y)))))))
   (if (<= x -4.8e+46)
     t_2
     (if (<= x 3.7e-47)
       (- (+ (* b c) (* -4.0 (* t a))) t_1)
       (if (<= x 3.2e+168) (- (- (* b c) (* (* x 4.0) i)) t_1) t_2)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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 * 27.0) * k;
	double t_2 = x * ((i * -4.0) + (t * (z * (18.0 * y))));
	double tmp;
	if (x <= -4.8e+46) {
		tmp = t_2;
	} else if (x <= 3.7e-47) {
		tmp = ((b * c) + (-4.0 * (t * a))) - t_1;
	} else if (x <= 3.2e+168) {
		tmp = ((b * c) - ((x * 4.0) * i)) - t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 * 27.0d0) * k
    t_2 = x * ((i * (-4.0d0)) + (t * (z * (18.0d0 * y))))
    if (x <= (-4.8d+46)) then
        tmp = t_2
    else if (x <= 3.7d-47) then
        tmp = ((b * c) + ((-4.0d0) * (t * a))) - t_1
    else if (x <= 3.2d+168) then
        tmp = ((b * c) - ((x * 4.0d0) * i)) - t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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 * 27.0) * k;
	double t_2 = x * ((i * -4.0) + (t * (z * (18.0 * y))));
	double tmp;
	if (x <= -4.8e+46) {
		tmp = t_2;
	} else if (x <= 3.7e-47) {
		tmp = ((b * c) + (-4.0 * (t * a))) - t_1;
	} else if (x <= 3.2e+168) {
		tmp = ((b * c) - ((x * 4.0) * i)) - t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	t_2 = x * ((i * -4.0) + (t * (z * (18.0 * y))))
	tmp = 0
	if x <= -4.8e+46:
		tmp = t_2
	elif x <= 3.7e-47:
		tmp = ((b * c) + (-4.0 * (t * a))) - t_1
	elif x <= 3.2e+168:
		tmp = ((b * c) - ((x * 4.0) * i)) - t_1
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	t_2 = Float64(x * Float64(Float64(i * -4.0) + Float64(t * Float64(z * Float64(18.0 * y)))))
	tmp = 0.0
	if (x <= -4.8e+46)
		tmp = t_2;
	elseif (x <= 3.7e-47)
		tmp = Float64(Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a))) - t_1);
	elseif (x <= 3.2e+168)
		tmp = Float64(Float64(Float64(b * c) - Float64(Float64(x * 4.0) * i)) - t_1);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * 27.0) * k;
	t_2 = x * ((i * -4.0) + (t * (z * (18.0 * y))));
	tmp = 0.0;
	if (x <= -4.8e+46)
		tmp = t_2;
	elseif (x <= 3.7e-47)
		tmp = ((b * c) + (-4.0 * (t * a))) - t_1;
	elseif (x <= 3.2e+168)
		tmp = ((b * c) - ((x * 4.0) * i)) - t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(i * -4.0), $MachinePrecision] + N[(t * N[(z * N[(18.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.8e+46], t$95$2, If[LessEqual[x, 3.7e-47], N[(N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[x, 3.2e+168], N[(N[(N[(b * c), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.80000000000000017e46 or 3.2000000000000001e168 < x

   1. Initial program 71.9%

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

      1. +-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

      2. associate-+r- N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\left(\left(b \cdot c + \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t\right) - \left(a \cdot 4\right) \cdot t\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t\right), \left(\left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(b \cdot c\right), \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t\right)\right), \left(\left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t\right)\right), \left(\left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      6. associate-*l* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot \left(z \cdot t\right)\right)\right), \left(\left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      7. associate-*l* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\left(x \cdot 18\right) \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\right), \left(\left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\left(x \cdot 18\right), \left(y \cdot \left(z \cdot t\right)\right)\right)\right), \left(\left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), \left(y \cdot \left(z \cdot t\right)\right)\right)\right), \left(\left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), \mathsf{*.f64}\left(y, \left(z \cdot t\right)\right)\right)\right), \left(\left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), \mathsf{*.f64}\left(y, \left(t \cdot z\right)\right)\right)\right), \left(\left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, z\right)\right)\right)\right), \left(\left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      13. associate-*l* N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, z\right)\right)\right)\right), \left(a \cdot \left(4 \cdot t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, z\right)\right)\right)\right), \mathsf{*.f64}\left(a, \left(4 \cdot t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      15. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, z\right)\right)\right)\right), \mathsf{*.f64}\left(a, \left(t \cdot 4\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      16. *-lowering-*.f64 82.3%

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, z\right)\right)\right)\right), \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(t, 4\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

   4. Applied egg-rr 82.3%

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

   5. Taylor expanded in y around inf

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\color{blue}{\left(y \cdot \left(18 \cdot \left(t \cdot \left(x \cdot z\right)\right) + \frac{b \cdot c}{y}\right)\right)}, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(t, 4\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \left(18 \cdot \left(t \cdot \left(x \cdot z\right)\right) + \frac{b \cdot c}{y}\right)\right), \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(t, 4\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\left(18 \cdot \left(t \cdot \left(x \cdot z\right)\right)\right), \left(\frac{b \cdot c}{y}\right)\right)\right), \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(t, 4\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\left(\left(18 \cdot t\right) \cdot \left(x \cdot z\right)\right), \left(\frac{b \cdot c}{y}\right)\right)\right), \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(t, 4\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(18 \cdot t\right), \left(x \cdot z\right)\right), \left(\frac{b \cdot c}{y}\right)\right)\right), \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(t, 4\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(18, t\right), \left(x \cdot z\right)\right), \left(\frac{b \cdot c}{y}\right)\right)\right), \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(t, 4\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(18, t\right), \mathsf{*.f64}\left(x, z\right)\right), \left(\frac{b \cdot c}{y}\right)\right)\right), \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(t, 4\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      7. associate-/l* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(18, t\right), \mathsf{*.f64}\left(x, z\right)\right), \left(b \cdot \frac{c}{y}\right)\right)\right), \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(t, 4\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(18, t\right), \mathsf{*.f64}\left(x, z\right)\right), \mathsf{*.f64}\left(b, \left(\frac{c}{y}\right)\right)\right)\right), \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(t, 4\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      9. /-lowering-/.f64 70.6%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(18, t\right), \mathsf{*.f64}\left(x, z\right)\right), \mathsf{*.f64}\left(b, \mathsf{/.f64}\left(c, y\right)\right)\right)\right), \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(t, 4\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

   7. Simplified 70.6%

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

   8. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)}\right) \]

      2. cancel-sign-sub-inv N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \color{blue}{\left(\mathsf{neg}\left(4\right)\right) \cdot i}\right)\right) \]

      3. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + -4 \cdot i\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right), \color{blue}{\left(-4 \cdot i\right)}\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(t \cdot \left(y \cdot z\right)\right) \cdot 18\right), \left(\color{blue}{-4} \cdot i\right)\right)\right) \]

      6. associate-*l* N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(t \cdot \left(\left(y \cdot z\right) \cdot 18\right)\right), \left(\color{blue}{-4} \cdot i\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(t \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right), \left(-4 \cdot i\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(18 \cdot \left(y \cdot z\right)\right)\right), \left(\color{blue}{-4} \cdot i\right)\right)\right) \]

      9. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(18 \cdot y\right) \cdot z\right)\right), \left(-4 \cdot i\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(z \cdot \left(18 \cdot y\right)\right)\right), \left(-4 \cdot i\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(z, \left(18 \cdot y\right)\right)\right), \left(-4 \cdot i\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(18, y\right)\right)\right), \left(-4 \cdot i\right)\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(18, y\right)\right)\right), \left(i \cdot \color{blue}{-4}\right)\right)\right) \]

      14. *-lowering-*.f64 72.8%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(18, y\right)\right)\right), \mathsf{*.f64}\left(i, \color{blue}{-4}\right)\right)\right) \]

   10. Simplified 72.8%

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

   if -4.80000000000000017e46 < x < 3.7e-47

   1. Initial program 96.6%

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

   3. Taylor expanded in x around 0

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(b \cdot c - 4 \cdot \left(a \cdot t\right)\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   4. Step-by-step derivation

      1. cancel-sign-sub-inv N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(a \cdot t\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + -4 \cdot \left(a \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(b \cdot c\right), \left(-4 \cdot \left(a \cdot t\right)\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(-4 \cdot \left(a \cdot t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(-4, \left(a \cdot t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, \color{blue}{27}\right), k\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(-4, \left(t \cdot a\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      7. *-lowering-*.f64 83.9%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(-4, \mathsf{*.f64}\left(t, a\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

   5. Simplified 83.9%

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

   if 3.7e-47 < x < 3.2000000000000001e168

   1. Initial program 79.8%

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

   3. Taylor expanded in t around 0

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\color{blue}{\left(b \cdot c\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 79.2%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

   5. Simplified 79.2%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{+46}:\\ \;\;\;\;x \cdot \left(i \cdot -4 + t \cdot \left(z \cdot \left(18 \cdot y\right)\right)\right)\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{-47}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+168}:\\ \;\;\;\;\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(i \cdot -4 + t \cdot \left(z \cdot \left(18 \cdot y\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 31.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := -4 \cdot \left(x \cdot i\right)\\ t_2 := -27 \cdot \left(j \cdot k\right)\\ \mathbf{if}\;k \leq -6.4 \cdot 10^{-97}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;k \leq -1.65 \cdot 10^{-270}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;k \leq 3.8 \cdot 10^{+55}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 1.2 \cdot 10^{+84}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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 (* -4.0 (* x i))) (t_2 (* -27.0 (* j k))))
   (if (<= k -6.4e-97)
     t_2
     (if (<= k -1.65e-270)
       t_1
       (if (<= k 3.8e+55) (* b c) (if (<= k 1.2e+84) 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 = -4.0 * (x * i);
	double t_2 = -27.0 * (j * k);
	double tmp;
	if (k <= -6.4e-97) {
		tmp = t_2;
	} else if (k <= -1.65e-270) {
		tmp = t_1;
	} else if (k <= 3.8e+55) {
		tmp = b * c;
	} else if (k <= 1.2e+84) {
		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 = (-4.0d0) * (x * i)
    t_2 = (-27.0d0) * (j * k)
    if (k <= (-6.4d-97)) then
        tmp = t_2
    else if (k <= (-1.65d-270)) then
        tmp = t_1
    else if (k <= 3.8d+55) then
        tmp = b * c
    else if (k <= 1.2d+84) 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 = -4.0 * (x * i);
	double t_2 = -27.0 * (j * k);
	double tmp;
	if (k <= -6.4e-97) {
		tmp = t_2;
	} else if (k <= -1.65e-270) {
		tmp = t_1;
	} else if (k <= 3.8e+55) {
		tmp = b * c;
	} else if (k <= 1.2e+84) {
		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 = -4.0 * (x * i)
	t_2 = -27.0 * (j * k)
	tmp = 0
	if k <= -6.4e-97:
		tmp = t_2
	elif k <= -1.65e-270:
		tmp = t_1
	elif k <= 3.8e+55:
		tmp = b * c
	elif k <= 1.2e+84:
		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(-4.0 * Float64(x * i))
	t_2 = Float64(-27.0 * Float64(j * k))
	tmp = 0.0
	if (k <= -6.4e-97)
		tmp = t_2;
	elseif (k <= -1.65e-270)
		tmp = t_1;
	elseif (k <= 3.8e+55)
		tmp = Float64(b * c);
	elseif (k <= 1.2e+84)
		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 = -4.0 * (x * i);
	t_2 = -27.0 * (j * k);
	tmp = 0.0;
	if (k <= -6.4e-97)
		tmp = t_2;
	elseif (k <= -1.65e-270)
		tmp = t_1;
	elseif (k <= 3.8e+55)
		tmp = b * c;
	elseif (k <= 1.2e+84)
		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[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[k, -6.4e-97], t$95$2, If[LessEqual[k, -1.65e-270], t$95$1, If[LessEqual[k, 3.8e+55], N[(b * c), $MachinePrecision], If[LessEqual[k, 1.2e+84], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if k < -6.39999999999999961e-97 or 1.2e84 < k

   1. Initial program 80.4%

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

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 80.3%

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

   5. Taylor expanded in j around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-27, \color{blue}{\left(j \cdot k\right)}\right) \]

      2. *-lowering-*.f64 43.2%

         \[\leadsto \mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, \color{blue}{k}\right)\right) \]

   7. Simplified 43.2%

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

   if -6.39999999999999961e-97 < k < -1.65000000000000009e-270 or 3.8e55 < k < 1.2e84

   1. Initial program 92.5%

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

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 92.5%

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

   5. Taylor expanded in i around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-4, \color{blue}{\left(i \cdot x\right)}\right) \]

      2. *-lowering-*.f64 32.9%

         \[\leadsto \mathsf{*.f64}\left(-4, \mathsf{*.f64}\left(i, \color{blue}{x}\right)\right) \]

   7. Simplified 32.9%

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

   if -1.65000000000000009e-270 < k < 3.8e55

   1. Initial program 87.2%

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

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 86.0%

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

   5. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot c} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 32.8%

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{c}\right) \]

   7. Simplified 32.8%

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

4. Final simplification 37.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -6.4 \cdot 10^{-97}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;k \leq -1.65 \cdot 10^{-270}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;k \leq 3.8 \cdot 10^{+55}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 1.2 \cdot 10^{+84}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 71.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := x \cdot \left(i \cdot -4 + t \cdot \left(z \cdot \left(18 \cdot y\right)\right)\right)\\ \mathbf{if}\;x \leq -2.8 \cdot 10^{+47}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-14}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (* x (+ (* i -4.0) (* t (* z (* 18.0 y)))))))
   (if (<= x -2.8e+47)
     t_1
     (if (<= x 1.4e-14)
       (- (+ (* b c) (* -4.0 (* t a))) (* (* j 27.0) 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 = x * ((i * -4.0) + (t * (z * (18.0 * y))));
	double tmp;
	if (x <= -2.8e+47) {
		tmp = t_1;
	} else if (x <= 1.4e-14) {
		tmp = ((b * c) + (-4.0 * (t * a))) - ((j * 27.0) * 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 = x * ((i * (-4.0d0)) + (t * (z * (18.0d0 * y))))
    if (x <= (-2.8d+47)) then
        tmp = t_1
    else if (x <= 1.4d-14) then
        tmp = ((b * c) + ((-4.0d0) * (t * a))) - ((j * 27.0d0) * 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 = x * ((i * -4.0) + (t * (z * (18.0 * y))));
	double tmp;
	if (x <= -2.8e+47) {
		tmp = t_1;
	} else if (x <= 1.4e-14) {
		tmp = ((b * c) + (-4.0 * (t * a))) - ((j * 27.0) * 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 = x * ((i * -4.0) + (t * (z * (18.0 * y))))
	tmp = 0
	if x <= -2.8e+47:
		tmp = t_1
	elif x <= 1.4e-14:
		tmp = ((b * c) + (-4.0 * (t * a))) - ((j * 27.0) * 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(x * Float64(Float64(i * -4.0) + Float64(t * Float64(z * Float64(18.0 * y)))))
	tmp = 0.0
	if (x <= -2.8e+47)
		tmp = t_1;
	elseif (x <= 1.4e-14)
		tmp = Float64(Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a))) - Float64(Float64(j * 27.0) * 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 = x * ((i * -4.0) + (t * (z * (18.0 * y))));
	tmp = 0.0;
	if (x <= -2.8e+47)
		tmp = t_1;
	elseif (x <= 1.4e-14)
		tmp = ((b * c) + (-4.0 * (t * a))) - ((j * 27.0) * 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[(x * N[(N[(i * -4.0), $MachinePrecision] + N[(t * N[(z * N[(18.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.8e+47], t$95$1, If[LessEqual[x, 1.4e-14], N[(N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.79999999999999988e47 or 1.4e-14 < x

   1. Initial program 73.1%

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

      1. +-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

      2. associate-+r- N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\left(\left(b \cdot c + \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t\right) - \left(a \cdot 4\right) \cdot t\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t\right), \left(\left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(b \cdot c\right), \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t\right)\right), \left(\left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t\right)\right), \left(\left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      6. associate-*l* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot \left(z \cdot t\right)\right)\right), \left(\left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      7. associate-*l* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\left(x \cdot 18\right) \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\right), \left(\left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\left(x \cdot 18\right), \left(y \cdot \left(z \cdot t\right)\right)\right)\right), \left(\left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), \left(y \cdot \left(z \cdot t\right)\right)\right)\right), \left(\left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), \mathsf{*.f64}\left(y, \left(z \cdot t\right)\right)\right)\right), \left(\left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), \mathsf{*.f64}\left(y, \left(t \cdot z\right)\right)\right)\right), \left(\left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, z\right)\right)\right)\right), \left(\left(a \cdot 4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      13. associate-*l* N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, z\right)\right)\right)\right), \left(a \cdot \left(4 \cdot t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, z\right)\right)\right)\right), \mathsf{*.f64}\left(a, \left(4 \cdot t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      15. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, z\right)\right)\right)\right), \mathsf{*.f64}\left(a, \left(t \cdot 4\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      16. *-lowering-*.f64 83.5%

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, z\right)\right)\right)\right), \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(t, 4\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

   4. Applied egg-rr 83.5%

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

   5. Taylor expanded in y around inf

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\color{blue}{\left(y \cdot \left(18 \cdot \left(t \cdot \left(x \cdot z\right)\right) + \frac{b \cdot c}{y}\right)\right)}, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(t, 4\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \left(18 \cdot \left(t \cdot \left(x \cdot z\right)\right) + \frac{b \cdot c}{y}\right)\right), \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(t, 4\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\left(18 \cdot \left(t \cdot \left(x \cdot z\right)\right)\right), \left(\frac{b \cdot c}{y}\right)\right)\right), \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(t, 4\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\left(\left(18 \cdot t\right) \cdot \left(x \cdot z\right)\right), \left(\frac{b \cdot c}{y}\right)\right)\right), \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(t, 4\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(18 \cdot t\right), \left(x \cdot z\right)\right), \left(\frac{b \cdot c}{y}\right)\right)\right), \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(t, 4\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(18, t\right), \left(x \cdot z\right)\right), \left(\frac{b \cdot c}{y}\right)\right)\right), \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(t, 4\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(18, t\right), \mathsf{*.f64}\left(x, z\right)\right), \left(\frac{b \cdot c}{y}\right)\right)\right), \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(t, 4\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      7. associate-/l* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(18, t\right), \mathsf{*.f64}\left(x, z\right)\right), \left(b \cdot \frac{c}{y}\right)\right)\right), \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(t, 4\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(18, t\right), \mathsf{*.f64}\left(x, z\right)\right), \mathsf{*.f64}\left(b, \left(\frac{c}{y}\right)\right)\right)\right), \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(t, 4\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      9. /-lowering-/.f64 70.6%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(18, t\right), \mathsf{*.f64}\left(x, z\right)\right), \mathsf{*.f64}\left(b, \mathsf{/.f64}\left(c, y\right)\right)\right)\right), \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(t, 4\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

   7. Simplified 70.6%

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

   8. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)}\right) \]

      2. cancel-sign-sub-inv N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \color{blue}{\left(\mathsf{neg}\left(4\right)\right) \cdot i}\right)\right) \]

      3. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + -4 \cdot i\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right), \color{blue}{\left(-4 \cdot i\right)}\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(t \cdot \left(y \cdot z\right)\right) \cdot 18\right), \left(\color{blue}{-4} \cdot i\right)\right)\right) \]

      6. associate-*l* N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(t \cdot \left(\left(y \cdot z\right) \cdot 18\right)\right), \left(\color{blue}{-4} \cdot i\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(t \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right), \left(-4 \cdot i\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(18 \cdot \left(y \cdot z\right)\right)\right), \left(\color{blue}{-4} \cdot i\right)\right)\right) \]

      9. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(18 \cdot y\right) \cdot z\right)\right), \left(-4 \cdot i\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(z \cdot \left(18 \cdot y\right)\right)\right), \left(-4 \cdot i\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(z, \left(18 \cdot y\right)\right)\right), \left(-4 \cdot i\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(18, y\right)\right)\right), \left(-4 \cdot i\right)\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(18, y\right)\right)\right), \left(i \cdot \color{blue}{-4}\right)\right)\right) \]

      14. *-lowering-*.f64 67.0%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(18, y\right)\right)\right), \mathsf{*.f64}\left(i, \color{blue}{-4}\right)\right)\right) \]

   10. Simplified 67.0%

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

   if -2.79999999999999988e47 < x < 1.4e-14

   1. Initial program 96.8%

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

   3. Taylor expanded in x around 0

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(b \cdot c - 4 \cdot \left(a \cdot t\right)\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   4. Step-by-step derivation

      1. cancel-sign-sub-inv N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(a \cdot t\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + -4 \cdot \left(a \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(b \cdot c\right), \left(-4 \cdot \left(a \cdot t\right)\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(-4 \cdot \left(a \cdot t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(-4, \left(a \cdot t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, \color{blue}{27}\right), k\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(-4, \left(t \cdot a\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      7. *-lowering-*.f64 84.8%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(-4, \mathsf{*.f64}\left(t, a\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

   5. Simplified 84.8%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{+47}:\\ \;\;\;\;x \cdot \left(i \cdot -4 + t \cdot \left(z \cdot \left(18 \cdot y\right)\right)\right)\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-14}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(i \cdot -4 + t \cdot \left(z \cdot \left(18 \cdot y\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 48.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c + x \cdot \left(i \cdot -4\right)\\ \mathbf{if}\;x \leq -6 \cdot 10^{+188}:\\ \;\;\;\;t \cdot \left(x \cdot \left(z \cdot \left(18 \cdot y\right)\right)\right)\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{+88}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{-47}:\\ \;\;\;\;b \cdot c + t \cdot \left(a \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (+ (* b c) (* x (* i -4.0)))))
   (if (<= x -6e+188)
     (* t (* x (* z (* 18.0 y))))
     (if (<= x -4.8e+88)
       t_1
       (if (<= x 4.4e-47) (+ (* b c) (* t (* a -4.0))) t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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) + (x * (i * -4.0));
	double tmp;
	if (x <= -6e+188) {
		tmp = t * (x * (z * (18.0 * y)));
	} else if (x <= -4.8e+88) {
		tmp = t_1;
	} else if (x <= 4.4e-47) {
		tmp = (b * c) + (t * (a * -4.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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) + (x * (i * (-4.0d0)))
    if (x <= (-6d+188)) then
        tmp = t * (x * (z * (18.0d0 * y)))
    else if (x <= (-4.8d+88)) then
        tmp = t_1
    else if (x <= 4.4d-47) then
        tmp = (b * c) + (t * (a * (-4.0d0)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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) + (x * (i * -4.0));
	double tmp;
	if (x <= -6e+188) {
		tmp = t * (x * (z * (18.0 * y)));
	} else if (x <= -4.8e+88) {
		tmp = t_1;
	} else if (x <= 4.4e-47) {
		tmp = (b * c) + (t * (a * -4.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) + (x * (i * -4.0))
	tmp = 0
	if x <= -6e+188:
		tmp = t * (x * (z * (18.0 * y)))
	elif x <= -4.8e+88:
		tmp = t_1
	elif x <= 4.4e-47:
		tmp = (b * c) + (t * (a * -4.0))
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) + Float64(x * Float64(i * -4.0)))
	tmp = 0.0
	if (x <= -6e+188)
		tmp = Float64(t * Float64(x * Float64(z * Float64(18.0 * y))));
	elseif (x <= -4.8e+88)
		tmp = t_1;
	elseif (x <= 4.4e-47)
		tmp = Float64(Float64(b * c) + Float64(t * Float64(a * -4.0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) + (x * (i * -4.0));
	tmp = 0.0;
	if (x <= -6e+188)
		tmp = t * (x * (z * (18.0 * y)));
	elseif (x <= -4.8e+88)
		tmp = t_1;
	elseif (x <= 4.4e-47)
		tmp = (b * c) + (t * (a * -4.0));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] + N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6e+188], N[(t * N[(x * N[(z * N[(18.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -4.8e+88], t$95$1, If[LessEqual[x, 4.4e-47], N[(N[(b * c), $MachinePrecision] + N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.0000000000000001e188

   1. Initial program 53.7%

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

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 53.7%

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

   5. Taylor expanded in t around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(-4 \cdot a\right), \color{blue}{\left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \left(\color{blue}{18} \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \left(\left(x \cdot \left(y \cdot z\right)\right) \cdot \color{blue}{18}\right)\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \left(x \cdot \color{blue}{\left(\left(y \cdot z\right) \cdot 18\right)}\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \left(x \cdot \left(18 \cdot \color{blue}{\left(y \cdot z\right)}\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \mathsf{*.f64}\left(x, \color{blue}{\left(18 \cdot \left(y \cdot z\right)\right)}\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(18, \color{blue}{\left(y \cdot z\right)}\right)\right)\right)\right) \]

      9. *-lowering-*.f64 69.2%

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(y, \color{blue}{z}\right)\right)\right)\right)\right) \]

   7. Simplified 69.2%

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

   8. Taylor expanded in a around 0

      \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)}\right) \]
   9. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(\left(18 \cdot x\right) \cdot \color{blue}{\left(y \cdot z\right)}\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(\left(x \cdot 18\right) \cdot \left(\color{blue}{y} \cdot z\right)\right)\right) \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(x \cdot \color{blue}{\left(18 \cdot \left(y \cdot z\right)\right)}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(x, \color{blue}{\left(18 \cdot \left(y \cdot z\right)\right)}\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(x, \left(\left(18 \cdot y\right) \cdot \color{blue}{z}\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(x, \left(z \cdot \color{blue}{\left(18 \cdot y\right)}\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(z, \color{blue}{\left(18 \cdot y\right)}\right)\right)\right) \]

      8. *-lowering-*.f64 61.8%

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(18, \color{blue}{y}\right)\right)\right)\right) \]

   10. Simplified 61.8%

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

   if -6.0000000000000001e188 < x < -4.7999999999999998e88 or 4.40000000000000037e-47 < x

   1. Initial program 77.5%

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

   3. Taylor expanded in t around 0

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\color{blue}{\left(b \cdot c\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 71.6%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

   5. Simplified 71.6%

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

   6. Taylor expanded in j around 0

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

      1. cancel-sign-sub-inv N/A

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

      2. metadata-eval N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(b \cdot c\right), \color{blue}{\left(-4 \cdot \left(i \cdot x\right)\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\color{blue}{-4} \cdot \left(i \cdot x\right)\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\left(-4 \cdot i\right) \cdot \color{blue}{x}\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(x \cdot \color{blue}{\left(-4 \cdot i\right)}\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \color{blue}{\left(-4 \cdot i\right)}\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \left(i \cdot \color{blue}{-4}\right)\right)\right) \]

      9. *-lowering-*.f64 59.9%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, \color{blue}{-4}\right)\right)\right) \]

   8. Simplified 59.9%

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

   if -4.7999999999999998e88 < x < 4.40000000000000037e-47

   1. Initial program 95.4%

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

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 94.6%

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

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \color{blue}{\left(b \cdot c\right)}\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 67.2%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \mathsf{*.f64}\left(b, \color{blue}{c}\right)\right) \]

   7. Simplified 67.2%

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

   8. Taylor expanded in x around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \color{blue}{\left(-4 \cdot a\right)}\right), \mathsf{*.f64}\left(b, c\right)\right) \]
   9. Step-by-step derivation

      1. *-lowering-*.f64 55.4%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(-4, a\right)\right), \mathsf{*.f64}\left(b, c\right)\right) \]

   10. Simplified 55.4%

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

4. Final simplification 57.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{+188}:\\ \;\;\;\;t \cdot \left(x \cdot \left(z \cdot \left(18 \cdot y\right)\right)\right)\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{+88}:\\ \;\;\;\;b \cdot c + x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{-47}:\\ \;\;\;\;b \cdot c + t \cdot \left(a \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + x \cdot \left(i \cdot -4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 41.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;k \leq -3.8 \cdot 10^{-88}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;k \leq 3 \cdot 10^{+215}:\\ \;\;\;\;b \cdot c + x \cdot \left(i \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= k -3.8e-88)
   (* j (* k -27.0))
   (if (<= k 3e+215) (+ (* b c) (* x (* i -4.0))) (* k (* j -27.0)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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 <= -3.8e-88) {
		tmp = j * (k * -27.0);
	} else if (k <= 3e+215) {
		tmp = (b * c) + (x * (i * -4.0));
	} else {
		tmp = k * (j * -27.0);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 <= (-3.8d-88)) then
        tmp = j * (k * (-27.0d0))
    else if (k <= 3d+215) then
        tmp = (b * c) + (x * (i * (-4.0d0)))
    else
        tmp = k * (j * (-27.0d0))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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 <= -3.8e-88) {
		tmp = j * (k * -27.0);
	} else if (k <= 3e+215) {
		tmp = (b * c) + (x * (i * -4.0));
	} else {
		tmp = k * (j * -27.0);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if k <= -3.8e-88:
		tmp = j * (k * -27.0)
	elif k <= 3e+215:
		tmp = (b * c) + (x * (i * -4.0))
	else:
		tmp = k * (j * -27.0)
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (k <= -3.8e-88)
		tmp = Float64(j * Float64(k * -27.0));
	elseif (k <= 3e+215)
		tmp = Float64(Float64(b * c) + Float64(x * Float64(i * -4.0)));
	else
		tmp = Float64(k * Float64(j * -27.0));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (k <= -3.8e-88)
		tmp = j * (k * -27.0);
	elseif (k <= 3e+215)
		tmp = (b * c) + (x * (i * -4.0));
	else
		tmp = k * (j * -27.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[k, -3.8e-88], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 3e+215], N[(N[(b * c), $MachinePrecision] + N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if k < -3.80000000000000011e-88

   1. Initial program 80.3%

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

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 80.3%

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

   5. Taylor expanded in j around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-27, \color{blue}{\left(j \cdot k\right)}\right) \]

      2. *-lowering-*.f64 35.6%

         \[\leadsto \mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, \color{blue}{k}\right)\right) \]

   7. Simplified 35.6%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-27 \cdot k\right), \color{blue}{j}\right) \]

      4. *-lowering-*.f64 35.6%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-27, k\right), j\right) \]

   9. Applied egg-rr 35.6%

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

   if -3.80000000000000011e-88 < k < 2.9999999999999999e215

   1. Initial program 88.9%

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

   3. Taylor expanded in t around 0

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\color{blue}{\left(b \cdot c\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 57.7%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

   5. Simplified 57.7%

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

   6. Taylor expanded in j around 0

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

      1. cancel-sign-sub-inv N/A

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

      2. metadata-eval N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(b \cdot c\right), \color{blue}{\left(-4 \cdot \left(i \cdot x\right)\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\color{blue}{-4} \cdot \left(i \cdot x\right)\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\left(-4 \cdot i\right) \cdot \color{blue}{x}\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(x \cdot \color{blue}{\left(-4 \cdot i\right)}\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \color{blue}{\left(-4 \cdot i\right)}\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \left(i \cdot \color{blue}{-4}\right)\right)\right) \]

      9. *-lowering-*.f64 48.2%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, \color{blue}{-4}\right)\right)\right) \]

   8. Simplified 48.2%

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

   if 2.9999999999999999e215 < k

   1. Initial program 70.2%

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

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 70.1%

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

   5. Taylor expanded in j around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-27, \color{blue}{\left(j \cdot k\right)}\right) \]

      2. *-lowering-*.f64 75.6%

         \[\leadsto \mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, \color{blue}{k}\right)\right) \]

   7. Simplified 75.6%

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

      1. associate-*r* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-27 \cdot j\right), \color{blue}{k}\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\left(j \cdot -27\right), k\right) \]

      4. *-lowering-*.f64 75.7%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, -27\right), k\right) \]

   9. Applied egg-rr 75.7%

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

4. Final simplification 46.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -3.8 \cdot 10^{-88}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;k \leq 3 \cdot 10^{+215}:\\ \;\;\;\;b \cdot c + x \cdot \left(i \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 31.2% accurate, 2.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := -27 \cdot \left(j \cdot k\right)\\ \mathbf{if}\;k \leq -2.8 \cdot 10^{-153}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;k \leq 2.1 \cdot 10^{+63}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* -27.0 (* j k))))
   (if (<= k -2.8e-153) t_1 (if (<= k 2.1e+63) (* b c) 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 = -27.0 * (j * k);
	double tmp;
	if (k <= -2.8e-153) {
		tmp = t_1;
	} else if (k <= 2.1e+63) {
		tmp = b * c;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 = (-27.0d0) * (j * k)
    if (k <= (-2.8d-153)) then
        tmp = t_1
    else if (k <= 2.1d+63) then
        tmp = b * c
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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 = -27.0 * (j * k);
	double tmp;
	if (k <= -2.8e-153) {
		tmp = t_1;
	} else if (k <= 2.1e+63) {
		tmp = b * c;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = -27.0 * (j * k)
	tmp = 0
	if k <= -2.8e-153:
		tmp = t_1
	elif k <= 2.1e+63:
		tmp = b * c
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(-27.0 * Float64(j * k))
	tmp = 0.0
	if (k <= -2.8e-153)
		tmp = t_1;
	elseif (k <= 2.1e+63)
		tmp = Float64(b * c);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = -27.0 * (j * k);
	tmp = 0.0;
	if (k <= -2.8e-153)
		tmp = t_1;
	elseif (k <= 2.1e+63)
		tmp = b * c;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[k, -2.8e-153], t$95$1, If[LessEqual[k, 2.1e+63], N[(b * c), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if k < -2.8000000000000001e-153 or 2.1000000000000002e63 < k

   1. Initial program 82.1%

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

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 82.0%

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

   5. Taylor expanded in j around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-27, \color{blue}{\left(j \cdot k\right)}\right) \]

      2. *-lowering-*.f64 38.3%

         \[\leadsto \mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, \color{blue}{k}\right)\right) \]

   7. Simplified 38.3%

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

   if -2.8000000000000001e-153 < k < 2.1000000000000002e63

   1. Initial program 88.5%

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

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 87.6%

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

   5. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot c} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 28.0%

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{c}\right) \]

   7. Simplified 28.0%

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

Alternative 26: 23.4% 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 84.9%

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

   1. associate--l+ N/A

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

   2. associate--l+ N/A

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

   3. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

   4. distribute-rgt-out-- N/A

      \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

   5. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

   6. sub-neg N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   7. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   8. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   9. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   10. *-lowering-*.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   11. distribute-rgt-neg-in N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   12. *-lowering-*.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   13. metadata-eval N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

3. Simplified 84.5%

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

5. Taylor expanded in b around inf

   \[\leadsto \color{blue}{b \cdot c} \]
6. Step-by-step derivation

   1. *-lowering-*.f64 23.0%

      \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{c}\right) \]

7. Simplified 23.0%

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

Developer Target 1: 89.3% 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 2024158 
(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
  (! :herbie-platform default (if (< t -8105407698770699/5000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (- (* (* 18 t) (* (* x y) z)) (* (+ (* a t) (* i x)) 4)) (- (* (* k j) 27) (* c b))) (if (< t 8284013971902611/50000000000000) (+ (- (* (* 18 y) (* x (* z t))) (* (+ (* a t) (* i x)) 4)) (- (* c b) (* 27 (* k j)))) (- (- (* (* 18 t) (* (* x y) z)) (* (+ (* a t) (* i x)) 4)) (- (* (* k j) 27) (* c b))))))

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