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

Percentage Accurate: 85.6% → 90.3%

Time: 32.1s

Alternatives: 24

Speedup: 0.5×

• 49.9% 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: 90.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;t \leq -6.5 \cdot 10^{-245}:\\ \;\;\;\;\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(-4 \cdot i\right)\right)\right) + t_1\\ \mathbf{elif}\;t \leq 6.4 \cdot 10^{-57}:\\ \;\;\;\;t_1 + \mathsf{fma}\left(x, \mathsf{fma}\left(18, y \cdot \left(t \cdot z\right), -4 \cdot i\right), b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(x, z \cdot \left(18 \cdot y\right), a \cdot \left(-4\right)\right), t, b \cdot c - \mathsf{fma}\left(j, k \cdot 27, i \cdot \left(x \cdot 4\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0))))
   (if (<= t -6.5e-245)
     (+
      (fma t (fma x (* 18.0 (* y z)) (* a -4.0)) (fma b c (* x (* -4.0 i))))
      t_1)
     (if (<= t 6.4e-57)
       (+ t_1 (fma x (fma 18.0 (* y (* t z)) (* -4.0 i)) (* b c)))
       (fma
        (fma x (* z (* 18.0 y)) (* a (- 4.0)))
        t
        (- (* b c) (fma j (* k 27.0) (* i (* x 4.0)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double tmp;
	if (t <= -6.5e-245) {
		tmp = fma(t, fma(x, (18.0 * (y * z)), (a * -4.0)), fma(b, c, (x * (-4.0 * i)))) + t_1;
	} else if (t <= 6.4e-57) {
		tmp = t_1 + fma(x, fma(18.0, (y * (t * z)), (-4.0 * i)), (b * c));
	} else {
		tmp = fma(fma(x, (z * (18.0 * y)), (a * -4.0)), t, ((b * c) - fma(j, (k * 27.0), (i * (x * 4.0)))));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * -27.0))
	tmp = 0.0
	if (t <= -6.5e-245)
		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)))) + t_1);
	elseif (t <= 6.4e-57)
		tmp = Float64(t_1 + fma(x, fma(18.0, Float64(y * Float64(t * z)), Float64(-4.0 * i)), Float64(b * c)));
	else
		tmp = fma(fma(x, Float64(z * Float64(18.0 * y)), Float64(a * Float64(-4.0))), t, Float64(Float64(b * c) - fma(j, Float64(k * 27.0), Float64(i * Float64(x * 4.0)))));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.5e-245], 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] + t$95$1), $MachinePrecision], If[LessEqual[t, 6.4e-57], N[(t$95$1 + N[(x * N[(18.0 * N[(y * N[(t * z), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * i), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(z * N[(18.0 * y), $MachinePrecision]), $MachinePrecision] + N[(a * (-4.0)), $MachinePrecision]), $MachinePrecision] * t + N[(N[(b * c), $MachinePrecision] - N[(j * N[(k * 27.0), $MachinePrecision] + N[(i * N[(x * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.5000000000000004e-245

   1. Initial program 84.7%

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

   3. Simplified 92.2%

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

   if -6.5000000000000004e-245 < t < 6.4000000000000002e-57

   1. Initial program 78.5%

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

   3. Simplified 79.9%

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

      1. associate-*r* 78.5%

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

      2. distribute-rgt-out-- 78.5%

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

      3. associate-*l* 85.3%

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

      4. *-commutative 85.3%

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

      5. *-commutative 85.3%

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

   6. Applied egg-rr 85.3%

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

   7. Taylor expanded in a around 0 77.1%

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

   9. Simplified 95.5%

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

   if 6.4000000000000002e-57 < t

   1. Initial program 89.9%

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

   3. Simplified 97.0%

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

      1. associate--l+ 97.0%

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

      2. *-commutative 97.0%

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

      3. fma-def 97.0%

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

      4. associate-*l* 97.0%

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

      5. fma-neg 97.0%

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

      6. associate-*r* 97.0%

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

      7. associate-*r* 97.0%

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

      8. +-commutative 97.0%

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

      9. fma-def 97.0%

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

      10. *-commutative 97.0%

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

      11. *-commutative 97.0%

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

   6. Applied egg-rr 97.0%

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

4. Final simplification 94.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{-245}:\\ \;\;\;\;\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(-4 \cdot i\right)\right)\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t \leq 6.4 \cdot 10^{-57}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + \mathsf{fma}\left(x, \mathsf{fma}\left(18, y \cdot \left(t \cdot z\right), -4 \cdot i\right), b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(x, z \cdot \left(18 \cdot y\right), a \cdot \left(-4\right)\right), t, b \cdot c - \mathsf{fma}\left(j, k \cdot 27, i \cdot \left(x \cdot 4\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 90.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;t \leq -6.5 \cdot 10^{-245} \lor \neg \left(t \leq 7 \cdot 10^{-57}\right):\\ \;\;\;\;\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(-4 \cdot i\right)\right)\right) + t_1\\ \mathbf{else}:\\ \;\;\;\;t_1 + \mathsf{fma}\left(x, \mathsf{fma}\left(18, y \cdot \left(t \cdot z\right), -4 \cdot i\right), b \cdot c\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 (or (<= t -6.5e-245) (not (<= t 7e-57)))
     (+
      (fma t (fma x (* 18.0 (* y z)) (* a -4.0)) (fma b c (* x (* -4.0 i))))
      t_1)
     (+ t_1 (fma x (fma 18.0 (* y (* t z)) (* -4.0 i)) (* b c))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double tmp;
	if ((t <= -6.5e-245) || !(t <= 7e-57)) {
		tmp = fma(t, fma(x, (18.0 * (y * z)), (a * -4.0)), fma(b, c, (x * (-4.0 * i)))) + t_1;
	} else {
		tmp = t_1 + fma(x, fma(18.0, (y * (t * z)), (-4.0 * i)), (b * c));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * -27.0))
	tmp = 0.0
	if ((t <= -6.5e-245) || !(t <= 7e-57))
		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)))) + t_1);
	else
		tmp = Float64(t_1 + fma(x, fma(18.0, Float64(y * Float64(t * z)), Float64(-4.0 * i)), Float64(b * c)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t, -6.5e-245], N[Not[LessEqual[t, 7e-57]], $MachinePrecision]], N[(N[(t * N[(x * N[(18.0 * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + N[(b * c + N[(x * N[(-4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(t$95$1 + N[(x * N[(18.0 * N[(y * N[(t * z), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * i), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -6.5000000000000004e-245 or 6.99999999999999983e-57 < t

   1. Initial program 86.6%

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

   3. Simplified 94.0%

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

   if -6.5000000000000004e-245 < t < 6.99999999999999983e-57

   1. Initial program 78.5%

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

   3. Simplified 79.9%

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

      1. associate-*r* 78.5%

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

      2. distribute-rgt-out-- 78.5%

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

      3. associate-*l* 85.3%

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

      4. *-commutative 85.3%

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

      5. *-commutative 85.3%

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

   6. Applied egg-rr 85.3%

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

   7. Taylor expanded in a around 0 77.1%

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

   9. Simplified 95.5%

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

4. Final simplification 94.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{-245} \lor \neg \left(t \leq 7 \cdot 10^{-57}\right):\\ \;\;\;\;\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(-4 \cdot i\right)\right)\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + \mathsf{fma}\left(x, \mathsf{fma}\left(18, y \cdot \left(t \cdot z\right), -4 \cdot i\right), b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 53.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := t_1 + b \cdot c\\ t_3 := t_1 + -4 \cdot \left(t \cdot a\right)\\ t_4 := t_1 + x \cdot \left(-4 \cdot i\right)\\ t_5 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;b \cdot c \leq -4.7 \cdot 10^{+39}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \cdot c \leq -2.7 \cdot 10^{-66}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;b \cdot c \leq -3.3 \cdot 10^{-166}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \cdot c \leq 1.65 \cdot 10^{-177}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;b \cdot c \leq 1.25 \cdot 10^{-110}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \cdot c \leq 1.4 \cdot 10^{-44}:\\ \;\;\;\;t_5 \cdot \left(t \cdot 18\right)\\ \mathbf{elif}\;b \cdot c \leq 4 \cdot 10^{+17}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \cdot c \leq 6.2 \cdot 10^{+35}:\\ \;\;\;\;18 \cdot \left(t \cdot t_5\right)\\ \mathbf{elif}\;b \cdot c \leq 2.25 \cdot 10^{+189}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0)))
        (t_2 (+ t_1 (* b c)))
        (t_3 (+ t_1 (* -4.0 (* t a))))
        (t_4 (+ t_1 (* x (* -4.0 i))))
        (t_5 (* x (* y z))))
   (if (<= (* b c) -4.7e+39)
     t_2
     (if (<= (* b c) -2.7e-66)
       t_4
       (if (<= (* b c) -3.3e-166)
         t_3
         (if (<= (* b c) 1.65e-177)
           t_4
           (if (<= (* b c) 1.25e-110)
             t_3
             (if (<= (* b c) 1.4e-44)
               (* t_5 (* t 18.0))
               (if (<= (* b c) 4e+17)
                 t_3
                 (if (<= (* b c) 6.2e+35)
                   (* 18.0 (* t t_5))
                   (if (<= (* b c) 2.25e+189) t_4 t_2)))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = t_1 + (b * c);
	double t_3 = t_1 + (-4.0 * (t * a));
	double t_4 = t_1 + (x * (-4.0 * i));
	double t_5 = x * (y * z);
	double tmp;
	if ((b * c) <= -4.7e+39) {
		tmp = t_2;
	} else if ((b * c) <= -2.7e-66) {
		tmp = t_4;
	} else if ((b * c) <= -3.3e-166) {
		tmp = t_3;
	} else if ((b * c) <= 1.65e-177) {
		tmp = t_4;
	} else if ((b * c) <= 1.25e-110) {
		tmp = t_3;
	} else if ((b * c) <= 1.4e-44) {
		tmp = t_5 * (t * 18.0);
	} else if ((b * c) <= 4e+17) {
		tmp = t_3;
	} else if ((b * c) <= 6.2e+35) {
		tmp = 18.0 * (t * t_5);
	} else if ((b * c) <= 2.25e+189) {
		tmp = t_4;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_1 = j * (k * (-27.0d0))
    t_2 = t_1 + (b * c)
    t_3 = t_1 + ((-4.0d0) * (t * a))
    t_4 = t_1 + (x * ((-4.0d0) * i))
    t_5 = x * (y * z)
    if ((b * c) <= (-4.7d+39)) then
        tmp = t_2
    else if ((b * c) <= (-2.7d-66)) then
        tmp = t_4
    else if ((b * c) <= (-3.3d-166)) then
        tmp = t_3
    else if ((b * c) <= 1.65d-177) then
        tmp = t_4
    else if ((b * c) <= 1.25d-110) then
        tmp = t_3
    else if ((b * c) <= 1.4d-44) then
        tmp = t_5 * (t * 18.0d0)
    else if ((b * c) <= 4d+17) then
        tmp = t_3
    else if ((b * c) <= 6.2d+35) then
        tmp = 18.0d0 * (t * t_5)
    else if ((b * c) <= 2.25d+189) then
        tmp = t_4
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = t_1 + (b * c);
	double t_3 = t_1 + (-4.0 * (t * a));
	double t_4 = t_1 + (x * (-4.0 * i));
	double t_5 = x * (y * z);
	double tmp;
	if ((b * c) <= -4.7e+39) {
		tmp = t_2;
	} else if ((b * c) <= -2.7e-66) {
		tmp = t_4;
	} else if ((b * c) <= -3.3e-166) {
		tmp = t_3;
	} else if ((b * c) <= 1.65e-177) {
		tmp = t_4;
	} else if ((b * c) <= 1.25e-110) {
		tmp = t_3;
	} else if ((b * c) <= 1.4e-44) {
		tmp = t_5 * (t * 18.0);
	} else if ((b * c) <= 4e+17) {
		tmp = t_3;
	} else if ((b * c) <= 6.2e+35) {
		tmp = 18.0 * (t * t_5);
	} else if ((b * c) <= 2.25e+189) {
		tmp = t_4;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	t_2 = t_1 + (b * c)
	t_3 = t_1 + (-4.0 * (t * a))
	t_4 = t_1 + (x * (-4.0 * i))
	t_5 = x * (y * z)
	tmp = 0
	if (b * c) <= -4.7e+39:
		tmp = t_2
	elif (b * c) <= -2.7e-66:
		tmp = t_4
	elif (b * c) <= -3.3e-166:
		tmp = t_3
	elif (b * c) <= 1.65e-177:
		tmp = t_4
	elif (b * c) <= 1.25e-110:
		tmp = t_3
	elif (b * c) <= 1.4e-44:
		tmp = t_5 * (t * 18.0)
	elif (b * c) <= 4e+17:
		tmp = t_3
	elif (b * c) <= 6.2e+35:
		tmp = 18.0 * (t * t_5)
	elif (b * c) <= 2.25e+189:
		tmp = t_4
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * -27.0))
	t_2 = Float64(t_1 + Float64(b * c))
	t_3 = Float64(t_1 + Float64(-4.0 * Float64(t * a)))
	t_4 = Float64(t_1 + Float64(x * Float64(-4.0 * i)))
	t_5 = Float64(x * Float64(y * z))
	tmp = 0.0
	if (Float64(b * c) <= -4.7e+39)
		tmp = t_2;
	elseif (Float64(b * c) <= -2.7e-66)
		tmp = t_4;
	elseif (Float64(b * c) <= -3.3e-166)
		tmp = t_3;
	elseif (Float64(b * c) <= 1.65e-177)
		tmp = t_4;
	elseif (Float64(b * c) <= 1.25e-110)
		tmp = t_3;
	elseif (Float64(b * c) <= 1.4e-44)
		tmp = Float64(t_5 * Float64(t * 18.0));
	elseif (Float64(b * c) <= 4e+17)
		tmp = t_3;
	elseif (Float64(b * c) <= 6.2e+35)
		tmp = Float64(18.0 * Float64(t * t_5));
	elseif (Float64(b * c) <= 2.25e+189)
		tmp = t_4;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * -27.0);
	t_2 = t_1 + (b * c);
	t_3 = t_1 + (-4.0 * (t * a));
	t_4 = t_1 + (x * (-4.0 * i));
	t_5 = x * (y * z);
	tmp = 0.0;
	if ((b * c) <= -4.7e+39)
		tmp = t_2;
	elseif ((b * c) <= -2.7e-66)
		tmp = t_4;
	elseif ((b * c) <= -3.3e-166)
		tmp = t_3;
	elseif ((b * c) <= 1.65e-177)
		tmp = t_4;
	elseif ((b * c) <= 1.25e-110)
		tmp = t_3;
	elseif ((b * c) <= 1.4e-44)
		tmp = t_5 * (t * 18.0);
	elseif ((b * c) <= 4e+17)
		tmp = t_3;
	elseif ((b * c) <= 6.2e+35)
		tmp = 18.0 * (t * t_5);
	elseif ((b * c) <= 2.25e+189)
		tmp = t_4;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(b * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$1 + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$1 + N[(x * N[(-4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -4.7e+39], t$95$2, If[LessEqual[N[(b * c), $MachinePrecision], -2.7e-66], t$95$4, If[LessEqual[N[(b * c), $MachinePrecision], -3.3e-166], t$95$3, If[LessEqual[N[(b * c), $MachinePrecision], 1.65e-177], t$95$4, If[LessEqual[N[(b * c), $MachinePrecision], 1.25e-110], t$95$3, If[LessEqual[N[(b * c), $MachinePrecision], 1.4e-44], N[(t$95$5 * N[(t * 18.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 4e+17], t$95$3, If[LessEqual[N[(b * c), $MachinePrecision], 6.2e+35], N[(18.0 * N[(t * t$95$5), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 2.25e+189], t$95$4, t$95$2]]]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 b c) < -4.6999999999999999e39 or 2.24999999999999987e189 < (*.f64 b c)

   1. Initial program 82.9%

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

   3. Simplified 86.4%

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

   5. Taylor expanded in b around inf 77.7%

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

   if -4.6999999999999999e39 < (*.f64 b c) < -2.69999999999999996e-66 or -3.30000000000000018e-166 < (*.f64 b c) < 1.65e-177 or 6.19999999999999973e35 < (*.f64 b c) < 2.24999999999999987e189

   1. Initial program 84.6%

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

   3. Simplified 89.6%

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

   5. Taylor expanded in i around inf 62.9%

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

      1. associate-*r* 62.9%

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

      2. *-commutative 62.9%

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

   7. Simplified 62.9%

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

   if -2.69999999999999996e-66 < (*.f64 b c) < -3.30000000000000018e-166 or 1.65e-177 < (*.f64 b c) < 1.25e-110 or 1.4e-44 < (*.f64 b c) < 4e17

   1. Initial program 93.1%

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

   3. Simplified 96.3%

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

   5. Taylor expanded in a around inf 79.8%

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

      1. *-commutative 79.8%

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

   7. Simplified 79.8%

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

   if 1.25e-110 < (*.f64 b c) < 1.4e-44

   1. Initial program 84.9%

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

   3. Simplified 99.7%

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

      1. associate--l+ 99.7%

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

      2. *-commutative 99.7%

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

      3. fma-def 99.7%

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

      4. associate-*l* 99.7%

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

      5. fma-neg 99.7%

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

      6. associate-*r* 94.8%

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

      7. associate-*r* 94.8%

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

      8. +-commutative 94.8%

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

      9. fma-def 94.8%

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

      10. *-commutative 94.8%

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

      11. *-commutative 94.8%

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

   6. Applied egg-rr 94.8%

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

   7. Taylor expanded in y around inf 50.5%

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

      1. associate-*r* 50.6%

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

      2. *-commutative 50.6%

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

      3. *-commutative 50.6%

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

   9. Simplified 50.6%

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

   if 4e17 < (*.f64 b c) < 6.19999999999999973e35

   1. Initial program 50.0%

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

   3. Simplified 100.0%

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

      1. associate--l+ 100.0%

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

      2. *-commutative 100.0%

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

      3. fma-def 100.0%

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

      4. associate-*l* 100.0%

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

      5. fma-neg 100.0%

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

      6. associate-*r* 100.0%

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

      7. associate-*r* 100.0%

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

      8. +-commutative 100.0%

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

      9. fma-def 100.0%

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

      10. *-commutative 100.0%

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

      11. *-commutative 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in y around inf 100.0%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -4.7 \cdot 10^{+39}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -2.7 \cdot 10^{-66}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + x \cdot \left(-4 \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq -3.3 \cdot 10^{-166}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;b \cdot c \leq 1.65 \cdot 10^{-177}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + x \cdot \left(-4 \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 1.25 \cdot 10^{-110}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;b \cdot c \leq 1.4 \cdot 10^{-44}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z\right)\right) \cdot \left(t \cdot 18\right)\\ \mathbf{elif}\;b \cdot c \leq 4 \cdot 10^{+17}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;b \cdot c \leq 6.2 \cdot 10^{+35}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 2.25 \cdot 10^{+189}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + x \cdot \left(-4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 91.0% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (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))) <= Inf)
		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(z * Float64(t * y))) - Float64(i * 4.0)));
	end
	return tmp
end

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 96.1%

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

   3. Simplified 96.0%

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

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

   1. Initial program 0.0%

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

   3. Simplified 35.5%

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

   5. Taylor expanded in x around inf 61.6%

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

      1. expm1-log1p-u 32.5%

         \[\leadsto x \cdot \left(18 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(t \cdot \left(y \cdot z\right)\right)\right)} - 4 \cdot i\right) \]

      2. expm1-udef 32.5%

         \[\leadsto x \cdot \left(18 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(t \cdot \left(y \cdot z\right)\right)} - 1\right)} - 4 \cdot i\right) \]

   7. Applied egg-rr 32.5%

      \[\leadsto x \cdot \left(18 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(t \cdot \left(y \cdot z\right)\right)} - 1\right)} - 4 \cdot i\right) \]
   8. Step-by-step derivation

      1. expm1-def 32.5%

         \[\leadsto x \cdot \left(18 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(t \cdot \left(y \cdot z\right)\right)\right)} - 4 \cdot i\right) \]

      2. expm1-log1p 61.6%

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

      3. associate-*r* 61.6%

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

   9. Simplified 61.6%

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

4. Final simplification 91.8%

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

Alternative 5: 51.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := t_1 + b \cdot c\\ t_3 := t_1 + -4 \cdot \left(t \cdot a\right)\\ \mathbf{if}\;b \cdot c \leq -5.8 \cdot 10^{-42}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \cdot c \leq 1.22 \cdot 10^{-110}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \cdot c \leq 1.5 \cdot 10^{-44}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z\right)\right) \cdot \left(t \cdot 18\right)\\ \mathbf{elif}\;b \cdot c \leq 5 \cdot 10^{+139}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \cdot c \leq 2.4 \cdot 10^{+169}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 5.6 \cdot 10^{+247}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0)))
        (t_2 (+ t_1 (* b c)))
        (t_3 (+ t_1 (* -4.0 (* t a)))))
   (if (<= (* b c) -5.8e-42)
     t_2
     (if (<= (* b c) 1.22e-110)
       t_3
       (if (<= (* b c) 1.5e-44)
         (* (* x (* y z)) (* t 18.0))
         (if (<= (* b c) 5e+139)
           t_3
           (if (<= (* b c) 2.4e+169)
             (* -4.0 (* x i))
             (if (<= (* b c) 5.6e+247) t_3 t_2))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = t_1 + (b * c);
	double t_3 = t_1 + (-4.0 * (t * a));
	double tmp;
	if ((b * c) <= -5.8e-42) {
		tmp = t_2;
	} else if ((b * c) <= 1.22e-110) {
		tmp = t_3;
	} else if ((b * c) <= 1.5e-44) {
		tmp = (x * (y * z)) * (t * 18.0);
	} else if ((b * c) <= 5e+139) {
		tmp = t_3;
	} else if ((b * c) <= 2.4e+169) {
		tmp = -4.0 * (x * i);
	} else if ((b * c) <= 5.6e+247) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = j * (k * (-27.0d0))
    t_2 = t_1 + (b * c)
    t_3 = t_1 + ((-4.0d0) * (t * a))
    if ((b * c) <= (-5.8d-42)) then
        tmp = t_2
    else if ((b * c) <= 1.22d-110) then
        tmp = t_3
    else if ((b * c) <= 1.5d-44) then
        tmp = (x * (y * z)) * (t * 18.0d0)
    else if ((b * c) <= 5d+139) then
        tmp = t_3
    else if ((b * c) <= 2.4d+169) then
        tmp = (-4.0d0) * (x * i)
    else if ((b * c) <= 5.6d+247) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = t_1 + (b * c);
	double t_3 = t_1 + (-4.0 * (t * a));
	double tmp;
	if ((b * c) <= -5.8e-42) {
		tmp = t_2;
	} else if ((b * c) <= 1.22e-110) {
		tmp = t_3;
	} else if ((b * c) <= 1.5e-44) {
		tmp = (x * (y * z)) * (t * 18.0);
	} else if ((b * c) <= 5e+139) {
		tmp = t_3;
	} else if ((b * c) <= 2.4e+169) {
		tmp = -4.0 * (x * i);
	} else if ((b * c) <= 5.6e+247) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	t_2 = t_1 + (b * c)
	t_3 = t_1 + (-4.0 * (t * a))
	tmp = 0
	if (b * c) <= -5.8e-42:
		tmp = t_2
	elif (b * c) <= 1.22e-110:
		tmp = t_3
	elif (b * c) <= 1.5e-44:
		tmp = (x * (y * z)) * (t * 18.0)
	elif (b * c) <= 5e+139:
		tmp = t_3
	elif (b * c) <= 2.4e+169:
		tmp = -4.0 * (x * i)
	elif (b * c) <= 5.6e+247:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * -27.0))
	t_2 = Float64(t_1 + Float64(b * c))
	t_3 = Float64(t_1 + Float64(-4.0 * Float64(t * a)))
	tmp = 0.0
	if (Float64(b * c) <= -5.8e-42)
		tmp = t_2;
	elseif (Float64(b * c) <= 1.22e-110)
		tmp = t_3;
	elseif (Float64(b * c) <= 1.5e-44)
		tmp = Float64(Float64(x * Float64(y * z)) * Float64(t * 18.0));
	elseif (Float64(b * c) <= 5e+139)
		tmp = t_3;
	elseif (Float64(b * c) <= 2.4e+169)
		tmp = Float64(-4.0 * Float64(x * i));
	elseif (Float64(b * c) <= 5.6e+247)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * -27.0);
	t_2 = t_1 + (b * c);
	t_3 = t_1 + (-4.0 * (t * a));
	tmp = 0.0;
	if ((b * c) <= -5.8e-42)
		tmp = t_2;
	elseif ((b * c) <= 1.22e-110)
		tmp = t_3;
	elseif ((b * c) <= 1.5e-44)
		tmp = (x * (y * z)) * (t * 18.0);
	elseif ((b * c) <= 5e+139)
		tmp = t_3;
	elseif ((b * c) <= 2.4e+169)
		tmp = -4.0 * (x * i);
	elseif ((b * c) <= 5.6e+247)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(b * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$1 + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -5.8e-42], t$95$2, If[LessEqual[N[(b * c), $MachinePrecision], 1.22e-110], t$95$3, If[LessEqual[N[(b * c), $MachinePrecision], 1.5e-44], N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] * N[(t * 18.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 5e+139], t$95$3, If[LessEqual[N[(b * c), $MachinePrecision], 2.4e+169], N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 5.6e+247], t$95$3, t$95$2]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 b c) < -5.8000000000000006e-42 or 5.59999999999999961e247 < (*.f64 b c)

   1. Initial program 84.0%

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

   3. Simplified 87.3%

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

   5. Taylor expanded in b around inf 72.2%

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

   if -5.8000000000000006e-42 < (*.f64 b c) < 1.22e-110 or 1.5000000000000001e-44 < (*.f64 b c) < 5.0000000000000003e139 or 2.3999999999999998e169 < (*.f64 b c) < 5.59999999999999961e247

   1. Initial program 84.7%

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

   3. Simplified 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 a around inf 60.2%

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

      1. *-commutative 60.2%

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

   7. Simplified 60.2%

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

   if 1.22e-110 < (*.f64 b c) < 1.5000000000000001e-44

   1. Initial program 84.9%

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

   3. Simplified 99.7%

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

      1. associate--l+ 99.7%

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

      2. *-commutative 99.7%

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

      3. fma-def 99.7%

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

      4. associate-*l* 99.7%

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

      5. fma-neg 99.7%

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

      6. associate-*r* 94.8%

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

      7. associate-*r* 94.8%

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

      8. +-commutative 94.8%

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

      9. fma-def 94.8%

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

      10. *-commutative 94.8%

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

      11. *-commutative 94.8%

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

   6. Applied egg-rr 94.8%

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

   7. Taylor expanded in y around inf 50.5%

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

      1. associate-*r* 50.6%

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

      2. *-commutative 50.6%

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

      3. *-commutative 50.6%

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

   9. Simplified 50.6%

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

   if 5.0000000000000003e139 < (*.f64 b c) < 2.3999999999999998e169

   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 84.4%

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

      1. associate--l+ 84.4%

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

      2. *-commutative 84.4%

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

      3. fma-def 84.4%

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

      4. associate-*l* 84.4%

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

      5. fma-neg 84.4%

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

      6. associate-*r* 84.4%

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

      7. associate-*r* 84.4%

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

      8. +-commutative 84.4%

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

      9. fma-def 84.4%

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

      10. *-commutative 84.4%

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

      11. *-commutative 84.4%

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

   6. Applied egg-rr 84.4%

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

   7. Taylor expanded in i around inf 68.0%

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

      1. *-commutative 68.0%

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

   9. Simplified 68.0%

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

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -5.8 \cdot 10^{-42}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \mathbf{elif}\;b \cdot c \leq 1.22 \cdot 10^{-110}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;b \cdot c \leq 1.5 \cdot 10^{-44}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z\right)\right) \cdot \left(t \cdot 18\right)\\ \mathbf{elif}\;b \cdot c \leq 5 \cdot 10^{+139}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;b \cdot c \leq 2.4 \cdot 10^{+169}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 5.6 \cdot 10^{+247}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 69.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := 4 \cdot \left(x \cdot i\right)\\ t_2 := k \cdot \left(j \cdot 27\right)\\ t_3 := \left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - t_1\\ \mathbf{if}\;t_2 \leq -4 \cdot 10^{+53}:\\ \;\;\;\;\left(b \cdot c - t_1\right) - t_2\\ \mathbf{elif}\;t_2 \leq 500:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_2 \leq 3 \cdot 10^{+48}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(t \cdot y\right)\right) - i \cdot 4\right)\\ \mathbf{elif}\;t_2 \leq 10^{+106}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* 4.0 (* x i)))
        (t_2 (* k (* j 27.0)))
        (t_3 (- (+ (* b c) (* -4.0 (* t a))) t_1)))
   (if (<= t_2 -4e+53)
     (- (- (* b c) t_1) t_2)
     (if (<= t_2 500.0)
       t_3
       (if (<= t_2 3e+48)
         (* x (- (* 18.0 (* z (* t y))) (* i 4.0)))
         (if (<= t_2 1e+106) t_3 (+ (* j (* k -27.0)) (* b c))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 4.0 * (x * i);
	double t_2 = k * (j * 27.0);
	double t_3 = ((b * c) + (-4.0 * (t * a))) - t_1;
	double tmp;
	if (t_2 <= -4e+53) {
		tmp = ((b * c) - t_1) - t_2;
	} else if (t_2 <= 500.0) {
		tmp = t_3;
	} else if (t_2 <= 3e+48) {
		tmp = x * ((18.0 * (z * (t * y))) - (i * 4.0));
	} else if (t_2 <= 1e+106) {
		tmp = t_3;
	} else {
		tmp = (j * (k * -27.0)) + (b * c);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = 4.0d0 * (x * i)
    t_2 = k * (j * 27.0d0)
    t_3 = ((b * c) + ((-4.0d0) * (t * a))) - t_1
    if (t_2 <= (-4d+53)) then
        tmp = ((b * c) - t_1) - t_2
    else if (t_2 <= 500.0d0) then
        tmp = t_3
    else if (t_2 <= 3d+48) then
        tmp = x * ((18.0d0 * (z * (t * y))) - (i * 4.0d0))
    else if (t_2 <= 1d+106) then
        tmp = t_3
    else
        tmp = (j * (k * (-27.0d0))) + (b * c)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 4.0 * (x * i);
	double t_2 = k * (j * 27.0);
	double t_3 = ((b * c) + (-4.0 * (t * a))) - t_1;
	double tmp;
	if (t_2 <= -4e+53) {
		tmp = ((b * c) - t_1) - t_2;
	} else if (t_2 <= 500.0) {
		tmp = t_3;
	} else if (t_2 <= 3e+48) {
		tmp = x * ((18.0 * (z * (t * y))) - (i * 4.0));
	} else if (t_2 <= 1e+106) {
		tmp = t_3;
	} else {
		tmp = (j * (k * -27.0)) + (b * c);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = 4.0 * (x * i)
	t_2 = k * (j * 27.0)
	t_3 = ((b * c) + (-4.0 * (t * a))) - t_1
	tmp = 0
	if t_2 <= -4e+53:
		tmp = ((b * c) - t_1) - t_2
	elif t_2 <= 500.0:
		tmp = t_3
	elif t_2 <= 3e+48:
		tmp = x * ((18.0 * (z * (t * y))) - (i * 4.0))
	elif t_2 <= 1e+106:
		tmp = t_3
	else:
		tmp = (j * (k * -27.0)) + (b * c)
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(4.0 * Float64(x * i))
	t_2 = Float64(k * Float64(j * 27.0))
	t_3 = Float64(Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a))) - t_1)
	tmp = 0.0
	if (t_2 <= -4e+53)
		tmp = Float64(Float64(Float64(b * c) - t_1) - t_2);
	elseif (t_2 <= 500.0)
		tmp = t_3;
	elseif (t_2 <= 3e+48)
		tmp = Float64(x * Float64(Float64(18.0 * Float64(z * Float64(t * y))) - Float64(i * 4.0)));
	elseif (t_2 <= 1e+106)
		tmp = t_3;
	else
		tmp = Float64(Float64(j * Float64(k * -27.0)) + Float64(b * c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = 4.0 * (x * i);
	t_2 = k * (j * 27.0);
	t_3 = ((b * c) + (-4.0 * (t * a))) - t_1;
	tmp = 0.0;
	if (t_2 <= -4e+53)
		tmp = ((b * c) - t_1) - t_2;
	elseif (t_2 <= 500.0)
		tmp = t_3;
	elseif (t_2 <= 3e+48)
		tmp = x * ((18.0 * (z * (t * y))) - (i * 4.0));
	elseif (t_2 <= 1e+106)
		tmp = t_3;
	else
		tmp = (j * (k * -27.0)) + (b * c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]}, If[LessEqual[t$95$2, -4e+53], N[(N[(N[(b * c), $MachinePrecision] - t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision], If[LessEqual[t$95$2, 500.0], t$95$3, If[LessEqual[t$95$2, 3e+48], N[(x * N[(N[(18.0 * N[(z * N[(t * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+106], t$95$3, N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 j 27) k) < -4e53

   1. Initial program 80.1%

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

   3. Taylor expanded in t around 0 78.9%

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

   if -4e53 < (*.f64 (*.f64 j 27) k) < 500 or 3e48 < (*.f64 (*.f64 j 27) k) < 1.00000000000000009e106

   1. Initial program 86.2%

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

   3. Simplified 89.6%

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

      1. associate--l+ 89.6%

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

      2. *-commutative 89.6%

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

      3. fma-def 91.7%

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

      4. associate-*l* 91.7%

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

      5. fma-neg 91.7%

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

      6. associate-*r* 91.0%

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

      7. associate-*r* 91.0%

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

      8. +-commutative 91.0%

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

      9. fma-def 91.0%

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

      10. *-commutative 91.0%

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

      11. *-commutative 91.0%

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

   6. Applied egg-rr 91.0%

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

   7. Taylor expanded in x around 0 81.9%

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

   8. Taylor expanded in j around 0 78.7%

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

   if 500 < (*.f64 (*.f64 j 27) k) < 3e48

   1. Initial program 61.5%

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

   3. Simplified 71.2%

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

   5. Taylor expanded in x around inf 70.9%

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

      1. expm1-log1p-u 58.5%

         \[\leadsto x \cdot \left(18 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(t \cdot \left(y \cdot z\right)\right)\right)} - 4 \cdot i\right) \]

      2. expm1-udef 58.5%

         \[\leadsto x \cdot \left(18 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(t \cdot \left(y \cdot z\right)\right)} - 1\right)} - 4 \cdot i\right) \]

   7. Applied egg-rr 58.5%

      \[\leadsto x \cdot \left(18 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(t \cdot \left(y \cdot z\right)\right)} - 1\right)} - 4 \cdot i\right) \]
   8. Step-by-step derivation

      1. expm1-def 58.5%

         \[\leadsto x \cdot \left(18 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(t \cdot \left(y \cdot z\right)\right)\right)} - 4 \cdot i\right) \]

      2. expm1-log1p 70.9%

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

      3. associate-*r* 61.4%

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

   9. Simplified 61.4%

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

   if 1.00000000000000009e106 < (*.f64 (*.f64 j 27) k)

   1. Initial program 90.3%

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

   3. Simplified 90.5%

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

   5. Taylor expanded in b around inf 81.0%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \cdot \left(j \cdot 27\right) \leq -4 \cdot 10^{+53}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 500:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 3 \cdot 10^{+48}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(t \cdot y\right)\right) - i \cdot 4\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 10^{+106}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 54.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;x \leq -5.2 \cdot 10^{+85}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(t \cdot y\right)\right) - i \cdot 4\right)\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{-36}:\\ \;\;\;\;t_1 + b \cdot c\\ \mathbf{elif}\;x \leq 112000000:\\ \;\;\;\;t_1 + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{+135} \lor \neg \left(x \leq 1.6 \cdot 10^{+237}\right):\\ \;\;\;\;t_1 + x \cdot \left(-4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t_1 + 18 \cdot \left(\left(y \cdot z\right) \cdot \left(t \cdot x\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0))))
   (if (<= x -5.2e+85)
     (* x (- (* 18.0 (* z (* t y))) (* i 4.0)))
     (if (<= x 9.2e-36)
       (+ t_1 (* b c))
       (if (<= x 112000000.0)
         (+ t_1 (* -4.0 (* t a)))
         (if (or (<= x 3.9e+135) (not (<= x 1.6e+237)))
           (+ t_1 (* x (* -4.0 i)))
           (+ t_1 (* 18.0 (* (* y z) (* t x))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double tmp;
	if (x <= -5.2e+85) {
		tmp = x * ((18.0 * (z * (t * y))) - (i * 4.0));
	} else if (x <= 9.2e-36) {
		tmp = t_1 + (b * c);
	} else if (x <= 112000000.0) {
		tmp = t_1 + (-4.0 * (t * a));
	} else if ((x <= 3.9e+135) || !(x <= 1.6e+237)) {
		tmp = t_1 + (x * (-4.0 * i));
	} else {
		tmp = t_1 + (18.0 * ((y * z) * (t * x)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * (k * (-27.0d0))
    if (x <= (-5.2d+85)) then
        tmp = x * ((18.0d0 * (z * (t * y))) - (i * 4.0d0))
    else if (x <= 9.2d-36) then
        tmp = t_1 + (b * c)
    else if (x <= 112000000.0d0) then
        tmp = t_1 + ((-4.0d0) * (t * a))
    else if ((x <= 3.9d+135) .or. (.not. (x <= 1.6d+237))) then
        tmp = t_1 + (x * ((-4.0d0) * i))
    else
        tmp = t_1 + (18.0d0 * ((y * z) * (t * x)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double tmp;
	if (x <= -5.2e+85) {
		tmp = x * ((18.0 * (z * (t * y))) - (i * 4.0));
	} else if (x <= 9.2e-36) {
		tmp = t_1 + (b * c);
	} else if (x <= 112000000.0) {
		tmp = t_1 + (-4.0 * (t * a));
	} else if ((x <= 3.9e+135) || !(x <= 1.6e+237)) {
		tmp = t_1 + (x * (-4.0 * i));
	} else {
		tmp = t_1 + (18.0 * ((y * z) * (t * x)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	tmp = 0
	if x <= -5.2e+85:
		tmp = x * ((18.0 * (z * (t * y))) - (i * 4.0))
	elif x <= 9.2e-36:
		tmp = t_1 + (b * c)
	elif x <= 112000000.0:
		tmp = t_1 + (-4.0 * (t * a))
	elif (x <= 3.9e+135) or not (x <= 1.6e+237):
		tmp = t_1 + (x * (-4.0 * i))
	else:
		tmp = t_1 + (18.0 * ((y * z) * (t * x)))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * -27.0))
	tmp = 0.0
	if (x <= -5.2e+85)
		tmp = Float64(x * Float64(Float64(18.0 * Float64(z * Float64(t * y))) - Float64(i * 4.0)));
	elseif (x <= 9.2e-36)
		tmp = Float64(t_1 + Float64(b * c));
	elseif (x <= 112000000.0)
		tmp = Float64(t_1 + Float64(-4.0 * Float64(t * a)));
	elseif ((x <= 3.9e+135) || !(x <= 1.6e+237))
		tmp = Float64(t_1 + Float64(x * Float64(-4.0 * i)));
	else
		tmp = Float64(t_1 + Float64(18.0 * Float64(Float64(y * z) * Float64(t * x))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * -27.0);
	tmp = 0.0;
	if (x <= -5.2e+85)
		tmp = x * ((18.0 * (z * (t * y))) - (i * 4.0));
	elseif (x <= 9.2e-36)
		tmp = t_1 + (b * c);
	elseif (x <= 112000000.0)
		tmp = t_1 + (-4.0 * (t * a));
	elseif ((x <= 3.9e+135) || ~((x <= 1.6e+237)))
		tmp = t_1 + (x * (-4.0 * i));
	else
		tmp = t_1 + (18.0 * ((y * z) * (t * x)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5.2e+85], N[(x * N[(N[(18.0 * N[(z * N[(t * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9.2e-36], N[(t$95$1 + N[(b * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 112000000.0], N[(t$95$1 + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, 3.9e+135], N[Not[LessEqual[x, 1.6e+237]], $MachinePrecision]], N[(t$95$1 + N[(x * N[(-4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(18.0 * N[(N[(y * z), $MachinePrecision] * N[(t * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -5.20000000000000021e85

   1. Initial program 69.6%

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

   3. Simplified 84.7%

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

   5. Taylor expanded in x around inf 77.5%

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

      1. expm1-log1p-u 61.5%

         \[\leadsto x \cdot \left(18 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(t \cdot \left(y \cdot z\right)\right)\right)} - 4 \cdot i\right) \]

      2. expm1-udef 59.8%

         \[\leadsto x \cdot \left(18 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(t \cdot \left(y \cdot z\right)\right)} - 1\right)} - 4 \cdot i\right) \]

   7. Applied egg-rr 59.8%

      \[\leadsto x \cdot \left(18 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(t \cdot \left(y \cdot z\right)\right)} - 1\right)} - 4 \cdot i\right) \]
   8. Step-by-step derivation

      1. expm1-def 61.5%

         \[\leadsto x \cdot \left(18 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(t \cdot \left(y \cdot z\right)\right)\right)} - 4 \cdot i\right) \]

      2. expm1-log1p 77.5%

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

      3. associate-*r* 75.8%

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

   9. Simplified 75.8%

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

   if -5.20000000000000021e85 < x < 9.19999999999999986e-36

   1. Initial program 92.0%

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

   3. Simplified 91.9%

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

   5. Taylor expanded in b around inf 63.9%

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

   if 9.19999999999999986e-36 < x < 1.12e8

   1. Initial program 85.5%

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

   3. Simplified 93.3%

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

   5. Taylor expanded in a around inf 71.6%

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

      1. *-commutative 71.6%

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

   7. Simplified 71.6%

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

   if 1.12e8 < x < 3.90000000000000032e135 or 1.60000000000000009e237 < x

   1. Initial program 87.5%

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

   3. Simplified 95.0%

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

   5. Taylor expanded in i around inf 66.4%

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

      1. associate-*r* 66.4%

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

      2. *-commutative 66.4%

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

   7. Simplified 66.4%

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

   if 3.90000000000000032e135 < x < 1.60000000000000009e237

   1. Initial program 72.1%

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

   3. Simplified 80.1%

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

   5. Taylor expanded in y around inf 74.7%

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

      1. associate-*r* 74.4%

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

   7. Simplified 74.4%

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

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{+85}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(t \cdot y\right)\right) - i \cdot 4\right)\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{-36}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \mathbf{elif}\;x \leq 112000000:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{+135} \lor \neg \left(x \leq 1.6 \cdot 10^{+237}\right):\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + x \cdot \left(-4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + 18 \cdot \left(\left(y \cdot z\right) \cdot \left(t \cdot x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 55.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;x \leq -8.8 \cdot 10^{+85}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(t \cdot y\right)\right) - i \cdot 4\right)\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-37}:\\ \;\;\;\;t_1 + b \cdot c\\ \mathbf{elif}\;x \leq 112000000:\\ \;\;\;\;t_1 + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq 5.3 \cdot 10^{+143} \lor \neg \left(x \leq 1.05 \cdot 10^{+241}\right):\\ \;\;\;\;t_1 + x \cdot \left(-4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t_1 + x \cdot \left(\left(t \cdot y\right) \cdot \left(18 \cdot z\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0))))
   (if (<= x -8.8e+85)
     (* x (- (* 18.0 (* z (* t y))) (* i 4.0)))
     (if (<= x 7e-37)
       (+ t_1 (* b c))
       (if (<= x 112000000.0)
         (+ t_1 (* -4.0 (* t a)))
         (if (or (<= x 5.3e+143) (not (<= x 1.05e+241)))
           (+ t_1 (* x (* -4.0 i)))
           (+ t_1 (* x (* (* t y) (* 18.0 z))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double tmp;
	if (x <= -8.8e+85) {
		tmp = x * ((18.0 * (z * (t * y))) - (i * 4.0));
	} else if (x <= 7e-37) {
		tmp = t_1 + (b * c);
	} else if (x <= 112000000.0) {
		tmp = t_1 + (-4.0 * (t * a));
	} else if ((x <= 5.3e+143) || !(x <= 1.05e+241)) {
		tmp = t_1 + (x * (-4.0 * i));
	} else {
		tmp = t_1 + (x * ((t * y) * (18.0 * 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.
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 (x <= (-8.8d+85)) then
        tmp = x * ((18.0d0 * (z * (t * y))) - (i * 4.0d0))
    else if (x <= 7d-37) then
        tmp = t_1 + (b * c)
    else if (x <= 112000000.0d0) then
        tmp = t_1 + ((-4.0d0) * (t * a))
    else if ((x <= 5.3d+143) .or. (.not. (x <= 1.05d+241))) then
        tmp = t_1 + (x * ((-4.0d0) * i))
    else
        tmp = t_1 + (x * ((t * y) * (18.0d0 * 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;
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 (x <= -8.8e+85) {
		tmp = x * ((18.0 * (z * (t * y))) - (i * 4.0));
	} else if (x <= 7e-37) {
		tmp = t_1 + (b * c);
	} else if (x <= 112000000.0) {
		tmp = t_1 + (-4.0 * (t * a));
	} else if ((x <= 5.3e+143) || !(x <= 1.05e+241)) {
		tmp = t_1 + (x * (-4.0 * i));
	} else {
		tmp = t_1 + (x * ((t * y) * (18.0 * 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])
[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 x <= -8.8e+85:
		tmp = x * ((18.0 * (z * (t * y))) - (i * 4.0))
	elif x <= 7e-37:
		tmp = t_1 + (b * c)
	elif x <= 112000000.0:
		tmp = t_1 + (-4.0 * (t * a))
	elif (x <= 5.3e+143) or not (x <= 1.05e+241):
		tmp = t_1 + (x * (-4.0 * i))
	else:
		tmp = t_1 + (x * ((t * y) * (18.0 * 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])
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 (x <= -8.8e+85)
		tmp = Float64(x * Float64(Float64(18.0 * Float64(z * Float64(t * y))) - Float64(i * 4.0)));
	elseif (x <= 7e-37)
		tmp = Float64(t_1 + Float64(b * c));
	elseif (x <= 112000000.0)
		tmp = Float64(t_1 + Float64(-4.0 * Float64(t * a)));
	elseif ((x <= 5.3e+143) || !(x <= 1.05e+241))
		tmp = Float64(t_1 + Float64(x * Float64(-4.0 * i)));
	else
		tmp = Float64(t_1 + Float64(x * Float64(Float64(t * y) * Float64(18.0 * 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])){:}
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 (x <= -8.8e+85)
		tmp = x * ((18.0 * (z * (t * y))) - (i * 4.0));
	elseif (x <= 7e-37)
		tmp = t_1 + (b * c);
	elseif (x <= 112000000.0)
		tmp = t_1 + (-4.0 * (t * a));
	elseif ((x <= 5.3e+143) || ~((x <= 1.05e+241)))
		tmp = t_1 + (x * (-4.0 * i));
	else
		tmp = t_1 + (x * ((t * y) * (18.0 * 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.
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[x, -8.8e+85], N[(x * N[(N[(18.0 * N[(z * N[(t * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7e-37], N[(t$95$1 + N[(b * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 112000000.0], N[(t$95$1 + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, 5.3e+143], N[Not[LessEqual[x, 1.05e+241]], $MachinePrecision]], N[(t$95$1 + N[(x * N[(-4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(x * N[(N[(t * y), $MachinePrecision] * N[(18.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -8.8000000000000007e85

   1. Initial program 69.6%

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

   3. Simplified 84.7%

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

   5. Taylor expanded in x around inf 77.5%

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

      1. expm1-log1p-u 61.5%

         \[\leadsto x \cdot \left(18 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(t \cdot \left(y \cdot z\right)\right)\right)} - 4 \cdot i\right) \]

      2. expm1-udef 59.8%

         \[\leadsto x \cdot \left(18 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(t \cdot \left(y \cdot z\right)\right)} - 1\right)} - 4 \cdot i\right) \]

   7. Applied egg-rr 59.8%

      \[\leadsto x \cdot \left(18 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(t \cdot \left(y \cdot z\right)\right)} - 1\right)} - 4 \cdot i\right) \]
   8. Step-by-step derivation

      1. expm1-def 61.5%

         \[\leadsto x \cdot \left(18 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(t \cdot \left(y \cdot z\right)\right)\right)} - 4 \cdot i\right) \]

      2. expm1-log1p 77.5%

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

      3. associate-*r* 75.8%

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

   9. Simplified 75.8%

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

   if -8.8000000000000007e85 < x < 7.0000000000000003e-37

   1. Initial program 92.0%

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

   3. Simplified 91.9%

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

   5. Taylor expanded in b around inf 63.9%

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

   if 7.0000000000000003e-37 < x < 1.12e8

   1. Initial program 85.5%

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

   3. Simplified 93.3%

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

   5. Taylor expanded in a around inf 71.6%

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

      1. *-commutative 71.6%

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

   7. Simplified 71.6%

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

   if 1.12e8 < x < 5.3e143 or 1.05e241 < x

   1. Initial program 87.5%

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

   3. Simplified 95.0%

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

   5. Taylor expanded in i around inf 66.4%

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

      1. associate-*r* 66.4%

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

      2. *-commutative 66.4%

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

   7. Simplified 66.4%

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

   if 5.3e143 < x < 1.05e241

   1. Initial program 72.1%

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

   3. Simplified 80.1%

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

   5. Taylor expanded in y around inf 74.7%

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

      1. *-commutative 74.7%

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

      2. *-commutative 74.7%

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

      3. associate-*l* 78.3%

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

      4. *-commutative 78.3%

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

      5. associate-*r* 78.3%

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

      6. associate-*r* 77.4%

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

      7. associate-*l* 77.4%

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

   7. Simplified 77.4%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.8 \cdot 10^{+85}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(t \cdot y\right)\right) - i \cdot 4\right)\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-37}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \mathbf{elif}\;x \leq 112000000:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq 5.3 \cdot 10^{+143} \lor \neg \left(x \leq 1.05 \cdot 10^{+241}\right):\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + x \cdot \left(-4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + x \cdot \left(\left(t \cdot y\right) \cdot \left(18 \cdot z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 59.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - 4 \cdot \left(x \cdot i\right)\\ t_2 := j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;x \leq -5.2 \cdot 10^{+85}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(t \cdot y\right)\right) - i \cdot 4\right)\\ \mathbf{elif}\;x \leq 10^{-217}:\\ \;\;\;\;t_2 + b \cdot c\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+59}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+112}:\\ \;\;\;\;t_2 + x \cdot \left(-4 \cdot i\right)\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{+162}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - i \cdot 4\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (- (+ (* b c) (* -4.0 (* t a))) (* 4.0 (* x i))))
        (t_2 (* j (* k -27.0))))
   (if (<= x -5.2e+85)
     (* x (- (* 18.0 (* z (* t y))) (* i 4.0)))
     (if (<= x 1e-217)
       (+ t_2 (* b c))
       (if (<= x 1.3e+59)
         t_1
         (if (<= x 1.7e+112)
           (+ t_2 (* x (* -4.0 i)))
           (if (<= x 1.2e+162)
             t_1
             (* x (- (* 18.0 (* t (* y z))) (* i 4.0))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((b * c) + (-4.0 * (t * a))) - (4.0 * (x * i));
	double t_2 = j * (k * -27.0);
	double tmp;
	if (x <= -5.2e+85) {
		tmp = x * ((18.0 * (z * (t * y))) - (i * 4.0));
	} else if (x <= 1e-217) {
		tmp = t_2 + (b * c);
	} else if (x <= 1.3e+59) {
		tmp = t_1;
	} else if (x <= 1.7e+112) {
		tmp = t_2 + (x * (-4.0 * i));
	} else if (x <= 1.2e+162) {
		tmp = t_1;
	} else {
		tmp = x * ((18.0 * (t * (y * z))) - (i * 4.0));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((b * c) + ((-4.0d0) * (t * a))) - (4.0d0 * (x * i))
    t_2 = j * (k * (-27.0d0))
    if (x <= (-5.2d+85)) then
        tmp = x * ((18.0d0 * (z * (t * y))) - (i * 4.0d0))
    else if (x <= 1d-217) then
        tmp = t_2 + (b * c)
    else if (x <= 1.3d+59) then
        tmp = t_1
    else if (x <= 1.7d+112) then
        tmp = t_2 + (x * ((-4.0d0) * i))
    else if (x <= 1.2d+162) then
        tmp = t_1
    else
        tmp = x * ((18.0d0 * (t * (y * z))) - (i * 4.0d0))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((b * c) + (-4.0 * (t * a))) - (4.0 * (x * i));
	double t_2 = j * (k * -27.0);
	double tmp;
	if (x <= -5.2e+85) {
		tmp = x * ((18.0 * (z * (t * y))) - (i * 4.0));
	} else if (x <= 1e-217) {
		tmp = t_2 + (b * c);
	} else if (x <= 1.3e+59) {
		tmp = t_1;
	} else if (x <= 1.7e+112) {
		tmp = t_2 + (x * (-4.0 * i));
	} else if (x <= 1.2e+162) {
		tmp = t_1;
	} else {
		tmp = x * ((18.0 * (t * (y * z))) - (i * 4.0));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = ((b * c) + (-4.0 * (t * a))) - (4.0 * (x * i))
	t_2 = j * (k * -27.0)
	tmp = 0
	if x <= -5.2e+85:
		tmp = x * ((18.0 * (z * (t * y))) - (i * 4.0))
	elif x <= 1e-217:
		tmp = t_2 + (b * c)
	elif x <= 1.3e+59:
		tmp = t_1
	elif x <= 1.7e+112:
		tmp = t_2 + (x * (-4.0 * i))
	elif x <= 1.2e+162:
		tmp = t_1
	else:
		tmp = x * ((18.0 * (t * (y * z))) - (i * 4.0))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a))) - Float64(4.0 * Float64(x * i)))
	t_2 = Float64(j * Float64(k * -27.0))
	tmp = 0.0
	if (x <= -5.2e+85)
		tmp = Float64(x * Float64(Float64(18.0 * Float64(z * Float64(t * y))) - Float64(i * 4.0)));
	elseif (x <= 1e-217)
		tmp = Float64(t_2 + Float64(b * c));
	elseif (x <= 1.3e+59)
		tmp = t_1;
	elseif (x <= 1.7e+112)
		tmp = Float64(t_2 + Float64(x * Float64(-4.0 * i)));
	elseif (x <= 1.2e+162)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(i * 4.0)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = ((b * c) + (-4.0 * (t * a))) - (4.0 * (x * i));
	t_2 = j * (k * -27.0);
	tmp = 0.0;
	if (x <= -5.2e+85)
		tmp = x * ((18.0 * (z * (t * y))) - (i * 4.0));
	elseif (x <= 1e-217)
		tmp = t_2 + (b * c);
	elseif (x <= 1.3e+59)
		tmp = t_1;
	elseif (x <= 1.7e+112)
		tmp = t_2 + (x * (-4.0 * i));
	elseif (x <= 1.2e+162)
		tmp = t_1;
	else
		tmp = x * ((18.0 * (t * (y * z))) - (i * 4.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5.2e+85], N[(x * N[(N[(18.0 * N[(z * N[(t * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1e-217], N[(t$95$2 + N[(b * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.3e+59], t$95$1, If[LessEqual[x, 1.7e+112], N[(t$95$2 + N[(x * N[(-4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.2e+162], t$95$1, 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 5 regimes

2. if x < -5.20000000000000021e85

   1. Initial program 69.6%

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

   3. Simplified 84.7%

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

   5. Taylor expanded in x around inf 77.5%

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

      1. expm1-log1p-u 61.5%

         \[\leadsto x \cdot \left(18 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(t \cdot \left(y \cdot z\right)\right)\right)} - 4 \cdot i\right) \]

      2. expm1-udef 59.8%

         \[\leadsto x \cdot \left(18 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(t \cdot \left(y \cdot z\right)\right)} - 1\right)} - 4 \cdot i\right) \]

   7. Applied egg-rr 59.8%

      \[\leadsto x \cdot \left(18 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(t \cdot \left(y \cdot z\right)\right)} - 1\right)} - 4 \cdot i\right) \]
   8. Step-by-step derivation

      1. expm1-def 61.5%

         \[\leadsto x \cdot \left(18 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(t \cdot \left(y \cdot z\right)\right)\right)} - 4 \cdot i\right) \]

      2. expm1-log1p 77.5%

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

      3. associate-*r* 75.8%

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

   9. Simplified 75.8%

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

   if -5.20000000000000021e85 < x < 1.00000000000000008e-217

   1. Initial program 92.0%

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

   3. Simplified 91.9%

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

   5. Taylor expanded in b around inf 68.5%

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

   if 1.00000000000000008e-217 < x < 1.3e59 or 1.69999999999999997e112 < x < 1.20000000000000005e162

   1. Initial program 89.2%

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

   3. Simplified 90.6%

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

      1. associate--l+ 90.6%

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

      2. *-commutative 90.6%

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

      3. fma-def 93.4%

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

      4. associate-*l* 92.0%

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

      5. fma-neg 92.0%

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

      6. associate-*r* 92.0%

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

      7. associate-*r* 92.0%

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

      8. +-commutative 92.0%

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

      9. fma-def 92.0%

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

      10. *-commutative 92.0%

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

      11. *-commutative 92.0%

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

   6. Applied egg-rr 92.0%

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

   7. Taylor expanded in x around 0 84.2%

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

   8. Taylor expanded in j around 0 64.9%

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

   if 1.3e59 < x < 1.69999999999999997e112

   1. Initial program 88.2%

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

   3. Simplified 94.0%

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

   5. Taylor expanded in i around inf 76.8%

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

      1. associate-*r* 76.8%

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

      2. *-commutative 76.8%

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

   7. Simplified 76.8%

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

   if 1.20000000000000005e162 < x

   1. Initial program 73.0%

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

   3. Simplified 80.7%

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

   5. Taylor expanded in x around inf 77.1%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{+85}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(t \cdot y\right)\right) - i \cdot 4\right)\\ \mathbf{elif}\;x \leq 10^{-217}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+59}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+112}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + x \cdot \left(-4 \cdot i\right)\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{+162}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - i \cdot 4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 75.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.38 \cdot 10^{+73} \lor \neg \left(t \leq 3.4 \cdot 10^{-93} \lor \neg \left(t \leq 1.4 \cdot 10^{-42}\right) \land t \leq 51000000\right):\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= t -1.38e+73)
         (not
          (or (<= t 3.4e-93) (and (not (<= t 1.4e-42)) (<= t 51000000.0)))))
   (+ (* j (* k -27.0)) (* t (+ (* 18.0 (* x (* y z))) (* a -4.0))))
   (- (- (* b c) (* 4.0 (* x i))) (* k (* j 27.0)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((t <= -1.38e+73) || !((t <= 3.4e-93) || (!(t <= 1.4e-42) && (t <= 51000000.0)))) {
		tmp = (j * (k * -27.0)) + (t * ((18.0 * (x * (y * z))) + (a * -4.0)));
	} else {
		tmp = ((b * c) - (4.0 * (x * i))) - (k * (j * 27.0));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((t <= (-1.38d+73)) .or. (.not. (t <= 3.4d-93) .or. (.not. (t <= 1.4d-42)) .and. (t <= 51000000.0d0))) then
        tmp = (j * (k * (-27.0d0))) + (t * ((18.0d0 * (x * (y * z))) + (a * (-4.0d0))))
    else
        tmp = ((b * c) - (4.0d0 * (x * i))) - (k * (j * 27.0d0))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((t <= -1.38e+73) || !((t <= 3.4e-93) || (!(t <= 1.4e-42) && (t <= 51000000.0)))) {
		tmp = (j * (k * -27.0)) + (t * ((18.0 * (x * (y * z))) + (a * -4.0)));
	} else {
		tmp = ((b * c) - (4.0 * (x * i))) - (k * (j * 27.0));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (t <= -1.38e+73) or not ((t <= 3.4e-93) or (not (t <= 1.4e-42) and (t <= 51000000.0))):
		tmp = (j * (k * -27.0)) + (t * ((18.0 * (x * (y * z))) + (a * -4.0)))
	else:
		tmp = ((b * c) - (4.0 * (x * i))) - (k * (j * 27.0))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((t <= -1.38e+73) || !((t <= 3.4e-93) || (!(t <= 1.4e-42) && (t <= 51000000.0))))
		tmp = Float64(Float64(j * Float64(k * -27.0)) + Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) + Float64(a * -4.0))));
	else
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(x * i))) - Float64(k * Float64(j * 27.0)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((t <= -1.38e+73) || ~(((t <= 3.4e-93) || (~((t <= 1.4e-42)) && (t <= 51000000.0)))))
		tmp = (j * (k * -27.0)) + (t * ((18.0 * (x * (y * z))) + (a * -4.0)));
	else
		tmp = ((b * c) - (4.0 * (x * i))) - (k * (j * 27.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[t, -1.38e+73], N[Not[Or[LessEqual[t, 3.4e-93], And[N[Not[LessEqual[t, 1.4e-42]], $MachinePrecision], LessEqual[t, 51000000.0]]]], $MachinePrecision]], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.38000000000000007e73 or 3.40000000000000001e-93 < t < 1.39999999999999999e-42 or 5.1e7 < t

   1. Initial program 79.7%

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

   3. Simplified 92.3%

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

   5. Taylor expanded in t around inf 79.7%

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

   if -1.38000000000000007e73 < t < 3.40000000000000001e-93 or 1.39999999999999999e-42 < t < 5.1e7

   1. Initial program 88.5%

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

   3. Taylor expanded in t around 0 84.3%

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

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.38 \cdot 10^{+73} \lor \neg \left(t \leq 3.4 \cdot 10^{-93} \lor \neg \left(t \leq 1.4 \cdot 10^{-42}\right) \land t \leq 51000000\right):\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 75.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ t_2 := k \cdot \left(j \cdot 27\right)\\ t_3 := \left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - t_2\\ t_4 := j \cdot \left(k \cdot -27\right) + t \cdot \left(18 \cdot t_1 + a \cdot -4\right)\\ \mathbf{if}\;t \leq -1.35 \cdot 10^{+73}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-97}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-43}:\\ \;\;\;\;\left(18 \cdot \left(t \cdot t_1\right) - 4 \cdot \left(t \cdot a\right)\right) - t_2\\ \mathbf{elif}\;t \leq 57000000:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* x (* y z)))
        (t_2 (* k (* j 27.0)))
        (t_3 (- (- (* b c) (* 4.0 (* x i))) t_2))
        (t_4 (+ (* j (* k -27.0)) (* t (+ (* 18.0 t_1) (* a -4.0))))))
   (if (<= t -1.35e+73)
     t_4
     (if (<= t 5.8e-97)
       t_3
       (if (<= t 1.25e-43)
         (- (- (* 18.0 (* t t_1)) (* 4.0 (* t a))) t_2)
         (if (<= t 57000000.0) t_3 t_4))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = x * (y * z);
	double t_2 = k * (j * 27.0);
	double t_3 = ((b * c) - (4.0 * (x * i))) - t_2;
	double t_4 = (j * (k * -27.0)) + (t * ((18.0 * t_1) + (a * -4.0)));
	double tmp;
	if (t <= -1.35e+73) {
		tmp = t_4;
	} else if (t <= 5.8e-97) {
		tmp = t_3;
	} else if (t <= 1.25e-43) {
		tmp = ((18.0 * (t * t_1)) - (4.0 * (t * a))) - t_2;
	} else if (t <= 57000000.0) {
		tmp = t_3;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = x * (y * z)
    t_2 = k * (j * 27.0d0)
    t_3 = ((b * c) - (4.0d0 * (x * i))) - t_2
    t_4 = (j * (k * (-27.0d0))) + (t * ((18.0d0 * t_1) + (a * (-4.0d0))))
    if (t <= (-1.35d+73)) then
        tmp = t_4
    else if (t <= 5.8d-97) then
        tmp = t_3
    else if (t <= 1.25d-43) then
        tmp = ((18.0d0 * (t * t_1)) - (4.0d0 * (t * a))) - t_2
    else if (t <= 57000000.0d0) then
        tmp = t_3
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = x * (y * z);
	double t_2 = k * (j * 27.0);
	double t_3 = ((b * c) - (4.0 * (x * i))) - t_2;
	double t_4 = (j * (k * -27.0)) + (t * ((18.0 * t_1) + (a * -4.0)));
	double tmp;
	if (t <= -1.35e+73) {
		tmp = t_4;
	} else if (t <= 5.8e-97) {
		tmp = t_3;
	} else if (t <= 1.25e-43) {
		tmp = ((18.0 * (t * t_1)) - (4.0 * (t * a))) - t_2;
	} else if (t <= 57000000.0) {
		tmp = t_3;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = x * (y * z)
	t_2 = k * (j * 27.0)
	t_3 = ((b * c) - (4.0 * (x * i))) - t_2
	t_4 = (j * (k * -27.0)) + (t * ((18.0 * t_1) + (a * -4.0)))
	tmp = 0
	if t <= -1.35e+73:
		tmp = t_4
	elif t <= 5.8e-97:
		tmp = t_3
	elif t <= 1.25e-43:
		tmp = ((18.0 * (t * t_1)) - (4.0 * (t * a))) - t_2
	elif t <= 57000000.0:
		tmp = t_3
	else:
		tmp = t_4
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(x * Float64(y * z))
	t_2 = Float64(k * Float64(j * 27.0))
	t_3 = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(x * i))) - t_2)
	t_4 = Float64(Float64(j * Float64(k * -27.0)) + Float64(t * Float64(Float64(18.0 * t_1) + Float64(a * -4.0))))
	tmp = 0.0
	if (t <= -1.35e+73)
		tmp = t_4;
	elseif (t <= 5.8e-97)
		tmp = t_3;
	elseif (t <= 1.25e-43)
		tmp = Float64(Float64(Float64(18.0 * Float64(t * t_1)) - Float64(4.0 * Float64(t * a))) - t_2);
	elseif (t <= 57000000.0)
		tmp = t_3;
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = x * (y * z);
	t_2 = k * (j * 27.0);
	t_3 = ((b * c) - (4.0 * (x * i))) - t_2;
	t_4 = (j * (k * -27.0)) + (t * ((18.0 * t_1) + (a * -4.0)));
	tmp = 0.0;
	if (t <= -1.35e+73)
		tmp = t_4;
	elseif (t <= 5.8e-97)
		tmp = t_3;
	elseif (t <= 1.25e-43)
		tmp = ((18.0 * (t * t_1)) - (4.0 * (t * a))) - t_2;
	elseif (t <= 57000000.0)
		tmp = t_3;
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(18.0 * t$95$1), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.35e+73], t$95$4, If[LessEqual[t, 5.8e-97], t$95$3, If[LessEqual[t, 1.25e-43], N[(N[(N[(18.0 * N[(t * t$95$1), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], If[LessEqual[t, 57000000.0], t$95$3, t$95$4]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.35e73 or 5.7e7 < t

   1. Initial program 79.5%

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

   3. Simplified 93.9%

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

   5. Taylor expanded in t around inf 79.5%

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

   if -1.35e73 < t < 5.7999999999999999e-97 or 1.25000000000000005e-43 < t < 5.7e7

   1. Initial program 88.5%

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

   3. Taylor expanded in t around 0 84.2%

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

   if 5.7999999999999999e-97 < t < 1.25000000000000005e-43

   1. Initial program 82.2%

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

   3. Taylor expanded in i around 0 82.3%

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

   4. Taylor expanded in b around 0 82.3%

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

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{+73}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-97}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-43}:\\ \;\;\;\;\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) - 4 \cdot \left(t \cdot a\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;t \leq 57000000:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 58.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - i \cdot 4\right)\\ t_2 := j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;x \leq -8.5 \cdot 10^{+85}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.28 \cdot 10^{-36}:\\ \;\;\;\;t_2 + b \cdot c\\ \mathbf{elif}\;x \leq 96000000:\\ \;\;\;\;t_2 + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{+131}:\\ \;\;\;\;t_2 + x \cdot \left(-4 \cdot i\right)\\ \mathbf{elif}\;x \leq 2.15 \cdot 10^{+131}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* x (- (* 18.0 (* t (* y z))) (* i 4.0))))
        (t_2 (* j (* k -27.0))))
   (if (<= x -8.5e+85)
     t_1
     (if (<= x 1.28e-36)
       (+ t_2 (* b c))
       (if (<= x 96000000.0)
         (+ t_2 (* -4.0 (* t a)))
         (if (<= x 1.9e+131)
           (+ t_2 (* x (* -4.0 i)))
           (if (<= x 2.15e+131) (* t (* a -4.0)) t_1)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = x * ((18.0 * (t * (y * z))) - (i * 4.0));
	double t_2 = j * (k * -27.0);
	double tmp;
	if (x <= -8.5e+85) {
		tmp = t_1;
	} else if (x <= 1.28e-36) {
		tmp = t_2 + (b * c);
	} else if (x <= 96000000.0) {
		tmp = t_2 + (-4.0 * (t * a));
	} else if (x <= 1.9e+131) {
		tmp = t_2 + (x * (-4.0 * i));
	} else if (x <= 2.15e+131) {
		tmp = t * (a * -4.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * ((18.0d0 * (t * (y * z))) - (i * 4.0d0))
    t_2 = j * (k * (-27.0d0))
    if (x <= (-8.5d+85)) then
        tmp = t_1
    else if (x <= 1.28d-36) then
        tmp = t_2 + (b * c)
    else if (x <= 96000000.0d0) then
        tmp = t_2 + ((-4.0d0) * (t * a))
    else if (x <= 1.9d+131) then
        tmp = t_2 + (x * ((-4.0d0) * i))
    else if (x <= 2.15d+131) then
        tmp = t * (a * (-4.0d0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = x * ((18.0 * (t * (y * z))) - (i * 4.0));
	double t_2 = j * (k * -27.0);
	double tmp;
	if (x <= -8.5e+85) {
		tmp = t_1;
	} else if (x <= 1.28e-36) {
		tmp = t_2 + (b * c);
	} else if (x <= 96000000.0) {
		tmp = t_2 + (-4.0 * (t * a));
	} else if (x <= 1.9e+131) {
		tmp = t_2 + (x * (-4.0 * i));
	} else if (x <= 2.15e+131) {
		tmp = t * (a * -4.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = x * ((18.0 * (t * (y * z))) - (i * 4.0))
	t_2 = j * (k * -27.0)
	tmp = 0
	if x <= -8.5e+85:
		tmp = t_1
	elif x <= 1.28e-36:
		tmp = t_2 + (b * c)
	elif x <= 96000000.0:
		tmp = t_2 + (-4.0 * (t * a))
	elif x <= 1.9e+131:
		tmp = t_2 + (x * (-4.0 * i))
	elif x <= 2.15e+131:
		tmp = t * (a * -4.0)
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(i * 4.0)))
	t_2 = Float64(j * Float64(k * -27.0))
	tmp = 0.0
	if (x <= -8.5e+85)
		tmp = t_1;
	elseif (x <= 1.28e-36)
		tmp = Float64(t_2 + Float64(b * c));
	elseif (x <= 96000000.0)
		tmp = Float64(t_2 + Float64(-4.0 * Float64(t * a)));
	elseif (x <= 1.9e+131)
		tmp = Float64(t_2 + Float64(x * Float64(-4.0 * i)));
	elseif (x <= 2.15e+131)
		tmp = Float64(t * Float64(a * -4.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = x * ((18.0 * (t * (y * z))) - (i * 4.0));
	t_2 = j * (k * -27.0);
	tmp = 0.0;
	if (x <= -8.5e+85)
		tmp = t_1;
	elseif (x <= 1.28e-36)
		tmp = t_2 + (b * c);
	elseif (x <= 96000000.0)
		tmp = t_2 + (-4.0 * (t * a));
	elseif (x <= 1.9e+131)
		tmp = t_2 + (x * (-4.0 * i));
	elseif (x <= 2.15e+131)
		tmp = t * (a * -4.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(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]}, If[LessEqual[x, -8.5e+85], t$95$1, If[LessEqual[x, 1.28e-36], N[(t$95$2 + N[(b * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 96000000.0], N[(t$95$2 + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.9e+131], N[(t$95$2 + N[(x * N[(-4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.15e+131], N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -8.4999999999999994e85 or 2.1500000000000001e131 < x

   1. Initial program 71.2%

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

   3. Simplified 82.7%

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

   5. Taylor expanded in x around inf 74.9%

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

   if -8.4999999999999994e85 < x < 1.28e-36

   1. Initial program 92.0%

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

   3. Simplified 91.9%

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

   5. Taylor expanded in b around inf 63.9%

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

   if 1.28e-36 < x < 9.6e7

   1. Initial program 85.5%

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

   3. Simplified 93.3%

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

   5. Taylor expanded in a around inf 71.6%

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

      1. *-commutative 71.6%

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

   7. Simplified 71.6%

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

   if 9.6e7 < x < 1.9000000000000002e131

   1. Initial program 89.9%

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

   3. Simplified 96.6%

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

   5. Taylor expanded in i around inf 64.9%

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

      1. associate-*r* 64.9%

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

      2. *-commutative 64.9%

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

   7. Simplified 64.9%

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

   if 1.9000000000000002e131 < x < 2.1500000000000001e131

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

      1. associate--l+ 100.0%

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

      2. *-commutative 100.0%

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

      3. fma-def 100.0%

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

      4. associate-*l* 100.0%

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

      5. fma-neg 100.0%

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

      6. associate-*r* 100.0%

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

      7. associate-*r* 100.0%

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

      8. +-commutative 100.0%

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

      9. fma-def 100.0%

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

      10. *-commutative 100.0%

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

      11. *-commutative 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in a around inf 100.0%

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

      1. *-commutative 100.0%

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

      2. *-commutative 100.0%

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

      3. associate-*l* 100.0%

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

      4. *-commutative 100.0%

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

   9. Simplified 100.0%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{+85}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - i \cdot 4\right)\\ \mathbf{elif}\;x \leq 1.28 \cdot 10^{-36}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \mathbf{elif}\;x \leq 96000000:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{+131}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + x \cdot \left(-4 \cdot i\right)\\ \mathbf{elif}\;x \leq 2.15 \cdot 10^{+131}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - i \cdot 4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 58.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;x \leq -6 \cdot 10^{+85}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(t \cdot y\right)\right) - i \cdot 4\right)\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{-36}:\\ \;\;\;\;t_1 + b \cdot c\\ \mathbf{elif}\;x \leq 62000000:\\ \;\;\;\;t_1 + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{+131}:\\ \;\;\;\;t_1 + x \cdot \left(-4 \cdot i\right)\\ \mathbf{elif}\;x \leq 2.15 \cdot 10^{+131}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - i \cdot 4\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 (<= x -6e+85)
     (* x (- (* 18.0 (* z (* t y))) (* i 4.0)))
     (if (<= x 3.9e-36)
       (+ t_1 (* b c))
       (if (<= x 62000000.0)
         (+ t_1 (* -4.0 (* t a)))
         (if (<= x 2.1e+131)
           (+ t_1 (* x (* -4.0 i)))
           (if (<= x 2.15e+131)
             (* t (* a -4.0))
             (* 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);
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 (x <= -6e+85) {
		tmp = x * ((18.0 * (z * (t * y))) - (i * 4.0));
	} else if (x <= 3.9e-36) {
		tmp = t_1 + (b * c);
	} else if (x <= 62000000.0) {
		tmp = t_1 + (-4.0 * (t * a));
	} else if (x <= 2.1e+131) {
		tmp = t_1 + (x * (-4.0 * i));
	} else if (x <= 2.15e+131) {
		tmp = t * (a * -4.0);
	} 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.
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 (x <= (-6d+85)) then
        tmp = x * ((18.0d0 * (z * (t * y))) - (i * 4.0d0))
    else if (x <= 3.9d-36) then
        tmp = t_1 + (b * c)
    else if (x <= 62000000.0d0) then
        tmp = t_1 + ((-4.0d0) * (t * a))
    else if (x <= 2.1d+131) then
        tmp = t_1 + (x * ((-4.0d0) * i))
    else if (x <= 2.15d+131) then
        tmp = t * (a * (-4.0d0))
    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;
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 (x <= -6e+85) {
		tmp = x * ((18.0 * (z * (t * y))) - (i * 4.0));
	} else if (x <= 3.9e-36) {
		tmp = t_1 + (b * c);
	} else if (x <= 62000000.0) {
		tmp = t_1 + (-4.0 * (t * a));
	} else if (x <= 2.1e+131) {
		tmp = t_1 + (x * (-4.0 * i));
	} else if (x <= 2.15e+131) {
		tmp = t * (a * -4.0);
	} 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])
[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 x <= -6e+85:
		tmp = x * ((18.0 * (z * (t * y))) - (i * 4.0))
	elif x <= 3.9e-36:
		tmp = t_1 + (b * c)
	elif x <= 62000000.0:
		tmp = t_1 + (-4.0 * (t * a))
	elif x <= 2.1e+131:
		tmp = t_1 + (x * (-4.0 * i))
	elif x <= 2.15e+131:
		tmp = t * (a * -4.0)
	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])
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 (x <= -6e+85)
		tmp = Float64(x * Float64(Float64(18.0 * Float64(z * Float64(t * y))) - Float64(i * 4.0)));
	elseif (x <= 3.9e-36)
		tmp = Float64(t_1 + Float64(b * c));
	elseif (x <= 62000000.0)
		tmp = Float64(t_1 + Float64(-4.0 * Float64(t * a)));
	elseif (x <= 2.1e+131)
		tmp = Float64(t_1 + Float64(x * Float64(-4.0 * i)));
	elseif (x <= 2.15e+131)
		tmp = Float64(t * Float64(a * -4.0));
	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])){:}
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 (x <= -6e+85)
		tmp = x * ((18.0 * (z * (t * y))) - (i * 4.0));
	elseif (x <= 3.9e-36)
		tmp = t_1 + (b * c);
	elseif (x <= 62000000.0)
		tmp = t_1 + (-4.0 * (t * a));
	elseif (x <= 2.1e+131)
		tmp = t_1 + (x * (-4.0 * i));
	elseif (x <= 2.15e+131)
		tmp = t * (a * -4.0);
	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.
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[x, -6e+85], N[(x * N[(N[(18.0 * N[(z * N[(t * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.9e-36], N[(t$95$1 + N[(b * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 62000000.0], N[(t$95$1 + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.1e+131], N[(t$95$1 + N[(x * N[(-4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.15e+131], N[(t * N[(a * -4.0), $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 6 regimes

2. if x < -6.0000000000000001e85

   1. Initial program 69.6%

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

   3. Simplified 84.7%

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

   5. Taylor expanded in x around inf 77.5%

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

      1. expm1-log1p-u 61.5%

         \[\leadsto x \cdot \left(18 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(t \cdot \left(y \cdot z\right)\right)\right)} - 4 \cdot i\right) \]

      2. expm1-udef 59.8%

         \[\leadsto x \cdot \left(18 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(t \cdot \left(y \cdot z\right)\right)} - 1\right)} - 4 \cdot i\right) \]

   7. Applied egg-rr 59.8%

      \[\leadsto x \cdot \left(18 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(t \cdot \left(y \cdot z\right)\right)} - 1\right)} - 4 \cdot i\right) \]
   8. Step-by-step derivation

      1. expm1-def 61.5%

         \[\leadsto x \cdot \left(18 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(t \cdot \left(y \cdot z\right)\right)\right)} - 4 \cdot i\right) \]

      2. expm1-log1p 77.5%

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

      3. associate-*r* 75.8%

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

   9. Simplified 75.8%

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

   if -6.0000000000000001e85 < x < 3.9000000000000001e-36

   1. Initial program 92.0%

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

   3. Simplified 91.9%

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

   5. Taylor expanded in b around inf 63.9%

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

   if 3.9000000000000001e-36 < x < 6.2e7

   1. Initial program 85.5%

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

   3. Simplified 93.3%

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

   5. Taylor expanded in a around inf 71.6%

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

      1. *-commutative 71.6%

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

   7. Simplified 71.6%

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

   if 6.2e7 < x < 2.09999999999999985e131

   1. Initial program 89.9%

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

   3. Simplified 96.6%

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

   5. Taylor expanded in i around inf 64.9%

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

      1. associate-*r* 64.9%

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

      2. *-commutative 64.9%

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

   7. Simplified 64.9%

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

   if 2.09999999999999985e131 < x < 2.1500000000000001e131

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

      1. associate--l+ 100.0%

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

      2. *-commutative 100.0%

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

      3. fma-def 100.0%

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

      4. associate-*l* 100.0%

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

      5. fma-neg 100.0%

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

      6. associate-*r* 100.0%

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

      7. associate-*r* 100.0%

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

      8. +-commutative 100.0%

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

      9. fma-def 100.0%

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

      10. *-commutative 100.0%

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

      11. *-commutative 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in a around inf 100.0%

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

      1. *-commutative 100.0%

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

      2. *-commutative 100.0%

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

      3. associate-*l* 100.0%

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

      4. *-commutative 100.0%

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

   9. Simplified 100.0%

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

   if 2.1500000000000001e131 < x

   1. Initial program 73.6%

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

   3. Simplified 79.6%

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

   5. Taylor expanded in x around inf 70.9%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{+85}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(t \cdot y\right)\right) - i \cdot 4\right)\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{-36}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \mathbf{elif}\;x \leq 62000000:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{+131}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + x \cdot \left(-4 \cdot i\right)\\ \mathbf{elif}\;x \leq 2.15 \cdot 10^{+131}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - i \cdot 4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 81.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := k \cdot \left(j \cdot 27\right)\\ t_2 := 4 \cdot \left(t \cdot a\right)\\ \mathbf{if}\;i \leq -8.5 \cdot 10^{-140} \lor \neg \left(i \leq 5.5 \cdot 10^{-16}\right):\\ \;\;\;\;\left(b \cdot c - \left(t_2 + 4 \cdot \left(x \cdot i\right)\right)\right) - t_1\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b \cdot c + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) - t_2\right) - t_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* k (* j 27.0))) (t_2 (* 4.0 (* t a))))
   (if (or (<= i -8.5e-140) (not (<= i 5.5e-16)))
     (- (- (* b c) (+ t_2 (* 4.0 (* x i)))) t_1)
     (- (- (+ (* b c) (* 18.0 (* t (* x (* y z))))) t_2) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = k * (j * 27.0);
	double t_2 = 4.0 * (t * a);
	double tmp;
	if ((i <= -8.5e-140) || !(i <= 5.5e-16)) {
		tmp = ((b * c) - (t_2 + (4.0 * (x * i)))) - t_1;
	} else {
		tmp = (((b * c) + (18.0 * (t * (x * (y * z))))) - t_2) - t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 = 4.0d0 * (t * a)
    if ((i <= (-8.5d-140)) .or. (.not. (i <= 5.5d-16))) then
        tmp = ((b * c) - (t_2 + (4.0d0 * (x * i)))) - t_1
    else
        tmp = (((b * c) + (18.0d0 * (t * (x * (y * z))))) - t_2) - t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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 = 4.0 * (t * a);
	double tmp;
	if ((i <= -8.5e-140) || !(i <= 5.5e-16)) {
		tmp = ((b * c) - (t_2 + (4.0 * (x * i)))) - t_1;
	} else {
		tmp = (((b * c) + (18.0 * (t * (x * (y * z))))) - t_2) - t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[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 = 4.0 * (t * a)
	tmp = 0
	if (i <= -8.5e-140) or not (i <= 5.5e-16):
		tmp = ((b * c) - (t_2 + (4.0 * (x * i)))) - t_1
	else:
		tmp = (((b * c) + (18.0 * (t * (x * (y * z))))) - t_2) - t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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(4.0 * Float64(t * a))
	tmp = 0.0
	if ((i <= -8.5e-140) || !(i <= 5.5e-16))
		tmp = Float64(Float64(Float64(b * c) - Float64(t_2 + Float64(4.0 * Float64(x * i)))) - t_1);
	else
		tmp = Float64(Float64(Float64(Float64(b * c) + Float64(18.0 * Float64(t * Float64(x * Float64(y * z))))) - t_2) - t_1);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
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 = 4.0 * (t * a);
	tmp = 0.0;
	if ((i <= -8.5e-140) || ~((i <= 5.5e-16)))
		tmp = ((b * c) - (t_2 + (4.0 * (x * i)))) - t_1;
	else
		tmp = (((b * c) + (18.0 * (t * (x * (y * z))))) - t_2) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[i, -8.5e-140], N[Not[LessEqual[i, 5.5e-16]], $MachinePrecision]], N[(N[(N[(b * c), $MachinePrecision] - N[(t$95$2 + N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(N[(N[(b * c), $MachinePrecision] + N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision] - t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if i < -8.49999999999999997e-140 or 5.49999999999999964e-16 < i

   1. Initial program 82.6%

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

   3. Taylor expanded in y around 0 86.8%

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

   if -8.49999999999999997e-140 < i < 5.49999999999999964e-16

   1. Initial program 87.9%

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

   3. Taylor expanded in i around 0 88.1%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -8.5 \cdot 10^{-140} \lor \neg \left(i \leq 5.5 \cdot 10^{-16}\right):\\ \;\;\;\;\left(b \cdot c - \left(4 \cdot \left(t \cdot a\right) + 4 \cdot \left(x \cdot i\right)\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b \cdot c + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) - 4 \cdot \left(t \cdot a\right)\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 59.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ t_2 := j \cdot \left(k \cdot -27\right)\\ t_3 := t_2 + b \cdot c\\ \mathbf{if}\;t \leq -5.5 \cdot 10^{+86}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-189}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-121}:\\ \;\;\;\;t_2 + x \cdot \left(-4 \cdot i\right)\\ \mathbf{elif}\;t \leq 520000000:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 (* b c))))
   (if (<= t -5.5e+86)
     t_1
     (if (<= t 6.8e-189)
       t_3
       (if (<= t 3.6e-121)
         (+ t_2 (* x (* -4.0 i)))
         (if (<= t 520000000.0) t_3 t_1))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	double t_2 = j * (k * -27.0);
	double t_3 = t_2 + (b * c);
	double tmp;
	if (t <= -5.5e+86) {
		tmp = t_1;
	} else if (t <= 6.8e-189) {
		tmp = t_3;
	} else if (t <= 3.6e-121) {
		tmp = t_2 + (x * (-4.0 * i));
	} else if (t <= 520000000.0) {
		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.
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 = t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0))
    t_2 = j * (k * (-27.0d0))
    t_3 = t_2 + (b * c)
    if (t <= (-5.5d+86)) then
        tmp = t_1
    else if (t <= 6.8d-189) then
        tmp = t_3
    else if (t <= 3.6d-121) then
        tmp = t_2 + (x * ((-4.0d0) * i))
    else if (t <= 520000000.0d0) 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;
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 + (b * c);
	double tmp;
	if (t <= -5.5e+86) {
		tmp = t_1;
	} else if (t <= 6.8e-189) {
		tmp = t_3;
	} else if (t <= 3.6e-121) {
		tmp = t_2 + (x * (-4.0 * i));
	} else if (t <= 520000000.0) {
		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])
[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 + (b * c)
	tmp = 0
	if t <= -5.5e+86:
		tmp = t_1
	elif t <= 6.8e-189:
		tmp = t_3
	elif t <= 3.6e-121:
		tmp = t_2 + (x * (-4.0 * i))
	elif t <= 520000000.0:
		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])
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(b * c))
	tmp = 0.0
	if (t <= -5.5e+86)
		tmp = t_1;
	elseif (t <= 6.8e-189)
		tmp = t_3;
	elseif (t <= 3.6e-121)
		tmp = Float64(t_2 + Float64(x * Float64(-4.0 * i)));
	elseif (t <= 520000000.0)
		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])){:}
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 + (b * c);
	tmp = 0.0;
	if (t <= -5.5e+86)
		tmp = t_1;
	elseif (t <= 6.8e-189)
		tmp = t_3;
	elseif (t <= 3.6e-121)
		tmp = t_2 + (x * (-4.0 * i));
	elseif (t <= 520000000.0)
		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.
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[(b * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.5e+86], t$95$1, If[LessEqual[t, 6.8e-189], t$95$3, If[LessEqual[t, 3.6e-121], N[(t$95$2 + N[(x * N[(-4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 520000000.0], t$95$3, t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.5000000000000002e86 or 5.2e8 < t

   1. Initial program 78.9%

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

   3. Simplified 90.7%

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

      1. associate--l+ 90.7%

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

      2. *-commutative 90.7%

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

      3. fma-def 94.8%

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

      4. associate-*l* 93.8%

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

      5. fma-neg 93.8%

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

      6. associate-*r* 93.8%

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

      7. associate-*r* 93.8%

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

      8. +-commutative 93.8%

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

      9. fma-def 93.8%

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

      10. *-commutative 93.8%

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

      11. *-commutative 93.8%

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

   6. Applied egg-rr 93.8%

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

   7. Taylor expanded in t around inf 65.0%

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

   if -5.5000000000000002e86 < t < 6.8000000000000002e-189 or 3.59999999999999984e-121 < t < 5.2e8

   1. Initial program 87.6%

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

   3. Simplified 87.6%

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

   5. Taylor expanded in b around inf 61.5%

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

   if 6.8000000000000002e-189 < t < 3.59999999999999984e-121

   1. Initial program 92.9%

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

   3. Simplified 92.9%

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

   5. Taylor expanded in i around inf 78.3%

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

      1. associate-*r* 78.3%

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

      2. *-commutative 78.3%

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

   7. Simplified 78.3%

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

4. Final simplification 63.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{+86}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-189}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-121}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + x \cdot \left(-4 \cdot i\right)\\ \mathbf{elif}\;t \leq 520000000:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 79.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ t_2 := 4 \cdot \left(x \cdot i\right)\\ t_3 := k \cdot \left(j \cdot 27\right)\\ \mathbf{if}\;k \leq -3.9 \cdot 10^{-118}:\\ \;\;\;\;\left(b \cdot c + 18 \cdot \left(t \cdot t_1\right)\right) - t_3\\ \mathbf{elif}\;k \leq 7.4 \cdot 10^{+74}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot t_1 - a \cdot 4\right)\right) - t_2\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - \left(4 \cdot \left(t \cdot a\right) + t_2\right)\right) - t_3\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* x (* y z))) (t_2 (* 4.0 (* x i))) (t_3 (* k (* j 27.0))))
   (if (<= k -3.9e-118)
     (- (+ (* b c) (* 18.0 (* t t_1))) t_3)
     (if (<= k 7.4e+74)
       (- (+ (* b c) (* t (- (* 18.0 t_1) (* a 4.0)))) t_2)
       (- (- (* b c) (+ (* 4.0 (* t a)) t_2)) t_3)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = x * (y * z);
	double t_2 = 4.0 * (x * i);
	double t_3 = k * (j * 27.0);
	double tmp;
	if (k <= -3.9e-118) {
		tmp = ((b * c) + (18.0 * (t * t_1))) - t_3;
	} else if (k <= 7.4e+74) {
		tmp = ((b * c) + (t * ((18.0 * t_1) - (a * 4.0)))) - t_2;
	} else {
		tmp = ((b * c) - ((4.0 * (t * a)) + t_2)) - t_3;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x * (y * z)
    t_2 = 4.0d0 * (x * i)
    t_3 = k * (j * 27.0d0)
    if (k <= (-3.9d-118)) then
        tmp = ((b * c) + (18.0d0 * (t * t_1))) - t_3
    else if (k <= 7.4d+74) then
        tmp = ((b * c) + (t * ((18.0d0 * t_1) - (a * 4.0d0)))) - t_2
    else
        tmp = ((b * c) - ((4.0d0 * (t * a)) + t_2)) - t_3
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = x * (y * z);
	double t_2 = 4.0 * (x * i);
	double t_3 = k * (j * 27.0);
	double tmp;
	if (k <= -3.9e-118) {
		tmp = ((b * c) + (18.0 * (t * t_1))) - t_3;
	} else if (k <= 7.4e+74) {
		tmp = ((b * c) + (t * ((18.0 * t_1) - (a * 4.0)))) - t_2;
	} else {
		tmp = ((b * c) - ((4.0 * (t * a)) + t_2)) - t_3;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = x * (y * z)
	t_2 = 4.0 * (x * i)
	t_3 = k * (j * 27.0)
	tmp = 0
	if k <= -3.9e-118:
		tmp = ((b * c) + (18.0 * (t * t_1))) - t_3
	elif k <= 7.4e+74:
		tmp = ((b * c) + (t * ((18.0 * t_1) - (a * 4.0)))) - t_2
	else:
		tmp = ((b * c) - ((4.0 * (t * a)) + t_2)) - t_3
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(x * Float64(y * z))
	t_2 = Float64(4.0 * Float64(x * i))
	t_3 = Float64(k * Float64(j * 27.0))
	tmp = 0.0
	if (k <= -3.9e-118)
		tmp = Float64(Float64(Float64(b * c) + Float64(18.0 * Float64(t * t_1))) - t_3);
	elseif (k <= 7.4e+74)
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(18.0 * t_1) - Float64(a * 4.0)))) - t_2);
	else
		tmp = Float64(Float64(Float64(b * c) - Float64(Float64(4.0 * Float64(t * a)) + t_2)) - t_3);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = x * (y * z);
	t_2 = 4.0 * (x * i);
	t_3 = k * (j * 27.0);
	tmp = 0.0;
	if (k <= -3.9e-118)
		tmp = ((b * c) + (18.0 * (t * t_1))) - t_3;
	elseif (k <= 7.4e+74)
		tmp = ((b * c) + (t * ((18.0 * t_1) - (a * 4.0)))) - t_2;
	else
		tmp = ((b * c) - ((4.0 * (t * a)) + t_2)) - t_3;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[k, -3.9e-118], N[(N[(N[(b * c), $MachinePrecision] + N[(18.0 * N[(t * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$3), $MachinePrecision], If[LessEqual[k, 7.4e+74], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(18.0 * t$95$1), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] - N[(N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision] - t$95$3), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if k < -3.90000000000000001e-118

   1. Initial program 82.2%

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

   3. Taylor expanded in i around 0 78.5%

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

   4. Taylor expanded in a around 0 77.3%

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

   if -3.90000000000000001e-118 < k < 7.4000000000000002e74

   1. Initial program 82.9%

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

   3. Simplified 88.2%

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

   5. Taylor expanded in j around 0 81.7%

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

   if 7.4000000000000002e74 < k

   1. Initial program 92.2%

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

   3. Taylor expanded in y around 0 92.1%

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

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -3.9 \cdot 10^{-118}:\\ \;\;\;\;\left(b \cdot c + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;k \leq 7.4 \cdot 10^{+74}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - \left(4 \cdot \left(t \cdot a\right) + 4 \cdot \left(x \cdot i\right)\right)\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 79.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -3.3 \cdot 10^{+86}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(t \cdot y\right)\right) - i \cdot 4\right)\\ \mathbf{elif}\;x \leq 6 \cdot 10^{+167}:\\ \;\;\;\;\left(b \cdot c - \left(4 \cdot \left(t \cdot a\right) + 4 \cdot \left(x \cdot i\right)\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - i \cdot 4\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= x -3.3e+86)
   (* x (- (* 18.0 (* z (* t y))) (* i 4.0)))
   (if (<= x 6e+167)
     (- (- (* b c) (+ (* 4.0 (* t a)) (* 4.0 (* x i)))) (* k (* j 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);
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 <= -3.3e+86) {
		tmp = x * ((18.0 * (z * (t * y))) - (i * 4.0));
	} else if (x <= 6e+167) {
		tmp = ((b * c) - ((4.0 * (t * a)) + (4.0 * (x * i)))) - (k * (j * 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.
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 <= (-3.3d+86)) then
        tmp = x * ((18.0d0 * (z * (t * y))) - (i * 4.0d0))
    else if (x <= 6d+167) then
        tmp = ((b * c) - ((4.0d0 * (t * a)) + (4.0d0 * (x * i)))) - (k * (j * 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;
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 <= -3.3e+86) {
		tmp = x * ((18.0 * (z * (t * y))) - (i * 4.0));
	} else if (x <= 6e+167) {
		tmp = ((b * c) - ((4.0 * (t * a)) + (4.0 * (x * i)))) - (k * (j * 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])
[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 <= -3.3e+86:
		tmp = x * ((18.0 * (z * (t * y))) - (i * 4.0))
	elif x <= 6e+167:
		tmp = ((b * c) - ((4.0 * (t * a)) + (4.0 * (x * i)))) - (k * (j * 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])
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 <= -3.3e+86)
		tmp = Float64(x * Float64(Float64(18.0 * Float64(z * Float64(t * y))) - Float64(i * 4.0)));
	elseif (x <= 6e+167)
		tmp = Float64(Float64(Float64(b * c) - Float64(Float64(4.0 * Float64(t * a)) + Float64(4.0 * Float64(x * i)))) - Float64(k * Float64(j * 27.0)));
	else
		tmp = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(i * 4.0)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (x <= -3.3e+86)
		tmp = x * ((18.0 * (z * (t * y))) - (i * 4.0));
	elseif (x <= 6e+167)
		tmp = ((b * c) - ((4.0 * (t * a)) + (4.0 * (x * i)))) - (k * (j * 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.
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, -3.3e+86], N[(x * N[(N[(18.0 * N[(z * N[(t * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6e+167], N[(N[(N[(b * c), $MachinePrecision] - N[(N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.2999999999999999e86

   1. Initial program 69.6%

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

   3. Simplified 84.7%

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

   5. Taylor expanded in x around inf 77.5%

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

      1. expm1-log1p-u 61.5%

         \[\leadsto x \cdot \left(18 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(t \cdot \left(y \cdot z\right)\right)\right)} - 4 \cdot i\right) \]

      2. expm1-udef 59.8%

         \[\leadsto x \cdot \left(18 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(t \cdot \left(y \cdot z\right)\right)} - 1\right)} - 4 \cdot i\right) \]

   7. Applied egg-rr 59.8%

      \[\leadsto x \cdot \left(18 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(t \cdot \left(y \cdot z\right)\right)} - 1\right)} - 4 \cdot i\right) \]
   8. Step-by-step derivation

      1. expm1-def 61.5%

         \[\leadsto x \cdot \left(18 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(t \cdot \left(y \cdot z\right)\right)\right)} - 4 \cdot i\right) \]

      2. expm1-log1p 77.5%

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

      3. associate-*r* 75.8%

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

   9. Simplified 75.8%

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

   if -3.2999999999999999e86 < x < 6.00000000000000023e167

   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. Taylor expanded in y around 0 87.3%

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

   if 6.00000000000000023e167 < x

   1. Initial program 73.0%

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

   3. Simplified 80.7%

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

   5. Taylor expanded in x around inf 77.1%

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

4. Final simplification 83.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.3 \cdot 10^{+86}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(t \cdot y\right)\right) - i \cdot 4\right)\\ \mathbf{elif}\;x \leq 6 \cdot 10^{+167}:\\ \;\;\;\;\left(b \cdot c - \left(4 \cdot \left(t \cdot a\right) + 4 \cdot \left(x \cdot i\right)\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - i \cdot 4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 33.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;k \leq -1.45 \cdot 10^{-60}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;k \leq 1.4 \cdot 10^{-196}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 9.5 \cdot 10^{-123}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;k \leq 3.3 \cdot 10^{+75}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= k -1.45e-60)
   (* -27.0 (* j k))
   (if (<= k 1.4e-196)
     (* b c)
     (if (<= k 9.5e-123)
       (* -4.0 (* x i))
       (if (<= k 3.3e+75) (* 18.0 (* t (* x (* y z)))) (* k (* j -27.0)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (k <= -1.45e-60) {
		tmp = -27.0 * (j * k);
	} else if (k <= 1.4e-196) {
		tmp = b * c;
	} else if (k <= 9.5e-123) {
		tmp = -4.0 * (x * i);
	} else if (k <= 3.3e+75) {
		tmp = 18.0 * (t * (x * (y * z)));
	} else {
		tmp = k * (j * -27.0);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (k <= (-1.45d-60)) then
        tmp = (-27.0d0) * (j * k)
    else if (k <= 1.4d-196) then
        tmp = b * c
    else if (k <= 9.5d-123) then
        tmp = (-4.0d0) * (x * i)
    else if (k <= 3.3d+75) then
        tmp = 18.0d0 * (t * (x * (y * z)))
    else
        tmp = k * (j * (-27.0d0))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (k <= -1.45e-60) {
		tmp = -27.0 * (j * k);
	} else if (k <= 1.4e-196) {
		tmp = b * c;
	} else if (k <= 9.5e-123) {
		tmp = -4.0 * (x * i);
	} else if (k <= 3.3e+75) {
		tmp = 18.0 * (t * (x * (y * z)));
	} else {
		tmp = k * (j * -27.0);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if k <= -1.45e-60:
		tmp = -27.0 * (j * k)
	elif k <= 1.4e-196:
		tmp = b * c
	elif k <= 9.5e-123:
		tmp = -4.0 * (x * i)
	elif k <= 3.3e+75:
		tmp = 18.0 * (t * (x * (y * z)))
	else:
		tmp = k * (j * -27.0)
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (k <= -1.45e-60)
		tmp = Float64(-27.0 * Float64(j * k));
	elseif (k <= 1.4e-196)
		tmp = Float64(b * c);
	elseif (k <= 9.5e-123)
		tmp = Float64(-4.0 * Float64(x * i));
	elseif (k <= 3.3e+75)
		tmp = Float64(18.0 * Float64(t * Float64(x * Float64(y * z))));
	else
		tmp = Float64(k * Float64(j * -27.0));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (k <= -1.45e-60)
		tmp = -27.0 * (j * k);
	elseif (k <= 1.4e-196)
		tmp = b * c;
	elseif (k <= 9.5e-123)
		tmp = -4.0 * (x * i);
	elseif (k <= 3.3e+75)
		tmp = 18.0 * (t * (x * (y * z)));
	else
		tmp = k * (j * -27.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[k, -1.45e-60], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 1.4e-196], N[(b * c), $MachinePrecision], If[LessEqual[k, 9.5e-123], N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 3.3e+75], N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if k < -1.45e-60

   1. Initial program 81.3%

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

   3. Simplified 88.5%

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

   5. Taylor expanded in j around inf 40.3%

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

   if -1.45e-60 < k < 1.3999999999999999e-196

   1. Initial program 88.6%

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

   3. Simplified 88.5%

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

      1. associate--l+ 88.5%

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

      2. *-commutative 88.5%

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

      3. fma-def 89.9%

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

      4. associate-*l* 89.9%

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

      5. fma-neg 89.9%

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

      6. associate-*r* 88.6%

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

      7. associate-*r* 88.6%

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

      8. +-commutative 88.6%

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

      9. fma-def 88.6%

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

      10. *-commutative 88.6%

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

      11. *-commutative 88.6%

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

   6. Applied egg-rr 88.6%

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

   7. Taylor expanded in b around inf 28.8%

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

   if 1.3999999999999999e-196 < k < 9.5000000000000002e-123

   1. Initial program 81.4%

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

   3. Simplified 85.6%

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

      1. associate--l+ 85.6%

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

      2. *-commutative 85.6%

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

      3. fma-def 90.5%

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

      4. associate-*l* 90.5%

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

      5. fma-neg 90.5%

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

      6. associate-*r* 90.5%

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

      7. associate-*r* 90.5%

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

      8. +-commutative 90.5%

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

      9. fma-def 90.5%

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

      10. *-commutative 90.5%

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

      11. *-commutative 90.5%

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

   6. Applied egg-rr 90.5%

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

   7. Taylor expanded in i around inf 41.4%

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

      1. *-commutative 41.4%

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

   9. Simplified 41.4%

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

   if 9.5000000000000002e-123 < k < 3.29999999999999998e75

   1. Initial program 75.9%

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

   3. Simplified 89.1%

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

      1. associate--l+ 89.1%

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

      2. *-commutative 89.1%

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

      3. fma-def 89.1%

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

      4. associate-*l* 89.0%

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

      5. fma-neg 89.0%

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

      6. associate-*r* 89.1%

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

      7. associate-*r* 89.1%

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

      8. +-commutative 89.1%

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

      9. fma-def 89.1%

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

      10. *-commutative 89.1%

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

      11. *-commutative 89.1%

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

   6. Applied egg-rr 89.1%

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

   7. Taylor expanded in y around inf 32.5%

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

   if 3.29999999999999998e75 < k

   1. Initial program 92.2%

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

   3. Simplified 92.2%

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

   5. Taylor expanded in j around inf 52.0%

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

      1. associate-*r* 52.1%

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

   7. Simplified 52.1%

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

4. Final simplification 38.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -1.45 \cdot 10^{-60}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;k \leq 1.4 \cdot 10^{-196}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 9.5 \cdot 10^{-123}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;k \leq 3.3 \cdot 10^{+75}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 33.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := -27 \cdot \left(j \cdot k\right)\\ \mathbf{if}\;k \leq -1.45 \cdot 10^{-60}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 1.5 \cdot 10^{-196}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 8 \cdot 10^{+21}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;k \leq 6.8 \cdot 10^{+96}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* -27.0 (* j k))))
   (if (<= k -1.45e-60)
     t_1
     (if (<= k 1.5e-196)
       (* b c)
       (if (<= k 8e+21) (* -4.0 (* x i)) (if (<= k 6.8e+96) (* b c) t_1))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -27.0 * (j * k);
	double tmp;
	if (k <= -1.45e-60) {
		tmp = t_1;
	} else if (k <= 1.5e-196) {
		tmp = b * c;
	} else if (k <= 8e+21) {
		tmp = -4.0 * (x * i);
	} else if (k <= 6.8e+96) {
		tmp = b * c;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-27.0d0) * (j * k)
    if (k <= (-1.45d-60)) then
        tmp = t_1
    else if (k <= 1.5d-196) then
        tmp = b * c
    else if (k <= 8d+21) then
        tmp = (-4.0d0) * (x * i)
    else if (k <= 6.8d+96) then
        tmp = b * c
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -27.0 * (j * k);
	double tmp;
	if (k <= -1.45e-60) {
		tmp = t_1;
	} else if (k <= 1.5e-196) {
		tmp = b * c;
	} else if (k <= 8e+21) {
		tmp = -4.0 * (x * i);
	} else if (k <= 6.8e+96) {
		tmp = b * c;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = -27.0 * (j * k)
	tmp = 0
	if k <= -1.45e-60:
		tmp = t_1
	elif k <= 1.5e-196:
		tmp = b * c
	elif k <= 8e+21:
		tmp = -4.0 * (x * i)
	elif k <= 6.8e+96:
		tmp = b * c
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(-27.0 * Float64(j * k))
	tmp = 0.0
	if (k <= -1.45e-60)
		tmp = t_1;
	elseif (k <= 1.5e-196)
		tmp = Float64(b * c);
	elseif (k <= 8e+21)
		tmp = Float64(-4.0 * Float64(x * i));
	elseif (k <= 6.8e+96)
		tmp = Float64(b * c);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = -27.0 * (j * k);
	tmp = 0.0;
	if (k <= -1.45e-60)
		tmp = t_1;
	elseif (k <= 1.5e-196)
		tmp = b * c;
	elseif (k <= 8e+21)
		tmp = -4.0 * (x * i);
	elseif (k <= 6.8e+96)
		tmp = b * c;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[k, -1.45e-60], t$95$1, If[LessEqual[k, 1.5e-196], N[(b * c), $MachinePrecision], If[LessEqual[k, 8e+21], N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 6.8e+96], N[(b * c), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if k < -1.45e-60 or 6.8000000000000002e96 < k

   1. Initial program 85.4%

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

   3. Simplified 89.8%

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

   5. Taylor expanded in j around inf 46.2%

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

   if -1.45e-60 < k < 1.5e-196 or 8e21 < k < 6.8000000000000002e96

   1. Initial program 86.2%

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

   3. Simplified 88.4%

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

      1. associate--l+ 88.4%

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

      2. *-commutative 88.4%

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

      3. fma-def 89.5%

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

      4. associate-*l* 89.5%

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

      5. fma-neg 89.5%

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

      6. associate-*r* 88.4%

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

      7. associate-*r* 88.4%

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

      8. +-commutative 88.4%

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

      9. fma-def 88.4%

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

      10. *-commutative 88.4%

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

      11. *-commutative 88.4%

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

   6. Applied egg-rr 88.4%

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

   7. Taylor expanded in b around inf 29.5%

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

   if 1.5e-196 < k < 8e21

   1. Initial program 79.6%

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

   3. Simplified 88.7%

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

      1. associate--l+ 88.7%

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

      2. *-commutative 88.7%

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

      3. fma-def 90.6%

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

      4. associate-*l* 90.6%

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

      5. fma-neg 90.6%

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

      6. associate-*r* 90.6%

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

      7. associate-*r* 90.6%

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

      8. +-commutative 90.6%

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

      9. fma-def 90.6%

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

      10. *-commutative 90.6%

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

      11. *-commutative 90.6%

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

   6. Applied egg-rr 90.6%

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

   7. Taylor expanded in i around inf 32.9%

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

      1. *-commutative 32.9%

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

   9. Simplified 32.9%

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

4. Final simplification 37.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -1.45 \cdot 10^{-60}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;k \leq 1.5 \cdot 10^{-196}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 8 \cdot 10^{+21}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;k \leq 6.8 \cdot 10^{+96}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 33.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;k \leq -1.4 \cdot 10^{-60}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;k \leq 1.4 \cdot 10^{-196}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 1.1 \cdot 10^{+22}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;k \leq 7.2 \cdot 10^{+96}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= k -1.4e-60)
   (* -27.0 (* j k))
   (if (<= k 1.4e-196)
     (* b c)
     (if (<= k 1.1e+22)
       (* -4.0 (* x i))
       (if (<= k 7.2e+96) (* b c) (* j (* k -27.0)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (k <= -1.4e-60) {
		tmp = -27.0 * (j * k);
	} else if (k <= 1.4e-196) {
		tmp = b * c;
	} else if (k <= 1.1e+22) {
		tmp = -4.0 * (x * i);
	} else if (k <= 7.2e+96) {
		tmp = b * c;
	} else {
		tmp = j * (k * -27.0);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (k <= (-1.4d-60)) then
        tmp = (-27.0d0) * (j * k)
    else if (k <= 1.4d-196) then
        tmp = b * c
    else if (k <= 1.1d+22) then
        tmp = (-4.0d0) * (x * i)
    else if (k <= 7.2d+96) then
        tmp = b * c
    else
        tmp = j * (k * (-27.0d0))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (k <= -1.4e-60) {
		tmp = -27.0 * (j * k);
	} else if (k <= 1.4e-196) {
		tmp = b * c;
	} else if (k <= 1.1e+22) {
		tmp = -4.0 * (x * i);
	} else if (k <= 7.2e+96) {
		tmp = b * c;
	} else {
		tmp = j * (k * -27.0);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if k <= -1.4e-60:
		tmp = -27.0 * (j * k)
	elif k <= 1.4e-196:
		tmp = b * c
	elif k <= 1.1e+22:
		tmp = -4.0 * (x * i)
	elif k <= 7.2e+96:
		tmp = b * c
	else:
		tmp = j * (k * -27.0)
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (k <= -1.4e-60)
		tmp = Float64(-27.0 * Float64(j * k));
	elseif (k <= 1.4e-196)
		tmp = Float64(b * c);
	elseif (k <= 1.1e+22)
		tmp = Float64(-4.0 * Float64(x * i));
	elseif (k <= 7.2e+96)
		tmp = Float64(b * c);
	else
		tmp = Float64(j * Float64(k * -27.0));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (k <= -1.4e-60)
		tmp = -27.0 * (j * k);
	elseif (k <= 1.4e-196)
		tmp = b * c;
	elseif (k <= 1.1e+22)
		tmp = -4.0 * (x * i);
	elseif (k <= 7.2e+96)
		tmp = b * c;
	else
		tmp = j * (k * -27.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[k, -1.4e-60], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 1.4e-196], N[(b * c), $MachinePrecision], If[LessEqual[k, 1.1e+22], N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 7.2e+96], N[(b * c), $MachinePrecision], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if k < -1.4000000000000001e-60

   1. Initial program 81.3%

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

   3. Simplified 88.5%

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

   5. Taylor expanded in j around inf 40.3%

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

   if -1.4000000000000001e-60 < k < 1.3999999999999999e-196 or 1.1e22 < k < 7.20000000000000026e96

   1. Initial program 86.2%

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

   3. Simplified 88.4%

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

      1. associate--l+ 88.4%

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

      2. *-commutative 88.4%

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

      3. fma-def 89.5%

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

      4. associate-*l* 89.5%

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

      5. fma-neg 89.5%

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

      6. associate-*r* 88.4%

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

      7. associate-*r* 88.4%

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

      8. +-commutative 88.4%

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

      9. fma-def 88.4%

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

      10. *-commutative 88.4%

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

      11. *-commutative 88.4%

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

   6. Applied egg-rr 88.4%

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

   7. Taylor expanded in b around inf 29.5%

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

   if 1.3999999999999999e-196 < k < 1.1e22

   1. Initial program 79.6%

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

   3. Simplified 88.7%

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

      1. associate--l+ 88.7%

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

      2. *-commutative 88.7%

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

      3. fma-def 90.6%

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

      4. associate-*l* 90.6%

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

      5. fma-neg 90.6%

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

      6. associate-*r* 90.6%

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

      7. associate-*r* 90.6%

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

      8. +-commutative 90.6%

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

      9. fma-def 90.6%

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

      10. *-commutative 90.6%

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

      11. *-commutative 90.6%

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

   6. Applied egg-rr 90.6%

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

   7. Taylor expanded in i around inf 32.9%

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

      1. *-commutative 32.9%

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

   9. Simplified 32.9%

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

   if 7.20000000000000026e96 < k

   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 91.7%

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

      1. associate--l+ 91.7%

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

      2. *-commutative 91.7%

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

      3. fma-def 91.7%

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

      4. associate-*l* 91.7%

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

      5. fma-neg 91.7%

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

      6. associate-*r* 91.7%

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

      7. associate-*r* 91.7%

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

      8. +-commutative 91.7%

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

      9. fma-def 91.7%

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

      10. *-commutative 91.7%

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

      11. *-commutative 91.7%

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

   6. Applied egg-rr 91.7%

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

   7. Taylor expanded in j around inf 55.2%

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

      1. *-commutative 55.2%

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

      2. associate-*r* 55.1%

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

   9. Simplified 55.1%

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

4. Final simplification 37.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -1.4 \cdot 10^{-60}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;k \leq 1.4 \cdot 10^{-196}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 1.1 \cdot 10^{+22}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;k \leq 7.2 \cdot 10^{+96}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 33.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;k \leq -1.22 \cdot 10^{-60}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;k \leq 1.4 \cdot 10^{-196}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 3.2 \cdot 10^{+22}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;k \leq 7.8 \cdot 10^{+97}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= k -1.22e-60)
   (* -27.0 (* j k))
   (if (<= k 1.4e-196)
     (* b c)
     (if (<= k 3.2e+22)
       (* -4.0 (* x i))
       (if (<= k 7.8e+97) (* b c) (* k (* j -27.0)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (k <= -1.22e-60) {
		tmp = -27.0 * (j * k);
	} else if (k <= 1.4e-196) {
		tmp = b * c;
	} else if (k <= 3.2e+22) {
		tmp = -4.0 * (x * i);
	} else if (k <= 7.8e+97) {
		tmp = b * c;
	} else {
		tmp = k * (j * -27.0);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (k <= (-1.22d-60)) then
        tmp = (-27.0d0) * (j * k)
    else if (k <= 1.4d-196) then
        tmp = b * c
    else if (k <= 3.2d+22) then
        tmp = (-4.0d0) * (x * i)
    else if (k <= 7.8d+97) then
        tmp = b * c
    else
        tmp = k * (j * (-27.0d0))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (k <= -1.22e-60) {
		tmp = -27.0 * (j * k);
	} else if (k <= 1.4e-196) {
		tmp = b * c;
	} else if (k <= 3.2e+22) {
		tmp = -4.0 * (x * i);
	} else if (k <= 7.8e+97) {
		tmp = b * c;
	} else {
		tmp = k * (j * -27.0);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if k <= -1.22e-60:
		tmp = -27.0 * (j * k)
	elif k <= 1.4e-196:
		tmp = b * c
	elif k <= 3.2e+22:
		tmp = -4.0 * (x * i)
	elif k <= 7.8e+97:
		tmp = b * c
	else:
		tmp = k * (j * -27.0)
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (k <= -1.22e-60)
		tmp = Float64(-27.0 * Float64(j * k));
	elseif (k <= 1.4e-196)
		tmp = Float64(b * c);
	elseif (k <= 3.2e+22)
		tmp = Float64(-4.0 * Float64(x * i));
	elseif (k <= 7.8e+97)
		tmp = Float64(b * c);
	else
		tmp = Float64(k * Float64(j * -27.0));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (k <= -1.22e-60)
		tmp = -27.0 * (j * k);
	elseif (k <= 1.4e-196)
		tmp = b * c;
	elseif (k <= 3.2e+22)
		tmp = -4.0 * (x * i);
	elseif (k <= 7.8e+97)
		tmp = b * c;
	else
		tmp = k * (j * -27.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[k, -1.22e-60], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 1.4e-196], N[(b * c), $MachinePrecision], If[LessEqual[k, 3.2e+22], N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 7.8e+97], N[(b * c), $MachinePrecision], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if k < -1.22e-60

   1. Initial program 81.3%

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

   3. Simplified 88.5%

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

   5. Taylor expanded in j around inf 40.3%

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

   if -1.22e-60 < k < 1.3999999999999999e-196 or 3.2e22 < k < 7.7999999999999999e97

   1. Initial program 86.2%

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

   3. Simplified 88.4%

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

      1. associate--l+ 88.4%

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

      2. *-commutative 88.4%

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

      3. fma-def 89.5%

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

      4. associate-*l* 89.5%

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

      5. fma-neg 89.5%

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

      6. associate-*r* 88.4%

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

      7. associate-*r* 88.4%

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

      8. +-commutative 88.4%

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

      9. fma-def 88.4%

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

      10. *-commutative 88.4%

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

      11. *-commutative 88.4%

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

   6. Applied egg-rr 88.4%

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

   7. Taylor expanded in b around inf 29.5%

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

   if 1.3999999999999999e-196 < k < 3.2e22

   1. Initial program 79.6%

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

   3. Simplified 88.7%

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

      1. associate--l+ 88.7%

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

      2. *-commutative 88.7%

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

      3. fma-def 90.6%

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

      4. associate-*l* 90.6%

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

      5. fma-neg 90.6%

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

      6. associate-*r* 90.6%

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

      7. associate-*r* 90.6%

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

      8. +-commutative 90.6%

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

      9. fma-def 90.6%

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

      10. *-commutative 90.6%

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

      11. *-commutative 90.6%

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

   6. Applied egg-rr 90.6%

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

   7. Taylor expanded in i around inf 32.9%

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

      1. *-commutative 32.9%

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

   9. Simplified 32.9%

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

   if 7.7999999999999999e97 < k

   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 91.7%

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

   5. Taylor expanded in j around inf 55.2%

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

      1. associate-*r* 55.2%

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

   7. Simplified 55.2%

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

4. Final simplification 37.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -1.22 \cdot 10^{-60}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;k \leq 1.4 \cdot 10^{-196}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 3.2 \cdot 10^{+22}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;k \leq 7.8 \cdot 10^{+97}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 47.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{+89}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{+126}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \mathbf{else}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= x -2.3e+89)
   (* -4.0 (* x i))
   (if (<= x 1.9e+126)
     (+ (* 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);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (x <= -2.3e+89) {
		tmp = -4.0 * (x * i);
	} else if (x <= 1.9e+126) {
		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.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (x <= (-2.3d+89)) then
        tmp = (-4.0d0) * (x * i)
    else if (x <= 1.9d+126) 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;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (x <= -2.3e+89) {
		tmp = -4.0 * (x * i);
	} else if (x <= 1.9e+126) {
		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])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if x <= -2.3e+89:
		tmp = -4.0 * (x * i)
	elif x <= 1.9e+126:
		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])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (x <= -2.3e+89)
		tmp = Float64(-4.0 * Float64(x * i));
	elseif (x <= 1.9e+126)
		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])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (x <= -2.3e+89)
		tmp = -4.0 * (x * i);
	elseif (x <= 1.9e+126)
		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.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[x, -2.3e+89], N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.9e+126], 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 x < -2.2999999999999999e89

   1. Initial program 68.4%

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

   3. Simplified 84.1%

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

      1. associate--l+ 84.1%

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

      2. *-commutative 84.1%

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

      3. fma-def 84.1%

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

      4. associate-*l* 84.1%

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

      5. fma-neg 84.1%

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

      6. associate-*r* 84.1%

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

      7. associate-*r* 84.1%

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

      8. +-commutative 84.1%

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

      9. fma-def 84.1%

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

      10. *-commutative 84.1%

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

      11. *-commutative 84.1%

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

   6. Applied egg-rr 84.1%

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

   7. Taylor expanded in i around inf 49.5%

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

      1. *-commutative 49.5%

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

   9. Simplified 49.5%

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

   if -2.2999999999999999e89 < x < 1.90000000000000008e126

   1. Initial program 91.1%

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

   3. Simplified 92.9%

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

   5. Taylor expanded in b around inf 59.5%

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

   if 1.90000000000000008e126 < x

   1. Initial program 75.1%

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

   3. Simplified 80.7%

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

      1. associate--l+ 80.7%

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

      2. *-commutative 80.7%

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

      3. fma-def 86.2%

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

      4. associate-*l* 86.2%

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

      5. fma-neg 86.2%

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

      6. associate-*r* 86.2%

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

      7. associate-*r* 86.2%

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

      8. +-commutative 86.2%

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

      9. fma-def 86.2%

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

      10. *-commutative 86.2%

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

      11. *-commutative 86.2%

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

   6. Applied egg-rr 86.2%

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

   7. Taylor expanded in y around inf 47.0%

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

4. Final simplification 55.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{+89}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{+126}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \mathbf{else}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 33.4% accurate, 2.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;k \leq -1.45 \cdot 10^{-60} \lor \neg \left(k \leq 1.25 \cdot 10^{+98}\right):\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= k -1.45e-60) (not (<= k 1.25e+98))) (* -27.0 (* j k)) (* b c)))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((k <= -1.45e-60) || !(k <= 1.25e+98)) {
		tmp = -27.0 * (j * k);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((k <= (-1.45d-60)) .or. (.not. (k <= 1.25d+98))) then
        tmp = (-27.0d0) * (j * k)
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((k <= -1.45e-60) || !(k <= 1.25e+98)) {
		tmp = -27.0 * (j * k);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (k <= -1.45e-60) or not (k <= 1.25e+98):
		tmp = -27.0 * (j * k)
	else:
		tmp = b * c
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((k <= -1.45e-60) || !(k <= 1.25e+98))
		tmp = Float64(-27.0 * Float64(j * k));
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((k <= -1.45e-60) || ~((k <= 1.25e+98)))
		tmp = -27.0 * (j * k);
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[k, -1.45e-60], N[Not[LessEqual[k, 1.25e+98]], $MachinePrecision]], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if k < -1.45e-60 or 1.25e98 < k

   1. Initial program 85.4%

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

   3. Simplified 89.8%

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

   5. Taylor expanded in j around inf 46.2%

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

   if -1.45e-60 < k < 1.25e98

   1. Initial program 83.7%

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

   3. Simplified 88.5%

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

      1. associate--l+ 88.5%

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

      2. *-commutative 88.5%

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

      3. fma-def 89.9%

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

      4. associate-*l* 89.9%

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

      5. fma-neg 89.9%

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

      6. associate-*r* 89.3%

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

      7. associate-*r* 89.3%

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

      8. +-commutative 89.3%

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

      9. fma-def 89.3%

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

      10. *-commutative 89.3%

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

      11. *-commutative 89.3%

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

   6. Applied egg-rr 89.3%

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

   7. Taylor expanded in b around inf 26.3%

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

4. Final simplification 35.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -1.45 \cdot 10^{-60} \lor \neg \left(k \leq 1.25 \cdot 10^{+98}\right):\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 23.5% accurate, 10.3× speedup

Math

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

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k) :precision binary64 (* b c))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	return b * c;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    code = b * c
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	return b * c;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	return b * c

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	return Float64(b * c)
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp = code(x, y, z, t, a, b, c, i, j, k)
	tmp = b * c;
end

Wolfram

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

Derivation

1. Initial program 84.5%

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

3. Simplified 88.7%

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

   1. associate--l+ 88.7%

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

   2. *-commutative 88.7%

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

   3. fma-def 90.6%

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

   4. associate-*l* 90.3%

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

   5. fma-neg 90.3%

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

   6. associate-*r* 89.9%

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

   7. associate-*r* 89.9%

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

   8. +-commutative 89.9%

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

   9. fma-def 89.9%

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

   10. *-commutative 89.9%

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

   11. *-commutative 89.9%

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

6. Applied egg-rr 89.9%

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

7. Taylor expanded in b around inf 25.9%

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

8. Final simplification 25.9%

   \[\leadsto b \cdot c \]
9. Add Preprocessing

Developer target: 89.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a \cdot t + i \cdot x\right) \cdot 4\\ t_2 := \left(\left(18 \cdot t\right) \cdot \left(\left(x \cdot y\right) \cdot z\right) - t_1\right) - \left(\left(k \cdot j\right) \cdot 27 - c \cdot b\right)\\ \mathbf{if}\;t < -1.6210815397541398 \cdot 10^{-69}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t < 165.68027943805222:\\ \;\;\;\;\left(\left(18 \cdot y\right) \cdot \left(x \cdot \left(z \cdot t\right)\right) - t_1\right) + \left(c \cdot b - 27 \cdot \left(k \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (+ (* a t) (* i x)) 4.0))
        (t_2
         (-
          (- (* (* 18.0 t) (* (* x y) z)) t_1)
          (- (* (* k j) 27.0) (* c b)))))
   (if (< t -1.6210815397541398e-69)
     t_2
     (if (< t 165.68027943805222)
       (+ (- (* (* 18.0 y) (* x (* z t))) t_1) (- (* c b) (* 27.0 (* k j))))
       t_2))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((a * t) + (i * x)) * 4.0;
	double t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b));
	double tmp;
	if (t < -1.6210815397541398e-69) {
		tmp = t_2;
	} else if (t < 165.68027943805222) {
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((a * t) + (i * x)) * 4.0d0
    t_2 = (((18.0d0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0d0) - (c * b))
    if (t < (-1.6210815397541398d-69)) then
        tmp = t_2
    else if (t < 165.68027943805222d0) then
        tmp = (((18.0d0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0d0 * (k * j)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((a * t) + (i * x)) * 4.0;
	double t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b));
	double tmp;
	if (t < -1.6210815397541398e-69) {
		tmp = t_2;
	} else if (t < 165.68027943805222) {
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = ((a * t) + (i * x)) * 4.0
	t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b))
	tmp = 0
	if t < -1.6210815397541398e-69:
		tmp = t_2
	elif t < 165.68027943805222:
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(Float64(a * t) + Float64(i * x)) * 4.0)
	t_2 = Float64(Float64(Float64(Float64(18.0 * t) * Float64(Float64(x * y) * z)) - t_1) - Float64(Float64(Float64(k * j) * 27.0) - Float64(c * b)))
	tmp = 0.0
	if (t < -1.6210815397541398e-69)
		tmp = t_2;
	elseif (t < 165.68027943805222)
		tmp = Float64(Float64(Float64(Float64(18.0 * y) * Float64(x * Float64(z * t))) - t_1) + Float64(Float64(c * b) - Float64(27.0 * Float64(k * j))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = ((a * t) + (i * x)) * 4.0;
	t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b));
	tmp = 0.0;
	if (t < -1.6210815397541398e-69)
		tmp = t_2;
	elseif (t < 165.68027943805222)
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(N[(a * t), $MachinePrecision] + N[(i * x), $MachinePrecision]), $MachinePrecision] * 4.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(18.0 * t), $MachinePrecision] * N[(N[(x * y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] - N[(N[(N[(k * j), $MachinePrecision] * 27.0), $MachinePrecision] - N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -1.6210815397541398e-69], t$95$2, If[Less[t, 165.68027943805222], N[(N[(N[(N[(18.0 * y), $MachinePrecision] * N[(x * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] + N[(N[(c * b), $MachinePrecision] - N[(27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2024020 
(FPCore (x y z t a b c i j k)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, E"
  :precision binary64

  :herbie-target
  (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)))