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

Percentage Accurate: 85.6% → 91.9%

Time: 33.3s

Alternatives: 27

Speedup: 0.9×

• 49.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 91.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{-59}:\\ \;\;\;\;\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(-4 \cdot i\right)\right)\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-30}:\\ \;\;\;\;\left(\left(\left(y \cdot \left(\left(x \cdot 18\right) \cdot \left(t \cdot z\right)\right) - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - i \cdot \left(x \cdot 4\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + \frac{b \cdot c}{t}\right) - \left(a \cdot 4 + \left(4 \cdot \frac{x \cdot i}{t} + 27 \cdot \frac{j \cdot k}{t}\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= t -9.5e-59)
   (+
    (fma t (fma x (* 18.0 (* y z)) (* a -4.0)) (fma b c (* x (* -4.0 i))))
    (* j (* k -27.0)))
   (if (<= t 5.5e-30)
     (-
      (-
       (+ (- (* y (* (* x 18.0) (* t z))) (* t (* a 4.0))) (* b c))
       (* i (* x 4.0)))
      (* k (* j 27.0)))
     (*
      t
      (-
       (+ (* 18.0 (* x (* y z))) (/ (* b c) t))
       (+ (* a 4.0) (+ (* 4.0 (/ (* x i) t)) (* 27.0 (/ (* j k) t)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (t <= -9.5e-59) {
		tmp = fma(t, fma(x, (18.0 * (y * z)), (a * -4.0)), fma(b, c, (x * (-4.0 * i)))) + (j * (k * -27.0));
	} else if (t <= 5.5e-30) {
		tmp = ((((y * ((x * 18.0) * (t * z))) - (t * (a * 4.0))) + (b * c)) - (i * (x * 4.0))) - (k * (j * 27.0));
	} else {
		tmp = t * (((18.0 * (x * (y * z))) + ((b * c) / t)) - ((a * 4.0) + ((4.0 * ((x * i) / t)) + (27.0 * ((j * k) / t)))));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (t <= -9.5e-59)
		tmp = Float64(fma(t, fma(x, Float64(18.0 * Float64(y * z)), Float64(a * -4.0)), fma(b, c, Float64(x * Float64(-4.0 * i)))) + Float64(j * Float64(k * -27.0)));
	elseif (t <= 5.5e-30)
		tmp = Float64(Float64(Float64(Float64(Float64(y * Float64(Float64(x * 18.0) * Float64(t * z))) - Float64(t * Float64(a * 4.0))) + Float64(b * c)) - Float64(i * Float64(x * 4.0))) - Float64(k * Float64(j * 27.0)));
	else
		tmp = Float64(t * Float64(Float64(Float64(18.0 * Float64(x * Float64(y * z))) + Float64(Float64(b * c) / t)) - Float64(Float64(a * 4.0) + Float64(Float64(4.0 * Float64(Float64(x * i) / t)) + Float64(27.0 * Float64(Float64(j * k) / t))))));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[t, -9.5e-59], N[(N[(t * N[(x * N[(18.0 * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + N[(b * c + N[(x * N[(-4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.5e-30], N[(N[(N[(N[(N[(y * N[(N[(x * 18.0), $MachinePrecision] * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - N[(i * N[(x * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(b * c), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] - N[(N[(a * 4.0), $MachinePrecision] + N[(N[(4.0 * N[(N[(x * i), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] + N[(27.0 * N[(N[(j * k), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.4999999999999994e-59

   1. Initial program 81.6%

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

   3. Simplified 85.8%

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

   if -9.4999999999999994e-59 < t < 5.49999999999999976e-30

   1. Initial program 90.5%

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

      1. pow1 90.5%

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

      2. associate-*l* 92.1%

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

      3. *-commutative 92.1%

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

   4. Applied egg-rr 92.1%

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

      1. unpow1 92.1%

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

      2. associate-*l* 96.4%

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

      3. *-commutative 96.4%

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

   6. Simplified 96.4%

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

   if 5.49999999999999976e-30 < t

   1. Initial program 82.8%

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

   3. Simplified 91.3%

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

   5. Taylor expanded in t around inf 94.1%

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

4. Final simplification 92.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{-59}:\\ \;\;\;\;\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(-4 \cdot i\right)\right)\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-30}:\\ \;\;\;\;\left(\left(\left(y \cdot \left(\left(x \cdot 18\right) \cdot \left(t \cdot z\right)\right) - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - i \cdot \left(x \cdot 4\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + \frac{b \cdot c}{t}\right) - \left(a \cdot 4 + \left(4 \cdot \frac{x \cdot i}{t} + 27 \cdot \frac{j \cdot k}{t}\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 89.4% accurate, 0.5× speedup

Math

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

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
         (-
          (-
           (+ (* b c) (- (* t (* z (* y (* x 18.0)))) (* t (* a 4.0))))
           (* i (* x 4.0)))
          (* k (* j 27.0)))))
   (if (<= t_1 INFINITY) t_1 (* c (+ b (* t (* -4.0 (/ a 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) + ((t * (z * (y * (x * 18.0)))) - (t * (a * 4.0)))) - (i * (x * 4.0))) - (k * (j * 27.0));
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = c * (b + (t * (-4.0 * (a / 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 = (((b * c) + ((t * (z * (y * (x * 18.0)))) - (t * (a * 4.0)))) - (i * (x * 4.0))) - (k * (j * 27.0));
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = c * (b + (t * (-4.0 * (a / 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) + ((t * (z * (y * (x * 18.0)))) - (t * (a * 4.0)))) - (i * (x * 4.0))) - (k * (j * 27.0))
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = c * (b + (t * (-4.0 * (a / 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(b * c) + Float64(Float64(t * Float64(z * Float64(y * Float64(x * 18.0)))) - Float64(t * Float64(a * 4.0)))) - Float64(i * Float64(x * 4.0))) - Float64(k * Float64(j * 27.0)))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(c * Float64(b + Float64(t * Float64(-4.0 * Float64(a / 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) + ((t * (z * (y * (x * 18.0)))) - (t * (a * 4.0)))) - (i * (x * 4.0))) - (k * (j * 27.0));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = c * (b + (t * (-4.0 * (a / 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[(b * c), $MachinePrecision] + N[(N[(t * N[(z * N[(y * N[(x * 18.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * N[(x * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(c * N[(b + N[(t * N[(-4.0 * N[(a / c), $MachinePrecision]), $MachinePrecision]), $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 96.9%

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

   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. Add Preprocessing

   3. Taylor expanded in x around 0 44.9%

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

   4. Taylor expanded in c around inf 51.8%

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

      1. associate-*r/ 51.8%

         \[\leadsto c \cdot \left(b + \color{blue}{\frac{-1 \cdot \left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)}{c}}\right) \]

      2. mul-1-neg 51.8%

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

      3. *-commutative 51.8%

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

      4. *-commutative 51.8%

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

      5. associate-*r* 51.8%

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

      6. *-commutative 51.8%

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

      7. associate-*l* 51.8%

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

      8. *-commutative 51.8%

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

      9. distribute-neg-in 51.8%

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

      10. distribute-rgt-neg-in 51.8%

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

      11. distribute-rgt-neg-in 51.8%

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

      12. metadata-eval 51.8%

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

      13. distribute-rgt-neg-in 51.8%

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

      14. distribute-lft-neg-in 51.8%

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

      15. metadata-eval 51.8%

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

      16. *-commutative 51.8%

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

   6. Simplified 51.8%

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

   7. Taylor expanded in t around inf 45.3%

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

      1. associate-*r/ 45.3%

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

      2. *-commutative 45.3%

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

      3. *-commutative 45.3%

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

      4. associate-*r* 45.3%

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

      5. *-commutative 45.3%

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

      6. associate-*r/ 48.8%

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

      7. associate-*r/ 48.8%

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

   9. Simplified 48.8%

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

4. Final simplification 91.5%

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

Alternative 3: 56.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ t_2 := j \cdot \left(k \cdot -27\right)\\ t_3 := t\_2 + i \cdot \left(x \cdot -4\right)\\ t_4 := t\_2 + b \cdot c\\ \mathbf{if}\;t \leq -1.5 \cdot 10^{+214}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{-31}:\\ \;\;\;\;t\_2 + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{-109}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t \leq -4.6 \cdot 10^{-216}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{-231}:\\ \;\;\;\;c \cdot \left(b + t \cdot \left(-4 \cdot \frac{a}{c}\right)\right)\\ \mathbf{elif}\;t \leq 2.95 \cdot 10^{-269}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-140}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+106}:\\ \;\;\;\;t\_4\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (- (* 18.0 (* x (* y z))) (* a 4.0))))
        (t_2 (* j (* k -27.0)))
        (t_3 (+ t_2 (* i (* x -4.0))))
        (t_4 (+ t_2 (* b c))))
   (if (<= t -1.5e+214)
     t_1
     (if (<= t -2.8e-31)
       (+ t_2 (* -4.0 (* t a)))
       (if (<= t -2.6e-109)
         t_4
         (if (<= t -4.6e-216)
           t_3
           (if (<= t -1.3e-231)
             (* c (+ b (* t (* -4.0 (/ a c)))))
             (if (<= t 2.95e-269)
               t_4
               (if (<= t 7e-140) t_3 (if (<= t 1.7e+106) t_4 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 * ((18.0 * (x * (y * z))) - (a * 4.0));
	double t_2 = j * (k * -27.0);
	double t_3 = t_2 + (i * (x * -4.0));
	double t_4 = t_2 + (b * c);
	double tmp;
	if (t <= -1.5e+214) {
		tmp = t_1;
	} else if (t <= -2.8e-31) {
		tmp = t_2 + (-4.0 * (t * a));
	} else if (t <= -2.6e-109) {
		tmp = t_4;
	} else if (t <= -4.6e-216) {
		tmp = t_3;
	} else if (t <= -1.3e-231) {
		tmp = c * (b + (t * (-4.0 * (a / c))));
	} else if (t <= 2.95e-269) {
		tmp = t_4;
	} else if (t <= 7e-140) {
		tmp = t_3;
	} else if (t <= 1.7e+106) {
		tmp = t_4;
	} 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) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0))
    t_2 = j * (k * (-27.0d0))
    t_3 = t_2 + (i * (x * (-4.0d0)))
    t_4 = t_2 + (b * c)
    if (t <= (-1.5d+214)) then
        tmp = t_1
    else if (t <= (-2.8d-31)) then
        tmp = t_2 + ((-4.0d0) * (t * a))
    else if (t <= (-2.6d-109)) then
        tmp = t_4
    else if (t <= (-4.6d-216)) then
        tmp = t_3
    else if (t <= (-1.3d-231)) then
        tmp = c * (b + (t * ((-4.0d0) * (a / c))))
    else if (t <= 2.95d-269) then
        tmp = t_4
    else if (t <= 7d-140) then
        tmp = t_3
    else if (t <= 1.7d+106) then
        tmp = t_4
    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 * ((18.0 * (x * (y * z))) - (a * 4.0));
	double t_2 = j * (k * -27.0);
	double t_3 = t_2 + (i * (x * -4.0));
	double t_4 = t_2 + (b * c);
	double tmp;
	if (t <= -1.5e+214) {
		tmp = t_1;
	} else if (t <= -2.8e-31) {
		tmp = t_2 + (-4.0 * (t * a));
	} else if (t <= -2.6e-109) {
		tmp = t_4;
	} else if (t <= -4.6e-216) {
		tmp = t_3;
	} else if (t <= -1.3e-231) {
		tmp = c * (b + (t * (-4.0 * (a / c))));
	} else if (t <= 2.95e-269) {
		tmp = t_4;
	} else if (t <= 7e-140) {
		tmp = t_3;
	} else if (t <= 1.7e+106) {
		tmp = t_4;
	} 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 * ((18.0 * (x * (y * z))) - (a * 4.0))
	t_2 = j * (k * -27.0)
	t_3 = t_2 + (i * (x * -4.0))
	t_4 = t_2 + (b * c)
	tmp = 0
	if t <= -1.5e+214:
		tmp = t_1
	elif t <= -2.8e-31:
		tmp = t_2 + (-4.0 * (t * a))
	elif t <= -2.6e-109:
		tmp = t_4
	elif t <= -4.6e-216:
		tmp = t_3
	elif t <= -1.3e-231:
		tmp = c * (b + (t * (-4.0 * (a / c))))
	elif t <= 2.95e-269:
		tmp = t_4
	elif t <= 7e-140:
		tmp = t_3
	elif t <= 1.7e+106:
		tmp = t_4
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)))
	t_2 = Float64(j * Float64(k * -27.0))
	t_3 = Float64(t_2 + Float64(i * Float64(x * -4.0)))
	t_4 = Float64(t_2 + Float64(b * c))
	tmp = 0.0
	if (t <= -1.5e+214)
		tmp = t_1;
	elseif (t <= -2.8e-31)
		tmp = Float64(t_2 + Float64(-4.0 * Float64(t * a)));
	elseif (t <= -2.6e-109)
		tmp = t_4;
	elseif (t <= -4.6e-216)
		tmp = t_3;
	elseif (t <= -1.3e-231)
		tmp = Float64(c * Float64(b + Float64(t * Float64(-4.0 * Float64(a / c)))));
	elseif (t <= 2.95e-269)
		tmp = t_4;
	elseif (t <= 7e-140)
		tmp = t_3;
	elseif (t <= 1.7e+106)
		tmp = t_4;
	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 * ((18.0 * (x * (y * z))) - (a * 4.0));
	t_2 = j * (k * -27.0);
	t_3 = t_2 + (i * (x * -4.0));
	t_4 = t_2 + (b * c);
	tmp = 0.0;
	if (t <= -1.5e+214)
		tmp = t_1;
	elseif (t <= -2.8e-31)
		tmp = t_2 + (-4.0 * (t * a));
	elseif (t <= -2.6e-109)
		tmp = t_4;
	elseif (t <= -4.6e-216)
		tmp = t_3;
	elseif (t <= -1.3e-231)
		tmp = c * (b + (t * (-4.0 * (a / c))));
	elseif (t <= 2.95e-269)
		tmp = t_4;
	elseif (t <= 7e-140)
		tmp = t_3;
	elseif (t <= 1.7e+106)
		tmp = t_4;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 + N[(i * N[(x * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$2 + N[(b * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.5e+214], t$95$1, If[LessEqual[t, -2.8e-31], N[(t$95$2 + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.6e-109], t$95$4, If[LessEqual[t, -4.6e-216], t$95$3, If[LessEqual[t, -1.3e-231], N[(c * N[(b + N[(t * N[(-4.0 * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.95e-269], t$95$4, If[LessEqual[t, 7e-140], t$95$3, If[LessEqual[t, 1.7e+106], t$95$4, t$95$1]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.5000000000000001e214 or 1.69999999999999997e106 < t

   1. Initial program 84.4%

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

   3. Simplified 93.7%

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

   5. Taylor expanded in t around inf 87.2%

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

   if -1.5000000000000001e214 < t < -2.7999999999999999e-31

   1. Initial program 78.4%

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

   3. Simplified 83.2%

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

   5. Taylor expanded in a around inf 60.9%

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

      1. *-commutative 60.9%

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

   7. Simplified 60.9%

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

   if -2.7999999999999999e-31 < t < -2.5999999999999998e-109 or -1.30000000000000001e-231 < t < 2.95e-269 or 6.9999999999999996e-140 < t < 1.69999999999999997e106

   1. Initial program 89.8%

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

   3. Simplified 91.2%

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

   5. Taylor expanded in b around inf 61.4%

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

   if -2.5999999999999998e-109 < t < -4.59999999999999993e-216 or 2.95e-269 < t < 6.9999999999999996e-140

   1. Initial program 88.1%

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

   3. Simplified 86.6%

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

   5. Taylor expanded in i around inf 69.6%

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

      1. metadata-eval 69.6%

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

      2. distribute-lft-neg-in 69.6%

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

      3. *-commutative 69.6%

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

      4. associate-*r* 69.6%

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

      5. distribute-rgt-neg-in 69.6%

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

      6. distribute-rgt-neg-in 69.6%

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

      7. metadata-eval 69.6%

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

      8. *-commutative 69.6%

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

   7. Simplified 69.6%

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

   if -4.59999999999999993e-216 < t < -1.30000000000000001e-231

   1. Initial program 66.7%

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

   3. Taylor expanded in x around 0 100.0%

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

   4. Taylor expanded in c around inf 100.0%

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

      1. associate-*r/ 100.0%

         \[\leadsto c \cdot \left(b + \color{blue}{\frac{-1 \cdot \left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)}{c}}\right) \]

      2. mul-1-neg 100.0%

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

      3. *-commutative 100.0%

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

      4. *-commutative 100.0%

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

      5. associate-*r* 100.0%

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

      6. *-commutative 100.0%

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

      7. associate-*l* 100.0%

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

      8. *-commutative 100.0%

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

      9. distribute-neg-in 100.0%

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

      10. distribute-rgt-neg-in 100.0%

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

      11. distribute-rgt-neg-in 100.0%

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

      12. metadata-eval 100.0%

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

      13. distribute-rgt-neg-in 100.0%

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

      14. distribute-lft-neg-in 100.0%

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

      15. metadata-eval 100.0%

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

      16. *-commutative 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in t around inf 100.0%

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

      1. associate-*r/ 100.0%

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

      2. *-commutative 100.0%

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

      3. *-commutative 100.0%

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

      4. associate-*r* 100.0%

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

      5. *-commutative 100.0%

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

      6. associate-*r/ 100.0%

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

      7. associate-*r/ 100.0%

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

   9. Simplified 100.0%

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

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{+214}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{-31}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{-109}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \mathbf{elif}\;t \leq -4.6 \cdot 10^{-216}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + i \cdot \left(x \cdot -4\right)\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{-231}:\\ \;\;\;\;c \cdot \left(b + t \cdot \left(-4 \cdot \frac{a}{c}\right)\right)\\ \mathbf{elif}\;t \leq 2.95 \cdot 10^{-269}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-140}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + i \cdot \left(x \cdot -4\right)\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+106}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 56.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := t\_1 + i \cdot \left(x \cdot -4\right)\\ t_3 := t\_1 + b \cdot c\\ \mathbf{if}\;t \leq -2.2 \cdot 10^{+216}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq -1.85 \cdot 10^{-20}:\\ \;\;\;\;t\_1 + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{-108}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq -3.3 \cdot 10^{-216}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{-231}:\\ \;\;\;\;c \cdot \left(b + t \cdot \left(-4 \cdot \frac{a}{c}\right)\right)\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-269}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-139}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+105}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot 18\right) - a \cdot 4\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0)))
        (t_2 (+ t_1 (* i (* x -4.0))))
        (t_3 (+ t_1 (* b c))))
   (if (<= t -2.2e+216)
     (* t (- (* 18.0 (* x (* y z))) (* a 4.0)))
     (if (<= t -1.85e-20)
       (+ t_1 (* -4.0 (* t a)))
       (if (<= t -1.2e-108)
         t_3
         (if (<= t -3.3e-216)
           t_2
           (if (<= t -1.3e-231)
             (* c (+ b (* t (* -4.0 (/ a c)))))
             (if (<= t 3.6e-269)
               t_3
               (if (<= t 1.05e-139)
                 t_2
                 (if (<= t 2e+105)
                   t_3
                   (* t (- (* (* y z) (* x 18.0)) (* a 4.0)))))))))))))

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 = j * (k * -27.0);
	double t_2 = t_1 + (i * (x * -4.0));
	double t_3 = t_1 + (b * c);
	double tmp;
	if (t <= -2.2e+216) {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	} else if (t <= -1.85e-20) {
		tmp = t_1 + (-4.0 * (t * a));
	} else if (t <= -1.2e-108) {
		tmp = t_3;
	} else if (t <= -3.3e-216) {
		tmp = t_2;
	} else if (t <= -1.3e-231) {
		tmp = c * (b + (t * (-4.0 * (a / c))));
	} else if (t <= 3.6e-269) {
		tmp = t_3;
	} else if (t <= 1.05e-139) {
		tmp = t_2;
	} else if (t <= 2e+105) {
		tmp = t_3;
	} else {
		tmp = t * (((y * z) * (x * 18.0)) - (a * 4.0));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = j * (k * (-27.0d0))
    t_2 = t_1 + (i * (x * (-4.0d0)))
    t_3 = t_1 + (b * c)
    if (t <= (-2.2d+216)) then
        tmp = t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0))
    else if (t <= (-1.85d-20)) then
        tmp = t_1 + ((-4.0d0) * (t * a))
    else if (t <= (-1.2d-108)) then
        tmp = t_3
    else if (t <= (-3.3d-216)) then
        tmp = t_2
    else if (t <= (-1.3d-231)) then
        tmp = c * (b + (t * ((-4.0d0) * (a / c))))
    else if (t <= 3.6d-269) then
        tmp = t_3
    else if (t <= 1.05d-139) then
        tmp = t_2
    else if (t <= 2d+105) then
        tmp = t_3
    else
        tmp = t * (((y * z) * (x * 18.0d0)) - (a * 4.0d0))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = t_1 + (i * (x * -4.0));
	double t_3 = t_1 + (b * c);
	double tmp;
	if (t <= -2.2e+216) {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	} else if (t <= -1.85e-20) {
		tmp = t_1 + (-4.0 * (t * a));
	} else if (t <= -1.2e-108) {
		tmp = t_3;
	} else if (t <= -3.3e-216) {
		tmp = t_2;
	} else if (t <= -1.3e-231) {
		tmp = c * (b + (t * (-4.0 * (a / c))));
	} else if (t <= 3.6e-269) {
		tmp = t_3;
	} else if (t <= 1.05e-139) {
		tmp = t_2;
	} else if (t <= 2e+105) {
		tmp = t_3;
	} else {
		tmp = t * (((y * z) * (x * 18.0)) - (a * 4.0));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	t_2 = t_1 + (i * (x * -4.0))
	t_3 = t_1 + (b * c)
	tmp = 0
	if t <= -2.2e+216:
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0))
	elif t <= -1.85e-20:
		tmp = t_1 + (-4.0 * (t * a))
	elif t <= -1.2e-108:
		tmp = t_3
	elif t <= -3.3e-216:
		tmp = t_2
	elif t <= -1.3e-231:
		tmp = c * (b + (t * (-4.0 * (a / c))))
	elif t <= 3.6e-269:
		tmp = t_3
	elif t <= 1.05e-139:
		tmp = t_2
	elif t <= 2e+105:
		tmp = t_3
	else:
		tmp = t * (((y * z) * (x * 18.0)) - (a * 4.0))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * -27.0))
	t_2 = Float64(t_1 + Float64(i * Float64(x * -4.0)))
	t_3 = Float64(t_1 + Float64(b * c))
	tmp = 0.0
	if (t <= -2.2e+216)
		tmp = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)));
	elseif (t <= -1.85e-20)
		tmp = Float64(t_1 + Float64(-4.0 * Float64(t * a)));
	elseif (t <= -1.2e-108)
		tmp = t_3;
	elseif (t <= -3.3e-216)
		tmp = t_2;
	elseif (t <= -1.3e-231)
		tmp = Float64(c * Float64(b + Float64(t * Float64(-4.0 * Float64(a / c)))));
	elseif (t <= 3.6e-269)
		tmp = t_3;
	elseif (t <= 1.05e-139)
		tmp = t_2;
	elseif (t <= 2e+105)
		tmp = t_3;
	else
		tmp = Float64(t * Float64(Float64(Float64(y * z) * Float64(x * 18.0)) - Float64(a * 4.0)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * -27.0);
	t_2 = t_1 + (i * (x * -4.0));
	t_3 = t_1 + (b * c);
	tmp = 0.0;
	if (t <= -2.2e+216)
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	elseif (t <= -1.85e-20)
		tmp = t_1 + (-4.0 * (t * a));
	elseif (t <= -1.2e-108)
		tmp = t_3;
	elseif (t <= -3.3e-216)
		tmp = t_2;
	elseif (t <= -1.3e-231)
		tmp = c * (b + (t * (-4.0 * (a / c))));
	elseif (t <= 3.6e-269)
		tmp = t_3;
	elseif (t <= 1.05e-139)
		tmp = t_2;
	elseif (t <= 2e+105)
		tmp = t_3;
	else
		tmp = t * (((y * z) * (x * 18.0)) - (a * 4.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(i * N[(x * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$1 + N[(b * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.2e+216], N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.85e-20], N[(t$95$1 + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.2e-108], t$95$3, If[LessEqual[t, -3.3e-216], t$95$2, If[LessEqual[t, -1.3e-231], N[(c * N[(b + N[(t * N[(-4.0 * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.6e-269], t$95$3, If[LessEqual[t, 1.05e-139], t$95$2, If[LessEqual[t, 2e+105], t$95$3, N[(t * N[(N[(N[(y * z), $MachinePrecision] * N[(x * 18.0), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -2.2e216

   1. Initial program 91.7%

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

   3. Simplified 95.8%

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

   5. Taylor expanded in t around inf 83.8%

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

   if -2.2e216 < t < -1.85e-20

   1. Initial program 78.4%

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

   3. Simplified 83.2%

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

   5. Taylor expanded in a around inf 60.9%

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

      1. *-commutative 60.9%

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

   7. Simplified 60.9%

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

   if -1.85e-20 < t < -1.20000000000000009e-108 or -1.30000000000000001e-231 < t < 3.59999999999999998e-269 or 1.05000000000000004e-139 < t < 1.9999999999999999e105

   1. Initial program 89.8%

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

   3. Simplified 91.2%

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

   5. Taylor expanded in b around inf 61.4%

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

   if -1.20000000000000009e-108 < t < -3.29999999999999969e-216 or 3.59999999999999998e-269 < t < 1.05000000000000004e-139

   1. Initial program 88.1%

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

   3. Simplified 86.6%

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

   5. Taylor expanded in i around inf 69.6%

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

      1. metadata-eval 69.6%

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

      2. distribute-lft-neg-in 69.6%

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

      3. *-commutative 69.6%

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

      4. associate-*r* 69.6%

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

      5. distribute-rgt-neg-in 69.6%

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

      6. distribute-rgt-neg-in 69.6%

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

      7. metadata-eval 69.6%

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

      8. *-commutative 69.6%

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

   7. Simplified 69.6%

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

   if -3.29999999999999969e-216 < t < -1.30000000000000001e-231

   1. Initial program 66.7%

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

   3. Taylor expanded in x around 0 100.0%

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

   4. Taylor expanded in c around inf 100.0%

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

      1. associate-*r/ 100.0%

         \[\leadsto c \cdot \left(b + \color{blue}{\frac{-1 \cdot \left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)}{c}}\right) \]

      2. mul-1-neg 100.0%

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

      3. *-commutative 100.0%

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

      4. *-commutative 100.0%

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

      5. associate-*r* 100.0%

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

      6. *-commutative 100.0%

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

      7. associate-*l* 100.0%

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

      8. *-commutative 100.0%

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

      9. distribute-neg-in 100.0%

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

      10. distribute-rgt-neg-in 100.0%

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

      11. distribute-rgt-neg-in 100.0%

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

      12. metadata-eval 100.0%

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

      13. distribute-rgt-neg-in 100.0%

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

      14. distribute-lft-neg-in 100.0%

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

      15. metadata-eval 100.0%

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

      16. *-commutative 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in t around inf 100.0%

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

      1. associate-*r/ 100.0%

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

      2. *-commutative 100.0%

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

      3. *-commutative 100.0%

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

      4. associate-*r* 100.0%

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

      5. *-commutative 100.0%

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

      6. associate-*r/ 100.0%

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

      7. associate-*r/ 100.0%

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

   9. Simplified 100.0%

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

   if 1.9999999999999999e105 < t

   1. Initial program 80.0%

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

   3. Simplified 92.4%

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

   5. Taylor expanded in t around inf 89.2%

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

      1. pow1 89.2%

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

      2. associate-*r* 86.9%

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

   7. Applied egg-rr 86.9%

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

      1. unpow1 86.9%

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

      2. associate-*r* 89.2%

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

      3. associate-*r* 89.4%

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

   9. Simplified 89.4%

      \[\leadsto t \cdot \left(\color{blue}{\left(18 \cdot x\right) \cdot \left(y \cdot z\right)} - 4 \cdot a\right) \]
3. Recombined 6 regimes into one program.

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{+216}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq -1.85 \cdot 10^{-20}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{-108}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \mathbf{elif}\;t \leq -3.3 \cdot 10^{-216}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + i \cdot \left(x \cdot -4\right)\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{-231}:\\ \;\;\;\;c \cdot \left(b + t \cdot \left(-4 \cdot \frac{a}{c}\right)\right)\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-269}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-139}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + i \cdot \left(x \cdot -4\right)\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+105}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot 18\right) - a \cdot 4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 65.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := k \cdot \left(j \cdot 27\right)\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+131}:\\ \;\;\;\;t\_1 + b \cdot c\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{+80}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - i \cdot 4\right)\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{-8}:\\ \;\;\;\;t\_1 + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;t\_2 \leq 4 \cdot 10^{+175}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 + i \cdot \left(x \cdot -4\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0))) (t_2 (* k (* j 27.0))))
   (if (<= t_2 -2e+131)
     (+ t_1 (* b c))
     (if (<= t_2 -5e+80)
       (* x (- (* 18.0 (* t (* y z))) (* i 4.0)))
       (if (<= t_2 -5e-8)
         (+ t_1 (* -4.0 (* t a)))
         (if (<= t_2 4e+175)
           (- (* b c) (* 4.0 (+ (* x i) (* t a))))
           (+ t_1 (* i (* x -4.0)))))))))

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 = j * (k * -27.0);
	double t_2 = k * (j * 27.0);
	double tmp;
	if (t_2 <= -2e+131) {
		tmp = t_1 + (b * c);
	} else if (t_2 <= -5e+80) {
		tmp = x * ((18.0 * (t * (y * z))) - (i * 4.0));
	} else if (t_2 <= -5e-8) {
		tmp = t_1 + (-4.0 * (t * a));
	} else if (t_2 <= 4e+175) {
		tmp = (b * c) - (4.0 * ((x * i) + (t * a)));
	} else {
		tmp = t_1 + (i * (x * -4.0));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * (k * (-27.0d0))
    t_2 = k * (j * 27.0d0)
    if (t_2 <= (-2d+131)) then
        tmp = t_1 + (b * c)
    else if (t_2 <= (-5d+80)) then
        tmp = x * ((18.0d0 * (t * (y * z))) - (i * 4.0d0))
    else if (t_2 <= (-5d-8)) then
        tmp = t_1 + ((-4.0d0) * (t * a))
    else if (t_2 <= 4d+175) then
        tmp = (b * c) - (4.0d0 * ((x * i) + (t * a)))
    else
        tmp = t_1 + (i * (x * (-4.0d0)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = k * (j * 27.0);
	double tmp;
	if (t_2 <= -2e+131) {
		tmp = t_1 + (b * c);
	} else if (t_2 <= -5e+80) {
		tmp = x * ((18.0 * (t * (y * z))) - (i * 4.0));
	} else if (t_2 <= -5e-8) {
		tmp = t_1 + (-4.0 * (t * a));
	} else if (t_2 <= 4e+175) {
		tmp = (b * c) - (4.0 * ((x * i) + (t * a)));
	} else {
		tmp = t_1 + (i * (x * -4.0));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	t_2 = k * (j * 27.0)
	tmp = 0
	if t_2 <= -2e+131:
		tmp = t_1 + (b * c)
	elif t_2 <= -5e+80:
		tmp = x * ((18.0 * (t * (y * z))) - (i * 4.0))
	elif t_2 <= -5e-8:
		tmp = t_1 + (-4.0 * (t * a))
	elif t_2 <= 4e+175:
		tmp = (b * c) - (4.0 * ((x * i) + (t * a)))
	else:
		tmp = t_1 + (i * (x * -4.0))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * -27.0))
	t_2 = Float64(k * Float64(j * 27.0))
	tmp = 0.0
	if (t_2 <= -2e+131)
		tmp = Float64(t_1 + Float64(b * c));
	elseif (t_2 <= -5e+80)
		tmp = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(i * 4.0)));
	elseif (t_2 <= -5e-8)
		tmp = Float64(t_1 + Float64(-4.0 * Float64(t * a)));
	elseif (t_2 <= 4e+175)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(Float64(x * i) + Float64(t * a))));
	else
		tmp = Float64(t_1 + Float64(i * Float64(x * -4.0)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * -27.0);
	t_2 = k * (j * 27.0);
	tmp = 0.0;
	if (t_2 <= -2e+131)
		tmp = t_1 + (b * c);
	elseif (t_2 <= -5e+80)
		tmp = x * ((18.0 * (t * (y * z))) - (i * 4.0));
	elseif (t_2 <= -5e-8)
		tmp = t_1 + (-4.0 * (t * a));
	elseif (t_2 <= 4e+175)
		tmp = (b * c) - (4.0 * ((x * i) + (t * a)));
	else
		tmp = t_1 + (i * (x * -4.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+131], N[(t$95$1 + N[(b * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -5e+80], N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -5e-8], N[(t$95$1 + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 4e+175], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(N[(x * i), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(i * N[(x * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -1.9999999999999998e131

   1. Initial program 90.1%

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

   3. Simplified 90.1%

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

   5. Taylor expanded in b around inf 75.4%

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

   if -1.9999999999999998e131 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -4.99999999999999961e80

   1. Initial program 88.7%

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

   3. Simplified 88.7%

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

   5. Taylor expanded in x around inf 84.1%

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

   if -4.99999999999999961e80 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -4.9999999999999998e-8

   1. Initial program 88.0%

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

   3. Simplified 76.5%

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

   5. Taylor expanded in a around inf 65.5%

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

      1. *-commutative 65.5%

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

   7. Simplified 65.5%

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

   if -4.9999999999999998e-8 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 3.9999999999999997e175

   1. Initial program 87.1%

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

      1. pow1 87.1%

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

      2. associate-*l* 84.2%

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

      3. *-commutative 84.2%

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

   4. Applied egg-rr 84.2%

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

      1. unpow1 84.2%

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

      2. associate-*l* 86.4%

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

      3. *-commutative 86.4%

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

   6. Simplified 86.4%

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

   7. Taylor expanded in y around 0 79.3%

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

      1. distribute-lft-out 79.3%

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

      2. *-commutative 79.3%

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

      3. *-commutative 79.3%

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

   9. Simplified 79.3%

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

   10. Taylor expanded in j around 0 77.3%

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

   if 3.9999999999999997e175 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 70.9%

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

   3. Simplified 71.3%

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

   5. Taylor expanded in i around inf 71.1%

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

      1. metadata-eval 71.1%

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

      2. distribute-lft-neg-in 71.1%

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

      3. *-commutative 71.1%

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

      4. associate-*r* 71.1%

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

      5. distribute-rgt-neg-in 71.1%

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

      6. distribute-rgt-neg-in 71.1%

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

      7. metadata-eval 71.1%

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

      8. *-commutative 71.1%

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

   7. Simplified 71.1%

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

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \cdot \left(j \cdot 27\right) \leq -2 \cdot 10^{+131}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq -5 \cdot 10^{+80}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - i \cdot 4\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq -5 \cdot 10^{-8}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 4 \cdot 10^{+175}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + i \cdot \left(x \cdot -4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 66.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := k \cdot \left(j \cdot 27\right)\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+131}:\\ \;\;\;\;t\_1 + 18 \cdot \left(\left(y \cdot z\right) \cdot \left(t \cdot x\right)\right)\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{+80}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - i \cdot 4\right)\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{-8}:\\ \;\;\;\;t\_1 + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;t\_2 \leq 4 \cdot 10^{+175}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 + i \cdot \left(x \cdot -4\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0))) (t_2 (* k (* j 27.0))))
   (if (<= t_2 -2e+131)
     (+ t_1 (* 18.0 (* (* y z) (* t x))))
     (if (<= t_2 -5e+80)
       (* x (- (* 18.0 (* t (* y z))) (* i 4.0)))
       (if (<= t_2 -5e-8)
         (+ t_1 (* -4.0 (* t a)))
         (if (<= t_2 4e+175)
           (- (* b c) (* 4.0 (+ (* x i) (* t a))))
           (+ t_1 (* i (* x -4.0)))))))))

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 = j * (k * -27.0);
	double t_2 = k * (j * 27.0);
	double tmp;
	if (t_2 <= -2e+131) {
		tmp = t_1 + (18.0 * ((y * z) * (t * x)));
	} else if (t_2 <= -5e+80) {
		tmp = x * ((18.0 * (t * (y * z))) - (i * 4.0));
	} else if (t_2 <= -5e-8) {
		tmp = t_1 + (-4.0 * (t * a));
	} else if (t_2 <= 4e+175) {
		tmp = (b * c) - (4.0 * ((x * i) + (t * a)));
	} else {
		tmp = t_1 + (i * (x * -4.0));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * (k * (-27.0d0))
    t_2 = k * (j * 27.0d0)
    if (t_2 <= (-2d+131)) then
        tmp = t_1 + (18.0d0 * ((y * z) * (t * x)))
    else if (t_2 <= (-5d+80)) then
        tmp = x * ((18.0d0 * (t * (y * z))) - (i * 4.0d0))
    else if (t_2 <= (-5d-8)) then
        tmp = t_1 + ((-4.0d0) * (t * a))
    else if (t_2 <= 4d+175) then
        tmp = (b * c) - (4.0d0 * ((x * i) + (t * a)))
    else
        tmp = t_1 + (i * (x * (-4.0d0)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = k * (j * 27.0);
	double tmp;
	if (t_2 <= -2e+131) {
		tmp = t_1 + (18.0 * ((y * z) * (t * x)));
	} else if (t_2 <= -5e+80) {
		tmp = x * ((18.0 * (t * (y * z))) - (i * 4.0));
	} else if (t_2 <= -5e-8) {
		tmp = t_1 + (-4.0 * (t * a));
	} else if (t_2 <= 4e+175) {
		tmp = (b * c) - (4.0 * ((x * i) + (t * a)));
	} else {
		tmp = t_1 + (i * (x * -4.0));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	t_2 = k * (j * 27.0)
	tmp = 0
	if t_2 <= -2e+131:
		tmp = t_1 + (18.0 * ((y * z) * (t * x)))
	elif t_2 <= -5e+80:
		tmp = x * ((18.0 * (t * (y * z))) - (i * 4.0))
	elif t_2 <= -5e-8:
		tmp = t_1 + (-4.0 * (t * a))
	elif t_2 <= 4e+175:
		tmp = (b * c) - (4.0 * ((x * i) + (t * a)))
	else:
		tmp = t_1 + (i * (x * -4.0))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * -27.0))
	t_2 = Float64(k * Float64(j * 27.0))
	tmp = 0.0
	if (t_2 <= -2e+131)
		tmp = Float64(t_1 + Float64(18.0 * Float64(Float64(y * z) * Float64(t * x))));
	elseif (t_2 <= -5e+80)
		tmp = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(i * 4.0)));
	elseif (t_2 <= -5e-8)
		tmp = Float64(t_1 + Float64(-4.0 * Float64(t * a)));
	elseif (t_2 <= 4e+175)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(Float64(x * i) + Float64(t * a))));
	else
		tmp = Float64(t_1 + Float64(i * Float64(x * -4.0)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * -27.0);
	t_2 = k * (j * 27.0);
	tmp = 0.0;
	if (t_2 <= -2e+131)
		tmp = t_1 + (18.0 * ((y * z) * (t * x)));
	elseif (t_2 <= -5e+80)
		tmp = x * ((18.0 * (t * (y * z))) - (i * 4.0));
	elseif (t_2 <= -5e-8)
		tmp = t_1 + (-4.0 * (t * a));
	elseif (t_2 <= 4e+175)
		tmp = (b * c) - (4.0 * ((x * i) + (t * a)));
	else
		tmp = t_1 + (i * (x * -4.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+131], N[(t$95$1 + N[(18.0 * N[(N[(y * z), $MachinePrecision] * N[(t * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -5e+80], N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -5e-8], N[(t$95$1 + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 4e+175], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(N[(x * i), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(i * N[(x * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -1.9999999999999998e131

   1. Initial program 90.1%

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

   3. Simplified 90.1%

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

   5. Taylor expanded in y around inf 77.9%

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

      1. associate-*r* 76.2%

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

   7. Simplified 76.2%

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

   if -1.9999999999999998e131 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -4.99999999999999961e80

   1. Initial program 88.7%

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

   3. Simplified 88.7%

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

   5. Taylor expanded in x around inf 84.1%

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

   if -4.99999999999999961e80 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -4.9999999999999998e-8

   1. Initial program 88.0%

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

   3. Simplified 76.5%

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

   5. Taylor expanded in a around inf 65.5%

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

      1. *-commutative 65.5%

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

   7. Simplified 65.5%

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

   if -4.9999999999999998e-8 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 3.9999999999999997e175

   1. Initial program 87.1%

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

      1. pow1 87.1%

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

      2. associate-*l* 84.2%

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

      3. *-commutative 84.2%

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

   4. Applied egg-rr 84.2%

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

      1. unpow1 84.2%

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

      2. associate-*l* 86.4%

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

      3. *-commutative 86.4%

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

   6. Simplified 86.4%

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

   7. Taylor expanded in y around 0 79.3%

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

      1. distribute-lft-out 79.3%

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

      2. *-commutative 79.3%

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

      3. *-commutative 79.3%

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

   9. Simplified 79.3%

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

   10. Taylor expanded in j around 0 77.3%

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

   if 3.9999999999999997e175 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 70.9%

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

   3. Simplified 71.3%

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

   5. Taylor expanded in i around inf 71.1%

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

      1. metadata-eval 71.1%

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

      2. distribute-lft-neg-in 71.1%

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

      3. *-commutative 71.1%

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

      4. associate-*r* 71.1%

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

      5. distribute-rgt-neg-in 71.1%

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

      6. distribute-rgt-neg-in 71.1%

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

      7. metadata-eval 71.1%

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

      8. *-commutative 71.1%

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

   7. Simplified 71.1%

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

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \cdot \left(j \cdot 27\right) \leq -2 \cdot 10^{+131}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + 18 \cdot \left(\left(y \cdot z\right) \cdot \left(t \cdot x\right)\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq -5 \cdot 10^{+80}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - i \cdot 4\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq -5 \cdot 10^{-8}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 4 \cdot 10^{+175}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + i \cdot \left(x \cdot -4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 36.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := -27 \cdot \left(j \cdot k\right)\\ t_2 := -4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;b \cdot c \leq -6.2 \cdot 10^{+171}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -7.8 \cdot 10^{-8}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq -1.35 \cdot 10^{-129}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \cdot c \leq 1.25 \cdot 10^{-228}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq 1.6 \cdot 10^{-87}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \cdot c \leq 3.2 \cdot 10^{+112}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* -27.0 (* j k))) (t_2 (* -4.0 (* x i))))
   (if (<= (* b c) -6.2e+171)
     (* b c)
     (if (<= (* b c) -7.8e-8)
       t_1
       (if (<= (* b c) -1.35e-129)
         t_2
         (if (<= (* b c) 1.25e-228)
           t_1
           (if (<= (* b c) 1.6e-87)
             t_2
             (if (<= (* b c) 3.2e+112) t_1 (* b c)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -27.0 * (j * k);
	double t_2 = -4.0 * (x * i);
	double tmp;
	if ((b * c) <= -6.2e+171) {
		tmp = b * c;
	} else if ((b * c) <= -7.8e-8) {
		tmp = t_1;
	} else if ((b * c) <= -1.35e-129) {
		tmp = t_2;
	} else if ((b * c) <= 1.25e-228) {
		tmp = t_1;
	} else if ((b * c) <= 1.6e-87) {
		tmp = t_2;
	} else if ((b * c) <= 3.2e+112) {
		tmp = t_1;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (-27.0d0) * (j * k)
    t_2 = (-4.0d0) * (x * i)
    if ((b * c) <= (-6.2d+171)) then
        tmp = b * c
    else if ((b * c) <= (-7.8d-8)) then
        tmp = t_1
    else if ((b * c) <= (-1.35d-129)) then
        tmp = t_2
    else if ((b * c) <= 1.25d-228) then
        tmp = t_1
    else if ((b * c) <= 1.6d-87) then
        tmp = t_2
    else if ((b * c) <= 3.2d+112) then
        tmp = t_1
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -27.0 * (j * k);
	double t_2 = -4.0 * (x * i);
	double tmp;
	if ((b * c) <= -6.2e+171) {
		tmp = b * c;
	} else if ((b * c) <= -7.8e-8) {
		tmp = t_1;
	} else if ((b * c) <= -1.35e-129) {
		tmp = t_2;
	} else if ((b * c) <= 1.25e-228) {
		tmp = t_1;
	} else if ((b * c) <= 1.6e-87) {
		tmp = t_2;
	} else if ((b * c) <= 3.2e+112) {
		tmp = t_1;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = -27.0 * (j * k)
	t_2 = -4.0 * (x * i)
	tmp = 0
	if (b * c) <= -6.2e+171:
		tmp = b * c
	elif (b * c) <= -7.8e-8:
		tmp = t_1
	elif (b * c) <= -1.35e-129:
		tmp = t_2
	elif (b * c) <= 1.25e-228:
		tmp = t_1
	elif (b * c) <= 1.6e-87:
		tmp = t_2
	elif (b * c) <= 3.2e+112:
		tmp = t_1
	else:
		tmp = b * c
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(-27.0 * Float64(j * k))
	t_2 = Float64(-4.0 * Float64(x * i))
	tmp = 0.0
	if (Float64(b * c) <= -6.2e+171)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -7.8e-8)
		tmp = t_1;
	elseif (Float64(b * c) <= -1.35e-129)
		tmp = t_2;
	elseif (Float64(b * c) <= 1.25e-228)
		tmp = t_1;
	elseif (Float64(b * c) <= 1.6e-87)
		tmp = t_2;
	elseif (Float64(b * c) <= 3.2e+112)
		tmp = t_1;
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = -27.0 * (j * k);
	t_2 = -4.0 * (x * i);
	tmp = 0.0;
	if ((b * c) <= -6.2e+171)
		tmp = b * c;
	elseif ((b * c) <= -7.8e-8)
		tmp = t_1;
	elseif ((b * c) <= -1.35e-129)
		tmp = t_2;
	elseif ((b * c) <= 1.25e-228)
		tmp = t_1;
	elseif ((b * c) <= 1.6e-87)
		tmp = t_2;
	elseif ((b * c) <= 3.2e+112)
		tmp = t_1;
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -6.2e+171], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -7.8e-8], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], -1.35e-129], t$95$2, If[LessEqual[N[(b * c), $MachinePrecision], 1.25e-228], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 1.6e-87], t$95$2, If[LessEqual[N[(b * c), $MachinePrecision], 3.2e+112], t$95$1, N[(b * c), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -6.1999999999999998e171 or 3.19999999999999986e112 < (*.f64 b c)

   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. pow1 80.7%

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

      2. associate-*l* 75.3%

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

      3. *-commutative 75.3%

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

   4. Applied egg-rr 75.3%

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

      1. unpow1 75.3%

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

      2. associate-*l* 75.3%

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

      3. *-commutative 75.3%

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

   6. Simplified 75.3%

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

   7. Taylor expanded in y around 0 79.7%

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

      1. distribute-lft-out 79.7%

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

      2. *-commutative 79.7%

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

      3. *-commutative 79.7%

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

   9. Simplified 79.7%

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

   10. Taylor expanded in b around inf 59.0%

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

   if -6.1999999999999998e171 < (*.f64 b c) < -7.7999999999999997e-8 or -1.35e-129 < (*.f64 b c) < 1.24999999999999993e-228 or 1.59999999999999989e-87 < (*.f64 b c) < 3.19999999999999986e112

   1. Initial program 88.8%

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

   3. Simplified 90.9%

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

   5. Taylor expanded in j around inf 40.1%

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

   if -7.7999999999999997e-8 < (*.f64 b c) < -1.35e-129 or 1.24999999999999993e-228 < (*.f64 b c) < 1.59999999999999989e-87

   1. Initial program 85.1%

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

      1. pow1 85.1%

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

      2. associate-*l* 87.3%

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

      3. *-commutative 87.3%

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

   4. Applied egg-rr 87.3%

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

      1. unpow1 87.3%

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

      2. associate-*l* 89.9%

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

      3. *-commutative 89.9%

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

   6. Simplified 89.9%

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

   7. Taylor expanded in y around 0 75.3%

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

      1. distribute-lft-out 75.3%

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

      2. *-commutative 75.3%

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

      3. *-commutative 75.3%

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

   9. Simplified 75.3%

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

   10. Taylor expanded in x around inf 38.9%

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

4. Final simplification 45.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -6.2 \cdot 10^{+171}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -7.8 \cdot 10^{-8}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq -1.35 \cdot 10^{-129}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 1.25 \cdot 10^{-228}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq 1.6 \cdot 10^{-87}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 3.2 \cdot 10^{+112}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 36.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := -4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;b \cdot c \leq -7.8 \cdot 10^{+172}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -7.8 \cdot 10^{-8}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq -8 \cdot 10^{-128}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \cdot c \leq 10^{-227}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq 6.4 \cdot 10^{-89}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \cdot c \leq 3.7 \cdot 10^{+107}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0))) (t_2 (* -4.0 (* x i))))
   (if (<= (* b c) -7.8e+172)
     (* b c)
     (if (<= (* b c) -7.8e-8)
       (* -27.0 (* j k))
       (if (<= (* b c) -8e-128)
         t_2
         (if (<= (* b c) 1e-227)
           t_1
           (if (<= (* b c) 6.4e-89)
             t_2
             (if (<= (* b c) 3.7e+107) t_1 (* b c)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = -4.0 * (x * i);
	double tmp;
	if ((b * c) <= -7.8e+172) {
		tmp = b * c;
	} else if ((b * c) <= -7.8e-8) {
		tmp = -27.0 * (j * k);
	} else if ((b * c) <= -8e-128) {
		tmp = t_2;
	} else if ((b * c) <= 1e-227) {
		tmp = t_1;
	} else if ((b * c) <= 6.4e-89) {
		tmp = t_2;
	} else if ((b * c) <= 3.7e+107) {
		tmp = t_1;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * (k * (-27.0d0))
    t_2 = (-4.0d0) * (x * i)
    if ((b * c) <= (-7.8d+172)) then
        tmp = b * c
    else if ((b * c) <= (-7.8d-8)) then
        tmp = (-27.0d0) * (j * k)
    else if ((b * c) <= (-8d-128)) then
        tmp = t_2
    else if ((b * c) <= 1d-227) then
        tmp = t_1
    else if ((b * c) <= 6.4d-89) then
        tmp = t_2
    else if ((b * c) <= 3.7d+107) then
        tmp = t_1
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = -4.0 * (x * i);
	double tmp;
	if ((b * c) <= -7.8e+172) {
		tmp = b * c;
	} else if ((b * c) <= -7.8e-8) {
		tmp = -27.0 * (j * k);
	} else if ((b * c) <= -8e-128) {
		tmp = t_2;
	} else if ((b * c) <= 1e-227) {
		tmp = t_1;
	} else if ((b * c) <= 6.4e-89) {
		tmp = t_2;
	} else if ((b * c) <= 3.7e+107) {
		tmp = t_1;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	t_2 = -4.0 * (x * i)
	tmp = 0
	if (b * c) <= -7.8e+172:
		tmp = b * c
	elif (b * c) <= -7.8e-8:
		tmp = -27.0 * (j * k)
	elif (b * c) <= -8e-128:
		tmp = t_2
	elif (b * c) <= 1e-227:
		tmp = t_1
	elif (b * c) <= 6.4e-89:
		tmp = t_2
	elif (b * c) <= 3.7e+107:
		tmp = t_1
	else:
		tmp = b * c
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * -27.0))
	t_2 = Float64(-4.0 * Float64(x * i))
	tmp = 0.0
	if (Float64(b * c) <= -7.8e+172)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -7.8e-8)
		tmp = Float64(-27.0 * Float64(j * k));
	elseif (Float64(b * c) <= -8e-128)
		tmp = t_2;
	elseif (Float64(b * c) <= 1e-227)
		tmp = t_1;
	elseif (Float64(b * c) <= 6.4e-89)
		tmp = t_2;
	elseif (Float64(b * c) <= 3.7e+107)
		tmp = t_1;
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * -27.0);
	t_2 = -4.0 * (x * i);
	tmp = 0.0;
	if ((b * c) <= -7.8e+172)
		tmp = b * c;
	elseif ((b * c) <= -7.8e-8)
		tmp = -27.0 * (j * k);
	elseif ((b * c) <= -8e-128)
		tmp = t_2;
	elseif ((b * c) <= 1e-227)
		tmp = t_1;
	elseif ((b * c) <= 6.4e-89)
		tmp = t_2;
	elseif ((b * c) <= 3.7e+107)
		tmp = t_1;
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -7.8e+172], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -7.8e-8], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -8e-128], t$95$2, If[LessEqual[N[(b * c), $MachinePrecision], 1e-227], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 6.4e-89], t$95$2, If[LessEqual[N[(b * c), $MachinePrecision], 3.7e+107], t$95$1, N[(b * c), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 b c) < -7.79999999999999934e172 or 3.7e107 < (*.f64 b c)

   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. pow1 80.7%

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

      2. associate-*l* 75.3%

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

      3. *-commutative 75.3%

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

   4. Applied egg-rr 75.3%

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

      1. unpow1 75.3%

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

      2. associate-*l* 75.3%

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

      3. *-commutative 75.3%

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

   6. Simplified 75.3%

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

   7. Taylor expanded in y around 0 79.7%

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

      1. distribute-lft-out 79.7%

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

      2. *-commutative 79.7%

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

      3. *-commutative 79.7%

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

   9. Simplified 79.7%

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

   10. Taylor expanded in b around inf 59.0%

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

   if -7.79999999999999934e172 < (*.f64 b c) < -7.7999999999999997e-8

   1. Initial program 88.3%

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

   3. Simplified 91.4%

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

   5. Taylor expanded in j around inf 45.2%

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

   if -7.7999999999999997e-8 < (*.f64 b c) < -8.00000000000000043e-128 or 9.99999999999999945e-228 < (*.f64 b c) < 6.39999999999999997e-89

   1. Initial program 85.1%

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

      1. pow1 85.1%

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

      2. associate-*l* 87.3%

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

      3. *-commutative 87.3%

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

   4. Applied egg-rr 87.3%

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

      1. unpow1 87.3%

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

      2. associate-*l* 89.9%

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

      3. *-commutative 89.9%

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

   6. Simplified 89.9%

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

   7. Taylor expanded in y around 0 75.3%

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

      1. distribute-lft-out 75.3%

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

      2. *-commutative 75.3%

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

      3. *-commutative 75.3%

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

   9. Simplified 75.3%

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

   10. Taylor expanded in x around inf 38.9%

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

   if -8.00000000000000043e-128 < (*.f64 b c) < 9.99999999999999945e-228 or 6.39999999999999997e-89 < (*.f64 b c) < 3.7e107

   1. Initial program 89.0%

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

      1. pow1 89.0%

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

      2. associate-*l* 85.4%

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

      3. *-commutative 85.4%

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

   4. Applied egg-rr 85.4%

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

      1. unpow1 85.4%

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

      2. associate-*l* 89.1%

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

      3. *-commutative 89.1%

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

   6. Simplified 89.1%

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

   7. Taylor expanded in j around inf 38.5%

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

      1. *-commutative 38.5%

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

      2. associate-*r* 38.5%

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

   9. Simplified 38.5%

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

4. Final simplification 45.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -7.8 \cdot 10^{+172}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -7.8 \cdot 10^{-8}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq -8 \cdot 10^{-128}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 10^{-227}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 6.4 \cdot 10^{-89}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 3.7 \cdot 10^{+107}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 36.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := -4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;b \cdot c \leq -1.06 \cdot 10^{+176}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -9.5 \cdot 10^{-8}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq -3.6 \cdot 10^{-129}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \cdot c \leq 1.06 \cdot 10^{-226}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq 10^{-88}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \cdot c \leq 1.85 \cdot 10^{+114}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0))) (t_2 (* -4.0 (* x i))))
   (if (<= (* b c) -1.06e+176)
     (* b c)
     (if (<= (* b c) -9.5e-8)
       (* k (* j -27.0))
       (if (<= (* b c) -3.6e-129)
         t_2
         (if (<= (* b c) 1.06e-226)
           t_1
           (if (<= (* b c) 1e-88)
             t_2
             (if (<= (* b c) 1.85e+114) t_1 (* b c)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = -4.0 * (x * i);
	double tmp;
	if ((b * c) <= -1.06e+176) {
		tmp = b * c;
	} else if ((b * c) <= -9.5e-8) {
		tmp = k * (j * -27.0);
	} else if ((b * c) <= -3.6e-129) {
		tmp = t_2;
	} else if ((b * c) <= 1.06e-226) {
		tmp = t_1;
	} else if ((b * c) <= 1e-88) {
		tmp = t_2;
	} else if ((b * c) <= 1.85e+114) {
		tmp = t_1;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * (k * (-27.0d0))
    t_2 = (-4.0d0) * (x * i)
    if ((b * c) <= (-1.06d+176)) then
        tmp = b * c
    else if ((b * c) <= (-9.5d-8)) then
        tmp = k * (j * (-27.0d0))
    else if ((b * c) <= (-3.6d-129)) then
        tmp = t_2
    else if ((b * c) <= 1.06d-226) then
        tmp = t_1
    else if ((b * c) <= 1d-88) then
        tmp = t_2
    else if ((b * c) <= 1.85d+114) then
        tmp = t_1
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = -4.0 * (x * i);
	double tmp;
	if ((b * c) <= -1.06e+176) {
		tmp = b * c;
	} else if ((b * c) <= -9.5e-8) {
		tmp = k * (j * -27.0);
	} else if ((b * c) <= -3.6e-129) {
		tmp = t_2;
	} else if ((b * c) <= 1.06e-226) {
		tmp = t_1;
	} else if ((b * c) <= 1e-88) {
		tmp = t_2;
	} else if ((b * c) <= 1.85e+114) {
		tmp = t_1;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	t_2 = -4.0 * (x * i)
	tmp = 0
	if (b * c) <= -1.06e+176:
		tmp = b * c
	elif (b * c) <= -9.5e-8:
		tmp = k * (j * -27.0)
	elif (b * c) <= -3.6e-129:
		tmp = t_2
	elif (b * c) <= 1.06e-226:
		tmp = t_1
	elif (b * c) <= 1e-88:
		tmp = t_2
	elif (b * c) <= 1.85e+114:
		tmp = t_1
	else:
		tmp = b * c
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * -27.0))
	t_2 = Float64(-4.0 * Float64(x * i))
	tmp = 0.0
	if (Float64(b * c) <= -1.06e+176)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -9.5e-8)
		tmp = Float64(k * Float64(j * -27.0));
	elseif (Float64(b * c) <= -3.6e-129)
		tmp = t_2;
	elseif (Float64(b * c) <= 1.06e-226)
		tmp = t_1;
	elseif (Float64(b * c) <= 1e-88)
		tmp = t_2;
	elseif (Float64(b * c) <= 1.85e+114)
		tmp = t_1;
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * -27.0);
	t_2 = -4.0 * (x * i);
	tmp = 0.0;
	if ((b * c) <= -1.06e+176)
		tmp = b * c;
	elseif ((b * c) <= -9.5e-8)
		tmp = k * (j * -27.0);
	elseif ((b * c) <= -3.6e-129)
		tmp = t_2;
	elseif ((b * c) <= 1.06e-226)
		tmp = t_1;
	elseif ((b * c) <= 1e-88)
		tmp = t_2;
	elseif ((b * c) <= 1.85e+114)
		tmp = t_1;
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -1.06e+176], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -9.5e-8], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -3.6e-129], t$95$2, If[LessEqual[N[(b * c), $MachinePrecision], 1.06e-226], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 1e-88], t$95$2, If[LessEqual[N[(b * c), $MachinePrecision], 1.85e+114], t$95$1, N[(b * c), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 b c) < -1.06000000000000002e176 or 1.85e114 < (*.f64 b c)

   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. pow1 80.7%

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

      2. associate-*l* 75.3%

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

      3. *-commutative 75.3%

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

   4. Applied egg-rr 75.3%

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

      1. unpow1 75.3%

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

      2. associate-*l* 75.3%

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

      3. *-commutative 75.3%

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

   6. Simplified 75.3%

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

   7. Taylor expanded in y around 0 79.7%

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

      1. distribute-lft-out 79.7%

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

      2. *-commutative 79.7%

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

      3. *-commutative 79.7%

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

   9. Simplified 79.7%

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

   10. Taylor expanded in b around inf 59.0%

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

   if -1.06000000000000002e176 < (*.f64 b c) < -9.50000000000000036e-8

   1. Initial program 88.3%

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

   3. Simplified 91.4%

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

   5. Taylor expanded in j around inf 45.2%

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

      1. associate-*r* 45.2%

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

      2. *-commutative 45.2%

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

   7. Simplified 45.2%

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

   if -9.50000000000000036e-8 < (*.f64 b c) < -3.6e-129 or 1.0599999999999999e-226 < (*.f64 b c) < 9.99999999999999934e-89

   1. Initial program 85.1%

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

      1. pow1 85.1%

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

      2. associate-*l* 87.3%

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

      3. *-commutative 87.3%

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

   4. Applied egg-rr 87.3%

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

      1. unpow1 87.3%

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

      2. associate-*l* 89.9%

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

      3. *-commutative 89.9%

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

   6. Simplified 89.9%

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

   7. Taylor expanded in y around 0 75.3%

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

      1. distribute-lft-out 75.3%

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

      2. *-commutative 75.3%

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

      3. *-commutative 75.3%

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

   9. Simplified 75.3%

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

   10. Taylor expanded in x around inf 38.9%

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

   if -3.6e-129 < (*.f64 b c) < 1.0599999999999999e-226 or 9.99999999999999934e-89 < (*.f64 b c) < 1.85e114

   1. Initial program 89.0%

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

      1. pow1 89.0%

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

      2. associate-*l* 85.4%

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

      3. *-commutative 85.4%

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

   4. Applied egg-rr 85.4%

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

      1. unpow1 85.4%

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

      2. associate-*l* 89.1%

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

      3. *-commutative 89.1%

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

   6. Simplified 89.1%

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

   7. Taylor expanded in j around inf 38.5%

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

      1. *-commutative 38.5%

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

      2. associate-*r* 38.5%

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

   9. Simplified 38.5%

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

4. Final simplification 45.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.06 \cdot 10^{+176}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -9.5 \cdot 10^{-8}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq -3.6 \cdot 10^{-129}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 1.06 \cdot 10^{-226}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 10^{-88}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 1.85 \cdot 10^{+114}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 37.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;b \cdot c \leq -1.15 \cdot 10^{+172}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -2.35 \cdot 10^{-7}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq -8.5 \cdot 10^{-220}:\\ \;\;\;\;18 \cdot \left(z \cdot \left(y \cdot \left(t \cdot x\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 5.5 \cdot 10^{-226}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq 5.5 \cdot 10^{-89}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 2.6 \cdot 10^{+105}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0))))
   (if (<= (* b c) -1.15e+172)
     (* b c)
     (if (<= (* b c) -2.35e-7)
       (* k (* j -27.0))
       (if (<= (* b c) -8.5e-220)
         (* 18.0 (* z (* y (* t x))))
         (if (<= (* b c) 5.5e-226)
           t_1
           (if (<= (* b c) 5.5e-89)
             (* -4.0 (* x i))
             (if (<= (* b c) 2.6e+105) t_1 (* b c)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double tmp;
	if ((b * c) <= -1.15e+172) {
		tmp = b * c;
	} else if ((b * c) <= -2.35e-7) {
		tmp = k * (j * -27.0);
	} else if ((b * c) <= -8.5e-220) {
		tmp = 18.0 * (z * (y * (t * x)));
	} else if ((b * c) <= 5.5e-226) {
		tmp = t_1;
	} else if ((b * c) <= 5.5e-89) {
		tmp = -4.0 * (x * i);
	} else if ((b * c) <= 2.6e+105) {
		tmp = t_1;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * (k * (-27.0d0))
    if ((b * c) <= (-1.15d+172)) then
        tmp = b * c
    else if ((b * c) <= (-2.35d-7)) then
        tmp = k * (j * (-27.0d0))
    else if ((b * c) <= (-8.5d-220)) then
        tmp = 18.0d0 * (z * (y * (t * x)))
    else if ((b * c) <= 5.5d-226) then
        tmp = t_1
    else if ((b * c) <= 5.5d-89) then
        tmp = (-4.0d0) * (x * i)
    else if ((b * c) <= 2.6d+105) then
        tmp = t_1
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double tmp;
	if ((b * c) <= -1.15e+172) {
		tmp = b * c;
	} else if ((b * c) <= -2.35e-7) {
		tmp = k * (j * -27.0);
	} else if ((b * c) <= -8.5e-220) {
		tmp = 18.0 * (z * (y * (t * x)));
	} else if ((b * c) <= 5.5e-226) {
		tmp = t_1;
	} else if ((b * c) <= 5.5e-89) {
		tmp = -4.0 * (x * i);
	} else if ((b * c) <= 2.6e+105) {
		tmp = t_1;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	tmp = 0
	if (b * c) <= -1.15e+172:
		tmp = b * c
	elif (b * c) <= -2.35e-7:
		tmp = k * (j * -27.0)
	elif (b * c) <= -8.5e-220:
		tmp = 18.0 * (z * (y * (t * x)))
	elif (b * c) <= 5.5e-226:
		tmp = t_1
	elif (b * c) <= 5.5e-89:
		tmp = -4.0 * (x * i)
	elif (b * c) <= 2.6e+105:
		tmp = t_1
	else:
		tmp = b * c
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * -27.0))
	tmp = 0.0
	if (Float64(b * c) <= -1.15e+172)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -2.35e-7)
		tmp = Float64(k * Float64(j * -27.0));
	elseif (Float64(b * c) <= -8.5e-220)
		tmp = Float64(18.0 * Float64(z * Float64(y * Float64(t * x))));
	elseif (Float64(b * c) <= 5.5e-226)
		tmp = t_1;
	elseif (Float64(b * c) <= 5.5e-89)
		tmp = Float64(-4.0 * Float64(x * i));
	elseif (Float64(b * c) <= 2.6e+105)
		tmp = t_1;
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * -27.0);
	tmp = 0.0;
	if ((b * c) <= -1.15e+172)
		tmp = b * c;
	elseif ((b * c) <= -2.35e-7)
		tmp = k * (j * -27.0);
	elseif ((b * c) <= -8.5e-220)
		tmp = 18.0 * (z * (y * (t * x)));
	elseif ((b * c) <= 5.5e-226)
		tmp = t_1;
	elseif ((b * c) <= 5.5e-89)
		tmp = -4.0 * (x * i);
	elseif ((b * c) <= 2.6e+105)
		tmp = t_1;
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -1.15e+172], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -2.35e-7], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -8.5e-220], N[(18.0 * N[(z * N[(y * N[(t * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 5.5e-226], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 5.5e-89], N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 2.6e+105], t$95$1, N[(b * c), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 b c) < -1.15e172 or 2.6000000000000002e105 < (*.f64 b c)

   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. pow1 80.7%

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

      2. associate-*l* 75.3%

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

      3. *-commutative 75.3%

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

   4. Applied egg-rr 75.3%

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

      1. unpow1 75.3%

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

      2. associate-*l* 75.3%

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

      3. *-commutative 75.3%

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

   6. Simplified 75.3%

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

   7. Taylor expanded in y around 0 79.7%

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

      1. distribute-lft-out 79.7%

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

      2. *-commutative 79.7%

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

      3. *-commutative 79.7%

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

   9. Simplified 79.7%

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

   10. Taylor expanded in b around inf 59.0%

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

   if -1.15e172 < (*.f64 b c) < -2.35e-7

   1. Initial program 88.3%

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

   3. Simplified 91.4%

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

   5. Taylor expanded in j around inf 45.2%

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

      1. associate-*r* 45.2%

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

      2. *-commutative 45.2%

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

   7. Simplified 45.2%

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

   if -2.35e-7 < (*.f64 b c) < -8.4999999999999996e-220

   1. Initial program 89.4%

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

   3. Simplified 92.1%

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

   5. Taylor expanded in t around inf 55.5%

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

   6. Taylor expanded in x around inf 30.5%

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

      1. associate-*r* 33.1%

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

      2. associate-*r* 33.1%

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

      3. associate-*r* 38.2%

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

   8. Simplified 38.2%

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

   if -8.4999999999999996e-220 < (*.f64 b c) < 5.5e-226 or 5.50000000000000012e-89 < (*.f64 b c) < 2.6000000000000002e105

   1. Initial program 89.5%

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

      1. pow1 89.5%

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

      2. associate-*l* 86.4%

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

      3. *-commutative 86.4%

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

   4. Applied egg-rr 86.4%

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

      1. unpow1 86.4%

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

      2. associate-*l* 89.6%

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

      3. *-commutative 89.6%

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

   6. Simplified 89.6%

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

   7. Taylor expanded in j around inf 39.7%

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

      1. *-commutative 39.7%

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

      2. associate-*r* 39.7%

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

   9. Simplified 39.7%

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

   if 5.5e-226 < (*.f64 b c) < 5.50000000000000012e-89

   1. Initial program 75.5%

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

      1. pow1 75.5%

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

      2. associate-*l* 81.1%

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

      3. *-commutative 81.1%

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

   4. Applied egg-rr 81.1%

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

      1. unpow1 81.1%

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

      2. associate-*l* 81.1%

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

      3. *-commutative 81.1%

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

   6. Simplified 81.1%

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

   7. Taylor expanded in y around 0 75.0%

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

      1. distribute-lft-out 75.0%

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

      2. *-commutative 75.0%

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

      3. *-commutative 75.0%

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

   9. Simplified 75.0%

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

   10. Taylor expanded in x around inf 44.8%

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

4. Final simplification 46.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.15 \cdot 10^{+172}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -2.35 \cdot 10^{-7}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq -8.5 \cdot 10^{-220}:\\ \;\;\;\;18 \cdot \left(z \cdot \left(y \cdot \left(t \cdot x\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 5.5 \cdot 10^{-226}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 5.5 \cdot 10^{-89}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 2.6 \cdot 10^{+105}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 91.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{+53} \lor \neg \left(t \leq 5.5 \cdot 10^{-30}\right):\\ \;\;\;\;t \cdot \left(\left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + \frac{b \cdot c}{t}\right) - \left(a \cdot 4 + \left(4 \cdot \frac{x \cdot i}{t} + 27 \cdot \frac{j \cdot k}{t}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(y \cdot \left(\left(x \cdot 18\right) \cdot \left(t \cdot z\right)\right) - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - i \cdot \left(x \cdot 4\right)\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= t -3.2e+53) (not (<= t 5.5e-30)))
   (*
    t
    (-
     (+ (* 18.0 (* x (* y z))) (/ (* b c) t))
     (+ (* a 4.0) (+ (* 4.0 (/ (* x i) t)) (* 27.0 (/ (* j k) t))))))
   (-
    (-
     (+ (- (* y (* (* x 18.0) (* t z))) (* t (* a 4.0))) (* b c))
     (* i (* x 4.0)))
    (* k (* j 27.0)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((t <= -3.2e+53) || !(t <= 5.5e-30)) {
		tmp = t * (((18.0 * (x * (y * z))) + ((b * c) / t)) - ((a * 4.0) + ((4.0 * ((x * i) / t)) + (27.0 * ((j * k) / t)))));
	} else {
		tmp = ((((y * ((x * 18.0) * (t * z))) - (t * (a * 4.0))) + (b * c)) - (i * (x * 4.0))) - (k * (j * 27.0));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((t <= (-3.2d+53)) .or. (.not. (t <= 5.5d-30))) then
        tmp = t * (((18.0d0 * (x * (y * z))) + ((b * c) / t)) - ((a * 4.0d0) + ((4.0d0 * ((x * i) / t)) + (27.0d0 * ((j * k) / t)))))
    else
        tmp = ((((y * ((x * 18.0d0) * (t * z))) - (t * (a * 4.0d0))) + (b * c)) - (i * (x * 4.0d0))) - (k * (j * 27.0d0))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((t <= -3.2e+53) || !(t <= 5.5e-30)) {
		tmp = t * (((18.0 * (x * (y * z))) + ((b * c) / t)) - ((a * 4.0) + ((4.0 * ((x * i) / t)) + (27.0 * ((j * k) / t)))));
	} else {
		tmp = ((((y * ((x * 18.0) * (t * z))) - (t * (a * 4.0))) + (b * c)) - (i * (x * 4.0))) - (k * (j * 27.0));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (t <= -3.2e+53) or not (t <= 5.5e-30):
		tmp = t * (((18.0 * (x * (y * z))) + ((b * c) / t)) - ((a * 4.0) + ((4.0 * ((x * i) / t)) + (27.0 * ((j * k) / t)))))
	else:
		tmp = ((((y * ((x * 18.0) * (t * z))) - (t * (a * 4.0))) + (b * c)) - (i * (x * 4.0))) - (k * (j * 27.0))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((t <= -3.2e+53) || !(t <= 5.5e-30))
		tmp = Float64(t * Float64(Float64(Float64(18.0 * Float64(x * Float64(y * z))) + Float64(Float64(b * c) / t)) - Float64(Float64(a * 4.0) + Float64(Float64(4.0 * Float64(Float64(x * i) / t)) + Float64(27.0 * Float64(Float64(j * k) / t))))));
	else
		tmp = Float64(Float64(Float64(Float64(Float64(y * Float64(Float64(x * 18.0) * Float64(t * z))) - Float64(t * Float64(a * 4.0))) + Float64(b * c)) - Float64(i * Float64(x * 4.0))) - Float64(k * Float64(j * 27.0)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((t <= -3.2e+53) || ~((t <= 5.5e-30)))
		tmp = t * (((18.0 * (x * (y * z))) + ((b * c) / t)) - ((a * 4.0) + ((4.0 * ((x * i) / t)) + (27.0 * ((j * k) / t)))));
	else
		tmp = ((((y * ((x * 18.0) * (t * z))) - (t * (a * 4.0))) + (b * c)) - (i * (x * 4.0))) - (k * (j * 27.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[t, -3.2e+53], N[Not[LessEqual[t, 5.5e-30]], $MachinePrecision]], N[(t * N[(N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(b * c), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] - N[(N[(a * 4.0), $MachinePrecision] + N[(N[(4.0 * N[(N[(x * i), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] + N[(27.0 * N[(N[(j * k), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(y * N[(N[(x * 18.0), $MachinePrecision] * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - N[(i * N[(x * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.2e53 or 5.49999999999999976e-30 < t

   1. Initial program 82.6%

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

   3. Simplified 89.2%

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

   5. Taylor expanded in t around inf 91.6%

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

   if -3.2e53 < t < 5.49999999999999976e-30

   1. Initial program 89.0%

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

      1. pow1 89.0%

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

      2. associate-*l* 90.3%

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

      3. *-commutative 90.3%

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

   4. Applied egg-rr 90.3%

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

      1. unpow1 90.3%

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

      2. associate-*l* 94.0%

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

      3. *-commutative 94.0%

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

   6. Simplified 94.0%

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

4. Final simplification 92.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{+53} \lor \neg \left(t \leq 5.5 \cdot 10^{-30}\right):\\ \;\;\;\;t \cdot \left(\left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + \frac{b \cdot c}{t}\right) - \left(a \cdot 4 + \left(4 \cdot \frac{x \cdot i}{t} + 27 \cdot \frac{j \cdot k}{t}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(y \cdot \left(\left(x \cdot 18\right) \cdot \left(t \cdot z\right)\right) - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - i \cdot \left(x \cdot 4\right)\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 69.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := k \cdot \left(j \cdot 27\right)\\ t_2 := \left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - t\_1\\ \mathbf{if}\;t \leq -2.8 \cdot 10^{+241}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq -7 \cdot 10^{+191}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -7 \cdot 10^{+127}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - i \cdot 4\right)\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-57}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - t\_1\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{+105}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot 18\right) - a \cdot 4\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* k (* j 27.0))) (t_2 (- (- (* b c) (* 4.0 (* x i))) t_1)))
   (if (<= t -2.8e+241)
     (* t (- (* 18.0 (* x (* y z))) (* a 4.0)))
     (if (<= t -7e+191)
       t_2
       (if (<= t -7e+127)
         (* x (- (* 18.0 (* t (* y z))) (* i 4.0)))
         (if (<= t -2e-57)
           (- (- (* b c) (* 4.0 (* t a))) t_1)
           (if (<= t 1.65e+105)
             t_2
             (* t (- (* (* y z) (* x 18.0)) (* a 4.0))))))))))

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 = k * (j * 27.0);
	double t_2 = ((b * c) - (4.0 * (x * i))) - t_1;
	double tmp;
	if (t <= -2.8e+241) {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	} else if (t <= -7e+191) {
		tmp = t_2;
	} else if (t <= -7e+127) {
		tmp = x * ((18.0 * (t * (y * z))) - (i * 4.0));
	} else if (t <= -2e-57) {
		tmp = ((b * c) - (4.0 * (t * a))) - t_1;
	} else if (t <= 1.65e+105) {
		tmp = t_2;
	} else {
		tmp = t * (((y * z) * (x * 18.0)) - (a * 4.0));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = k * (j * 27.0d0)
    t_2 = ((b * c) - (4.0d0 * (x * i))) - t_1
    if (t <= (-2.8d+241)) then
        tmp = t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0))
    else if (t <= (-7d+191)) then
        tmp = t_2
    else if (t <= (-7d+127)) then
        tmp = x * ((18.0d0 * (t * (y * z))) - (i * 4.0d0))
    else if (t <= (-2d-57)) then
        tmp = ((b * c) - (4.0d0 * (t * a))) - t_1
    else if (t <= 1.65d+105) then
        tmp = t_2
    else
        tmp = t * (((y * z) * (x * 18.0d0)) - (a * 4.0d0))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = k * (j * 27.0);
	double t_2 = ((b * c) - (4.0 * (x * i))) - t_1;
	double tmp;
	if (t <= -2.8e+241) {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	} else if (t <= -7e+191) {
		tmp = t_2;
	} else if (t <= -7e+127) {
		tmp = x * ((18.0 * (t * (y * z))) - (i * 4.0));
	} else if (t <= -2e-57) {
		tmp = ((b * c) - (4.0 * (t * a))) - t_1;
	} else if (t <= 1.65e+105) {
		tmp = t_2;
	} else {
		tmp = t * (((y * z) * (x * 18.0)) - (a * 4.0));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = k * (j * 27.0)
	t_2 = ((b * c) - (4.0 * (x * i))) - t_1
	tmp = 0
	if t <= -2.8e+241:
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0))
	elif t <= -7e+191:
		tmp = t_2
	elif t <= -7e+127:
		tmp = x * ((18.0 * (t * (y * z))) - (i * 4.0))
	elif t <= -2e-57:
		tmp = ((b * c) - (4.0 * (t * a))) - t_1
	elif t <= 1.65e+105:
		tmp = t_2
	else:
		tmp = t * (((y * z) * (x * 18.0)) - (a * 4.0))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(k * Float64(j * 27.0))
	t_2 = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(x * i))) - t_1)
	tmp = 0.0
	if (t <= -2.8e+241)
		tmp = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)));
	elseif (t <= -7e+191)
		tmp = t_2;
	elseif (t <= -7e+127)
		tmp = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(i * 4.0)));
	elseif (t <= -2e-57)
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(t * a))) - t_1);
	elseif (t <= 1.65e+105)
		tmp = t_2;
	else
		tmp = Float64(t * Float64(Float64(Float64(y * z) * Float64(x * 18.0)) - Float64(a * 4.0)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = k * (j * 27.0);
	t_2 = ((b * c) - (4.0 * (x * i))) - t_1;
	tmp = 0.0;
	if (t <= -2.8e+241)
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	elseif (t <= -7e+191)
		tmp = t_2;
	elseif (t <= -7e+127)
		tmp = x * ((18.0 * (t * (y * z))) - (i * 4.0));
	elseif (t <= -2e-57)
		tmp = ((b * c) - (4.0 * (t * a))) - t_1;
	elseif (t <= 1.65e+105)
		tmp = t_2;
	else
		tmp = t * (((y * z) * (x * 18.0)) - (a * 4.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]}, If[LessEqual[t, -2.8e+241], N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -7e+191], t$95$2, If[LessEqual[t, -7e+127], N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2e-57], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[t, 1.65e+105], t$95$2, N[(t * N[(N[(N[(y * z), $MachinePrecision] * N[(x * 18.0), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -2.80000000000000026e241

   1. Initial program 94.1%

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

   3. Simplified 94.1%

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

   5. Taylor expanded in t around inf 94.3%

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

   if -2.80000000000000026e241 < t < -6.9999999999999994e191 or -1.99999999999999991e-57 < t < 1.64999999999999999e105

   1. Initial program 89.4%

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

   3. Taylor expanded in t around 0 82.7%

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

   if -6.9999999999999994e191 < t < -6.99999999999999956e127

   1. Initial program 28.3%

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

   3. Simplified 28.6%

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

   5. Taylor expanded in x around inf 57.7%

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

   if -6.99999999999999956e127 < t < -1.99999999999999991e-57

   1. Initial program 84.2%

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

   3. Taylor expanded in x around 0 72.6%

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

   if 1.64999999999999999e105 < t

   1. Initial program 80.0%

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

   3. Simplified 92.4%

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

   5. Taylor expanded in t around inf 89.2%

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

      1. pow1 89.2%

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

      2. associate-*r* 86.9%

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

   7. Applied egg-rr 86.9%

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

      1. unpow1 86.9%

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

      2. associate-*r* 89.2%

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

      3. associate-*r* 89.4%

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

   9. Simplified 89.4%

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

4. Final simplification 82.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+241}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq -7 \cdot 10^{+191}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;t \leq -7 \cdot 10^{+127}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - i \cdot 4\right)\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-57}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{+105}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot 18\right) - a \cdot 4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 46.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right) + b \cdot c\\ t_2 := -4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;x \leq -3.2 \cdot 10^{+271}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;x \leq -4.6 \cdot 10^{+193}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{-287}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{-308}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{+54}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 5.3 \cdot 10^{+187}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(z \cdot \left(18 \cdot \left(x \cdot y\right)\right)\right)\\ \end{array} \end{array} \]

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 (* k -27.0)) (* b c))) (t_2 (* -4.0 (* x i))))
   (if (<= x -3.2e+271)
     (* 18.0 (* t (* x (* y z))))
     (if (<= x -4.6e+193)
       t_2
       (if (<= x -3.5e-287)
         t_1
         (if (<= x -1.9e-308)
           (* t (* a -4.0))
           (if (<= x 2.2e+54)
             t_1
             (if (<= x 5.3e+187) t_2 (* t (* z (* 18.0 (* x y))))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * (k * -27.0)) + (b * c);
	double t_2 = -4.0 * (x * i);
	double tmp;
	if (x <= -3.2e+271) {
		tmp = 18.0 * (t * (x * (y * z)));
	} else if (x <= -4.6e+193) {
		tmp = t_2;
	} else if (x <= -3.5e-287) {
		tmp = t_1;
	} else if (x <= -1.9e-308) {
		tmp = t * (a * -4.0);
	} else if (x <= 2.2e+54) {
		tmp = t_1;
	} else if (x <= 5.3e+187) {
		tmp = t_2;
	} else {
		tmp = t * (z * (18.0 * (x * y)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (j * (k * (-27.0d0))) + (b * c)
    t_2 = (-4.0d0) * (x * i)
    if (x <= (-3.2d+271)) then
        tmp = 18.0d0 * (t * (x * (y * z)))
    else if (x <= (-4.6d+193)) then
        tmp = t_2
    else if (x <= (-3.5d-287)) then
        tmp = t_1
    else if (x <= (-1.9d-308)) then
        tmp = t * (a * (-4.0d0))
    else if (x <= 2.2d+54) then
        tmp = t_1
    else if (x <= 5.3d+187) then
        tmp = t_2
    else
        tmp = t * (z * (18.0d0 * (x * y)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * (k * -27.0)) + (b * c);
	double t_2 = -4.0 * (x * i);
	double tmp;
	if (x <= -3.2e+271) {
		tmp = 18.0 * (t * (x * (y * z)));
	} else if (x <= -4.6e+193) {
		tmp = t_2;
	} else if (x <= -3.5e-287) {
		tmp = t_1;
	} else if (x <= -1.9e-308) {
		tmp = t * (a * -4.0);
	} else if (x <= 2.2e+54) {
		tmp = t_1;
	} else if (x <= 5.3e+187) {
		tmp = t_2;
	} else {
		tmp = t * (z * (18.0 * (x * y)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * (k * -27.0)) + (b * c)
	t_2 = -4.0 * (x * i)
	tmp = 0
	if x <= -3.2e+271:
		tmp = 18.0 * (t * (x * (y * z)))
	elif x <= -4.6e+193:
		tmp = t_2
	elif x <= -3.5e-287:
		tmp = t_1
	elif x <= -1.9e-308:
		tmp = t * (a * -4.0)
	elif x <= 2.2e+54:
		tmp = t_1
	elif x <= 5.3e+187:
		tmp = t_2
	else:
		tmp = t * (z * (18.0 * (x * y)))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * Float64(k * -27.0)) + Float64(b * c))
	t_2 = Float64(-4.0 * Float64(x * i))
	tmp = 0.0
	if (x <= -3.2e+271)
		tmp = Float64(18.0 * Float64(t * Float64(x * Float64(y * z))));
	elseif (x <= -4.6e+193)
		tmp = t_2;
	elseif (x <= -3.5e-287)
		tmp = t_1;
	elseif (x <= -1.9e-308)
		tmp = Float64(t * Float64(a * -4.0));
	elseif (x <= 2.2e+54)
		tmp = t_1;
	elseif (x <= 5.3e+187)
		tmp = t_2;
	else
		tmp = Float64(t * Float64(z * Float64(18.0 * Float64(x * y))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * (k * -27.0)) + (b * c);
	t_2 = -4.0 * (x * i);
	tmp = 0.0;
	if (x <= -3.2e+271)
		tmp = 18.0 * (t * (x * (y * z)));
	elseif (x <= -4.6e+193)
		tmp = t_2;
	elseif (x <= -3.5e-287)
		tmp = t_1;
	elseif (x <= -1.9e-308)
		tmp = t * (a * -4.0);
	elseif (x <= 2.2e+54)
		tmp = t_1;
	elseif (x <= 5.3e+187)
		tmp = t_2;
	else
		tmp = t * (z * (18.0 * (x * y)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.2e+271], N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -4.6e+193], t$95$2, If[LessEqual[x, -3.5e-287], t$95$1, If[LessEqual[x, -1.9e-308], N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.2e+54], t$95$1, If[LessEqual[x, 5.3e+187], t$95$2, N[(t * N[(z * N[(18.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -3.2000000000000001e271

   1. Initial program 62.5%

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

   3. Simplified 75.0%

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

   5. Taylor expanded in t around inf 76.3%

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

   6. Taylor expanded in x around inf 64.0%

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

   if -3.2000000000000001e271 < x < -4.60000000000000026e193 or 2.1999999999999999e54 < x < 5.30000000000000034e187

   1. Initial program 75.6%

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

      1. pow1 75.6%

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

      2. associate-*l* 73.1%

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

      3. *-commutative 73.1%

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

   4. Applied egg-rr 73.1%

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

      1. unpow1 73.1%

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

      2. associate-*l* 85.4%

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

      3. *-commutative 85.4%

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

   6. Simplified 85.4%

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

   7. Taylor expanded in y around 0 78.4%

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

      1. distribute-lft-out 78.4%

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

      2. *-commutative 78.4%

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

      3. *-commutative 78.4%

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

   9. Simplified 78.4%

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

   10. Taylor expanded in x around inf 56.3%

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

   if -4.60000000000000026e193 < x < -3.5e-287 or -1.9000000000000001e-308 < x < 2.1999999999999999e54

   1. Initial program 91.4%

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

   3. Simplified 90.9%

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

   5. Taylor expanded in b around inf 57.3%

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

   if -3.5e-287 < x < -1.9000000000000001e-308

   1. Initial program 99.8%

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

      1. pow1 99.8%

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

      2. associate-*l* 85.5%

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

      3. *-commutative 85.5%

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

   4. Applied egg-rr 85.5%

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

      1. unpow1 85.5%

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

      2. associate-*l* 85.5%

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

      3. *-commutative 85.5%

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

   6. Simplified 85.5%

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

   7. Taylor expanded in y around 0 99.8%

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

      1. distribute-lft-out 99.8%

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

      2. *-commutative 99.8%

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

      3. *-commutative 99.8%

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

   9. Simplified 99.8%

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

   10. Taylor expanded in t around inf 82.2%

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

       1. *-commutative 82.2%

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

       2. *-commutative 82.2%

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

       3. associate-*r* 82.2%

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

   12. Simplified 82.2%

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

   if 5.30000000000000034e187 < x

   1. Initial program 69.2%

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

   3. Simplified 76.9%

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

   5. Taylor expanded in t around inf 66.0%

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

      1. pow1 66.0%

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

      2. associate-*r* 69.5%

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

   7. Applied egg-rr 69.5%

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

      1. unpow1 69.5%

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

      2. associate-*r* 66.0%

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

      3. associate-*r* 66.0%

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

   9. Simplified 66.0%

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

   10. Taylor expanded in x around inf 59.0%

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

       1. associate-*r* 66.4%

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

       2. *-commutative 66.4%

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

       3. associate-*l* 66.4%

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

       4. *-commutative 66.4%

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

       5. associate-*r* 66.4%

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

       6. *-commutative 66.4%

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

   12. Simplified 66.4%

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

4. Final simplification 59.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{+271}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;x \leq -4.6 \cdot 10^{+193}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{-287}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{-308}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{+54}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \mathbf{elif}\;x \leq 5.3 \cdot 10^{+187}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(z \cdot \left(18 \cdot \left(x \cdot y\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 56.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - i \cdot 4\right)\\ t_2 := j \cdot \left(k \cdot -27\right)\\ t_3 := t\_2 + -4 \cdot \left(t \cdot a\right)\\ \mathbf{if}\;x \leq -2.3 \cdot 10^{+192}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -2.9 \cdot 10^{+51}:\\ \;\;\;\;t\_2 + b \cdot c\\ \mathbf{elif}\;x \leq 10^{-308}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-289}:\\ \;\;\;\;c \cdot \left(b + t \cdot \left(-4 \cdot \frac{a}{c}\right)\right)\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{+41}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (- (* 18.0 (* t (* y z))) (* i 4.0))))
        (t_2 (* j (* k -27.0)))
        (t_3 (+ t_2 (* -4.0 (* t a)))))
   (if (<= x -2.3e+192)
     t_1
     (if (<= x -2.9e+51)
       (+ t_2 (* b c))
       (if (<= x 1e-308)
         t_3
         (if (<= x 1.3e-289)
           (* c (+ b (* t (* -4.0 (/ a c)))))
           (if (<= x 3.8e+41) t_3 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 * ((18.0 * (t * (y * z))) - (i * 4.0));
	double t_2 = j * (k * -27.0);
	double t_3 = t_2 + (-4.0 * (t * a));
	double tmp;
	if (x <= -2.3e+192) {
		tmp = t_1;
	} else if (x <= -2.9e+51) {
		tmp = t_2 + (b * c);
	} else if (x <= 1e-308) {
		tmp = t_3;
	} else if (x <= 1.3e-289) {
		tmp = c * (b + (t * (-4.0 * (a / c))));
	} else if (x <= 3.8e+41) {
		tmp = t_3;
	} 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) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x * ((18.0d0 * (t * (y * z))) - (i * 4.0d0))
    t_2 = j * (k * (-27.0d0))
    t_3 = t_2 + ((-4.0d0) * (t * a))
    if (x <= (-2.3d+192)) then
        tmp = t_1
    else if (x <= (-2.9d+51)) then
        tmp = t_2 + (b * c)
    else if (x <= 1d-308) then
        tmp = t_3
    else if (x <= 1.3d-289) then
        tmp = c * (b + (t * ((-4.0d0) * (a / c))))
    else if (x <= 3.8d+41) then
        tmp = t_3
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && 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 * (t * (y * z))) - (i * 4.0));
	double t_2 = j * (k * -27.0);
	double t_3 = t_2 + (-4.0 * (t * a));
	double tmp;
	if (x <= -2.3e+192) {
		tmp = t_1;
	} else if (x <= -2.9e+51) {
		tmp = t_2 + (b * c);
	} else if (x <= 1e-308) {
		tmp = t_3;
	} else if (x <= 1.3e-289) {
		tmp = c * (b + (t * (-4.0 * (a / c))));
	} else if (x <= 3.8e+41) {
		tmp = t_3;
	} 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 * ((18.0 * (t * (y * z))) - (i * 4.0))
	t_2 = j * (k * -27.0)
	t_3 = t_2 + (-4.0 * (t * a))
	tmp = 0
	if x <= -2.3e+192:
		tmp = t_1
	elif x <= -2.9e+51:
		tmp = t_2 + (b * c)
	elif x <= 1e-308:
		tmp = t_3
	elif x <= 1.3e-289:
		tmp = c * (b + (t * (-4.0 * (a / c))))
	elif x <= 3.8e+41:
		tmp = t_3
	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(18.0 * Float64(t * Float64(y * z))) - Float64(i * 4.0)))
	t_2 = Float64(j * Float64(k * -27.0))
	t_3 = Float64(t_2 + Float64(-4.0 * Float64(t * a)))
	tmp = 0.0
	if (x <= -2.3e+192)
		tmp = t_1;
	elseif (x <= -2.9e+51)
		tmp = Float64(t_2 + Float64(b * c));
	elseif (x <= 1e-308)
		tmp = t_3;
	elseif (x <= 1.3e-289)
		tmp = Float64(c * Float64(b + Float64(t * Float64(-4.0 * Float64(a / c)))));
	elseif (x <= 3.8e+41)
		tmp = t_3;
	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 * ((18.0 * (t * (y * z))) - (i * 4.0));
	t_2 = j * (k * -27.0);
	t_3 = t_2 + (-4.0 * (t * a));
	tmp = 0.0;
	if (x <= -2.3e+192)
		tmp = t_1;
	elseif (x <= -2.9e+51)
		tmp = t_2 + (b * c);
	elseif (x <= 1e-308)
		tmp = t_3;
	elseif (x <= 1.3e-289)
		tmp = c * (b + (t * (-4.0 * (a / c))));
	elseif (x <= 3.8e+41)
		tmp = t_3;
	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[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.3e+192], t$95$1, If[LessEqual[x, -2.9e+51], N[(t$95$2 + N[(b * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1e-308], t$95$3, If[LessEqual[x, 1.3e-289], N[(c * N[(b + N[(t * N[(-4.0 * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.8e+41], t$95$3, t$95$1]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.2999999999999999e192 or 3.8000000000000001e41 < x

   1. Initial program 72.5%

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

   3. Simplified 82.5%

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

   5. Taylor expanded in x around inf 73.8%

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

   if -2.2999999999999999e192 < x < -2.8999999999999998e51

   1. Initial program 91.5%

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

   3. Simplified 95.8%

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

   5. Taylor expanded in b around inf 67.4%

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

   if -2.8999999999999998e51 < x < 9.9999999999999991e-309 or 1.2999999999999999e-289 < x < 3.8000000000000001e41

   1. Initial program 91.6%

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

   3. Simplified 90.3%

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

   5. Taylor expanded in a around inf 63.5%

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

      1. *-commutative 63.5%

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

   7. Simplified 63.5%

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

   if 9.9999999999999991e-309 < x < 1.2999999999999999e-289

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 99.8%

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

   4. Taylor expanded in c around inf 99.8%

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

      1. associate-*r/ 99.8%

         \[\leadsto c \cdot \left(b + \color{blue}{\frac{-1 \cdot \left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)}{c}}\right) \]

      2. mul-1-neg 99.8%

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

      3. *-commutative 99.8%

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

      4. *-commutative 99.8%

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

      5. associate-*r* 99.8%

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

      6. *-commutative 99.8%

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

      7. associate-*l* 99.8%

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

      8. *-commutative 99.8%

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

      9. distribute-neg-in 99.8%

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

      10. distribute-rgt-neg-in 99.8%

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

      11. distribute-rgt-neg-in 99.8%

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

      12. metadata-eval 99.8%

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

      13. distribute-rgt-neg-in 99.8%

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

      14. distribute-lft-neg-in 99.8%

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

      15. metadata-eval 99.8%

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

      16. *-commutative 99.8%

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

   6. Simplified 99.8%

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

   7. Taylor expanded in t around inf 89.6%

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

      1. associate-*r/ 89.6%

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

      2. *-commutative 89.6%

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

      3. *-commutative 89.6%

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

      4. associate-*r* 89.6%

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

      5. *-commutative 89.6%

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

      6. associate-*r/ 89.4%

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

      7. associate-*r/ 89.4%

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

   9. Simplified 89.4%

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

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{+192}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - i \cdot 4\right)\\ \mathbf{elif}\;x \leq -2.9 \cdot 10^{+51}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \mathbf{elif}\;x \leq 10^{-308}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-289}:\\ \;\;\;\;c \cdot \left(b + t \cdot \left(-4 \cdot \frac{a}{c}\right)\right)\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{+41}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - i \cdot 4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 58.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\\ t_2 := x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - i \cdot 4\right)\\ \mathbf{if}\;x \leq -1.02 \cdot 10^{+118}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{+51}:\\ \;\;\;\;b \cdot c + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-310}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-290}:\\ \;\;\;\;c \cdot \left(b + t \cdot \left(-4 \cdot \frac{a}{c}\right)\right)\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{+41}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (+ (* j (* k -27.0)) (* -4.0 (* t a))))
        (t_2 (* x (- (* 18.0 (* t (* y z))) (* i 4.0)))))
   (if (<= x -1.02e+118)
     t_2
     (if (<= x -3.2e+51)
       (+ (* b c) (* 18.0 (* t (* x (* y z)))))
       (if (<= x 5e-310)
         t_1
         (if (<= x 2.4e-290)
           (* c (+ b (* t (* -4.0 (/ a c)))))
           (if (<= x 4.8e+41) t_1 t_2)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * (k * -27.0)) + (-4.0 * (t * a));
	double t_2 = x * ((18.0 * (t * (y * z))) - (i * 4.0));
	double tmp;
	if (x <= -1.02e+118) {
		tmp = t_2;
	} else if (x <= -3.2e+51) {
		tmp = (b * c) + (18.0 * (t * (x * (y * z))));
	} else if (x <= 5e-310) {
		tmp = t_1;
	} else if (x <= 2.4e-290) {
		tmp = c * (b + (t * (-4.0 * (a / c))));
	} else if (x <= 4.8e+41) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (j * (k * (-27.0d0))) + ((-4.0d0) * (t * a))
    t_2 = x * ((18.0d0 * (t * (y * z))) - (i * 4.0d0))
    if (x <= (-1.02d+118)) then
        tmp = t_2
    else if (x <= (-3.2d+51)) then
        tmp = (b * c) + (18.0d0 * (t * (x * (y * z))))
    else if (x <= 5d-310) then
        tmp = t_1
    else if (x <= 2.4d-290) then
        tmp = c * (b + (t * ((-4.0d0) * (a / c))))
    else if (x <= 4.8d+41) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * (k * -27.0)) + (-4.0 * (t * a));
	double t_2 = x * ((18.0 * (t * (y * z))) - (i * 4.0));
	double tmp;
	if (x <= -1.02e+118) {
		tmp = t_2;
	} else if (x <= -3.2e+51) {
		tmp = (b * c) + (18.0 * (t * (x * (y * z))));
	} else if (x <= 5e-310) {
		tmp = t_1;
	} else if (x <= 2.4e-290) {
		tmp = c * (b + (t * (-4.0 * (a / c))));
	} else if (x <= 4.8e+41) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * (k * -27.0)) + (-4.0 * (t * a))
	t_2 = x * ((18.0 * (t * (y * z))) - (i * 4.0))
	tmp = 0
	if x <= -1.02e+118:
		tmp = t_2
	elif x <= -3.2e+51:
		tmp = (b * c) + (18.0 * (t * (x * (y * z))))
	elif x <= 5e-310:
		tmp = t_1
	elif x <= 2.4e-290:
		tmp = c * (b + (t * (-4.0 * (a / c))))
	elif x <= 4.8e+41:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * Float64(k * -27.0)) + Float64(-4.0 * Float64(t * a)))
	t_2 = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(i * 4.0)))
	tmp = 0.0
	if (x <= -1.02e+118)
		tmp = t_2;
	elseif (x <= -3.2e+51)
		tmp = Float64(Float64(b * c) + Float64(18.0 * Float64(t * Float64(x * Float64(y * z)))));
	elseif (x <= 5e-310)
		tmp = t_1;
	elseif (x <= 2.4e-290)
		tmp = Float64(c * Float64(b + Float64(t * Float64(-4.0 * Float64(a / c)))));
	elseif (x <= 4.8e+41)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * (k * -27.0)) + (-4.0 * (t * a));
	t_2 = x * ((18.0 * (t * (y * z))) - (i * 4.0));
	tmp = 0.0;
	if (x <= -1.02e+118)
		tmp = t_2;
	elseif (x <= -3.2e+51)
		tmp = (b * c) + (18.0 * (t * (x * (y * z))));
	elseif (x <= 5e-310)
		tmp = t_1;
	elseif (x <= 2.4e-290)
		tmp = c * (b + (t * (-4.0 * (a / c))));
	elseif (x <= 4.8e+41)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.02e+118], t$95$2, If[LessEqual[x, -3.2e+51], N[(N[(b * c), $MachinePrecision] + N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5e-310], t$95$1, If[LessEqual[x, 2.4e-290], N[(c * N[(b + N[(t * N[(-4.0 * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.8e+41], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.0199999999999999e118 or 4.8000000000000003e41 < x

   1. Initial program 75.8%

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

   3. Simplified 85.2%

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

   5. Taylor expanded in x around inf 69.9%

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

   if -1.0199999999999999e118 < x < -3.2000000000000002e51

   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 a around 0 88.9%

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

   4. Taylor expanded in i around 0 100.0%

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

   5. Taylor expanded in j around 0 100.0%

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

   if -3.2000000000000002e51 < x < 4.999999999999985e-310 or 2.4000000000000001e-290 < x < 4.8000000000000003e41

   1. Initial program 91.6%

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

   3. Simplified 90.3%

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

   5. Taylor expanded in a around inf 63.5%

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

      1. *-commutative 63.5%

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

   7. Simplified 63.5%

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

   if 4.999999999999985e-310 < x < 2.4000000000000001e-290

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 99.8%

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

   4. Taylor expanded in c around inf 99.8%

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

      1. associate-*r/ 99.8%

         \[\leadsto c \cdot \left(b + \color{blue}{\frac{-1 \cdot \left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)}{c}}\right) \]

      2. mul-1-neg 99.8%

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

      3. *-commutative 99.8%

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

      4. *-commutative 99.8%

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

      5. associate-*r* 99.8%

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

      6. *-commutative 99.8%

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

      7. associate-*l* 99.8%

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

      8. *-commutative 99.8%

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

      9. distribute-neg-in 99.8%

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

      10. distribute-rgt-neg-in 99.8%

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

      11. distribute-rgt-neg-in 99.8%

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

      12. metadata-eval 99.8%

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

      13. distribute-rgt-neg-in 99.8%

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

      14. distribute-lft-neg-in 99.8%

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

      15. metadata-eval 99.8%

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

      16. *-commutative 99.8%

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

   6. Simplified 99.8%

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

   7. Taylor expanded in t around inf 89.6%

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

      1. associate-*r/ 89.6%

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

      2. *-commutative 89.6%

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

      3. *-commutative 89.6%

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

      4. associate-*r* 89.6%

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

      5. *-commutative 89.6%

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

      6. associate-*r/ 89.4%

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

      7. associate-*r/ 89.4%

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

   9. Simplified 89.4%

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

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.02 \cdot 10^{+118}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - i \cdot 4\right)\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{+51}:\\ \;\;\;\;b \cdot c + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-310}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-290}:\\ \;\;\;\;c \cdot \left(b + t \cdot \left(-4 \cdot \frac{a}{c}\right)\right)\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{+41}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - i \cdot 4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 86.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;c \leq 10^{-232}:\\ \;\;\;\;\left(\left(\left(y \cdot \left(\left(x \cdot 18\right) \cdot \left(t \cdot z\right)\right) - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - i \cdot \left(x \cdot 4\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot 18\right) - a \cdot 4\right)\right) - \left(x \cdot \left(i \cdot 4\right) + j \cdot \left(k \cdot 27\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= c 1e-232)
   (-
    (-
     (+ (- (* y (* (* x 18.0) (* t z))) (* t (* a 4.0))) (* b c))
     (* i (* x 4.0)))
    (* k (* j 27.0)))
   (-
    (+ (* b c) (* t (- (* (* y z) (* x 18.0)) (* a 4.0))))
    (+ (* x (* i 4.0)) (* j (* k 27.0))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (c <= 1e-232) {
		tmp = ((((y * ((x * 18.0) * (t * z))) - (t * (a * 4.0))) + (b * c)) - (i * (x * 4.0))) - (k * (j * 27.0));
	} else {
		tmp = ((b * c) + (t * (((y * z) * (x * 18.0)) - (a * 4.0)))) - ((x * (i * 4.0)) + (j * (k * 27.0)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (c <= 1d-232) then
        tmp = ((((y * ((x * 18.0d0) * (t * z))) - (t * (a * 4.0d0))) + (b * c)) - (i * (x * 4.0d0))) - (k * (j * 27.0d0))
    else
        tmp = ((b * c) + (t * (((y * z) * (x * 18.0d0)) - (a * 4.0d0)))) - ((x * (i * 4.0d0)) + (j * (k * 27.0d0)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (c <= 1e-232) {
		tmp = ((((y * ((x * 18.0) * (t * z))) - (t * (a * 4.0))) + (b * c)) - (i * (x * 4.0))) - (k * (j * 27.0));
	} else {
		tmp = ((b * c) + (t * (((y * z) * (x * 18.0)) - (a * 4.0)))) - ((x * (i * 4.0)) + (j * (k * 27.0)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if c <= 1e-232:
		tmp = ((((y * ((x * 18.0) * (t * z))) - (t * (a * 4.0))) + (b * c)) - (i * (x * 4.0))) - (k * (j * 27.0))
	else:
		tmp = ((b * c) + (t * (((y * z) * (x * 18.0)) - (a * 4.0)))) - ((x * (i * 4.0)) + (j * (k * 27.0)))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (c <= 1e-232)
		tmp = Float64(Float64(Float64(Float64(Float64(y * Float64(Float64(x * 18.0) * Float64(t * z))) - Float64(t * Float64(a * 4.0))) + Float64(b * c)) - Float64(i * Float64(x * 4.0))) - Float64(k * Float64(j * 27.0)));
	else
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(Float64(y * z) * Float64(x * 18.0)) - Float64(a * 4.0)))) - Float64(Float64(x * Float64(i * 4.0)) + Float64(j * Float64(k * 27.0))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (c <= 1e-232)
		tmp = ((((y * ((x * 18.0) * (t * z))) - (t * (a * 4.0))) + (b * c)) - (i * (x * 4.0))) - (k * (j * 27.0));
	else
		tmp = ((b * c) + (t * (((y * z) * (x * 18.0)) - (a * 4.0)))) - ((x * (i * 4.0)) + (j * (k * 27.0)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[c, 1e-232], N[(N[(N[(N[(N[(y * N[(N[(x * 18.0), $MachinePrecision] * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - N[(i * N[(x * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(N[(y * z), $MachinePrecision] * N[(x * 18.0), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * N[(i * 4.0), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < 1.00000000000000002e-232

   1. Initial program 85.5%

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

      1. pow1 85.5%

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

      2. associate-*l* 85.3%

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

      3. *-commutative 85.3%

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

   4. Applied egg-rr 85.3%

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

      1. unpow1 85.3%

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

      2. associate-*l* 86.0%

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

      3. *-commutative 86.0%

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

   6. Simplified 86.0%

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

   if 1.00000000000000002e-232 < c

   1. Initial program 86.5%

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

   3. Simplified 90.1%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq 10^{-232}:\\ \;\;\;\;\left(\left(\left(y \cdot \left(\left(x \cdot 18\right) \cdot \left(t \cdot z\right)\right) - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - i \cdot \left(x \cdot 4\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot 18\right) - a \cdot 4\right)\right) - \left(x \cdot \left(i \cdot 4\right) + j \cdot \left(k \cdot 27\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 69.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - i \cdot 4\right)\\ \mathbf{if}\;x \leq -2.3 \cdot 10^{+192}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 32500:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{+177}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{+210}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + 18 \cdot \left(\left(y \cdot z\right) \cdot \left(t \cdot x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* x (- (* 18.0 (* t (* y z))) (* i 4.0)))))
   (if (<= x -2.3e+192)
     t_1
     (if (<= x 32500.0)
       (- (- (* b c) (* 4.0 (* t a))) (* k (* j 27.0)))
       (if (<= x 3.6e+177)
         (- (* b c) (* 4.0 (+ (* x i) (* t a))))
         (if (<= x 3.8e+210)
           (+ (* j (* k -27.0)) (* 18.0 (* (* y z) (* t x))))
           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 * ((18.0 * (t * (y * z))) - (i * 4.0));
	double tmp;
	if (x <= -2.3e+192) {
		tmp = t_1;
	} else if (x <= 32500.0) {
		tmp = ((b * c) - (4.0 * (t * a))) - (k * (j * 27.0));
	} else if (x <= 3.6e+177) {
		tmp = (b * c) - (4.0 * ((x * i) + (t * a)));
	} else if (x <= 3.8e+210) {
		tmp = (j * (k * -27.0)) + (18.0 * ((y * z) * (t * x)));
	} 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 * ((18.0d0 * (t * (y * z))) - (i * 4.0d0))
    if (x <= (-2.3d+192)) then
        tmp = t_1
    else if (x <= 32500.0d0) then
        tmp = ((b * c) - (4.0d0 * (t * a))) - (k * (j * 27.0d0))
    else if (x <= 3.6d+177) then
        tmp = (b * c) - (4.0d0 * ((x * i) + (t * a)))
    else if (x <= 3.8d+210) then
        tmp = (j * (k * (-27.0d0))) + (18.0d0 * ((y * z) * (t * x)))
    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 * ((18.0 * (t * (y * z))) - (i * 4.0));
	double tmp;
	if (x <= -2.3e+192) {
		tmp = t_1;
	} else if (x <= 32500.0) {
		tmp = ((b * c) - (4.0 * (t * a))) - (k * (j * 27.0));
	} else if (x <= 3.6e+177) {
		tmp = (b * c) - (4.0 * ((x * i) + (t * a)));
	} else if (x <= 3.8e+210) {
		tmp = (j * (k * -27.0)) + (18.0 * ((y * z) * (t * x)));
	} 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 * ((18.0 * (t * (y * z))) - (i * 4.0))
	tmp = 0
	if x <= -2.3e+192:
		tmp = t_1
	elif x <= 32500.0:
		tmp = ((b * c) - (4.0 * (t * a))) - (k * (j * 27.0))
	elif x <= 3.6e+177:
		tmp = (b * c) - (4.0 * ((x * i) + (t * a)))
	elif x <= 3.8e+210:
		tmp = (j * (k * -27.0)) + (18.0 * ((y * z) * (t * x)))
	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(18.0 * Float64(t * Float64(y * z))) - Float64(i * 4.0)))
	tmp = 0.0
	if (x <= -2.3e+192)
		tmp = t_1;
	elseif (x <= 32500.0)
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(t * a))) - Float64(k * Float64(j * 27.0)));
	elseif (x <= 3.6e+177)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(Float64(x * i) + Float64(t * a))));
	elseif (x <= 3.8e+210)
		tmp = Float64(Float64(j * Float64(k * -27.0)) + Float64(18.0 * Float64(Float64(y * z) * Float64(t * x))));
	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 * ((18.0 * (t * (y * z))) - (i * 4.0));
	tmp = 0.0;
	if (x <= -2.3e+192)
		tmp = t_1;
	elseif (x <= 32500.0)
		tmp = ((b * c) - (4.0 * (t * a))) - (k * (j * 27.0));
	elseif (x <= 3.6e+177)
		tmp = (b * c) - (4.0 * ((x * i) + (t * a)));
	elseif (x <= 3.8e+210)
		tmp = (j * (k * -27.0)) + (18.0 * ((y * z) * (t * x)));
	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[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.3e+192], t$95$1, If[LessEqual[x, 32500.0], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.6e+177], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(N[(x * i), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.8e+210], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(18.0 * N[(N[(y * z), $MachinePrecision] * N[(t * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.2999999999999999e192 or 3.80000000000000028e210 < x

   1. Initial program 64.5%

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

   3. Simplified 77.8%

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

   5. Taylor expanded in x around inf 81.5%

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

   if -2.2999999999999999e192 < x < 32500

   1. Initial program 92.7%

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

   3. Taylor expanded in x around 0 79.0%

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

   if 32500 < x < 3.60000000000000003e177

   1. Initial program 86.6%

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

      1. pow1 86.6%

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

      2. associate-*l* 91.8%

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

      3. *-commutative 91.8%

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

   4. Applied egg-rr 91.8%

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

      1. unpow1 91.8%

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

      2. associate-*l* 91.8%

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

      3. *-commutative 91.8%

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

   6. Simplified 91.8%

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

   7. Taylor expanded in y around 0 81.3%

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

      1. distribute-lft-out 81.3%

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

      2. *-commutative 81.3%

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

      3. *-commutative 81.3%

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

   9. Simplified 81.3%

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

   10. Taylor expanded in j around 0 71.0%

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

   if 3.60000000000000003e177 < x < 3.80000000000000028e210

   1. Initial program 62.5%

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

   3. Simplified 87.5%

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

   5. Taylor expanded in y around inf 75.1%

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

      1. associate-*r* 87.6%

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

   7. Simplified 87.6%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{+192}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - i \cdot 4\right)\\ \mathbf{elif}\;x \leq 32500:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{+177}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{+210}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + 18 \cdot \left(\left(y \cdot z\right) \cdot \left(t \cdot x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - i \cdot 4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 69.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{if}\;t \leq -2.8 \cdot 10^{+241}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{+173}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -6 \cdot 10^{-58}:\\ \;\;\;\;c \cdot \left(b + \frac{j \cdot \left(k \cdot -27\right) + t \cdot \left(a \cdot -4\right)}{c}\right)\\ \mathbf{elif}\;t \leq 10^{+106}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot 18\right) - a \cdot 4\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (- (- (* b c) (* 4.0 (* x i))) (* k (* j 27.0)))))
   (if (<= t -2.8e+241)
     (* t (- (* 18.0 (* x (* y z))) (* a 4.0)))
     (if (<= t -2.9e+173)
       t_1
       (if (<= t -6e-58)
         (* c (+ b (/ (+ (* j (* k -27.0)) (* t (* a -4.0))) c)))
         (if (<= t 1e+106) t_1 (* t (- (* (* y z) (* x 18.0)) (* a 4.0)))))))))

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) - (4.0 * (x * i))) - (k * (j * 27.0));
	double tmp;
	if (t <= -2.8e+241) {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	} else if (t <= -2.9e+173) {
		tmp = t_1;
	} else if (t <= -6e-58) {
		tmp = c * (b + (((j * (k * -27.0)) + (t * (a * -4.0))) / c));
	} else if (t <= 1e+106) {
		tmp = t_1;
	} else {
		tmp = t * (((y * z) * (x * 18.0)) - (a * 4.0));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((b * c) - (4.0d0 * (x * i))) - (k * (j * 27.0d0))
    if (t <= (-2.8d+241)) then
        tmp = t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0))
    else if (t <= (-2.9d+173)) then
        tmp = t_1
    else if (t <= (-6d-58)) then
        tmp = c * (b + (((j * (k * (-27.0d0))) + (t * (a * (-4.0d0)))) / c))
    else if (t <= 1d+106) then
        tmp = t_1
    else
        tmp = t * (((y * z) * (x * 18.0d0)) - (a * 4.0d0))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((b * c) - (4.0 * (x * i))) - (k * (j * 27.0));
	double tmp;
	if (t <= -2.8e+241) {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	} else if (t <= -2.9e+173) {
		tmp = t_1;
	} else if (t <= -6e-58) {
		tmp = c * (b + (((j * (k * -27.0)) + (t * (a * -4.0))) / c));
	} else if (t <= 1e+106) {
		tmp = t_1;
	} else {
		tmp = t * (((y * z) * (x * 18.0)) - (a * 4.0));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = ((b * c) - (4.0 * (x * i))) - (k * (j * 27.0))
	tmp = 0
	if t <= -2.8e+241:
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0))
	elif t <= -2.9e+173:
		tmp = t_1
	elif t <= -6e-58:
		tmp = c * (b + (((j * (k * -27.0)) + (t * (a * -4.0))) / c))
	elif t <= 1e+106:
		tmp = t_1
	else:
		tmp = t * (((y * z) * (x * 18.0)) - (a * 4.0))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(x * i))) - Float64(k * Float64(j * 27.0)))
	tmp = 0.0
	if (t <= -2.8e+241)
		tmp = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)));
	elseif (t <= -2.9e+173)
		tmp = t_1;
	elseif (t <= -6e-58)
		tmp = Float64(c * Float64(b + Float64(Float64(Float64(j * Float64(k * -27.0)) + Float64(t * Float64(a * -4.0))) / c)));
	elseif (t <= 1e+106)
		tmp = t_1;
	else
		tmp = Float64(t * Float64(Float64(Float64(y * z) * Float64(x * 18.0)) - Float64(a * 4.0)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = ((b * c) - (4.0 * (x * i))) - (k * (j * 27.0));
	tmp = 0.0;
	if (t <= -2.8e+241)
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	elseif (t <= -2.9e+173)
		tmp = t_1;
	elseif (t <= -6e-58)
		tmp = c * (b + (((j * (k * -27.0)) + (t * (a * -4.0))) / c));
	elseif (t <= 1e+106)
		tmp = t_1;
	else
		tmp = t * (((y * z) * (x * 18.0)) - (a * 4.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.8e+241], N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.9e+173], t$95$1, If[LessEqual[t, -6e-58], N[(c * N[(b + N[(N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1e+106], t$95$1, N[(t * N[(N[(N[(y * z), $MachinePrecision] * N[(x * 18.0), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.80000000000000026e241

   1. Initial program 94.1%

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

   3. Simplified 94.1%

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

   5. Taylor expanded in t around inf 94.3%

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

   if -2.80000000000000026e241 < t < -2.90000000000000007e173 or -6.00000000000000015e-58 < t < 1.00000000000000009e106

   1. Initial program 87.8%

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

   3. Taylor expanded in t around 0 81.3%

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

   if -2.90000000000000007e173 < t < -6.00000000000000015e-58

   1. Initial program 79.9%

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

   3. Taylor expanded in x around 0 72.1%

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

   4. Taylor expanded in c around inf 69.4%

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

      1. associate-*r/ 69.4%

         \[\leadsto c \cdot \left(b + \color{blue}{\frac{-1 \cdot \left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)}{c}}\right) \]

      2. mul-1-neg 69.4%

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

      3. *-commutative 69.4%

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

      4. *-commutative 69.4%

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

      5. associate-*r* 69.4%

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

      6. *-commutative 69.4%

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

      7. associate-*l* 69.5%

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

      8. *-commutative 69.5%

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

      9. distribute-neg-in 69.5%

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

      10. distribute-rgt-neg-in 69.5%

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

      11. distribute-rgt-neg-in 69.5%

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

      12. metadata-eval 69.5%

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

      13. distribute-rgt-neg-in 69.5%

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

      14. distribute-lft-neg-in 69.5%

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

      15. metadata-eval 69.5%

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

      16. *-commutative 69.5%

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

   6. Simplified 69.5%

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

   if 1.00000000000000009e106 < t

   1. Initial program 80.0%

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

   3. Simplified 92.4%

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

   5. Taylor expanded in t around inf 89.2%

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

      1. pow1 89.2%

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

      2. associate-*r* 86.9%

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

   7. Applied egg-rr 86.9%

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

      1. unpow1 86.9%

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

      2. associate-*r* 89.2%

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

      3. associate-*r* 89.4%

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

   9. Simplified 89.4%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+241}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{+173}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;t \leq -6 \cdot 10^{-58}:\\ \;\;\;\;c \cdot \left(b + \frac{j \cdot \left(k \cdot -27\right) + t \cdot \left(a \cdot -4\right)}{c}\right)\\ \mathbf{elif}\;t \leq 10^{+106}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot 18\right) - a \cdot 4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 87.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq 3.6 \cdot 10^{+210}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot 18\right) - a \cdot 4\right)\right) - \left(x \cdot \left(i \cdot 4\right) + j \cdot \left(k \cdot 27\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - i \cdot 4\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= x 3.6e+210)
   (-
    (+ (* b c) (* t (- (* (* y z) (* x 18.0)) (* a 4.0))))
    (+ (* x (* i 4.0)) (* j (* k 27.0))))
   (* x (- (* 18.0 (* t (* y z))) (* i 4.0)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (x <= 3.6e+210) {
		tmp = ((b * c) + (t * (((y * z) * (x * 18.0)) - (a * 4.0)))) - ((x * (i * 4.0)) + (j * (k * 27.0)));
	} else {
		tmp = x * ((18.0 * (t * (y * z))) - (i * 4.0));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (x <= 3.6d+210) then
        tmp = ((b * c) + (t * (((y * z) * (x * 18.0d0)) - (a * 4.0d0)))) - ((x * (i * 4.0d0)) + (j * (k * 27.0d0)))
    else
        tmp = x * ((18.0d0 * (t * (y * z))) - (i * 4.0d0))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (x <= 3.6e+210) {
		tmp = ((b * c) + (t * (((y * z) * (x * 18.0)) - (a * 4.0)))) - ((x * (i * 4.0)) + (j * (k * 27.0)));
	} else {
		tmp = x * ((18.0 * (t * (y * z))) - (i * 4.0));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if x <= 3.6e+210:
		tmp = ((b * c) + (t * (((y * z) * (x * 18.0)) - (a * 4.0)))) - ((x * (i * 4.0)) + (j * (k * 27.0)))
	else:
		tmp = x * ((18.0 * (t * (y * z))) - (i * 4.0))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (x <= 3.6e+210)
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(Float64(y * z) * Float64(x * 18.0)) - Float64(a * 4.0)))) - Float64(Float64(x * Float64(i * 4.0)) + Float64(j * Float64(k * 27.0))));
	else
		tmp = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(i * 4.0)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (x <= 3.6e+210)
		tmp = ((b * c) + (t * (((y * z) * (x * 18.0)) - (a * 4.0)))) - ((x * (i * 4.0)) + (j * (k * 27.0)));
	else
		tmp = x * ((18.0 * (t * (y * z))) - (i * 4.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[x, 3.6e+210], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(N[(y * z), $MachinePrecision] * N[(x * 18.0), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * N[(i * 4.0), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 3.6000000000000003e210

   1. Initial program 88.1%

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

   3. Simplified 90.3%

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

   if 3.6000000000000003e210 < x

   1. Initial program 61.9%

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

   3. Simplified 71.4%

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

   5. Taylor expanded in x around inf 90.5%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 3.6 \cdot 10^{+210}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot 18\right) - a \cdot 4\right)\right) - \left(x \cdot \left(i \cdot 4\right) + j \cdot \left(k \cdot 27\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - i \cdot 4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 83.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{-57} \lor \neg \left(t \leq 6.4 \cdot 10^{+44}\right):\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot 18\right) - a \cdot 4\right)\right) - j \cdot \left(k \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= t -1e-57) (not (<= t 6.4e+44)))
   (- (+ (* b c) (* t (- (* (* y z) (* x 18.0)) (* a 4.0)))) (* j (* k 27.0)))
   (- (- (* b c) (* 4.0 (+ (* x i) (* t a)))) (* 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 ((t <= -1e-57) || !(t <= 6.4e+44)) {
		tmp = ((b * c) + (t * (((y * z) * (x * 18.0)) - (a * 4.0)))) - (j * (k * 27.0));
	} else {
		tmp = ((b * c) - (4.0 * ((x * i) + (t * a)))) - (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 ((t <= (-1d-57)) .or. (.not. (t <= 6.4d+44))) then
        tmp = ((b * c) + (t * (((y * z) * (x * 18.0d0)) - (a * 4.0d0)))) - (j * (k * 27.0d0))
    else
        tmp = ((b * c) - (4.0d0 * ((x * i) + (t * a)))) - (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 ((t <= -1e-57) || !(t <= 6.4e+44)) {
		tmp = ((b * c) + (t * (((y * z) * (x * 18.0)) - (a * 4.0)))) - (j * (k * 27.0));
	} else {
		tmp = ((b * c) - (4.0 * ((x * i) + (t * a)))) - (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 (t <= -1e-57) or not (t <= 6.4e+44):
		tmp = ((b * c) + (t * (((y * z) * (x * 18.0)) - (a * 4.0)))) - (j * (k * 27.0))
	else:
		tmp = ((b * c) - (4.0 * ((x * i) + (t * a)))) - (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 ((t <= -1e-57) || !(t <= 6.4e+44))
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(Float64(y * z) * Float64(x * 18.0)) - Float64(a * 4.0)))) - Float64(j * Float64(k * 27.0)));
	else
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(Float64(x * i) + Float64(t * a)))) - 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 ((t <= -1e-57) || ~((t <= 6.4e+44)))
		tmp = ((b * c) + (t * (((y * z) * (x * 18.0)) - (a * 4.0)))) - (j * (k * 27.0));
	else
		tmp = ((b * c) - (4.0 * ((x * i) + (t * a)))) - (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[Or[LessEqual[t, -1e-57], N[Not[LessEqual[t, 6.4e+44]], $MachinePrecision]], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(N[(y * z), $MachinePrecision] * N[(x * 18.0), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(j * N[(k * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(N[(x * i), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -9.99999999999999955e-58 or 6.40000000000000009e44 < t

   1. Initial program 83.1%

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

   3. Simplified 88.7%

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

   5. Taylor expanded in x around 0 85.7%

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

      1. *-commutative 85.7%

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

      2. associate-*r* 85.8%

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

   7. Simplified 85.8%

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

   if -9.99999999999999955e-58 < t < 6.40000000000000009e44

   1. Initial program 88.6%

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

   3. Taylor expanded in y around 0 93.6%

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

      1. distribute-lft-out 93.6%

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

      2. *-commutative 93.6%

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

   5. Simplified 93.6%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{-57} \lor \neg \left(t \leq 6.4 \cdot 10^{+44}\right):\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot 18\right) - a \cdot 4\right)\right) - j \cdot \left(k \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 80.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := k \cdot \left(j \cdot 27\right)\\ \mathbf{if}\;t \leq -2.8 \cdot 10^{+241} \lor \neg \left(t \leq 4.4 \cdot 10^{+106}\right):\\ \;\;\;\;t \cdot \left(a \cdot \left(-4\right) - \left(z \cdot \left(x \cdot y\right)\right) \cdot -18\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\right) - t\_1\\ \end{array} \end{array} \]

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 (* k (* j 27.0))))
   (if (or (<= t -2.8e+241) (not (<= t 4.4e+106)))
     (- (* t (- (* a (- 4.0)) (* (* z (* x y)) -18.0))) t_1)
     (- (- (* b c) (* 4.0 (+ (* x i) (* t a)))) 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 = k * (j * 27.0);
	double tmp;
	if ((t <= -2.8e+241) || !(t <= 4.4e+106)) {
		tmp = (t * ((a * -4.0) - ((z * (x * y)) * -18.0))) - t_1;
	} else {
		tmp = ((b * c) - (4.0 * ((x * i) + (t * a)))) - 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 = k * (j * 27.0d0)
    if ((t <= (-2.8d+241)) .or. (.not. (t <= 4.4d+106))) then
        tmp = (t * ((a * -4.0d0) - ((z * (x * y)) * (-18.0d0)))) - t_1
    else
        tmp = ((b * c) - (4.0d0 * ((x * i) + (t * a)))) - 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 = k * (j * 27.0);
	double tmp;
	if ((t <= -2.8e+241) || !(t <= 4.4e+106)) {
		tmp = (t * ((a * -4.0) - ((z * (x * y)) * -18.0))) - t_1;
	} else {
		tmp = ((b * c) - (4.0 * ((x * i) + (t * a)))) - 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 = k * (j * 27.0)
	tmp = 0
	if (t <= -2.8e+241) or not (t <= 4.4e+106):
		tmp = (t * ((a * -4.0) - ((z * (x * y)) * -18.0))) - t_1
	else:
		tmp = ((b * c) - (4.0 * ((x * i) + (t * a)))) - 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(k * Float64(j * 27.0))
	tmp = 0.0
	if ((t <= -2.8e+241) || !(t <= 4.4e+106))
		tmp = Float64(Float64(t * Float64(Float64(a * Float64(-4.0)) - Float64(Float64(z * Float64(x * y)) * -18.0))) - t_1);
	else
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(Float64(x * i) + Float64(t * a)))) - 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 = k * (j * 27.0);
	tmp = 0.0;
	if ((t <= -2.8e+241) || ~((t <= 4.4e+106)))
		tmp = (t * ((a * -4.0) - ((z * (x * y)) * -18.0))) - t_1;
	else
		tmp = ((b * c) - (4.0 * ((x * i) + (t * a)))) - 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[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t, -2.8e+241], N[Not[LessEqual[t, 4.4e+106]], $MachinePrecision]], N[(N[(t * N[(N[(a * (-4.0)), $MachinePrecision] - N[(N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision] * -18.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(N[(x * i), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -2.80000000000000026e241 or 4.39999999999999983e106 < t

   1. Initial program 84.2%

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

      1. pow1 84.2%

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

      2. associate-*l* 75.7%

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

      3. *-commutative 75.7%

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

   4. Applied egg-rr 75.7%

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

      1. unpow1 75.7%

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

      2. associate-*l* 74.0%

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

      3. *-commutative 74.0%

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

   6. Simplified 74.0%

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

   7. Taylor expanded in t around -inf 94.3%

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

      1. associate-*r* 94.3%

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

      2. neg-mul-1 94.3%

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

      3. cancel-sign-sub-inv 94.3%

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

      4. metadata-eval 94.3%

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

      5. *-commutative 94.3%

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

      6. associate-*r* 92.6%

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

   9. Simplified 92.6%

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

   if -2.80000000000000026e241 < t < 4.39999999999999983e106

   1. Initial program 86.4%

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

   3. Taylor expanded in y around 0 87.3%

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

      1. distribute-lft-out 87.3%

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

      2. *-commutative 87.3%

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

   5. Simplified 87.3%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+241} \lor \neg \left(t \leq 4.4 \cdot 10^{+106}\right):\\ \;\;\;\;t \cdot \left(a \cdot \left(-4\right) - \left(z \cdot \left(x \cdot y\right)\right) \cdot -18\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 49.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := t\_1 + b \cdot c\\ \mathbf{if}\;t \leq -3.6 \cdot 10^{-24}:\\ \;\;\;\;t\_1 + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-269}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-140}:\\ \;\;\;\;t\_1 + i \cdot \left(x \cdot -4\right)\\ \mathbf{elif}\;t \leq 3.55 \cdot 10^{+106}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0))) (t_2 (+ t_1 (* b c))))
   (if (<= t -3.6e-24)
     (+ t_1 (* -4.0 (* t a)))
     (if (<= t 2.3e-269)
       t_2
       (if (<= t 4.5e-140)
         (+ t_1 (* i (* x -4.0)))
         (if (<= t 3.55e+106) t_2 (* 18.0 (* t (* x (* y z))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = t_1 + (b * c);
	double tmp;
	if (t <= -3.6e-24) {
		tmp = t_1 + (-4.0 * (t * a));
	} else if (t <= 2.3e-269) {
		tmp = t_2;
	} else if (t <= 4.5e-140) {
		tmp = t_1 + (i * (x * -4.0));
	} else if (t <= 3.55e+106) {
		tmp = t_2;
	} else {
		tmp = 18.0 * (t * (x * (y * z)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * (k * (-27.0d0))
    t_2 = t_1 + (b * c)
    if (t <= (-3.6d-24)) then
        tmp = t_1 + ((-4.0d0) * (t * a))
    else if (t <= 2.3d-269) then
        tmp = t_2
    else if (t <= 4.5d-140) then
        tmp = t_1 + (i * (x * (-4.0d0)))
    else if (t <= 3.55d+106) then
        tmp = t_2
    else
        tmp = 18.0d0 * (t * (x * (y * z)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = t_1 + (b * c);
	double tmp;
	if (t <= -3.6e-24) {
		tmp = t_1 + (-4.0 * (t * a));
	} else if (t <= 2.3e-269) {
		tmp = t_2;
	} else if (t <= 4.5e-140) {
		tmp = t_1 + (i * (x * -4.0));
	} else if (t <= 3.55e+106) {
		tmp = t_2;
	} else {
		tmp = 18.0 * (t * (x * (y * z)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	t_2 = t_1 + (b * c)
	tmp = 0
	if t <= -3.6e-24:
		tmp = t_1 + (-4.0 * (t * a))
	elif t <= 2.3e-269:
		tmp = t_2
	elif t <= 4.5e-140:
		tmp = t_1 + (i * (x * -4.0))
	elif t <= 3.55e+106:
		tmp = t_2
	else:
		tmp = 18.0 * (t * (x * (y * z)))
	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(j * Float64(k * -27.0))
	t_2 = Float64(t_1 + Float64(b * c))
	tmp = 0.0
	if (t <= -3.6e-24)
		tmp = Float64(t_1 + Float64(-4.0 * Float64(t * a)));
	elseif (t <= 2.3e-269)
		tmp = t_2;
	elseif (t <= 4.5e-140)
		tmp = Float64(t_1 + Float64(i * Float64(x * -4.0)));
	elseif (t <= 3.55e+106)
		tmp = t_2;
	else
		tmp = Float64(18.0 * Float64(t * Float64(x * Float64(y * z))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * -27.0);
	t_2 = t_1 + (b * c);
	tmp = 0.0;
	if (t <= -3.6e-24)
		tmp = t_1 + (-4.0 * (t * a));
	elseif (t <= 2.3e-269)
		tmp = t_2;
	elseif (t <= 4.5e-140)
		tmp = t_1 + (i * (x * -4.0));
	elseif (t <= 3.55e+106)
		tmp = t_2;
	else
		tmp = 18.0 * (t * (x * (y * z)));
	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[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(b * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.6e-24], N[(t$95$1 + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.3e-269], t$95$2, If[LessEqual[t, 4.5e-140], N[(t$95$1 + N[(i * N[(x * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.55e+106], t$95$2, N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3.6000000000000001e-24

   1. Initial program 83.2%

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

   3. Simplified 87.8%

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

   5. Taylor expanded in a around inf 61.6%

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

      1. *-commutative 61.6%

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

   7. Simplified 61.6%

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

   if -3.6000000000000001e-24 < t < 2.3e-269 or 4.50000000000000004e-140 < t < 3.55000000000000015e106

   1. Initial program 88.4%

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

   3. Simplified 90.4%

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

   5. Taylor expanded in b around inf 60.3%

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

   if 2.3e-269 < t < 4.50000000000000004e-140

   1. Initial program 89.5%

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

   3. Simplified 86.9%

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

   5. Taylor expanded in i around inf 69.2%

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

      1. metadata-eval 69.2%

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

      2. distribute-lft-neg-in 69.2%

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

      3. *-commutative 69.2%

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

      4. associate-*r* 69.2%

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

      5. distribute-rgt-neg-in 69.2%

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

      6. distribute-rgt-neg-in 69.2%

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

      7. metadata-eval 69.2%

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

      8. *-commutative 69.2%

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

   7. Simplified 69.2%

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

   if 3.55000000000000015e106 < t

   1. Initial program 80.0%

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

   3. Simplified 92.4%

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

   5. Taylor expanded in t around inf 89.2%

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

   6. Taylor expanded in x around inf 57.1%

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

4. Final simplification 61.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{-24}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-269}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-140}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + i \cdot \left(x \cdot -4\right)\\ \mathbf{elif}\;t \leq 3.55 \cdot 10^{+106}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \mathbf{else}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 78.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{+245}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+105}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot 18\right) - a \cdot 4\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= t -8.5e+245)
   (* t (- (* 18.0 (* x (* y z))) (* a 4.0)))
   (if (<= t 5.2e+105)
     (- (- (* b c) (* 4.0 (+ (* x i) (* t a)))) (* k (* j 27.0)))
     (* t (- (* (* y z) (* x 18.0)) (* a 4.0))))))

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 (t <= -8.5e+245) {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	} else if (t <= 5.2e+105) {
		tmp = ((b * c) - (4.0 * ((x * i) + (t * a)))) - (k * (j * 27.0));
	} else {
		tmp = t * (((y * z) * (x * 18.0)) - (a * 4.0));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (t <= (-8.5d+245)) then
        tmp = t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0))
    else if (t <= 5.2d+105) then
        tmp = ((b * c) - (4.0d0 * ((x * i) + (t * a)))) - (k * (j * 27.0d0))
    else
        tmp = t * (((y * z) * (x * 18.0d0)) - (a * 4.0d0))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (t <= -8.5e+245) {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	} else if (t <= 5.2e+105) {
		tmp = ((b * c) - (4.0 * ((x * i) + (t * a)))) - (k * (j * 27.0));
	} else {
		tmp = t * (((y * z) * (x * 18.0)) - (a * 4.0));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if t <= -8.5e+245:
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0))
	elif t <= 5.2e+105:
		tmp = ((b * c) - (4.0 * ((x * i) + (t * a)))) - (k * (j * 27.0))
	else:
		tmp = t * (((y * z) * (x * 18.0)) - (a * 4.0))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (t <= -8.5e+245)
		tmp = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)));
	elseif (t <= 5.2e+105)
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(Float64(x * i) + Float64(t * a)))) - Float64(k * Float64(j * 27.0)));
	else
		tmp = Float64(t * Float64(Float64(Float64(y * z) * Float64(x * 18.0)) - Float64(a * 4.0)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (t <= -8.5e+245)
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	elseif (t <= 5.2e+105)
		tmp = ((b * c) - (4.0 * ((x * i) + (t * a)))) - (k * (j * 27.0));
	else
		tmp = t * (((y * z) * (x * 18.0)) - (a * 4.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[t, -8.5e+245], N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.2e+105], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(N[(x * i), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(N[(y * z), $MachinePrecision] * N[(x * 18.0), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.49999999999999971e245

   1. Initial program 94.1%

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

   3. Simplified 94.1%

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

   5. Taylor expanded in t around inf 94.3%

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

   if -8.49999999999999971e245 < t < 5.2000000000000004e105

   1. Initial program 86.4%

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

   3. Taylor expanded in y around 0 87.3%

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

      1. distribute-lft-out 87.3%

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

      2. *-commutative 87.3%

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

   5. Simplified 87.3%

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

   if 5.2000000000000004e105 < t

   1. Initial program 80.0%

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

   3. Simplified 92.4%

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

   5. Taylor expanded in t around inf 89.2%

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

      1. pow1 89.2%

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

      2. associate-*r* 86.9%

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

   7. Applied egg-rr 86.9%

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

      1. unpow1 86.9%

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

      2. associate-*r* 89.2%

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

      3. associate-*r* 89.4%

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

   9. Simplified 89.4%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{+245}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+105}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot 18\right) - a \cdot 4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 36.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -6.2 \cdot 10^{+171} \lor \neg \left(b \cdot c \leq 6.2 \cdot 10^{+103}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= (* b c) -6.2e+171) (not (<= (* b c) 6.2e+103)))
   (* b c)
   (* -27.0 (* j k))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (((b * c) <= -6.2e+171) || !((b * c) <= 6.2e+103)) {
		tmp = b * c;
	} else {
		tmp = -27.0 * (j * k);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (((b * c) <= (-6.2d+171)) .or. (.not. ((b * c) <= 6.2d+103))) then
        tmp = b * c
    else
        tmp = (-27.0d0) * (j * k)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (((b * c) <= -6.2e+171) || !((b * c) <= 6.2e+103)) {
		tmp = b * c;
	} else {
		tmp = -27.0 * (j * k);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if ((b * c) <= -6.2e+171) or not ((b * c) <= 6.2e+103):
		tmp = b * c
	else:
		tmp = -27.0 * (j * k)
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((Float64(b * c) <= -6.2e+171) || !(Float64(b * c) <= 6.2e+103))
		tmp = Float64(b * c);
	else
		tmp = Float64(-27.0 * Float64(j * k));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (((b * c) <= -6.2e+171) || ~(((b * c) <= 6.2e+103)))
		tmp = b * c;
	else
		tmp = -27.0 * (j * k);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[N[(b * c), $MachinePrecision], -6.2e+171], N[Not[LessEqual[N[(b * c), $MachinePrecision], 6.2e+103]], $MachinePrecision]], N[(b * c), $MachinePrecision], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -6.1999999999999998e171 or 6.2000000000000003e103 < (*.f64 b c)

   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. pow1 80.7%

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

      2. associate-*l* 75.3%

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

      3. *-commutative 75.3%

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

   4. Applied egg-rr 75.3%

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

      1. unpow1 75.3%

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

      2. associate-*l* 75.3%

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

      3. *-commutative 75.3%

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

   6. Simplified 75.3%

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

   7. Taylor expanded in y around 0 79.7%

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

      1. distribute-lft-out 79.7%

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

      2. *-commutative 79.7%

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

      3. *-commutative 79.7%

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

   9. Simplified 79.7%

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

   10. Taylor expanded in b around inf 59.0%

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

   if -6.1999999999999998e171 < (*.f64 b c) < 6.2000000000000003e103

   1. Initial program 88.0%

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

   3. Simplified 90.2%

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

   5. Taylor expanded in j around inf 33.4%

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

4. Final simplification 40.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -6.2 \cdot 10^{+171} \lor \neg \left(b \cdot c \leq 6.2 \cdot 10^{+103}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 49.6% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{+121}:\\ \;\;\;\;c \cdot \left(b + t \cdot \left(-4 \cdot \frac{a}{c}\right)\right)\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+106}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \mathbf{else}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= t -9.5e+121)
   (* c (+ b (* t (* -4.0 (/ a c)))))
   (if (<= t 7e+106)
     (+ (* j (* k -27.0)) (* b c))
     (* 18.0 (* t (* x (* y z)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (t <= -9.5e+121) {
		tmp = c * (b + (t * (-4.0 * (a / c))));
	} else if (t <= 7e+106) {
		tmp = (j * (k * -27.0)) + (b * c);
	} else {
		tmp = 18.0 * (t * (x * (y * z)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (t <= (-9.5d+121)) then
        tmp = c * (b + (t * ((-4.0d0) * (a / c))))
    else if (t <= 7d+106) then
        tmp = (j * (k * (-27.0d0))) + (b * c)
    else
        tmp = 18.0d0 * (t * (x * (y * z)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (t <= -9.5e+121) {
		tmp = c * (b + (t * (-4.0 * (a / c))));
	} else if (t <= 7e+106) {
		tmp = (j * (k * -27.0)) + (b * c);
	} else {
		tmp = 18.0 * (t * (x * (y * z)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if t <= -9.5e+121:
		tmp = c * (b + (t * (-4.0 * (a / c))))
	elif t <= 7e+106:
		tmp = (j * (k * -27.0)) + (b * c)
	else:
		tmp = 18.0 * (t * (x * (y * z)))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (t <= -9.5e+121)
		tmp = Float64(c * Float64(b + Float64(t * Float64(-4.0 * Float64(a / c)))));
	elseif (t <= 7e+106)
		tmp = Float64(Float64(j * Float64(k * -27.0)) + Float64(b * c));
	else
		tmp = Float64(18.0 * Float64(t * Float64(x * Float64(y * z))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (t <= -9.5e+121)
		tmp = c * (b + (t * (-4.0 * (a / c))));
	elseif (t <= 7e+106)
		tmp = (j * (k * -27.0)) + (b * c);
	else
		tmp = 18.0 * (t * (x * (y * z)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[t, -9.5e+121], N[(c * N[(b + N[(t * N[(-4.0 * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7e+106], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision], N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.49999999999999949e121

   1. Initial program 79.9%

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

   3. Taylor expanded in x around 0 63.0%

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

   4. Taylor expanded in c around inf 60.6%

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

      1. associate-*r/ 60.6%

         \[\leadsto c \cdot \left(b + \color{blue}{\frac{-1 \cdot \left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)}{c}}\right) \]

      2. mul-1-neg 60.6%

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

      3. *-commutative 60.6%

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

      4. *-commutative 60.6%

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

      5. associate-*r* 60.6%

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

      6. *-commutative 60.6%

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

      7. associate-*l* 60.6%

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

      8. *-commutative 60.6%

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

      9. distribute-neg-in 60.6%

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

      10. distribute-rgt-neg-in 60.6%

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

      11. distribute-rgt-neg-in 60.6%

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

      12. metadata-eval 60.6%

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

      13. distribute-rgt-neg-in 60.6%

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

      14. distribute-lft-neg-in 60.6%

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

      15. metadata-eval 60.6%

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

      16. *-commutative 60.6%

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

   6. Simplified 60.6%

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

   7. Taylor expanded in t around inf 50.7%

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

      1. associate-*r/ 50.7%

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

      2. *-commutative 50.7%

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

      3. *-commutative 50.7%

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

      4. associate-*r* 50.7%

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

      5. *-commutative 50.7%

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

      6. associate-*r/ 50.7%

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

      7. associate-*r/ 50.7%

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

   9. Simplified 50.7%

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

   if -9.49999999999999949e121 < t < 6.99999999999999962e106

   1. Initial program 88.7%

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

   3. Simplified 89.9%

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

   5. Taylor expanded in b around inf 55.8%

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

   if 6.99999999999999962e106 < t

   1. Initial program 80.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 92.4%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 89.2%

      \[\leadsto \color{blue}{t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)} \]

   6. Taylor expanded in x around inf 57.1%

      \[\leadsto \color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 55.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{+121}:\\ \;\;\;\;c \cdot \left(b + t \cdot \left(-4 \cdot \frac{a}{c}\right)\right)\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+106}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \mathbf{else}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 49.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;t \leq -9.5 \cdot 10^{-20}:\\ \;\;\;\;t\_1 + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{+106}:\\ \;\;\;\;t\_1 + b \cdot c\\ \mathbf{else}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0))))
   (if (<= t -9.5e-20)
     (+ t_1 (* -4.0 (* t a)))
     (if (<= t 2.4e+106) (+ t_1 (* b c)) (* 18.0 (* t (* x (* y z))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double tmp;
	if (t <= -9.5e-20) {
		tmp = t_1 + (-4.0 * (t * a));
	} else if (t <= 2.4e+106) {
		tmp = t_1 + (b * c);
	} else {
		tmp = 18.0 * (t * (x * (y * z)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * (k * (-27.0d0))
    if (t <= (-9.5d-20)) then
        tmp = t_1 + ((-4.0d0) * (t * a))
    else if (t <= 2.4d+106) then
        tmp = t_1 + (b * c)
    else
        tmp = 18.0d0 * (t * (x * (y * z)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double tmp;
	if (t <= -9.5e-20) {
		tmp = t_1 + (-4.0 * (t * a));
	} else if (t <= 2.4e+106) {
		tmp = t_1 + (b * c);
	} else {
		tmp = 18.0 * (t * (x * (y * z)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	tmp = 0
	if t <= -9.5e-20:
		tmp = t_1 + (-4.0 * (t * a))
	elif t <= 2.4e+106:
		tmp = t_1 + (b * c)
	else:
		tmp = 18.0 * (t * (x * (y * z)))
	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(j * Float64(k * -27.0))
	tmp = 0.0
	if (t <= -9.5e-20)
		tmp = Float64(t_1 + Float64(-4.0 * Float64(t * a)));
	elseif (t <= 2.4e+106)
		tmp = Float64(t_1 + Float64(b * c));
	else
		tmp = Float64(18.0 * Float64(t * Float64(x * Float64(y * z))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * -27.0);
	tmp = 0.0;
	if (t <= -9.5e-20)
		tmp = t_1 + (-4.0 * (t * a));
	elseif (t <= 2.4e+106)
		tmp = t_1 + (b * c);
	else
		tmp = 18.0 * (t * (x * (y * z)));
	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[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -9.5e-20], N[(t$95$1 + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.4e+106], N[(t$95$1 + N[(b * c), $MachinePrecision]), $MachinePrecision], N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.5e-20

   1. Initial program 83.2%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 87.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 61.6%

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t\right)} + j \cdot \left(k \cdot -27\right) \]
   6. Step-by-step derivation

      1. *-commutative 61.6%

         \[\leadsto -4 \cdot \color{blue}{\left(t \cdot a\right)} + j \cdot \left(k \cdot -27\right) \]

   7. Simplified 61.6%

      \[\leadsto \color{blue}{-4 \cdot \left(t \cdot a\right)} + j \cdot \left(k \cdot -27\right) \]

   if -9.5e-20 < t < 2.4000000000000001e106

   1. Initial program 88.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 89.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 57.9%

      \[\leadsto \color{blue}{b \cdot c} + j \cdot \left(k \cdot -27\right) \]

   if 2.4000000000000001e106 < t

   1. Initial program 80.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 92.4%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 89.2%

      \[\leadsto \color{blue}{t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)} \]

   6. Taylor expanded in x around inf 57.1%

      \[\leadsto \color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 58.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{-20}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{+106}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \mathbf{else}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 22.9% accurate, 10.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ b \cdot c \end{array} \]

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 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. Step-by-step derivation

   1. pow1 85.9%

      \[\leadsto \left(\left(\left(\color{blue}{{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t\right)}^{1}} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. associate-*l* 83.2%

      \[\leadsto \left(\left(\left({\color{blue}{\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot \left(z \cdot t\right)\right)}}^{1} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. *-commutative 83.2%

      \[\leadsto \left(\left(\left({\left(\color{blue}{\left(y \cdot \left(x \cdot 18\right)\right)} \cdot \left(z \cdot t\right)\right)}^{1} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

4. Applied egg-rr 83.2%

   \[\leadsto \left(\left(\left(\color{blue}{{\left(\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right)\right)}^{1}} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
5. Step-by-step derivation

   1. unpow1 83.2%

      \[\leadsto \left(\left(\left(\color{blue}{\left(y \cdot \left(x \cdot 18\right)\right) \cdot \left(z \cdot t\right)} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. associate-*l* 85.1%

      \[\leadsto \left(\left(\left(\color{blue}{y \cdot \left(\left(x \cdot 18\right) \cdot \left(z \cdot t\right)\right)} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. *-commutative 85.1%

      \[\leadsto \left(\left(\left(y \cdot \left(\left(x \cdot 18\right) \cdot \color{blue}{\left(t \cdot z\right)}\right) - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

6. Simplified 85.1%

   \[\leadsto \left(\left(\left(\color{blue}{y \cdot \left(\left(x \cdot 18\right) \cdot \left(t \cdot z\right)\right)} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

7. Taylor expanded in y around 0 79.8%

   \[\leadsto \color{blue}{\left(b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]
8. Step-by-step derivation

   1. distribute-lft-out 79.8%

      \[\leadsto \left(b \cdot c - \color{blue}{4 \cdot \left(a \cdot t + i \cdot x\right)}\right) - \left(j \cdot 27\right) \cdot k \]

   2. *-commutative 79.8%

      \[\leadsto \left(b \cdot c - 4 \cdot \left(\color{blue}{t \cdot a} + i \cdot x\right)\right) - \left(j \cdot 27\right) \cdot k \]

   3. *-commutative 79.8%

      \[\leadsto \left(b \cdot c - 4 \cdot \left(t \cdot a + \color{blue}{x \cdot i}\right)\right) - \left(j \cdot 27\right) \cdot k \]

9. Simplified 79.8%

   \[\leadsto \color{blue}{\left(b \cdot c - 4 \cdot \left(t \cdot a + x \cdot i\right)\right)} - \left(j \cdot 27\right) \cdot k \]

10. Taylor expanded in b around inf 22.7%

    \[\leadsto \color{blue}{b \cdot c} \]

11. Final simplification 22.7%

    \[\leadsto b \cdot c \]
12. Add Preprocessing

Developer target: 89.6% 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 2024058 
(FPCore (x y z t a b c i j k)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, E"
  :precision binary64

  :alt
  (if (< t -1.6210815397541398e-69) (- (- (* (* 18.0 t) (* (* x y) z)) (* (+ (* a t) (* i x)) 4.0)) (- (* (* k j) 27.0) (* c b))) (if (< t 165.68027943805222) (+ (- (* (* 18.0 y) (* x (* z t))) (* (+ (* a t) (* i x)) 4.0)) (- (* c b) (* 27.0 (* k j)))) (- (- (* (* 18.0 t) (* (* x y) z)) (* (+ (* a t) (* i x)) 4.0)) (- (* (* k j) 27.0) (* c b)))))

  (- (- (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i)) (* (* j 27.0) k)))