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

Percentage Accurate: 85.7% → 91.4%

Time: 26.2s

Alternatives: 27

Speedup: 0.9×

• 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: 85.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 91.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+47}:\\ \;\;\;\;y \cdot \left(\frac{\mathsf{fma}\left(b, c, -4 \cdot \left(x \cdot i + t \cdot a\right) + k \cdot \left(-27 \cdot j\right)\right)}{y} - \left(-18 \cdot t\right) \cdot \left(x \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), -4 \cdot a\right), \mathsf{fma}\left(b, c, x \cdot \left(-4 \cdot i\right)\right)\right) + j \cdot \left(k \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= y -1.5e+47)
   (*
    y
    (-
     (/ (fma b c (+ (* -4.0 (+ (* x i) (* t a))) (* k (* -27.0 j)))) y)
     (* (* -18.0 t) (* x z))))
   (+
    (fma t (fma x (* 18.0 (* y z)) (* -4.0 a)) (fma b c (* x (* -4.0 i))))
    (* 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 (y <= -1.5e+47) {
		tmp = y * ((fma(b, c, ((-4.0 * ((x * i) + (t * a))) + (k * (-27.0 * j)))) / y) - ((-18.0 * t) * (x * z)));
	} else {
		tmp = fma(t, fma(x, (18.0 * (y * z)), (-4.0 * a)), fma(b, c, (x * (-4.0 * i)))) + (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 (y <= -1.5e+47)
		tmp = Float64(y * Float64(Float64(fma(b, c, Float64(Float64(-4.0 * Float64(Float64(x * i) + Float64(t * a))) + Float64(k * Float64(-27.0 * j)))) / y) - Float64(Float64(-18.0 * t) * Float64(x * z))));
	else
		tmp = Float64(fma(t, fma(x, Float64(18.0 * Float64(y * z)), Float64(-4.0 * a)), fma(b, c, Float64(x * Float64(-4.0 * i)))) + Float64(j * Float64(k * -27.0)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[y, -1.5e+47], N[(y * N[(N[(N[(b * c + N[(N[(-4.0 * N[(N[(x * i), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(k * N[(-27.0 * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] - N[(N[(-18.0 * t), $MachinePrecision] * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t * N[(x * N[(18.0 * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] + N[(b * c + N[(x * N[(-4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.5000000000000001e47

   1. Initial program 76.9%

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

   3. Simplified 75.1%

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

   5. Taylor expanded in y around -inf 86.1%

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

   7. Simplified 88.1%

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

   if -1.5000000000000001e47 < y

   1. Initial program 83.8%

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

   3. Simplified 88.7%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+47}:\\ \;\;\;\;y \cdot \left(\frac{\mathsf{fma}\left(b, c, -4 \cdot \left(x \cdot i + t \cdot a\right) + k \cdot \left(-27 \cdot j\right)\right)}{y} - \left(-18 \cdot t\right) \cdot \left(x \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), -4 \cdot a\right), \mathsf{fma}\left(b, c, x \cdot \left(-4 \cdot i\right)\right)\right) + j \cdot \left(k \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 90.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{-13}:\\ \;\;\;\;y \cdot \left(\frac{\mathsf{fma}\left(b, c, -4 \cdot \left(x \cdot i + t \cdot a\right) + k \cdot \left(-27 \cdot j\right)\right)}{y} - \left(-18 \cdot t\right) \cdot \left(x \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - t \cdot \left(a \cdot 4 - \left(y \cdot z\right) \cdot \left(x \cdot 18\right)\right)\right) - \left(x \cdot \left(i \cdot 4\right) + j \cdot \left(k \cdot 27\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= y -2.6e-13)
   (*
    y
    (-
     (/ (fma b c (+ (* -4.0 (+ (* x i) (* t a))) (* k (* -27.0 j)))) y)
     (* (* -18.0 t) (* x z))))
   (-
    (- (* b c) (* t (- (* a 4.0) (* (* y z) (* x 18.0)))))
    (+ (* x (* i 4.0)) (* j (* k 27.0))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (y <= -2.6e-13) {
		tmp = y * ((fma(b, c, ((-4.0 * ((x * i) + (t * a))) + (k * (-27.0 * j)))) / y) - ((-18.0 * t) * (x * z)));
	} else {
		tmp = ((b * c) - (t * ((a * 4.0) - ((y * z) * (x * 18.0))))) - ((x * (i * 4.0)) + (j * (k * 27.0)));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (y <= -2.6e-13)
		tmp = Float64(y * Float64(Float64(fma(b, c, Float64(Float64(-4.0 * Float64(Float64(x * i) + Float64(t * a))) + Float64(k * Float64(-27.0 * j)))) / y) - Float64(Float64(-18.0 * t) * Float64(x * z))));
	else
		tmp = Float64(Float64(Float64(b * c) - Float64(t * Float64(Float64(a * 4.0) - Float64(Float64(y * z) * Float64(x * 18.0))))) - Float64(Float64(x * Float64(i * 4.0)) + Float64(j * Float64(k * 27.0))));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[y, -2.6e-13], N[(y * N[(N[(N[(b * c + N[(N[(-4.0 * N[(N[(x * i), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(k * N[(-27.0 * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] - N[(N[(-18.0 * t), $MachinePrecision] * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] - N[(t * N[(N[(a * 4.0), $MachinePrecision] - N[(N[(y * z), $MachinePrecision] * N[(x * 18.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * N[(i * 4.0), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.6e-13

   1. Initial program 75.6%

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

   3. Simplified 75.7%

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

   5. Taylor expanded in y around -inf 83.4%

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

   7. Simplified 84.8%

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

   if -2.6e-13 < y

   1. Initial program 85.2%

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

   3. Simplified 87.3%

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

4. Final simplification 86.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{-13}:\\ \;\;\;\;y \cdot \left(\frac{\mathsf{fma}\left(b, c, -4 \cdot \left(x \cdot i + t \cdot a\right) + k \cdot \left(-27 \cdot j\right)\right)}{y} - \left(-18 \cdot t\right) \cdot \left(x \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - t \cdot \left(a \cdot 4 - \left(y \cdot z\right) \cdot \left(x \cdot 18\right)\right)\right) - \left(x \cdot \left(i \cdot 4\right) + j \cdot \left(k \cdot 27\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 91.9% accurate, 0.5× speedup

Math

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

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1
         (-
          (-
           (+ (* b c) (- (* t (* z (* y (* x 18.0)))) (* t (* a 4.0))))
           (* i (* x 4.0)))
          (* k (* j 27.0)))))
   (if (<= t_1 INFINITY)
     t_1
     (* x (* i (- (* 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) + ((t * (z * (y * (x * 18.0)))) - (t * (a * 4.0)))) - (i * (x * 4.0))) - (k * (j * 27.0));
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = x * (i * ((18.0 * ((t * (y * z)) / 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 t_1 = (((b * c) + ((t * (z * (y * (x * 18.0)))) - (t * (a * 4.0)))) - (i * (x * 4.0))) - (k * (j * 27.0));
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = x * (i * ((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) + ((t * (z * (y * (x * 18.0)))) - (t * (a * 4.0)))) - (i * (x * 4.0))) - (k * (j * 27.0))
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = x * (i * ((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(Float64(b * c) + Float64(Float64(t * Float64(z * Float64(y * Float64(x * 18.0)))) - Float64(t * Float64(a * 4.0)))) - Float64(i * Float64(x * 4.0))) - Float64(k * Float64(j * 27.0)))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(i * Float64(Float64(18.0 * Float64(Float64(t * Float64(y * z)) / 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) + ((t * (z * (y * (x * 18.0)))) - (t * (a * 4.0)))) - (i * (x * 4.0))) - (k * (j * 27.0));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = x * (i * ((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[(N[(b * c), $MachinePrecision] + N[(N[(t * N[(z * N[(y * N[(x * 18.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * N[(x * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(x * N[(i * N[(N[(18.0 * N[(N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision]), $MachinePrecision] - 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 95.5%

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

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

   1. Initial program 0.0%

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

   3. Simplified 17.1%

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

   5. Taylor expanded in x around inf 54.6%

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

   6. Taylor expanded in i around inf 57.4%

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

4. Final simplification 90.3%

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

Alternative 4: 36.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := t \cdot \left(-4 \cdot a\right)\\ \mathbf{if}\;b \cdot c \leq -2.9 \cdot 10^{+79}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -1 \cdot 10^{+27}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq -9.2 \cdot 10^{+26}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -2.5 \cdot 10^{-45}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq -9.4 \cdot 10^{-119}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq -1.8 \cdot 10^{-308}:\\ \;\;\;\;k \cdot \left(-27 \cdot j\right)\\ \mathbf{elif}\;b \cdot c \leq 2.5 \cdot 10^{-267}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 3.9 \cdot 10^{+50}:\\ \;\;\;\;-27 \cdot \left(k \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* t (* -4.0 a))))
   (if (<= (* b c) -2.9e+79)
     (* b c)
     (if (<= (* b c) -1e+27)
       t_1
       (if (<= (* b c) -9.2e+26)
         (* b c)
         (if (<= (* b c) -2.5e-45)
           (* j (* k -27.0))
           (if (<= (* b c) -9.4e-119)
             t_1
             (if (<= (* b c) -1.8e-308)
               (* k (* -27.0 j))
               (if (<= (* b c) 2.5e-267)
                 (* -4.0 (* x i))
                 (if (<= (* b c) 3.9e+50) (* -27.0 (* k j)) (* b c)))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * (-4.0 * a);
	double tmp;
	if ((b * c) <= -2.9e+79) {
		tmp = b * c;
	} else if ((b * c) <= -1e+27) {
		tmp = t_1;
	} else if ((b * c) <= -9.2e+26) {
		tmp = b * c;
	} else if ((b * c) <= -2.5e-45) {
		tmp = j * (k * -27.0);
	} else if ((b * c) <= -9.4e-119) {
		tmp = t_1;
	} else if ((b * c) <= -1.8e-308) {
		tmp = k * (-27.0 * j);
	} else if ((b * c) <= 2.5e-267) {
		tmp = -4.0 * (x * i);
	} else if ((b * c) <= 3.9e+50) {
		tmp = -27.0 * (k * j);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((-4.0d0) * a)
    if ((b * c) <= (-2.9d+79)) then
        tmp = b * c
    else if ((b * c) <= (-1d+27)) then
        tmp = t_1
    else if ((b * c) <= (-9.2d+26)) then
        tmp = b * c
    else if ((b * c) <= (-2.5d-45)) then
        tmp = j * (k * (-27.0d0))
    else if ((b * c) <= (-9.4d-119)) then
        tmp = t_1
    else if ((b * c) <= (-1.8d-308)) then
        tmp = k * ((-27.0d0) * j)
    else if ((b * c) <= 2.5d-267) then
        tmp = (-4.0d0) * (x * i)
    else if ((b * c) <= 3.9d+50) then
        tmp = (-27.0d0) * (k * j)
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * (-4.0 * a);
	double tmp;
	if ((b * c) <= -2.9e+79) {
		tmp = b * c;
	} else if ((b * c) <= -1e+27) {
		tmp = t_1;
	} else if ((b * c) <= -9.2e+26) {
		tmp = b * c;
	} else if ((b * c) <= -2.5e-45) {
		tmp = j * (k * -27.0);
	} else if ((b * c) <= -9.4e-119) {
		tmp = t_1;
	} else if ((b * c) <= -1.8e-308) {
		tmp = k * (-27.0 * j);
	} else if ((b * c) <= 2.5e-267) {
		tmp = -4.0 * (x * i);
	} else if ((b * c) <= 3.9e+50) {
		tmp = -27.0 * (k * j);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = t * (-4.0 * a)
	tmp = 0
	if (b * c) <= -2.9e+79:
		tmp = b * c
	elif (b * c) <= -1e+27:
		tmp = t_1
	elif (b * c) <= -9.2e+26:
		tmp = b * c
	elif (b * c) <= -2.5e-45:
		tmp = j * (k * -27.0)
	elif (b * c) <= -9.4e-119:
		tmp = t_1
	elif (b * c) <= -1.8e-308:
		tmp = k * (-27.0 * j)
	elif (b * c) <= 2.5e-267:
		tmp = -4.0 * (x * i)
	elif (b * c) <= 3.9e+50:
		tmp = -27.0 * (k * j)
	else:
		tmp = b * c
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(t * Float64(-4.0 * a))
	tmp = 0.0
	if (Float64(b * c) <= -2.9e+79)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -1e+27)
		tmp = t_1;
	elseif (Float64(b * c) <= -9.2e+26)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -2.5e-45)
		tmp = Float64(j * Float64(k * -27.0));
	elseif (Float64(b * c) <= -9.4e-119)
		tmp = t_1;
	elseif (Float64(b * c) <= -1.8e-308)
		tmp = Float64(k * Float64(-27.0 * j));
	elseif (Float64(b * c) <= 2.5e-267)
		tmp = Float64(-4.0 * Float64(x * i));
	elseif (Float64(b * c) <= 3.9e+50)
		tmp = Float64(-27.0 * Float64(k * j));
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = t * (-4.0 * a);
	tmp = 0.0;
	if ((b * c) <= -2.9e+79)
		tmp = b * c;
	elseif ((b * c) <= -1e+27)
		tmp = t_1;
	elseif ((b * c) <= -9.2e+26)
		tmp = b * c;
	elseif ((b * c) <= -2.5e-45)
		tmp = j * (k * -27.0);
	elseif ((b * c) <= -9.4e-119)
		tmp = t_1;
	elseif ((b * c) <= -1.8e-308)
		tmp = k * (-27.0 * j);
	elseif ((b * c) <= 2.5e-267)
		tmp = -4.0 * (x * i);
	elseif ((b * c) <= 3.9e+50)
		tmp = -27.0 * (k * j);
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(t * N[(-4.0 * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -2.9e+79], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -1e+27], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], -9.2e+26], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -2.5e-45], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -9.4e-119], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], -1.8e-308], N[(k * N[(-27.0 * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 2.5e-267], N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 3.9e+50], N[(-27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if (*.f64 b c) < -2.89999999999999992e79 or -1e27 < (*.f64 b c) < -9.2000000000000002e26 or 3.89999999999999967e50 < (*.f64 b c)

   1. Initial program 77.9%

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

      1. pow1 77.9%

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

      2. associate-*l* 77.9%

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

      3. *-commutative 77.9%

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

   4. Applied egg-rr 77.9%

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

      1. unpow1 77.9%

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

      2. associate-*l* 79.8%

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

      3. *-commutative 79.8%

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

   6. Simplified 79.8%

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

   7. Taylor expanded in b around inf 54.1%

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

   if -2.89999999999999992e79 < (*.f64 b c) < -1e27 or -2.49999999999999988e-45 < (*.f64 b c) < -9.40000000000000004e-119

   1. Initial program 85.4%

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

      1. pow1 85.4%

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

      2. associate-*l* 85.4%

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

      3. *-commutative 85.4%

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

   4. Applied egg-rr 85.4%

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

      1. unpow1 85.4%

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

      2. associate-*l* 85.4%

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

      3. *-commutative 85.4%

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

   6. Simplified 85.4%

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

   7. Taylor expanded in a around inf 46.4%

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

      1. associate-*r* 46.4%

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

      2. *-commutative 46.4%

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

   9. Simplified 46.4%

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

   if -9.2000000000000002e26 < (*.f64 b c) < -2.49999999999999988e-45

   1. Initial program 76.8%

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

      1. pow1 76.8%

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

      2. associate-*l* 76.8%

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

      3. *-commutative 76.8%

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

   4. Applied egg-rr 76.8%

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

      1. unpow1 76.8%

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

      2. associate-*l* 84.5%

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

      3. *-commutative 84.5%

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

   6. Simplified 84.5%

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

   7. Taylor expanded in j around inf 48.4%

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

      1. metadata-eval 48.4%

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

      2. distribute-lft-neg-in 48.4%

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

      3. associate-*r* 48.5%

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

      4. *-commutative 48.5%

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

      5. associate-*r* 48.5%

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

      6. distribute-rgt-neg-in 48.5%

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

      7. distribute-lft-neg-in 48.5%

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

      8. metadata-eval 48.5%

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

      9. *-commutative 48.5%

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

   9. Simplified 48.5%

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

   if -9.40000000000000004e-119 < (*.f64 b c) < -1.7999999999999999e-308

   1. Initial program 77.5%

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

   3. Simplified 84.9%

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

   5. Taylor expanded in j around inf 39.8%

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

      1. associate-*r* 39.9%

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

      2. *-commutative 39.9%

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

      3. metadata-eval 39.9%

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

      4. distribute-rgt-neg-in 39.9%

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

      5. *-commutative 39.9%

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

      6. distribute-rgt-neg-in 39.9%

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

      7. metadata-eval 39.9%

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

      8. *-commutative 39.9%

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

   7. Simplified 39.9%

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

   if -1.7999999999999999e-308 < (*.f64 b c) < 2.5e-267

   1. Initial program 89.1%

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

      1. pow1 89.1%

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

      2. associate-*l* 89.1%

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

      3. *-commutative 89.1%

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

   4. Applied egg-rr 89.1%

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

      1. unpow1 89.1%

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

      2. associate-*l* 92.4%

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

      3. *-commutative 92.4%

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

   6. Simplified 92.4%

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

   7. Taylor expanded in i around inf 42.1%

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

      1. *-commutative 42.1%

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

      2. *-commutative 42.1%

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

   9. Simplified 42.1%

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

   if 2.5e-267 < (*.f64 b c) < 3.89999999999999967e50

   1. Initial program 90.6%

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

   3. Simplified 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 j around inf 44.8%

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

4. Final simplification 48.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2.9 \cdot 10^{+79}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -1 \cdot 10^{+27}:\\ \;\;\;\;t \cdot \left(-4 \cdot a\right)\\ \mathbf{elif}\;b \cdot c \leq -9.2 \cdot 10^{+26}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -2.5 \cdot 10^{-45}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq -9.4 \cdot 10^{-119}:\\ \;\;\;\;t \cdot \left(-4 \cdot a\right)\\ \mathbf{elif}\;b \cdot c \leq -1.8 \cdot 10^{-308}:\\ \;\;\;\;k \cdot \left(-27 \cdot j\right)\\ \mathbf{elif}\;b \cdot c \leq 2.5 \cdot 10^{-267}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 3.9 \cdot 10^{+50}:\\ \;\;\;\;-27 \cdot \left(k \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 37.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := t \cdot \left(-4 \cdot a\right)\\ \mathbf{if}\;b \cdot c \leq -3 \cdot 10^{+79}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -3.2 \cdot 10^{+27}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq -9.2 \cdot 10^{+26}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -2.4 \cdot 10^{-51}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq -1.55 \cdot 10^{-117}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq 4.2 \cdot 10^{+50}:\\ \;\;\;\;k \cdot \left(-27 \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* t (* -4.0 a))))
   (if (<= (* b c) -3e+79)
     (* b c)
     (if (<= (* b c) -3.2e+27)
       t_1
       (if (<= (* b c) -9.2e+26)
         (* b c)
         (if (<= (* b c) -2.4e-51)
           (* j (* k -27.0))
           (if (<= (* b c) -1.55e-117)
             t_1
             (if (<= (* b c) 4.2e+50) (* k (* -27.0 j)) (* b c)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * (-4.0 * a);
	double tmp;
	if ((b * c) <= -3e+79) {
		tmp = b * c;
	} else if ((b * c) <= -3.2e+27) {
		tmp = t_1;
	} else if ((b * c) <= -9.2e+26) {
		tmp = b * c;
	} else if ((b * c) <= -2.4e-51) {
		tmp = j * (k * -27.0);
	} else if ((b * c) <= -1.55e-117) {
		tmp = t_1;
	} else if ((b * c) <= 4.2e+50) {
		tmp = k * (-27.0 * j);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((-4.0d0) * a)
    if ((b * c) <= (-3d+79)) then
        tmp = b * c
    else if ((b * c) <= (-3.2d+27)) then
        tmp = t_1
    else if ((b * c) <= (-9.2d+26)) then
        tmp = b * c
    else if ((b * c) <= (-2.4d-51)) then
        tmp = j * (k * (-27.0d0))
    else if ((b * c) <= (-1.55d-117)) then
        tmp = t_1
    else if ((b * c) <= 4.2d+50) then
        tmp = k * ((-27.0d0) * j)
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * (-4.0 * a);
	double tmp;
	if ((b * c) <= -3e+79) {
		tmp = b * c;
	} else if ((b * c) <= -3.2e+27) {
		tmp = t_1;
	} else if ((b * c) <= -9.2e+26) {
		tmp = b * c;
	} else if ((b * c) <= -2.4e-51) {
		tmp = j * (k * -27.0);
	} else if ((b * c) <= -1.55e-117) {
		tmp = t_1;
	} else if ((b * c) <= 4.2e+50) {
		tmp = k * (-27.0 * j);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = t * (-4.0 * a)
	tmp = 0
	if (b * c) <= -3e+79:
		tmp = b * c
	elif (b * c) <= -3.2e+27:
		tmp = t_1
	elif (b * c) <= -9.2e+26:
		tmp = b * c
	elif (b * c) <= -2.4e-51:
		tmp = j * (k * -27.0)
	elif (b * c) <= -1.55e-117:
		tmp = t_1
	elif (b * c) <= 4.2e+50:
		tmp = k * (-27.0 * j)
	else:
		tmp = b * c
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(t * Float64(-4.0 * a))
	tmp = 0.0
	if (Float64(b * c) <= -3e+79)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -3.2e+27)
		tmp = t_1;
	elseif (Float64(b * c) <= -9.2e+26)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -2.4e-51)
		tmp = Float64(j * Float64(k * -27.0));
	elseif (Float64(b * c) <= -1.55e-117)
		tmp = t_1;
	elseif (Float64(b * c) <= 4.2e+50)
		tmp = Float64(k * Float64(-27.0 * j));
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = t * (-4.0 * a);
	tmp = 0.0;
	if ((b * c) <= -3e+79)
		tmp = b * c;
	elseif ((b * c) <= -3.2e+27)
		tmp = t_1;
	elseif ((b * c) <= -9.2e+26)
		tmp = b * c;
	elseif ((b * c) <= -2.4e-51)
		tmp = j * (k * -27.0);
	elseif ((b * c) <= -1.55e-117)
		tmp = t_1;
	elseif ((b * c) <= 4.2e+50)
		tmp = k * (-27.0 * j);
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(t * N[(-4.0 * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -3e+79], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -3.2e+27], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], -9.2e+26], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -2.4e-51], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -1.55e-117], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 4.2e+50], N[(k * N[(-27.0 * j), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 b c) < -2.99999999999999974e79 or -3.20000000000000015e27 < (*.f64 b c) < -9.2000000000000002e26 or 4.1999999999999999e50 < (*.f64 b c)

   1. Initial program 77.9%

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

      1. pow1 77.9%

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

      2. associate-*l* 77.9%

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

      3. *-commutative 77.9%

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

   4. Applied egg-rr 77.9%

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

      1. unpow1 77.9%

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

      2. associate-*l* 79.8%

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

      3. *-commutative 79.8%

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

   6. Simplified 79.8%

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

   7. Taylor expanded in b around inf 54.1%

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

   if -2.99999999999999974e79 < (*.f64 b c) < -3.20000000000000015e27 or -2.4e-51 < (*.f64 b c) < -1.55000000000000005e-117

   1. Initial program 85.4%

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

      1. pow1 85.4%

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

      2. associate-*l* 85.4%

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

      3. *-commutative 85.4%

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

   4. Applied egg-rr 85.4%

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

      1. unpow1 85.4%

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

      2. associate-*l* 85.4%

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

      3. *-commutative 85.4%

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

   6. Simplified 85.4%

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

   7. Taylor expanded in a around inf 46.4%

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

      1. associate-*r* 46.4%

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

      2. *-commutative 46.4%

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

   9. Simplified 46.4%

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

   if -9.2000000000000002e26 < (*.f64 b c) < -2.4e-51

   1. Initial program 76.8%

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

      1. pow1 76.8%

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

      2. associate-*l* 76.8%

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

      3. *-commutative 76.8%

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

   4. Applied egg-rr 76.8%

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

      1. unpow1 76.8%

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

      2. associate-*l* 84.5%

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

      3. *-commutative 84.5%

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

   6. Simplified 84.5%

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

   7. Taylor expanded in j around inf 48.4%

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

      1. metadata-eval 48.4%

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

      2. distribute-lft-neg-in 48.4%

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

      3. associate-*r* 48.5%

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

      4. *-commutative 48.5%

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

      5. associate-*r* 48.5%

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

      6. distribute-rgt-neg-in 48.5%

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

      7. distribute-lft-neg-in 48.5%

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

      8. metadata-eval 48.5%

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

      9. *-commutative 48.5%

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

   9. Simplified 48.5%

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

   if -1.55000000000000005e-117 < (*.f64 b c) < 4.1999999999999999e50

   1. Initial program 87.0%

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

   3. Simplified 89.6%

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

   5. Taylor expanded in j around inf 37.5%

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

      1. associate-*r* 37.5%

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

      2. *-commutative 37.5%

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

      3. metadata-eval 37.5%

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

      4. distribute-rgt-neg-in 37.5%

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

      5. *-commutative 37.5%

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

      6. distribute-rgt-neg-in 37.5%

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

      7. metadata-eval 37.5%

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

      8. *-commutative 37.5%

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

   7. Simplified 37.5%

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

4. Final simplification 46.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -3 \cdot 10^{+79}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -3.2 \cdot 10^{+27}:\\ \;\;\;\;t \cdot \left(-4 \cdot a\right)\\ \mathbf{elif}\;b \cdot c \leq -9.2 \cdot 10^{+26}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -2.4 \cdot 10^{-51}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq -1.55 \cdot 10^{-117}:\\ \;\;\;\;t \cdot \left(-4 \cdot a\right)\\ \mathbf{elif}\;b \cdot c \leq 4.2 \cdot 10^{+50}:\\ \;\;\;\;k \cdot \left(-27 \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 86.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := k \cdot \left(j \cdot 27\right)\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;-27 \cdot \left(k \cdot j\right)\\ \mathbf{elif}\;t\_1 \leq 10^{+125}:\\ \;\;\;\;\left(b \cdot c - t \cdot \left(a \cdot 4 - \left(y \cdot z\right) \cdot \left(x \cdot 18\right)\right)\right) - \left(x \cdot \left(i \cdot 4\right) + j \cdot \left(k \cdot 27\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(b + -4 \cdot \frac{t \cdot a}{c}\right) - 27 \cdot \left(k \cdot j\right)\\ \end{array} \end{array} \]

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 (* k (* j 27.0))))
   (if (<= t_1 (- INFINITY))
     (* -27.0 (* k j))
     (if (<= t_1 1e+125)
       (-
        (- (* b c) (* t (- (* a 4.0) (* (* y z) (* x 18.0)))))
        (+ (* x (* i 4.0)) (* j (* k 27.0))))
       (- (* c (+ b (* -4.0 (/ (* t a) c)))) (* 27.0 (* k j)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = k * (j * 27.0);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = -27.0 * (k * j);
	} else if (t_1 <= 1e+125) {
		tmp = ((b * c) - (t * ((a * 4.0) - ((y * z) * (x * 18.0))))) - ((x * (i * 4.0)) + (j * (k * 27.0)));
	} else {
		tmp = (c * (b + (-4.0 * ((t * a) / c)))) - (27.0 * (k * j));
	}
	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 t_1 = k * (j * 27.0);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = -27.0 * (k * j);
	} else if (t_1 <= 1e+125) {
		tmp = ((b * c) - (t * ((a * 4.0) - ((y * z) * (x * 18.0))))) - ((x * (i * 4.0)) + (j * (k * 27.0)));
	} else {
		tmp = (c * (b + (-4.0 * ((t * a) / c)))) - (27.0 * (k * j));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = k * (j * 27.0)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = -27.0 * (k * j)
	elif t_1 <= 1e+125:
		tmp = ((b * c) - (t * ((a * 4.0) - ((y * z) * (x * 18.0))))) - ((x * (i * 4.0)) + (j * (k * 27.0)))
	else:
		tmp = (c * (b + (-4.0 * ((t * a) / c)))) - (27.0 * (k * j))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(k * Float64(j * 27.0))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(-27.0 * Float64(k * j));
	elseif (t_1 <= 1e+125)
		tmp = Float64(Float64(Float64(b * c) - Float64(t * Float64(Float64(a * 4.0) - Float64(Float64(y * z) * Float64(x * 18.0))))) - Float64(Float64(x * Float64(i * 4.0)) + Float64(j * Float64(k * 27.0))));
	else
		tmp = Float64(Float64(c * Float64(b + Float64(-4.0 * Float64(Float64(t * a) / c)))) - Float64(27.0 * Float64(k * j)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = k * (j * 27.0);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = -27.0 * (k * j);
	elseif (t_1 <= 1e+125)
		tmp = ((b * c) - (t * ((a * 4.0) - ((y * z) * (x * 18.0))))) - ((x * (i * 4.0)) + (j * (k * 27.0)));
	else
		tmp = (c * (b + (-4.0 * ((t * a) / c)))) - (27.0 * (k * j));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(-27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+125], N[(N[(N[(b * c), $MachinePrecision] - N[(t * N[(N[(a * 4.0), $MachinePrecision] - N[(N[(y * z), $MachinePrecision] * N[(x * 18.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * N[(i * 4.0), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c * N[(b + N[(-4.0 * N[(N[(t * a), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -inf.0

   1. Initial program 45.5%

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

   3. Simplified 45.5%

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

   5. Taylor expanded in j around inf 90.9%

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

   if -inf.0 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 9.9999999999999992e124

   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 90.0%

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

   if 9.9999999999999992e124 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 73.2%

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

   3. Simplified 66.8%

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

   5. Taylor expanded in c around inf 62.6%

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

   6. Taylor expanded in x around 0 72.0%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \cdot \left(j \cdot 27\right) \leq -\infty:\\ \;\;\;\;-27 \cdot \left(k \cdot j\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 10^{+125}:\\ \;\;\;\;\left(b \cdot c - t \cdot \left(a \cdot 4 - \left(y \cdot z\right) \cdot \left(x \cdot 18\right)\right)\right) - \left(x \cdot \left(i \cdot 4\right) + j \cdot \left(k \cdot 27\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(b + -4 \cdot \frac{t \cdot a}{c}\right) - 27 \cdot \left(k \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 69.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(x \cdot i\right) \cdot 4\\ t_2 := b \cdot c - \left(t\_1 + 27 \cdot \left(k \cdot j\right)\right)\\ t_3 := t \cdot \left(-18 \cdot \left(z \cdot \left(x \cdot \left(-y\right)\right)\right) - a \cdot 4\right)\\ \mathbf{if}\;t \leq -7.5 \cdot 10^{+131}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{+78}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + a \cdot \left(t \cdot -4\right)\\ \mathbf{elif}\;t \leq -6.2 \cdot 10^{-14}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+51}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+118}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - t\_1\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{+180}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* x i) 4.0))
        (t_2 (- (* b c) (+ t_1 (* 27.0 (* k j)))))
        (t_3 (* t (- (* -18.0 (* z (* x (- y)))) (* a 4.0)))))
   (if (<= t -7.5e+131)
     t_3
     (if (<= t -3.5e+78)
       (+ (* j (* k -27.0)) (* a (* t -4.0)))
       (if (<= t -6.2e-14)
         t_3
         (if (<= t 9e+51)
           t_2
           (if (<= t 4e+118)
             (- (+ (* b c) (* -4.0 (* t a))) t_1)
             (if (<= t 3.3e+180) 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 * i) * 4.0;
	double t_2 = (b * c) - (t_1 + (27.0 * (k * j)));
	double t_3 = t * ((-18.0 * (z * (x * -y))) - (a * 4.0));
	double tmp;
	if (t <= -7.5e+131) {
		tmp = t_3;
	} else if (t <= -3.5e+78) {
		tmp = (j * (k * -27.0)) + (a * (t * -4.0));
	} else if (t <= -6.2e-14) {
		tmp = t_3;
	} else if (t <= 9e+51) {
		tmp = t_2;
	} else if (t <= 4e+118) {
		tmp = ((b * c) + (-4.0 * (t * a))) - t_1;
	} else if (t <= 3.3e+180) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (x * i) * 4.0d0
    t_2 = (b * c) - (t_1 + (27.0d0 * (k * j)))
    t_3 = t * (((-18.0d0) * (z * (x * -y))) - (a * 4.0d0))
    if (t <= (-7.5d+131)) then
        tmp = t_3
    else if (t <= (-3.5d+78)) then
        tmp = (j * (k * (-27.0d0))) + (a * (t * (-4.0d0)))
    else if (t <= (-6.2d-14)) then
        tmp = t_3
    else if (t <= 9d+51) then
        tmp = t_2
    else if (t <= 4d+118) then
        tmp = ((b * c) + ((-4.0d0) * (t * a))) - t_1
    else if (t <= 3.3d+180) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (x * i) * 4.0;
	double t_2 = (b * c) - (t_1 + (27.0 * (k * j)));
	double t_3 = t * ((-18.0 * (z * (x * -y))) - (a * 4.0));
	double tmp;
	if (t <= -7.5e+131) {
		tmp = t_3;
	} else if (t <= -3.5e+78) {
		tmp = (j * (k * -27.0)) + (a * (t * -4.0));
	} else if (t <= -6.2e-14) {
		tmp = t_3;
	} else if (t <= 9e+51) {
		tmp = t_2;
	} else if (t <= 4e+118) {
		tmp = ((b * c) + (-4.0 * (t * a))) - t_1;
	} else if (t <= 3.3e+180) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (x * i) * 4.0
	t_2 = (b * c) - (t_1 + (27.0 * (k * j)))
	t_3 = t * ((-18.0 * (z * (x * -y))) - (a * 4.0))
	tmp = 0
	if t <= -7.5e+131:
		tmp = t_3
	elif t <= -3.5e+78:
		tmp = (j * (k * -27.0)) + (a * (t * -4.0))
	elif t <= -6.2e-14:
		tmp = t_3
	elif t <= 9e+51:
		tmp = t_2
	elif t <= 4e+118:
		tmp = ((b * c) + (-4.0 * (t * a))) - t_1
	elif t <= 3.3e+180:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(x * i) * 4.0)
	t_2 = Float64(Float64(b * c) - Float64(t_1 + Float64(27.0 * Float64(k * j))))
	t_3 = Float64(t * Float64(Float64(-18.0 * Float64(z * Float64(x * Float64(-y)))) - Float64(a * 4.0)))
	tmp = 0.0
	if (t <= -7.5e+131)
		tmp = t_3;
	elseif (t <= -3.5e+78)
		tmp = Float64(Float64(j * Float64(k * -27.0)) + Float64(a * Float64(t * -4.0)));
	elseif (t <= -6.2e-14)
		tmp = t_3;
	elseif (t <= 9e+51)
		tmp = t_2;
	elseif (t <= 4e+118)
		tmp = Float64(Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a))) - t_1);
	elseif (t <= 3.3e+180)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (x * i) * 4.0;
	t_2 = (b * c) - (t_1 + (27.0 * (k * j)));
	t_3 = t * ((-18.0 * (z * (x * -y))) - (a * 4.0));
	tmp = 0.0;
	if (t <= -7.5e+131)
		tmp = t_3;
	elseif (t <= -3.5e+78)
		tmp = (j * (k * -27.0)) + (a * (t * -4.0));
	elseif (t <= -6.2e-14)
		tmp = t_3;
	elseif (t <= 9e+51)
		tmp = t_2;
	elseif (t <= 4e+118)
		tmp = ((b * c) + (-4.0 * (t * a))) - t_1;
	elseif (t <= 3.3e+180)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(x * i), $MachinePrecision] * 4.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] - N[(t$95$1 + N[(27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(N[(-18.0 * N[(z * N[(x * (-y)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.5e+131], t$95$3, If[LessEqual[t, -3.5e+78], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(a * N[(t * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -6.2e-14], t$95$3, If[LessEqual[t, 9e+51], t$95$2, If[LessEqual[t, 4e+118], N[(N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[t, 3.3e+180], t$95$2, t$95$3]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -7.4999999999999995e131 or -3.5000000000000001e78 < t < -6.20000000000000009e-14 or 3.29999999999999989e180 < t

   1. Initial program 75.6%

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

      1. pow1 75.6%

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

      2. associate-*l* 70.3%

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

      3. *-commutative 70.3%

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

   4. Applied egg-rr 70.3%

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

      1. unpow1 70.3%

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

      2. associate-*l* 71.7%

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

      3. *-commutative 71.7%

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

   6. Simplified 71.7%

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

   7. Taylor expanded in t around -inf 77.5%

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

      1. mul-1-neg 77.5%

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

      2. cancel-sign-sub-inv 77.5%

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

      3. *-commutative 77.5%

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

      4. associate-*r* 78.7%

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

      5. metadata-eval 78.7%

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

   9. Simplified 78.7%

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

   if -7.4999999999999995e131 < t < -3.5000000000000001e78

   1. Initial program 71.4%

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

   3. Simplified 71.2%

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

   5. Taylor expanded in a around inf 85.6%

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

      1. metadata-eval 85.6%

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

      2. distribute-lft-neg-in 85.6%

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

      3. *-commutative 85.6%

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

      4. associate-*l* 85.6%

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

      5. distribute-lft-neg-in 85.6%

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

      6. distribute-lft-neg-in 85.6%

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

      7. metadata-eval 85.6%

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

   7. Simplified 85.6%

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

   if -6.20000000000000009e-14 < t < 8.9999999999999999e51 or 3.99999999999999987e118 < t < 3.29999999999999989e180

   1. Initial program 85.1%

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

   3. Simplified 85.1%

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

   5. Taylor expanded in t around 0 74.3%

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

   if 8.9999999999999999e51 < t < 3.99999999999999987e118

   1. Initial program 90.4%

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

   3. Simplified 95.0%

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

   5. Taylor expanded in j around 0 81.2%

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

   6. Taylor expanded in x around 0 76.4%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{+131}:\\ \;\;\;\;t \cdot \left(-18 \cdot \left(z \cdot \left(x \cdot \left(-y\right)\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{+78}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + a \cdot \left(t \cdot -4\right)\\ \mathbf{elif}\;t \leq -6.2 \cdot 10^{-14}:\\ \;\;\;\;t \cdot \left(-18 \cdot \left(z \cdot \left(x \cdot \left(-y\right)\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+51}:\\ \;\;\;\;b \cdot c - \left(\left(x \cdot i\right) \cdot 4 + 27 \cdot \left(k \cdot j\right)\right)\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+118}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - \left(x \cdot i\right) \cdot 4\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{+180}:\\ \;\;\;\;b \cdot c - \left(\left(x \cdot i\right) \cdot 4 + 27 \cdot \left(k \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-18 \cdot \left(z \cdot \left(x \cdot \left(-y\right)\right)\right) - a \cdot 4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 56.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ t_2 := j \cdot \left(k \cdot -27\right)\\ t_3 := t\_2 + a \cdot \left(t \cdot -4\right)\\ \mathbf{if}\;t \leq -3.1 \cdot 10^{+132}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{+78}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq -1.55 \cdot 10^{-58}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-33}:\\ \;\;\;\;t\_2 + b \cdot c\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+153}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{+180}:\\ \;\;\;\;b \cdot c - \left(x \cdot i\right) \cdot 4\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 (* a (* t -4.0)))))
   (if (<= t -3.1e+132)
     t_1
     (if (<= t -1.1e+78)
       t_3
       (if (<= t -1.55e-58)
         t_1
         (if (<= t 2.2e-33)
           (+ t_2 (* b c))
           (if (<= t 3e+153)
             t_3
             (if (<= t 3.3e+180) (- (* b c) (* (* x i) 4.0)) t_1))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	double t_2 = j * (k * -27.0);
	double t_3 = t_2 + (a * (t * -4.0));
	double tmp;
	if (t <= -3.1e+132) {
		tmp = t_1;
	} else if (t <= -1.1e+78) {
		tmp = t_3;
	} else if (t <= -1.55e-58) {
		tmp = t_1;
	} else if (t <= 2.2e-33) {
		tmp = t_2 + (b * c);
	} else if (t <= 3e+153) {
		tmp = t_3;
	} else if (t <= 3.3e+180) {
		tmp = (b * c) - ((x * i) * 4.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: 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 + (a * (t * (-4.0d0)))
    if (t <= (-3.1d+132)) then
        tmp = t_1
    else if (t <= (-1.1d+78)) then
        tmp = t_3
    else if (t <= (-1.55d-58)) then
        tmp = t_1
    else if (t <= 2.2d-33) then
        tmp = t_2 + (b * c)
    else if (t <= 3d+153) then
        tmp = t_3
    else if (t <= 3.3d+180) then
        tmp = (b * c) - ((x * i) * 4.0d0)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	double t_2 = j * (k * -27.0);
	double t_3 = t_2 + (a * (t * -4.0));
	double tmp;
	if (t <= -3.1e+132) {
		tmp = t_1;
	} else if (t <= -1.1e+78) {
		tmp = t_3;
	} else if (t <= -1.55e-58) {
		tmp = t_1;
	} else if (t <= 2.2e-33) {
		tmp = t_2 + (b * c);
	} else if (t <= 3e+153) {
		tmp = t_3;
	} else if (t <= 3.3e+180) {
		tmp = (b * c) - ((x * i) * 4.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = t * ((18.0 * (x * (y * z))) - (a * 4.0))
	t_2 = j * (k * -27.0)
	t_3 = t_2 + (a * (t * -4.0))
	tmp = 0
	if t <= -3.1e+132:
		tmp = t_1
	elif t <= -1.1e+78:
		tmp = t_3
	elif t <= -1.55e-58:
		tmp = t_1
	elif t <= 2.2e-33:
		tmp = t_2 + (b * c)
	elif t <= 3e+153:
		tmp = t_3
	elif t <= 3.3e+180:
		tmp = (b * c) - ((x * i) * 4.0)
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(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(a * Float64(t * -4.0)))
	tmp = 0.0
	if (t <= -3.1e+132)
		tmp = t_1;
	elseif (t <= -1.1e+78)
		tmp = t_3;
	elseif (t <= -1.55e-58)
		tmp = t_1;
	elseif (t <= 2.2e-33)
		tmp = Float64(t_2 + Float64(b * c));
	elseif (t <= 3e+153)
		tmp = t_3;
	elseif (t <= 3.3e+180)
		tmp = Float64(Float64(b * c) - Float64(Float64(x * i) * 4.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	t_2 = j * (k * -27.0);
	t_3 = t_2 + (a * (t * -4.0));
	tmp = 0.0;
	if (t <= -3.1e+132)
		tmp = t_1;
	elseif (t <= -1.1e+78)
		tmp = t_3;
	elseif (t <= -1.55e-58)
		tmp = t_1;
	elseif (t <= 2.2e-33)
		tmp = t_2 + (b * c);
	elseif (t <= 3e+153)
		tmp = t_3;
	elseif (t <= 3.3e+180)
		tmp = (b * c) - ((x * i) * 4.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(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[(a * N[(t * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.1e+132], t$95$1, If[LessEqual[t, -1.1e+78], t$95$3, If[LessEqual[t, -1.55e-58], t$95$1, If[LessEqual[t, 2.2e-33], N[(t$95$2 + N[(b * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3e+153], t$95$3, If[LessEqual[t, 3.3e+180], N[(N[(b * c), $MachinePrecision] - N[(N[(x * i), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3.0999999999999998e132 or -1.10000000000000007e78 < t < -1.55e-58 or 3.29999999999999989e180 < t

   1. Initial program 77.2%

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

   3. Simplified 80.7%

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

   5. Taylor expanded in t around inf 73.3%

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

   if -3.0999999999999998e132 < t < -1.10000000000000007e78 or 2.20000000000000005e-33 < t < 3.00000000000000019e153

   1. Initial program 87.9%

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

   3. Simplified 91.3%

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

   5. Taylor expanded in a around inf 58.7%

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

      1. metadata-eval 58.7%

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

      2. distribute-lft-neg-in 58.7%

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

      3. *-commutative 58.7%

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

      4. associate-*l* 58.7%

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

      5. distribute-lft-neg-in 58.7%

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

      6. distribute-lft-neg-in 58.7%

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

      7. metadata-eval 58.7%

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

   7. Simplified 58.7%

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

   if -1.55e-58 < t < 2.20000000000000005e-33

   1. Initial program 83.6%

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

   3. Simplified 84.7%

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

   5. Taylor expanded in b around inf 64.8%

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

   if 3.00000000000000019e153 < t < 3.29999999999999989e180

   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 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. Taylor expanded in j around 0 99.7%

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

   6. Taylor expanded in t around 0 76.8%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{+132}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{+78}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + a \cdot \left(t \cdot -4\right)\\ \mathbf{elif}\;t \leq -1.55 \cdot 10^{-58}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-33}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+153}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + a \cdot \left(t \cdot -4\right)\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{+180}:\\ \;\;\;\;b \cdot c - \left(x \cdot i\right) \cdot 4\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 78.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := t \cdot \left(y \cdot z\right)\\ t_2 := x \cdot \left(18 \cdot t\_1 - i \cdot 4\right)\\ \mathbf{if}\;x \leq -2.6 \cdot 10^{+243}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -5.5 \cdot 10^{+171}:\\ \;\;\;\;b \cdot c - \left(\left(x \cdot i\right) \cdot 4 + 27 \cdot \left(k \cdot j\right)\right)\\ \mathbf{elif}\;x \leq -1.05 \cdot 10^{+119}:\\ \;\;\;\;x \cdot \left(i \cdot \left(18 \cdot \frac{t\_1}{i} - 4\right)\right)\\ \mathbf{elif}\;x \leq 5.1 \cdot 10^{+233}:\\ \;\;\;\;\left(\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - i \cdot \left(x \cdot 4\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* t (* y z))) (t_2 (* x (- (* 18.0 t_1) (* i 4.0)))))
   (if (<= x -2.6e+243)
     t_2
     (if (<= x -5.5e+171)
       (- (* b c) (+ (* (* x i) 4.0) (* 27.0 (* k j))))
       (if (<= x -1.05e+119)
         (* x (* i (- (* 18.0 (/ t_1 i)) 4.0)))
         (if (<= x 5.1e+233)
           (- (- (- (* b c) (* 4.0 (* t a))) (* i (* x 4.0))) (* k (* j 27.0)))
           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 = t * (y * z);
	double t_2 = x * ((18.0 * t_1) - (i * 4.0));
	double tmp;
	if (x <= -2.6e+243) {
		tmp = t_2;
	} else if (x <= -5.5e+171) {
		tmp = (b * c) - (((x * i) * 4.0) + (27.0 * (k * j)));
	} else if (x <= -1.05e+119) {
		tmp = x * (i * ((18.0 * (t_1 / i)) - 4.0));
	} else if (x <= 5.1e+233) {
		tmp = (((b * c) - (4.0 * (t * a))) - (i * (x * 4.0))) - (k * (j * 27.0));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * (y * z)
    t_2 = x * ((18.0d0 * t_1) - (i * 4.0d0))
    if (x <= (-2.6d+243)) then
        tmp = t_2
    else if (x <= (-5.5d+171)) then
        tmp = (b * c) - (((x * i) * 4.0d0) + (27.0d0 * (k * j)))
    else if (x <= (-1.05d+119)) then
        tmp = x * (i * ((18.0d0 * (t_1 / i)) - 4.0d0))
    else if (x <= 5.1d+233) then
        tmp = (((b * c) - (4.0d0 * (t * a))) - (i * (x * 4.0d0))) - (k * (j * 27.0d0))
    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 = t * (y * z);
	double t_2 = x * ((18.0 * t_1) - (i * 4.0));
	double tmp;
	if (x <= -2.6e+243) {
		tmp = t_2;
	} else if (x <= -5.5e+171) {
		tmp = (b * c) - (((x * i) * 4.0) + (27.0 * (k * j)));
	} else if (x <= -1.05e+119) {
		tmp = x * (i * ((18.0 * (t_1 / i)) - 4.0));
	} else if (x <= 5.1e+233) {
		tmp = (((b * c) - (4.0 * (t * a))) - (i * (x * 4.0))) - (k * (j * 27.0));
	} 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 = t * (y * z)
	t_2 = x * ((18.0 * t_1) - (i * 4.0))
	tmp = 0
	if x <= -2.6e+243:
		tmp = t_2
	elif x <= -5.5e+171:
		tmp = (b * c) - (((x * i) * 4.0) + (27.0 * (k * j)))
	elif x <= -1.05e+119:
		tmp = x * (i * ((18.0 * (t_1 / i)) - 4.0))
	elif x <= 5.1e+233:
		tmp = (((b * c) - (4.0 * (t * a))) - (i * (x * 4.0))) - (k * (j * 27.0))
	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(t * Float64(y * z))
	t_2 = Float64(x * Float64(Float64(18.0 * t_1) - Float64(i * 4.0)))
	tmp = 0.0
	if (x <= -2.6e+243)
		tmp = t_2;
	elseif (x <= -5.5e+171)
		tmp = Float64(Float64(b * c) - Float64(Float64(Float64(x * i) * 4.0) + Float64(27.0 * Float64(k * j))));
	elseif (x <= -1.05e+119)
		tmp = Float64(x * Float64(i * Float64(Float64(18.0 * Float64(t_1 / i)) - 4.0)));
	elseif (x <= 5.1e+233)
		tmp = Float64(Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(t * a))) - Float64(i * Float64(x * 4.0))) - Float64(k * Float64(j * 27.0)));
	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 = t * (y * z);
	t_2 = x * ((18.0 * t_1) - (i * 4.0));
	tmp = 0.0;
	if (x <= -2.6e+243)
		tmp = t_2;
	elseif (x <= -5.5e+171)
		tmp = (b * c) - (((x * i) * 4.0) + (27.0 * (k * j)));
	elseif (x <= -1.05e+119)
		tmp = x * (i * ((18.0 * (t_1 / i)) - 4.0));
	elseif (x <= 5.1e+233)
		tmp = (((b * c) - (4.0 * (t * a))) - (i * (x * 4.0))) - (k * (j * 27.0));
	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[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(18.0 * t$95$1), $MachinePrecision] - N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.6e+243], t$95$2, If[LessEqual[x, -5.5e+171], N[(N[(b * c), $MachinePrecision] - N[(N[(N[(x * i), $MachinePrecision] * 4.0), $MachinePrecision] + N[(27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.05e+119], N[(x * N[(i * N[(N[(18.0 * N[(t$95$1 / i), $MachinePrecision]), $MachinePrecision] - 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.1e+233], N[(N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * N[(x * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.59999999999999997e243 or 5.10000000000000011e233 < x

   1. Initial program 55.8%

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

   3. Simplified 68.7%

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

   5. Taylor expanded in x around inf 84.2%

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

   if -2.59999999999999997e243 < x < -5.5000000000000003e171

   1. Initial program 56.2%

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

   3. Simplified 62.4%

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

   5. Taylor expanded in t around 0 81.7%

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

   if -5.5000000000000003e171 < x < -1.04999999999999991e119

   1. Initial program 68.9%

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

   3. Simplified 69.0%

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

   5. Taylor expanded in x around inf 75.7%

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

   6. Taylor expanded in i around inf 75.9%

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

   if -1.04999999999999991e119 < x < 5.10000000000000011e233

   1. Initial program 91.3%

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

   3. Taylor expanded in x around 0 85.5%

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

4. Final simplification 84.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{+243}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - i \cdot 4\right)\\ \mathbf{elif}\;x \leq -5.5 \cdot 10^{+171}:\\ \;\;\;\;b \cdot c - \left(\left(x \cdot i\right) \cdot 4 + 27 \cdot \left(k \cdot j\right)\right)\\ \mathbf{elif}\;x \leq -1.05 \cdot 10^{+119}:\\ \;\;\;\;x \cdot \left(i \cdot \left(18 \cdot \frac{t \cdot \left(y \cdot z\right)}{i} - 4\right)\right)\\ \mathbf{elif}\;x \leq 5.1 \cdot 10^{+233}:\\ \;\;\;\;\left(\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - i \cdot \left(x \cdot 4\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - i \cdot 4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 81.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := k \cdot \left(j \cdot 27\right)\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+83}:\\ \;\;\;\;\left(\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - i \cdot \left(x \cdot 4\right)\right) - t\_1\\ \mathbf{elif}\;t\_1 \leq 10^{+125}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\right) - \left(x \cdot i\right) \cdot 4\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(b + -4 \cdot \frac{t \cdot a}{c}\right) - 27 \cdot \left(k \cdot j\right)\\ \end{array} \end{array} \]

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 (* k (* j 27.0))))
   (if (<= t_1 -2e+83)
     (- (- (- (* b c) (* 4.0 (* t a))) (* i (* x 4.0))) t_1)
     (if (<= t_1 1e+125)
       (-
        (+ (* b c) (* t (- (* 18.0 (* x (* y z))) (* a 4.0))))
        (* (* x i) 4.0))
       (- (* c (+ b (* -4.0 (/ (* t a) c)))) (* 27.0 (* k j)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = k * (j * 27.0);
	double tmp;
	if (t_1 <= -2e+83) {
		tmp = (((b * c) - (4.0 * (t * a))) - (i * (x * 4.0))) - t_1;
	} else if (t_1 <= 1e+125) {
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - ((x * i) * 4.0);
	} else {
		tmp = (c * (b + (-4.0 * ((t * a) / c)))) - (27.0 * (k * j));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = k * (j * 27.0d0)
    if (t_1 <= (-2d+83)) then
        tmp = (((b * c) - (4.0d0 * (t * a))) - (i * (x * 4.0d0))) - t_1
    else if (t_1 <= 1d+125) then
        tmp = ((b * c) + (t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0)))) - ((x * i) * 4.0d0)
    else
        tmp = (c * (b + ((-4.0d0) * ((t * a) / c)))) - (27.0d0 * (k * j))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = k * (j * 27.0);
	double tmp;
	if (t_1 <= -2e+83) {
		tmp = (((b * c) - (4.0 * (t * a))) - (i * (x * 4.0))) - t_1;
	} else if (t_1 <= 1e+125) {
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - ((x * i) * 4.0);
	} else {
		tmp = (c * (b + (-4.0 * ((t * a) / c)))) - (27.0 * (k * j));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = k * (j * 27.0)
	tmp = 0
	if t_1 <= -2e+83:
		tmp = (((b * c) - (4.0 * (t * a))) - (i * (x * 4.0))) - t_1
	elif t_1 <= 1e+125:
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - ((x * i) * 4.0)
	else:
		tmp = (c * (b + (-4.0 * ((t * a) / c)))) - (27.0 * (k * j))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(k * Float64(j * 27.0))
	tmp = 0.0
	if (t_1 <= -2e+83)
		tmp = Float64(Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(t * a))) - Float64(i * Float64(x * 4.0))) - t_1);
	elseif (t_1 <= 1e+125)
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)))) - Float64(Float64(x * i) * 4.0));
	else
		tmp = Float64(Float64(c * Float64(b + Float64(-4.0 * Float64(Float64(t * a) / c)))) - Float64(27.0 * Float64(k * j)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = k * (j * 27.0);
	tmp = 0.0;
	if (t_1 <= -2e+83)
		tmp = (((b * c) - (4.0 * (t * a))) - (i * (x * 4.0))) - t_1;
	elseif (t_1 <= 1e+125)
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - ((x * i) * 4.0);
	else
		tmp = (c * (b + (-4.0 * ((t * a) / c)))) - (27.0 * (k * j));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+83], N[(N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * N[(x * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[t$95$1, 1e+125], N[(N[(N[(b * c), $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[(x * i), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision], N[(N[(c * N[(b + N[(-4.0 * N[(N[(t * a), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -2.00000000000000006e83

   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 x around 0 82.7%

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

   if -2.00000000000000006e83 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 9.9999999999999992e124

   1. Initial program 85.0%

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

   3. Simplified 88.0%

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

   5. Taylor expanded in j around 0 86.0%

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

   if 9.9999999999999992e124 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 73.2%

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

   3. Simplified 66.8%

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

   5. Taylor expanded in c around inf 62.6%

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

   6. Taylor expanded in x around 0 72.0%

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

4. Final simplification 82.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \cdot \left(j \cdot 27\right) \leq -2 \cdot 10^{+83}:\\ \;\;\;\;\left(\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - i \cdot \left(x \cdot 4\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 10^{+125}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\right) - \left(x \cdot i\right) \cdot 4\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(b + -4 \cdot \frac{t \cdot a}{c}\right) - 27 \cdot \left(k \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 71.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := 27 \cdot \left(k \cdot j\right)\\ t_2 := b \cdot c + -4 \cdot \left(t \cdot a\right)\\ t_3 := t \cdot \left(y \cdot z\right)\\ t_4 := \left(x \cdot i\right) \cdot 4\\ \mathbf{if}\;x \leq -1.6 \cdot 10^{+243}:\\ \;\;\;\;x \cdot \left(18 \cdot t\_3 - i \cdot 4\right)\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{+172}:\\ \;\;\;\;b \cdot c - \left(t\_4 + t\_1\right)\\ \mathbf{elif}\;x \leq -1.08 \cdot 10^{+120}:\\ \;\;\;\;x \cdot \left(i \cdot \left(18 \cdot \frac{t\_3}{i} - 4\right)\right)\\ \mathbf{elif}\;x \leq 9 \cdot 10^{+56}:\\ \;\;\;\;t\_2 - t\_1\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{+198}:\\ \;\;\;\;t\_2 - t\_4\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot \left(-4 \cdot \frac{i}{z} + 18 \cdot \left(y \cdot t\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 (* k j)))
        (t_2 (+ (* b c) (* -4.0 (* t a))))
        (t_3 (* t (* y z)))
        (t_4 (* (* x i) 4.0)))
   (if (<= x -1.6e+243)
     (* x (- (* 18.0 t_3) (* i 4.0)))
     (if (<= x -1.3e+172)
       (- (* b c) (+ t_4 t_1))
       (if (<= x -1.08e+120)
         (* x (* i (- (* 18.0 (/ t_3 i)) 4.0)))
         (if (<= x 9e+56)
           (- t_2 t_1)
           (if (<= x 4.5e+198)
             (- t_2 t_4)
             (* x (* z (+ (* -4.0 (/ i z)) (* 18.0 (* y t))))))))))))

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 * (k * j);
	double t_2 = (b * c) + (-4.0 * (t * a));
	double t_3 = t * (y * z);
	double t_4 = (x * i) * 4.0;
	double tmp;
	if (x <= -1.6e+243) {
		tmp = x * ((18.0 * t_3) - (i * 4.0));
	} else if (x <= -1.3e+172) {
		tmp = (b * c) - (t_4 + t_1);
	} else if (x <= -1.08e+120) {
		tmp = x * (i * ((18.0 * (t_3 / i)) - 4.0));
	} else if (x <= 9e+56) {
		tmp = t_2 - t_1;
	} else if (x <= 4.5e+198) {
		tmp = t_2 - t_4;
	} else {
		tmp = x * (z * ((-4.0 * (i / z)) + (18.0 * (y * t))));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 = 27.0d0 * (k * j)
    t_2 = (b * c) + ((-4.0d0) * (t * a))
    t_3 = t * (y * z)
    t_4 = (x * i) * 4.0d0
    if (x <= (-1.6d+243)) then
        tmp = x * ((18.0d0 * t_3) - (i * 4.0d0))
    else if (x <= (-1.3d+172)) then
        tmp = (b * c) - (t_4 + t_1)
    else if (x <= (-1.08d+120)) then
        tmp = x * (i * ((18.0d0 * (t_3 / i)) - 4.0d0))
    else if (x <= 9d+56) then
        tmp = t_2 - t_1
    else if (x <= 4.5d+198) then
        tmp = t_2 - t_4
    else
        tmp = x * (z * (((-4.0d0) * (i / z)) + (18.0d0 * (y * t))))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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 * (k * j);
	double t_2 = (b * c) + (-4.0 * (t * a));
	double t_3 = t * (y * z);
	double t_4 = (x * i) * 4.0;
	double tmp;
	if (x <= -1.6e+243) {
		tmp = x * ((18.0 * t_3) - (i * 4.0));
	} else if (x <= -1.3e+172) {
		tmp = (b * c) - (t_4 + t_1);
	} else if (x <= -1.08e+120) {
		tmp = x * (i * ((18.0 * (t_3 / i)) - 4.0));
	} else if (x <= 9e+56) {
		tmp = t_2 - t_1;
	} else if (x <= 4.5e+198) {
		tmp = t_2 - t_4;
	} else {
		tmp = x * (z * ((-4.0 * (i / z)) + (18.0 * (y * t))));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[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 * (k * j)
	t_2 = (b * c) + (-4.0 * (t * a))
	t_3 = t * (y * z)
	t_4 = (x * i) * 4.0
	tmp = 0
	if x <= -1.6e+243:
		tmp = x * ((18.0 * t_3) - (i * 4.0))
	elif x <= -1.3e+172:
		tmp = (b * c) - (t_4 + t_1)
	elif x <= -1.08e+120:
		tmp = x * (i * ((18.0 * (t_3 / i)) - 4.0))
	elif x <= 9e+56:
		tmp = t_2 - t_1
	elif x <= 4.5e+198:
		tmp = t_2 - t_4
	else:
		tmp = x * (z * ((-4.0 * (i / z)) + (18.0 * (y * t))))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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(k * j))
	t_2 = Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a)))
	t_3 = Float64(t * Float64(y * z))
	t_4 = Float64(Float64(x * i) * 4.0)
	tmp = 0.0
	if (x <= -1.6e+243)
		tmp = Float64(x * Float64(Float64(18.0 * t_3) - Float64(i * 4.0)));
	elseif (x <= -1.3e+172)
		tmp = Float64(Float64(b * c) - Float64(t_4 + t_1));
	elseif (x <= -1.08e+120)
		tmp = Float64(x * Float64(i * Float64(Float64(18.0 * Float64(t_3 / i)) - 4.0)));
	elseif (x <= 9e+56)
		tmp = Float64(t_2 - t_1);
	elseif (x <= 4.5e+198)
		tmp = Float64(t_2 - t_4);
	else
		tmp = Float64(x * Float64(z * Float64(Float64(-4.0 * Float64(i / z)) + Float64(18.0 * Float64(y * t)))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
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 * (k * j);
	t_2 = (b * c) + (-4.0 * (t * a));
	t_3 = t * (y * z);
	t_4 = (x * i) * 4.0;
	tmp = 0.0;
	if (x <= -1.6e+243)
		tmp = x * ((18.0 * t_3) - (i * 4.0));
	elseif (x <= -1.3e+172)
		tmp = (b * c) - (t_4 + t_1);
	elseif (x <= -1.08e+120)
		tmp = x * (i * ((18.0 * (t_3 / i)) - 4.0));
	elseif (x <= 9e+56)
		tmp = t_2 - t_1;
	elseif (x <= 4.5e+198)
		tmp = t_2 - t_4;
	else
		tmp = x * (z * ((-4.0 * (i / z)) + (18.0 * (y * t))));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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[(k * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x * i), $MachinePrecision] * 4.0), $MachinePrecision]}, If[LessEqual[x, -1.6e+243], N[(x * N[(N[(18.0 * t$95$3), $MachinePrecision] - N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.3e+172], N[(N[(b * c), $MachinePrecision] - N[(t$95$4 + t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.08e+120], N[(x * N[(i * N[(N[(18.0 * N[(t$95$3 / i), $MachinePrecision]), $MachinePrecision] - 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9e+56], N[(t$95$2 - t$95$1), $MachinePrecision], If[LessEqual[x, 4.5e+198], N[(t$95$2 - t$95$4), $MachinePrecision], N[(x * N[(z * N[(N[(-4.0 * N[(i / z), $MachinePrecision]), $MachinePrecision] + N[(18.0 * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -1.60000000000000008e243

   1. Initial program 64.8%

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

   3. Simplified 71.9%

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

   5. Taylor expanded in x around inf 85.6%

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

   if -1.60000000000000008e243 < x < -1.3e172

   1. Initial program 56.2%

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

   3. Simplified 62.4%

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

   5. Taylor expanded in t around 0 81.7%

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

   if -1.3e172 < x < -1.0799999999999999e120

   1. Initial program 68.9%

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

   3. Simplified 69.0%

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

   5. Taylor expanded in x around inf 75.7%

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

   6. Taylor expanded in i around inf 75.9%

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

   if -1.0799999999999999e120 < x < 9.0000000000000006e56

   1. Initial program 94.6%

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

   3. Simplified 92.8%

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

   5. Taylor expanded in x around 0 80.9%

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

   if 9.0000000000000006e56 < x < 4.50000000000000001e198

   1. Initial program 79.3%

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

   3. Simplified 79.3%

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

   5. Taylor expanded in j around 0 83.6%

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

   6. Taylor expanded in x around 0 79.5%

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

   if 4.50000000000000001e198 < x

   1. Initial program 54.9%

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

   3. Simplified 69.7%

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

   5. Taylor expanded in x around inf 78.8%

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

   6. Taylor expanded in z around inf 78.9%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{+243}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - i \cdot 4\right)\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{+172}:\\ \;\;\;\;b \cdot c - \left(\left(x \cdot i\right) \cdot 4 + 27 \cdot \left(k \cdot j\right)\right)\\ \mathbf{elif}\;x \leq -1.08 \cdot 10^{+120}:\\ \;\;\;\;x \cdot \left(i \cdot \left(18 \cdot \frac{t \cdot \left(y \cdot z\right)}{i} - 4\right)\right)\\ \mathbf{elif}\;x \leq 9 \cdot 10^{+56}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - 27 \cdot \left(k \cdot j\right)\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{+198}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - \left(x \cdot i\right) \cdot 4\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot \left(-4 \cdot \frac{i}{z} + 18 \cdot \left(y \cdot t\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 55.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;x \leq -9.2 \cdot 10^{+115}:\\ \;\;\;\;x \cdot \left(i \cdot \left(18 \cdot \frac{t \cdot \left(y \cdot z\right)}{i} - 4\right)\right)\\ \mathbf{elif}\;x \leq -1.12 \cdot 10^{-145}:\\ \;\;\;\;t\_1 + a \cdot \left(t \cdot -4\right)\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{-284}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+56}:\\ \;\;\;\;t\_1 + b \cdot c\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{+198}:\\ \;\;\;\;b \cdot c - \left(x \cdot i\right) \cdot 4\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot \left(-4 \cdot \frac{i}{z} + 18 \cdot \left(y \cdot t\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 -9.2e+115)
     (* x (* i (- (* 18.0 (/ (* t (* y z)) i)) 4.0)))
     (if (<= x -1.12e-145)
       (+ t_1 (* a (* t -4.0)))
       (if (<= x -3.5e-284)
         (+ (* b c) (* -4.0 (* t a)))
         (if (<= x 3.2e+56)
           (+ t_1 (* b c))
           (if (<= x 4.1e+198)
             (- (* b c) (* (* x i) 4.0))
             (* x (* z (+ (* -4.0 (/ i z)) (* 18.0 (* y t))))))))))))

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 <= -9.2e+115) {
		tmp = x * (i * ((18.0 * ((t * (y * z)) / i)) - 4.0));
	} else if (x <= -1.12e-145) {
		tmp = t_1 + (a * (t * -4.0));
	} else if (x <= -3.5e-284) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else if (x <= 3.2e+56) {
		tmp = t_1 + (b * c);
	} else if (x <= 4.1e+198) {
		tmp = (b * c) - ((x * i) * 4.0);
	} else {
		tmp = x * (z * ((-4.0 * (i / z)) + (18.0 * (y * t))));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 <= (-9.2d+115)) then
        tmp = x * (i * ((18.0d0 * ((t * (y * z)) / i)) - 4.0d0))
    else if (x <= (-1.12d-145)) then
        tmp = t_1 + (a * (t * (-4.0d0)))
    else if (x <= (-3.5d-284)) then
        tmp = (b * c) + ((-4.0d0) * (t * a))
    else if (x <= 3.2d+56) then
        tmp = t_1 + (b * c)
    else if (x <= 4.1d+198) then
        tmp = (b * c) - ((x * i) * 4.0d0)
    else
        tmp = x * (z * (((-4.0d0) * (i / z)) + (18.0d0 * (y * t))))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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 <= -9.2e+115) {
		tmp = x * (i * ((18.0 * ((t * (y * z)) / i)) - 4.0));
	} else if (x <= -1.12e-145) {
		tmp = t_1 + (a * (t * -4.0));
	} else if (x <= -3.5e-284) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else if (x <= 3.2e+56) {
		tmp = t_1 + (b * c);
	} else if (x <= 4.1e+198) {
		tmp = (b * c) - ((x * i) * 4.0);
	} else {
		tmp = x * (z * ((-4.0 * (i / z)) + (18.0 * (y * t))));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[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 <= -9.2e+115:
		tmp = x * (i * ((18.0 * ((t * (y * z)) / i)) - 4.0))
	elif x <= -1.12e-145:
		tmp = t_1 + (a * (t * -4.0))
	elif x <= -3.5e-284:
		tmp = (b * c) + (-4.0 * (t * a))
	elif x <= 3.2e+56:
		tmp = t_1 + (b * c)
	elif x <= 4.1e+198:
		tmp = (b * c) - ((x * i) * 4.0)
	else:
		tmp = x * (z * ((-4.0 * (i / z)) + (18.0 * (y * t))))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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 <= -9.2e+115)
		tmp = Float64(x * Float64(i * Float64(Float64(18.0 * Float64(Float64(t * Float64(y * z)) / i)) - 4.0)));
	elseif (x <= -1.12e-145)
		tmp = Float64(t_1 + Float64(a * Float64(t * -4.0)));
	elseif (x <= -3.5e-284)
		tmp = Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a)));
	elseif (x <= 3.2e+56)
		tmp = Float64(t_1 + Float64(b * c));
	elseif (x <= 4.1e+198)
		tmp = Float64(Float64(b * c) - Float64(Float64(x * i) * 4.0));
	else
		tmp = Float64(x * Float64(z * Float64(Float64(-4.0 * Float64(i / z)) + Float64(18.0 * Float64(y * t)))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
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 <= -9.2e+115)
		tmp = x * (i * ((18.0 * ((t * (y * z)) / i)) - 4.0));
	elseif (x <= -1.12e-145)
		tmp = t_1 + (a * (t * -4.0));
	elseif (x <= -3.5e-284)
		tmp = (b * c) + (-4.0 * (t * a));
	elseif (x <= 3.2e+56)
		tmp = t_1 + (b * c);
	elseif (x <= 4.1e+198)
		tmp = (b * c) - ((x * i) * 4.0);
	else
		tmp = x * (z * ((-4.0 * (i / z)) + (18.0 * (y * t))));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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, -9.2e+115], N[(x * N[(i * N[(N[(18.0 * N[(N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision]), $MachinePrecision] - 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.12e-145], N[(t$95$1 + N[(a * N[(t * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3.5e-284], N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.2e+56], N[(t$95$1 + N[(b * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.1e+198], N[(N[(b * c), $MachinePrecision] - N[(N[(x * i), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision], N[(x * N[(z * N[(N[(-4.0 * N[(i / z), $MachinePrecision]), $MachinePrecision] + N[(18.0 * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -9.20000000000000014e115

   1. Initial program 63.2%

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

   3. Simplified 67.6%

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

   5. Taylor expanded in x around inf 67.7%

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

   6. Taylor expanded in i around inf 67.8%

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

   if -9.20000000000000014e115 < x < -1.12000000000000001e-145

   1. Initial program 95.9%

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

   3. Simplified 95.9%

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

   5. Taylor expanded in a around inf 58.8%

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

      1. metadata-eval 58.8%

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

      2. distribute-lft-neg-in 58.8%

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

      3. *-commutative 58.8%

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

      4. associate-*l* 58.8%

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

      5. distribute-lft-neg-in 58.8%

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

      6. distribute-lft-neg-in 58.8%

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

      7. metadata-eval 58.8%

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

   7. Simplified 58.8%

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

   if -1.12000000000000001e-145 < x < -3.49999999999999975e-284

   1. Initial program 92.1%

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

   3. Simplified 88.7%

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

   5. Taylor expanded in j around 0 80.8%

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

   6. Taylor expanded in i around 0 78.1%

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

   7. Taylor expanded in x around 0 74.1%

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

   if -3.49999999999999975e-284 < x < 3.20000000000000003e56

   1. Initial program 94.7%

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

   3. Simplified 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 b around inf 62.5%

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

   if 3.20000000000000003e56 < x < 4.1000000000000002e198

   1. Initial program 79.3%

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

   3. Simplified 79.3%

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

   5. Taylor expanded in j around 0 83.6%

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

   6. Taylor expanded in t around 0 75.8%

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

   if 4.1000000000000002e198 < x

   1. Initial program 54.9%

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

   3. Simplified 69.7%

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

   5. Taylor expanded in x around inf 78.8%

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

   6. Taylor expanded in z around inf 78.9%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.2 \cdot 10^{+115}:\\ \;\;\;\;x \cdot \left(i \cdot \left(18 \cdot \frac{t \cdot \left(y \cdot z\right)}{i} - 4\right)\right)\\ \mathbf{elif}\;x \leq -1.12 \cdot 10^{-145}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + a \cdot \left(t \cdot -4\right)\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{-284}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+56}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{+198}:\\ \;\;\;\;b \cdot c - \left(x \cdot i\right) \cdot 4\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot \left(-4 \cdot \frac{i}{z} + 18 \cdot \left(y \cdot t\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 36.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -4.6 \cdot 10^{+82}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -2.25 \cdot 10^{-123}:\\ \;\;\;\;t \cdot \left(x \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq -3.05 \cdot 10^{-180}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 2.6 \cdot 10^{-60}:\\ \;\;\;\;18 \cdot \left(\left(y \cdot z\right) \cdot \left(t \cdot x\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 2.9 \cdot 10^{+50}:\\ \;\;\;\;-27 \cdot \left(k \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

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 (<= (* b c) -4.6e+82)
   (* b c)
   (if (<= (* b c) -2.25e-123)
     (* t (* x (* 18.0 (* y z))))
     (if (<= (* b c) -3.05e-180)
       (* j (* k -27.0))
       (if (<= (* b c) 2.6e-60)
         (* 18.0 (* (* y z) (* t x)))
         (if (<= (* b c) 2.9e+50) (* -27.0 (* k j)) (* 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 ((b * c) <= -4.6e+82) {
		tmp = b * c;
	} else if ((b * c) <= -2.25e-123) {
		tmp = t * (x * (18.0 * (y * z)));
	} else if ((b * c) <= -3.05e-180) {
		tmp = j * (k * -27.0);
	} else if ((b * c) <= 2.6e-60) {
		tmp = 18.0 * ((y * z) * (t * x));
	} else if ((b * c) <= 2.9e+50) {
		tmp = -27.0 * (k * j);
	} 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 ((b * c) <= (-4.6d+82)) then
        tmp = b * c
    else if ((b * c) <= (-2.25d-123)) then
        tmp = t * (x * (18.0d0 * (y * z)))
    else if ((b * c) <= (-3.05d-180)) then
        tmp = j * (k * (-27.0d0))
    else if ((b * c) <= 2.6d-60) then
        tmp = 18.0d0 * ((y * z) * (t * x))
    else if ((b * c) <= 2.9d+50) then
        tmp = (-27.0d0) * (k * j)
    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 ((b * c) <= -4.6e+82) {
		tmp = b * c;
	} else if ((b * c) <= -2.25e-123) {
		tmp = t * (x * (18.0 * (y * z)));
	} else if ((b * c) <= -3.05e-180) {
		tmp = j * (k * -27.0);
	} else if ((b * c) <= 2.6e-60) {
		tmp = 18.0 * ((y * z) * (t * x));
	} else if ((b * c) <= 2.9e+50) {
		tmp = -27.0 * (k * j);
	} 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 (b * c) <= -4.6e+82:
		tmp = b * c
	elif (b * c) <= -2.25e-123:
		tmp = t * (x * (18.0 * (y * z)))
	elif (b * c) <= -3.05e-180:
		tmp = j * (k * -27.0)
	elif (b * c) <= 2.6e-60:
		tmp = 18.0 * ((y * z) * (t * x))
	elif (b * c) <= 2.9e+50:
		tmp = -27.0 * (k * j)
	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 (Float64(b * c) <= -4.6e+82)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -2.25e-123)
		tmp = Float64(t * Float64(x * Float64(18.0 * Float64(y * z))));
	elseif (Float64(b * c) <= -3.05e-180)
		tmp = Float64(j * Float64(k * -27.0));
	elseif (Float64(b * c) <= 2.6e-60)
		tmp = Float64(18.0 * Float64(Float64(y * z) * Float64(t * x)));
	elseif (Float64(b * c) <= 2.9e+50)
		tmp = Float64(-27.0 * Float64(k * j));
	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 ((b * c) <= -4.6e+82)
		tmp = b * c;
	elseif ((b * c) <= -2.25e-123)
		tmp = t * (x * (18.0 * (y * z)));
	elseif ((b * c) <= -3.05e-180)
		tmp = j * (k * -27.0);
	elseif ((b * c) <= 2.6e-60)
		tmp = 18.0 * ((y * z) * (t * x));
	elseif ((b * c) <= 2.9e+50)
		tmp = -27.0 * (k * j);
	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[LessEqual[N[(b * c), $MachinePrecision], -4.6e+82], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -2.25e-123], N[(t * N[(x * N[(18.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -3.05e-180], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 2.6e-60], N[(18.0 * N[(N[(y * z), $MachinePrecision] * N[(t * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 2.9e+50], N[(-27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 b c) < -4.59999999999999976e82 or 2.9e50 < (*.f64 b c)

   1. Initial program 77.1%

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

      1. pow1 77.1%

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

      2. associate-*l* 77.1%

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

      3. *-commutative 77.1%

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

   4. Applied egg-rr 77.1%

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

      1. unpow1 77.1%

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

      2. associate-*l* 79.1%

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

      3. *-commutative 79.1%

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

   6. Simplified 79.1%

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

   7. Taylor expanded in b around inf 55.1%

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

   if -4.59999999999999976e82 < (*.f64 b c) < -2.24999999999999997e-123

   1. Initial program 84.2%

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

   3. Simplified 88.6%

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

   5. Taylor expanded in c around inf 82.0%

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

   6. Taylor expanded in y around inf 46.2%

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

      1. *-commutative 46.2%

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

      2. associate-*l* 46.2%

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

      3. *-commutative 46.2%

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

      4. associate-*r* 46.2%

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

      5. *-commutative 46.2%

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

      6. associate-*l* 46.2%

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

   8. Simplified 46.2%

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

   if -2.24999999999999997e-123 < (*.f64 b c) < -3.05e-180

   1. Initial program 89.8%

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

      1. pow1 89.8%

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

      2. associate-*l* 79.8%

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

      3. *-commutative 79.8%

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

   4. Applied egg-rr 79.8%

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

      1. unpow1 79.8%

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

      2. associate-*l* 79.8%

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

      3. *-commutative 79.8%

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

   6. Simplified 79.8%

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

   7. Taylor expanded in j around inf 60.4%

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

      1. metadata-eval 60.4%

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

      2. distribute-lft-neg-in 60.4%

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

      3. associate-*r* 60.5%

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

      4. *-commutative 60.5%

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

      5. associate-*r* 60.5%

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

      6. distribute-rgt-neg-in 60.5%

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

      7. distribute-lft-neg-in 60.5%

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

      8. metadata-eval 60.5%

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

      9. *-commutative 60.5%

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

   9. Simplified 60.5%

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

   if -3.05e-180 < (*.f64 b c) < 2.5999999999999998e-60

   1. Initial program 84.3%

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

   3. Simplified 89.0%

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

   5. Taylor expanded in c around inf 65.5%

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

   6. Taylor expanded in y around inf 33.7%

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

      1. associate-*r* 38.4%

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

   8. Simplified 38.4%

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

   if 2.5999999999999998e-60 < (*.f64 b c) < 2.9e50

   1. Initial program 99.8%

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

   3. Simplified 92.8%

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

   5. Taylor expanded in j around inf 74.2%

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

4. Final simplification 49.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -4.6 \cdot 10^{+82}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -2.25 \cdot 10^{-123}:\\ \;\;\;\;t \cdot \left(x \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq -3.05 \cdot 10^{-180}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 2.6 \cdot 10^{-60}:\\ \;\;\;\;18 \cdot \left(\left(y \cdot z\right) \cdot \left(t \cdot x\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 2.9 \cdot 10^{+50}:\\ \;\;\;\;-27 \cdot \left(k \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 36.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := 18 \cdot \left(\left(y \cdot z\right) \cdot \left(t \cdot x\right)\right)\\ \mathbf{if}\;b \cdot c \leq -1.38 \cdot 10^{+82}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -1.7 \cdot 10^{-121}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq -1.6 \cdot 10^{-179}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 9.5 \cdot 10^{-39}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq 4.2 \cdot 10^{+50}:\\ \;\;\;\;-27 \cdot \left(k \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* 18.0 (* (* y z) (* t x)))))
   (if (<= (* b c) -1.38e+82)
     (* b c)
     (if (<= (* b c) -1.7e-121)
       t_1
       (if (<= (* b c) -1.6e-179)
         (* j (* k -27.0))
         (if (<= (* b c) 9.5e-39)
           t_1
           (if (<= (* b c) 4.2e+50) (* -27.0 (* k j)) (* 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 = 18.0 * ((y * z) * (t * x));
	double tmp;
	if ((b * c) <= -1.38e+82) {
		tmp = b * c;
	} else if ((b * c) <= -1.7e-121) {
		tmp = t_1;
	} else if ((b * c) <= -1.6e-179) {
		tmp = j * (k * -27.0);
	} else if ((b * c) <= 9.5e-39) {
		tmp = t_1;
	} else if ((b * c) <= 4.2e+50) {
		tmp = -27.0 * (k * j);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 18.0d0 * ((y * z) * (t * x))
    if ((b * c) <= (-1.38d+82)) then
        tmp = b * c
    else if ((b * c) <= (-1.7d-121)) then
        tmp = t_1
    else if ((b * c) <= (-1.6d-179)) then
        tmp = j * (k * (-27.0d0))
    else if ((b * c) <= 9.5d-39) then
        tmp = t_1
    else if ((b * c) <= 4.2d+50) then
        tmp = (-27.0d0) * (k * j)
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 18.0 * ((y * z) * (t * x));
	double tmp;
	if ((b * c) <= -1.38e+82) {
		tmp = b * c;
	} else if ((b * c) <= -1.7e-121) {
		tmp = t_1;
	} else if ((b * c) <= -1.6e-179) {
		tmp = j * (k * -27.0);
	} else if ((b * c) <= 9.5e-39) {
		tmp = t_1;
	} else if ((b * c) <= 4.2e+50) {
		tmp = -27.0 * (k * j);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = 18.0 * ((y * z) * (t * x))
	tmp = 0
	if (b * c) <= -1.38e+82:
		tmp = b * c
	elif (b * c) <= -1.7e-121:
		tmp = t_1
	elif (b * c) <= -1.6e-179:
		tmp = j * (k * -27.0)
	elif (b * c) <= 9.5e-39:
		tmp = t_1
	elif (b * c) <= 4.2e+50:
		tmp = -27.0 * (k * j)
	else:
		tmp = b * c
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(18.0 * Float64(Float64(y * z) * Float64(t * x)))
	tmp = 0.0
	if (Float64(b * c) <= -1.38e+82)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -1.7e-121)
		tmp = t_1;
	elseif (Float64(b * c) <= -1.6e-179)
		tmp = Float64(j * Float64(k * -27.0));
	elseif (Float64(b * c) <= 9.5e-39)
		tmp = t_1;
	elseif (Float64(b * c) <= 4.2e+50)
		tmp = Float64(-27.0 * Float64(k * j));
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = 18.0 * ((y * z) * (t * x));
	tmp = 0.0;
	if ((b * c) <= -1.38e+82)
		tmp = b * c;
	elseif ((b * c) <= -1.7e-121)
		tmp = t_1;
	elseif ((b * c) <= -1.6e-179)
		tmp = j * (k * -27.0);
	elseif ((b * c) <= 9.5e-39)
		tmp = t_1;
	elseif ((b * c) <= 4.2e+50)
		tmp = -27.0 * (k * j);
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(18.0 * N[(N[(y * z), $MachinePrecision] * N[(t * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -1.38e+82], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -1.7e-121], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], -1.6e-179], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 9.5e-39], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 4.2e+50], N[(-27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 b c) < -1.3799999999999999e82 or 4.1999999999999999e50 < (*.f64 b c)

   1. Initial program 77.1%

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

      1. pow1 77.1%

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

      2. associate-*l* 77.1%

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

      3. *-commutative 77.1%

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

   4. Applied egg-rr 77.1%

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

      1. unpow1 77.1%

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

      2. associate-*l* 79.1%

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

      3. *-commutative 79.1%

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

   6. Simplified 79.1%

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

   7. Taylor expanded in b around inf 55.1%

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

   if -1.3799999999999999e82 < (*.f64 b c) < -1.70000000000000001e-121 or -1.6e-179 < (*.f64 b c) < 9.4999999999999999e-39

   1. Initial program 84.2%

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

   3. Simplified 88.9%

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

   5. Taylor expanded in c around inf 71.4%

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

   6. Taylor expanded in y around inf 38.2%

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

      1. associate-*r* 40.4%

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

   8. Simplified 40.4%

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

   if -1.70000000000000001e-121 < (*.f64 b c) < -1.6e-179

   1. Initial program 89.8%

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

      1. pow1 89.8%

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

      2. associate-*l* 79.8%

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

      3. *-commutative 79.8%

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

   4. Applied egg-rr 79.8%

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

      1. unpow1 79.8%

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

      2. associate-*l* 79.8%

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

      3. *-commutative 79.8%

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

   6. Simplified 79.8%

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

   7. Taylor expanded in j around inf 60.4%

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

      1. metadata-eval 60.4%

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

      2. distribute-lft-neg-in 60.4%

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

      3. associate-*r* 60.5%

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

      4. *-commutative 60.5%

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

      5. associate-*r* 60.5%

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

      6. distribute-rgt-neg-in 60.5%

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

      7. distribute-lft-neg-in 60.5%

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

      8. metadata-eval 60.5%

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

      9. *-commutative 60.5%

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

   9. Simplified 60.5%

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

   if 9.4999999999999999e-39 < (*.f64 b c) < 4.1999999999999999e50

   1. Initial program 99.8%

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

   3. Simplified 92.8%

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

   5. Taylor expanded in j around inf 74.2%

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

4. Final simplification 49.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.38 \cdot 10^{+82}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -1.7 \cdot 10^{-121}:\\ \;\;\;\;18 \cdot \left(\left(y \cdot z\right) \cdot \left(t \cdot x\right)\right)\\ \mathbf{elif}\;b \cdot c \leq -1.6 \cdot 10^{-179}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 9.5 \cdot 10^{-39}:\\ \;\;\;\;18 \cdot \left(\left(y \cdot z\right) \cdot \left(t \cdot x\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 4.2 \cdot 10^{+50}:\\ \;\;\;\;-27 \cdot \left(k \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 55.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - i \cdot 4\right)\\ t_2 := j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;x \leq -1.05 \cdot 10^{+116}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -3.8 \cdot 10^{-146}:\\ \;\;\;\;t\_2 + a \cdot \left(t \cdot -4\right)\\ \mathbf{elif}\;x \leq -8.2 \cdot 10^{-284}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{+56}:\\ \;\;\;\;t\_2 + b \cdot c\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+198}:\\ \;\;\;\;b \cdot c - \left(x \cdot i\right) \cdot 4\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 -1.05e+116)
     t_1
     (if (<= x -3.8e-146)
       (+ t_2 (* a (* t -4.0)))
       (if (<= x -8.2e-284)
         (+ (* b c) (* -4.0 (* t a)))
         (if (<= x 2.7e+56)
           (+ t_2 (* b c))
           (if (<= x 5e+198) (- (* b c) (* (* x i) 4.0)) t_1)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = x * ((18.0 * (t * (y * z))) - (i * 4.0));
	double t_2 = j * (k * -27.0);
	double tmp;
	if (x <= -1.05e+116) {
		tmp = t_1;
	} else if (x <= -3.8e-146) {
		tmp = t_2 + (a * (t * -4.0));
	} else if (x <= -8.2e-284) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else if (x <= 2.7e+56) {
		tmp = t_2 + (b * c);
	} else if (x <= 5e+198) {
		tmp = (b * c) - ((x * i) * 4.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * ((18.0d0 * (t * (y * z))) - (i * 4.0d0))
    t_2 = j * (k * (-27.0d0))
    if (x <= (-1.05d+116)) then
        tmp = t_1
    else if (x <= (-3.8d-146)) then
        tmp = t_2 + (a * (t * (-4.0d0)))
    else if (x <= (-8.2d-284)) then
        tmp = (b * c) + ((-4.0d0) * (t * a))
    else if (x <= 2.7d+56) then
        tmp = t_2 + (b * c)
    else if (x <= 5d+198) then
        tmp = (b * c) - ((x * i) * 4.0d0)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = x * ((18.0 * (t * (y * z))) - (i * 4.0));
	double t_2 = j * (k * -27.0);
	double tmp;
	if (x <= -1.05e+116) {
		tmp = t_1;
	} else if (x <= -3.8e-146) {
		tmp = t_2 + (a * (t * -4.0));
	} else if (x <= -8.2e-284) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else if (x <= 2.7e+56) {
		tmp = t_2 + (b * c);
	} else if (x <= 5e+198) {
		tmp = (b * c) - ((x * i) * 4.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = x * ((18.0 * (t * (y * z))) - (i * 4.0))
	t_2 = j * (k * -27.0)
	tmp = 0
	if x <= -1.05e+116:
		tmp = t_1
	elif x <= -3.8e-146:
		tmp = t_2 + (a * (t * -4.0))
	elif x <= -8.2e-284:
		tmp = (b * c) + (-4.0 * (t * a))
	elif x <= 2.7e+56:
		tmp = t_2 + (b * c)
	elif x <= 5e+198:
		tmp = (b * c) - ((x * i) * 4.0)
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(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 <= -1.05e+116)
		tmp = t_1;
	elseif (x <= -3.8e-146)
		tmp = Float64(t_2 + Float64(a * Float64(t * -4.0)));
	elseif (x <= -8.2e-284)
		tmp = Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a)));
	elseif (x <= 2.7e+56)
		tmp = Float64(t_2 + Float64(b * c));
	elseif (x <= 5e+198)
		tmp = Float64(Float64(b * c) - Float64(Float64(x * i) * 4.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = x * ((18.0 * (t * (y * z))) - (i * 4.0));
	t_2 = j * (k * -27.0);
	tmp = 0.0;
	if (x <= -1.05e+116)
		tmp = t_1;
	elseif (x <= -3.8e-146)
		tmp = t_2 + (a * (t * -4.0));
	elseif (x <= -8.2e-284)
		tmp = (b * c) + (-4.0 * (t * a));
	elseif (x <= 2.7e+56)
		tmp = t_2 + (b * c);
	elseif (x <= 5e+198)
		tmp = (b * c) - ((x * i) * 4.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(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, -1.05e+116], t$95$1, If[LessEqual[x, -3.8e-146], N[(t$95$2 + N[(a * N[(t * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -8.2e-284], N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.7e+56], N[(t$95$2 + N[(b * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5e+198], N[(N[(b * c), $MachinePrecision] - N[(N[(x * i), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -1.0500000000000001e116 or 5.00000000000000049e198 < x

   1. Initial program 59.7%

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

   3. Simplified 68.5%

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

   5. Taylor expanded in x around inf 72.4%

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

   if -1.0500000000000001e116 < x < -3.79999999999999994e-146

   1. Initial program 95.9%

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

   3. Simplified 95.9%

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

   5. Taylor expanded in a around inf 58.8%

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

      1. metadata-eval 58.8%

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

      2. distribute-lft-neg-in 58.8%

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

      3. *-commutative 58.8%

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

      4. associate-*l* 58.8%

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

      5. distribute-lft-neg-in 58.8%

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

      6. distribute-lft-neg-in 58.8%

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

      7. metadata-eval 58.8%

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

   7. Simplified 58.8%

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

   if -3.79999999999999994e-146 < x < -8.19999999999999997e-284

   1. Initial program 92.1%

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

   3. Simplified 88.7%

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

   5. Taylor expanded in j around 0 80.8%

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

   6. Taylor expanded in i around 0 78.1%

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

   7. Taylor expanded in x around 0 74.1%

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

   if -8.19999999999999997e-284 < x < 2.7000000000000001e56

   1. Initial program 94.7%

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

   3. Simplified 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 b around inf 62.5%

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

   if 2.7000000000000001e56 < x < 5.00000000000000049e198

   1. Initial program 79.3%

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

   3. Simplified 79.3%

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

   5. Taylor expanded in j around 0 83.6%

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

   6. Taylor expanded in t around 0 75.8%

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

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{+116}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - i \cdot 4\right)\\ \mathbf{elif}\;x \leq -3.8 \cdot 10^{-146}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + a \cdot \left(t \cdot -4\right)\\ \mathbf{elif}\;x \leq -8.2 \cdot 10^{-284}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{+56}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+198}:\\ \;\;\;\;b \cdot c - \left(x \cdot i\right) \cdot 4\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - i \cdot 4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 89.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -0.01:\\ \;\;\;\;\left(\left(b \cdot c + \left(y \cdot \left(\left(x \cdot 18\right) \cdot \left(t \cdot z\right)\right) - t \cdot \left(a \cdot 4\right)\right)\right) - i \cdot \left(x \cdot 4\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - t \cdot \left(a \cdot 4 - \left(y \cdot z\right) \cdot \left(x \cdot 18\right)\right)\right) - \left(x \cdot \left(i \cdot 4\right) + j \cdot \left(k \cdot 27\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= y -0.01)
   (-
    (-
     (+ (* b c) (- (* y (* (* x 18.0) (* t z))) (* t (* a 4.0))))
     (* i (* x 4.0)))
    (* k (* j 27.0)))
   (-
    (- (* b c) (* t (- (* a 4.0) (* (* y z) (* x 18.0)))))
    (+ (* x (* i 4.0)) (* j (* k 27.0))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (y <= -0.01) {
		tmp = (((b * c) + ((y * ((x * 18.0) * (t * z))) - (t * (a * 4.0)))) - (i * (x * 4.0))) - (k * (j * 27.0));
	} else {
		tmp = ((b * c) - (t * ((a * 4.0) - ((y * z) * (x * 18.0))))) - ((x * (i * 4.0)) + (j * (k * 27.0)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (y <= (-0.01d0)) then
        tmp = (((b * c) + ((y * ((x * 18.0d0) * (t * z))) - (t * (a * 4.0d0)))) - (i * (x * 4.0d0))) - (k * (j * 27.0d0))
    else
        tmp = ((b * c) - (t * ((a * 4.0d0) - ((y * z) * (x * 18.0d0))))) - ((x * (i * 4.0d0)) + (j * (k * 27.0d0)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (y <= -0.01) {
		tmp = (((b * c) + ((y * ((x * 18.0) * (t * z))) - (t * (a * 4.0)))) - (i * (x * 4.0))) - (k * (j * 27.0));
	} else {
		tmp = ((b * c) - (t * ((a * 4.0) - ((y * z) * (x * 18.0))))) - ((x * (i * 4.0)) + (j * (k * 27.0)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if y <= -0.01:
		tmp = (((b * c) + ((y * ((x * 18.0) * (t * z))) - (t * (a * 4.0)))) - (i * (x * 4.0))) - (k * (j * 27.0))
	else:
		tmp = ((b * c) - (t * ((a * 4.0) - ((y * z) * (x * 18.0))))) - ((x * (i * 4.0)) + (j * (k * 27.0)))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (y <= -0.01)
		tmp = Float64(Float64(Float64(Float64(b * c) + Float64(Float64(y * Float64(Float64(x * 18.0) * Float64(t * z))) - Float64(t * Float64(a * 4.0)))) - Float64(i * Float64(x * 4.0))) - Float64(k * Float64(j * 27.0)));
	else
		tmp = Float64(Float64(Float64(b * c) - Float64(t * Float64(Float64(a * 4.0) - Float64(Float64(y * z) * Float64(x * 18.0))))) - Float64(Float64(x * Float64(i * 4.0)) + Float64(j * Float64(k * 27.0))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (y <= -0.01)
		tmp = (((b * c) + ((y * ((x * 18.0) * (t * z))) - (t * (a * 4.0)))) - (i * (x * 4.0))) - (k * (j * 27.0));
	else
		tmp = ((b * c) - (t * ((a * 4.0) - ((y * z) * (x * 18.0))))) - ((x * (i * 4.0)) + (j * (k * 27.0)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[y, -0.01], N[(N[(N[(N[(b * c), $MachinePrecision] + N[(N[(y * N[(N[(x * 18.0), $MachinePrecision] * N[(t * z), $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], N[(N[(N[(b * c), $MachinePrecision] - N[(t * N[(N[(a * 4.0), $MachinePrecision] - N[(N[(y * z), $MachinePrecision] * N[(x * 18.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * N[(i * 4.0), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.0100000000000000002

   1. Initial program 73.0%

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

      1. pow1 73.0%

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

      2. associate-*l* 77.4%

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

      3. *-commutative 77.4%

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

   4. Applied egg-rr 77.4%

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

      1. unpow1 77.4%

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

      2. associate-*l* 81.7%

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

      3. *-commutative 81.7%

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

   6. Simplified 81.7%

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

   if -0.0100000000000000002 < y

   1. Initial program 85.7%

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

   3. Simplified 87.8%

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

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.01:\\ \;\;\;\;\left(\left(b \cdot c + \left(y \cdot \left(\left(x \cdot 18\right) \cdot \left(t \cdot z\right)\right) - t \cdot \left(a \cdot 4\right)\right)\right) - i \cdot \left(x \cdot 4\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - t \cdot \left(a \cdot 4 - \left(y \cdot z\right) \cdot \left(x \cdot 18\right)\right)\right) - \left(x \cdot \left(i \cdot 4\right) + j \cdot \left(k \cdot 27\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 69.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := t \cdot \left(-18 \cdot \left(z \cdot \left(x \cdot \left(-y\right)\right)\right) - a \cdot 4\right)\\ \mathbf{if}\;t \leq -7.2 \cdot 10^{+131}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -3.2 \cdot 10^{+85}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + a \cdot \left(t \cdot -4\right)\\ \mathbf{elif}\;t \leq -6.6 \cdot 10^{-13} \lor \neg \left(t \leq 3.3 \cdot 10^{+180}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - \left(\left(x \cdot i\right) \cdot 4 + 27 \cdot \left(k \cdot j\right)\right)\\ \end{array} \end{array} \]

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 (* t (- (* -18.0 (* z (* x (- y)))) (* a 4.0)))))
   (if (<= t -7.2e+131)
     t_1
     (if (<= t -3.2e+85)
       (+ (* j (* k -27.0)) (* a (* t -4.0)))
       (if (or (<= t -6.6e-13) (not (<= t 3.3e+180)))
         t_1
         (- (* b c) (+ (* (* x i) 4.0) (* 27.0 (* k j)))))))))

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 * (z * (x * -y))) - (a * 4.0));
	double tmp;
	if (t <= -7.2e+131) {
		tmp = t_1;
	} else if (t <= -3.2e+85) {
		tmp = (j * (k * -27.0)) + (a * (t * -4.0));
	} else if ((t <= -6.6e-13) || !(t <= 3.3e+180)) {
		tmp = t_1;
	} else {
		tmp = (b * c) - (((x * i) * 4.0) + (27.0 * (k * j)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (((-18.0d0) * (z * (x * -y))) - (a * 4.0d0))
    if (t <= (-7.2d+131)) then
        tmp = t_1
    else if (t <= (-3.2d+85)) then
        tmp = (j * (k * (-27.0d0))) + (a * (t * (-4.0d0)))
    else if ((t <= (-6.6d-13)) .or. (.not. (t <= 3.3d+180))) then
        tmp = t_1
    else
        tmp = (b * c) - (((x * i) * 4.0d0) + (27.0d0 * (k * j)))
    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 * (z * (x * -y))) - (a * 4.0));
	double tmp;
	if (t <= -7.2e+131) {
		tmp = t_1;
	} else if (t <= -3.2e+85) {
		tmp = (j * (k * -27.0)) + (a * (t * -4.0));
	} else if ((t <= -6.6e-13) || !(t <= 3.3e+180)) {
		tmp = t_1;
	} else {
		tmp = (b * c) - (((x * i) * 4.0) + (27.0 * (k * j)));
	}
	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 * (z * (x * -y))) - (a * 4.0))
	tmp = 0
	if t <= -7.2e+131:
		tmp = t_1
	elif t <= -3.2e+85:
		tmp = (j * (k * -27.0)) + (a * (t * -4.0))
	elif (t <= -6.6e-13) or not (t <= 3.3e+180):
		tmp = t_1
	else:
		tmp = (b * c) - (((x * i) * 4.0) + (27.0 * (k * j)))
	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(z * Float64(x * Float64(-y)))) - Float64(a * 4.0)))
	tmp = 0.0
	if (t <= -7.2e+131)
		tmp = t_1;
	elseif (t <= -3.2e+85)
		tmp = Float64(Float64(j * Float64(k * -27.0)) + Float64(a * Float64(t * -4.0)));
	elseif ((t <= -6.6e-13) || !(t <= 3.3e+180))
		tmp = t_1;
	else
		tmp = Float64(Float64(b * c) - Float64(Float64(Float64(x * i) * 4.0) + Float64(27.0 * Float64(k * j))));
	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 * (z * (x * -y))) - (a * 4.0));
	tmp = 0.0;
	if (t <= -7.2e+131)
		tmp = t_1;
	elseif (t <= -3.2e+85)
		tmp = (j * (k * -27.0)) + (a * (t * -4.0));
	elseif ((t <= -6.6e-13) || ~((t <= 3.3e+180)))
		tmp = t_1;
	else
		tmp = (b * c) - (((x * i) * 4.0) + (27.0 * (k * j)));
	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[(z * N[(x * (-y)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.2e+131], t$95$1, If[LessEqual[t, -3.2e+85], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(a * N[(t * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, -6.6e-13], N[Not[LessEqual[t, 3.3e+180]], $MachinePrecision]], t$95$1, N[(N[(b * c), $MachinePrecision] - N[(N[(N[(x * i), $MachinePrecision] * 4.0), $MachinePrecision] + N[(27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.20000000000000063e131 or -3.20000000000000018e85 < t < -6.6000000000000001e-13 or 3.29999999999999989e180 < t

   1. Initial program 75.6%

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

      1. pow1 75.6%

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

      2. associate-*l* 70.3%

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

      3. *-commutative 70.3%

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

   4. Applied egg-rr 70.3%

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

      1. unpow1 70.3%

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

      2. associate-*l* 71.7%

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

      3. *-commutative 71.7%

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

   6. Simplified 71.7%

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

   7. Taylor expanded in t around -inf 77.5%

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

      1. mul-1-neg 77.5%

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

      2. cancel-sign-sub-inv 77.5%

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

      3. *-commutative 77.5%

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

      4. associate-*r* 78.7%

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

      5. metadata-eval 78.7%

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

   9. Simplified 78.7%

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

   if -7.20000000000000063e131 < t < -3.20000000000000018e85

   1. Initial program 71.4%

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

   3. Simplified 71.2%

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

   5. Taylor expanded in a around inf 85.6%

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

      1. metadata-eval 85.6%

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

      2. distribute-lft-neg-in 85.6%

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

      3. *-commutative 85.6%

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

      4. associate-*l* 85.6%

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

      5. distribute-lft-neg-in 85.6%

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

      6. distribute-lft-neg-in 85.6%

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

      7. metadata-eval 85.6%

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

   7. Simplified 85.6%

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

   if -6.6000000000000001e-13 < t < 3.29999999999999989e180

   1. Initial program 85.8%

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

   3. Simplified 86.3%

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

   5. Taylor expanded in t around 0 72.0%

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

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{+131}:\\ \;\;\;\;t \cdot \left(-18 \cdot \left(z \cdot \left(x \cdot \left(-y\right)\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq -3.2 \cdot 10^{+85}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + a \cdot \left(t \cdot -4\right)\\ \mathbf{elif}\;t \leq -6.6 \cdot 10^{-13} \lor \neg \left(t \leq 3.3 \cdot 10^{+180}\right):\\ \;\;\;\;t \cdot \left(-18 \cdot \left(z \cdot \left(x \cdot \left(-y\right)\right)\right) - a \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - \left(\left(x \cdot i\right) \cdot 4 + 27 \cdot \left(k \cdot j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 57.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := x \cdot \left(i \cdot \left(18 \cdot \frac{t \cdot \left(y \cdot z\right)}{i} - 4\right)\right)\\ t_2 := j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;x \leq -9 \cdot 10^{+117}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -3.4 \cdot 10^{-147}:\\ \;\;\;\;t\_2 + a \cdot \left(t \cdot -4\right)\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{-284}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{+80}:\\ \;\;\;\;t\_2 + b \cdot c\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (* x (* i (- (* 18.0 (/ (* t (* y z)) i)) 4.0))))
        (t_2 (* j (* k -27.0))))
   (if (<= x -9e+117)
     t_1
     (if (<= x -3.4e-147)
       (+ t_2 (* a (* t -4.0)))
       (if (<= x -4.2e-284)
         (+ (* b c) (* -4.0 (* t a)))
         (if (<= x 1.9e+80) (+ t_2 (* 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 = x * (i * ((18.0 * ((t * (y * z)) / i)) - 4.0));
	double t_2 = j * (k * -27.0);
	double tmp;
	if (x <= -9e+117) {
		tmp = t_1;
	} else if (x <= -3.4e-147) {
		tmp = t_2 + (a * (t * -4.0));
	} else if (x <= -4.2e-284) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else if (x <= 1.9e+80) {
		tmp = t_2 + (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) :: t_2
    real(8) :: tmp
    t_1 = x * (i * ((18.0d0 * ((t * (y * z)) / i)) - 4.0d0))
    t_2 = j * (k * (-27.0d0))
    if (x <= (-9d+117)) then
        tmp = t_1
    else if (x <= (-3.4d-147)) then
        tmp = t_2 + (a * (t * (-4.0d0)))
    else if (x <= (-4.2d-284)) then
        tmp = (b * c) + ((-4.0d0) * (t * a))
    else if (x <= 1.9d+80) then
        tmp = t_2 + (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 = x * (i * ((18.0 * ((t * (y * z)) / i)) - 4.0));
	double t_2 = j * (k * -27.0);
	double tmp;
	if (x <= -9e+117) {
		tmp = t_1;
	} else if (x <= -3.4e-147) {
		tmp = t_2 + (a * (t * -4.0));
	} else if (x <= -4.2e-284) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else if (x <= 1.9e+80) {
		tmp = t_2 + (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 = x * (i * ((18.0 * ((t * (y * z)) / i)) - 4.0))
	t_2 = j * (k * -27.0)
	tmp = 0
	if x <= -9e+117:
		tmp = t_1
	elif x <= -3.4e-147:
		tmp = t_2 + (a * (t * -4.0))
	elif x <= -4.2e-284:
		tmp = (b * c) + (-4.0 * (t * a))
	elif x <= 1.9e+80:
		tmp = t_2 + (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(x * Float64(i * Float64(Float64(18.0 * Float64(Float64(t * Float64(y * z)) / i)) - 4.0)))
	t_2 = Float64(j * Float64(k * -27.0))
	tmp = 0.0
	if (x <= -9e+117)
		tmp = t_1;
	elseif (x <= -3.4e-147)
		tmp = Float64(t_2 + Float64(a * Float64(t * -4.0)));
	elseif (x <= -4.2e-284)
		tmp = Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a)));
	elseif (x <= 1.9e+80)
		tmp = Float64(t_2 + 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 = x * (i * ((18.0 * ((t * (y * z)) / i)) - 4.0));
	t_2 = j * (k * -27.0);
	tmp = 0.0;
	if (x <= -9e+117)
		tmp = t_1;
	elseif (x <= -3.4e-147)
		tmp = t_2 + (a * (t * -4.0));
	elseif (x <= -4.2e-284)
		tmp = (b * c) + (-4.0 * (t * a));
	elseif (x <= 1.9e+80)
		tmp = t_2 + (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[(x * N[(i * N[(N[(18.0 * N[(N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision]), $MachinePrecision] - 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -9e+117], t$95$1, If[LessEqual[x, -3.4e-147], N[(t$95$2 + N[(a * N[(t * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -4.2e-284], N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.9e+80], N[(t$95$2 + N[(b * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -9e117 or 1.89999999999999999e80 < x

   1. Initial program 64.2%

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

   3. Simplified 71.1%

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

   5. Taylor expanded in x around inf 69.3%

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

   6. Taylor expanded in i around inf 70.3%

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

   if -9e117 < x < -3.39999999999999996e-147

   1. Initial program 95.9%

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

   3. Simplified 95.9%

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

   5. Taylor expanded in a around inf 58.8%

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

      1. metadata-eval 58.8%

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

      2. distribute-lft-neg-in 58.8%

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

      3. *-commutative 58.8%

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

      4. associate-*l* 58.8%

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

      5. distribute-lft-neg-in 58.8%

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

      6. distribute-lft-neg-in 58.8%

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

      7. metadata-eval 58.8%

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

   7. Simplified 58.8%

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

   if -3.39999999999999996e-147 < x < -4.19999999999999982e-284

   1. Initial program 92.1%

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

   3. Simplified 88.7%

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

   5. Taylor expanded in j around 0 80.8%

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

   6. Taylor expanded in i around 0 78.1%

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

   7. Taylor expanded in x around 0 74.1%

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

   if -4.19999999999999982e-284 < x < 1.89999999999999999e80

   1. Initial program 93.6%

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

   3. Simplified 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 b around inf 61.5%

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

4. Final simplification 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+117}:\\ \;\;\;\;x \cdot \left(i \cdot \left(18 \cdot \frac{t \cdot \left(y \cdot z\right)}{i} - 4\right)\right)\\ \mathbf{elif}\;x \leq -3.4 \cdot 10^{-147}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + a \cdot \left(t \cdot -4\right)\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{-284}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{+80}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(i \cdot \left(18 \cdot \frac{t \cdot \left(y \cdot z\right)}{i} - 4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 51.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := t\_1 + b \cdot c\\ \mathbf{if}\;k \leq -4.8 \cdot 10^{-29}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;k \leq 2.05 \cdot 10^{+62}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;k \leq 1.35 \cdot 10^{+85}:\\ \;\;\;\;t\_1 + a \cdot \left(t \cdot -4\right)\\ \mathbf{elif}\;k \leq 5.6 \cdot 10^{+99}:\\ \;\;\;\;b \cdot c - \left(x \cdot i\right) \cdot 4\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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))))
   (if (<= k -4.8e-29)
     t_2
     (if (<= k 2.05e+62)
       (+ (* b c) (* -4.0 (* t a)))
       (if (<= k 1.35e+85)
         (+ t_1 (* a (* t -4.0)))
         (if (<= k 5.6e+99) (- (* b c) (* (* x i) 4.0)) 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 tmp;
	if (k <= -4.8e-29) {
		tmp = t_2;
	} else if (k <= 2.05e+62) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else if (k <= 1.35e+85) {
		tmp = t_1 + (a * (t * -4.0));
	} else if (k <= 5.6e+99) {
		tmp = (b * c) - ((x * i) * 4.0);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * (k * (-27.0d0))
    t_2 = t_1 + (b * c)
    if (k <= (-4.8d-29)) then
        tmp = t_2
    else if (k <= 2.05d+62) then
        tmp = (b * c) + ((-4.0d0) * (t * a))
    else if (k <= 1.35d+85) then
        tmp = t_1 + (a * (t * (-4.0d0)))
    else if (k <= 5.6d+99) then
        tmp = (b * c) - ((x * i) * 4.0d0)
    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 tmp;
	if (k <= -4.8e-29) {
		tmp = t_2;
	} else if (k <= 2.05e+62) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else if (k <= 1.35e+85) {
		tmp = t_1 + (a * (t * -4.0));
	} else if (k <= 5.6e+99) {
		tmp = (b * c) - ((x * i) * 4.0);
	} 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)
	tmp = 0
	if k <= -4.8e-29:
		tmp = t_2
	elif k <= 2.05e+62:
		tmp = (b * c) + (-4.0 * (t * a))
	elif k <= 1.35e+85:
		tmp = t_1 + (a * (t * -4.0))
	elif k <= 5.6e+99:
		tmp = (b * c) - ((x * i) * 4.0)
	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))
	tmp = 0.0
	if (k <= -4.8e-29)
		tmp = t_2;
	elseif (k <= 2.05e+62)
		tmp = Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a)));
	elseif (k <= 1.35e+85)
		tmp = Float64(t_1 + Float64(a * Float64(t * -4.0)));
	elseif (k <= 5.6e+99)
		tmp = Float64(Float64(b * c) - Float64(Float64(x * i) * 4.0));
	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);
	tmp = 0.0;
	if (k <= -4.8e-29)
		tmp = t_2;
	elseif (k <= 2.05e+62)
		tmp = (b * c) + (-4.0 * (t * a));
	elseif (k <= 1.35e+85)
		tmp = t_1 + (a * (t * -4.0));
	elseif (k <= 5.6e+99)
		tmp = (b * c) - ((x * i) * 4.0);
	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]}, If[LessEqual[k, -4.8e-29], t$95$2, If[LessEqual[k, 2.05e+62], N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 1.35e+85], N[(t$95$1 + N[(a * N[(t * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 5.6e+99], N[(N[(b * c), $MachinePrecision] - N[(N[(x * i), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if k < -4.79999999999999984e-29 or 5.6e99 < k

   1. Initial program 78.6%

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

   3. Simplified 82.0%

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

   5. Taylor expanded in b around inf 61.0%

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

   if -4.79999999999999984e-29 < k < 2.04999999999999992e62

   1. Initial program 87.3%

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

   3. Simplified 87.5%

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

   5. Taylor expanded in j around 0 82.8%

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

   6. Taylor expanded in i around 0 72.4%

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

   7. Taylor expanded in x around 0 56.7%

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

   if 2.04999999999999992e62 < k < 1.34999999999999992e85

   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 85.3%

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

   5. Taylor expanded in a around inf 99.6%

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

      1. metadata-eval 99.6%

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

      2. distribute-lft-neg-in 99.6%

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

      3. *-commutative 99.6%

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

      4. associate-*l* 99.6%

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

      5. distribute-lft-neg-in 99.6%

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

      6. distribute-lft-neg-in 99.6%

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

      7. metadata-eval 99.6%

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

   7. Simplified 99.6%

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

   if 1.34999999999999992e85 < k < 5.6e99

   1. Initial program 68.0%

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

   3. Simplified 83.1%

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

   5. Taylor expanded in j around 0 82.8%

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

   6. Taylor expanded in t around 0 83.6%

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

4. Final simplification 60.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -4.8 \cdot 10^{-29}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \mathbf{elif}\;k \leq 2.05 \cdot 10^{+62}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;k \leq 1.35 \cdot 10^{+85}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + a \cdot \left(t \cdot -4\right)\\ \mathbf{elif}\;k \leq 5.6 \cdot 10^{+99}:\\ \;\;\;\;b \cdot c - \left(x \cdot i\right) \cdot 4\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 36.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1 \cdot 10^{+83}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq 2.5 \cdot 10^{-267}:\\ \;\;\;\;x \cdot \left(\left(y \cdot z\right) \cdot \left(t \cdot 18\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 4.2 \cdot 10^{+50}:\\ \;\;\;\;-27 \cdot \left(k \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

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 (<= (* b c) -1e+83)
   (* b c)
   (if (<= (* b c) 2.5e-267)
     (* x (* (* y z) (* t 18.0)))
     (if (<= (* b c) 4.2e+50) (* -27.0 (* k j)) (* 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 ((b * c) <= -1e+83) {
		tmp = b * c;
	} else if ((b * c) <= 2.5e-267) {
		tmp = x * ((y * z) * (t * 18.0));
	} else if ((b * c) <= 4.2e+50) {
		tmp = -27.0 * (k * j);
	} 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 ((b * c) <= (-1d+83)) then
        tmp = b * c
    else if ((b * c) <= 2.5d-267) then
        tmp = x * ((y * z) * (t * 18.0d0))
    else if ((b * c) <= 4.2d+50) then
        tmp = (-27.0d0) * (k * j)
    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 ((b * c) <= -1e+83) {
		tmp = b * c;
	} else if ((b * c) <= 2.5e-267) {
		tmp = x * ((y * z) * (t * 18.0));
	} else if ((b * c) <= 4.2e+50) {
		tmp = -27.0 * (k * j);
	} 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 (b * c) <= -1e+83:
		tmp = b * c
	elif (b * c) <= 2.5e-267:
		tmp = x * ((y * z) * (t * 18.0))
	elif (b * c) <= 4.2e+50:
		tmp = -27.0 * (k * j)
	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 (Float64(b * c) <= -1e+83)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= 2.5e-267)
		tmp = Float64(x * Float64(Float64(y * z) * Float64(t * 18.0)));
	elseif (Float64(b * c) <= 4.2e+50)
		tmp = Float64(-27.0 * Float64(k * j));
	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 ((b * c) <= -1e+83)
		tmp = b * c;
	elseif ((b * c) <= 2.5e-267)
		tmp = x * ((y * z) * (t * 18.0));
	elseif ((b * c) <= 4.2e+50)
		tmp = -27.0 * (k * j);
	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[LessEqual[N[(b * c), $MachinePrecision], -1e+83], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 2.5e-267], N[(x * N[(N[(y * z), $MachinePrecision] * N[(t * 18.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 4.2e+50], N[(-27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -1.00000000000000003e83 or 4.1999999999999999e50 < (*.f64 b c)

   1. Initial program 77.1%

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

      1. pow1 77.1%

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

      2. associate-*l* 77.1%

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

      3. *-commutative 77.1%

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

   4. Applied egg-rr 77.1%

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

      1. unpow1 77.1%

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

      2. associate-*l* 79.1%

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

      3. *-commutative 79.1%

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

   6. Simplified 79.1%

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

   7. Taylor expanded in b around inf 55.1%

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

   if -1.00000000000000003e83 < (*.f64 b c) < 2.5e-267

   1. Initial program 83.8%

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

   3. Simplified 88.7%

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

   5. Taylor expanded in x around inf 53.0%

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

   6. Taylor expanded in t around inf 40.4%

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

      1. associate-*r* 40.4%

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

      2. associate-*r* 38.6%

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

   8. Simplified 38.6%

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

      1. pow1 38.6%

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

      2. associate-*r* 38.6%

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

      3. *-commutative 38.6%

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

      4. associate-*r* 38.6%

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

      5. *-commutative 38.6%

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

      6. *-commutative 38.6%

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

   10. Applied egg-rr 38.6%

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

       1. unpow1 38.6%

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

       2. associate-*r* 40.4%

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

       3. *-commutative 40.4%

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

   12. Simplified 40.4%

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

   if 2.5e-267 < (*.f64 b c) < 4.1999999999999999e50

   1. Initial program 90.6%

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

   3. Simplified 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 j around inf 44.8%

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

4. Final simplification 47.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1 \cdot 10^{+83}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq 2.5 \cdot 10^{-267}:\\ \;\;\;\;x \cdot \left(\left(y \cdot z\right) \cdot \left(t \cdot 18\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 4.2 \cdot 10^{+50}:\\ \;\;\;\;-27 \cdot \left(k \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 36.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -4.8 \cdot 10^{+82}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq 1.05 \cdot 10^{-266}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 3.2 \cdot 10^{+50}:\\ \;\;\;\;-27 \cdot \left(k \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

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 (<= (* b c) -4.8e+82)
   (* b c)
   (if (<= (* b c) 1.05e-266)
     (* x (* 18.0 (* t (* y z))))
     (if (<= (* b c) 3.2e+50) (* -27.0 (* k j)) (* 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 ((b * c) <= -4.8e+82) {
		tmp = b * c;
	} else if ((b * c) <= 1.05e-266) {
		tmp = x * (18.0 * (t * (y * z)));
	} else if ((b * c) <= 3.2e+50) {
		tmp = -27.0 * (k * j);
	} 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 ((b * c) <= (-4.8d+82)) then
        tmp = b * c
    else if ((b * c) <= 1.05d-266) then
        tmp = x * (18.0d0 * (t * (y * z)))
    else if ((b * c) <= 3.2d+50) then
        tmp = (-27.0d0) * (k * j)
    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 ((b * c) <= -4.8e+82) {
		tmp = b * c;
	} else if ((b * c) <= 1.05e-266) {
		tmp = x * (18.0 * (t * (y * z)));
	} else if ((b * c) <= 3.2e+50) {
		tmp = -27.0 * (k * j);
	} 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 (b * c) <= -4.8e+82:
		tmp = b * c
	elif (b * c) <= 1.05e-266:
		tmp = x * (18.0 * (t * (y * z)))
	elif (b * c) <= 3.2e+50:
		tmp = -27.0 * (k * j)
	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 (Float64(b * c) <= -4.8e+82)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= 1.05e-266)
		tmp = Float64(x * Float64(18.0 * Float64(t * Float64(y * z))));
	elseif (Float64(b * c) <= 3.2e+50)
		tmp = Float64(-27.0 * Float64(k * j));
	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 ((b * c) <= -4.8e+82)
		tmp = b * c;
	elseif ((b * c) <= 1.05e-266)
		tmp = x * (18.0 * (t * (y * z)));
	elseif ((b * c) <= 3.2e+50)
		tmp = -27.0 * (k * j);
	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[LessEqual[N[(b * c), $MachinePrecision], -4.8e+82], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1.05e-266], N[(x * N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 3.2e+50], N[(-27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -4.79999999999999996e82 or 3.19999999999999983e50 < (*.f64 b c)

   1. Initial program 77.1%

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

      1. pow1 77.1%

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

      2. associate-*l* 77.1%

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

      3. *-commutative 77.1%

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

   4. Applied egg-rr 77.1%

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

      1. unpow1 77.1%

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

      2. associate-*l* 79.1%

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

      3. *-commutative 79.1%

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

   6. Simplified 79.1%

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

   7. Taylor expanded in b around inf 55.1%

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

   if -4.79999999999999996e82 < (*.f64 b c) < 1.04999999999999998e-266

   1. Initial program 83.8%

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

   3. Simplified 88.7%

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

   5. Taylor expanded in x around inf 53.0%

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

   6. Taylor expanded in t around inf 40.4%

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

   if 1.04999999999999998e-266 < (*.f64 b c) < 3.19999999999999983e50

   1. Initial program 90.6%

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

   3. Simplified 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 j around inf 44.8%

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

4. Final simplification 47.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -4.8 \cdot 10^{+82}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq 1.05 \cdot 10^{-266}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 3.2 \cdot 10^{+50}:\\ \;\;\;\;-27 \cdot \left(k \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 51.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;k \leq -2.1 \cdot 10^{-30} \lor \neg \left(k \leq 2.1 \cdot 10^{+77}\right):\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 -2.1e-30) (not (<= k 2.1e+77)))
   (+ (* j (* k -27.0)) (* b c))
   (+ (* b c) (* -4.0 (* t a)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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 <= -2.1e-30) || !(k <= 2.1e+77)) {
		tmp = (j * (k * -27.0)) + (b * c);
	} else {
		tmp = (b * c) + (-4.0 * (t * a));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 <= (-2.1d-30)) .or. (.not. (k <= 2.1d+77))) then
        tmp = (j * (k * (-27.0d0))) + (b * c)
    else
        tmp = (b * c) + ((-4.0d0) * (t * a))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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 <= -2.1e-30) || !(k <= 2.1e+77)) {
		tmp = (j * (k * -27.0)) + (b * c);
	} else {
		tmp = (b * c) + (-4.0 * (t * a));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[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 <= -2.1e-30) or not (k <= 2.1e+77):
		tmp = (j * (k * -27.0)) + (b * c)
	else:
		tmp = (b * c) + (-4.0 * (t * a))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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 <= -2.1e-30) || !(k <= 2.1e+77))
		tmp = Float64(Float64(j * Float64(k * -27.0)) + Float64(b * c));
	else
		tmp = Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
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 <= -2.1e-30) || ~((k <= 2.1e+77)))
		tmp = (j * (k * -27.0)) + (b * c);
	else
		tmp = (b * c) + (-4.0 * (t * a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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, -2.1e-30], N[Not[LessEqual[k, 2.1e+77]], $MachinePrecision]], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if k < -2.1000000000000002e-30 or 2.0999999999999999e77 < k

   1. Initial program 79.0%

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

   3. Simplified 82.7%

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

   5. Taylor expanded in b around inf 60.5%

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

   if -2.1000000000000002e-30 < k < 2.0999999999999999e77

   1. Initial program 85.9%

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

   3. Simplified 86.9%

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

   5. Taylor expanded in j around 0 82.3%

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

   6. Taylor expanded in i around 0 72.0%

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

   7. Taylor expanded in x around 0 56.7%

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

4. Final simplification 58.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -2.1 \cdot 10^{-30} \lor \neg \left(k \leq 2.1 \cdot 10^{+77}\right):\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 37.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -8.6 \cdot 10^{+26} \lor \neg \left(b \cdot c \leq 2.95 \cdot 10^{+50}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(-27 \cdot j\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= (* b c) -8.6e+26) (not (<= (* b c) 2.95e+50)))
   (* b c)
   (* k (* -27.0 j))))

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) <= -8.6e+26) || !((b * c) <= 2.95e+50)) {
		tmp = b * c;
	} else {
		tmp = k * (-27.0 * j);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (((b * c) <= (-8.6d+26)) .or. (.not. ((b * c) <= 2.95d+50))) then
        tmp = b * c
    else
        tmp = k * ((-27.0d0) * j)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (((b * c) <= -8.6e+26) || !((b * c) <= 2.95e+50)) {
		tmp = b * c;
	} else {
		tmp = k * (-27.0 * j);
	}
	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) <= -8.6e+26) or not ((b * c) <= 2.95e+50):
		tmp = b * c
	else:
		tmp = k * (-27.0 * j)
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((Float64(b * c) <= -8.6e+26) || !(Float64(b * c) <= 2.95e+50))
		tmp = Float64(b * c);
	else
		tmp = Float64(k * Float64(-27.0 * j));
	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) <= -8.6e+26) || ~(((b * c) <= 2.95e+50)))
		tmp = b * c;
	else
		tmp = k * (-27.0 * j);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[N[(b * c), $MachinePrecision], -8.6e+26], N[Not[LessEqual[N[(b * c), $MachinePrecision], 2.95e+50]], $MachinePrecision]], N[(b * c), $MachinePrecision], N[(k * N[(-27.0 * j), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -8.5999999999999996e26 or 2.9499999999999999e50 < (*.f64 b c)

   1. Initial program 77.3%

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

      1. pow1 77.3%

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

      2. associate-*l* 77.2%

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

      3. *-commutative 77.2%

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

   4. Applied egg-rr 77.2%

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

      1. unpow1 77.2%

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

      2. associate-*l* 79.0%

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

      3. *-commutative 79.0%

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

   6. Simplified 79.0%

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

   7. Taylor expanded in b around inf 50.3%

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

   if -8.5999999999999996e26 < (*.f64 b c) < 2.9499999999999999e50

   1. Initial program 86.9%

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

   3. Simplified 89.7%

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

   5. Taylor expanded in j around inf 34.6%

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

      1. associate-*r* 34.7%

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

      2. *-commutative 34.7%

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

      3. metadata-eval 34.7%

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

      4. distribute-rgt-neg-in 34.7%

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

      5. *-commutative 34.7%

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

      6. distribute-rgt-neg-in 34.7%

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

      7. metadata-eval 34.7%

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

      8. *-commutative 34.7%

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

   7. Simplified 34.7%

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

4. Final simplification 41.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -8.6 \cdot 10^{+26} \lor \neg \left(b \cdot c \leq 2.95 \cdot 10^{+50}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(-27 \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 37.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -5.7 \cdot 10^{+26} \lor \neg \left(b \cdot c \leq 3.6 \cdot 10^{+50}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= (* b c) -5.7e+26) (not (<= (* b c) 3.6e+50)))
   (* b c)
   (* j (* k -27.0))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (((b * c) <= -5.7e+26) || !((b * c) <= 3.6e+50)) {
		tmp = b * c;
	} else {
		tmp = j * (k * -27.0);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (((b * c) <= (-5.7d+26)) .or. (.not. ((b * c) <= 3.6d+50))) then
        tmp = b * c
    else
        tmp = j * (k * (-27.0d0))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (((b * c) <= -5.7e+26) || !((b * c) <= 3.6e+50)) {
		tmp = b * c;
	} else {
		tmp = j * (k * -27.0);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if ((b * c) <= -5.7e+26) or not ((b * c) <= 3.6e+50):
		tmp = b * c
	else:
		tmp = j * (k * -27.0)
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((Float64(b * c) <= -5.7e+26) || !(Float64(b * c) <= 3.6e+50))
		tmp = Float64(b * c);
	else
		tmp = Float64(j * Float64(k * -27.0));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (((b * c) <= -5.7e+26) || ~(((b * c) <= 3.6e+50)))
		tmp = b * c;
	else
		tmp = j * (k * -27.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[N[(b * c), $MachinePrecision], -5.7e+26], N[Not[LessEqual[N[(b * c), $MachinePrecision], 3.6e+50]], $MachinePrecision]], N[(b * c), $MachinePrecision], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -5.7000000000000003e26 or 3.59999999999999986e50 < (*.f64 b c)

   1. Initial program 77.3%

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

      1. pow1 77.3%

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

      2. associate-*l* 77.2%

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

      3. *-commutative 77.2%

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

   4. Applied egg-rr 77.2%

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

      1. unpow1 77.2%

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

      2. associate-*l* 79.0%

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

      3. *-commutative 79.0%

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

   6. Simplified 79.0%

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

   7. Taylor expanded in b around inf 50.3%

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

   if -5.7000000000000003e26 < (*.f64 b c) < 3.59999999999999986e50

   1. Initial program 86.9%

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

      1. pow1 86.9%

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

      2. associate-*l* 86.1%

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

      3. *-commutative 86.1%

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

   4. Applied egg-rr 86.1%

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

      1. unpow1 86.1%

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

      2. associate-*l* 88.4%

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

      3. *-commutative 88.4%

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

   6. Simplified 88.4%

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

   7. Taylor expanded in j around inf 34.6%

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

      1. metadata-eval 34.6%

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

      2. distribute-lft-neg-in 34.6%

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

      3. associate-*r* 34.7%

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

      4. *-commutative 34.7%

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

      5. associate-*r* 34.6%

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

      6. distribute-rgt-neg-in 34.6%

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

      7. distribute-lft-neg-in 34.6%

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

      8. metadata-eval 34.6%

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

      9. *-commutative 34.6%

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

   9. Simplified 34.6%

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

4. Final simplification 41.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -5.7 \cdot 10^{+26} \lor \neg \left(b \cdot c \leq 3.6 \cdot 10^{+50}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 37.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -9.2 \cdot 10^{+26} \lor \neg \left(b \cdot c \leq 1.95 \cdot 10^{+50}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(k \cdot j\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= (* b c) -9.2e+26) (not (<= (* b c) 1.95e+50)))
   (* b c)
   (* -27.0 (* k j))))

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) <= -9.2e+26) || !((b * c) <= 1.95e+50)) {
		tmp = b * c;
	} else {
		tmp = -27.0 * (k * j);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (((b * c) <= (-9.2d+26)) .or. (.not. ((b * c) <= 1.95d+50))) then
        tmp = b * c
    else
        tmp = (-27.0d0) * (k * j)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (((b * c) <= -9.2e+26) || !((b * c) <= 1.95e+50)) {
		tmp = b * c;
	} else {
		tmp = -27.0 * (k * j);
	}
	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) <= -9.2e+26) or not ((b * c) <= 1.95e+50):
		tmp = b * c
	else:
		tmp = -27.0 * (k * j)
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((Float64(b * c) <= -9.2e+26) || !(Float64(b * c) <= 1.95e+50))
		tmp = Float64(b * c);
	else
		tmp = Float64(-27.0 * Float64(k * j));
	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) <= -9.2e+26) || ~(((b * c) <= 1.95e+50)))
		tmp = b * c;
	else
		tmp = -27.0 * (k * j);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[N[(b * c), $MachinePrecision], -9.2e+26], N[Not[LessEqual[N[(b * c), $MachinePrecision], 1.95e+50]], $MachinePrecision]], N[(b * c), $MachinePrecision], N[(-27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -9.2000000000000002e26 or 1.94999999999999984e50 < (*.f64 b c)

   1. Initial program 77.3%

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

      1. pow1 77.3%

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

      2. associate-*l* 77.2%

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

      3. *-commutative 77.2%

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

   4. Applied egg-rr 77.2%

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

      1. unpow1 77.2%

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

      2. associate-*l* 79.0%

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

      3. *-commutative 79.0%

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

   6. Simplified 79.0%

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

   7. Taylor expanded in b around inf 50.3%

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

   if -9.2000000000000002e26 < (*.f64 b c) < 1.94999999999999984e50

   1. Initial program 86.9%

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

   3. Simplified 89.7%

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

   5. Taylor expanded in j around inf 34.6%

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

4. Final simplification 41.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -9.2 \cdot 10^{+26} \lor \neg \left(b \cdot c \leq 1.95 \cdot 10^{+50}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(k \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 48.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;k \leq -5.4 \cdot 10^{-14}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;k \leq 2.2 \cdot 10^{+133}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(-27 \cdot j\right)\\ \end{array} \end{array} \]

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 -5.4e-14)
   (* j (* k -27.0))
   (if (<= k 2.2e+133) (+ (* b c) (* -4.0 (* t a))) (* k (* -27.0 j)))))

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 <= -5.4e-14) {
		tmp = j * (k * -27.0);
	} else if (k <= 2.2e+133) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else {
		tmp = k * (-27.0 * j);
	}
	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 <= (-5.4d-14)) then
        tmp = j * (k * (-27.0d0))
    else if (k <= 2.2d+133) then
        tmp = (b * c) + ((-4.0d0) * (t * a))
    else
        tmp = k * ((-27.0d0) * j)
    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 <= -5.4e-14) {
		tmp = j * (k * -27.0);
	} else if (k <= 2.2e+133) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else {
		tmp = k * (-27.0 * j);
	}
	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 <= -5.4e-14:
		tmp = j * (k * -27.0)
	elif k <= 2.2e+133:
		tmp = (b * c) + (-4.0 * (t * a))
	else:
		tmp = k * (-27.0 * j)
	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 <= -5.4e-14)
		tmp = Float64(j * Float64(k * -27.0));
	elseif (k <= 2.2e+133)
		tmp = Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a)));
	else
		tmp = Float64(k * Float64(-27.0 * j));
	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 <= -5.4e-14)
		tmp = j * (k * -27.0);
	elseif (k <= 2.2e+133)
		tmp = (b * c) + (-4.0 * (t * a));
	else
		tmp = k * (-27.0 * j);
	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, -5.4e-14], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 2.2e+133], N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(k * N[(-27.0 * j), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if k < -5.3999999999999997e-14

   1. Initial program 83.1%

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

      1. pow1 83.1%

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

      2. associate-*l* 80.3%

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

      3. *-commutative 80.3%

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

   4. Applied egg-rr 80.3%

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

      1. unpow1 80.3%

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

      2. associate-*l* 83.1%

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

      3. *-commutative 83.1%

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

   6. Simplified 83.1%

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

   7. Taylor expanded in j around inf 35.3%

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

      1. metadata-eval 35.3%

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

      2. distribute-lft-neg-in 35.3%

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

      3. associate-*r* 35.4%

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

      4. *-commutative 35.4%

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

      5. associate-*r* 35.3%

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

      6. distribute-rgt-neg-in 35.3%

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

      7. distribute-lft-neg-in 35.3%

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

      8. metadata-eval 35.3%

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

      9. *-commutative 35.3%

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

   9. Simplified 35.3%

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

   if -5.3999999999999997e-14 < k < 2.2e133

   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 86.1%

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

   5. Taylor expanded in j around 0 78.2%

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

   6. Taylor expanded in i around 0 68.2%

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

   7. Taylor expanded in x around 0 53.2%

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

   if 2.2e133 < k

   1. Initial program 74.2%

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

   3. Simplified 74.1%

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

   5. Taylor expanded in j around inf 64.1%

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

      1. associate-*r* 64.1%

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

      2. *-commutative 64.1%

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

      3. metadata-eval 64.1%

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

      4. distribute-rgt-neg-in 64.1%

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

      5. *-commutative 64.1%

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

      6. distribute-rgt-neg-in 64.1%

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

      7. metadata-eval 64.1%

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

      8. *-commutative 64.1%

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

   7. Simplified 64.1%

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

4. Final simplification 49.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -5.4 \cdot 10^{-14}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;k \leq 2.2 \cdot 10^{+133}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(-27 \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 23.7% accurate, 10.3× speedup

Math

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

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 82.4%

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

   1. pow1 82.4%

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

   2. associate-*l* 82.0%

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

   3. *-commutative 82.0%

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

4. Applied egg-rr 82.0%

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

   1. unpow1 82.0%

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

   2. associate-*l* 84.0%

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

   3. *-commutative 84.0%

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

6. Simplified 84.0%

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

7. Taylor expanded in b around inf 27.3%

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

Developer target: 89.7% 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 2024105 
(FPCore (x y z t a b c i j k)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, E"
  :precision binary64

  :alt
  (if (< t -1.6210815397541398e-69) (- (- (* (* 18.0 t) (* (* x y) z)) (* (+ (* a t) (* i x)) 4.0)) (- (* (* k j) 27.0) (* c b))) (if (< t 165.68027943805222) (+ (- (* (* 18.0 y) (* x (* z t))) (* (+ (* a t) (* i x)) 4.0)) (- (* c b) (* 27.0 (* k j)))) (- (- (* (* 18.0 t) (* (* x y) z)) (* (+ (* a t) (* i x)) 4.0)) (- (* (* k j) 27.0) (* c b)))))

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