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

Percentage Accurate: 85.0% → 92.2%

Time: 20.7s

Alternatives: 23

Speedup: 0.8×

• 51.2% 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: 85.0% 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: 92.2% accurate, 0.5× speedup

Math

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

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1
         (-
          (-
           (- (* b c) (- (* t (* a 4.0)) (* (* (* (* x 18.0) y) z) t)))
           (* (* x 4.0) i))
          (* (* j 27.0) k))))
   (if (<= t_1 INFINITY) 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);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (((b * c) - ((t * (a * 4.0)) - ((((x * 18.0) * y) * z) * t))) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	}
	return tmp;
}

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (((b * c) - ((t * (a * 4.0)) - ((((x * 18.0) * y) * z) * t))) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = 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])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (((b * c) - ((t * (a * 4.0)) - ((((x * 18.0) * y) * z) * t))) - ((x * 4.0) * i)) - ((j * 27.0) * k)
	tmp = 0
	if t_1 <= math.inf:
		tmp = 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])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(Float64(Float64(b * c) - Float64(Float64(t * Float64(a * 4.0)) - Float64(Float64(Float64(Float64(x * 18.0) * y) * z) * t))) - 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(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])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (((b * c) - ((t * (a * 4.0)) - ((((x * 18.0) * y) * z) * t))) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = 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.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(N[(N[(b * c), $MachinePrecision] - N[(N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]), $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[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 95.6%

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

   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 32.4%

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

   5. Taylor expanded in x around inf 70.6%

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

4. Final simplification 91.9%

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

Alternative 2: 79.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + i \cdot -4\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;x \leq -3 \cdot 10^{+148}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -6.2 \cdot 10^{-81}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;x \leq 2.85 \cdot 10^{-129}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{+107}:\\ \;\;\;\;\left(b \cdot c + \left(x \cdot \left(18 \cdot y\right)\right) \cdot \left(z \cdot t\right)\right) - \left(j \cdot \left(27 \cdot k\right) + x \cdot \left(4 \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1
         (+ (* x (+ (* 18.0 (* t (* y z))) (* i -4.0))) (* j (* k -27.0)))))
   (if (<= x -3e+148)
     t_1
     (if (<= x -6.2e-81)
       (-
        (+ (* b c) (* t (- (* 18.0 (* x (* y z))) (* a 4.0))))
        (* 4.0 (* x i)))
       (if (<= x 2.85e-129)
         (- (- (* b c) (* 4.0 (* t a))) (* (* j 27.0) k))
         (if (<= x 1.4e+107)
           (-
            (+ (* b c) (* (* x (* 18.0 y)) (* z t)))
            (+ (* j (* 27.0 k)) (* x (* 4.0 i))))
           t_1))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (x * ((18.0 * (t * (y * z))) + (i * -4.0))) + (j * (k * -27.0));
	double tmp;
	if (x <= -3e+148) {
		tmp = t_1;
	} else if (x <= -6.2e-81) {
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - (4.0 * (x * i));
	} else if (x <= 2.85e-129) {
		tmp = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k);
	} else if (x <= 1.4e+107) {
		tmp = ((b * c) + ((x * (18.0 * y)) * (z * t))) - ((j * (27.0 * k)) + (x * (4.0 * i)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * ((18.0d0 * (t * (y * z))) + (i * (-4.0d0)))) + (j * (k * (-27.0d0)))
    if (x <= (-3d+148)) then
        tmp = t_1
    else if (x <= (-6.2d-81)) then
        tmp = ((b * c) + (t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0)))) - (4.0d0 * (x * i))
    else if (x <= 2.85d-129) then
        tmp = ((b * c) - (4.0d0 * (t * a))) - ((j * 27.0d0) * k)
    else if (x <= 1.4d+107) then
        tmp = ((b * c) + ((x * (18.0d0 * y)) * (z * t))) - ((j * (27.0d0 * k)) + (x * (4.0d0 * i)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (x * ((18.0 * (t * (y * z))) + (i * -4.0))) + (j * (k * -27.0));
	double tmp;
	if (x <= -3e+148) {
		tmp = t_1;
	} else if (x <= -6.2e-81) {
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - (4.0 * (x * i));
	} else if (x <= 2.85e-129) {
		tmp = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k);
	} else if (x <= 1.4e+107) {
		tmp = ((b * c) + ((x * (18.0 * y)) * (z * t))) - ((j * (27.0 * k)) + (x * (4.0 * i)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (x * ((18.0 * (t * (y * z))) + (i * -4.0))) + (j * (k * -27.0))
	tmp = 0
	if x <= -3e+148:
		tmp = t_1
	elif x <= -6.2e-81:
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - (4.0 * (x * i))
	elif x <= 2.85e-129:
		tmp = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k)
	elif x <= 1.4e+107:
		tmp = ((b * c) + ((x * (18.0 * y)) * (z * t))) - ((j * (27.0 * k)) + (x * (4.0 * i)))
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) + Float64(i * -4.0))) + Float64(j * Float64(k * -27.0)))
	tmp = 0.0
	if (x <= -3e+148)
		tmp = t_1;
	elseif (x <= -6.2e-81)
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)))) - Float64(4.0 * Float64(x * i)));
	elseif (x <= 2.85e-129)
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(t * a))) - Float64(Float64(j * 27.0) * k));
	elseif (x <= 1.4e+107)
		tmp = Float64(Float64(Float64(b * c) + Float64(Float64(x * Float64(18.0 * y)) * Float64(z * t))) - Float64(Float64(j * Float64(27.0 * k)) + Float64(x * Float64(4.0 * i))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (x * ((18.0 * (t * (y * z))) + (i * -4.0))) + (j * (k * -27.0));
	tmp = 0.0;
	if (x <= -3e+148)
		tmp = t_1;
	elseif (x <= -6.2e-81)
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - (4.0 * (x * i));
	elseif (x <= 2.85e-129)
		tmp = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k);
	elseif (x <= 1.4e+107)
		tmp = ((b * c) + ((x * (18.0 * y)) * (z * t))) - ((j * (27.0 * k)) + (x * (4.0 * i)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3e+148], t$95$1, If[LessEqual[x, -6.2e-81], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.85e-129], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.4e+107], N[(N[(N[(b * c), $MachinePrecision] + N[(N[(x * N[(18.0 * y), $MachinePrecision]), $MachinePrecision] * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision] + N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -3.00000000000000015e148 or 1.39999999999999992e107 < x

   1. Initial program 63.9%

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

   3. Simplified 77.9%

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

   5. Taylor expanded in x around inf 84.5%

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

   if -3.00000000000000015e148 < x < -6.19999999999999976e-81

   1. Initial program 77.0%

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

   3. Simplified 83.5%

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

   5. Taylor expanded in j around 0 87.9%

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

   if -6.19999999999999976e-81 < x < 2.85e-129

   1. Initial program 98.5%

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

   3. Taylor expanded in x around 0 90.9%

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

   if 2.85e-129 < x < 1.39999999999999992e107

   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 94.0%

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

      1. associate-*r* 92.0%

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

      2. distribute-rgt-out-- 92.0%

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

      3. associate-+l- 92.0%

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

      4. associate-*l* 95.9%

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

      5. fmm-def 95.9%

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

      6. associate-*l* 95.9%

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

      7. *-commutative 95.9%

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

   6. Applied egg-rr 95.9%

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

      1. fmm-undef 95.9%

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

      2. *-commutative 95.9%

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

      3. associate-*r* 95.9%

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

      4. *-commutative 95.9%

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

      5. *-commutative 95.9%

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

      6. *-commutative 95.9%

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

      7. associate-*l* 95.9%

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

      8. *-commutative 95.9%

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

      9. *-commutative 95.9%

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

   8. Simplified 95.9%

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

   9. Taylor expanded in a around 0 93.8%

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

       1. associate-*r* 93.8%

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

       2. *-commutative 93.8%

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

       3. neg-mul-1 93.8%

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

   11. Simplified 93.8%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{+148}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + i \cdot -4\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq -6.2 \cdot 10^{-81}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;x \leq 2.85 \cdot 10^{-129}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{+107}:\\ \;\;\;\;\left(b \cdot c + \left(x \cdot \left(18 \cdot y\right)\right) \cdot \left(z \cdot t\right)\right) - \left(j \cdot \left(27 \cdot k\right) + x \cdot \left(4 \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + i \cdot -4\right) + j \cdot \left(k \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 37.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := z \cdot \left(y \cdot \left(x \cdot \left(18 \cdot t\right)\right)\right)\\ \mathbf{if}\;b \cdot c \leq -9.5 \cdot 10^{+150}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -5 \cdot 10^{-311}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq 7.5 \cdot 10^{-59}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 1.58 \cdot 10^{+19}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 4.1 \cdot 10^{+220}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 (* z (* y (* x (* 18.0 t))))))
   (if (<= (* b c) -9.5e+150)
     (* b c)
     (if (<= (* b c) -5e-311)
       t_1
       (if (<= (* b c) 7.5e-59)
         (* x (* i -4.0))
         (if (<= (* b c) 1.58e+19)
           (* t (* a -4.0))
           (if (<= (* b c) 4.1e+220) t_1 (* b c))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = z * (y * (x * (18.0 * t)));
	double tmp;
	if ((b * c) <= -9.5e+150) {
		tmp = b * c;
	} else if ((b * c) <= -5e-311) {
		tmp = t_1;
	} else if ((b * c) <= 7.5e-59) {
		tmp = x * (i * -4.0);
	} else if ((b * c) <= 1.58e+19) {
		tmp = t * (a * -4.0);
	} else if ((b * c) <= 4.1e+220) {
		tmp = t_1;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 = z * (y * (x * (18.0d0 * t)))
    if ((b * c) <= (-9.5d+150)) then
        tmp = b * c
    else if ((b * c) <= (-5d-311)) then
        tmp = t_1
    else if ((b * c) <= 7.5d-59) then
        tmp = x * (i * (-4.0d0))
    else if ((b * c) <= 1.58d+19) then
        tmp = t * (a * (-4.0d0))
    else if ((b * c) <= 4.1d+220) then
        tmp = t_1
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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 = z * (y * (x * (18.0 * t)));
	double tmp;
	if ((b * c) <= -9.5e+150) {
		tmp = b * c;
	} else if ((b * c) <= -5e-311) {
		tmp = t_1;
	} else if ((b * c) <= 7.5e-59) {
		tmp = x * (i * -4.0);
	} else if ((b * c) <= 1.58e+19) {
		tmp = t * (a * -4.0);
	} else if ((b * c) <= 4.1e+220) {
		tmp = t_1;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[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 = z * (y * (x * (18.0 * t)))
	tmp = 0
	if (b * c) <= -9.5e+150:
		tmp = b * c
	elif (b * c) <= -5e-311:
		tmp = t_1
	elif (b * c) <= 7.5e-59:
		tmp = x * (i * -4.0)
	elif (b * c) <= 1.58e+19:
		tmp = t * (a * -4.0)
	elif (b * c) <= 4.1e+220:
		tmp = t_1
	else:
		tmp = b * c
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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(z * Float64(y * Float64(x * Float64(18.0 * t))))
	tmp = 0.0
	if (Float64(b * c) <= -9.5e+150)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -5e-311)
		tmp = t_1;
	elseif (Float64(b * c) <= 7.5e-59)
		tmp = Float64(x * Float64(i * -4.0));
	elseif (Float64(b * c) <= 1.58e+19)
		tmp = Float64(t * Float64(a * -4.0));
	elseif (Float64(b * c) <= 4.1e+220)
		tmp = t_1;
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
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 = z * (y * (x * (18.0 * t)));
	tmp = 0.0;
	if ((b * c) <= -9.5e+150)
		tmp = b * c;
	elseif ((b * c) <= -5e-311)
		tmp = t_1;
	elseif ((b * c) <= 7.5e-59)
		tmp = x * (i * -4.0);
	elseif ((b * c) <= 1.58e+19)
		tmp = t * (a * -4.0);
	elseif ((b * c) <= 4.1e+220)
		tmp = t_1;
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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[(z * N[(y * N[(x * N[(18.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -9.5e+150], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -5e-311], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 7.5e-59], N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1.58e+19], N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 4.1e+220], t$95$1, N[(b * c), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 b c) < -9.5000000000000001e150 or 4.09999999999999981e220 < (*.f64 b c)

   1. Initial program 75.7%

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

   3. Simplified 83.1%

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

      1. associate-*r* 81.8%

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

      2. distribute-rgt-out-- 75.7%

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

      3. associate-+l- 75.7%

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

      4. associate-*l* 76.9%

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

      5. fmm-def 76.9%

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

      6. associate-*l* 76.9%

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

      7. *-commutative 76.9%

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

   6. Applied egg-rr 76.9%

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

      1. fmm-undef 76.9%

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

      2. *-commutative 76.9%

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

      3. associate-*r* 76.9%

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

      4. *-commutative 76.9%

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

      5. *-commutative 76.9%

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

      6. *-commutative 76.9%

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

      7. associate-*l* 76.9%

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

      8. *-commutative 76.9%

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

      9. *-commutative 76.9%

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

   8. Simplified 76.9%

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

   9. Taylor expanded in b around inf 66.6%

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

   if -9.5000000000000001e150 < (*.f64 b c) < -5.00000000000023e-311 or 1.58e19 < (*.f64 b c) < 4.09999999999999981e220

   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 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 y around inf 58.6%

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

      1. associate-*r* 59.5%

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

   7. Simplified 59.5%

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

   8. Taylor expanded in z around inf 53.8%

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

   9. Taylor expanded in j around 0 40.0%

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

       1. associate-*r* 42.8%

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

       2. associate-*r* 42.8%

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

       3. associate-*r* 42.8%

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

       4. *-commutative 42.8%

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

   11. Simplified 42.8%

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

   if -5.00000000000023e-311 < (*.f64 b c) < 7.50000000000000019e-59

   1. Initial program 82.8%

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

   3. Simplified 77.7%

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

      1. associate-*r* 84.5%

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

      2. distribute-rgt-out-- 82.8%

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

      3. associate-+l- 82.8%

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

      4. associate-*l* 86.0%

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

      5. fmm-def 86.0%

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

      6. associate-*l* 86.1%

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

      7. *-commutative 86.1%

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

   6. Applied egg-rr 86.1%

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

      1. fmm-undef 86.1%

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

      2. *-commutative 86.1%

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

      3. associate-*r* 86.1%

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

      4. *-commutative 86.1%

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

      5. *-commutative 86.1%

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

      6. *-commutative 86.1%

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

      7. associate-*l* 86.1%

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

      8. *-commutative 86.1%

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

      9. *-commutative 86.1%

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

   8. Simplified 86.1%

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

   9. Taylor expanded in i around inf 37.4%

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

       1. metadata-eval 37.4%

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

       2. distribute-lft-neg-in 37.4%

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

       3. associate-*r* 37.4%

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

       4. *-commutative 37.4%

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

       5. distribute-rgt-neg-in 37.4%

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

       6. distribute-lft-neg-in 37.4%

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

       7. metadata-eval 37.4%

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

   11. Simplified 37.4%

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

   if 7.50000000000000019e-59 < (*.f64 b c) < 1.58e19

   1. Initial program 88.1%

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

   3. Simplified 76.7%

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

   5. Taylor expanded in j around 0 65.3%

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

   6. Taylor expanded in x around 0 54.5%

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

   7. Taylor expanded in a around inf 54.1%

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

      1. associate-*r* 54.1%

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

   9. Simplified 54.1%

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

4. Final simplification 50.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -9.5 \cdot 10^{+150}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -5 \cdot 10^{-311}:\\ \;\;\;\;z \cdot \left(y \cdot \left(x \cdot \left(18 \cdot t\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 7.5 \cdot 10^{-59}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 1.58 \cdot 10^{+19}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 4.1 \cdot 10^{+220}:\\ \;\;\;\;z \cdot \left(y \cdot \left(x \cdot \left(18 \cdot t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 78.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_1 \leq -5 \lor \neg \left(t\_1 \leq 10^{+133}\right):\\ \;\;\;\;\left(b \cdot c + \left(x \cdot \left(18 \cdot y\right)\right) \cdot \left(z \cdot t\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)))
   (if (or (<= t_1 -5.0) (not (<= t_1 1e+133)))
     (- (+ (* b c) (* (* x (* 18.0 y)) (* z t))) (* 27.0 (* j k)))
     (-
      (+ (* b c) (* t (- (* 18.0 (* x (* y z))) (* a 4.0))))
      (* 4.0 (* x i))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if ((t_1 <= -5.0) || !(t_1 <= 1e+133)) {
		tmp = ((b * c) + ((x * (18.0 * y)) * (z * t))) - (27.0 * (j * k));
	} else {
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - (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.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (j * 27.0d0) * k
    if ((t_1 <= (-5.0d0)) .or. (.not. (t_1 <= 1d+133))) then
        tmp = ((b * c) + ((x * (18.0d0 * y)) * (z * t))) - (27.0d0 * (j * k))
    else
        tmp = ((b * c) + (t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0)))) - (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;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if ((t_1 <= -5.0) || !(t_1 <= 1e+133)) {
		tmp = ((b * c) + ((x * (18.0 * y)) * (z * t))) - (27.0 * (j * k));
	} else {
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - (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])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	tmp = 0
	if (t_1 <= -5.0) or not (t_1 <= 1e+133):
		tmp = ((b * c) + ((x * (18.0 * y)) * (z * t))) - (27.0 * (j * k))
	else:
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - (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])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if ((t_1 <= -5.0) || !(t_1 <= 1e+133))
		tmp = Float64(Float64(Float64(b * c) + Float64(Float64(x * Float64(18.0 * y)) * Float64(z * t))) - Float64(27.0 * Float64(j * k)));
	else
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)))) - 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])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * 27.0) * k;
	tmp = 0.0;
	if ((t_1 <= -5.0) || ~((t_1 <= 1e+133)))
		tmp = ((b * c) + ((x * (18.0 * y)) * (z * t))) - (27.0 * (j * k));
	else
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - (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.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5.0], N[Not[LessEqual[t$95$1, 1e+133]], $MachinePrecision]], N[(N[(N[(b * c), $MachinePrecision] + N[(N[(x * N[(18.0 * y), $MachinePrecision]), $MachinePrecision] * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -5 or 1e133 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 79.7%

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

   3. Simplified 78.1%

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

      1. associate-*r* 83.2%

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

      2. distribute-rgt-out-- 79.7%

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

      3. associate-+l- 79.7%

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

      4. associate-*l* 78.9%

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

      5. fmm-def 78.9%

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

      6. associate-*l* 78.1%

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

      7. *-commutative 78.1%

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

   6. Applied egg-rr 78.1%

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

      1. fmm-undef 78.1%

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

      2. *-commutative 78.1%

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

      3. associate-*r* 78.1%

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

      4. *-commutative 78.1%

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

      5. *-commutative 78.1%

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

      6. *-commutative 78.1%

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

      7. associate-*l* 78.1%

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

      8. *-commutative 78.1%

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

      9. *-commutative 78.1%

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

   8. Simplified 78.1%

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

   9. Taylor expanded in a around 0 76.4%

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

       1. associate-*r* 76.4%

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

       2. *-commutative 76.4%

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

       3. neg-mul-1 76.4%

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

   11. Simplified 76.4%

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

   12. Taylor expanded in x around 0 75.6%

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

   if -5 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 1e133

   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 89.7%

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

   5. Taylor expanded in j around 0 88.4%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \leq -5 \lor \neg \left(\left(j \cdot 27\right) \cdot k \leq 10^{+133}\right):\\ \;\;\;\;\left(b \cdot c + \left(x \cdot \left(18 \cdot y\right)\right) \cdot \left(z \cdot t\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(27 \cdot k\right) + x \cdot \left(4 \cdot i\right)\\ \mathbf{if}\;t \leq -3.6 \cdot 10^{+123}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-4 \cdot \frac{a}{x} + 18 \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-52}:\\ \;\;\;\;\left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot \left(z \cdot t\right) - \left(a \cdot \left(t \cdot 4\right) - b \cdot c\right)\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + \frac{b \cdot c}{t}\right) - a \cdot 4\right) - t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (+ (* j (* 27.0 k)) (* x (* 4.0 i)))))
   (if (<= t -3.6e+123)
     (* t (* x (+ (* -4.0 (/ a x)) (* 18.0 (* y z)))))
     (if (<= t 1.35e-52)
       (- (- (* (* x (* 18.0 y)) (* z t)) (- (* a (* t 4.0)) (* b c))) t_1)
       (- (* t (- (+ (* 18.0 (* x (* y z))) (/ (* b c) t)) (* a 4.0))) t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * (27.0 * k)) + (x * (4.0 * i));
	double tmp;
	if (t <= -3.6e+123) {
		tmp = t * (x * ((-4.0 * (a / x)) + (18.0 * (y * z))));
	} else if (t <= 1.35e-52) {
		tmp = (((x * (18.0 * y)) * (z * t)) - ((a * (t * 4.0)) - (b * c))) - t_1;
	} else {
		tmp = (t * (((18.0 * (x * (y * z))) + ((b * c) / t)) - (a * 4.0))) - t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (j * (27.0d0 * k)) + (x * (4.0d0 * i))
    if (t <= (-3.6d+123)) then
        tmp = t * (x * (((-4.0d0) * (a / x)) + (18.0d0 * (y * z))))
    else if (t <= 1.35d-52) then
        tmp = (((x * (18.0d0 * y)) * (z * t)) - ((a * (t * 4.0d0)) - (b * c))) - t_1
    else
        tmp = (t * (((18.0d0 * (x * (y * z))) + ((b * c) / t)) - (a * 4.0d0))) - t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * (27.0 * k)) + (x * (4.0 * i));
	double tmp;
	if (t <= -3.6e+123) {
		tmp = t * (x * ((-4.0 * (a / x)) + (18.0 * (y * z))));
	} else if (t <= 1.35e-52) {
		tmp = (((x * (18.0 * y)) * (z * t)) - ((a * (t * 4.0)) - (b * c))) - t_1;
	} else {
		tmp = (t * (((18.0 * (x * (y * z))) + ((b * c) / t)) - (a * 4.0))) - t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * (27.0 * k)) + (x * (4.0 * i))
	tmp = 0
	if t <= -3.6e+123:
		tmp = t * (x * ((-4.0 * (a / x)) + (18.0 * (y * z))))
	elif t <= 1.35e-52:
		tmp = (((x * (18.0 * y)) * (z * t)) - ((a * (t * 4.0)) - (b * c))) - t_1
	else:
		tmp = (t * (((18.0 * (x * (y * z))) + ((b * c) / t)) - (a * 4.0))) - t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * Float64(27.0 * k)) + Float64(x * Float64(4.0 * i)))
	tmp = 0.0
	if (t <= -3.6e+123)
		tmp = Float64(t * Float64(x * Float64(Float64(-4.0 * Float64(a / x)) + Float64(18.0 * Float64(y * z)))));
	elseif (t <= 1.35e-52)
		tmp = Float64(Float64(Float64(Float64(x * Float64(18.0 * y)) * Float64(z * t)) - Float64(Float64(a * Float64(t * 4.0)) - Float64(b * c))) - t_1);
	else
		tmp = Float64(Float64(t * Float64(Float64(Float64(18.0 * Float64(x * Float64(y * z))) + Float64(Float64(b * c) / t)) - Float64(a * 4.0))) - t_1);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * (27.0 * k)) + (x * (4.0 * i));
	tmp = 0.0;
	if (t <= -3.6e+123)
		tmp = t * (x * ((-4.0 * (a / x)) + (18.0 * (y * z))));
	elseif (t <= 1.35e-52)
		tmp = (((x * (18.0 * y)) * (z * t)) - ((a * (t * 4.0)) - (b * c))) - t_1;
	else
		tmp = (t * (((18.0 * (x * (y * z))) + ((b * c) / t)) - (a * 4.0))) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision] + N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.6e+123], N[(t * N[(x * N[(N[(-4.0 * N[(a / x), $MachinePrecision]), $MachinePrecision] + N[(18.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.35e-52], N[(N[(N[(N[(x * N[(18.0 * y), $MachinePrecision]), $MachinePrecision] * N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(N[(a * N[(t * 4.0), $MachinePrecision]), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(t * N[(N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(b * c), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.59999999999999998e123

   1. Initial program 63.5%

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

   3. Simplified 84.7%

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

   5. Taylor expanded in t around inf 96.8%

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

   6. Taylor expanded in x around inf 96.8%

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

   if -3.59999999999999998e123 < t < 1.35000000000000005e-52

   1. Initial program 83.8%

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

   3. Simplified 81.1%

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

      1. associate-*r* 83.8%

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

      2. distribute-rgt-out-- 83.8%

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

      3. associate-+l- 83.8%

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

      4. associate-*l* 86.4%

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

      5. fmm-def 86.4%

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

      6. associate-*l* 86.4%

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

      7. *-commutative 86.4%

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

   6. Applied egg-rr 86.4%

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

      1. fmm-undef 86.4%

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

      2. *-commutative 86.4%

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

      3. associate-*r* 86.4%

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

      4. *-commutative 86.4%

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

      5. *-commutative 86.4%

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

      6. *-commutative 86.4%

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

      7. associate-*l* 86.4%

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

      8. *-commutative 86.4%

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

      9. *-commutative 86.4%

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

   8. Simplified 86.4%

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

   if 1.35000000000000005e-52 < t

   1. Initial program 85.6%

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

   3. Simplified 90.8%

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

   5. Taylor expanded in t around inf 90.8%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{+123}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-4 \cdot \frac{a}{x} + 18 \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-52}:\\ \;\;\;\;\left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot \left(z \cdot t\right) - \left(a \cdot \left(t \cdot 4\right) - b \cdot c\right)\right) - \left(j \cdot \left(27 \cdot k\right) + x \cdot \left(4 \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + \frac{b \cdot c}{t}\right) - a \cdot 4\right) - \left(j \cdot \left(27 \cdot k\right) + x \cdot \left(4 \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 75.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ t_2 := 4 \cdot \left(x \cdot i\right)\\ t_3 := x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + i \cdot -4\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;x \leq -8 \cdot 10^{+147}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq -1.32 \cdot 10^{-45}:\\ \;\;\;\;\left(b \cdot c + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) - t\_2\\ \mathbf{elif}\;x \leq 2 \cdot 10^{-93}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - t\_1\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+97}:\\ \;\;\;\;\left(b \cdot c - t\_2\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k))
        (t_2 (* 4.0 (* x i)))
        (t_3
         (+ (* x (+ (* 18.0 (* t (* y z))) (* i -4.0))) (* j (* k -27.0)))))
   (if (<= x -8e+147)
     t_3
     (if (<= x -1.32e-45)
       (- (+ (* b c) (* 18.0 (* t (* x (* y z))))) t_2)
       (if (<= x 2e-93)
         (- (- (* b c) (* 4.0 (* t a))) t_1)
         (if (<= x 3.2e+97) (- (- (* b c) t_2) t_1) t_3))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double t_2 = 4.0 * (x * i);
	double t_3 = (x * ((18.0 * (t * (y * z))) + (i * -4.0))) + (j * (k * -27.0));
	double tmp;
	if (x <= -8e+147) {
		tmp = t_3;
	} else if (x <= -1.32e-45) {
		tmp = ((b * c) + (18.0 * (t * (x * (y * z))))) - t_2;
	} else if (x <= 2e-93) {
		tmp = ((b * c) - (4.0 * (t * a))) - t_1;
	} else if (x <= 3.2e+97) {
		tmp = ((b * c) - t_2) - t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (j * 27.0d0) * k
    t_2 = 4.0d0 * (x * i)
    t_3 = (x * ((18.0d0 * (t * (y * z))) + (i * (-4.0d0)))) + (j * (k * (-27.0d0)))
    if (x <= (-8d+147)) then
        tmp = t_3
    else if (x <= (-1.32d-45)) then
        tmp = ((b * c) + (18.0d0 * (t * (x * (y * z))))) - t_2
    else if (x <= 2d-93) then
        tmp = ((b * c) - (4.0d0 * (t * a))) - t_1
    else if (x <= 3.2d+97) then
        tmp = ((b * c) - t_2) - t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double t_2 = 4.0 * (x * i);
	double t_3 = (x * ((18.0 * (t * (y * z))) + (i * -4.0))) + (j * (k * -27.0));
	double tmp;
	if (x <= -8e+147) {
		tmp = t_3;
	} else if (x <= -1.32e-45) {
		tmp = ((b * c) + (18.0 * (t * (x * (y * z))))) - t_2;
	} else if (x <= 2e-93) {
		tmp = ((b * c) - (4.0 * (t * a))) - t_1;
	} else if (x <= 3.2e+97) {
		tmp = ((b * c) - t_2) - t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	t_2 = 4.0 * (x * i)
	t_3 = (x * ((18.0 * (t * (y * z))) + (i * -4.0))) + (j * (k * -27.0))
	tmp = 0
	if x <= -8e+147:
		tmp = t_3
	elif x <= -1.32e-45:
		tmp = ((b * c) + (18.0 * (t * (x * (y * z))))) - t_2
	elif x <= 2e-93:
		tmp = ((b * c) - (4.0 * (t * a))) - t_1
	elif x <= 3.2e+97:
		tmp = ((b * c) - t_2) - t_1
	else:
		tmp = t_3
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	t_2 = Float64(4.0 * Float64(x * i))
	t_3 = Float64(Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) + Float64(i * -4.0))) + Float64(j * Float64(k * -27.0)))
	tmp = 0.0
	if (x <= -8e+147)
		tmp = t_3;
	elseif (x <= -1.32e-45)
		tmp = Float64(Float64(Float64(b * c) + Float64(18.0 * Float64(t * Float64(x * Float64(y * z))))) - t_2);
	elseif (x <= 2e-93)
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(t * a))) - t_1);
	elseif (x <= 3.2e+97)
		tmp = Float64(Float64(Float64(b * c) - t_2) - t_1);
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * 27.0) * k;
	t_2 = 4.0 * (x * i);
	t_3 = (x * ((18.0 * (t * (y * z))) + (i * -4.0))) + (j * (k * -27.0));
	tmp = 0.0;
	if (x <= -8e+147)
		tmp = t_3;
	elseif (x <= -1.32e-45)
		tmp = ((b * c) + (18.0 * (t * (x * (y * z))))) - t_2;
	elseif (x <= 2e-93)
		tmp = ((b * c) - (4.0 * (t * a))) - t_1;
	elseif (x <= 3.2e+97)
		tmp = ((b * c) - t_2) - t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, Block[{t$95$2 = N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -8e+147], t$95$3, If[LessEqual[x, -1.32e-45], N[(N[(N[(b * c), $MachinePrecision] + N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], If[LessEqual[x, 2e-93], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[x, 3.2e+97], N[(N[(N[(b * c), $MachinePrecision] - t$95$2), $MachinePrecision] - t$95$1), $MachinePrecision], t$95$3]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -7.9999999999999998e147 or 3.20000000000000016e97 < x

   1. Initial program 63.6%

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

   3. Simplified 78.4%

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

   5. Taylor expanded in x around inf 83.7%

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

   if -7.9999999999999998e147 < x < -1.32000000000000005e-45

   1. Initial program 74.3%

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

   3. Simplified 79.6%

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

   5. Taylor expanded in j around 0 90.1%

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

   6. Taylor expanded in a around 0 77.6%

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

   if -1.32000000000000005e-45 < x < 1.9999999999999998e-93

   1. Initial program 97.7%

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

   3. Taylor expanded in x around 0 87.0%

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

   if 1.9999999999999998e-93 < x < 3.20000000000000016e97

   1. Initial program 92.6%

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

   3. Taylor expanded in t around 0 85.2%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{+147}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + i \cdot -4\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq -1.32 \cdot 10^{-45}:\\ \;\;\;\;\left(b \cdot c + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;x \leq 2 \cdot 10^{-93}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+97}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + i \cdot -4\right) + j \cdot \left(k \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 81.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(27 \cdot k\right) + x \cdot \left(4 \cdot i\right)\\ \mathbf{if}\;t \leq -4 \cdot 10^{+123}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-4 \cdot \frac{a}{x} + 18 \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-124}:\\ \;\;\;\;\left(b \cdot c + \left(x \cdot \left(18 \cdot y\right)\right) \cdot \left(z \cdot t\right)\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - t \cdot \left(a \cdot 4 - \left(x \cdot 18\right) \cdot \left(y \cdot z\right)\right)\right) - t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (+ (* j (* 27.0 k)) (* x (* 4.0 i)))))
   (if (<= t -4e+123)
     (* t (* x (+ (* -4.0 (/ a x)) (* 18.0 (* y z)))))
     (if (<= t 2.4e-124)
       (- (+ (* b c) (* (* x (* 18.0 y)) (* z t))) t_1)
       (- (- (* b c) (* t (- (* a 4.0) (* (* x 18.0) (* y z))))) t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * (27.0 * k)) + (x * (4.0 * i));
	double tmp;
	if (t <= -4e+123) {
		tmp = t * (x * ((-4.0 * (a / x)) + (18.0 * (y * z))));
	} else if (t <= 2.4e-124) {
		tmp = ((b * c) + ((x * (18.0 * y)) * (z * t))) - t_1;
	} else {
		tmp = ((b * c) - (t * ((a * 4.0) - ((x * 18.0) * (y * z))))) - t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (j * (27.0d0 * k)) + (x * (4.0d0 * i))
    if (t <= (-4d+123)) then
        tmp = t * (x * (((-4.0d0) * (a / x)) + (18.0d0 * (y * z))))
    else if (t <= 2.4d-124) then
        tmp = ((b * c) + ((x * (18.0d0 * y)) * (z * t))) - t_1
    else
        tmp = ((b * c) - (t * ((a * 4.0d0) - ((x * 18.0d0) * (y * z))))) - t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * (27.0 * k)) + (x * (4.0 * i));
	double tmp;
	if (t <= -4e+123) {
		tmp = t * (x * ((-4.0 * (a / x)) + (18.0 * (y * z))));
	} else if (t <= 2.4e-124) {
		tmp = ((b * c) + ((x * (18.0 * y)) * (z * t))) - t_1;
	} else {
		tmp = ((b * c) - (t * ((a * 4.0) - ((x * 18.0) * (y * z))))) - t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * (27.0 * k)) + (x * (4.0 * i))
	tmp = 0
	if t <= -4e+123:
		tmp = t * (x * ((-4.0 * (a / x)) + (18.0 * (y * z))))
	elif t <= 2.4e-124:
		tmp = ((b * c) + ((x * (18.0 * y)) * (z * t))) - t_1
	else:
		tmp = ((b * c) - (t * ((a * 4.0) - ((x * 18.0) * (y * z))))) - t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * Float64(27.0 * k)) + Float64(x * Float64(4.0 * i)))
	tmp = 0.0
	if (t <= -4e+123)
		tmp = Float64(t * Float64(x * Float64(Float64(-4.0 * Float64(a / x)) + Float64(18.0 * Float64(y * z)))));
	elseif (t <= 2.4e-124)
		tmp = Float64(Float64(Float64(b * c) + Float64(Float64(x * Float64(18.0 * y)) * Float64(z * t))) - t_1);
	else
		tmp = Float64(Float64(Float64(b * c) - Float64(t * Float64(Float64(a * 4.0) - Float64(Float64(x * 18.0) * Float64(y * z))))) - t_1);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * (27.0 * k)) + (x * (4.0 * i));
	tmp = 0.0;
	if (t <= -4e+123)
		tmp = t * (x * ((-4.0 * (a / x)) + (18.0 * (y * z))));
	elseif (t <= 2.4e-124)
		tmp = ((b * c) + ((x * (18.0 * y)) * (z * t))) - t_1;
	else
		tmp = ((b * c) - (t * ((a * 4.0) - ((x * 18.0) * (y * z))))) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision] + N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4e+123], N[(t * N[(x * N[(N[(-4.0 * N[(a / x), $MachinePrecision]), $MachinePrecision] + N[(18.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.4e-124], N[(N[(N[(b * c), $MachinePrecision] + N[(N[(x * N[(18.0 * y), $MachinePrecision]), $MachinePrecision] * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] - N[(t * N[(N[(a * 4.0), $MachinePrecision] - N[(N[(x * 18.0), $MachinePrecision] * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.99999999999999991e123

   1. Initial program 63.5%

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

   3. Simplified 84.7%

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

   5. Taylor expanded in t around inf 96.8%

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

   6. Taylor expanded in x around inf 96.8%

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

   if -3.99999999999999991e123 < t < 2.39999999999999992e-124

   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 79.1%

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

      1. associate-*r* 82.2%

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

      2. distribute-rgt-out-- 82.2%

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

      3. associate-+l- 82.2%

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

      4. associate-*l* 85.1%

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

      5. fmm-def 85.1%

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

      6. associate-*l* 85.2%

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

      7. *-commutative 85.2%

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

   6. Applied egg-rr 85.2%

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

      1. fmm-undef 85.1%

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

      2. *-commutative 85.1%

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

      3. associate-*r* 85.1%

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

      4. *-commutative 85.1%

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

      5. *-commutative 85.1%

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

      6. *-commutative 85.1%

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

      7. associate-*l* 85.1%

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

      8. *-commutative 85.1%

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

      9. *-commutative 85.1%

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

   8. Simplified 85.1%

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

   9. Taylor expanded in a around 0 81.6%

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

       1. associate-*r* 81.6%

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

       2. *-commutative 81.6%

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

       3. neg-mul-1 81.6%

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

   11. Simplified 81.6%

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

   if 2.39999999999999992e-124 < t

   1. Initial program 87.4%

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

   3. Simplified 91.6%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+123}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-4 \cdot \frac{a}{x} + 18 \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-124}:\\ \;\;\;\;\left(b \cdot c + \left(x \cdot \left(18 \cdot y\right)\right) \cdot \left(z \cdot t\right)\right) - \left(j \cdot \left(27 \cdot k\right) + x \cdot \left(4 \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - t \cdot \left(a \cdot 4 - \left(x \cdot 18\right) \cdot \left(y \cdot z\right)\right)\right) - \left(j \cdot \left(27 \cdot k\right) + x \cdot \left(4 \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 37.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := y \cdot \left(t \cdot \left(x \cdot \left(18 \cdot z\right)\right)\right)\\ \mathbf{if}\;b \cdot c \leq -4.4 \cdot 10^{+153}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -1.5 \cdot 10^{-57}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq 6.5 \cdot 10^{-162}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq 5.8 \cdot 10^{+220}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 (* y (* t (* x (* 18.0 z))))))
   (if (<= (* b c) -4.4e+153)
     (* b c)
     (if (<= (* b c) -1.5e-57)
       t_1
       (if (<= (* b c) 6.5e-162)
         (* -27.0 (* j k))
         (if (<= (* b c) 5.8e+220) t_1 (* b c)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = y * (t * (x * (18.0 * z)));
	double tmp;
	if ((b * c) <= -4.4e+153) {
		tmp = b * c;
	} else if ((b * c) <= -1.5e-57) {
		tmp = t_1;
	} else if ((b * c) <= 6.5e-162) {
		tmp = -27.0 * (j * k);
	} else if ((b * c) <= 5.8e+220) {
		tmp = t_1;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 = y * (t * (x * (18.0d0 * z)))
    if ((b * c) <= (-4.4d+153)) then
        tmp = b * c
    else if ((b * c) <= (-1.5d-57)) then
        tmp = t_1
    else if ((b * c) <= 6.5d-162) then
        tmp = (-27.0d0) * (j * k)
    else if ((b * c) <= 5.8d+220) then
        tmp = t_1
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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 = y * (t * (x * (18.0 * z)));
	double tmp;
	if ((b * c) <= -4.4e+153) {
		tmp = b * c;
	} else if ((b * c) <= -1.5e-57) {
		tmp = t_1;
	} else if ((b * c) <= 6.5e-162) {
		tmp = -27.0 * (j * k);
	} else if ((b * c) <= 5.8e+220) {
		tmp = t_1;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[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 = y * (t * (x * (18.0 * z)))
	tmp = 0
	if (b * c) <= -4.4e+153:
		tmp = b * c
	elif (b * c) <= -1.5e-57:
		tmp = t_1
	elif (b * c) <= 6.5e-162:
		tmp = -27.0 * (j * k)
	elif (b * c) <= 5.8e+220:
		tmp = t_1
	else:
		tmp = b * c
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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(y * Float64(t * Float64(x * Float64(18.0 * z))))
	tmp = 0.0
	if (Float64(b * c) <= -4.4e+153)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -1.5e-57)
		tmp = t_1;
	elseif (Float64(b * c) <= 6.5e-162)
		tmp = Float64(-27.0 * Float64(j * k));
	elseif (Float64(b * c) <= 5.8e+220)
		tmp = t_1;
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
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 = y * (t * (x * (18.0 * z)));
	tmp = 0.0;
	if ((b * c) <= -4.4e+153)
		tmp = b * c;
	elseif ((b * c) <= -1.5e-57)
		tmp = t_1;
	elseif ((b * c) <= 6.5e-162)
		tmp = -27.0 * (j * k);
	elseif ((b * c) <= 5.8e+220)
		tmp = t_1;
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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[(y * N[(t * N[(x * N[(18.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -4.4e+153], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -1.5e-57], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 6.5e-162], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 5.8e+220], t$95$1, N[(b * c), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -4.3999999999999999e153 or 5.79999999999999983e220 < (*.f64 b c)

   1. Initial program 75.7%

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

   3. Simplified 83.1%

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

      1. associate-*r* 81.8%

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

      2. distribute-rgt-out-- 75.7%

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

      3. associate-+l- 75.7%

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

      4. associate-*l* 76.9%

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

      5. fmm-def 76.9%

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

      6. associate-*l* 76.9%

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

      7. *-commutative 76.9%

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

   6. Applied egg-rr 76.9%

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

      1. fmm-undef 76.9%

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

      2. *-commutative 76.9%

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

      3. associate-*r* 76.9%

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

      4. *-commutative 76.9%

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

      5. *-commutative 76.9%

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

      6. *-commutative 76.9%

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

      7. associate-*l* 76.9%

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

      8. *-commutative 76.9%

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

      9. *-commutative 76.9%

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

   8. Simplified 76.9%

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

   9. Taylor expanded in b around inf 66.6%

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

   if -4.3999999999999999e153 < (*.f64 b c) < -1.5e-57 or 6.49999999999999989e-162 < (*.f64 b c) < 5.79999999999999983e220

   1. Initial program 80.0%

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

   3. Simplified 83.0%

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

   5. Taylor expanded in t around inf 53.9%

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

   6. Taylor expanded in x around inf 35.4%

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

   7. Taylor expanded in t around 0 35.4%

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

      1. associate-*r* 35.4%

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

      2. *-commutative 35.4%

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

      3. associate-*r* 35.4%

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

      4. associate-*l* 38.1%

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

      5. associate-*r* 38.1%

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

      6. *-commutative 38.1%

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

      7. *-commutative 38.1%

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

      8. associate-*l* 38.2%

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

      9. associate-*l* 38.2%

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

      10. *-commutative 38.2%

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

   9. Simplified 38.2%

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

   if -1.5e-57 < (*.f64 b c) < 6.49999999999999989e-162

   1. Initial program 91.4%

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

   3. Simplified 88.5%

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

   5. Taylor expanded in j around inf 38.4%

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

Alternative 9: 37.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -4 \cdot 10^{+152}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -1.8 \cdot 10^{-58}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 2.3 \cdot 10^{+20}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq 4.8 \cdot 10^{+220}:\\ \;\;\;\;t \cdot \left(x \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= (* b c) -4e+152)
   (* b c)
   (if (<= (* b c) -1.8e-58)
     (* t (* 18.0 (* x (* y z))))
     (if (<= (* b c) 2.3e+20)
       (* -27.0 (* j k))
       (if (<= (* b c) 4.8e+220) (* t (* x (* 18.0 (* y z)))) (* b c))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b * c) <= -4e+152) {
		tmp = b * c;
	} else if ((b * c) <= -1.8e-58) {
		tmp = t * (18.0 * (x * (y * z)));
	} else if ((b * c) <= 2.3e+20) {
		tmp = -27.0 * (j * k);
	} else if ((b * c) <= 4.8e+220) {
		tmp = t * (x * (18.0 * (y * z)));
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((b * c) <= (-4d+152)) then
        tmp = b * c
    else if ((b * c) <= (-1.8d-58)) then
        tmp = t * (18.0d0 * (x * (y * z)))
    else if ((b * c) <= 2.3d+20) then
        tmp = (-27.0d0) * (j * k)
    else if ((b * c) <= 4.8d+220) then
        tmp = t * (x * (18.0d0 * (y * z)))
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b * c) <= -4e+152) {
		tmp = b * c;
	} else if ((b * c) <= -1.8e-58) {
		tmp = t * (18.0 * (x * (y * z)));
	} else if ((b * c) <= 2.3e+20) {
		tmp = -27.0 * (j * k);
	} else if ((b * c) <= 4.8e+220) {
		tmp = t * (x * (18.0 * (y * z)));
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (b * c) <= -4e+152:
		tmp = b * c
	elif (b * c) <= -1.8e-58:
		tmp = t * (18.0 * (x * (y * z)))
	elif (b * c) <= 2.3e+20:
		tmp = -27.0 * (j * k)
	elif (b * c) <= 4.8e+220:
		tmp = t * (x * (18.0 * (y * z)))
	else:
		tmp = b * c
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (Float64(b * c) <= -4e+152)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -1.8e-58)
		tmp = Float64(t * Float64(18.0 * Float64(x * Float64(y * z))));
	elseif (Float64(b * c) <= 2.3e+20)
		tmp = Float64(-27.0 * Float64(j * k));
	elseif (Float64(b * c) <= 4.8e+220)
		tmp = Float64(t * Float64(x * Float64(18.0 * Float64(y * z))));
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((b * c) <= -4e+152)
		tmp = b * c;
	elseif ((b * c) <= -1.8e-58)
		tmp = t * (18.0 * (x * (y * z)));
	elseif ((b * c) <= 2.3e+20)
		tmp = -27.0 * (j * k);
	elseif ((b * c) <= 4.8e+220)
		tmp = t * (x * (18.0 * (y * z)));
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[N[(b * c), $MachinePrecision], -4e+152], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -1.8e-58], N[(t * N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 2.3e+20], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 4.8e+220], N[(t * N[(x * N[(18.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 b c) < -4.0000000000000002e152 or 4.7999999999999996e220 < (*.f64 b c)

   1. Initial program 75.7%

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

   3. Simplified 83.1%

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

      1. associate-*r* 81.8%

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

      2. distribute-rgt-out-- 75.7%

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

      3. associate-+l- 75.7%

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

      4. associate-*l* 76.9%

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

      5. fmm-def 76.9%

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

      6. associate-*l* 76.9%

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

      7. *-commutative 76.9%

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

   6. Applied egg-rr 76.9%

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

      1. fmm-undef 76.9%

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

      2. *-commutative 76.9%

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

      3. associate-*r* 76.9%

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

      4. *-commutative 76.9%

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

      5. *-commutative 76.9%

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

      6. *-commutative 76.9%

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

      7. associate-*l* 76.9%

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

      8. *-commutative 76.9%

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

      9. *-commutative 76.9%

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

   8. Simplified 76.9%

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

   9. Taylor expanded in b around inf 66.6%

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

   if -4.0000000000000002e152 < (*.f64 b c) < -1.80000000000000005e-58

   1. Initial program 82.4%

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

   3. Simplified 92.7%

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

   5. Taylor expanded in t around inf 52.1%

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

   6. Taylor expanded in x around inf 37.7%

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

   if -1.80000000000000005e-58 < (*.f64 b c) < 2.3e20

   1. Initial program 86.0%

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

   3. Simplified 82.3%

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

   5. Taylor expanded in j around inf 34.9%

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

   if 2.3e20 < (*.f64 b c) < 4.7999999999999996e220

   1. Initial program 82.0%

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

   3. Simplified 85.8%

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

   5. Taylor expanded in t around inf 61.5%

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

   6. Taylor expanded in x around inf 61.5%

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

   7. Taylor expanded in a around 0 47.8%

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

Alternative 10: 37.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{if}\;b \cdot c \leq -2.2 \cdot 10^{+151}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -5.4 \cdot 10^{-59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq 6 \cdot 10^{+18}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq 1.1 \cdot 10^{+223}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* t (* 18.0 (* x (* y z))))))
   (if (<= (* b c) -2.2e+151)
     (* b c)
     (if (<= (* b c) -5.4e-59)
       t_1
       (if (<= (* b c) 6e+18)
         (* -27.0 (* j k))
         (if (<= (* b c) 1.1e+223) t_1 (* b c)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * (18.0 * (x * (y * z)));
	double tmp;
	if ((b * c) <= -2.2e+151) {
		tmp = b * c;
	} else if ((b * c) <= -5.4e-59) {
		tmp = t_1;
	} else if ((b * c) <= 6e+18) {
		tmp = -27.0 * (j * k);
	} else if ((b * c) <= 1.1e+223) {
		tmp = t_1;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (18.0d0 * (x * (y * z)))
    if ((b * c) <= (-2.2d+151)) then
        tmp = b * c
    else if ((b * c) <= (-5.4d-59)) then
        tmp = t_1
    else if ((b * c) <= 6d+18) then
        tmp = (-27.0d0) * (j * k)
    else if ((b * c) <= 1.1d+223) then
        tmp = t_1
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * (18.0 * (x * (y * z)));
	double tmp;
	if ((b * c) <= -2.2e+151) {
		tmp = b * c;
	} else if ((b * c) <= -5.4e-59) {
		tmp = t_1;
	} else if ((b * c) <= 6e+18) {
		tmp = -27.0 * (j * k);
	} else if ((b * c) <= 1.1e+223) {
		tmp = t_1;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = t * (18.0 * (x * (y * z)))
	tmp = 0
	if (b * c) <= -2.2e+151:
		tmp = b * c
	elif (b * c) <= -5.4e-59:
		tmp = t_1
	elif (b * c) <= 6e+18:
		tmp = -27.0 * (j * k)
	elif (b * c) <= 1.1e+223:
		tmp = t_1
	else:
		tmp = b * c
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(t * Float64(18.0 * Float64(x * Float64(y * z))))
	tmp = 0.0
	if (Float64(b * c) <= -2.2e+151)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -5.4e-59)
		tmp = t_1;
	elseif (Float64(b * c) <= 6e+18)
		tmp = Float64(-27.0 * Float64(j * k));
	elseif (Float64(b * c) <= 1.1e+223)
		tmp = t_1;
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = t * (18.0 * (x * (y * z)));
	tmp = 0.0;
	if ((b * c) <= -2.2e+151)
		tmp = b * c;
	elseif ((b * c) <= -5.4e-59)
		tmp = t_1;
	elseif ((b * c) <= 6e+18)
		tmp = -27.0 * (j * k);
	elseif ((b * c) <= 1.1e+223)
		tmp = t_1;
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(t * N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -2.2e+151], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -5.4e-59], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 6e+18], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1.1e+223], t$95$1, N[(b * c), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -2.20000000000000007e151 or 1.1e223 < (*.f64 b c)

   1. Initial program 75.7%

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

   3. Simplified 83.1%

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

      1. associate-*r* 81.8%

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

      2. distribute-rgt-out-- 75.7%

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

      3. associate-+l- 75.7%

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

      4. associate-*l* 76.9%

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

      5. fmm-def 76.9%

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

      6. associate-*l* 76.9%

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

      7. *-commutative 76.9%

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

   6. Applied egg-rr 76.9%

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

      1. fmm-undef 76.9%

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

      2. *-commutative 76.9%

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

      3. associate-*r* 76.9%

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

      4. *-commutative 76.9%

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

      5. *-commutative 76.9%

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

      6. *-commutative 76.9%

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

      7. associate-*l* 76.9%

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

      8. *-commutative 76.9%

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

      9. *-commutative 76.9%

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

   8. Simplified 76.9%

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

   9. Taylor expanded in b around inf 66.6%

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

   if -2.20000000000000007e151 < (*.f64 b c) < -5.3999999999999998e-59 or 6e18 < (*.f64 b c) < 1.1e223

   1. Initial program 82.3%

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

   3. Simplified 89.8%

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

   5. Taylor expanded in t around inf 56.0%

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

   6. Taylor expanded in x around inf 41.9%

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

   if -5.3999999999999998e-59 < (*.f64 b c) < 6e18

   1. Initial program 86.0%

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

   3. Simplified 82.3%

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

   5. Taylor expanded in j around inf 34.9%

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

Alternative 11: 71.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t \leq -6.1 \cdot 10^{+119}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-4 \cdot \frac{a}{x} + 18 \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{+14}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - t\_1\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{+64}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{+154}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot \left(-4\right) - \left(z \cdot \left(x \cdot y\right)\right) \cdot -18\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)))
   (if (<= t -6.1e+119)
     (* t (* x (+ (* -4.0 (/ a x)) (* 18.0 (* y z)))))
     (if (<= t 4.3e+14)
       (- (- (* b c) (* 4.0 (* x i))) t_1)
       (if (<= t 2.2e+64)
         (* t (- (* 18.0 (* x (* y z))) (* a 4.0)))
         (if (<= t 6.5e+154)
           (- (- (* b c) (* 4.0 (* t a))) t_1)
           (* t (- (* a (- 4.0)) (* (* z (* x y)) -18.0)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (t <= -6.1e+119) {
		tmp = t * (x * ((-4.0 * (a / x)) + (18.0 * (y * z))));
	} else if (t <= 4.3e+14) {
		tmp = ((b * c) - (4.0 * (x * i))) - t_1;
	} else if (t <= 2.2e+64) {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	} else if (t <= 6.5e+154) {
		tmp = ((b * c) - (4.0 * (t * a))) - t_1;
	} else {
		tmp = t * ((a * -4.0) - ((z * (x * y)) * -18.0));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (j * 27.0d0) * k
    if (t <= (-6.1d+119)) then
        tmp = t * (x * (((-4.0d0) * (a / x)) + (18.0d0 * (y * z))))
    else if (t <= 4.3d+14) then
        tmp = ((b * c) - (4.0d0 * (x * i))) - t_1
    else if (t <= 2.2d+64) then
        tmp = t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0))
    else if (t <= 6.5d+154) then
        tmp = ((b * c) - (4.0d0 * (t * a))) - t_1
    else
        tmp = t * ((a * -4.0d0) - ((z * (x * y)) * (-18.0d0)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (t <= -6.1e+119) {
		tmp = t * (x * ((-4.0 * (a / x)) + (18.0 * (y * z))));
	} else if (t <= 4.3e+14) {
		tmp = ((b * c) - (4.0 * (x * i))) - t_1;
	} else if (t <= 2.2e+64) {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	} else if (t <= 6.5e+154) {
		tmp = ((b * c) - (4.0 * (t * a))) - t_1;
	} else {
		tmp = t * ((a * -4.0) - ((z * (x * y)) * -18.0));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	tmp = 0
	if t <= -6.1e+119:
		tmp = t * (x * ((-4.0 * (a / x)) + (18.0 * (y * z))))
	elif t <= 4.3e+14:
		tmp = ((b * c) - (4.0 * (x * i))) - t_1
	elif t <= 2.2e+64:
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0))
	elif t <= 6.5e+154:
		tmp = ((b * c) - (4.0 * (t * a))) - t_1
	else:
		tmp = t * ((a * -4.0) - ((z * (x * y)) * -18.0))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t <= -6.1e+119)
		tmp = Float64(t * Float64(x * Float64(Float64(-4.0 * Float64(a / x)) + Float64(18.0 * Float64(y * z)))));
	elseif (t <= 4.3e+14)
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(x * i))) - t_1);
	elseif (t <= 2.2e+64)
		tmp = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)));
	elseif (t <= 6.5e+154)
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(t * a))) - t_1);
	else
		tmp = Float64(t * Float64(Float64(a * Float64(-4.0)) - Float64(Float64(z * Float64(x * y)) * -18.0)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * 27.0) * k;
	tmp = 0.0;
	if (t <= -6.1e+119)
		tmp = t * (x * ((-4.0 * (a / x)) + (18.0 * (y * z))));
	elseif (t <= 4.3e+14)
		tmp = ((b * c) - (4.0 * (x * i))) - t_1;
	elseif (t <= 2.2e+64)
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	elseif (t <= 6.5e+154)
		tmp = ((b * c) - (4.0 * (t * a))) - t_1;
	else
		tmp = t * ((a * -4.0) - ((z * (x * y)) * -18.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t, -6.1e+119], N[(t * N[(x * N[(N[(-4.0 * N[(a / x), $MachinePrecision]), $MachinePrecision] + N[(18.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.3e+14], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[t, 2.2e+64], N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.5e+154], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(t * N[(N[(a * (-4.0)), $MachinePrecision] - N[(N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision] * -18.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -6.1e119

   1. Initial program 63.5%

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

   3. Simplified 84.7%

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

   5. Taylor expanded in t around inf 96.8%

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

   6. Taylor expanded in x around inf 96.8%

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

   if -6.1e119 < t < 4.3e14

   1. Initial program 84.2%

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

   3. Taylor expanded in t around 0 81.0%

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

   if 4.3e14 < t < 2.20000000000000002e64

   1. Initial program 85.6%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 85.4%

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

   if 2.20000000000000002e64 < t < 6.5000000000000005e154

   1. Initial program 92.3%

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

   3. Taylor expanded in x around 0 81.0%

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

   if 6.5000000000000005e154 < t

   1. Initial program 77.6%

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

   3. Simplified 85.1%

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

      1. associate-*r* 85.1%

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

      2. distribute-rgt-out-- 77.7%

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

      3. associate-+l- 77.7%

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

      4. associate-*l* 66.9%

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

      5. fmm-def 66.9%

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

      6. associate-*l* 66.9%

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

      7. *-commutative 66.9%

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

   6. Applied egg-rr 66.9%

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

      1. fmm-undef 66.9%

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

      2. *-commutative 66.9%

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

      3. associate-*r* 66.9%

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

      4. *-commutative 66.9%

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

      5. *-commutative 66.9%

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

      6. *-commutative 66.9%

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

      7. associate-*l* 66.9%

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

      8. *-commutative 66.9%

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

      9. *-commutative 66.9%

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

   8. Simplified 66.9%

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

   9. Taylor expanded in t around -inf 77.3%

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

       1. mul-1-neg 77.3%

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

       2. cancel-sign-sub-inv 77.3%

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

       3. metadata-eval 77.3%

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

       4. *-commutative 77.3%

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

       5. associate-*r* 77.3%

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

       6. *-commutative 77.3%

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

   11. Simplified 77.3%

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

4. Final simplification 82.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.1 \cdot 10^{+119}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-4 \cdot \frac{a}{x} + 18 \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{+14}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{+64}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{+154}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot \left(-4\right) - \left(z \cdot \left(x \cdot y\right)\right) \cdot -18\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 71.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+120}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-4 \cdot \frac{a}{x} + 18 \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq 61000:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+132}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + i \cdot -4\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot \left(-4\right) - \left(z \cdot \left(x \cdot y\right)\right) \cdot -18\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= t -4e+120)
   (* t (* x (+ (* -4.0 (/ a x)) (* 18.0 (* y z)))))
   (if (<= t 61000.0)
     (- (- (* b c) (* 4.0 (* x i))) (* (* j 27.0) k))
     (if (<= t 3e+132)
       (+ (* x (+ (* 18.0 (* t (* y z))) (* i -4.0))) (* j (* k -27.0)))
       (* t (- (* a (- 4.0)) (* (* z (* x y)) -18.0)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (t <= -4e+120) {
		tmp = t * (x * ((-4.0 * (a / x)) + (18.0 * (y * z))));
	} else if (t <= 61000.0) {
		tmp = ((b * c) - (4.0 * (x * i))) - ((j * 27.0) * k);
	} else if (t <= 3e+132) {
		tmp = (x * ((18.0 * (t * (y * z))) + (i * -4.0))) + (j * (k * -27.0));
	} else {
		tmp = t * ((a * -4.0) - ((z * (x * y)) * -18.0));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (t <= (-4d+120)) then
        tmp = t * (x * (((-4.0d0) * (a / x)) + (18.0d0 * (y * z))))
    else if (t <= 61000.0d0) then
        tmp = ((b * c) - (4.0d0 * (x * i))) - ((j * 27.0d0) * k)
    else if (t <= 3d+132) then
        tmp = (x * ((18.0d0 * (t * (y * z))) + (i * (-4.0d0)))) + (j * (k * (-27.0d0)))
    else
        tmp = t * ((a * -4.0d0) - ((z * (x * y)) * (-18.0d0)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (t <= -4e+120) {
		tmp = t * (x * ((-4.0 * (a / x)) + (18.0 * (y * z))));
	} else if (t <= 61000.0) {
		tmp = ((b * c) - (4.0 * (x * i))) - ((j * 27.0) * k);
	} else if (t <= 3e+132) {
		tmp = (x * ((18.0 * (t * (y * z))) + (i * -4.0))) + (j * (k * -27.0));
	} else {
		tmp = t * ((a * -4.0) - ((z * (x * y)) * -18.0));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if t <= -4e+120:
		tmp = t * (x * ((-4.0 * (a / x)) + (18.0 * (y * z))))
	elif t <= 61000.0:
		tmp = ((b * c) - (4.0 * (x * i))) - ((j * 27.0) * k)
	elif t <= 3e+132:
		tmp = (x * ((18.0 * (t * (y * z))) + (i * -4.0))) + (j * (k * -27.0))
	else:
		tmp = t * ((a * -4.0) - ((z * (x * y)) * -18.0))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (t <= -4e+120)
		tmp = Float64(t * Float64(x * Float64(Float64(-4.0 * Float64(a / x)) + Float64(18.0 * Float64(y * z)))));
	elseif (t <= 61000.0)
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(x * i))) - Float64(Float64(j * 27.0) * k));
	elseif (t <= 3e+132)
		tmp = Float64(Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) + Float64(i * -4.0))) + Float64(j * Float64(k * -27.0)));
	else
		tmp = Float64(t * Float64(Float64(a * Float64(-4.0)) - Float64(Float64(z * Float64(x * y)) * -18.0)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (t <= -4e+120)
		tmp = t * (x * ((-4.0 * (a / x)) + (18.0 * (y * z))));
	elseif (t <= 61000.0)
		tmp = ((b * c) - (4.0 * (x * i))) - ((j * 27.0) * k);
	elseif (t <= 3e+132)
		tmp = (x * ((18.0 * (t * (y * z))) + (i * -4.0))) + (j * (k * -27.0));
	else
		tmp = t * ((a * -4.0) - ((z * (x * y)) * -18.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[t, -4e+120], N[(t * N[(x * N[(N[(-4.0 * N[(a / x), $MachinePrecision]), $MachinePrecision] + N[(18.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 61000.0], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3e+132], N[(N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(a * (-4.0)), $MachinePrecision] - N[(N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision] * -18.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3.9999999999999999e120

   1. Initial program 63.5%

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

   3. Simplified 84.7%

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

   5. Taylor expanded in t around inf 96.8%

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

   6. Taylor expanded in x around inf 96.8%

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

   if -3.9999999999999999e120 < t < 61000

   1. Initial program 84.2%

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

   3. Taylor expanded in t around 0 81.0%

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

   if 61000 < t < 2.9999999999999998e132

   1. Initial program 87.5%

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

   3. Simplified 96.8%

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

   5. Taylor expanded in x around inf 75.7%

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

   if 2.9999999999999998e132 < 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 85.7%

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

      1. associate-*r* 85.6%

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

      2. distribute-rgt-out-- 79.9%

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

      3. associate-+l- 79.9%

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

      4. associate-*l* 71.6%

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

      5. fmm-def 71.6%

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

      6. associate-*l* 71.6%

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

      7. *-commutative 71.6%

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

   6. Applied egg-rr 71.6%

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

      1. fmm-undef 71.6%

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

      2. *-commutative 71.6%

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

      3. associate-*r* 71.6%

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

      4. *-commutative 71.6%

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

      5. *-commutative 71.6%

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

      6. *-commutative 71.6%

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

      7. associate-*l* 71.6%

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

      8. *-commutative 71.6%

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

      9. *-commutative 71.6%

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

   8. Simplified 71.6%

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

   9. Taylor expanded in t around -inf 76.8%

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

       1. mul-1-neg 76.8%

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

       2. cancel-sign-sub-inv 76.8%

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

       3. metadata-eval 76.8%

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

       4. *-commutative 76.8%

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

       5. associate-*r* 76.8%

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

       6. *-commutative 76.8%

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

   11. Simplified 76.8%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+120}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-4 \cdot \frac{a}{x} + 18 \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq 61000:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+132}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + i \cdot -4\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot \left(-4\right) - \left(z \cdot \left(x \cdot y\right)\right) \cdot -18\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 57.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{+118}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-4 \cdot \frac{a}{x} + 18 \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-168}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq 0.003:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= t -1.65e+118)
   (* t (* x (+ (* -4.0 (/ a x)) (* 18.0 (* y z)))))
   (if (<= t 1.2e-168)
     (- (* b c) (* 4.0 (* x i)))
     (if (<= t 0.003)
       (+ (* b c) (* j (* k -27.0)))
       (* t (- (* 18.0 (* x (* y z))) (* a 4.0)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (t <= -1.65e+118) {
		tmp = t * (x * ((-4.0 * (a / x)) + (18.0 * (y * z))));
	} else if (t <= 1.2e-168) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if (t <= 0.003) {
		tmp = (b * c) + (j * (k * -27.0));
	} else {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (t <= (-1.65d+118)) then
        tmp = t * (x * (((-4.0d0) * (a / x)) + (18.0d0 * (y * z))))
    else if (t <= 1.2d-168) then
        tmp = (b * c) - (4.0d0 * (x * i))
    else if (t <= 0.003d0) then
        tmp = (b * c) + (j * (k * (-27.0d0)))
    else
        tmp = t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (t <= -1.65e+118) {
		tmp = t * (x * ((-4.0 * (a / x)) + (18.0 * (y * z))));
	} else if (t <= 1.2e-168) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if (t <= 0.003) {
		tmp = (b * c) + (j * (k * -27.0));
	} else {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if t <= -1.65e+118:
		tmp = t * (x * ((-4.0 * (a / x)) + (18.0 * (y * z))))
	elif t <= 1.2e-168:
		tmp = (b * c) - (4.0 * (x * i))
	elif t <= 0.003:
		tmp = (b * c) + (j * (k * -27.0))
	else:
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (t <= -1.65e+118)
		tmp = Float64(t * Float64(x * Float64(Float64(-4.0 * Float64(a / x)) + Float64(18.0 * Float64(y * z)))));
	elseif (t <= 1.2e-168)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)));
	elseif (t <= 0.003)
		tmp = Float64(Float64(b * c) + Float64(j * Float64(k * -27.0)));
	else
		tmp = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (t <= -1.65e+118)
		tmp = t * (x * ((-4.0 * (a / x)) + (18.0 * (y * z))));
	elseif (t <= 1.2e-168)
		tmp = (b * c) - (4.0 * (x * i));
	elseif (t <= 0.003)
		tmp = (b * c) + (j * (k * -27.0));
	else
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[t, -1.65e+118], N[(t * N[(x * N[(N[(-4.0 * N[(a / x), $MachinePrecision]), $MachinePrecision] + N[(18.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.2e-168], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 0.003], N[(N[(b * c), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.65e118

   1. Initial program 63.5%

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

   3. Simplified 84.7%

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

   5. Taylor expanded in t around inf 96.8%

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

   6. Taylor expanded in x around inf 96.8%

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

   if -1.65e118 < t < 1.2e-168

   1. Initial program 80.7%

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

   3. Simplified 78.2%

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

   5. Taylor expanded in j around 0 65.9%

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

   6. Taylor expanded in t around 0 62.9%

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

   if 1.2e-168 < t < 0.0030000000000000001

   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 94.8%

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

   5. Taylor expanded in b around inf 78.2%

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

   if 0.0030000000000000001 < t

   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 89.5%

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

   5. Taylor expanded in t around inf 66.1%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{+118}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-4 \cdot \frac{a}{x} + 18 \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-168}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq 0.003:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 57.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{if}\;t \leq -1.72 \cdot 10^{+118}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-159}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq 2.8:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* t (- (* 18.0 (* x (* y z))) (* a 4.0)))))
   (if (<= t -1.72e+118)
     t_1
     (if (<= t 9.5e-159)
       (- (* b c) (* 4.0 (* x i)))
       (if (<= t 2.8) (+ (* b c) (* j (* k -27.0))) t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	double tmp;
	if (t <= -1.72e+118) {
		tmp = t_1;
	} else if (t <= 9.5e-159) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if (t <= 2.8) {
		tmp = (b * c) + (j * (k * -27.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0))
    if (t <= (-1.72d+118)) then
        tmp = t_1
    else if (t <= 9.5d-159) then
        tmp = (b * c) - (4.0d0 * (x * i))
    else if (t <= 2.8d0) then
        tmp = (b * c) + (j * (k * (-27.0d0)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	double tmp;
	if (t <= -1.72e+118) {
		tmp = t_1;
	} else if (t <= 9.5e-159) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if (t <= 2.8) {
		tmp = (b * c) + (j * (k * -27.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = t * ((18.0 * (x * (y * z))) - (a * 4.0))
	tmp = 0
	if t <= -1.72e+118:
		tmp = t_1
	elif t <= 9.5e-159:
		tmp = (b * c) - (4.0 * (x * i))
	elif t <= 2.8:
		tmp = (b * c) + (j * (k * -27.0))
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)))
	tmp = 0.0
	if (t <= -1.72e+118)
		tmp = t_1;
	elseif (t <= 9.5e-159)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)));
	elseif (t <= 2.8)
		tmp = Float64(Float64(b * c) + Float64(j * Float64(k * -27.0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	tmp = 0.0;
	if (t <= -1.72e+118)
		tmp = t_1;
	elseif (t <= 9.5e-159)
		tmp = (b * c) - (4.0 * (x * i));
	elseif (t <= 2.8)
		tmp = (b * c) + (j * (k * -27.0));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.72e+118], t$95$1, If[LessEqual[t, 9.5e-159], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.8], N[(N[(b * c), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.71999999999999999e118 or 2.7999999999999998 < t

   1. Initial program 77.9%

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

   3. Simplified 87.9%

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

   5. Taylor expanded in t around inf 76.2%

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

   if -1.71999999999999999e118 < t < 9.4999999999999997e-159

   1. Initial program 80.7%

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

   3. Simplified 78.2%

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

   5. Taylor expanded in j around 0 65.9%

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

   6. Taylor expanded in t around 0 62.9%

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

   if 9.4999999999999997e-159 < t < 2.7999999999999998

   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 94.8%

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

   5. Taylor expanded in b around inf 78.2%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.72 \cdot 10^{+118}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-159}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq 2.8:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 49.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{+115}:\\ \;\;\;\;z \cdot \left(y \cdot \left(x \cdot \left(18 \cdot t\right)\right)\right)\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-168}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{+86}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(b + \frac{t \cdot \left(a \cdot -4\right)}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= t -1.2e+115)
   (* z (* y (* x (* 18.0 t))))
   (if (<= t 2.8e-168)
     (- (* b c) (* 4.0 (* x i)))
     (if (<= t 9.2e+86)
       (+ (* b c) (* j (* k -27.0)))
       (* c (+ b (/ (* t (* a -4.0)) c)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (t <= -1.2e+115) {
		tmp = z * (y * (x * (18.0 * t)));
	} else if (t <= 2.8e-168) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if (t <= 9.2e+86) {
		tmp = (b * c) + (j * (k * -27.0));
	} else {
		tmp = c * (b + ((t * (a * -4.0)) / c));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (t <= (-1.2d+115)) then
        tmp = z * (y * (x * (18.0d0 * t)))
    else if (t <= 2.8d-168) then
        tmp = (b * c) - (4.0d0 * (x * i))
    else if (t <= 9.2d+86) then
        tmp = (b * c) + (j * (k * (-27.0d0)))
    else
        tmp = c * (b + ((t * (a * (-4.0d0))) / c))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (t <= -1.2e+115) {
		tmp = z * (y * (x * (18.0 * t)));
	} else if (t <= 2.8e-168) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if (t <= 9.2e+86) {
		tmp = (b * c) + (j * (k * -27.0));
	} else {
		tmp = c * (b + ((t * (a * -4.0)) / c));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if t <= -1.2e+115:
		tmp = z * (y * (x * (18.0 * t)))
	elif t <= 2.8e-168:
		tmp = (b * c) - (4.0 * (x * i))
	elif t <= 9.2e+86:
		tmp = (b * c) + (j * (k * -27.0))
	else:
		tmp = c * (b + ((t * (a * -4.0)) / c))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (t <= -1.2e+115)
		tmp = Float64(z * Float64(y * Float64(x * Float64(18.0 * t))));
	elseif (t <= 2.8e-168)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)));
	elseif (t <= 9.2e+86)
		tmp = Float64(Float64(b * c) + Float64(j * Float64(k * -27.0)));
	else
		tmp = Float64(c * Float64(b + Float64(Float64(t * Float64(a * -4.0)) / c)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (t <= -1.2e+115)
		tmp = z * (y * (x * (18.0 * t)));
	elseif (t <= 2.8e-168)
		tmp = (b * c) - (4.0 * (x * i));
	elseif (t <= 9.2e+86)
		tmp = (b * c) + (j * (k * -27.0));
	else
		tmp = c * (b + ((t * (a * -4.0)) / c));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[t, -1.2e+115], N[(z * N[(y * N[(x * N[(18.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.8e-168], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.2e+86], N[(N[(b * c), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(b + N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.2e115

   1. Initial program 63.8%

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

   3. Simplified 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 y around inf 65.0%

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

      1. associate-*r* 70.2%

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

   7. Simplified 70.2%

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

   8. Taylor expanded in z around inf 64.6%

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

   9. Taylor expanded in j around 0 65.1%

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

       1. associate-*r* 75.6%

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

       2. associate-*r* 75.7%

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

       3. associate-*r* 75.6%

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

       4. *-commutative 75.6%

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

   11. Simplified 75.6%

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

   if -1.2e115 < t < 2.8000000000000002e-168

   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 78.5%

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

   5. Taylor expanded in j around 0 65.9%

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

   6. Taylor expanded in t around 0 62.8%

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

   if 2.8000000000000002e-168 < t < 9.19999999999999958e86

   1. Initial program 89.7%

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

   3. Simplified 94.8%

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

   5. Taylor expanded in b around inf 62.5%

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

   if 9.19999999999999958e86 < t

   1. Initial program 87.1%

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

   3. Simplified 89.3%

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

   5. Taylor expanded in j around 0 82.7%

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

   6. Taylor expanded in x around 0 52.1%

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

   7. Taylor expanded in c around inf 50.2%

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

      1. associate-*r/ 50.2%

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

      2. associate-*r* 50.2%

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

   9. Simplified 50.2%

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

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{+115}:\\ \;\;\;\;z \cdot \left(y \cdot \left(x \cdot \left(18 \cdot t\right)\right)\right)\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-168}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{+86}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(b + \frac{t \cdot \left(a \cdot -4\right)}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 38.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2.9 \cdot 10^{+148}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -1.25 \cdot 10^{+45}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 8.8 \cdot 10^{+140}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= (* b c) -2.9e+148)
   (* b c)
   (if (<= (* b c) -1.25e+45)
     (* x (* i -4.0))
     (if (<= (* b c) 8.8e+140) (* -27.0 (* j k)) (* b c)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b * c) <= -2.9e+148) {
		tmp = b * c;
	} else if ((b * c) <= -1.25e+45) {
		tmp = x * (i * -4.0);
	} else if ((b * c) <= 8.8e+140) {
		tmp = -27.0 * (j * k);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((b * c) <= (-2.9d+148)) then
        tmp = b * c
    else if ((b * c) <= (-1.25d+45)) then
        tmp = x * (i * (-4.0d0))
    else if ((b * c) <= 8.8d+140) then
        tmp = (-27.0d0) * (j * k)
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b * c) <= -2.9e+148) {
		tmp = b * c;
	} else if ((b * c) <= -1.25e+45) {
		tmp = x * (i * -4.0);
	} else if ((b * c) <= 8.8e+140) {
		tmp = -27.0 * (j * k);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (b * c) <= -2.9e+148:
		tmp = b * c
	elif (b * c) <= -1.25e+45:
		tmp = x * (i * -4.0)
	elif (b * c) <= 8.8e+140:
		tmp = -27.0 * (j * k)
	else:
		tmp = b * c
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (Float64(b * c) <= -2.9e+148)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -1.25e+45)
		tmp = Float64(x * Float64(i * -4.0));
	elseif (Float64(b * c) <= 8.8e+140)
		tmp = Float64(-27.0 * Float64(j * k));
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((b * c) <= -2.9e+148)
		tmp = b * c;
	elseif ((b * c) <= -1.25e+45)
		tmp = x * (i * -4.0);
	elseif ((b * c) <= 8.8e+140)
		tmp = -27.0 * (j * k);
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[N[(b * c), $MachinePrecision], -2.9e+148], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -1.25e+45], N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 8.8e+140], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -2.9e148 or 8.7999999999999993e140 < (*.f64 b c)

   1. Initial program 76.4%

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

   3. Simplified 84.0%

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

      1. associate-*r* 82.9%

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

      2. distribute-rgt-out-- 76.4%

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

      3. associate-+l- 76.4%

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

      4. associate-*l* 76.5%

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

      5. fmm-def 76.4%

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

      6. associate-*l* 76.5%

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

      7. *-commutative 76.5%

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

   6. Applied egg-rr 76.5%

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

      1. fmm-undef 76.5%

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

      2. *-commutative 76.5%

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

      3. associate-*r* 76.5%

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

      4. *-commutative 76.5%

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

      5. *-commutative 76.5%

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

      6. *-commutative 76.5%

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

      7. associate-*l* 76.5%

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

      8. *-commutative 76.5%

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

      9. *-commutative 76.5%

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

   8. Simplified 76.5%

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

   9. Taylor expanded in b around inf 62.3%

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

   if -2.9e148 < (*.f64 b c) < -1.25e45

   1. Initial program 77.4%

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

   3. Simplified 89.2%

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

      1. associate-*r* 83.3%

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

      2. distribute-rgt-out-- 77.4%

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

      3. associate-+l- 77.4%

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

      4. associate-*l* 71.6%

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

      5. fmm-def 71.6%

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

      6. associate-*l* 71.6%

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

      7. *-commutative 71.6%

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

   6. Applied egg-rr 71.6%

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

      1. fmm-undef 71.6%

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

      2. *-commutative 71.6%

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

      3. associate-*r* 71.6%

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

      4. *-commutative 71.6%

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

      5. *-commutative 71.6%

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

      6. *-commutative 71.6%

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

      7. associate-*l* 71.6%

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

      8. *-commutative 71.6%

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

      9. *-commutative 71.6%

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

   8. Simplified 71.6%

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

   9. Taylor expanded in i around inf 48.2%

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

       1. metadata-eval 48.2%

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

       2. distribute-lft-neg-in 48.2%

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

       3. associate-*r* 48.2%

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

       4. *-commutative 48.2%

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

       5. distribute-rgt-neg-in 48.2%

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

       6. distribute-lft-neg-in 48.2%

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

       7. metadata-eval 48.2%

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

   11. Simplified 48.2%

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

   if -1.25e45 < (*.f64 b c) < 8.7999999999999993e140

   1. Initial program 85.6%

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

   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 j around inf 32.9%

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

4. Final simplification 44.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2.9 \cdot 10^{+148}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -1.25 \cdot 10^{+45}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 8.8 \cdot 10^{+140}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 72.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{+28} \lor \neg \left(x \leq 3.4 \cdot 10^{+83}\right):\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 -4.2e+28) (not (<= x 3.4e+83)))
   (* x (- (* 18.0 (* t (* y z))) (* 4.0 i)))
   (- (- (* b c) (* 4.0 (* t a))) (* (* j 27.0) k))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((x <= -4.2e+28) || !(x <= 3.4e+83)) {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	} else {
		tmp = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 <= (-4.2d+28)) .or. (.not. (x <= 3.4d+83))) then
        tmp = x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i))
    else
        tmp = ((b * c) - (4.0d0 * (t * a))) - ((j * 27.0d0) * k)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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 <= -4.2e+28) || !(x <= 3.4e+83)) {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	} else {
		tmp = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[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 <= -4.2e+28) or not (x <= 3.4e+83):
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i))
	else:
		tmp = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k)
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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 <= -4.2e+28) || !(x <= 3.4e+83))
		tmp = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)));
	else
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(t * a))) - Float64(Float64(j * 27.0) * k));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
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 <= -4.2e+28) || ~((x <= 3.4e+83)))
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	else
		tmp = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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, -4.2e+28], N[Not[LessEqual[x, 3.4e+83]], $MachinePrecision]], N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.19999999999999978e28 or 3.3999999999999998e83 < x

   1. Initial program 65.5%

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

   3. Simplified 78.5%

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

   5. Taylor expanded in x around inf 72.6%

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

   if -4.19999999999999978e28 < x < 3.3999999999999998e83

   1. Initial program 95.0%

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

   3. Taylor expanded in x around 0 76.9%

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

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{+28} \lor \neg \left(x \leq 3.4 \cdot 10^{+83}\right):\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 55.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;b \cdot c \leq -2 \cdot 10^{+150}:\\ \;\;\;\;c \cdot \left(b + \frac{t \cdot \left(a \cdot -4\right)}{c}\right)\\ \mathbf{elif}\;b \cdot c \leq 10^{+22}:\\ \;\;\;\;t\_1 + i \cdot \left(x \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0))))
   (if (<= (* b c) -2e+150)
     (* c (+ b (/ (* t (* a -4.0)) c)))
     (if (<= (* b c) 1e+22) (+ t_1 (* i (* x -4.0))) (+ (* b c) t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double tmp;
	if ((b * c) <= -2e+150) {
		tmp = c * (b + ((t * (a * -4.0)) / c));
	} else if ((b * c) <= 1e+22) {
		tmp = t_1 + (i * (x * -4.0));
	} else {
		tmp = (b * c) + t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * (k * (-27.0d0))
    if ((b * c) <= (-2d+150)) then
        tmp = c * (b + ((t * (a * (-4.0d0))) / c))
    else if ((b * c) <= 1d+22) then
        tmp = t_1 + (i * (x * (-4.0d0)))
    else
        tmp = (b * c) + t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double tmp;
	if ((b * c) <= -2e+150) {
		tmp = c * (b + ((t * (a * -4.0)) / c));
	} else if ((b * c) <= 1e+22) {
		tmp = t_1 + (i * (x * -4.0));
	} else {
		tmp = (b * c) + t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	tmp = 0
	if (b * c) <= -2e+150:
		tmp = c * (b + ((t * (a * -4.0)) / c))
	elif (b * c) <= 1e+22:
		tmp = t_1 + (i * (x * -4.0))
	else:
		tmp = (b * c) + t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * -27.0))
	tmp = 0.0
	if (Float64(b * c) <= -2e+150)
		tmp = Float64(c * Float64(b + Float64(Float64(t * Float64(a * -4.0)) / c)));
	elseif (Float64(b * c) <= 1e+22)
		tmp = Float64(t_1 + Float64(i * Float64(x * -4.0)));
	else
		tmp = Float64(Float64(b * c) + t_1);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * -27.0);
	tmp = 0.0;
	if ((b * c) <= -2e+150)
		tmp = c * (b + ((t * (a * -4.0)) / c));
	elseif ((b * c) <= 1e+22)
		tmp = t_1 + (i * (x * -4.0));
	else
		tmp = (b * c) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -2e+150], N[(c * N[(b + N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1e+22], N[(t$95$1 + N[(i * N[(x * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -1.99999999999999996e150

   1. Initial program 77.7%

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

   3. Simplified 83.0%

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

   5. Taylor expanded in j around 0 81.6%

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

   6. Taylor expanded in x around 0 70.2%

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

   7. Taylor expanded in c around inf 70.3%

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

      1. associate-*r/ 70.3%

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

      2. associate-*r* 70.3%

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

   9. Simplified 70.3%

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

   if -1.99999999999999996e150 < (*.f64 b c) < 1e22

   1. Initial program 85.9%

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

   3. Simplified 85.9%

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

   5. Taylor expanded in i around inf 58.9%

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

      1. metadata-eval 58.9%

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

      2. distribute-lft-neg-in 58.9%

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

      3. *-commutative 58.9%

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

      4. associate-*r* 58.9%

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

      5. distribute-rgt-neg-in 58.9%

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

      6. distribute-rgt-neg-in 58.9%

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

      7. metadata-eval 58.9%

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

      8. *-commutative 58.9%

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

   7. Simplified 58.9%

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

   if 1e22 < (*.f64 b c)

   1. Initial program 74.4%

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

   3. Simplified 82.4%

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

   5. Taylor expanded in b around inf 63.1%

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

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2 \cdot 10^{+150}:\\ \;\;\;\;c \cdot \left(b + \frac{t \cdot \left(a \cdot -4\right)}{c}\right)\\ \mathbf{elif}\;b \cdot c \leq 10^{+22}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + i \cdot \left(x \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 49.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -3.85 \cdot 10^{+115}:\\ \;\;\;\;z \cdot \left(y \cdot \left(x \cdot \left(18 \cdot t\right)\right)\right)\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-165}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{+86}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= t -3.85e+115)
   (* z (* y (* x (* 18.0 t))))
   (if (<= t 3.2e-165)
     (- (* b c) (* 4.0 (* x i)))
     (if (<= t 8.2e+86)
       (+ (* b c) (* j (* k -27.0)))
       (+ (* b c) (* -4.0 (* t a)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (t <= -3.85e+115) {
		tmp = z * (y * (x * (18.0 * t)));
	} else if (t <= 3.2e-165) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if (t <= 8.2e+86) {
		tmp = (b * c) + (j * (k * -27.0));
	} else {
		tmp = (b * c) + (-4.0 * (t * a));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (t <= (-3.85d+115)) then
        tmp = z * (y * (x * (18.0d0 * t)))
    else if (t <= 3.2d-165) then
        tmp = (b * c) - (4.0d0 * (x * i))
    else if (t <= 8.2d+86) then
        tmp = (b * c) + (j * (k * (-27.0d0)))
    else
        tmp = (b * c) + ((-4.0d0) * (t * a))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (t <= -3.85e+115) {
		tmp = z * (y * (x * (18.0 * t)));
	} else if (t <= 3.2e-165) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if (t <= 8.2e+86) {
		tmp = (b * c) + (j * (k * -27.0));
	} else {
		tmp = (b * c) + (-4.0 * (t * a));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if t <= -3.85e+115:
		tmp = z * (y * (x * (18.0 * t)))
	elif t <= 3.2e-165:
		tmp = (b * c) - (4.0 * (x * i))
	elif t <= 8.2e+86:
		tmp = (b * c) + (j * (k * -27.0))
	else:
		tmp = (b * c) + (-4.0 * (t * a))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (t <= -3.85e+115)
		tmp = Float64(z * Float64(y * Float64(x * Float64(18.0 * t))));
	elseif (t <= 3.2e-165)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)));
	elseif (t <= 8.2e+86)
		tmp = Float64(Float64(b * c) + Float64(j * Float64(k * -27.0)));
	else
		tmp = Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (t <= -3.85e+115)
		tmp = z * (y * (x * (18.0 * t)));
	elseif (t <= 3.2e-165)
		tmp = (b * c) - (4.0 * (x * i));
	elseif (t <= 8.2e+86)
		tmp = (b * c) + (j * (k * -27.0));
	else
		tmp = (b * c) + (-4.0 * (t * a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[t, -3.85e+115], N[(z * N[(y * N[(x * N[(18.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.2e-165], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.2e+86], N[(N[(b * c), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3.84999999999999984e115

   1. Initial program 63.8%

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

   3. Simplified 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 y around inf 65.0%

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

      1. associate-*r* 70.2%

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

   7. Simplified 70.2%

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

   8. Taylor expanded in z around inf 64.6%

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

   9. Taylor expanded in j around 0 65.1%

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

       1. associate-*r* 75.6%

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

       2. associate-*r* 75.7%

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

       3. associate-*r* 75.6%

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

       4. *-commutative 75.6%

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

   11. Simplified 75.6%

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

   if -3.84999999999999984e115 < t < 3.20000000000000013e-165

   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 78.5%

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

   5. Taylor expanded in j around 0 65.9%

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

   6. Taylor expanded in t around 0 62.8%

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

   if 3.20000000000000013e-165 < t < 8.1999999999999998e86

   1. Initial program 89.7%

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

   3. Simplified 94.8%

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

   5. Taylor expanded in b around inf 62.5%

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

   if 8.1999999999999998e86 < t

   1. Initial program 87.1%

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

   3. Simplified 89.3%

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

   5. Taylor expanded in j around 0 82.7%

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

   6. Taylor expanded in x around 0 52.1%

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

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.85 \cdot 10^{+115}:\\ \;\;\;\;z \cdot \left(y \cdot \left(x \cdot \left(18 \cdot t\right)\right)\right)\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-165}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{+86}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 38.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2.9 \cdot 10^{+146} \lor \neg \left(b \cdot c \leq 1.65 \cdot 10^{+140}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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) -2.9e+146) (not (<= (* b c) 1.65e+140)))
   (* b c)
   (* -27.0 (* j k))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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) <= -2.9e+146) || !((b * c) <= 1.65e+140)) {
		tmp = b * c;
	} else {
		tmp = -27.0 * (j * k);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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) <= (-2.9d+146)) .or. (.not. ((b * c) <= 1.65d+140))) then
        tmp = b * c
    else
        tmp = (-27.0d0) * (j * k)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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) <= -2.9e+146) || !((b * c) <= 1.65e+140)) {
		tmp = b * c;
	} else {
		tmp = -27.0 * (j * k);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[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) <= -2.9e+146) or not ((b * c) <= 1.65e+140):
		tmp = b * c
	else:
		tmp = -27.0 * (j * k)
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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) <= -2.9e+146) || !(Float64(b * c) <= 1.65e+140))
		tmp = Float64(b * c);
	else
		tmp = Float64(-27.0 * Float64(j * k));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
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) <= -2.9e+146) || ~(((b * c) <= 1.65e+140)))
		tmp = b * c;
	else
		tmp = -27.0 * (j * k);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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], -2.9e+146], N[Not[LessEqual[N[(b * c), $MachinePrecision], 1.65e+140]], $MachinePrecision]], N[(b * c), $MachinePrecision], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -2.8999999999999998e146 or 1.6500000000000001e140 < (*.f64 b c)

   1. Initial program 76.4%

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

   3. Simplified 84.0%

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

      1. associate-*r* 82.9%

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

      2. distribute-rgt-out-- 76.4%

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

      3. associate-+l- 76.4%

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

      4. associate-*l* 76.5%

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

      5. fmm-def 76.4%

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

      6. associate-*l* 76.5%

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

      7. *-commutative 76.5%

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

   6. Applied egg-rr 76.5%

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

      1. fmm-undef 76.5%

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

      2. *-commutative 76.5%

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

      3. associate-*r* 76.5%

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

      4. *-commutative 76.5%

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

      5. *-commutative 76.5%

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

      6. *-commutative 76.5%

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

      7. associate-*l* 76.5%

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

      8. *-commutative 76.5%

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

      9. *-commutative 76.5%

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

   8. Simplified 76.5%

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

   9. Taylor expanded in b around inf 62.3%

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

   if -2.8999999999999998e146 < (*.f64 b c) < 1.6500000000000001e140

   1. Initial program 84.8%

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

   3. Simplified 84.8%

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

   5. Taylor expanded in j around inf 31.4%

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

4. Final simplification 42.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2.9 \cdot 10^{+146} \lor \neg \left(b \cdot c \leq 1.65 \cdot 10^{+140}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 50.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+115}:\\ \;\;\;\;z \cdot \left(y \cdot \left(x \cdot \left(18 \cdot t\right)\right)\right)\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+86}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= t -4e+115)
   (* z (* y (* x (* 18.0 t))))
   (if (<= t 7e+86)
     (+ (* b c) (* j (* k -27.0)))
     (+ (* b c) (* -4.0 (* t a))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (t <= -4e+115) {
		tmp = z * (y * (x * (18.0 * t)));
	} else if (t <= 7e+86) {
		tmp = (b * c) + (j * (k * -27.0));
	} else {
		tmp = (b * c) + (-4.0 * (t * a));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (t <= (-4d+115)) then
        tmp = z * (y * (x * (18.0d0 * t)))
    else if (t <= 7d+86) then
        tmp = (b * c) + (j * (k * (-27.0d0)))
    else
        tmp = (b * c) + ((-4.0d0) * (t * a))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (t <= -4e+115) {
		tmp = z * (y * (x * (18.0 * t)));
	} else if (t <= 7e+86) {
		tmp = (b * c) + (j * (k * -27.0));
	} else {
		tmp = (b * c) + (-4.0 * (t * a));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if t <= -4e+115:
		tmp = z * (y * (x * (18.0 * t)))
	elif t <= 7e+86:
		tmp = (b * c) + (j * (k * -27.0))
	else:
		tmp = (b * c) + (-4.0 * (t * a))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (t <= -4e+115)
		tmp = Float64(z * Float64(y * Float64(x * Float64(18.0 * t))));
	elseif (t <= 7e+86)
		tmp = Float64(Float64(b * c) + Float64(j * Float64(k * -27.0)));
	else
		tmp = Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (t <= -4e+115)
		tmp = z * (y * (x * (18.0 * t)));
	elseif (t <= 7e+86)
		tmp = (b * c) + (j * (k * -27.0));
	else
		tmp = (b * c) + (-4.0 * (t * a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[t, -4e+115], N[(z * N[(y * N[(x * N[(18.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7e+86], N[(N[(b * c), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.0000000000000001e115

   1. Initial program 63.8%

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

   3. Simplified 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 y around inf 65.0%

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

      1. associate-*r* 70.2%

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

   7. Simplified 70.2%

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

   8. Taylor expanded in z around inf 64.6%

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

   9. Taylor expanded in j around 0 65.1%

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

       1. associate-*r* 75.6%

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

       2. associate-*r* 75.7%

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

       3. associate-*r* 75.6%

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

       4. *-commutative 75.6%

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

   11. Simplified 75.6%

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

   if -4.0000000000000001e115 < t < 7.00000000000000038e86

   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 84.1%

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

   5. Taylor expanded in b around inf 55.0%

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

   if 7.00000000000000038e86 < t

   1. Initial program 87.1%

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

   3. Simplified 89.3%

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

   5. Taylor expanded in j around 0 82.7%

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

   6. Taylor expanded in x around 0 52.1%

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

4. Final simplification 57.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+115}:\\ \;\;\;\;z \cdot \left(y \cdot \left(x \cdot \left(18 \cdot t\right)\right)\right)\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+86}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 45.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+138}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x \cdot \left(18 \cdot z\right)\right)\right)\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-172}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot \left(x \cdot \left(18 \cdot t\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= y -2.1e+138)
   (* y (* t (* x (* 18.0 z))))
   (if (<= y 4.8e-172)
     (+ (* b c) (* -4.0 (* t a)))
     (* z (* y (* x (* 18.0 t)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (y <= -2.1e+138) {
		tmp = y * (t * (x * (18.0 * z)));
	} else if (y <= 4.8e-172) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else {
		tmp = z * (y * (x * (18.0 * t)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (y <= (-2.1d+138)) then
        tmp = y * (t * (x * (18.0d0 * z)))
    else if (y <= 4.8d-172) then
        tmp = (b * c) + ((-4.0d0) * (t * a))
    else
        tmp = z * (y * (x * (18.0d0 * t)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (y <= -2.1e+138) {
		tmp = y * (t * (x * (18.0 * z)));
	} else if (y <= 4.8e-172) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else {
		tmp = z * (y * (x * (18.0 * t)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if y <= -2.1e+138:
		tmp = y * (t * (x * (18.0 * z)))
	elif y <= 4.8e-172:
		tmp = (b * c) + (-4.0 * (t * a))
	else:
		tmp = z * (y * (x * (18.0 * t)))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (y <= -2.1e+138)
		tmp = Float64(y * Float64(t * Float64(x * Float64(18.0 * z))));
	elseif (y <= 4.8e-172)
		tmp = Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a)));
	else
		tmp = Float64(z * Float64(y * Float64(x * Float64(18.0 * t))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (y <= -2.1e+138)
		tmp = y * (t * (x * (18.0 * z)));
	elseif (y <= 4.8e-172)
		tmp = (b * c) + (-4.0 * (t * a));
	else
		tmp = z * (y * (x * (18.0 * t)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[y, -2.1e+138], N[(y * N[(t * N[(x * N[(18.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.8e-172], N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(y * N[(x * N[(18.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.10000000000000007e138

   1. Initial program 75.2%

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

   3. Simplified 69.6%

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

   5. Taylor expanded in t around inf 56.0%

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

   6. Taylor expanded in x around inf 55.5%

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

   7. Taylor expanded in t around 0 55.5%

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

      1. associate-*r* 55.5%

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

      2. *-commutative 55.5%

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

      3. associate-*r* 53.0%

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

      4. associate-*l* 55.5%

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

      5. associate-*r* 55.5%

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

      6. *-commutative 55.5%

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

      7. *-commutative 55.5%

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

      8. associate-*l* 55.6%

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

      9. associate-*l* 55.6%

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

      10. *-commutative 55.6%

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

   9. Simplified 55.6%

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

   if -2.10000000000000007e138 < y < 4.8000000000000002e-172

   1. Initial program 89.1%

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

   3. Simplified 90.0%

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

   5. Taylor expanded in j around 0 75.3%

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

   6. Taylor expanded in x around 0 50.3%

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

   if 4.8000000000000002e-172 < y

   1. Initial program 75.4%

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

   3. Simplified 84.4%

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

   5. Taylor expanded in y around inf 50.0%

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

      1. associate-*r* 50.9%

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

   7. Simplified 50.9%

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

   8. Taylor expanded in z around inf 48.1%

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

   9. Taylor expanded in j around 0 37.1%

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

       1. associate-*r* 37.2%

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

       2. associate-*r* 37.2%

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

       3. associate-*r* 37.2%

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

       4. *-commutative 37.2%

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

   11. Simplified 37.2%

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

4. Final simplification 45.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+138}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x \cdot \left(18 \cdot z\right)\right)\right)\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-172}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot \left(x \cdot \left(18 \cdot t\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 23.5% accurate, 10.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 81.7%

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

3. Simplified 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. Step-by-step derivation

   1. associate-*r* 85.7%

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

   2. distribute-rgt-out-- 81.4%

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

   3. associate-+l- 81.4%

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

   4. associate-*l* 80.9%

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

   5. fmm-def 80.9%

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

   6. associate-*l* 80.6%

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

   7. *-commutative 80.6%

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

6. Applied egg-rr 80.6%

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

   1. fmm-undef 80.6%

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

   2. *-commutative 80.6%

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

   3. associate-*r* 80.6%

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

   4. *-commutative 80.6%

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

   5. *-commutative 80.6%

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

   6. *-commutative 80.6%

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

   7. associate-*l* 80.6%

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

   8. *-commutative 80.6%

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

   9. *-commutative 80.6%

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

8. Simplified 80.6%

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

9. Taylor expanded in b around inf 25.9%

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

Developer Target 1: 89.2% 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 2024185 
(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)))