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

Percentage Accurate: 85.5% → 91.9%

Time: 18.2s

Alternatives: 22

Speedup: 0.8×

• 49.5% 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: 85.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 91.9% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x #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 94.4%

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

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

   1. Initial program 0.0%

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

   3. Simplified 27.3%

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

   5. Taylor expanded in z around inf 9.1%

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

   6. Taylor expanded in a around 0 30.3%

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

      1. associate-*r* 45.5%

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

      2. associate-*r* 45.5%

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

      3. associate-*r* 45.5%

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

      4. *-commutative 45.5%

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

   8. Simplified 45.5%

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

   9. Taylor expanded in x around inf 70.0%

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

       1. cancel-sign-sub-inv 70.0%

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

       2. associate-*r* 70.0%

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

       3. metadata-eval 70.0%

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

       4. *-commutative 70.0%

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

   11. Simplified 70.0%

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

4. Final simplification 91.3%

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

Alternative 2: 88.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\\ \mathbf{if}\;t \leq -1.5 \cdot 10^{-29} \lor \neg \left(t \leq 5 \cdot 10^{-79}\right):\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + z \cdot \left(y \cdot \left(x \cdot \left(18 \cdot t\right)\right)\right)\right) - t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (+ (* x (* 4.0 i)) (* j (* 27.0 k)))))
   (if (or (<= t -1.5e-29) (not (<= t 5e-79)))
     (- (+ (* b c) (* t (- (* (* x 18.0) (* y z)) (* a 4.0)))) t_1)
     (- (+ (* b c) (* z (* y (* x (* 18.0 t))))) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (x * (4.0 * i)) + (j * (27.0 * k));
	double tmp;
	if ((t <= -1.5e-29) || !(t <= 5e-79)) {
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - t_1;
	} else {
		tmp = ((b * c) + (z * (y * (x * (18.0 * t))))) - t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * (4.0d0 * i)) + (j * (27.0d0 * k))
    if ((t <= (-1.5d-29)) .or. (.not. (t <= 5d-79))) then
        tmp = ((b * c) + (t * (((x * 18.0d0) * (y * z)) - (a * 4.0d0)))) - t_1
    else
        tmp = ((b * c) + (z * (y * (x * (18.0d0 * t))))) - t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (x * (4.0 * i)) + (j * (27.0 * k));
	double tmp;
	if ((t <= -1.5e-29) || !(t <= 5e-79)) {
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - t_1;
	} else {
		tmp = ((b * c) + (z * (y * (x * (18.0 * t))))) - t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (x * (4.0 * i)) + (j * (27.0 * k))
	tmp = 0
	if (t <= -1.5e-29) or not (t <= 5e-79):
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - t_1
	else:
		tmp = ((b * c) + (z * (y * (x * (18.0 * t))))) - t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(x * Float64(4.0 * i)) + Float64(j * Float64(27.0 * k)))
	tmp = 0.0
	if ((t <= -1.5e-29) || !(t <= 5e-79))
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(Float64(x * 18.0) * Float64(y * z)) - Float64(a * 4.0)))) - t_1);
	else
		tmp = Float64(Float64(Float64(b * c) + Float64(z * Float64(y * Float64(x * Float64(18.0 * t))))) - t_1);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (x * (4.0 * i)) + (j * (27.0 * k));
	tmp = 0.0;
	if ((t <= -1.5e-29) || ~((t <= 5e-79)))
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - t_1;
	else
		tmp = ((b * c) + (z * (y * (x * (18.0 * t))))) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision] + N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t, -1.5e-29], N[Not[LessEqual[t, 5e-79]], $MachinePrecision]], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(N[(x * 18.0), $MachinePrecision] * N[(y * z), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] + N[(z * N[(y * N[(x * N[(18.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.5000000000000001e-29 or 4.99999999999999999e-79 < t

   1. Initial program 82.7%

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

   3. Simplified 85.5%

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

   if -1.5000000000000001e-29 < t < 4.99999999999999999e-79

   1. Initial program 81.5%

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

   3. Simplified 81.7%

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

   5. Taylor expanded in z around inf 86.1%

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

   6. Taylor expanded in a around 0 84.4%

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

      1. associate-*r* 92.3%

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

      2. associate-*r* 92.3%

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

      3. associate-*r* 92.3%

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

      4. *-commutative 92.3%

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

   8. Simplified 92.3%

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

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{-29} \lor \neg \left(t \leq 5 \cdot 10^{-79}\right):\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + z \cdot \left(y \cdot \left(x \cdot \left(18 \cdot t\right)\right)\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 81.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\\ \mathbf{if}\;a \cdot 4 \leq -2 \cdot 10^{+80}:\\ \;\;\;\;\left(b \cdot c + a \cdot \left(t \cdot -4\right)\right) - t\_1\\ \mathbf{elif}\;a \cdot 4 \leq 2 \cdot 10^{+122}:\\ \;\;\;\;\left(b \cdot c + z \cdot \left(y \cdot \left(x \cdot \left(18 \cdot t\right)\right)\right)\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (+ (* x (* 4.0 i)) (* j (* 27.0 k)))))
   (if (<= (* a 4.0) -2e+80)
     (- (+ (* b c) (* a (* t -4.0))) t_1)
     (if (<= (* a 4.0) 2e+122)
       (- (+ (* b c) (* z (* y (* x (* 18.0 t))))) t_1)
       (-
        (+ (* b c) (* -4.0 (* t a)))
        (+ (* 4.0 (* x i)) (* 27.0 (* j k))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (x * (4.0 * i)) + (j * (27.0 * k));
	double tmp;
	if ((a * 4.0) <= -2e+80) {
		tmp = ((b * c) + (a * (t * -4.0))) - t_1;
	} else if ((a * 4.0) <= 2e+122) {
		tmp = ((b * c) + (z * (y * (x * (18.0 * t))))) - t_1;
	} else {
		tmp = ((b * c) + (-4.0 * (t * a))) - ((4.0 * (x * i)) + (27.0 * (j * k)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * (4.0d0 * i)) + (j * (27.0d0 * k))
    if ((a * 4.0d0) <= (-2d+80)) then
        tmp = ((b * c) + (a * (t * (-4.0d0)))) - t_1
    else if ((a * 4.0d0) <= 2d+122) then
        tmp = ((b * c) + (z * (y * (x * (18.0d0 * t))))) - t_1
    else
        tmp = ((b * c) + ((-4.0d0) * (t * a))) - ((4.0d0 * (x * i)) + (27.0d0 * (j * k)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (x * (4.0 * i)) + (j * (27.0 * k));
	double tmp;
	if ((a * 4.0) <= -2e+80) {
		tmp = ((b * c) + (a * (t * -4.0))) - t_1;
	} else if ((a * 4.0) <= 2e+122) {
		tmp = ((b * c) + (z * (y * (x * (18.0 * t))))) - t_1;
	} else {
		tmp = ((b * c) + (-4.0 * (t * a))) - ((4.0 * (x * i)) + (27.0 * (j * k)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (x * (4.0 * i)) + (j * (27.0 * k))
	tmp = 0
	if (a * 4.0) <= -2e+80:
		tmp = ((b * c) + (a * (t * -4.0))) - t_1
	elif (a * 4.0) <= 2e+122:
		tmp = ((b * c) + (z * (y * (x * (18.0 * t))))) - t_1
	else:
		tmp = ((b * c) + (-4.0 * (t * a))) - ((4.0 * (x * i)) + (27.0 * (j * k)))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(x * Float64(4.0 * i)) + Float64(j * Float64(27.0 * k)))
	tmp = 0.0
	if (Float64(a * 4.0) <= -2e+80)
		tmp = Float64(Float64(Float64(b * c) + Float64(a * Float64(t * -4.0))) - t_1);
	elseif (Float64(a * 4.0) <= 2e+122)
		tmp = Float64(Float64(Float64(b * c) + Float64(z * Float64(y * Float64(x * Float64(18.0 * t))))) - t_1);
	else
		tmp = Float64(Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a))) - Float64(Float64(4.0 * Float64(x * i)) + Float64(27.0 * Float64(j * k))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (x * (4.0 * i)) + (j * (27.0 * k));
	tmp = 0.0;
	if ((a * 4.0) <= -2e+80)
		tmp = ((b * c) + (a * (t * -4.0))) - t_1;
	elseif ((a * 4.0) <= 2e+122)
		tmp = ((b * c) + (z * (y * (x * (18.0 * t))))) - t_1;
	else
		tmp = ((b * c) + (-4.0 * (t * a))) - ((4.0 * (x * i)) + (27.0 * (j * k)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision] + N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * 4.0), $MachinePrecision], -2e+80], N[(N[(N[(b * c), $MachinePrecision] + N[(a * N[(t * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[N[(a * 4.0), $MachinePrecision], 2e+122], N[(N[(N[(b * c), $MachinePrecision] + N[(z * N[(y * N[(x * N[(18.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision] + N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a #s(literal 4 binary64)) < -2e80

   1. Initial program 71.6%

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

   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 z around inf 64.3%

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

   6. Taylor expanded in z around 0 73.6%

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

      1. associate-*r* 73.6%

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

      2. *-commutative 73.6%

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

      3. associate-*r* 73.6%

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

   8. Simplified 73.6%

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

   if -2e80 < (*.f64 a #s(literal 4 binary64)) < 2.00000000000000003e122

   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 84.5%

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

   5. Taylor expanded in z around inf 83.7%

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

   6. Taylor expanded in a around 0 84.9%

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

      1. associate-*r* 86.0%

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

      2. associate-*r* 85.9%

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

      3. associate-*r* 85.9%

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

      4. *-commutative 85.9%

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

   8. Simplified 85.9%

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

   if 2.00000000000000003e122 < (*.f64 a #s(literal 4 binary64))

   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 87.2%

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

   5. Taylor expanded in y around 0 87.3%

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

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 4 \leq -2 \cdot 10^{+80}:\\ \;\;\;\;\left(b \cdot c + a \cdot \left(t \cdot -4\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{elif}\;a \cdot 4 \leq 2 \cdot 10^{+122}:\\ \;\;\;\;\left(b \cdot c + z \cdot \left(y \cdot \left(x \cdot \left(18 \cdot t\right)\right)\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 81.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\\ \mathbf{if}\;a \cdot 4 \leq -2 \cdot 10^{+80}:\\ \;\;\;\;\left(b \cdot c + a \cdot \left(t \cdot -4\right)\right) - t\_1\\ \mathbf{elif}\;a \cdot 4 \leq 2 \cdot 10^{+122}:\\ \;\;\;\;\left(b \cdot c + z \cdot \left(18 \cdot \left(t \cdot \left(x \cdot y\right)\right)\right)\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (+ (* x (* 4.0 i)) (* j (* 27.0 k)))))
   (if (<= (* a 4.0) -2e+80)
     (- (+ (* b c) (* a (* t -4.0))) t_1)
     (if (<= (* a 4.0) 2e+122)
       (- (+ (* b c) (* z (* 18.0 (* t (* x y))))) t_1)
       (-
        (+ (* b c) (* -4.0 (* t a)))
        (+ (* 4.0 (* x i)) (* 27.0 (* j k))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (x * (4.0 * i)) + (j * (27.0 * k));
	double tmp;
	if ((a * 4.0) <= -2e+80) {
		tmp = ((b * c) + (a * (t * -4.0))) - t_1;
	} else if ((a * 4.0) <= 2e+122) {
		tmp = ((b * c) + (z * (18.0 * (t * (x * y))))) - t_1;
	} else {
		tmp = ((b * c) + (-4.0 * (t * a))) - ((4.0 * (x * i)) + (27.0 * (j * k)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * (4.0d0 * i)) + (j * (27.0d0 * k))
    if ((a * 4.0d0) <= (-2d+80)) then
        tmp = ((b * c) + (a * (t * (-4.0d0)))) - t_1
    else if ((a * 4.0d0) <= 2d+122) then
        tmp = ((b * c) + (z * (18.0d0 * (t * (x * y))))) - t_1
    else
        tmp = ((b * c) + ((-4.0d0) * (t * a))) - ((4.0d0 * (x * i)) + (27.0d0 * (j * k)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (x * (4.0 * i)) + (j * (27.0 * k));
	double tmp;
	if ((a * 4.0) <= -2e+80) {
		tmp = ((b * c) + (a * (t * -4.0))) - t_1;
	} else if ((a * 4.0) <= 2e+122) {
		tmp = ((b * c) + (z * (18.0 * (t * (x * y))))) - t_1;
	} else {
		tmp = ((b * c) + (-4.0 * (t * a))) - ((4.0 * (x * i)) + (27.0 * (j * k)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (x * (4.0 * i)) + (j * (27.0 * k))
	tmp = 0
	if (a * 4.0) <= -2e+80:
		tmp = ((b * c) + (a * (t * -4.0))) - t_1
	elif (a * 4.0) <= 2e+122:
		tmp = ((b * c) + (z * (18.0 * (t * (x * y))))) - t_1
	else:
		tmp = ((b * c) + (-4.0 * (t * a))) - ((4.0 * (x * i)) + (27.0 * (j * k)))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(x * Float64(4.0 * i)) + Float64(j * Float64(27.0 * k)))
	tmp = 0.0
	if (Float64(a * 4.0) <= -2e+80)
		tmp = Float64(Float64(Float64(b * c) + Float64(a * Float64(t * -4.0))) - t_1);
	elseif (Float64(a * 4.0) <= 2e+122)
		tmp = Float64(Float64(Float64(b * c) + Float64(z * Float64(18.0 * Float64(t * Float64(x * y))))) - t_1);
	else
		tmp = Float64(Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a))) - Float64(Float64(4.0 * Float64(x * i)) + Float64(27.0 * Float64(j * k))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (x * (4.0 * i)) + (j * (27.0 * k));
	tmp = 0.0;
	if ((a * 4.0) <= -2e+80)
		tmp = ((b * c) + (a * (t * -4.0))) - t_1;
	elseif ((a * 4.0) <= 2e+122)
		tmp = ((b * c) + (z * (18.0 * (t * (x * y))))) - t_1;
	else
		tmp = ((b * c) + (-4.0 * (t * a))) - ((4.0 * (x * i)) + (27.0 * (j * k)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision] + N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * 4.0), $MachinePrecision], -2e+80], N[(N[(N[(b * c), $MachinePrecision] + N[(a * N[(t * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[N[(a * 4.0), $MachinePrecision], 2e+122], N[(N[(N[(b * c), $MachinePrecision] + N[(z * N[(18.0 * N[(t * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision] + N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a #s(literal 4 binary64)) < -2e80

   1. Initial program 71.6%

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

   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 z around inf 64.3%

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

   6. Taylor expanded in z around 0 73.6%

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

      1. associate-*r* 73.6%

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

      2. *-commutative 73.6%

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

      3. associate-*r* 73.6%

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

   8. Simplified 73.6%

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

   if -2e80 < (*.f64 a #s(literal 4 binary64)) < 2.00000000000000003e122

   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 84.5%

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

   5. Taylor expanded in z around inf 83.7%

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

   6. Taylor expanded in a around 0 84.9%

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

   if 2.00000000000000003e122 < (*.f64 a #s(literal 4 binary64))

   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 87.2%

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

   5. Taylor expanded in y around 0 87.3%

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

4. Final simplification 83.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 4 \leq -2 \cdot 10^{+80}:\\ \;\;\;\;\left(b \cdot c + a \cdot \left(t \cdot -4\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{elif}\;a \cdot 4 \leq 2 \cdot 10^{+122}:\\ \;\;\;\;\left(b \cdot c + z \cdot \left(18 \cdot \left(t \cdot \left(x \cdot y\right)\right)\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 69.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := 4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;b \cdot c \leq -2 \cdot 10^{+120}:\\ \;\;\;\;b \cdot c - \left(t\_1 + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 10^{+50}:\\ \;\;\;\;x \cdot \left(i \cdot -4 + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* 4.0 (* x i))))
   (if (<= (* b c) -2e+120)
     (- (* b c) (+ t_1 (* 27.0 (* j k))))
     (if (<= (* b c) 1e+50)
       (+ (* x (+ (* i -4.0) (* 18.0 (* t (* y z))))) (* j (* k -27.0)))
       (- (+ (* b c) (* -4.0 (* t a))) t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 4.0 * (x * i);
	double tmp;
	if ((b * c) <= -2e+120) {
		tmp = (b * c) - (t_1 + (27.0 * (j * k)));
	} else if ((b * c) <= 1e+50) {
		tmp = (x * ((i * -4.0) + (18.0 * (t * (y * z))))) + (j * (k * -27.0));
	} else {
		tmp = ((b * c) + (-4.0 * (t * a))) - t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 4.0d0 * (x * i)
    if ((b * c) <= (-2d+120)) then
        tmp = (b * c) - (t_1 + (27.0d0 * (j * k)))
    else if ((b * c) <= 1d+50) then
        tmp = (x * ((i * (-4.0d0)) + (18.0d0 * (t * (y * z))))) + (j * (k * (-27.0d0)))
    else
        tmp = ((b * c) + ((-4.0d0) * (t * a))) - t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 4.0 * (x * i);
	double tmp;
	if ((b * c) <= -2e+120) {
		tmp = (b * c) - (t_1 + (27.0 * (j * k)));
	} else if ((b * c) <= 1e+50) {
		tmp = (x * ((i * -4.0) + (18.0 * (t * (y * z))))) + (j * (k * -27.0));
	} else {
		tmp = ((b * c) + (-4.0 * (t * a))) - t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = 4.0 * (x * i)
	tmp = 0
	if (b * c) <= -2e+120:
		tmp = (b * c) - (t_1 + (27.0 * (j * k)))
	elif (b * c) <= 1e+50:
		tmp = (x * ((i * -4.0) + (18.0 * (t * (y * z))))) + (j * (k * -27.0))
	else:
		tmp = ((b * c) + (-4.0 * (t * a))) - t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(4.0 * Float64(x * i))
	tmp = 0.0
	if (Float64(b * c) <= -2e+120)
		tmp = Float64(Float64(b * c) - Float64(t_1 + Float64(27.0 * Float64(j * k))));
	elseif (Float64(b * c) <= 1e+50)
		tmp = Float64(Float64(x * Float64(Float64(i * -4.0) + Float64(18.0 * Float64(t * Float64(y * z))))) + Float64(j * Float64(k * -27.0)));
	else
		tmp = Float64(Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a))) - t_1);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = 4.0 * (x * i);
	tmp = 0.0;
	if ((b * c) <= -2e+120)
		tmp = (b * c) - (t_1 + (27.0 * (j * k)));
	elseif ((b * c) <= 1e+50)
		tmp = (x * ((i * -4.0) + (18.0 * (t * (y * z))))) + (j * (k * -27.0));
	else
		tmp = ((b * c) + (-4.0 * (t * a))) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -2e+120], N[(N[(b * c), $MachinePrecision] - N[(t$95$1 + N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1e+50], N[(N[(x * N[(N[(i * -4.0), $MachinePrecision] + N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -2e120

   1. Initial program 86.1%

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

   3. Simplified 88.9%

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

   5. Taylor expanded in t around 0 86.8%

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

   if -2e120 < (*.f64 b c) < 1.0000000000000001e50

   1. Initial program 81.8%

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

   3. Simplified 86.1%

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

   5. Taylor expanded in x around inf 69.6%

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

   if 1.0000000000000001e50 < (*.f64 b c)

   1. Initial program 81.1%

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

   3. Simplified 77.5%

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

   5. Taylor expanded in z around inf 83.0%

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

   6. Taylor expanded in z around 0 79.4%

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

      1. associate-*r* 79.4%

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

      2. *-commutative 79.4%

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

      3. associate-*r* 79.4%

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

   8. Simplified 79.4%

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

   9. Taylor expanded in j around 0 75.8%

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

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2 \cdot 10^{+120}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 10^{+50}:\\ \;\;\;\;x \cdot \left(i \cdot -4 + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 50.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := t\_1 + -4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;i \leq -2.06 \cdot 10^{+37}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq -8.5 \cdot 10^{-234}:\\ \;\;\;\;a \cdot \left(t \cdot -4\right) + t\_1\\ \mathbf{elif}\;i \leq 8.6 \cdot 10^{-305}:\\ \;\;\;\;x \cdot \left(t \cdot \left(z \cdot \left(y \cdot \left(--18\right)\right)\right)\right)\\ \mathbf{elif}\;i \leq 520000:\\ \;\;\;\;b \cdot c + t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0))) (t_2 (+ t_1 (* -4.0 (* x i)))))
   (if (<= i -2.06e+37)
     t_2
     (if (<= i -8.5e-234)
       (+ (* a (* t -4.0)) t_1)
       (if (<= i 8.6e-305)
         (* x (* t (* z (* y (- -18.0)))))
         (if (<= i 520000.0) (+ (* b c) t_1) t_2))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = t_1 + (-4.0 * (x * i));
	double tmp;
	if (i <= -2.06e+37) {
		tmp = t_2;
	} else if (i <= -8.5e-234) {
		tmp = (a * (t * -4.0)) + t_1;
	} else if (i <= 8.6e-305) {
		tmp = x * (t * (z * (y * -(-18.0))));
	} else if (i <= 520000.0) {
		tmp = (b * c) + t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * (k * (-27.0d0))
    t_2 = t_1 + ((-4.0d0) * (x * i))
    if (i <= (-2.06d+37)) then
        tmp = t_2
    else if (i <= (-8.5d-234)) then
        tmp = (a * (t * (-4.0d0))) + t_1
    else if (i <= 8.6d-305) then
        tmp = x * (t * (z * (y * -(-18.0d0))))
    else if (i <= 520000.0d0) then
        tmp = (b * c) + t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = t_1 + (-4.0 * (x * i));
	double tmp;
	if (i <= -2.06e+37) {
		tmp = t_2;
	} else if (i <= -8.5e-234) {
		tmp = (a * (t * -4.0)) + t_1;
	} else if (i <= 8.6e-305) {
		tmp = x * (t * (z * (y * -(-18.0))));
	} else if (i <= 520000.0) {
		tmp = (b * c) + t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	t_2 = t_1 + (-4.0 * (x * i))
	tmp = 0
	if i <= -2.06e+37:
		tmp = t_2
	elif i <= -8.5e-234:
		tmp = (a * (t * -4.0)) + t_1
	elif i <= 8.6e-305:
		tmp = x * (t * (z * (y * -(-18.0))))
	elif i <= 520000.0:
		tmp = (b * c) + t_1
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * -27.0))
	t_2 = Float64(t_1 + Float64(-4.0 * Float64(x * i)))
	tmp = 0.0
	if (i <= -2.06e+37)
		tmp = t_2;
	elseif (i <= -8.5e-234)
		tmp = Float64(Float64(a * Float64(t * -4.0)) + t_1);
	elseif (i <= 8.6e-305)
		tmp = Float64(x * Float64(t * Float64(z * Float64(y * Float64(-(-18.0))))));
	elseif (i <= 520000.0)
		tmp = Float64(Float64(b * c) + t_1);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * -27.0);
	t_2 = t_1 + (-4.0 * (x * i));
	tmp = 0.0;
	if (i <= -2.06e+37)
		tmp = t_2;
	elseif (i <= -8.5e-234)
		tmp = (a * (t * -4.0)) + t_1;
	elseif (i <= 8.6e-305)
		tmp = x * (t * (z * (y * -(-18.0))));
	elseif (i <= 520000.0)
		tmp = (b * c) + t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -2.06e+37], t$95$2, If[LessEqual[i, -8.5e-234], N[(N[(a * N[(t * -4.0), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[i, 8.6e-305], N[(x * N[(t * N[(z * N[(y * (--18.0)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 520000.0], N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if i < -2.05999999999999988e37 or 5.2e5 < i

   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 84.2%

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

   5. Taylor expanded in i around inf 59.7%

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

   if -2.05999999999999988e37 < i < -8.5000000000000005e-234

   1. Initial program 87.8%

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

   3. Simplified 86.0%

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

   5. Taylor expanded in a around inf 62.3%

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

      1. metadata-eval 62.3%

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

      2. distribute-lft-neg-in 62.3%

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

      3. *-commutative 62.3%

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

      4. associate-*l* 62.3%

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

      5. distribute-lft-neg-in 62.3%

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

      6. distribute-lft-neg-in 62.3%

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

      7. metadata-eval 62.3%

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

   7. Simplified 62.3%

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

   if -8.5000000000000005e-234 < i < 8.6000000000000004e-305

   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 90.9%

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

   5. Taylor expanded in z around inf 91.1%

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

   6. Taylor expanded in x around -inf 67.5%

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

      1. mul-1-neg 67.5%

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

      2. cancel-sign-sub-inv 67.5%

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

      3. associate-*r* 63.1%

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

      4. metadata-eval 63.1%

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

   8. Simplified 63.1%

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

   9. Taylor expanded in t around inf 53.9%

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

       1. *-commutative 53.9%

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

       2. *-commutative 53.9%

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

       3. associate-*l* 67.3%

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

       4. *-commutative 67.3%

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

       5. associate-*r* 67.4%

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

       6. associate-*r* 67.4%

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

       7. *-commutative 67.4%

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

       8. associate-*l* 67.4%

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

   11. Simplified 67.4%

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

   if 8.6000000000000004e-305 < i < 5.2e5

   1. Initial program 81.6%

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

   3. Simplified 84.3%

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

   5. Taylor expanded in b around inf 52.1%

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

4. Final simplification 58.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -2.06 \cdot 10^{+37}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;i \leq -8.5 \cdot 10^{-234}:\\ \;\;\;\;a \cdot \left(t \cdot -4\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;i \leq 8.6 \cdot 10^{-305}:\\ \;\;\;\;x \cdot \left(t \cdot \left(z \cdot \left(y \cdot \left(--18\right)\right)\right)\right)\\ \mathbf{elif}\;i \leq 520000:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(x \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 81.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{+50} \lor \neg \left(x \leq 3.3 \cdot 10^{+68}\right):\\ \;\;\;\;x \cdot \left(i \cdot -4 + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= x -3.6e+50) (not (<= x 3.3e+68)))
   (+ (* x (+ (* i -4.0) (* 18.0 (* t (* y z))))) (* j (* k -27.0)))
   (- (+ (* b c) (* -4.0 (* t a))) (+ (* 4.0 (* x i)) (* 27.0 (* j k))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((x <= -3.6e+50) || !(x <= 3.3e+68)) {
		tmp = (x * ((i * -4.0) + (18.0 * (t * (y * z))))) + (j * (k * -27.0));
	} else {
		tmp = ((b * c) + (-4.0 * (t * a))) - ((4.0 * (x * i)) + (27.0 * (j * k)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((x <= (-3.6d+50)) .or. (.not. (x <= 3.3d+68))) then
        tmp = (x * ((i * (-4.0d0)) + (18.0d0 * (t * (y * z))))) + (j * (k * (-27.0d0)))
    else
        tmp = ((b * c) + ((-4.0d0) * (t * a))) - ((4.0d0 * (x * i)) + (27.0d0 * (j * k)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((x <= -3.6e+50) || !(x <= 3.3e+68)) {
		tmp = (x * ((i * -4.0) + (18.0 * (t * (y * z))))) + (j * (k * -27.0));
	} else {
		tmp = ((b * c) + (-4.0 * (t * a))) - ((4.0 * (x * i)) + (27.0 * (j * k)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (x <= -3.6e+50) or not (x <= 3.3e+68):
		tmp = (x * ((i * -4.0) + (18.0 * (t * (y * z))))) + (j * (k * -27.0))
	else:
		tmp = ((b * c) + (-4.0 * (t * a))) - ((4.0 * (x * i)) + (27.0 * (j * k)))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((x <= -3.6e+50) || !(x <= 3.3e+68))
		tmp = Float64(Float64(x * Float64(Float64(i * -4.0) + Float64(18.0 * Float64(t * Float64(y * z))))) + Float64(j * Float64(k * -27.0)));
	else
		tmp = Float64(Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a))) - Float64(Float64(4.0 * Float64(x * i)) + Float64(27.0 * Float64(j * k))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((x <= -3.6e+50) || ~((x <= 3.3e+68)))
		tmp = (x * ((i * -4.0) + (18.0 * (t * (y * z))))) + (j * (k * -27.0));
	else
		tmp = ((b * c) + (-4.0 * (t * a))) - ((4.0 * (x * i)) + (27.0 * (j * k)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[x, -3.6e+50], N[Not[LessEqual[x, 3.3e+68]], $MachinePrecision]], N[(N[(x * N[(N[(i * -4.0), $MachinePrecision] + N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision] + N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.59999999999999986e50 or 3.3e68 < x

   1. Initial program 68.1%

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

   3. Simplified 79.2%

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

   5. Taylor expanded in x around inf 82.7%

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

   if -3.59999999999999986e50 < x < 3.3e68

   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 88.5%

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

   5. Taylor expanded in y around 0 85.2%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{+50} \lor \neg \left(x \leq 3.3 \cdot 10^{+68}\right):\\ \;\;\;\;x \cdot \left(i \cdot -4 + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 75.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{+43} \lor \neg \left(t \leq 1.25 \cdot 10^{+41}\right):\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(x \cdot \left(-4 \cdot \frac{a}{x} + 18 \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= t -6e+43) (not (<= t 1.25e+41)))
   (+ (* j (* k -27.0)) (* t (* x (+ (* -4.0 (/ a x)) (* 18.0 (* y z))))))
   (- (* b c) (+ (* 4.0 (* x i)) (* 27.0 (* j k))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((t <= -6e+43) || !(t <= 1.25e+41)) {
		tmp = (j * (k * -27.0)) + (t * (x * ((-4.0 * (a / x)) + (18.0 * (y * z)))));
	} else {
		tmp = (b * c) - ((4.0 * (x * i)) + (27.0 * (j * k)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((t <= (-6d+43)) .or. (.not. (t <= 1.25d+41))) then
        tmp = (j * (k * (-27.0d0))) + (t * (x * (((-4.0d0) * (a / x)) + (18.0d0 * (y * z)))))
    else
        tmp = (b * c) - ((4.0d0 * (x * i)) + (27.0d0 * (j * k)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((t <= -6e+43) || !(t <= 1.25e+41)) {
		tmp = (j * (k * -27.0)) + (t * (x * ((-4.0 * (a / x)) + (18.0 * (y * z)))));
	} else {
		tmp = (b * c) - ((4.0 * (x * i)) + (27.0 * (j * k)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (t <= -6e+43) or not (t <= 1.25e+41):
		tmp = (j * (k * -27.0)) + (t * (x * ((-4.0 * (a / x)) + (18.0 * (y * z)))))
	else:
		tmp = (b * c) - ((4.0 * (x * i)) + (27.0 * (j * k)))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((t <= -6e+43) || !(t <= 1.25e+41))
		tmp = Float64(Float64(j * Float64(k * -27.0)) + Float64(t * Float64(x * Float64(Float64(-4.0 * Float64(a / x)) + Float64(18.0 * Float64(y * z))))));
	else
		tmp = Float64(Float64(b * c) - Float64(Float64(4.0 * Float64(x * i)) + Float64(27.0 * Float64(j * k))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((t <= -6e+43) || ~((t <= 1.25e+41)))
		tmp = (j * (k * -27.0)) + (t * (x * ((-4.0 * (a / x)) + (18.0 * (y * z)))));
	else
		tmp = (b * c) - ((4.0 * (x * i)) + (27.0 * (j * k)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[t, -6e+43], N[Not[LessEqual[t, 1.25e+41]], $MachinePrecision]], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(t * N[(x * N[(N[(-4.0 * N[(a / x), $MachinePrecision]), $MachinePrecision] + N[(18.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] - N[(N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision] + N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6.00000000000000033e43 or 1.25000000000000006e41 < t

   1. Initial program 80.9%

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

   3. Simplified 88.2%

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

   5. Taylor expanded in x around inf 65.1%

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

   6. Taylor expanded in t around inf 76.0%

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

   if -6.00000000000000033e43 < t < 1.25000000000000006e41

   1. Initial program 83.3%

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

   3. Simplified 82.8%

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

   5. Taylor expanded in t around 0 74.4%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{+43} \lor \neg \left(t \leq 1.25 \cdot 10^{+41}\right):\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(x \cdot \left(-4 \cdot \frac{a}{x} + 18 \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 32.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := -4 \cdot \left(x \cdot i\right)\\ t_2 := j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;j \leq -4.8 \cdot 10^{+147}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -5.2 \cdot 10^{-65}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -2 \cdot 10^{-301}:\\ \;\;\;\;a \cdot \left(t \cdot -4\right)\\ \mathbf{elif}\;j \leq 3.5 \cdot 10^{-208}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 3.35 \cdot 10^{+41}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* -4.0 (* x i))) (t_2 (* j (* k -27.0))))
   (if (<= j -4.8e+147)
     t_2
     (if (<= j -5.2e-65)
       t_1
       (if (<= j -2e-301)
         (* a (* t -4.0))
         (if (<= j 3.5e-208) t_1 (if (<= j 3.35e+41) (* b c) t_2)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -4.0 * (x * i);
	double t_2 = j * (k * -27.0);
	double tmp;
	if (j <= -4.8e+147) {
		tmp = t_2;
	} else if (j <= -5.2e-65) {
		tmp = t_1;
	} else if (j <= -2e-301) {
		tmp = a * (t * -4.0);
	} else if (j <= 3.5e-208) {
		tmp = t_1;
	} else if (j <= 3.35e+41) {
		tmp = b * c;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (-4.0d0) * (x * i)
    t_2 = j * (k * (-27.0d0))
    if (j <= (-4.8d+147)) then
        tmp = t_2
    else if (j <= (-5.2d-65)) then
        tmp = t_1
    else if (j <= (-2d-301)) then
        tmp = a * (t * (-4.0d0))
    else if (j <= 3.5d-208) then
        tmp = t_1
    else if (j <= 3.35d+41) then
        tmp = b * c
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -4.0 * (x * i);
	double t_2 = j * (k * -27.0);
	double tmp;
	if (j <= -4.8e+147) {
		tmp = t_2;
	} else if (j <= -5.2e-65) {
		tmp = t_1;
	} else if (j <= -2e-301) {
		tmp = a * (t * -4.0);
	} else if (j <= 3.5e-208) {
		tmp = t_1;
	} else if (j <= 3.35e+41) {
		tmp = b * c;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = -4.0 * (x * i)
	t_2 = j * (k * -27.0)
	tmp = 0
	if j <= -4.8e+147:
		tmp = t_2
	elif j <= -5.2e-65:
		tmp = t_1
	elif j <= -2e-301:
		tmp = a * (t * -4.0)
	elif j <= 3.5e-208:
		tmp = t_1
	elif j <= 3.35e+41:
		tmp = b * c
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(-4.0 * Float64(x * i))
	t_2 = Float64(j * Float64(k * -27.0))
	tmp = 0.0
	if (j <= -4.8e+147)
		tmp = t_2;
	elseif (j <= -5.2e-65)
		tmp = t_1;
	elseif (j <= -2e-301)
		tmp = Float64(a * Float64(t * -4.0));
	elseif (j <= 3.5e-208)
		tmp = t_1;
	elseif (j <= 3.35e+41)
		tmp = Float64(b * c);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = -4.0 * (x * i);
	t_2 = j * (k * -27.0);
	tmp = 0.0;
	if (j <= -4.8e+147)
		tmp = t_2;
	elseif (j <= -5.2e-65)
		tmp = t_1;
	elseif (j <= -2e-301)
		tmp = a * (t * -4.0);
	elseif (j <= 3.5e-208)
		tmp = t_1;
	elseif (j <= 3.35e+41)
		tmp = b * c;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -4.8e+147], t$95$2, If[LessEqual[j, -5.2e-65], t$95$1, If[LessEqual[j, -2e-301], N[(a * N[(t * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.5e-208], t$95$1, If[LessEqual[j, 3.35e+41], N[(b * c), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -4.80000000000000004e147 or 3.3499999999999998e41 < j

   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 81.8%

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

   5. Taylor expanded in t around 0 69.5%

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

   6. Taylor expanded in i around 0 60.5%

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

      1. *-commutative 60.5%

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

      2. associate-*r* 60.5%

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

   8. Simplified 60.5%

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

   9. Taylor expanded in b around 0 52.5%

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

       1. *-commutative 52.5%

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

       2. *-commutative 52.5%

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

       3. associate-*r* 52.5%

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

   11. Simplified 52.5%

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

   12. Taylor expanded in k around 0 52.5%

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

       1. *-commutative 52.5%

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

       2. associate-*r* 52.5%

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

       3. *-commutative 52.5%

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

   14. Simplified 52.5%

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

   if -4.80000000000000004e147 < j < -5.20000000000000019e-65 or -2.00000000000000013e-301 < j < 3.49999999999999991e-208

   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 85.5%

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

   5. Taylor expanded in z around inf 84.1%

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

   6. Taylor expanded in i around inf 31.3%

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

      1. *-commutative 31.3%

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

   8. Simplified 31.3%

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

   if -5.20000000000000019e-65 < j < -2.00000000000000013e-301

   1. Initial program 80.3%

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

   3. Simplified 88.2%

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

   5. Taylor expanded in a around inf 37.4%

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

      1. metadata-eval 37.4%

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

      2. distribute-lft-neg-in 37.4%

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

      3. *-commutative 37.4%

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

      4. associate-*l* 37.4%

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

      5. distribute-lft-neg-in 37.4%

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

      6. distribute-lft-neg-in 37.4%

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

      7. metadata-eval 37.4%

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

   7. Simplified 37.4%

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

   8. Taylor expanded in j around inf 33.8%

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

   9. Taylor expanded in j around 0 29.6%

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

       1. *-commutative 29.6%

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

       2. associate-*r* 29.6%

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

       3. *-commutative 29.6%

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

   11. Simplified 29.6%

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

   if 3.49999999999999991e-208 < j < 3.3499999999999998e41

   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 85.0%

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

   5. Taylor expanded in z around inf 82.7%

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

   6. Taylor expanded in b around inf 35.5%

      \[\leadsto \color{blue}{b \cdot c} \]
3. Recombined 4 regimes into one program.

4. Final simplification 39.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -4.8 \cdot 10^{+147}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;j \leq -5.2 \cdot 10^{-65}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;j \leq -2 \cdot 10^{-301}:\\ \;\;\;\;a \cdot \left(t \cdot -4\right)\\ \mathbf{elif}\;j \leq 3.5 \cdot 10^{-208}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;j \leq 3.35 \cdot 10^{+41}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 59.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;x \leq -1.82 \cdot 10^{+31}:\\ \;\;\;\;x \cdot \left(4 \cdot \left(-i\right) - z \cdot \left(y \cdot \left(t \cdot -18\right)\right)\right)\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-244}:\\ \;\;\;\;b \cdot c + t\_1\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{+47}:\\ \;\;\;\;a \cdot \left(t \cdot -4\right) + t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0))))
   (if (<= x -1.82e+31)
     (* x (- (* 4.0 (- i)) (* z (* y (* t -18.0)))))
     (if (<= x 1.15e-244)
       (+ (* b c) t_1)
       (if (<= x 3.4e+47)
         (+ (* a (* t -4.0)) t_1)
         (* x (- (* 18.0 (* t (* y z))) (* 4.0 i))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double tmp;
	if (x <= -1.82e+31) {
		tmp = x * ((4.0 * -i) - (z * (y * (t * -18.0))));
	} else if (x <= 1.15e-244) {
		tmp = (b * c) + t_1;
	} else if (x <= 3.4e+47) {
		tmp = (a * (t * -4.0)) + t_1;
	} else {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * (k * (-27.0d0))
    if (x <= (-1.82d+31)) then
        tmp = x * ((4.0d0 * -i) - (z * (y * (t * (-18.0d0)))))
    else if (x <= 1.15d-244) then
        tmp = (b * c) + t_1
    else if (x <= 3.4d+47) then
        tmp = (a * (t * (-4.0d0))) + t_1
    else
        tmp = x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double tmp;
	if (x <= -1.82e+31) {
		tmp = x * ((4.0 * -i) - (z * (y * (t * -18.0))));
	} else if (x <= 1.15e-244) {
		tmp = (b * c) + t_1;
	} else if (x <= 3.4e+47) {
		tmp = (a * (t * -4.0)) + t_1;
	} else {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	tmp = 0
	if x <= -1.82e+31:
		tmp = x * ((4.0 * -i) - (z * (y * (t * -18.0))))
	elif x <= 1.15e-244:
		tmp = (b * c) + t_1
	elif x <= 3.4e+47:
		tmp = (a * (t * -4.0)) + t_1
	else:
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * -27.0))
	tmp = 0.0
	if (x <= -1.82e+31)
		tmp = Float64(x * Float64(Float64(4.0 * Float64(-i)) - Float64(z * Float64(y * Float64(t * -18.0)))));
	elseif (x <= 1.15e-244)
		tmp = Float64(Float64(b * c) + t_1);
	elseif (x <= 3.4e+47)
		tmp = Float64(Float64(a * Float64(t * -4.0)) + t_1);
	else
		tmp = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * -27.0);
	tmp = 0.0;
	if (x <= -1.82e+31)
		tmp = x * ((4.0 * -i) - (z * (y * (t * -18.0))));
	elseif (x <= 1.15e-244)
		tmp = (b * c) + t_1;
	elseif (x <= 3.4e+47)
		tmp = (a * (t * -4.0)) + t_1;
	else
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.82e+31], N[(x * N[(N[(4.0 * (-i)), $MachinePrecision] - N[(z * N[(y * N[(t * -18.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.15e-244], N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[x, 3.4e+47], N[(N[(a * N[(t * -4.0), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.8200000000000001e31

   1. Initial program 70.7%

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

   3. Simplified 75.7%

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

   5. Taylor expanded in z around inf 65.5%

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

   6. Taylor expanded in x around -inf 66.9%

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

      1. mul-1-neg 66.9%

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

      2. cancel-sign-sub-inv 66.9%

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

      3. associate-*r* 68.5%

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

      4. metadata-eval 68.5%

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

   8. Simplified 68.5%

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

   9. Taylor expanded in t around 0 66.9%

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

       1. associate-*r* 68.5%

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

       2. associate-*l* 68.5%

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

       3. *-commutative 68.5%

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

       4. associate-*r* 70.2%

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

   11. Simplified 70.2%

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

   if -1.8200000000000001e31 < x < 1.15e-244

   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 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 b around inf 63.2%

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

   if 1.15e-244 < x < 3.3999999999999998e47

   1. Initial program 92.0%

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

   3. Simplified 91.1%

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

   5. Taylor expanded in a around inf 53.6%

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

      1. metadata-eval 53.6%

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

      2. distribute-lft-neg-in 53.6%

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

      3. *-commutative 53.6%

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

      4. associate-*l* 53.6%

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

      5. distribute-lft-neg-in 53.6%

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

      6. distribute-lft-neg-in 53.6%

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

      7. metadata-eval 53.6%

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

   7. Simplified 53.6%

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

   if 3.3999999999999998e47 < x

   1. Initial program 66.7%

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

   3. Simplified 78.3%

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

   5. Taylor expanded in x around inf 82.6%

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

4. Final simplification 66.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.82 \cdot 10^{+31}:\\ \;\;\;\;x \cdot \left(4 \cdot \left(-i\right) - z \cdot \left(y \cdot \left(t \cdot -18\right)\right)\right)\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-244}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{+47}:\\ \;\;\;\;a \cdot \left(t \cdot -4\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 59.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;x \leq -3.6 \cdot 10^{+30}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) + i \cdot -4\right)\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-244}:\\ \;\;\;\;b \cdot c + t\_1\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{+46}:\\ \;\;\;\;a \cdot \left(t \cdot -4\right) + t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0))))
   (if (<= x -3.6e+30)
     (* x (+ (* 18.0 (* z (* y t))) (* i -4.0)))
     (if (<= x 1.2e-244)
       (+ (* b c) t_1)
       (if (<= x 1.8e+46)
         (+ (* a (* t -4.0)) t_1)
         (* x (- (* 18.0 (* t (* y z))) (* 4.0 i))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double tmp;
	if (x <= -3.6e+30) {
		tmp = x * ((18.0 * (z * (y * t))) + (i * -4.0));
	} else if (x <= 1.2e-244) {
		tmp = (b * c) + t_1;
	} else if (x <= 1.8e+46) {
		tmp = (a * (t * -4.0)) + t_1;
	} else {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * (k * (-27.0d0))
    if (x <= (-3.6d+30)) then
        tmp = x * ((18.0d0 * (z * (y * t))) + (i * (-4.0d0)))
    else if (x <= 1.2d-244) then
        tmp = (b * c) + t_1
    else if (x <= 1.8d+46) then
        tmp = (a * (t * (-4.0d0))) + t_1
    else
        tmp = x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double tmp;
	if (x <= -3.6e+30) {
		tmp = x * ((18.0 * (z * (y * t))) + (i * -4.0));
	} else if (x <= 1.2e-244) {
		tmp = (b * c) + t_1;
	} else if (x <= 1.8e+46) {
		tmp = (a * (t * -4.0)) + t_1;
	} else {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	tmp = 0
	if x <= -3.6e+30:
		tmp = x * ((18.0 * (z * (y * t))) + (i * -4.0))
	elif x <= 1.2e-244:
		tmp = (b * c) + t_1
	elif x <= 1.8e+46:
		tmp = (a * (t * -4.0)) + t_1
	else:
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * -27.0))
	tmp = 0.0
	if (x <= -3.6e+30)
		tmp = Float64(x * Float64(Float64(18.0 * Float64(z * Float64(y * t))) + Float64(i * -4.0)));
	elseif (x <= 1.2e-244)
		tmp = Float64(Float64(b * c) + t_1);
	elseif (x <= 1.8e+46)
		tmp = Float64(Float64(a * Float64(t * -4.0)) + t_1);
	else
		tmp = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * -27.0);
	tmp = 0.0;
	if (x <= -3.6e+30)
		tmp = x * ((18.0 * (z * (y * t))) + (i * -4.0));
	elseif (x <= 1.2e-244)
		tmp = (b * c) + t_1;
	elseif (x <= 1.8e+46)
		tmp = (a * (t * -4.0)) + t_1;
	else
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.6e+30], N[(x * N[(N[(18.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.2e-244], N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[x, 1.8e+46], N[(N[(a * N[(t * -4.0), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -3.6000000000000002e30

   1. Initial program 70.7%

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

   3. Simplified 75.7%

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

   5. Taylor expanded in z around inf 65.5%

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

   6. Taylor expanded in a around 0 63.9%

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

      1. associate-*r* 72.1%

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

      2. associate-*r* 72.1%

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

      3. associate-*r* 72.1%

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

      4. *-commutative 72.1%

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

   8. Simplified 72.1%

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

   9. Taylor expanded in x around inf 66.9%

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

       1. cancel-sign-sub-inv 66.9%

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

       2. associate-*r* 68.5%

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

       3. metadata-eval 68.5%

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

       4. *-commutative 68.5%

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

   11. Simplified 68.5%

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

   if -3.6000000000000002e30 < x < 1.20000000000000008e-244

   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 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 b around inf 63.2%

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

   if 1.20000000000000008e-244 < x < 1.7999999999999999e46

   1. Initial program 92.0%

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

   3. Simplified 91.1%

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

   5. Taylor expanded in a around inf 53.6%

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

      1. metadata-eval 53.6%

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

      2. distribute-lft-neg-in 53.6%

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

      3. *-commutative 53.6%

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

      4. associate-*l* 53.6%

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

      5. distribute-lft-neg-in 53.6%

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

      6. distribute-lft-neg-in 53.6%

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

      7. metadata-eval 53.6%

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

   7. Simplified 53.6%

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

   if 1.7999999999999999e46 < x

   1. Initial program 66.7%

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

   3. Simplified 78.3%

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

   5. Taylor expanded in x around inf 82.6%

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

4. Final simplification 66.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{+30}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) + i \cdot -4\right)\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-244}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{+46}:\\ \;\;\;\;a \cdot \left(t \cdot -4\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 59.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) + i \cdot -4\right)\\ \mathbf{if}\;x \leq -2.05 \cdot 10^{+33}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 10^{-244}:\\ \;\;\;\;b \cdot c + t\_1\\ \mathbf{elif}\;x \leq 5.7 \cdot 10^{+45}:\\ \;\;\;\;a \cdot \left(t \cdot -4\right) + t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0)))
        (t_2 (* x (+ (* 18.0 (* z (* y t))) (* i -4.0)))))
   (if (<= x -2.05e+33)
     t_2
     (if (<= x 1e-244)
       (+ (* b c) t_1)
       (if (<= x 5.7e+45) (+ (* a (* t -4.0)) t_1) t_2)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = x * ((18.0 * (z * (y * t))) + (i * -4.0));
	double tmp;
	if (x <= -2.05e+33) {
		tmp = t_2;
	} else if (x <= 1e-244) {
		tmp = (b * c) + t_1;
	} else if (x <= 5.7e+45) {
		tmp = (a * (t * -4.0)) + t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * (k * (-27.0d0))
    t_2 = x * ((18.0d0 * (z * (y * t))) + (i * (-4.0d0)))
    if (x <= (-2.05d+33)) then
        tmp = t_2
    else if (x <= 1d-244) then
        tmp = (b * c) + t_1
    else if (x <= 5.7d+45) then
        tmp = (a * (t * (-4.0d0))) + t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = x * ((18.0 * (z * (y * t))) + (i * -4.0));
	double tmp;
	if (x <= -2.05e+33) {
		tmp = t_2;
	} else if (x <= 1e-244) {
		tmp = (b * c) + t_1;
	} else if (x <= 5.7e+45) {
		tmp = (a * (t * -4.0)) + t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	t_2 = x * ((18.0 * (z * (y * t))) + (i * -4.0))
	tmp = 0
	if x <= -2.05e+33:
		tmp = t_2
	elif x <= 1e-244:
		tmp = (b * c) + t_1
	elif x <= 5.7e+45:
		tmp = (a * (t * -4.0)) + t_1
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * -27.0))
	t_2 = Float64(x * Float64(Float64(18.0 * Float64(z * Float64(y * t))) + Float64(i * -4.0)))
	tmp = 0.0
	if (x <= -2.05e+33)
		tmp = t_2;
	elseif (x <= 1e-244)
		tmp = Float64(Float64(b * c) + t_1);
	elseif (x <= 5.7e+45)
		tmp = Float64(Float64(a * Float64(t * -4.0)) + t_1);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * -27.0);
	t_2 = x * ((18.0 * (z * (y * t))) + (i * -4.0));
	tmp = 0.0;
	if (x <= -2.05e+33)
		tmp = t_2;
	elseif (x <= 1e-244)
		tmp = (b * c) + t_1;
	elseif (x <= 5.7e+45)
		tmp = (a * (t * -4.0)) + t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(18.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.05e+33], t$95$2, If[LessEqual[x, 1e-244], N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[x, 5.7e+45], N[(N[(a * N[(t * -4.0), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.04999999999999997e33 or 5.70000000000000027e45 < x

   1. Initial program 68.6%

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

   3. Simplified 77.0%

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

   5. Taylor expanded in z around inf 66.8%

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

   6. Taylor expanded in a around 0 67.8%

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

      1. associate-*r* 73.6%

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

      2. associate-*r* 72.8%

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

      3. associate-*r* 72.7%

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

      4. *-commutative 72.7%

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

   8. Simplified 72.7%

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

   9. Taylor expanded in x around inf 74.8%

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

       1. cancel-sign-sub-inv 74.8%

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

       2. associate-*r* 74.0%

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

       3. metadata-eval 74.0%

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

       4. *-commutative 74.0%

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

   11. Simplified 74.0%

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

   if -2.04999999999999997e33 < x < 9.9999999999999993e-245

   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 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 b around inf 63.2%

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

   if 9.9999999999999993e-245 < x < 5.70000000000000027e45

   1. Initial program 92.0%

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

   3. Simplified 91.1%

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

   5. Taylor expanded in a around inf 53.6%

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

      1. metadata-eval 53.6%

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

      2. distribute-lft-neg-in 53.6%

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

      3. *-commutative 53.6%

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

      4. associate-*l* 53.6%

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

      5. distribute-lft-neg-in 53.6%

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

      6. distribute-lft-neg-in 53.6%

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

      7. metadata-eval 53.6%

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

   7. Simplified 53.6%

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

4. Final simplification 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.05 \cdot 10^{+33}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) + i \cdot -4\right)\\ \mathbf{elif}\;x \leq 10^{-244}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq 5.7 \cdot 10^{+45}:\\ \;\;\;\;a \cdot \left(t \cdot -4\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) + i \cdot -4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 48.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{+50}:\\ \;\;\;\;-18 \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot \left(-t\right)\right)\right)\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{+55}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq 5.7 \cdot 10^{+259}:\\ \;\;\;\;x \cdot \left(t \cdot \left(z \cdot \left(y \cdot \left(--18\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(c + -4 \cdot \frac{x \cdot i}{b}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= x -3.6e+50)
   (* -18.0 (* (* y z) (* x (- t))))
   (if (<= x 4.6e+55)
     (+ (* b c) (* j (* k -27.0)))
     (if (<= x 5.7e+259)
       (* x (* t (* z (* y (- -18.0)))))
       (* b (+ c (* -4.0 (/ (* x i) b))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (x <= -3.6e+50) {
		tmp = -18.0 * ((y * z) * (x * -t));
	} else if (x <= 4.6e+55) {
		tmp = (b * c) + (j * (k * -27.0));
	} else if (x <= 5.7e+259) {
		tmp = x * (t * (z * (y * -(-18.0))));
	} else {
		tmp = b * (c + (-4.0 * ((x * i) / b)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (x <= (-3.6d+50)) then
        tmp = (-18.0d0) * ((y * z) * (x * -t))
    else if (x <= 4.6d+55) then
        tmp = (b * c) + (j * (k * (-27.0d0)))
    else if (x <= 5.7d+259) then
        tmp = x * (t * (z * (y * -(-18.0d0))))
    else
        tmp = b * (c + ((-4.0d0) * ((x * i) / b)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (x <= -3.6e+50) {
		tmp = -18.0 * ((y * z) * (x * -t));
	} else if (x <= 4.6e+55) {
		tmp = (b * c) + (j * (k * -27.0));
	} else if (x <= 5.7e+259) {
		tmp = x * (t * (z * (y * -(-18.0))));
	} else {
		tmp = b * (c + (-4.0 * ((x * i) / b)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if x <= -3.6e+50:
		tmp = -18.0 * ((y * z) * (x * -t))
	elif x <= 4.6e+55:
		tmp = (b * c) + (j * (k * -27.0))
	elif x <= 5.7e+259:
		tmp = x * (t * (z * (y * -(-18.0))))
	else:
		tmp = b * (c + (-4.0 * ((x * i) / b)))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (x <= -3.6e+50)
		tmp = Float64(-18.0 * Float64(Float64(y * z) * Float64(x * Float64(-t))));
	elseif (x <= 4.6e+55)
		tmp = Float64(Float64(b * c) + Float64(j * Float64(k * -27.0)));
	elseif (x <= 5.7e+259)
		tmp = Float64(x * Float64(t * Float64(z * Float64(y * Float64(-(-18.0))))));
	else
		tmp = Float64(b * Float64(c + Float64(-4.0 * Float64(Float64(x * i) / b))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (x <= -3.6e+50)
		tmp = -18.0 * ((y * z) * (x * -t));
	elseif (x <= 4.6e+55)
		tmp = (b * c) + (j * (k * -27.0));
	elseif (x <= 5.7e+259)
		tmp = x * (t * (z * (y * -(-18.0))));
	else
		tmp = b * (c + (-4.0 * ((x * i) / b)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[x, -3.6e+50], N[(-18.0 * N[(N[(y * z), $MachinePrecision] * N[(x * (-t)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.6e+55], N[(N[(b * c), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.7e+259], N[(x * N[(t * N[(z * N[(y * (--18.0)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(c + N[(-4.0 * N[(N[(x * i), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -3.59999999999999986e50

   1. Initial program 71.5%

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

   3. Simplified 77.1%

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

   5. Taylor expanded in z around inf 64.1%

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

   6. Taylor expanded in x around -inf 69.3%

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

      1. mul-1-neg 69.3%

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

      2. cancel-sign-sub-inv 69.3%

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

      3. associate-*r* 69.3%

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

      4. metadata-eval 69.3%

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

   8. Simplified 69.3%

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

   9. Taylor expanded in t around inf 44.7%

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

       1. associate-*r* 48.2%

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

   11. Simplified 48.2%

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

   if -3.59999999999999986e50 < x < 4.59999999999999975e55

   1. Initial program 92.6%

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

   3. Simplified 89.6%

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

   5. Taylor expanded in b around inf 52.3%

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

   if 4.59999999999999975e55 < x < 5.7e259

   1. Initial program 64.4%

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

   3. Simplified 79.0%

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

   5. Taylor expanded in z around inf 70.5%

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

   6. Taylor expanded in x around -inf 82.2%

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

      1. mul-1-neg 82.2%

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

      2. cancel-sign-sub-inv 82.2%

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

      3. associate-*r* 78.2%

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

      4. metadata-eval 78.2%

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

   8. Simplified 78.2%

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

   9. Taylor expanded in t around inf 59.2%

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

       1. *-commutative 59.2%

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

       2. *-commutative 59.2%

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

       3. associate-*l* 61.1%

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

       4. *-commutative 61.1%

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

       5. associate-*r* 61.1%

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

       6. associate-*r* 61.2%

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

       7. *-commutative 61.2%

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

       8. associate-*l* 61.2%

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

   11. Simplified 61.2%

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

   if 5.7e259 < x

   1. Initial program 67.3%

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

   3. Simplified 67.3%

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

   5. Taylor expanded in t around 0 78.6%

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

   6. Taylor expanded in b around inf 89.0%

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

   7. Taylor expanded in j around 0 89.0%

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

4. Final simplification 54.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{+50}:\\ \;\;\;\;-18 \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot \left(-t\right)\right)\right)\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{+55}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq 5.7 \cdot 10^{+259}:\\ \;\;\;\;x \cdot \left(t \cdot \left(z \cdot \left(y \cdot \left(--18\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(c + -4 \cdot \frac{x \cdot i}{b}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 71.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{+44} \lor \neg \left(t \leq 7.2 \cdot 10^{+41}\right):\\ \;\;\;\;t \cdot \left(-18 \cdot \left(\left(y \cdot z\right) \cdot \left(-x\right)\right) - a \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= t -3e+44) (not (<= t 7.2e+41)))
   (* t (- (* -18.0 (* (* y z) (- x))) (* a 4.0)))
   (- (* b c) (+ (* 4.0 (* x i)) (* 27.0 (* j k))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((t <= -3e+44) || !(t <= 7.2e+41)) {
		tmp = t * ((-18.0 * ((y * z) * -x)) - (a * 4.0));
	} else {
		tmp = (b * c) - ((4.0 * (x * i)) + (27.0 * (j * k)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((t <= (-3d+44)) .or. (.not. (t <= 7.2d+41))) then
        tmp = t * (((-18.0d0) * ((y * z) * -x)) - (a * 4.0d0))
    else
        tmp = (b * c) - ((4.0d0 * (x * i)) + (27.0d0 * (j * k)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((t <= -3e+44) || !(t <= 7.2e+41)) {
		tmp = t * ((-18.0 * ((y * z) * -x)) - (a * 4.0));
	} else {
		tmp = (b * c) - ((4.0 * (x * i)) + (27.0 * (j * k)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (t <= -3e+44) or not (t <= 7.2e+41):
		tmp = t * ((-18.0 * ((y * z) * -x)) - (a * 4.0))
	else:
		tmp = (b * c) - ((4.0 * (x * i)) + (27.0 * (j * k)))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((t <= -3e+44) || !(t <= 7.2e+41))
		tmp = Float64(t * Float64(Float64(-18.0 * Float64(Float64(y * z) * Float64(-x))) - Float64(a * 4.0)));
	else
		tmp = Float64(Float64(b * c) - Float64(Float64(4.0 * Float64(x * i)) + Float64(27.0 * Float64(j * k))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((t <= -3e+44) || ~((t <= 7.2e+41)))
		tmp = t * ((-18.0 * ((y * z) * -x)) - (a * 4.0));
	else
		tmp = (b * c) - ((4.0 * (x * i)) + (27.0 * (j * k)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[t, -3e+44], N[Not[LessEqual[t, 7.2e+41]], $MachinePrecision]], N[(t * N[(N[(-18.0 * N[(N[(y * z), $MachinePrecision] * (-x)), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] - N[(N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision] + N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.99999999999999987e44 or 7.20000000000000051e41 < t

   1. Initial program 80.7%

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

   3. Taylor expanded in t around -inf 70.5%

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

      1. associate-*r* 70.5%

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

      2. neg-mul-1 70.5%

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

      3. cancel-sign-sub-inv 70.5%

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

      4. metadata-eval 70.5%

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

      5. *-commutative 70.5%

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

      6. *-commutative 70.5%

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

   5. Simplified 70.5%

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

   if -2.99999999999999987e44 < t < 7.20000000000000051e41

   1. Initial program 83.4%

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

   3. Simplified 82.9%

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

   5. Taylor expanded in t around 0 74.6%

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

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{+44} \lor \neg \left(t \leq 7.2 \cdot 10^{+41}\right):\\ \;\;\;\;t \cdot \left(-18 \cdot \left(\left(y \cdot z\right) \cdot \left(-x\right)\right) - a \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 55.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;b \cdot c \leq -5 \cdot 10^{+113}:\\ \;\;\;\;b \cdot c + t\_1\\ \mathbf{elif}\;b \cdot c \leq 10^{+72}:\\ \;\;\;\;t\_1 + -4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(c + -4 \cdot \frac{x \cdot i}{b}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0))))
   (if (<= (* b c) -5e+113)
     (+ (* b c) t_1)
     (if (<= (* b c) 1e+72)
       (+ t_1 (* -4.0 (* x i)))
       (* b (+ c (* -4.0 (/ (* x i) b))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double tmp;
	if ((b * c) <= -5e+113) {
		tmp = (b * c) + t_1;
	} else if ((b * c) <= 1e+72) {
		tmp = t_1 + (-4.0 * (x * i));
	} else {
		tmp = b * (c + (-4.0 * ((x * i) / b)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * (k * (-27.0d0))
    if ((b * c) <= (-5d+113)) then
        tmp = (b * c) + t_1
    else if ((b * c) <= 1d+72) then
        tmp = t_1 + ((-4.0d0) * (x * i))
    else
        tmp = b * (c + ((-4.0d0) * ((x * i) / b)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double tmp;
	if ((b * c) <= -5e+113) {
		tmp = (b * c) + t_1;
	} else if ((b * c) <= 1e+72) {
		tmp = t_1 + (-4.0 * (x * i));
	} else {
		tmp = b * (c + (-4.0 * ((x * i) / b)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	tmp = 0
	if (b * c) <= -5e+113:
		tmp = (b * c) + t_1
	elif (b * c) <= 1e+72:
		tmp = t_1 + (-4.0 * (x * i))
	else:
		tmp = b * (c + (-4.0 * ((x * i) / b)))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * -27.0))
	tmp = 0.0
	if (Float64(b * c) <= -5e+113)
		tmp = Float64(Float64(b * c) + t_1);
	elseif (Float64(b * c) <= 1e+72)
		tmp = Float64(t_1 + Float64(-4.0 * Float64(x * i)));
	else
		tmp = Float64(b * Float64(c + Float64(-4.0 * Float64(Float64(x * i) / b))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * -27.0);
	tmp = 0.0;
	if ((b * c) <= -5e+113)
		tmp = (b * c) + t_1;
	elseif ((b * c) <= 1e+72)
		tmp = t_1 + (-4.0 * (x * i));
	else
		tmp = b * (c + (-4.0 * ((x * i) / b)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -5e+113], N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1e+72], N[(t$95$1 + N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(c + N[(-4.0 * N[(N[(x * i), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -5e113

   1. Initial program 86.5%

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

   3. Simplified 91.9%

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

   5. Taylor expanded in b around inf 76.8%

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

   if -5e113 < (*.f64 b c) < 9.99999999999999944e71

   1. Initial program 82.2%

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

   3. Simplified 86.4%

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

   5. Taylor expanded in i around inf 48.0%

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

   if 9.99999999999999944e71 < (*.f64 b c)

   1. Initial program 79.1%

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

   3. Simplified 75.2%

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

   5. Taylor expanded in t around 0 63.2%

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

   6. Taylor expanded in b around inf 65.3%

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

   7. Taylor expanded in j around 0 57.1%

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

4. Final simplification 53.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -5 \cdot 10^{+113}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 10^{+72}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(c + -4 \cdot \frac{x \cdot i}{b}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 48.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -3.7 \cdot 10^{+50} \lor \neg \left(x \leq 1.02 \cdot 10^{+56}\right):\\ \;\;\;\;-18 \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot \left(-t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= x -3.7e+50) (not (<= x 1.02e+56)))
   (* -18.0 (* (* y z) (* x (- t))))
   (+ (* 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);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((x <= -3.7e+50) || !(x <= 1.02e+56)) {
		tmp = -18.0 * ((y * z) * (x * -t));
	} else {
		tmp = (b * c) + (j * (k * -27.0));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((x <= (-3.7d+50)) .or. (.not. (x <= 1.02d+56))) then
        tmp = (-18.0d0) * ((y * z) * (x * -t))
    else
        tmp = (b * c) + (j * (k * (-27.0d0)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((x <= -3.7e+50) || !(x <= 1.02e+56)) {
		tmp = -18.0 * ((y * z) * (x * -t));
	} else {
		tmp = (b * c) + (j * (k * -27.0));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (x <= -3.7e+50) or not (x <= 1.02e+56):
		tmp = -18.0 * ((y * z) * (x * -t))
	else:
		tmp = (b * c) + (j * (k * -27.0))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((x <= -3.7e+50) || !(x <= 1.02e+56))
		tmp = Float64(-18.0 * Float64(Float64(y * z) * Float64(x * Float64(-t))));
	else
		tmp = Float64(Float64(b * c) + Float64(j * Float64(k * -27.0)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((x <= -3.7e+50) || ~((x <= 1.02e+56)))
		tmp = -18.0 * ((y * z) * (x * -t));
	else
		tmp = (b * c) + (j * (k * -27.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[x, -3.7e+50], N[Not[LessEqual[x, 1.02e+56]], $MachinePrecision]], N[(-18.0 * N[(N[(y * z), $MachinePrecision] * N[(x * (-t)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.7000000000000001e50 or 1.02e56 < x

   1. Initial program 68.1%

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

   3. Simplified 77.1%

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

   5. Taylor expanded in z around inf 65.3%

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

   6. Taylor expanded in x around -inf 76.6%

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

      1. mul-1-neg 76.6%

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

      2. cancel-sign-sub-inv 76.6%

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

      3. associate-*r* 74.8%

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

      4. metadata-eval 74.8%

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

   8. Simplified 74.8%

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

   9. Taylor expanded in t around inf 49.4%

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

       1. associate-*r* 52.8%

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

   11. Simplified 52.8%

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

   if -3.7000000000000001e50 < x < 1.02e56

   1. Initial program 92.6%

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

   3. Simplified 89.6%

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

   5. Taylor expanded in b around inf 52.3%

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

4. Final simplification 52.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.7 \cdot 10^{+50} \lor \neg \left(x \leq 1.02 \cdot 10^{+56}\right):\\ \;\;\;\;-18 \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot \left(-t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 32.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;j \leq -4 \cdot 10^{+147}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 4.2 \cdot 10^{-209}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;j \leq 4 \cdot 10^{+39}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0))))
   (if (<= j -4e+147)
     t_1
     (if (<= j 4.2e-209) (* -4.0 (* x i)) (if (<= j 4e+39) (* b c) t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double tmp;
	if (j <= -4e+147) {
		tmp = t_1;
	} else if (j <= 4.2e-209) {
		tmp = -4.0 * (x * i);
	} else if (j <= 4e+39) {
		tmp = b * c;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * (k * (-27.0d0))
    if (j <= (-4d+147)) then
        tmp = t_1
    else if (j <= 4.2d-209) then
        tmp = (-4.0d0) * (x * i)
    else if (j <= 4d+39) then
        tmp = b * c
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double tmp;
	if (j <= -4e+147) {
		tmp = t_1;
	} else if (j <= 4.2e-209) {
		tmp = -4.0 * (x * i);
	} else if (j <= 4e+39) {
		tmp = b * c;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	tmp = 0
	if j <= -4e+147:
		tmp = t_1
	elif j <= 4.2e-209:
		tmp = -4.0 * (x * i)
	elif j <= 4e+39:
		tmp = b * c
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * -27.0))
	tmp = 0.0
	if (j <= -4e+147)
		tmp = t_1;
	elseif (j <= 4.2e-209)
		tmp = Float64(-4.0 * Float64(x * i));
	elseif (j <= 4e+39)
		tmp = Float64(b * c);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * -27.0);
	tmp = 0.0;
	if (j <= -4e+147)
		tmp = t_1;
	elseif (j <= 4.2e-209)
		tmp = -4.0 * (x * i);
	elseif (j <= 4e+39)
		tmp = b * c;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -4e+147], t$95$1, If[LessEqual[j, 4.2e-209], N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 4e+39], N[(b * c), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if j < -3.9999999999999999e147 or 3.99999999999999976e39 < j

   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 81.8%

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

   5. Taylor expanded in t around 0 69.5%

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

   6. Taylor expanded in i around 0 60.5%

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

      1. *-commutative 60.5%

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

      2. associate-*r* 60.5%

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

   8. Simplified 60.5%

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

   9. Taylor expanded in b around 0 52.5%

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

       1. *-commutative 52.5%

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

       2. *-commutative 52.5%

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

       3. associate-*r* 52.5%

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

   11. Simplified 52.5%

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

   12. Taylor expanded in k around 0 52.5%

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

       1. *-commutative 52.5%

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

       2. associate-*r* 52.5%

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

       3. *-commutative 52.5%

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

   14. Simplified 52.5%

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

   if -3.9999999999999999e147 < j < 4.19999999999999991e-209

   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 85.0%

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

   5. Taylor expanded in z around inf 78.6%

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

   6. Taylor expanded in i around inf 27.1%

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

      1. *-commutative 27.1%

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

   8. Simplified 27.1%

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

   if 4.19999999999999991e-209 < j < 3.99999999999999976e39

   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 85.0%

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

   5. Taylor expanded in z around inf 82.7%

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

   6. Taylor expanded in b around inf 35.5%

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

4. Final simplification 37.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -4 \cdot 10^{+147}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;j \leq 4.2 \cdot 10^{-209}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;j \leq 4 \cdot 10^{+39}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 32.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot k\right) \cdot -27\\ \mathbf{if}\;j \leq -4.1 \cdot 10^{+147}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 9.2 \cdot 10^{-209}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;j \leq 3.4 \cdot 10^{+39}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j k) -27.0)))
   (if (<= j -4.1e+147)
     t_1
     (if (<= j 9.2e-209) (* -4.0 (* x i)) (if (<= j 3.4e+39) (* b c) t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * k) * -27.0;
	double tmp;
	if (j <= -4.1e+147) {
		tmp = t_1;
	} else if (j <= 9.2e-209) {
		tmp = -4.0 * (x * i);
	} else if (j <= 3.4e+39) {
		tmp = b * c;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (j * k) * (-27.0d0)
    if (j <= (-4.1d+147)) then
        tmp = t_1
    else if (j <= 9.2d-209) then
        tmp = (-4.0d0) * (x * i)
    else if (j <= 3.4d+39) then
        tmp = b * c
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * k) * -27.0;
	double tmp;
	if (j <= -4.1e+147) {
		tmp = t_1;
	} else if (j <= 9.2e-209) {
		tmp = -4.0 * (x * i);
	} else if (j <= 3.4e+39) {
		tmp = b * c;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * k) * -27.0
	tmp = 0
	if j <= -4.1e+147:
		tmp = t_1
	elif j <= 9.2e-209:
		tmp = -4.0 * (x * i)
	elif j <= 3.4e+39:
		tmp = b * c
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * k) * -27.0)
	tmp = 0.0
	if (j <= -4.1e+147)
		tmp = t_1;
	elseif (j <= 9.2e-209)
		tmp = Float64(-4.0 * Float64(x * i));
	elseif (j <= 3.4e+39)
		tmp = Float64(b * c);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * k) * -27.0;
	tmp = 0.0;
	if (j <= -4.1e+147)
		tmp = t_1;
	elseif (j <= 9.2e-209)
		tmp = -4.0 * (x * i);
	elseif (j <= 3.4e+39)
		tmp = b * c;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * k), $MachinePrecision] * -27.0), $MachinePrecision]}, If[LessEqual[j, -4.1e+147], t$95$1, If[LessEqual[j, 9.2e-209], N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.4e+39], N[(b * c), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if j < -4.09999999999999966e147 or 3.3999999999999999e39 < j

   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 81.8%

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

   5. Taylor expanded in j around inf 52.5%

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

   if -4.09999999999999966e147 < j < 9.1999999999999999e-209

   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 85.0%

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

   5. Taylor expanded in z around inf 78.6%

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

   6. Taylor expanded in i around inf 27.1%

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

      1. *-commutative 27.1%

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

   8. Simplified 27.1%

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

   if 9.1999999999999999e-209 < j < 3.3999999999999999e39

   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 85.0%

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

   5. Taylor expanded in z around inf 82.7%

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

   6. Taylor expanded in b around inf 35.5%

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

4. Final simplification 37.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -4.1 \cdot 10^{+147}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \mathbf{elif}\;j \leq 9.2 \cdot 10^{-209}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;j \leq 3.4 \cdot 10^{+39}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 50.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;k \leq -1.3 \cdot 10^{-109} \lor \neg \left(k \leq 1.4 \cdot 10^{+37}\right):\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= k -1.3e-109) (not (<= k 1.4e+37)))
   (+ (* b c) (* j (* k -27.0)))
   (- (* b c) (* 4.0 (* x i)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((k <= -1.3e-109) || !(k <= 1.4e+37)) {
		tmp = (b * c) + (j * (k * -27.0));
	} else {
		tmp = (b * c) - (4.0 * (x * i));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((k <= (-1.3d-109)) .or. (.not. (k <= 1.4d+37))) then
        tmp = (b * c) + (j * (k * (-27.0d0)))
    else
        tmp = (b * c) - (4.0d0 * (x * i))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((k <= -1.3e-109) || !(k <= 1.4e+37)) {
		tmp = (b * c) + (j * (k * -27.0));
	} else {
		tmp = (b * c) - (4.0 * (x * i));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (k <= -1.3e-109) or not (k <= 1.4e+37):
		tmp = (b * c) + (j * (k * -27.0))
	else:
		tmp = (b * c) - (4.0 * (x * i))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((k <= -1.3e-109) || !(k <= 1.4e+37))
		tmp = Float64(Float64(b * c) + Float64(j * Float64(k * -27.0)));
	else
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((k <= -1.3e-109) || ~((k <= 1.4e+37)))
		tmp = (b * c) + (j * (k * -27.0));
	else
		tmp = (b * c) - (4.0 * (x * i));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[k, -1.3e-109], N[Not[LessEqual[k, 1.4e+37]], $MachinePrecision]], N[(N[(b * c), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if k < -1.2999999999999999e-109 or 1.3999999999999999e37 < k

   1. Initial program 81.0%

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

   3. Simplified 83.2%

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

   5. Taylor expanded in b around inf 49.4%

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

   if -1.2999999999999999e-109 < k < 1.3999999999999999e37

   1. Initial program 84.1%

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

   3. Simplified 86.0%

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

   5. Taylor expanded in t around 0 51.7%

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

   6. Taylor expanded in i around inf 48.7%

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

      1. *-commutative 48.7%

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

   8. Simplified 48.7%

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

4. Final simplification 49.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -1.3 \cdot 10^{-109} \lor \neg \left(k \leq 1.4 \cdot 10^{+37}\right):\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 47.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;i \leq -1.32 \cdot 10^{+186} \lor \neg \left(i \leq 1.32 \cdot 10^{+108}\right):\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= i -1.32e+186) (not (<= i 1.32e+108)))
   (* -4.0 (* x i))
   (+ (* 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);
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 ((i <= -1.32e+186) || !(i <= 1.32e+108)) {
		tmp = -4.0 * (x * i);
	} else {
		tmp = (b * c) + (j * (k * -27.0));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((i <= (-1.32d+186)) .or. (.not. (i <= 1.32d+108))) then
        tmp = (-4.0d0) * (x * i)
    else
        tmp = (b * c) + (j * (k * (-27.0d0)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((i <= -1.32e+186) || !(i <= 1.32e+108)) {
		tmp = -4.0 * (x * i);
	} else {
		tmp = (b * c) + (j * (k * -27.0));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (i <= -1.32e+186) or not (i <= 1.32e+108):
		tmp = -4.0 * (x * i)
	else:
		tmp = (b * c) + (j * (k * -27.0))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((i <= -1.32e+186) || !(i <= 1.32e+108))
		tmp = Float64(-4.0 * Float64(x * i));
	else
		tmp = Float64(Float64(b * c) + Float64(j * Float64(k * -27.0)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((i <= -1.32e+186) || ~((i <= 1.32e+108)))
		tmp = -4.0 * (x * i);
	else
		tmp = (b * c) + (j * (k * -27.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[i, -1.32e+186], N[Not[LessEqual[i, 1.32e+108]], $MachinePrecision]], N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -1.32000000000000005e186 or 1.32000000000000013e108 < i

   1. Initial program 75.1%

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

   3. Simplified 83.9%

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

   5. Taylor expanded in z around inf 69.9%

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

   6. Taylor expanded in i around inf 59.5%

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

      1. *-commutative 59.5%

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

   8. Simplified 59.5%

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

   if -1.32000000000000005e186 < i < 1.32000000000000013e108

   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 84.4%

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

   5. Taylor expanded in b around inf 45.8%

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

4. Final simplification 48.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.32 \cdot 10^{+186} \lor \neg \left(i \leq 1.32 \cdot 10^{+108}\right):\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 36.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -4.5 \cdot 10^{+305} \lor \neg \left(b \cdot c \leq 1.46 \cdot 10^{+138}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= (* b c) -4.5e+305) (not (<= (* b c) 1.46e+138)))
   (* 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);
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) <= -4.5e+305) || !((b * c) <= 1.46e+138)) {
		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.
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) <= (-4.5d+305)) .or. (.not. ((b * c) <= 1.46d+138))) 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;
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) <= -4.5e+305) || !((b * c) <= 1.46e+138)) {
		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])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if ((b * c) <= -4.5e+305) or not ((b * c) <= 1.46e+138):
		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])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((Float64(b * c) <= -4.5e+305) || !(Float64(b * c) <= 1.46e+138))
		tmp = Float64(b * c);
	else
		tmp = Float64(Float64(j * k) * -27.0);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (((b * c) <= -4.5e+305) || ~(((b * c) <= 1.46e+138)))
		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.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[N[(b * c), $MachinePrecision], -4.5e+305], N[Not[LessEqual[N[(b * c), $MachinePrecision], 1.46e+138]], $MachinePrecision]], N[(b * c), $MachinePrecision], N[(N[(j * k), $MachinePrecision] * -27.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -4.5000000000000003e305 or 1.45999999999999995e138 < (*.f64 b c)

   1. Initial program 78.0%

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

   3. Simplified 76.1%

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

   5. Taylor expanded in z around inf 82.0%

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

   6. Taylor expanded in b around inf 61.3%

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

   if -4.5000000000000003e305 < (*.f64 b c) < 1.45999999999999995e138

   1. Initial program 83.3%

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

   3. Simplified 86.8%

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

   5. Taylor expanded in j around inf 27.8%

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

4. Final simplification 34.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -4.5 \cdot 10^{+305} \lor \neg \left(b \cdot c \leq 1.46 \cdot 10^{+138}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 22.6% accurate, 10.3× speedup

Math

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

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k) :precision binary64 (* b c))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	return b * c;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    code = b * c
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	return b * c;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	return b * c

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	return Float64(b * c)
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp = code(x, y, z, t, a, b, c, i, j, k)
	tmp = b * c;
end

Wolfram

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

Derivation

1. Initial program 82.2%

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

3. Simplified 83.9%

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

5. Taylor expanded in z around inf 78.4%

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

6. Taylor expanded in b around inf 18.6%

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

Developer Target 1: 89.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a \cdot t + i \cdot x\right) \cdot 4\\ t_2 := \left(\left(18 \cdot t\right) \cdot \left(\left(x \cdot y\right) \cdot z\right) - t\_1\right) - \left(\left(k \cdot j\right) \cdot 27 - c \cdot b\right)\\ \mathbf{if}\;t < -1.6210815397541398 \cdot 10^{-69}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t < 165.68027943805222:\\ \;\;\;\;\left(\left(18 \cdot y\right) \cdot \left(x \cdot \left(z \cdot t\right)\right) - t\_1\right) + \left(c \cdot b - 27 \cdot \left(k \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (+ (* a t) (* i x)) 4.0))
        (t_2
         (-
          (- (* (* 18.0 t) (* (* x y) z)) t_1)
          (- (* (* k j) 27.0) (* c b)))))
   (if (< t -1.6210815397541398e-69)
     t_2
     (if (< t 165.68027943805222)
       (+ (- (* (* 18.0 y) (* x (* z t))) t_1) (- (* c b) (* 27.0 (* k j))))
       t_2))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((a * t) + (i * x)) * 4.0;
	double t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b));
	double tmp;
	if (t < -1.6210815397541398e-69) {
		tmp = t_2;
	} else if (t < 165.68027943805222) {
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((a * t) + (i * x)) * 4.0d0
    t_2 = (((18.0d0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0d0) - (c * b))
    if (t < (-1.6210815397541398d-69)) then
        tmp = t_2
    else if (t < 165.68027943805222d0) then
        tmp = (((18.0d0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0d0 * (k * j)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((a * t) + (i * x)) * 4.0;
	double t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b));
	double tmp;
	if (t < -1.6210815397541398e-69) {
		tmp = t_2;
	} else if (t < 165.68027943805222) {
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = ((a * t) + (i * x)) * 4.0
	t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b))
	tmp = 0
	if t < -1.6210815397541398e-69:
		tmp = t_2
	elif t < 165.68027943805222:
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(Float64(a * t) + Float64(i * x)) * 4.0)
	t_2 = Float64(Float64(Float64(Float64(18.0 * t) * Float64(Float64(x * y) * z)) - t_1) - Float64(Float64(Float64(k * j) * 27.0) - Float64(c * b)))
	tmp = 0.0
	if (t < -1.6210815397541398e-69)
		tmp = t_2;
	elseif (t < 165.68027943805222)
		tmp = Float64(Float64(Float64(Float64(18.0 * y) * Float64(x * Float64(z * t))) - t_1) + Float64(Float64(c * b) - Float64(27.0 * Float64(k * j))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = ((a * t) + (i * x)) * 4.0;
	t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b));
	tmp = 0.0;
	if (t < -1.6210815397541398e-69)
		tmp = t_2;
	elseif (t < 165.68027943805222)
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(N[(a * t), $MachinePrecision] + N[(i * x), $MachinePrecision]), $MachinePrecision] * 4.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(18.0 * t), $MachinePrecision] * N[(N[(x * y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] - N[(N[(N[(k * j), $MachinePrecision] * 27.0), $MachinePrecision] - N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -1.6210815397541398e-69], t$95$2, If[Less[t, 165.68027943805222], N[(N[(N[(N[(18.0 * y), $MachinePrecision] * N[(x * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] + N[(N[(c * b), $MachinePrecision] - N[(27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2024160 
(FPCore (x y z t a b c i j k)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, E"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< t -8105407698770699/5000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (- (* (* 18 t) (* (* x y) z)) (* (+ (* a t) (* i x)) 4)) (- (* (* k j) 27) (* c b))) (if (< t 8284013971902611/50000000000000) (+ (- (* (* 18 y) (* x (* z t))) (* (+ (* a t) (* i x)) 4)) (- (* c b) (* 27 (* k j)))) (- (- (* (* 18 t) (* (* x y) z)) (* (+ (* a t) (* i x)) 4)) (- (* (* k j) 27) (* c b))))))

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