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

Percentage Accurate: 85.7% → 92.3%

Time: 36.3s

Alternatives: 32

Speedup: 0.9×

• 50.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 92.3% accurate, 0.2× speedup

Math

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

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1
         (-
          (+ (* b c) (* y (+ (* 18.0 (* t (* x z))) (* (/ (* t a) y) -4.0))))
          (+ (* x (* 4.0 i)) (* j (* 27.0 k)))))
        (t_2
         (-
          (-
           (+ (* b c) (- (* t (* z (* y (* 18.0 x)))) (* t (* 4.0 a))))
           (* (* x 4.0) i))
          (* (* j 27.0) k))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 1e+308)
       t_2
       (if (<= t_2 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);
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) + (y * ((18.0 * (t * (x * z))) + (((t * a) / y) * -4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	double t_2 = (((b * c) + ((t * (z * (y * (18.0 * x)))) - (t * (4.0 * a)))) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= 1e+308) {
		tmp = t_2;
	} else if (t_2 <= ((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;
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) + (y * ((18.0 * (t * (x * z))) + (((t * a) / y) * -4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	double t_2 = (((b * c) + ((t * (z * (y * (18.0 * x)))) - (t * (4.0 * a)))) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= 1e+308) {
		tmp = t_2;
	} else if (t_2 <= 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])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = ((b * c) + (y * ((18.0 * (t * (x * z))) + (((t * a) / y) * -4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)))
	t_2 = (((b * c) + ((t * (z * (y * (18.0 * x)))) - (t * (4.0 * a)))) - ((x * 4.0) * i)) - ((j * 27.0) * k)
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= 1e+308:
		tmp = t_2
	elif t_2 <= 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])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(Float64(b * c) + Float64(y * Float64(Float64(18.0 * Float64(t * Float64(x * z))) + Float64(Float64(Float64(t * a) / y) * -4.0)))) - Float64(Float64(x * Float64(4.0 * i)) + Float64(j * Float64(27.0 * k))))
	t_2 = Float64(Float64(Float64(Float64(b * c) + Float64(Float64(t * Float64(z * Float64(y * Float64(18.0 * x)))) - Float64(t * Float64(4.0 * a)))) - Float64(Float64(x * 4.0) * i)) - Float64(Float64(j * 27.0) * k))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= 1e+308)
		tmp = t_2;
	elseif (t_2 <= 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])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = ((b * c) + (y * ((18.0 * (t * (x * z))) + (((t * a) / y) * -4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	t_2 = (((b * c) + ((t * (z * (y * (18.0 * x)))) - (t * (4.0 * a)))) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= 1e+308)
		tmp = t_2;
	elseif (t_2 <= 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.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(N[(b * c), $MachinePrecision] + N[(y * N[(N[(18.0 * N[(t * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(t * a), $MachinePrecision] / y), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision] + N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(b * c), $MachinePrecision] + N[(N[(t * N[(z * N[(y * N[(18.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * N[(4.0 * a), $MachinePrecision]), $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$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, 1e+308], t$95$2, If[LessEqual[t$95$2, 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 3 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 or 1e308 < (-.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 90.2%

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

   3. Simplified 92.9%

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

   5. Taylor expanded in y around inf 98.1%

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

   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)) < 1e308

   1. Initial program 99.7%

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

   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 19.0%

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

   5. Taylor expanded in x around inf 71.5%

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

4. Final simplification 96.7%

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

Alternative 2: 89.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+154}:\\ \;\;\;\;\left(y \cdot \left(\left(18 \cdot \left(t \cdot \left(x \cdot z\right)\right) + \frac{b \cdot c}{y}\right) - 4 \cdot \frac{t \cdot a}{y}\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= y -1.2e+154)
   (-
    (-
     (* y (- (+ (* 18.0 (* t (* x z))) (/ (* b c) y)) (* 4.0 (/ (* t a) y))))
     (* (* x 4.0) i))
    (* (* j 27.0) k))
   (+
    (fma t (fma x (* 18.0 (* y z)) (* a -4.0)) (fma b c (* x (* i -4.0))))
    (* j (* k -27.0)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (y <= -1.2e+154) {
		tmp = ((y * (((18.0 * (t * (x * z))) + ((b * c) / y)) - (4.0 * ((t * a) / y)))) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	} else {
		tmp = fma(t, fma(x, (18.0 * (y * z)), (a * -4.0)), fma(b, c, (x * (i * -4.0)))) + (j * (k * -27.0));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (y <= -1.2e+154)
		tmp = Float64(Float64(Float64(y * Float64(Float64(Float64(18.0 * Float64(t * Float64(x * z))) + Float64(Float64(b * c) / y)) - Float64(4.0 * Float64(Float64(t * a) / y)))) - Float64(Float64(x * 4.0) * i)) - Float64(Float64(j * 27.0) * k));
	else
		tmp = Float64(fma(t, fma(x, Float64(18.0 * Float64(y * z)), Float64(a * -4.0)), fma(b, c, Float64(x * Float64(i * -4.0)))) + Float64(j * Float64(k * -27.0)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[y, -1.2e+154], N[(N[(N[(y * N[(N[(N[(18.0 * N[(t * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(b * c), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(N[(t * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], N[(N[(t * N[(x * N[(18.0 * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + N[(b * c + N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.20000000000000007e154

   1. Initial program 74.0%

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

   3. Taylor expanded in y around inf 97.2%

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

   if -1.20000000000000007e154 < y

   1. Initial program 89.9%

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

   3. Simplified 92.3%

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

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+154}:\\ \;\;\;\;\left(y \cdot \left(\left(18 \cdot \left(t \cdot \left(x \cdot z\right)\right) + \frac{b \cdot c}{y}\right) - 4 \cdot \frac{t \cdot a}{y}\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 90.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ t_2 := \left(b \cdot c + \left(t \cdot \left(z \cdot \left(y \cdot \left(18 \cdot x\right)\right)\right) - t \cdot \left(4 \cdot a\right)\right)\right) - \left(x \cdot 4\right) \cdot i\\ t_3 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;\left(\left(b \cdot c + t\_1\right) - 4 \cdot \left(t \cdot a\right)\right) - t\_3\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+254}:\\ \;\;\;\;t\_2 - t\_3\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;y \cdot \left(\left(18 \cdot \left(t \cdot \left(x \cdot z\right)\right) + \frac{b \cdot c}{y}\right) + \frac{t \cdot a}{y} \cdot -4\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* x (- (* 18.0 (* t (* y z))) (* 4.0 i))))
        (t_2
         (-
          (+ (* b c) (- (* t (* z (* y (* 18.0 x)))) (* t (* 4.0 a))))
          (* (* x 4.0) i)))
        (t_3 (* (* j 27.0) k)))
   (if (<= t_2 (- INFINITY))
     (- (- (+ (* b c) t_1) (* 4.0 (* t a))) t_3)
     (if (<= t_2 5e+254)
       (- t_2 t_3)
       (if (<= t_2 INFINITY)
         (-
          (*
           y
           (+ (+ (* 18.0 (* t (* x z))) (/ (* b c) y)) (* (/ (* t a) y) -4.0)))
          (* 4.0 (* x i)))
         t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	double t_2 = ((b * c) + ((t * (z * (y * (18.0 * x)))) - (t * (4.0 * a)))) - ((x * 4.0) * i);
	double t_3 = (j * 27.0) * k;
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = (((b * c) + t_1) - (4.0 * (t * a))) - t_3;
	} else if (t_2 <= 5e+254) {
		tmp = t_2 - t_3;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = (y * (((18.0 * (t * (x * z))) + ((b * c) / y)) + (((t * a) / y) * -4.0))) - (4.0 * (x * i));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	double t_2 = ((b * c) + ((t * (z * (y * (18.0 * x)))) - (t * (4.0 * a)))) - ((x * 4.0) * i);
	double t_3 = (j * 27.0) * k;
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = (((b * c) + t_1) - (4.0 * (t * a))) - t_3;
	} else if (t_2 <= 5e+254) {
		tmp = t_2 - t_3;
	} else if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = (y * (((18.0 * (t * (x * z))) + ((b * c) / y)) + (((t * a) / y) * -4.0))) - (4.0 * (x * 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])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = x * ((18.0 * (t * (y * z))) - (4.0 * i))
	t_2 = ((b * c) + ((t * (z * (y * (18.0 * x)))) - (t * (4.0 * a)))) - ((x * 4.0) * i)
	t_3 = (j * 27.0) * k
	tmp = 0
	if t_2 <= -math.inf:
		tmp = (((b * c) + t_1) - (4.0 * (t * a))) - t_3
	elif t_2 <= 5e+254:
		tmp = t_2 - t_3
	elif t_2 <= math.inf:
		tmp = (y * (((18.0 * (t * (x * z))) + ((b * c) / y)) + (((t * a) / y) * -4.0))) - (4.0 * (x * 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])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)))
	t_2 = Float64(Float64(Float64(b * c) + Float64(Float64(t * Float64(z * Float64(y * Float64(18.0 * x)))) - Float64(t * Float64(4.0 * a)))) - Float64(Float64(x * 4.0) * i))
	t_3 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(Float64(Float64(Float64(b * c) + t_1) - Float64(4.0 * Float64(t * a))) - t_3);
	elseif (t_2 <= 5e+254)
		tmp = Float64(t_2 - t_3);
	elseif (t_2 <= Inf)
		tmp = Float64(Float64(y * Float64(Float64(Float64(18.0 * Float64(t * Float64(x * z))) + Float64(Float64(b * c) / y)) + Float64(Float64(Float64(t * a) / y) * -4.0))) - Float64(4.0 * Float64(x * 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])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	t_2 = ((b * c) + ((t * (z * (y * (18.0 * x)))) - (t * (4.0 * a)))) - ((x * 4.0) * i);
	t_3 = (j * 27.0) * k;
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = (((b * c) + t_1) - (4.0 * (t * a))) - t_3;
	elseif (t_2 <= 5e+254)
		tmp = t_2 - t_3;
	elseif (t_2 <= Inf)
		tmp = (y * (((18.0 * (t * (x * z))) + ((b * c) / y)) + (((t * a) / y) * -4.0))) - (4.0 * (x * 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.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(b * c), $MachinePrecision] + N[(N[(t * N[(z * N[(y * N[(18.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * N[(4.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(N[(N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$3), $MachinePrecision], If[LessEqual[t$95$2, 5e+254], N[(t$95$2 - t$95$3), $MachinePrecision], If[LessEqual[t$95$2, Infinity], N[(N[(y * N[(N[(N[(18.0 * N[(t * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(b * c), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(t * a), $MachinePrecision] / y), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if (-.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)) < -inf.0

   1. Initial program 80.4%

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

   3. Taylor expanded in x around 0 89.1%

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

   if -inf.0 < (-.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)) < 4.99999999999999994e254

   1. Initial program 99.8%

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

   if 4.99999999999999994e254 < (-.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)) < +inf.0

   1. Initial program 88.7%

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

   3. Simplified 88.7%

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

   5. Taylor expanded in j around 0 88.9%

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

   6. Taylor expanded in y around inf 87.3%

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

   if +inf.0 < (-.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))

   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 25.0%

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

   5. Taylor expanded in x around inf 75.2%

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

4. Final simplification 93.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(b \cdot c + \left(t \cdot \left(z \cdot \left(y \cdot \left(18 \cdot x\right)\right)\right) - t \cdot \left(4 \cdot a\right)\right)\right) - \left(x \cdot 4\right) \cdot i \leq -\infty:\\ \;\;\;\;\left(\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;\left(b \cdot c + \left(t \cdot \left(z \cdot \left(y \cdot \left(18 \cdot x\right)\right)\right) - t \cdot \left(4 \cdot a\right)\right)\right) - \left(x \cdot 4\right) \cdot i \leq 5 \cdot 10^{+254}:\\ \;\;\;\;\left(\left(b \cdot c + \left(t \cdot \left(z \cdot \left(y \cdot \left(18 \cdot x\right)\right)\right) - t \cdot \left(4 \cdot a\right)\right)\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;\left(b \cdot c + \left(t \cdot \left(z \cdot \left(y \cdot \left(18 \cdot x\right)\right)\right) - t \cdot \left(4 \cdot a\right)\right)\right) - \left(x \cdot 4\right) \cdot i \leq \infty:\\ \;\;\;\;y \cdot \left(\left(18 \cdot \left(t \cdot \left(x \cdot z\right)\right) + \frac{b \cdot c}{y}\right) + \frac{t \cdot a}{y} \cdot -4\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 36.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ t_2 := 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{if}\;b \cdot c \leq -1.62 \cdot 10^{+152}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -2.4 \cdot 10^{+29}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq -5 \cdot 10^{-69}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq -4.15 \cdot 10^{-190}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq 7 \cdot 10^{-184}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \cdot c \leq 1.6 \cdot 10^{-109}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq 1.9 \cdot 10^{+129}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* t (* a -4.0))) (t_2 (* 18.0 (* t (* x (* y z))))))
   (if (<= (* b c) -1.62e+152)
     (* b c)
     (if (<= (* b c) -2.4e+29)
       t_1
       (if (<= (* b c) -5e-69)
         (* -27.0 (* j k))
         (if (<= (* b c) -4.15e-190)
           t_1
           (if (<= (* b c) 7e-184)
             t_2
             (if (<= (* b c) 1.6e-109)
               t_1
               (if (<= (* b c) 1.9e+129) t_2 (* b c))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * (a * -4.0);
	double t_2 = 18.0 * (t * (x * (y * z)));
	double tmp;
	if ((b * c) <= -1.62e+152) {
		tmp = b * c;
	} else if ((b * c) <= -2.4e+29) {
		tmp = t_1;
	} else if ((b * c) <= -5e-69) {
		tmp = -27.0 * (j * k);
	} else if ((b * c) <= -4.15e-190) {
		tmp = t_1;
	} else if ((b * c) <= 7e-184) {
		tmp = t_2;
	} else if ((b * c) <= 1.6e-109) {
		tmp = t_1;
	} else if ((b * c) <= 1.9e+129) {
		tmp = t_2;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * (a * (-4.0d0))
    t_2 = 18.0d0 * (t * (x * (y * z)))
    if ((b * c) <= (-1.62d+152)) then
        tmp = b * c
    else if ((b * c) <= (-2.4d+29)) then
        tmp = t_1
    else if ((b * c) <= (-5d-69)) then
        tmp = (-27.0d0) * (j * k)
    else if ((b * c) <= (-4.15d-190)) then
        tmp = t_1
    else if ((b * c) <= 7d-184) then
        tmp = t_2
    else if ((b * c) <= 1.6d-109) then
        tmp = t_1
    else if ((b * c) <= 1.9d+129) then
        tmp = t_2
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * (a * -4.0);
	double t_2 = 18.0 * (t * (x * (y * z)));
	double tmp;
	if ((b * c) <= -1.62e+152) {
		tmp = b * c;
	} else if ((b * c) <= -2.4e+29) {
		tmp = t_1;
	} else if ((b * c) <= -5e-69) {
		tmp = -27.0 * (j * k);
	} else if ((b * c) <= -4.15e-190) {
		tmp = t_1;
	} else if ((b * c) <= 7e-184) {
		tmp = t_2;
	} else if ((b * c) <= 1.6e-109) {
		tmp = t_1;
	} else if ((b * c) <= 1.9e+129) {
		tmp = t_2;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = t * (a * -4.0)
	t_2 = 18.0 * (t * (x * (y * z)))
	tmp = 0
	if (b * c) <= -1.62e+152:
		tmp = b * c
	elif (b * c) <= -2.4e+29:
		tmp = t_1
	elif (b * c) <= -5e-69:
		tmp = -27.0 * (j * k)
	elif (b * c) <= -4.15e-190:
		tmp = t_1
	elif (b * c) <= 7e-184:
		tmp = t_2
	elif (b * c) <= 1.6e-109:
		tmp = t_1
	elif (b * c) <= 1.9e+129:
		tmp = t_2
	else:
		tmp = b * c
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(t * Float64(a * -4.0))
	t_2 = Float64(18.0 * Float64(t * Float64(x * Float64(y * z))))
	tmp = 0.0
	if (Float64(b * c) <= -1.62e+152)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -2.4e+29)
		tmp = t_1;
	elseif (Float64(b * c) <= -5e-69)
		tmp = Float64(-27.0 * Float64(j * k));
	elseif (Float64(b * c) <= -4.15e-190)
		tmp = t_1;
	elseif (Float64(b * c) <= 7e-184)
		tmp = t_2;
	elseif (Float64(b * c) <= 1.6e-109)
		tmp = t_1;
	elseif (Float64(b * c) <= 1.9e+129)
		tmp = t_2;
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = t * (a * -4.0);
	t_2 = 18.0 * (t * (x * (y * z)));
	tmp = 0.0;
	if ((b * c) <= -1.62e+152)
		tmp = b * c;
	elseif ((b * c) <= -2.4e+29)
		tmp = t_1;
	elseif ((b * c) <= -5e-69)
		tmp = -27.0 * (j * k);
	elseif ((b * c) <= -4.15e-190)
		tmp = t_1;
	elseif ((b * c) <= 7e-184)
		tmp = t_2;
	elseif ((b * c) <= 1.6e-109)
		tmp = t_1;
	elseif ((b * c) <= 1.9e+129)
		tmp = t_2;
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -1.62e+152], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -2.4e+29], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], -5e-69], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -4.15e-190], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 7e-184], t$95$2, If[LessEqual[N[(b * c), $MachinePrecision], 1.6e-109], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 1.9e+129], t$95$2, N[(b * c), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 b c) < -1.6200000000000001e152 or 1.90000000000000003e129 < (*.f64 b c)

   1. Initial program 83.2%

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

   3. Simplified 82.0%

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

   5. Taylor expanded in c around inf 84.8%

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

   6. Taylor expanded in c around inf 70.5%

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

   if -1.6200000000000001e152 < (*.f64 b c) < -2.4000000000000001e29 or -5.00000000000000033e-69 < (*.f64 b c) < -4.15000000000000002e-190 or 6.99999999999999962e-184 < (*.f64 b c) < 1.6000000000000001e-109

   1. Initial program 87.2%

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

   3. Simplified 87.3%

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

   5. Taylor expanded in c around inf 73.0%

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

   6. Taylor expanded in a around inf 47.4%

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

      1. *-commutative 47.4%

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

      2. *-commutative 47.4%

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

      3. associate-*r* 47.4%

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

   8. Simplified 47.4%

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

   if -2.4000000000000001e29 < (*.f64 b c) < -5.00000000000000033e-69

   1. Initial program 93.4%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in j around inf 51.0%

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

   if -4.15000000000000002e-190 < (*.f64 b c) < 6.99999999999999962e-184 or 1.6000000000000001e-109 < (*.f64 b c) < 1.90000000000000003e129

   1. Initial program 90.1%

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

   3. Simplified 92.8%

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

   5. Taylor expanded in c around inf 71.0%

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

   6. Taylor expanded in y around inf 32.9%

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

4. Final simplification 48.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.62 \cdot 10^{+152}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -2.4 \cdot 10^{+29}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq -5 \cdot 10^{-69}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq -4.15 \cdot 10^{-190}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 7 \cdot 10^{-184}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 1.6 \cdot 10^{-109}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 1.9 \cdot 10^{+129}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 36.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ t_2 := 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{if}\;b \cdot c \leq -2 \cdot 10^{+153}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -2 \cdot 10^{+31}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq -1 \cdot 10^{-66}:\\ \;\;\;\;c \cdot \left(-27 \cdot \frac{j \cdot k}{c}\right)\\ \mathbf{elif}\;b \cdot c \leq -2 \cdot 10^{-186}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq 5 \cdot 10^{-184}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \cdot c \leq 2 \cdot 10^{-109}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq 2 \cdot 10^{+129}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* t (* a -4.0))) (t_2 (* 18.0 (* t (* x (* y z))))))
   (if (<= (* b c) -2e+153)
     (* b c)
     (if (<= (* b c) -2e+31)
       t_1
       (if (<= (* b c) -1e-66)
         (* c (* -27.0 (/ (* j k) c)))
         (if (<= (* b c) -2e-186)
           t_1
           (if (<= (* b c) 5e-184)
             t_2
             (if (<= (* b c) 2e-109)
               t_1
               (if (<= (* b c) 2e+129) t_2 (* b c))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * (a * -4.0);
	double t_2 = 18.0 * (t * (x * (y * z)));
	double tmp;
	if ((b * c) <= -2e+153) {
		tmp = b * c;
	} else if ((b * c) <= -2e+31) {
		tmp = t_1;
	} else if ((b * c) <= -1e-66) {
		tmp = c * (-27.0 * ((j * k) / c));
	} else if ((b * c) <= -2e-186) {
		tmp = t_1;
	} else if ((b * c) <= 5e-184) {
		tmp = t_2;
	} else if ((b * c) <= 2e-109) {
		tmp = t_1;
	} else if ((b * c) <= 2e+129) {
		tmp = t_2;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * (a * (-4.0d0))
    t_2 = 18.0d0 * (t * (x * (y * z)))
    if ((b * c) <= (-2d+153)) then
        tmp = b * c
    else if ((b * c) <= (-2d+31)) then
        tmp = t_1
    else if ((b * c) <= (-1d-66)) then
        tmp = c * ((-27.0d0) * ((j * k) / c))
    else if ((b * c) <= (-2d-186)) then
        tmp = t_1
    else if ((b * c) <= 5d-184) then
        tmp = t_2
    else if ((b * c) <= 2d-109) then
        tmp = t_1
    else if ((b * c) <= 2d+129) then
        tmp = t_2
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * (a * -4.0);
	double t_2 = 18.0 * (t * (x * (y * z)));
	double tmp;
	if ((b * c) <= -2e+153) {
		tmp = b * c;
	} else if ((b * c) <= -2e+31) {
		tmp = t_1;
	} else if ((b * c) <= -1e-66) {
		tmp = c * (-27.0 * ((j * k) / c));
	} else if ((b * c) <= -2e-186) {
		tmp = t_1;
	} else if ((b * c) <= 5e-184) {
		tmp = t_2;
	} else if ((b * c) <= 2e-109) {
		tmp = t_1;
	} else if ((b * c) <= 2e+129) {
		tmp = t_2;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = t * (a * -4.0)
	t_2 = 18.0 * (t * (x * (y * z)))
	tmp = 0
	if (b * c) <= -2e+153:
		tmp = b * c
	elif (b * c) <= -2e+31:
		tmp = t_1
	elif (b * c) <= -1e-66:
		tmp = c * (-27.0 * ((j * k) / c))
	elif (b * c) <= -2e-186:
		tmp = t_1
	elif (b * c) <= 5e-184:
		tmp = t_2
	elif (b * c) <= 2e-109:
		tmp = t_1
	elif (b * c) <= 2e+129:
		tmp = t_2
	else:
		tmp = b * c
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(t * Float64(a * -4.0))
	t_2 = Float64(18.0 * Float64(t * Float64(x * Float64(y * z))))
	tmp = 0.0
	if (Float64(b * c) <= -2e+153)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -2e+31)
		tmp = t_1;
	elseif (Float64(b * c) <= -1e-66)
		tmp = Float64(c * Float64(-27.0 * Float64(Float64(j * k) / c)));
	elseif (Float64(b * c) <= -2e-186)
		tmp = t_1;
	elseif (Float64(b * c) <= 5e-184)
		tmp = t_2;
	elseif (Float64(b * c) <= 2e-109)
		tmp = t_1;
	elseif (Float64(b * c) <= 2e+129)
		tmp = t_2;
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = t * (a * -4.0);
	t_2 = 18.0 * (t * (x * (y * z)));
	tmp = 0.0;
	if ((b * c) <= -2e+153)
		tmp = b * c;
	elseif ((b * c) <= -2e+31)
		tmp = t_1;
	elseif ((b * c) <= -1e-66)
		tmp = c * (-27.0 * ((j * k) / c));
	elseif ((b * c) <= -2e-186)
		tmp = t_1;
	elseif ((b * c) <= 5e-184)
		tmp = t_2;
	elseif ((b * c) <= 2e-109)
		tmp = t_1;
	elseif ((b * c) <= 2e+129)
		tmp = t_2;
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -2e+153], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -2e+31], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], -1e-66], N[(c * N[(-27.0 * N[(N[(j * k), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -2e-186], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 5e-184], t$95$2, If[LessEqual[N[(b * c), $MachinePrecision], 2e-109], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 2e+129], t$95$2, N[(b * c), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 b c) < -2e153 or 2e129 < (*.f64 b c)

   1. Initial program 83.2%

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

   3. Simplified 82.0%

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

   5. Taylor expanded in c around inf 84.8%

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

   6. Taylor expanded in c around inf 70.5%

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

   if -2e153 < (*.f64 b c) < -1.9999999999999999e31 or -9.9999999999999998e-67 < (*.f64 b c) < -1.9999999999999998e-186 or 5.00000000000000003e-184 < (*.f64 b c) < 2e-109

   1. Initial program 87.2%

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

   3. Simplified 87.3%

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

   5. Taylor expanded in c around inf 73.0%

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

   6. Taylor expanded in a around inf 47.4%

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

      1. *-commutative 47.4%

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

      2. *-commutative 47.4%

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

      3. associate-*r* 47.4%

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

   8. Simplified 47.4%

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

   if -1.9999999999999999e31 < (*.f64 b c) < -9.9999999999999998e-67

   1. Initial program 93.4%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in c around inf 87.6%

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

   6. Taylor expanded in x around 0 75.3%

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

   7. Taylor expanded in j around inf 51.1%

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

   if -1.9999999999999998e-186 < (*.f64 b c) < 5.00000000000000003e-184 or 2e-109 < (*.f64 b c) < 2e129

   1. Initial program 90.1%

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

   3. Simplified 92.8%

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

   5. Taylor expanded in c around inf 71.0%

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

   6. Taylor expanded in y around inf 32.9%

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

4. Final simplification 48.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2 \cdot 10^{+153}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -2 \cdot 10^{+31}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq -1 \cdot 10^{-66}:\\ \;\;\;\;c \cdot \left(-27 \cdot \frac{j \cdot k}{c}\right)\\ \mathbf{elif}\;b \cdot c \leq -2 \cdot 10^{-186}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 5 \cdot 10^{-184}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 2 \cdot 10^{-109}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 2 \cdot 10^{+129}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 36.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ \mathbf{if}\;b \cdot c \leq -2 \cdot 10^{+153}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -2 \cdot 10^{+31}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq -1 \cdot 10^{-66}:\\ \;\;\;\;c \cdot \left(-27 \cdot \frac{j \cdot k}{c}\right)\\ \mathbf{elif}\;b \cdot c \leq -2 \cdot 10^{-186}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq 5 \cdot 10^{-184}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 2 \cdot 10^{-109}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq 2 \cdot 10^{+129}:\\ \;\;\;\;t \cdot \left(\left(18 \cdot z\right) \cdot \left(y \cdot x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* t (* a -4.0))))
   (if (<= (* b c) -2e+153)
     (* b c)
     (if (<= (* b c) -2e+31)
       t_1
       (if (<= (* b c) -1e-66)
         (* c (* -27.0 (/ (* j k) c)))
         (if (<= (* b c) -2e-186)
           t_1
           (if (<= (* b c) 5e-184)
             (* 18.0 (* t (* x (* y z))))
             (if (<= (* b c) 2e-109)
               t_1
               (if (<= (* b c) 2e+129)
                 (* t (* (* 18.0 z) (* y x)))
                 (* b c))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * (a * -4.0);
	double tmp;
	if ((b * c) <= -2e+153) {
		tmp = b * c;
	} else if ((b * c) <= -2e+31) {
		tmp = t_1;
	} else if ((b * c) <= -1e-66) {
		tmp = c * (-27.0 * ((j * k) / c));
	} else if ((b * c) <= -2e-186) {
		tmp = t_1;
	} else if ((b * c) <= 5e-184) {
		tmp = 18.0 * (t * (x * (y * z)));
	} else if ((b * c) <= 2e-109) {
		tmp = t_1;
	} else if ((b * c) <= 2e+129) {
		tmp = t * ((18.0 * z) * (y * x));
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (a * (-4.0d0))
    if ((b * c) <= (-2d+153)) then
        tmp = b * c
    else if ((b * c) <= (-2d+31)) then
        tmp = t_1
    else if ((b * c) <= (-1d-66)) then
        tmp = c * ((-27.0d0) * ((j * k) / c))
    else if ((b * c) <= (-2d-186)) then
        tmp = t_1
    else if ((b * c) <= 5d-184) then
        tmp = 18.0d0 * (t * (x * (y * z)))
    else if ((b * c) <= 2d-109) then
        tmp = t_1
    else if ((b * c) <= 2d+129) then
        tmp = t * ((18.0d0 * z) * (y * x))
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * (a * -4.0);
	double tmp;
	if ((b * c) <= -2e+153) {
		tmp = b * c;
	} else if ((b * c) <= -2e+31) {
		tmp = t_1;
	} else if ((b * c) <= -1e-66) {
		tmp = c * (-27.0 * ((j * k) / c));
	} else if ((b * c) <= -2e-186) {
		tmp = t_1;
	} else if ((b * c) <= 5e-184) {
		tmp = 18.0 * (t * (x * (y * z)));
	} else if ((b * c) <= 2e-109) {
		tmp = t_1;
	} else if ((b * c) <= 2e+129) {
		tmp = t * ((18.0 * z) * (y * x));
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = t * (a * -4.0)
	tmp = 0
	if (b * c) <= -2e+153:
		tmp = b * c
	elif (b * c) <= -2e+31:
		tmp = t_1
	elif (b * c) <= -1e-66:
		tmp = c * (-27.0 * ((j * k) / c))
	elif (b * c) <= -2e-186:
		tmp = t_1
	elif (b * c) <= 5e-184:
		tmp = 18.0 * (t * (x * (y * z)))
	elif (b * c) <= 2e-109:
		tmp = t_1
	elif (b * c) <= 2e+129:
		tmp = t * ((18.0 * z) * (y * x))
	else:
		tmp = b * c
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(t * Float64(a * -4.0))
	tmp = 0.0
	if (Float64(b * c) <= -2e+153)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -2e+31)
		tmp = t_1;
	elseif (Float64(b * c) <= -1e-66)
		tmp = Float64(c * Float64(-27.0 * Float64(Float64(j * k) / c)));
	elseif (Float64(b * c) <= -2e-186)
		tmp = t_1;
	elseif (Float64(b * c) <= 5e-184)
		tmp = Float64(18.0 * Float64(t * Float64(x * Float64(y * z))));
	elseif (Float64(b * c) <= 2e-109)
		tmp = t_1;
	elseif (Float64(b * c) <= 2e+129)
		tmp = Float64(t * Float64(Float64(18.0 * z) * Float64(y * x)));
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = t * (a * -4.0);
	tmp = 0.0;
	if ((b * c) <= -2e+153)
		tmp = b * c;
	elseif ((b * c) <= -2e+31)
		tmp = t_1;
	elseif ((b * c) <= -1e-66)
		tmp = c * (-27.0 * ((j * k) / c));
	elseif ((b * c) <= -2e-186)
		tmp = t_1;
	elseif ((b * c) <= 5e-184)
		tmp = 18.0 * (t * (x * (y * z)));
	elseif ((b * c) <= 2e-109)
		tmp = t_1;
	elseif ((b * c) <= 2e+129)
		tmp = t * ((18.0 * z) * (y * x));
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -2e+153], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -2e+31], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], -1e-66], N[(c * N[(-27.0 * N[(N[(j * k), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -2e-186], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 5e-184], N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 2e-109], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 2e+129], N[(t * N[(N[(18.0 * z), $MachinePrecision] * N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 b c) < -2e153 or 2e129 < (*.f64 b c)

   1. Initial program 83.2%

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

   3. Simplified 82.0%

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

   5. Taylor expanded in c around inf 84.8%

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

   6. Taylor expanded in c around inf 70.5%

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

   if -2e153 < (*.f64 b c) < -1.9999999999999999e31 or -9.9999999999999998e-67 < (*.f64 b c) < -1.9999999999999998e-186 or 5.00000000000000003e-184 < (*.f64 b c) < 2e-109

   1. Initial program 87.2%

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

   3. Simplified 87.3%

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

   5. Taylor expanded in c around inf 73.0%

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

   6. Taylor expanded in a around inf 47.4%

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

      1. *-commutative 47.4%

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

      2. *-commutative 47.4%

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

      3. associate-*r* 47.4%

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

   8. Simplified 47.4%

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

   if -1.9999999999999999e31 < (*.f64 b c) < -9.9999999999999998e-67

   1. Initial program 93.4%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in c around inf 87.6%

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

   6. Taylor expanded in x around 0 75.3%

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

   7. Taylor expanded in j around inf 51.1%

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

   if -1.9999999999999998e-186 < (*.f64 b c) < 5.00000000000000003e-184

   1. Initial program 96.1%

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

   3. Simplified 98.0%

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

   5. Taylor expanded in c around inf 68.7%

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

   6. Taylor expanded in y around inf 31.0%

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

   if 2e-109 < (*.f64 b c) < 2e129

   1. Initial program 84.5%

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

   3. Simplified 88.1%

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

   5. Taylor expanded in c around inf 73.1%

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

   6. Taylor expanded in y around inf 34.7%

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

      1. *-commutative 34.7%

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

      2. associate-*r* 34.7%

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

      3. associate-*r* 36.3%

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

      4. *-commutative 36.3%

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

      5. associate-*r* 36.4%

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

   8. Simplified 36.4%

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

4. Final simplification 48.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2 \cdot 10^{+153}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -2 \cdot 10^{+31}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq -1 \cdot 10^{-66}:\\ \;\;\;\;c \cdot \left(-27 \cdot \frac{j \cdot k}{c}\right)\\ \mathbf{elif}\;b \cdot c \leq -2 \cdot 10^{-186}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 5 \cdot 10^{-184}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 2 \cdot 10^{-109}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 2 \cdot 10^{+129}:\\ \;\;\;\;t \cdot \left(\left(18 \cdot z\right) \cdot \left(y \cdot x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 56.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := x \cdot \left(y \cdot z\right)\\ t_3 := t\_1 + 18 \cdot \left(t \cdot t\_2\right)\\ t_4 := b \cdot c - 4 \cdot \left(x \cdot i\right)\\ t_5 := t \cdot \left(18 \cdot t\_2 - 4 \cdot a\right)\\ \mathbf{if}\;t \leq -4 \cdot 10^{-50}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{-271}:\\ \;\;\;\;b \cdot c + t\_1\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-32}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+50}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+87}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{+116}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{+161}:\\ \;\;\;\;c \cdot \left(b + -4 \cdot \frac{t \cdot a}{c}\right)\\ \mathbf{elif}\;t \leq 6.9 \cdot 10^{+186}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_5\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0)))
        (t_2 (* x (* y z)))
        (t_3 (+ t_1 (* 18.0 (* t t_2))))
        (t_4 (- (* b c) (* 4.0 (* x i))))
        (t_5 (* t (- (* 18.0 t_2) (* 4.0 a)))))
   (if (<= t -4e-50)
     t_5
     (if (<= t -2.9e-271)
       (+ (* b c) t_1)
       (if (<= t 7e-32)
         t_4
         (if (<= t 3.2e+50)
           t_5
           (if (<= t 2e+87)
             t_4
             (if (<= t 1.5e+116)
               t_3
               (if (<= t 5.6e+161)
                 (* c (+ b (* -4.0 (/ (* t a) c))))
                 (if (<= t 6.9e+186) t_3 t_5))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = x * (y * z);
	double t_3 = t_1 + (18.0 * (t * t_2));
	double t_4 = (b * c) - (4.0 * (x * i));
	double t_5 = t * ((18.0 * t_2) - (4.0 * a));
	double tmp;
	if (t <= -4e-50) {
		tmp = t_5;
	} else if (t <= -2.9e-271) {
		tmp = (b * c) + t_1;
	} else if (t <= 7e-32) {
		tmp = t_4;
	} else if (t <= 3.2e+50) {
		tmp = t_5;
	} else if (t <= 2e+87) {
		tmp = t_4;
	} else if (t <= 1.5e+116) {
		tmp = t_3;
	} else if (t <= 5.6e+161) {
		tmp = c * (b + (-4.0 * ((t * a) / c)));
	} else if (t <= 6.9e+186) {
		tmp = t_3;
	} else {
		tmp = t_5;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_1 = j * (k * (-27.0d0))
    t_2 = x * (y * z)
    t_3 = t_1 + (18.0d0 * (t * t_2))
    t_4 = (b * c) - (4.0d0 * (x * i))
    t_5 = t * ((18.0d0 * t_2) - (4.0d0 * a))
    if (t <= (-4d-50)) then
        tmp = t_5
    else if (t <= (-2.9d-271)) then
        tmp = (b * c) + t_1
    else if (t <= 7d-32) then
        tmp = t_4
    else if (t <= 3.2d+50) then
        tmp = t_5
    else if (t <= 2d+87) then
        tmp = t_4
    else if (t <= 1.5d+116) then
        tmp = t_3
    else if (t <= 5.6d+161) then
        tmp = c * (b + ((-4.0d0) * ((t * a) / c)))
    else if (t <= 6.9d+186) then
        tmp = t_3
    else
        tmp = t_5
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = x * (y * z);
	double t_3 = t_1 + (18.0 * (t * t_2));
	double t_4 = (b * c) - (4.0 * (x * i));
	double t_5 = t * ((18.0 * t_2) - (4.0 * a));
	double tmp;
	if (t <= -4e-50) {
		tmp = t_5;
	} else if (t <= -2.9e-271) {
		tmp = (b * c) + t_1;
	} else if (t <= 7e-32) {
		tmp = t_4;
	} else if (t <= 3.2e+50) {
		tmp = t_5;
	} else if (t <= 2e+87) {
		tmp = t_4;
	} else if (t <= 1.5e+116) {
		tmp = t_3;
	} else if (t <= 5.6e+161) {
		tmp = c * (b + (-4.0 * ((t * a) / c)));
	} else if (t <= 6.9e+186) {
		tmp = t_3;
	} else {
		tmp = t_5;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	t_2 = x * (y * z)
	t_3 = t_1 + (18.0 * (t * t_2))
	t_4 = (b * c) - (4.0 * (x * i))
	t_5 = t * ((18.0 * t_2) - (4.0 * a))
	tmp = 0
	if t <= -4e-50:
		tmp = t_5
	elif t <= -2.9e-271:
		tmp = (b * c) + t_1
	elif t <= 7e-32:
		tmp = t_4
	elif t <= 3.2e+50:
		tmp = t_5
	elif t <= 2e+87:
		tmp = t_4
	elif t <= 1.5e+116:
		tmp = t_3
	elif t <= 5.6e+161:
		tmp = c * (b + (-4.0 * ((t * a) / c)))
	elif t <= 6.9e+186:
		tmp = t_3
	else:
		tmp = t_5
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * -27.0))
	t_2 = Float64(x * Float64(y * z))
	t_3 = Float64(t_1 + Float64(18.0 * Float64(t * t_2)))
	t_4 = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)))
	t_5 = Float64(t * Float64(Float64(18.0 * t_2) - Float64(4.0 * a)))
	tmp = 0.0
	if (t <= -4e-50)
		tmp = t_5;
	elseif (t <= -2.9e-271)
		tmp = Float64(Float64(b * c) + t_1);
	elseif (t <= 7e-32)
		tmp = t_4;
	elseif (t <= 3.2e+50)
		tmp = t_5;
	elseif (t <= 2e+87)
		tmp = t_4;
	elseif (t <= 1.5e+116)
		tmp = t_3;
	elseif (t <= 5.6e+161)
		tmp = Float64(c * Float64(b + Float64(-4.0 * Float64(Float64(t * a) / c))));
	elseif (t <= 6.9e+186)
		tmp = t_3;
	else
		tmp = t_5;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * -27.0);
	t_2 = x * (y * z);
	t_3 = t_1 + (18.0 * (t * t_2));
	t_4 = (b * c) - (4.0 * (x * i));
	t_5 = t * ((18.0 * t_2) - (4.0 * a));
	tmp = 0.0;
	if (t <= -4e-50)
		tmp = t_5;
	elseif (t <= -2.9e-271)
		tmp = (b * c) + t_1;
	elseif (t <= 7e-32)
		tmp = t_4;
	elseif (t <= 3.2e+50)
		tmp = t_5;
	elseif (t <= 2e+87)
		tmp = t_4;
	elseif (t <= 1.5e+116)
		tmp = t_3;
	elseif (t <= 5.6e+161)
		tmp = c * (b + (-4.0 * ((t * a) / c)));
	elseif (t <= 6.9e+186)
		tmp = t_3;
	else
		tmp = t_5;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$1 + N[(18.0 * N[(t * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(t * N[(N[(18.0 * t$95$2), $MachinePrecision] - N[(4.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4e-50], t$95$5, If[LessEqual[t, -2.9e-271], N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[t, 7e-32], t$95$4, If[LessEqual[t, 3.2e+50], t$95$5, If[LessEqual[t, 2e+87], t$95$4, If[LessEqual[t, 1.5e+116], t$95$3, If[LessEqual[t, 5.6e+161], N[(c * N[(b + N[(-4.0 * N[(N[(t * a), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.9e+186], t$95$3, t$95$5]]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -4.00000000000000003e-50 or 6.9999999999999997e-32 < t < 3.19999999999999983e50 or 6.89999999999999992e186 < t

   1. Initial program 89.2%

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

   3. Simplified 90.3%

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

   5. Taylor expanded in c around inf 77.7%

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

   6. Taylor expanded in t around -inf 69.1%

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

   if -4.00000000000000003e-50 < t < -2.90000000000000014e-271

   1. Initial program 91.8%

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

   3. Simplified 93.7%

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

   5. Taylor expanded in b around inf 72.9%

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

   if -2.90000000000000014e-271 < t < 6.9999999999999997e-32 or 3.19999999999999983e50 < t < 1.9999999999999999e87

   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 80.0%

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

   5. Taylor expanded in j around 0 69.8%

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

   6. Taylor expanded in t around 0 64.6%

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

   if 1.9999999999999999e87 < t < 1.4999999999999999e116 or 5.60000000000000041e161 < t < 6.89999999999999992e186

   1. Initial program 92.6%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around inf 85.8%

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

   if 1.4999999999999999e116 < t < 5.60000000000000041e161

   1. Initial program 92.7%

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

   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 c around inf 92.6%

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

   6. Taylor expanded in x around 0 79.8%

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

   7. Taylor expanded in j around 0 80.0%

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

4. Final simplification 70.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{-50}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{-271}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-32}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+50}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+87}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{+116}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{+161}:\\ \;\;\;\;c \cdot \left(b + -4 \cdot \frac{t \cdot a}{c}\right)\\ \mathbf{elif}\;t \leq 6.9 \cdot 10^{+186}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 56.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := x \cdot \left(y \cdot z\right)\\ t_3 := b \cdot c - 4 \cdot \left(x \cdot i\right)\\ t_4 := t \cdot \left(18 \cdot t\_2 - 4 \cdot a\right)\\ \mathbf{if}\;t \leq -3.85 \cdot 10^{-50}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t \leq -4.8 \cdot 10^{-274}:\\ \;\;\;\;b \cdot c + t\_1\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-29}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{+53}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+82}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{+116}:\\ \;\;\;\;t\_1 + 18 \cdot \left(t \cdot t\_2\right)\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+160}:\\ \;\;\;\;c \cdot \left(b + -4 \cdot \frac{t \cdot a}{c}\right)\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+182}:\\ \;\;\;\;t\_1 + 18 \cdot \left(\left(y \cdot z\right) \cdot \left(t \cdot x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0)))
        (t_2 (* x (* y z)))
        (t_3 (- (* b c) (* 4.0 (* x i))))
        (t_4 (* t (- (* 18.0 t_2) (* 4.0 a)))))
   (if (<= t -3.85e-50)
     t_4
     (if (<= t -4.8e-274)
       (+ (* b c) t_1)
       (if (<= t 5e-29)
         t_3
         (if (<= t 3.8e+53)
           t_4
           (if (<= t 9e+82)
             t_3
             (if (<= t 1.35e+116)
               (+ t_1 (* 18.0 (* t t_2)))
               (if (<= t 9.5e+160)
                 (* c (+ b (* -4.0 (/ (* t a) c))))
                 (if (<= t 8e+182)
                   (+ t_1 (* 18.0 (* (* y z) (* t x))))
                   t_4))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = x * (y * z);
	double t_3 = (b * c) - (4.0 * (x * i));
	double t_4 = t * ((18.0 * t_2) - (4.0 * a));
	double tmp;
	if (t <= -3.85e-50) {
		tmp = t_4;
	} else if (t <= -4.8e-274) {
		tmp = (b * c) + t_1;
	} else if (t <= 5e-29) {
		tmp = t_3;
	} else if (t <= 3.8e+53) {
		tmp = t_4;
	} else if (t <= 9e+82) {
		tmp = t_3;
	} else if (t <= 1.35e+116) {
		tmp = t_1 + (18.0 * (t * t_2));
	} else if (t <= 9.5e+160) {
		tmp = c * (b + (-4.0 * ((t * a) / c)));
	} else if (t <= 8e+182) {
		tmp = t_1 + (18.0 * ((y * z) * (t * x)));
	} else {
		tmp = t_4;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = j * (k * (-27.0d0))
    t_2 = x * (y * z)
    t_3 = (b * c) - (4.0d0 * (x * i))
    t_4 = t * ((18.0d0 * t_2) - (4.0d0 * a))
    if (t <= (-3.85d-50)) then
        tmp = t_4
    else if (t <= (-4.8d-274)) then
        tmp = (b * c) + t_1
    else if (t <= 5d-29) then
        tmp = t_3
    else if (t <= 3.8d+53) then
        tmp = t_4
    else if (t <= 9d+82) then
        tmp = t_3
    else if (t <= 1.35d+116) then
        tmp = t_1 + (18.0d0 * (t * t_2))
    else if (t <= 9.5d+160) then
        tmp = c * (b + ((-4.0d0) * ((t * a) / c)))
    else if (t <= 8d+182) then
        tmp = t_1 + (18.0d0 * ((y * z) * (t * x)))
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = x * (y * z);
	double t_3 = (b * c) - (4.0 * (x * i));
	double t_4 = t * ((18.0 * t_2) - (4.0 * a));
	double tmp;
	if (t <= -3.85e-50) {
		tmp = t_4;
	} else if (t <= -4.8e-274) {
		tmp = (b * c) + t_1;
	} else if (t <= 5e-29) {
		tmp = t_3;
	} else if (t <= 3.8e+53) {
		tmp = t_4;
	} else if (t <= 9e+82) {
		tmp = t_3;
	} else if (t <= 1.35e+116) {
		tmp = t_1 + (18.0 * (t * t_2));
	} else if (t <= 9.5e+160) {
		tmp = c * (b + (-4.0 * ((t * a) / c)));
	} else if (t <= 8e+182) {
		tmp = t_1 + (18.0 * ((y * z) * (t * x)));
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	t_2 = x * (y * z)
	t_3 = (b * c) - (4.0 * (x * i))
	t_4 = t * ((18.0 * t_2) - (4.0 * a))
	tmp = 0
	if t <= -3.85e-50:
		tmp = t_4
	elif t <= -4.8e-274:
		tmp = (b * c) + t_1
	elif t <= 5e-29:
		tmp = t_3
	elif t <= 3.8e+53:
		tmp = t_4
	elif t <= 9e+82:
		tmp = t_3
	elif t <= 1.35e+116:
		tmp = t_1 + (18.0 * (t * t_2))
	elif t <= 9.5e+160:
		tmp = c * (b + (-4.0 * ((t * a) / c)))
	elif t <= 8e+182:
		tmp = t_1 + (18.0 * ((y * z) * (t * x)))
	else:
		tmp = t_4
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * -27.0))
	t_2 = Float64(x * Float64(y * z))
	t_3 = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)))
	t_4 = Float64(t * Float64(Float64(18.0 * t_2) - Float64(4.0 * a)))
	tmp = 0.0
	if (t <= -3.85e-50)
		tmp = t_4;
	elseif (t <= -4.8e-274)
		tmp = Float64(Float64(b * c) + t_1);
	elseif (t <= 5e-29)
		tmp = t_3;
	elseif (t <= 3.8e+53)
		tmp = t_4;
	elseif (t <= 9e+82)
		tmp = t_3;
	elseif (t <= 1.35e+116)
		tmp = Float64(t_1 + Float64(18.0 * Float64(t * t_2)));
	elseif (t <= 9.5e+160)
		tmp = Float64(c * Float64(b + Float64(-4.0 * Float64(Float64(t * a) / c))));
	elseif (t <= 8e+182)
		tmp = Float64(t_1 + Float64(18.0 * Float64(Float64(y * z) * Float64(t * x))));
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * -27.0);
	t_2 = x * (y * z);
	t_3 = (b * c) - (4.0 * (x * i));
	t_4 = t * ((18.0 * t_2) - (4.0 * a));
	tmp = 0.0;
	if (t <= -3.85e-50)
		tmp = t_4;
	elseif (t <= -4.8e-274)
		tmp = (b * c) + t_1;
	elseif (t <= 5e-29)
		tmp = t_3;
	elseif (t <= 3.8e+53)
		tmp = t_4;
	elseif (t <= 9e+82)
		tmp = t_3;
	elseif (t <= 1.35e+116)
		tmp = t_1 + (18.0 * (t * t_2));
	elseif (t <= 9.5e+160)
		tmp = c * (b + (-4.0 * ((t * a) / c)));
	elseif (t <= 8e+182)
		tmp = t_1 + (18.0 * ((y * z) * (t * x)));
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t * N[(N[(18.0 * t$95$2), $MachinePrecision] - N[(4.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.85e-50], t$95$4, If[LessEqual[t, -4.8e-274], N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[t, 5e-29], t$95$3, If[LessEqual[t, 3.8e+53], t$95$4, If[LessEqual[t, 9e+82], t$95$3, If[LessEqual[t, 1.35e+116], N[(t$95$1 + N[(18.0 * N[(t * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.5e+160], N[(c * N[(b + N[(-4.0 * N[(N[(t * a), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8e+182], N[(t$95$1 + N[(18.0 * N[(N[(y * z), $MachinePrecision] * N[(t * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$4]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -3.84999999999999982e-50 or 4.99999999999999986e-29 < t < 3.79999999999999997e53 or 8.0000000000000005e182 < t

   1. Initial program 89.3%

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

   3. Simplified 90.3%

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

   5. Taylor expanded in c around inf 77.1%

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

   6. Taylor expanded in t around -inf 69.4%

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

   if -3.84999999999999982e-50 < t < -4.8e-274

   1. Initial program 91.8%

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

   3. Simplified 93.7%

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

   5. Taylor expanded in b around inf 72.9%

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

   if -4.8e-274 < t < 4.99999999999999986e-29 or 3.79999999999999997e53 < t < 8.9999999999999993e82

   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 80.0%

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

   5. Taylor expanded in j around 0 69.8%

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

   6. Taylor expanded in t around 0 64.6%

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

   if 8.9999999999999993e82 < t < 1.35e116

   1. Initial program 87.3%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 87.3%

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

   if 1.35e116 < t < 9.5000000000000006e160

   1. Initial program 92.7%

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

   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 c around inf 92.6%

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

   6. Taylor expanded in x around 0 79.8%

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

   7. Taylor expanded in j around 0 80.0%

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

   if 9.5000000000000006e160 < t < 8.0000000000000005e182

   1. Initial program 100.0%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around inf 80.5%

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

      1. associate-*r* 81.3%

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

   7. Simplified 81.3%

      \[\leadsto \color{blue}{18 \cdot \left(\left(t \cdot x\right) \cdot \left(y \cdot z\right)\right)} + j \cdot \left(k \cdot -27\right) \]
3. Recombined 6 regimes into one program.

4. Final simplification 70.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.85 \cdot 10^{-50}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)\\ \mathbf{elif}\;t \leq -4.8 \cdot 10^{-274}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-29}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{+53}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+82}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{+116}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+160}:\\ \;\;\;\;c \cdot \left(b + -4 \cdot \frac{t \cdot a}{c}\right)\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+182}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + 18 \cdot \left(\left(y \cdot z\right) \cdot \left(t \cdot x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 70.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := 4 \cdot \left(x \cdot i\right)\\ t_2 := \left(j \cdot 27\right) \cdot k\\ t_3 := \left(b \cdot c + \left(t \cdot a\right) \cdot -4\right) - t\_1\\ t_4 := 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\\ \mathbf{if}\;t\_2 \leq -10000000:\\ \;\;\;\;\left(b \cdot c + 18 \cdot \left(t \cdot \left(z \cdot \left(y \cdot x\right)\right)\right)\right) - t\_2\\ \mathbf{elif}\;t\_2 \leq 10^{-305}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{-179}:\\ \;\;\;\;t \cdot \left(t\_4 - 4 \cdot a\right) - t\_1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+69}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(t\_4 + a \cdot -4\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* 4.0 (* x i)))
        (t_2 (* (* j 27.0) k))
        (t_3 (- (+ (* b c) (* (* t a) -4.0)) t_1))
        (t_4 (* 18.0 (* x (* y z)))))
   (if (<= t_2 -10000000.0)
     (- (+ (* b c) (* 18.0 (* t (* z (* y x))))) t_2)
     (if (<= t_2 1e-305)
       t_3
       (if (<= t_2 2e-179)
         (- (* t (- t_4 (* 4.0 a))) t_1)
         (if (<= t_2 2e+69)
           t_3
           (+ (* j (* k -27.0)) (* t (+ t_4 (* a -4.0))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 4.0 * (x * i);
	double t_2 = (j * 27.0) * k;
	double t_3 = ((b * c) + ((t * a) * -4.0)) - t_1;
	double t_4 = 18.0 * (x * (y * z));
	double tmp;
	if (t_2 <= -10000000.0) {
		tmp = ((b * c) + (18.0 * (t * (z * (y * x))))) - t_2;
	} else if (t_2 <= 1e-305) {
		tmp = t_3;
	} else if (t_2 <= 2e-179) {
		tmp = (t * (t_4 - (4.0 * a))) - t_1;
	} else if (t_2 <= 2e+69) {
		tmp = t_3;
	} else {
		tmp = (j * (k * -27.0)) + (t * (t_4 + (a * -4.0)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = 4.0d0 * (x * i)
    t_2 = (j * 27.0d0) * k
    t_3 = ((b * c) + ((t * a) * (-4.0d0))) - t_1
    t_4 = 18.0d0 * (x * (y * z))
    if (t_2 <= (-10000000.0d0)) then
        tmp = ((b * c) + (18.0d0 * (t * (z * (y * x))))) - t_2
    else if (t_2 <= 1d-305) then
        tmp = t_3
    else if (t_2 <= 2d-179) then
        tmp = (t * (t_4 - (4.0d0 * a))) - t_1
    else if (t_2 <= 2d+69) then
        tmp = t_3
    else
        tmp = (j * (k * (-27.0d0))) + (t * (t_4 + (a * (-4.0d0))))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 4.0 * (x * i);
	double t_2 = (j * 27.0) * k;
	double t_3 = ((b * c) + ((t * a) * -4.0)) - t_1;
	double t_4 = 18.0 * (x * (y * z));
	double tmp;
	if (t_2 <= -10000000.0) {
		tmp = ((b * c) + (18.0 * (t * (z * (y * x))))) - t_2;
	} else if (t_2 <= 1e-305) {
		tmp = t_3;
	} else if (t_2 <= 2e-179) {
		tmp = (t * (t_4 - (4.0 * a))) - t_1;
	} else if (t_2 <= 2e+69) {
		tmp = t_3;
	} else {
		tmp = (j * (k * -27.0)) + (t * (t_4 + (a * -4.0)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = 4.0 * (x * i)
	t_2 = (j * 27.0) * k
	t_3 = ((b * c) + ((t * a) * -4.0)) - t_1
	t_4 = 18.0 * (x * (y * z))
	tmp = 0
	if t_2 <= -10000000.0:
		tmp = ((b * c) + (18.0 * (t * (z * (y * x))))) - t_2
	elif t_2 <= 1e-305:
		tmp = t_3
	elif t_2 <= 2e-179:
		tmp = (t * (t_4 - (4.0 * a))) - t_1
	elif t_2 <= 2e+69:
		tmp = t_3
	else:
		tmp = (j * (k * -27.0)) + (t * (t_4 + (a * -4.0)))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(4.0 * Float64(x * i))
	t_2 = Float64(Float64(j * 27.0) * k)
	t_3 = Float64(Float64(Float64(b * c) + Float64(Float64(t * a) * -4.0)) - t_1)
	t_4 = Float64(18.0 * Float64(x * Float64(y * z)))
	tmp = 0.0
	if (t_2 <= -10000000.0)
		tmp = Float64(Float64(Float64(b * c) + Float64(18.0 * Float64(t * Float64(z * Float64(y * x))))) - t_2);
	elseif (t_2 <= 1e-305)
		tmp = t_3;
	elseif (t_2 <= 2e-179)
		tmp = Float64(Float64(t * Float64(t_4 - Float64(4.0 * a))) - t_1);
	elseif (t_2 <= 2e+69)
		tmp = t_3;
	else
		tmp = Float64(Float64(j * Float64(k * -27.0)) + Float64(t * Float64(t_4 + Float64(a * -4.0))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = 4.0 * (x * i);
	t_2 = (j * 27.0) * k;
	t_3 = ((b * c) + ((t * a) * -4.0)) - t_1;
	t_4 = 18.0 * (x * (y * z));
	tmp = 0.0;
	if (t_2 <= -10000000.0)
		tmp = ((b * c) + (18.0 * (t * (z * (y * x))))) - t_2;
	elseif (t_2 <= 1e-305)
		tmp = t_3;
	elseif (t_2 <= 2e-179)
		tmp = (t * (t_4 - (4.0 * a))) - t_1;
	elseif (t_2 <= 2e+69)
		tmp = t_3;
	else
		tmp = (j * (k * -27.0)) + (t * (t_4 + (a * -4.0)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(b * c), $MachinePrecision] + N[(N[(t * a), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]}, Block[{t$95$4 = N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -10000000.0], N[(N[(N[(b * c), $MachinePrecision] + N[(18.0 * N[(t * N[(z * N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], If[LessEqual[t$95$2, 1e-305], t$95$3, If[LessEqual[t$95$2, 2e-179], N[(N[(t * N[(t$95$4 - N[(4.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[t$95$2, 2e+69], t$95$3, N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(t * N[(t$95$4 + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -1e7

   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 81.9%

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

   4. Taylor expanded in a around 0 78.6%

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

      1. pow1 78.6%

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

   6. Applied egg-rr 78.6%

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

      1. unpow1 78.6%

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

      2. associate-*r* 76.9%

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

   8. Simplified 76.9%

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

   9. Taylor expanded in t around inf 79.9%

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

       1. associate-*r* 83.4%

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

       2. *-commutative 83.4%

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

   11. Simplified 83.4%

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

   if -1e7 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 9.99999999999999996e-306 or 2e-179 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 2.0000000000000001e69

   1. Initial program 90.5%

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

   3. Simplified 91.9%

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

   5. Taylor expanded in j around 0 90.5%

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

   6. Taylor expanded in x around 0 80.4%

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

   if 9.99999999999999996e-306 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 2e-179

   1. Initial program 67.1%

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

   3. Simplified 73.7%

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

   5. Taylor expanded in j around 0 73.7%

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

   6. Taylor expanded in b around 0 87.1%

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

   if 2.0000000000000001e69 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 79.1%

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

   3. Simplified 86.0%

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

   5. Taylor expanded in t around inf 81.5%

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

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \leq -10000000:\\ \;\;\;\;\left(b \cdot c + 18 \cdot \left(t \cdot \left(z \cdot \left(y \cdot x\right)\right)\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 10^{-305}:\\ \;\;\;\;\left(b \cdot c + \left(t \cdot a\right) \cdot -4\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 2 \cdot 10^{-179}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 2 \cdot 10^{+69}:\\ \;\;\;\;\left(b \cdot c + \left(t \cdot a\right) \cdot -4\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 71.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := 4 \cdot \left(x \cdot i\right)\\ t_2 := \left(b \cdot c + \left(t \cdot a\right) \cdot -4\right) - t\_1\\ t_3 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_3 \leq -10000000:\\ \;\;\;\;\left(b \cdot c + 18 \cdot \left(t \cdot \left(z \cdot \left(y \cdot x\right)\right)\right)\right) - t\_3\\ \mathbf{elif}\;t\_3 \leq 10^{-305}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_3 \leq 2 \cdot 10^{-179}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right) - t\_1\\ \mathbf{elif}\;t\_3 \leq 2 \cdot 10^{+33}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + y \cdot \left(z \cdot \left(t \cdot \left(18 \cdot x\right)\right)\right)\right) - t\_3\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* 4.0 (* x i)))
        (t_2 (- (+ (* b c) (* (* t a) -4.0)) t_1))
        (t_3 (* (* j 27.0) k)))
   (if (<= t_3 -10000000.0)
     (- (+ (* b c) (* 18.0 (* t (* z (* y x))))) t_3)
     (if (<= t_3 1e-305)
       t_2
       (if (<= t_3 2e-179)
         (- (* t (- (* 18.0 (* x (* y z))) (* 4.0 a))) t_1)
         (if (<= t_3 2e+33)
           t_2
           (- (+ (* b c) (* y (* z (* t (* 18.0 x))))) t_3)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 4.0 * (x * i);
	double t_2 = ((b * c) + ((t * a) * -4.0)) - t_1;
	double t_3 = (j * 27.0) * k;
	double tmp;
	if (t_3 <= -10000000.0) {
		tmp = ((b * c) + (18.0 * (t * (z * (y * x))))) - t_3;
	} else if (t_3 <= 1e-305) {
		tmp = t_2;
	} else if (t_3 <= 2e-179) {
		tmp = (t * ((18.0 * (x * (y * z))) - (4.0 * a))) - t_1;
	} else if (t_3 <= 2e+33) {
		tmp = t_2;
	} else {
		tmp = ((b * c) + (y * (z * (t * (18.0 * x))))) - 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.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = 4.0d0 * (x * i)
    t_2 = ((b * c) + ((t * a) * (-4.0d0))) - t_1
    t_3 = (j * 27.0d0) * k
    if (t_3 <= (-10000000.0d0)) then
        tmp = ((b * c) + (18.0d0 * (t * (z * (y * x))))) - t_3
    else if (t_3 <= 1d-305) then
        tmp = t_2
    else if (t_3 <= 2d-179) then
        tmp = (t * ((18.0d0 * (x * (y * z))) - (4.0d0 * a))) - t_1
    else if (t_3 <= 2d+33) then
        tmp = t_2
    else
        tmp = ((b * c) + (y * (z * (t * (18.0d0 * x))))) - 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;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 4.0 * (x * i);
	double t_2 = ((b * c) + ((t * a) * -4.0)) - t_1;
	double t_3 = (j * 27.0) * k;
	double tmp;
	if (t_3 <= -10000000.0) {
		tmp = ((b * c) + (18.0 * (t * (z * (y * x))))) - t_3;
	} else if (t_3 <= 1e-305) {
		tmp = t_2;
	} else if (t_3 <= 2e-179) {
		tmp = (t * ((18.0 * (x * (y * z))) - (4.0 * a))) - t_1;
	} else if (t_3 <= 2e+33) {
		tmp = t_2;
	} else {
		tmp = ((b * c) + (y * (z * (t * (18.0 * x))))) - 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])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = 4.0 * (x * i)
	t_2 = ((b * c) + ((t * a) * -4.0)) - t_1
	t_3 = (j * 27.0) * k
	tmp = 0
	if t_3 <= -10000000.0:
		tmp = ((b * c) + (18.0 * (t * (z * (y * x))))) - t_3
	elif t_3 <= 1e-305:
		tmp = t_2
	elif t_3 <= 2e-179:
		tmp = (t * ((18.0 * (x * (y * z))) - (4.0 * a))) - t_1
	elif t_3 <= 2e+33:
		tmp = t_2
	else:
		tmp = ((b * c) + (y * (z * (t * (18.0 * x))))) - 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])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(4.0 * Float64(x * i))
	t_2 = Float64(Float64(Float64(b * c) + Float64(Float64(t * a) * -4.0)) - t_1)
	t_3 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_3 <= -10000000.0)
		tmp = Float64(Float64(Float64(b * c) + Float64(18.0 * Float64(t * Float64(z * Float64(y * x))))) - t_3);
	elseif (t_3 <= 1e-305)
		tmp = t_2;
	elseif (t_3 <= 2e-179)
		tmp = Float64(Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(4.0 * a))) - t_1);
	elseif (t_3 <= 2e+33)
		tmp = t_2;
	else
		tmp = Float64(Float64(Float64(b * c) + Float64(y * Float64(z * Float64(t * Float64(18.0 * x))))) - 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])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = 4.0 * (x * i);
	t_2 = ((b * c) + ((t * a) * -4.0)) - t_1;
	t_3 = (j * 27.0) * k;
	tmp = 0.0;
	if (t_3 <= -10000000.0)
		tmp = ((b * c) + (18.0 * (t * (z * (y * x))))) - t_3;
	elseif (t_3 <= 1e-305)
		tmp = t_2;
	elseif (t_3 <= 2e-179)
		tmp = (t * ((18.0 * (x * (y * z))) - (4.0 * a))) - t_1;
	elseif (t_3 <= 2e+33)
		tmp = t_2;
	else
		tmp = ((b * c) + (y * (z * (t * (18.0 * x))))) - 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.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(b * c), $MachinePrecision] + N[(N[(t * a), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$3, -10000000.0], N[(N[(N[(b * c), $MachinePrecision] + N[(18.0 * N[(t * N[(z * N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$3), $MachinePrecision], If[LessEqual[t$95$3, 1e-305], t$95$2, If[LessEqual[t$95$3, 2e-179], N[(N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[t$95$3, 2e+33], t$95$2, N[(N[(N[(b * c), $MachinePrecision] + N[(y * N[(z * N[(t * N[(18.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$3), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -1e7

   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 81.9%

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

   4. Taylor expanded in a around 0 78.6%

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

      1. pow1 78.6%

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

   6. Applied egg-rr 78.6%

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

      1. unpow1 78.6%

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

      2. associate-*r* 76.9%

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

   8. Simplified 76.9%

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

   9. Taylor expanded in t around inf 79.9%

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

       1. associate-*r* 83.4%

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

       2. *-commutative 83.4%

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

   11. Simplified 83.4%

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

   if -1e7 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 9.99999999999999996e-306 or 2e-179 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 1.9999999999999999e33

   1. Initial program 91.1%

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

   3. Simplified 92.5%

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

   5. Taylor expanded in j around 0 91.1%

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

   6. Taylor expanded in x around 0 80.3%

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

   if 9.99999999999999996e-306 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 2e-179

   1. Initial program 67.1%

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

   3. Simplified 73.7%

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

   5. Taylor expanded in j around 0 73.7%

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

   6. Taylor expanded in b around 0 87.1%

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

   if 1.9999999999999999e33 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 77.8%

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

   3. Taylor expanded in x around 0 82.4%

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

   4. Taylor expanded in a around 0 80.4%

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

      1. pow1 80.4%

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

   6. Applied egg-rr 80.4%

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

      1. unpow1 80.4%

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

      2. associate-*r* 84.6%

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

   8. Simplified 84.6%

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

   9. Taylor expanded in t around inf 77.9%

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

       1. associate-*r* 78.0%

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

       2. associate-*r* 78.0%

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

       3. *-commutative 78.0%

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

       4. associate-*r* 80.1%

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

       5. *-commutative 80.1%

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

       6. associate-*r* 80.1%

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

   11. Simplified 80.1%

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

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \leq -10000000:\\ \;\;\;\;\left(b \cdot c + 18 \cdot \left(t \cdot \left(z \cdot \left(y \cdot x\right)\right)\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 10^{-305}:\\ \;\;\;\;\left(b \cdot c + \left(t \cdot a\right) \cdot -4\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 2 \cdot 10^{-179}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 2 \cdot 10^{+33}:\\ \;\;\;\;\left(b \cdot c + \left(t \cdot a\right) \cdot -4\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + y \cdot \left(z \cdot \left(t \cdot \left(18 \cdot x\right)\right)\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 50.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c - 4 \cdot \left(x \cdot i\right)\\ t_2 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+84}:\\ \;\;\;\;b \cdot c - t\_2\\ \mathbf{elif}\;t\_2 \leq 10^{-290}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{-167}:\\ \;\;\;\;t \cdot \left(\left(18 \cdot z\right) \cdot \left(y \cdot x\right)\right)\\ \mathbf{elif}\;t\_2 \leq 10^{+77}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+274}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(-27 \cdot \frac{j \cdot k}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (- (* b c) (* 4.0 (* x i)))) (t_2 (* (* j 27.0) k)))
   (if (<= t_2 -5e+84)
     (- (* b c) t_2)
     (if (<= t_2 1e-290)
       t_1
       (if (<= t_2 1e-167)
         (* t (* (* 18.0 z) (* y x)))
         (if (<= t_2 1e+77)
           t_1
           (if (<= t_2 5e+274)
             (* 18.0 (* t (* x (* y z))))
             (* c (* -27.0 (/ (* j k) c))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) - (4.0 * (x * i));
	double t_2 = (j * 27.0) * k;
	double tmp;
	if (t_2 <= -5e+84) {
		tmp = (b * c) - t_2;
	} else if (t_2 <= 1e-290) {
		tmp = t_1;
	} else if (t_2 <= 1e-167) {
		tmp = t * ((18.0 * z) * (y * x));
	} else if (t_2 <= 1e+77) {
		tmp = t_1;
	} else if (t_2 <= 5e+274) {
		tmp = 18.0 * (t * (x * (y * z)));
	} else {
		tmp = c * (-27.0 * ((j * k) / c));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (b * c) - (4.0d0 * (x * i))
    t_2 = (j * 27.0d0) * k
    if (t_2 <= (-5d+84)) then
        tmp = (b * c) - t_2
    else if (t_2 <= 1d-290) then
        tmp = t_1
    else if (t_2 <= 1d-167) then
        tmp = t * ((18.0d0 * z) * (y * x))
    else if (t_2 <= 1d+77) then
        tmp = t_1
    else if (t_2 <= 5d+274) then
        tmp = 18.0d0 * (t * (x * (y * z)))
    else
        tmp = c * ((-27.0d0) * ((j * k) / c))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) - (4.0 * (x * i));
	double t_2 = (j * 27.0) * k;
	double tmp;
	if (t_2 <= -5e+84) {
		tmp = (b * c) - t_2;
	} else if (t_2 <= 1e-290) {
		tmp = t_1;
	} else if (t_2 <= 1e-167) {
		tmp = t * ((18.0 * z) * (y * x));
	} else if (t_2 <= 1e+77) {
		tmp = t_1;
	} else if (t_2 <= 5e+274) {
		tmp = 18.0 * (t * (x * (y * z)));
	} else {
		tmp = c * (-27.0 * ((j * k) / c));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) - (4.0 * (x * i))
	t_2 = (j * 27.0) * k
	tmp = 0
	if t_2 <= -5e+84:
		tmp = (b * c) - t_2
	elif t_2 <= 1e-290:
		tmp = t_1
	elif t_2 <= 1e-167:
		tmp = t * ((18.0 * z) * (y * x))
	elif t_2 <= 1e+77:
		tmp = t_1
	elif t_2 <= 5e+274:
		tmp = 18.0 * (t * (x * (y * z)))
	else:
		tmp = c * (-27.0 * ((j * k) / c))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)))
	t_2 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_2 <= -5e+84)
		tmp = Float64(Float64(b * c) - t_2);
	elseif (t_2 <= 1e-290)
		tmp = t_1;
	elseif (t_2 <= 1e-167)
		tmp = Float64(t * Float64(Float64(18.0 * z) * Float64(y * x)));
	elseif (t_2 <= 1e+77)
		tmp = t_1;
	elseif (t_2 <= 5e+274)
		tmp = Float64(18.0 * Float64(t * Float64(x * Float64(y * z))));
	else
		tmp = Float64(c * Float64(-27.0 * Float64(Float64(j * k) / c)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) - (4.0 * (x * i));
	t_2 = (j * 27.0) * k;
	tmp = 0.0;
	if (t_2 <= -5e+84)
		tmp = (b * c) - t_2;
	elseif (t_2 <= 1e-290)
		tmp = t_1;
	elseif (t_2 <= 1e-167)
		tmp = t * ((18.0 * z) * (y * x));
	elseif (t_2 <= 1e+77)
		tmp = t_1;
	elseif (t_2 <= 5e+274)
		tmp = 18.0 * (t * (x * (y * z)));
	else
		tmp = c * (-27.0 * ((j * k) / c));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+84], N[(N[(b * c), $MachinePrecision] - t$95$2), $MachinePrecision], If[LessEqual[t$95$2, 1e-290], t$95$1, If[LessEqual[t$95$2, 1e-167], N[(t * N[(N[(18.0 * z), $MachinePrecision] * N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+77], t$95$1, If[LessEqual[t$95$2, 5e+274], N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(-27.0 * N[(N[(j * k), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -5.0000000000000001e84

   1. Initial program 90.6%

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

   3. Taylor expanded in x around 0 86.4%

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

   4. Taylor expanded in b around inf 68.8%

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

   if -5.0000000000000001e84 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 1.0000000000000001e-290 or 1e-167 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 9.99999999999999983e76

   1. Initial program 90.6%

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

   3. Simplified 91.3%

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

   5. Taylor expanded in j around 0 89.4%

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

   6. Taylor expanded in t around 0 54.7%

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

   if 1.0000000000000001e-290 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 1e-167

   1. Initial program 71.9%

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

   3. Simplified 79.0%

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

   5. Taylor expanded in c around inf 86.6%

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

   6. Taylor expanded in y around inf 44.8%

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

      1. *-commutative 44.8%

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

      2. associate-*r* 44.8%

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

      3. associate-*r* 44.8%

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

      4. *-commutative 44.8%

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

      5. associate-*r* 44.8%

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

   8. Simplified 44.8%

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

   if 9.99999999999999983e76 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 4.9999999999999998e274

   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 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 c around inf 61.4%

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

   6. Taylor expanded in y around inf 51.9%

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

   if 4.9999999999999998e274 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 71.4%

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

   3. Simplified 71.3%

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

   5. Taylor expanded in c around inf 64.3%

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

   6. Taylor expanded in x around 0 85.7%

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

   7. Taylor expanded in j around inf 85.7%

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

4. Final simplification 58.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \leq -5 \cdot 10^{+84}:\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 10^{-290}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 10^{-167}:\\ \;\;\;\;t \cdot \left(\left(18 \cdot z\right) \cdot \left(y \cdot x\right)\right)\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 10^{+77}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 5 \cdot 10^{+274}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(-27 \cdot \frac{j \cdot k}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 66.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(b \cdot c + \left(t \cdot a\right) \cdot -4\right) - 4 \cdot \left(x \cdot i\right)\\ t_2 := j \cdot \left(k \cdot -27\right)\\ t_3 := x \cdot \left(y \cdot z\right)\\ t_4 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_4 \leq -5 \cdot 10^{+84}:\\ \;\;\;\;t\_2 + 18 \cdot \left(t \cdot t\_3\right)\\ \mathbf{elif}\;t\_4 \leq 10^{-305}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_4 \leq 2 \cdot 10^{-179}:\\ \;\;\;\;t \cdot \left(18 \cdot t\_3 - 4 \cdot a\right)\\ \mathbf{elif}\;t\_4 \leq 2 \cdot 10^{+69}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2 + 18 \cdot \left(\left(y \cdot z\right) \cdot \left(t \cdot x\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (- (+ (* b c) (* (* t a) -4.0)) (* 4.0 (* x i))))
        (t_2 (* j (* k -27.0)))
        (t_3 (* x (* y z)))
        (t_4 (* (* j 27.0) k)))
   (if (<= t_4 -5e+84)
     (+ t_2 (* 18.0 (* t t_3)))
     (if (<= t_4 1e-305)
       t_1
       (if (<= t_4 2e-179)
         (* t (- (* 18.0 t_3) (* 4.0 a)))
         (if (<= t_4 2e+69) t_1 (+ t_2 (* 18.0 (* (* y z) (* t x))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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)) - (4.0 * (x * i));
	double t_2 = j * (k * -27.0);
	double t_3 = x * (y * z);
	double t_4 = (j * 27.0) * k;
	double tmp;
	if (t_4 <= -5e+84) {
		tmp = t_2 + (18.0 * (t * t_3));
	} else if (t_4 <= 1e-305) {
		tmp = t_1;
	} else if (t_4 <= 2e-179) {
		tmp = t * ((18.0 * t_3) - (4.0 * a));
	} else if (t_4 <= 2e+69) {
		tmp = t_1;
	} else {
		tmp = t_2 + (18.0 * ((y * z) * (t * x)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = ((b * c) + ((t * a) * (-4.0d0))) - (4.0d0 * (x * i))
    t_2 = j * (k * (-27.0d0))
    t_3 = x * (y * z)
    t_4 = (j * 27.0d0) * k
    if (t_4 <= (-5d+84)) then
        tmp = t_2 + (18.0d0 * (t * t_3))
    else if (t_4 <= 1d-305) then
        tmp = t_1
    else if (t_4 <= 2d-179) then
        tmp = t * ((18.0d0 * t_3) - (4.0d0 * a))
    else if (t_4 <= 2d+69) then
        tmp = t_1
    else
        tmp = t_2 + (18.0d0 * ((y * z) * (t * x)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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)) - (4.0 * (x * i));
	double t_2 = j * (k * -27.0);
	double t_3 = x * (y * z);
	double t_4 = (j * 27.0) * k;
	double tmp;
	if (t_4 <= -5e+84) {
		tmp = t_2 + (18.0 * (t * t_3));
	} else if (t_4 <= 1e-305) {
		tmp = t_1;
	} else if (t_4 <= 2e-179) {
		tmp = t * ((18.0 * t_3) - (4.0 * a));
	} else if (t_4 <= 2e+69) {
		tmp = t_1;
	} else {
		tmp = t_2 + (18.0 * ((y * z) * (t * x)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = ((b * c) + ((t * a) * -4.0)) - (4.0 * (x * i))
	t_2 = j * (k * -27.0)
	t_3 = x * (y * z)
	t_4 = (j * 27.0) * k
	tmp = 0
	if t_4 <= -5e+84:
		tmp = t_2 + (18.0 * (t * t_3))
	elif t_4 <= 1e-305:
		tmp = t_1
	elif t_4 <= 2e-179:
		tmp = t * ((18.0 * t_3) - (4.0 * a))
	elif t_4 <= 2e+69:
		tmp = t_1
	else:
		tmp = t_2 + (18.0 * ((y * z) * (t * x)))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(Float64(b * c) + Float64(Float64(t * a) * -4.0)) - Float64(4.0 * Float64(x * i)))
	t_2 = Float64(j * Float64(k * -27.0))
	t_3 = Float64(x * Float64(y * z))
	t_4 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_4 <= -5e+84)
		tmp = Float64(t_2 + Float64(18.0 * Float64(t * t_3)));
	elseif (t_4 <= 1e-305)
		tmp = t_1;
	elseif (t_4 <= 2e-179)
		tmp = Float64(t * Float64(Float64(18.0 * t_3) - Float64(4.0 * a)));
	elseif (t_4 <= 2e+69)
		tmp = t_1;
	else
		tmp = Float64(t_2 + Float64(18.0 * Float64(Float64(y * z) * Float64(t * x))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = ((b * c) + ((t * a) * -4.0)) - (4.0 * (x * i));
	t_2 = j * (k * -27.0);
	t_3 = x * (y * z);
	t_4 = (j * 27.0) * k;
	tmp = 0.0;
	if (t_4 <= -5e+84)
		tmp = t_2 + (18.0 * (t * t_3));
	elseif (t_4 <= 1e-305)
		tmp = t_1;
	elseif (t_4 <= 2e-179)
		tmp = t * ((18.0 * t_3) - (4.0 * a));
	elseif (t_4 <= 2e+69)
		tmp = t_1;
	else
		tmp = t_2 + (18.0 * ((y * z) * (t * x)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(N[(b * c), $MachinePrecision] + N[(N[(t * a), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$4, -5e+84], N[(t$95$2 + N[(18.0 * N[(t * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, 1e-305], t$95$1, If[LessEqual[t$95$4, 2e-179], N[(t * N[(N[(18.0 * t$95$3), $MachinePrecision] - N[(4.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, 2e+69], t$95$1, N[(t$95$2 + N[(18.0 * N[(N[(y * z), $MachinePrecision] * N[(t * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -5.0000000000000001e84

   1. Initial program 90.6%

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

   3. Simplified 93.3%

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

   5. Taylor expanded in y around inf 70.2%

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

   if -5.0000000000000001e84 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 9.99999999999999996e-306 or 2e-179 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 2.0000000000000001e69

   1. Initial program 91.1%

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

   3. Simplified 91.8%

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

   5. Taylor expanded in j around 0 90.5%

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

   6. Taylor expanded in x around 0 79.7%

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

   if 9.99999999999999996e-306 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 2e-179

   1. Initial program 67.1%

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

   3. Simplified 73.7%

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

   5. Taylor expanded in c around inf 80.8%

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

   6. Taylor expanded in t around -inf 75.4%

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

   if 2.0000000000000001e69 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 79.1%

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

   3. Simplified 86.0%

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

   5. Taylor expanded in y around inf 77.0%

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

      1. associate-*r* 77.0%

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

   7. Simplified 77.0%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \leq -5 \cdot 10^{+84}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 10^{-305}:\\ \;\;\;\;\left(b \cdot c + \left(t \cdot a\right) \cdot -4\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 2 \cdot 10^{-179}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 2 \cdot 10^{+69}:\\ \;\;\;\;\left(b \cdot c + \left(t \cdot a\right) \cdot -4\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + 18 \cdot \left(\left(y \cdot z\right) \cdot \left(t \cdot x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 37.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ \mathbf{if}\;b \cdot c \leq -5.6 \cdot 10^{+151}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -6.8 \cdot 10^{+28}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq -2.5 \cdot 10^{-74}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq -3.15 \cdot 10^{-186}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq 5.8 \cdot 10^{-184}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 3.8 \cdot 10^{+148}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* t (* a -4.0))))
   (if (<= (* b c) -5.6e+151)
     (* b c)
     (if (<= (* b c) -6.8e+28)
       t_1
       (if (<= (* b c) -2.5e-74)
         (* -27.0 (* j k))
         (if (<= (* b c) -3.15e-186)
           t_1
           (if (<= (* b c) 5.8e-184)
             (* j (* k -27.0))
             (if (<= (* b c) 3.8e+148) t_1 (* b c)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * (a * -4.0);
	double tmp;
	if ((b * c) <= -5.6e+151) {
		tmp = b * c;
	} else if ((b * c) <= -6.8e+28) {
		tmp = t_1;
	} else if ((b * c) <= -2.5e-74) {
		tmp = -27.0 * (j * k);
	} else if ((b * c) <= -3.15e-186) {
		tmp = t_1;
	} else if ((b * c) <= 5.8e-184) {
		tmp = j * (k * -27.0);
	} else if ((b * c) <= 3.8e+148) {
		tmp = t_1;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (a * (-4.0d0))
    if ((b * c) <= (-5.6d+151)) then
        tmp = b * c
    else if ((b * c) <= (-6.8d+28)) then
        tmp = t_1
    else if ((b * c) <= (-2.5d-74)) then
        tmp = (-27.0d0) * (j * k)
    else if ((b * c) <= (-3.15d-186)) then
        tmp = t_1
    else if ((b * c) <= 5.8d-184) then
        tmp = j * (k * (-27.0d0))
    else if ((b * c) <= 3.8d+148) then
        tmp = t_1
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * (a * -4.0);
	double tmp;
	if ((b * c) <= -5.6e+151) {
		tmp = b * c;
	} else if ((b * c) <= -6.8e+28) {
		tmp = t_1;
	} else if ((b * c) <= -2.5e-74) {
		tmp = -27.0 * (j * k);
	} else if ((b * c) <= -3.15e-186) {
		tmp = t_1;
	} else if ((b * c) <= 5.8e-184) {
		tmp = j * (k * -27.0);
	} else if ((b * c) <= 3.8e+148) {
		tmp = t_1;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = t * (a * -4.0)
	tmp = 0
	if (b * c) <= -5.6e+151:
		tmp = b * c
	elif (b * c) <= -6.8e+28:
		tmp = t_1
	elif (b * c) <= -2.5e-74:
		tmp = -27.0 * (j * k)
	elif (b * c) <= -3.15e-186:
		tmp = t_1
	elif (b * c) <= 5.8e-184:
		tmp = j * (k * -27.0)
	elif (b * c) <= 3.8e+148:
		tmp = t_1
	else:
		tmp = b * c
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(t * Float64(a * -4.0))
	tmp = 0.0
	if (Float64(b * c) <= -5.6e+151)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -6.8e+28)
		tmp = t_1;
	elseif (Float64(b * c) <= -2.5e-74)
		tmp = Float64(-27.0 * Float64(j * k));
	elseif (Float64(b * c) <= -3.15e-186)
		tmp = t_1;
	elseif (Float64(b * c) <= 5.8e-184)
		tmp = Float64(j * Float64(k * -27.0));
	elseif (Float64(b * c) <= 3.8e+148)
		tmp = t_1;
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = t * (a * -4.0);
	tmp = 0.0;
	if ((b * c) <= -5.6e+151)
		tmp = b * c;
	elseif ((b * c) <= -6.8e+28)
		tmp = t_1;
	elseif ((b * c) <= -2.5e-74)
		tmp = -27.0 * (j * k);
	elseif ((b * c) <= -3.15e-186)
		tmp = t_1;
	elseif ((b * c) <= 5.8e-184)
		tmp = j * (k * -27.0);
	elseif ((b * c) <= 3.8e+148)
		tmp = t_1;
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -5.6e+151], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -6.8e+28], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], -2.5e-74], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -3.15e-186], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 5.8e-184], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 3.8e+148], t$95$1, N[(b * c), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 b c) < -5.59999999999999975e151 or 3.7999999999999998e148 < (*.f64 b c)

   1. Initial program 82.5%

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

   3. Simplified 81.4%

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

   5. Taylor expanded in c around inf 84.2%

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

   6. Taylor expanded in c around inf 73.1%

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

   if -5.59999999999999975e151 < (*.f64 b c) < -6.8e28 or -2.49999999999999999e-74 < (*.f64 b c) < -3.1499999999999999e-186 or 5.80000000000000028e-184 < (*.f64 b c) < 3.7999999999999998e148

   1. Initial program 86.2%

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

   3. Simplified 88.0%

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

   5. Taylor expanded in c around inf 73.8%

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

   6. Taylor expanded in a around inf 31.9%

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

      1. *-commutative 31.9%

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

      2. *-commutative 31.9%

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

      3. associate-*r* 31.9%

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

   8. Simplified 31.9%

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

   if -6.8e28 < (*.f64 b c) < -2.49999999999999999e-74

   1. Initial program 93.4%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in j around inf 51.0%

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

   if -3.1499999999999999e-186 < (*.f64 b c) < 5.80000000000000028e-184

   1. Initial program 96.1%

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

   3. Simplified 98.0%

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

   5. Taylor expanded in y around inf 60.1%

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

   6. Taylor expanded in t around 0 29.9%

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

      1. associate-*r* 29.9%

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

      2. *-commutative 29.9%

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

      3. associate-*r* 29.9%

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

   8. Simplified 29.9%

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

4. Final simplification 44.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -5.6 \cdot 10^{+151}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -6.8 \cdot 10^{+28}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq -2.5 \cdot 10^{-74}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq -3.15 \cdot 10^{-186}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 5.8 \cdot 10^{-184}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 3.8 \cdot 10^{+148}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 73.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\\ t_2 := 4 \cdot \left(x \cdot i\right)\\ t_3 := \left(b \cdot c - t\_2\right) - \left(j \cdot 27\right) \cdot k\\ t_4 := j \cdot \left(k \cdot -27\right) + t \cdot \left(t\_1 + a \cdot -4\right)\\ \mathbf{if}\;t \leq -4.3 \cdot 10^{-50}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{-182}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-103}:\\ \;\;\;\;\left(b \cdot c + \left(t \cdot a\right) \cdot -4\right) - t\_2\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{-44}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{+55}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{+90}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + t \cdot \left(t\_1 - 4 \cdot a\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* 18.0 (* x (* y z))))
        (t_2 (* 4.0 (* x i)))
        (t_3 (- (- (* b c) t_2) (* (* j 27.0) k)))
        (t_4 (+ (* j (* k -27.0)) (* t (+ t_1 (* a -4.0))))))
   (if (<= t -4.3e-50)
     t_4
     (if (<= t 5.4e-182)
       t_3
       (if (<= t 7.5e-103)
         (- (+ (* b c) (* (* t a) -4.0)) t_2)
         (if (<= t 8.8e-44)
           t_3
           (if (<= t 5.4e+55)
             t_4
             (if (<= t 2.9e+90) t_3 (+ (* b c) (* t (- t_1 (* 4.0 a))))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 18.0 * (x * (y * z));
	double t_2 = 4.0 * (x * i);
	double t_3 = ((b * c) - t_2) - ((j * 27.0) * k);
	double t_4 = (j * (k * -27.0)) + (t * (t_1 + (a * -4.0)));
	double tmp;
	if (t <= -4.3e-50) {
		tmp = t_4;
	} else if (t <= 5.4e-182) {
		tmp = t_3;
	} else if (t <= 7.5e-103) {
		tmp = ((b * c) + ((t * a) * -4.0)) - t_2;
	} else if (t <= 8.8e-44) {
		tmp = t_3;
	} else if (t <= 5.4e+55) {
		tmp = t_4;
	} else if (t <= 2.9e+90) {
		tmp = t_3;
	} else {
		tmp = (b * c) + (t * (t_1 - (4.0 * 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.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = 18.0d0 * (x * (y * z))
    t_2 = 4.0d0 * (x * i)
    t_3 = ((b * c) - t_2) - ((j * 27.0d0) * k)
    t_4 = (j * (k * (-27.0d0))) + (t * (t_1 + (a * (-4.0d0))))
    if (t <= (-4.3d-50)) then
        tmp = t_4
    else if (t <= 5.4d-182) then
        tmp = t_3
    else if (t <= 7.5d-103) then
        tmp = ((b * c) + ((t * a) * (-4.0d0))) - t_2
    else if (t <= 8.8d-44) then
        tmp = t_3
    else if (t <= 5.4d+55) then
        tmp = t_4
    else if (t <= 2.9d+90) then
        tmp = t_3
    else
        tmp = (b * c) + (t * (t_1 - (4.0d0 * 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;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 18.0 * (x * (y * z));
	double t_2 = 4.0 * (x * i);
	double t_3 = ((b * c) - t_2) - ((j * 27.0) * k);
	double t_4 = (j * (k * -27.0)) + (t * (t_1 + (a * -4.0)));
	double tmp;
	if (t <= -4.3e-50) {
		tmp = t_4;
	} else if (t <= 5.4e-182) {
		tmp = t_3;
	} else if (t <= 7.5e-103) {
		tmp = ((b * c) + ((t * a) * -4.0)) - t_2;
	} else if (t <= 8.8e-44) {
		tmp = t_3;
	} else if (t <= 5.4e+55) {
		tmp = t_4;
	} else if (t <= 2.9e+90) {
		tmp = t_3;
	} else {
		tmp = (b * c) + (t * (t_1 - (4.0 * 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])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = 18.0 * (x * (y * z))
	t_2 = 4.0 * (x * i)
	t_3 = ((b * c) - t_2) - ((j * 27.0) * k)
	t_4 = (j * (k * -27.0)) + (t * (t_1 + (a * -4.0)))
	tmp = 0
	if t <= -4.3e-50:
		tmp = t_4
	elif t <= 5.4e-182:
		tmp = t_3
	elif t <= 7.5e-103:
		tmp = ((b * c) + ((t * a) * -4.0)) - t_2
	elif t <= 8.8e-44:
		tmp = t_3
	elif t <= 5.4e+55:
		tmp = t_4
	elif t <= 2.9e+90:
		tmp = t_3
	else:
		tmp = (b * c) + (t * (t_1 - (4.0 * 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])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(18.0 * Float64(x * Float64(y * z)))
	t_2 = Float64(4.0 * Float64(x * i))
	t_3 = Float64(Float64(Float64(b * c) - t_2) - Float64(Float64(j * 27.0) * k))
	t_4 = Float64(Float64(j * Float64(k * -27.0)) + Float64(t * Float64(t_1 + Float64(a * -4.0))))
	tmp = 0.0
	if (t <= -4.3e-50)
		tmp = t_4;
	elseif (t <= 5.4e-182)
		tmp = t_3;
	elseif (t <= 7.5e-103)
		tmp = Float64(Float64(Float64(b * c) + Float64(Float64(t * a) * -4.0)) - t_2);
	elseif (t <= 8.8e-44)
		tmp = t_3;
	elseif (t <= 5.4e+55)
		tmp = t_4;
	elseif (t <= 2.9e+90)
		tmp = t_3;
	else
		tmp = Float64(Float64(b * c) + Float64(t * Float64(t_1 - Float64(4.0 * 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])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = 18.0 * (x * (y * z));
	t_2 = 4.0 * (x * i);
	t_3 = ((b * c) - t_2) - ((j * 27.0) * k);
	t_4 = (j * (k * -27.0)) + (t * (t_1 + (a * -4.0)));
	tmp = 0.0;
	if (t <= -4.3e-50)
		tmp = t_4;
	elseif (t <= 5.4e-182)
		tmp = t_3;
	elseif (t <= 7.5e-103)
		tmp = ((b * c) + ((t * a) * -4.0)) - t_2;
	elseif (t <= 8.8e-44)
		tmp = t_3;
	elseif (t <= 5.4e+55)
		tmp = t_4;
	elseif (t <= 2.9e+90)
		tmp = t_3;
	else
		tmp = (b * c) + (t * (t_1 - (4.0 * 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.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(b * c), $MachinePrecision] - t$95$2), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(t * N[(t$95$1 + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.3e-50], t$95$4, If[LessEqual[t, 5.4e-182], t$95$3, If[LessEqual[t, 7.5e-103], N[(N[(N[(b * c), $MachinePrecision] + N[(N[(t * a), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], If[LessEqual[t, 8.8e-44], t$95$3, If[LessEqual[t, 5.4e+55], t$95$4, If[LessEqual[t, 2.9e+90], t$95$3, N[(N[(b * c), $MachinePrecision] + N[(t * N[(t$95$1 - N[(4.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -4.29999999999999997e-50 or 8.80000000000000048e-44 < t < 5.39999999999999954e55

   1. Initial program 91.6%

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

   3. Simplified 92.8%

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

   5. Taylor expanded in t around inf 80.8%

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

   if -4.29999999999999997e-50 < t < 5.39999999999999999e-182 or 7.5e-103 < t < 8.80000000000000048e-44 or 5.39999999999999954e55 < t < 2.9000000000000001e90

   1. Initial program 86.4%

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

   3. Taylor expanded in t around 0 87.1%

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

   if 5.39999999999999999e-182 < t < 7.5e-103

   1. Initial program 81.8%

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

   3. Simplified 77.6%

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

   5. Taylor expanded in j around 0 72.9%

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

   6. Taylor expanded in x around 0 72.1%

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

   if 2.9000000000000001e90 < t

   1. Initial program 84.3%

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

   3. Simplified 88.6%

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

   5. Taylor expanded in j around 0 84.4%

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

   6. Taylor expanded in i around 0 82.2%

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

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.3 \cdot 10^{-50}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{-182}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-103}:\\ \;\;\;\;\left(b \cdot c + \left(t \cdot a\right) \cdot -4\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{-44}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{+55}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{+90}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 72.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\\ t_2 := 4 \cdot \left(x \cdot i\right)\\ t_3 := \left(b \cdot c - t\_2\right) - \left(j \cdot 27\right) \cdot k\\ t_4 := t \cdot \left(t\_1 - 4 \cdot a\right)\\ t_5 := t\_4 - t\_2\\ \mathbf{if}\;t \leq -3.35 \cdot 10^{-50}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(t\_1 + a \cdot -4\right)\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-161}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-103}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;t \leq 1.62 \cdot 10^{-43}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+52}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+89}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + t\_4\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* 18.0 (* x (* y z))))
        (t_2 (* 4.0 (* x i)))
        (t_3 (- (- (* b c) t_2) (* (* j 27.0) k)))
        (t_4 (* t (- t_1 (* 4.0 a))))
        (t_5 (- t_4 t_2)))
   (if (<= t -3.35e-50)
     (+ (* j (* k -27.0)) (* t (+ t_1 (* a -4.0))))
     (if (<= t 6.5e-161)
       t_3
       (if (<= t 5.5e-103)
         t_5
         (if (<= t 1.62e-43)
           t_3
           (if (<= t 1.1e+52)
             t_5
             (if (<= t 9.5e+89) t_3 (+ (* b c) t_4)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 18.0 * (x * (y * z));
	double t_2 = 4.0 * (x * i);
	double t_3 = ((b * c) - t_2) - ((j * 27.0) * k);
	double t_4 = t * (t_1 - (4.0 * a));
	double t_5 = t_4 - t_2;
	double tmp;
	if (t <= -3.35e-50) {
		tmp = (j * (k * -27.0)) + (t * (t_1 + (a * -4.0)));
	} else if (t <= 6.5e-161) {
		tmp = t_3;
	} else if (t <= 5.5e-103) {
		tmp = t_5;
	} else if (t <= 1.62e-43) {
		tmp = t_3;
	} else if (t <= 1.1e+52) {
		tmp = t_5;
	} else if (t <= 9.5e+89) {
		tmp = t_3;
	} else {
		tmp = (b * c) + t_4;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_1 = 18.0d0 * (x * (y * z))
    t_2 = 4.0d0 * (x * i)
    t_3 = ((b * c) - t_2) - ((j * 27.0d0) * k)
    t_4 = t * (t_1 - (4.0d0 * a))
    t_5 = t_4 - t_2
    if (t <= (-3.35d-50)) then
        tmp = (j * (k * (-27.0d0))) + (t * (t_1 + (a * (-4.0d0))))
    else if (t <= 6.5d-161) then
        tmp = t_3
    else if (t <= 5.5d-103) then
        tmp = t_5
    else if (t <= 1.62d-43) then
        tmp = t_3
    else if (t <= 1.1d+52) then
        tmp = t_5
    else if (t <= 9.5d+89) then
        tmp = t_3
    else
        tmp = (b * c) + t_4
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 18.0 * (x * (y * z));
	double t_2 = 4.0 * (x * i);
	double t_3 = ((b * c) - t_2) - ((j * 27.0) * k);
	double t_4 = t * (t_1 - (4.0 * a));
	double t_5 = t_4 - t_2;
	double tmp;
	if (t <= -3.35e-50) {
		tmp = (j * (k * -27.0)) + (t * (t_1 + (a * -4.0)));
	} else if (t <= 6.5e-161) {
		tmp = t_3;
	} else if (t <= 5.5e-103) {
		tmp = t_5;
	} else if (t <= 1.62e-43) {
		tmp = t_3;
	} else if (t <= 1.1e+52) {
		tmp = t_5;
	} else if (t <= 9.5e+89) {
		tmp = t_3;
	} else {
		tmp = (b * c) + t_4;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = 18.0 * (x * (y * z))
	t_2 = 4.0 * (x * i)
	t_3 = ((b * c) - t_2) - ((j * 27.0) * k)
	t_4 = t * (t_1 - (4.0 * a))
	t_5 = t_4 - t_2
	tmp = 0
	if t <= -3.35e-50:
		tmp = (j * (k * -27.0)) + (t * (t_1 + (a * -4.0)))
	elif t <= 6.5e-161:
		tmp = t_3
	elif t <= 5.5e-103:
		tmp = t_5
	elif t <= 1.62e-43:
		tmp = t_3
	elif t <= 1.1e+52:
		tmp = t_5
	elif t <= 9.5e+89:
		tmp = t_3
	else:
		tmp = (b * c) + t_4
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(18.0 * Float64(x * Float64(y * z)))
	t_2 = Float64(4.0 * Float64(x * i))
	t_3 = Float64(Float64(Float64(b * c) - t_2) - Float64(Float64(j * 27.0) * k))
	t_4 = Float64(t * Float64(t_1 - Float64(4.0 * a)))
	t_5 = Float64(t_4 - t_2)
	tmp = 0.0
	if (t <= -3.35e-50)
		tmp = Float64(Float64(j * Float64(k * -27.0)) + Float64(t * Float64(t_1 + Float64(a * -4.0))));
	elseif (t <= 6.5e-161)
		tmp = t_3;
	elseif (t <= 5.5e-103)
		tmp = t_5;
	elseif (t <= 1.62e-43)
		tmp = t_3;
	elseif (t <= 1.1e+52)
		tmp = t_5;
	elseif (t <= 9.5e+89)
		tmp = t_3;
	else
		tmp = Float64(Float64(b * c) + t_4);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = 18.0 * (x * (y * z));
	t_2 = 4.0 * (x * i);
	t_3 = ((b * c) - t_2) - ((j * 27.0) * k);
	t_4 = t * (t_1 - (4.0 * a));
	t_5 = t_4 - t_2;
	tmp = 0.0;
	if (t <= -3.35e-50)
		tmp = (j * (k * -27.0)) + (t * (t_1 + (a * -4.0)));
	elseif (t <= 6.5e-161)
		tmp = t_3;
	elseif (t <= 5.5e-103)
		tmp = t_5;
	elseif (t <= 1.62e-43)
		tmp = t_3;
	elseif (t <= 1.1e+52)
		tmp = t_5;
	elseif (t <= 9.5e+89)
		tmp = t_3;
	else
		tmp = (b * c) + t_4;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(b * c), $MachinePrecision] - t$95$2), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t * N[(t$95$1 - N[(4.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$4 - t$95$2), $MachinePrecision]}, If[LessEqual[t, -3.35e-50], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(t * N[(t$95$1 + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.5e-161], t$95$3, If[LessEqual[t, 5.5e-103], t$95$5, If[LessEqual[t, 1.62e-43], t$95$3, If[LessEqual[t, 1.1e+52], t$95$5, If[LessEqual[t, 9.5e+89], t$95$3, N[(N[(b * c), $MachinePrecision] + t$95$4), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3.3500000000000002e-50

   1. Initial program 91.1%

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

   3. Simplified 92.5%

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

   5. Taylor expanded in t around inf 81.7%

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

   if -3.3500000000000002e-50 < t < 6.50000000000000008e-161 or 5.50000000000000032e-103 < t < 1.6199999999999999e-43 or 1.1e52 < t < 9.5000000000000003e89

   1. Initial program 86.1%

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

   3. Taylor expanded in t around 0 86.8%

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

   if 6.50000000000000008e-161 < t < 5.50000000000000032e-103 or 1.6199999999999999e-43 < t < 1.1e52

   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 88.3%

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

   5. Taylor expanded in j around 0 82.5%

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

   6. Taylor expanded in b around 0 79.8%

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

   if 9.5000000000000003e89 < t

   1. Initial program 84.3%

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

   3. Simplified 88.6%

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

   5. Taylor expanded in j around 0 84.4%

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

   6. Taylor expanded in i around 0 82.2%

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

4. Final simplification 83.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.35 \cdot 10^{-50}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-161}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-103}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq 1.62 \cdot 10^{-43}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+52}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+89}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 53.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+84}:\\ \;\;\;\;b \cdot c - t\_1\\ \mathbf{elif}\;t\_1 \leq 10^{-167}:\\ \;\;\;\;c \cdot \left(b + -4 \cdot \frac{t \cdot a}{c}\right)\\ \mathbf{elif}\;t\_1 \leq 10^{+77}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t\_1 \leq 10^{+230}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right) + -4 \cdot \left(x \cdot i\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)))
   (if (<= t_1 -5e+84)
     (- (* b c) t_1)
     (if (<= t_1 1e-167)
       (* c (+ b (* -4.0 (/ (* t a) c))))
       (if (<= t_1 1e+77)
         (- (* b c) (* 4.0 (* x i)))
         (if (<= t_1 1e+230)
           (* 18.0 (* t (* x (* y z))))
           (+ (* -27.0 (* j k)) (* -4.0 (* x i)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (t_1 <= -5e+84) {
		tmp = (b * c) - t_1;
	} else if (t_1 <= 1e-167) {
		tmp = c * (b + (-4.0 * ((t * a) / c)));
	} else if (t_1 <= 1e+77) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if (t_1 <= 1e+230) {
		tmp = 18.0 * (t * (x * (y * z)));
	} else {
		tmp = (-27.0 * (j * k)) + (-4.0 * (x * i));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (j * 27.0d0) * k
    if (t_1 <= (-5d+84)) then
        tmp = (b * c) - t_1
    else if (t_1 <= 1d-167) then
        tmp = c * (b + ((-4.0d0) * ((t * a) / c)))
    else if (t_1 <= 1d+77) then
        tmp = (b * c) - (4.0d0 * (x * i))
    else if (t_1 <= 1d+230) then
        tmp = 18.0d0 * (t * (x * (y * z)))
    else
        tmp = ((-27.0d0) * (j * k)) + ((-4.0d0) * (x * i))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (t_1 <= -5e+84) {
		tmp = (b * c) - t_1;
	} else if (t_1 <= 1e-167) {
		tmp = c * (b + (-4.0 * ((t * a) / c)));
	} else if (t_1 <= 1e+77) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if (t_1 <= 1e+230) {
		tmp = 18.0 * (t * (x * (y * z)));
	} else {
		tmp = (-27.0 * (j * k)) + (-4.0 * (x * i));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	tmp = 0
	if t_1 <= -5e+84:
		tmp = (b * c) - t_1
	elif t_1 <= 1e-167:
		tmp = c * (b + (-4.0 * ((t * a) / c)))
	elif t_1 <= 1e+77:
		tmp = (b * c) - (4.0 * (x * i))
	elif t_1 <= 1e+230:
		tmp = 18.0 * (t * (x * (y * z)))
	else:
		tmp = (-27.0 * (j * k)) + (-4.0 * (x * i))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_1 <= -5e+84)
		tmp = Float64(Float64(b * c) - t_1);
	elseif (t_1 <= 1e-167)
		tmp = Float64(c * Float64(b + Float64(-4.0 * Float64(Float64(t * a) / c))));
	elseif (t_1 <= 1e+77)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)));
	elseif (t_1 <= 1e+230)
		tmp = Float64(18.0 * Float64(t * Float64(x * Float64(y * z))));
	else
		tmp = Float64(Float64(-27.0 * Float64(j * k)) + Float64(-4.0 * Float64(x * i)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * 27.0) * k;
	tmp = 0.0;
	if (t_1 <= -5e+84)
		tmp = (b * c) - t_1;
	elseif (t_1 <= 1e-167)
		tmp = c * (b + (-4.0 * ((t * a) / c)));
	elseif (t_1 <= 1e+77)
		tmp = (b * c) - (4.0 * (x * i));
	elseif (t_1 <= 1e+230)
		tmp = 18.0 * (t * (x * (y * z)));
	else
		tmp = (-27.0 * (j * k)) + (-4.0 * (x * i));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+84], N[(N[(b * c), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[t$95$1, 1e-167], N[(c * N[(b + N[(-4.0 * N[(N[(t * a), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+77], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+230], N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -5.0000000000000001e84

   1. Initial program 90.6%

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

   3. Taylor expanded in x around 0 86.4%

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

   4. Taylor expanded in b around inf 68.8%

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

   if -5.0000000000000001e84 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 1e-167

   1. Initial program 87.6%

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

   3. Simplified 88.5%

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

   5. Taylor expanded in c around inf 81.0%

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

   6. Taylor expanded in x around 0 55.8%

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

   7. Taylor expanded in j around 0 55.1%

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

   if 1e-167 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 9.99999999999999983e76

   1. Initial program 93.2%

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

   3. Simplified 95.4%

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

   5. Taylor expanded in j around 0 90.9%

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

   6. Taylor expanded in t around 0 65.3%

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

   if 9.99999999999999983e76 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 1.0000000000000001e230

   1. Initial program 91.8%

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

   3. Simplified 91.7%

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

   5. Taylor expanded in c around inf 71.6%

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

   6. Taylor expanded in y around inf 56.3%

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

   if 1.0000000000000001e230 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 61.1%

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

   3. Simplified 77.7%

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

   5. Taylor expanded in i around inf 72.6%

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

      1. associate-*r* 72.6%

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

      2. *-commutative 72.6%

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

      3. associate-*r* 72.6%

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

      4. *-commutative 72.6%

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

      5. *-commutative 72.6%

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

   7. Simplified 72.6%

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

   8. Taylor expanded in i around 0 72.6%

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

4. Final simplification 60.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \leq -5 \cdot 10^{+84}:\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 10^{-167}:\\ \;\;\;\;c \cdot \left(b + -4 \cdot \frac{t \cdot a}{c}\right)\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 10^{+77}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 10^{+230}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right) + -4 \cdot \left(x \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 52.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+84}:\\ \;\;\;\;b \cdot c - t\_1\\ \mathbf{elif}\;t\_1 \leq 10^{-167}:\\ \;\;\;\;c \cdot \left(b + -4 \cdot \frac{t \cdot a}{c}\right)\\ \mathbf{elif}\;t\_1 \leq 10^{+77}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+274}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(-27 \cdot \frac{j \cdot k}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)))
   (if (<= t_1 -5e+84)
     (- (* b c) t_1)
     (if (<= t_1 1e-167)
       (* c (+ b (* -4.0 (/ (* t a) c))))
       (if (<= t_1 1e+77)
         (- (* b c) (* 4.0 (* x i)))
         (if (<= t_1 5e+274)
           (* 18.0 (* t (* x (* y z))))
           (* c (* -27.0 (/ (* j k) c)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (t_1 <= -5e+84) {
		tmp = (b * c) - t_1;
	} else if (t_1 <= 1e-167) {
		tmp = c * (b + (-4.0 * ((t * a) / c)));
	} else if (t_1 <= 1e+77) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if (t_1 <= 5e+274) {
		tmp = 18.0 * (t * (x * (y * z)));
	} else {
		tmp = c * (-27.0 * ((j * k) / c));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (j * 27.0d0) * k
    if (t_1 <= (-5d+84)) then
        tmp = (b * c) - t_1
    else if (t_1 <= 1d-167) then
        tmp = c * (b + ((-4.0d0) * ((t * a) / c)))
    else if (t_1 <= 1d+77) then
        tmp = (b * c) - (4.0d0 * (x * i))
    else if (t_1 <= 5d+274) then
        tmp = 18.0d0 * (t * (x * (y * z)))
    else
        tmp = c * ((-27.0d0) * ((j * k) / c))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (t_1 <= -5e+84) {
		tmp = (b * c) - t_1;
	} else if (t_1 <= 1e-167) {
		tmp = c * (b + (-4.0 * ((t * a) / c)));
	} else if (t_1 <= 1e+77) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if (t_1 <= 5e+274) {
		tmp = 18.0 * (t * (x * (y * z)));
	} else {
		tmp = c * (-27.0 * ((j * k) / c));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	tmp = 0
	if t_1 <= -5e+84:
		tmp = (b * c) - t_1
	elif t_1 <= 1e-167:
		tmp = c * (b + (-4.0 * ((t * a) / c)))
	elif t_1 <= 1e+77:
		tmp = (b * c) - (4.0 * (x * i))
	elif t_1 <= 5e+274:
		tmp = 18.0 * (t * (x * (y * z)))
	else:
		tmp = c * (-27.0 * ((j * k) / c))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_1 <= -5e+84)
		tmp = Float64(Float64(b * c) - t_1);
	elseif (t_1 <= 1e-167)
		tmp = Float64(c * Float64(b + Float64(-4.0 * Float64(Float64(t * a) / c))));
	elseif (t_1 <= 1e+77)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)));
	elseif (t_1 <= 5e+274)
		tmp = Float64(18.0 * Float64(t * Float64(x * Float64(y * z))));
	else
		tmp = Float64(c * Float64(-27.0 * Float64(Float64(j * k) / c)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * 27.0) * k;
	tmp = 0.0;
	if (t_1 <= -5e+84)
		tmp = (b * c) - t_1;
	elseif (t_1 <= 1e-167)
		tmp = c * (b + (-4.0 * ((t * a) / c)));
	elseif (t_1 <= 1e+77)
		tmp = (b * c) - (4.0 * (x * i));
	elseif (t_1 <= 5e+274)
		tmp = 18.0 * (t * (x * (y * z)));
	else
		tmp = c * (-27.0 * ((j * k) / c));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+84], N[(N[(b * c), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[t$95$1, 1e-167], N[(c * N[(b + N[(-4.0 * N[(N[(t * a), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+77], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+274], N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(-27.0 * N[(N[(j * k), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -5.0000000000000001e84

   1. Initial program 90.6%

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

   3. Taylor expanded in x around 0 86.4%

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

   4. Taylor expanded in b around inf 68.8%

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

   if -5.0000000000000001e84 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 1e-167

   1. Initial program 87.6%

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

   3. Simplified 88.5%

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

   5. Taylor expanded in c around inf 81.0%

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

   6. Taylor expanded in x around 0 55.8%

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

   7. Taylor expanded in j around 0 55.1%

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

   if 1e-167 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 9.99999999999999983e76

   1. Initial program 93.2%

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

   3. Simplified 95.4%

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

   5. Taylor expanded in j around 0 90.9%

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

   6. Taylor expanded in t around 0 65.3%

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

   if 9.99999999999999983e76 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 4.9999999999999998e274

   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 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 c around inf 61.4%

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

   6. Taylor expanded in y around inf 51.9%

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

   if 4.9999999999999998e274 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 71.4%

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

   3. Simplified 71.3%

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

   5. Taylor expanded in c around inf 64.3%

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

   6. Taylor expanded in x around 0 85.7%

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

   7. Taylor expanded in j around inf 85.7%

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

4. Final simplification 60.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \leq -5 \cdot 10^{+84}:\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 10^{-167}:\\ \;\;\;\;c \cdot \left(b + -4 \cdot \frac{t \cdot a}{c}\right)\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 10^{+77}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 5 \cdot 10^{+274}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(-27 \cdot \frac{j \cdot k}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 57.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c + j \cdot \left(k \cdot -27\right)\\ t_2 := t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)\\ \mathbf{if}\;t \leq -3.7 \cdot 10^{-50}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -6.2 \cdot 10^{-274}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.7 \cdot 10^{-31}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+55}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{+90}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{+112}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (+ (* b c) (* j (* k -27.0))))
        (t_2 (* t (- (* 18.0 (* x (* y z))) (* 4.0 a)))))
   (if (<= t -3.7e-50)
     t_2
     (if (<= t -6.2e-274)
       t_1
       (if (<= t 4.7e-31)
         (- (* b c) (* 4.0 (* x i)))
         (if (<= t 1.15e+55)
           t_2
           (if (<= t 1.55e+90)
             t_1
             (if (<= t 6.5e+112)
               (* x (- (* 18.0 (* t (* y z))) (* 4.0 i)))
               t_2))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) + (j * (k * -27.0));
	double t_2 = t * ((18.0 * (x * (y * z))) - (4.0 * a));
	double tmp;
	if (t <= -3.7e-50) {
		tmp = t_2;
	} else if (t <= -6.2e-274) {
		tmp = t_1;
	} else if (t <= 4.7e-31) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if (t <= 1.15e+55) {
		tmp = t_2;
	} else if (t <= 1.55e+90) {
		tmp = t_1;
	} else if (t <= 6.5e+112) {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (b * c) + (j * (k * (-27.0d0)))
    t_2 = t * ((18.0d0 * (x * (y * z))) - (4.0d0 * a))
    if (t <= (-3.7d-50)) then
        tmp = t_2
    else if (t <= (-6.2d-274)) then
        tmp = t_1
    else if (t <= 4.7d-31) then
        tmp = (b * c) - (4.0d0 * (x * i))
    else if (t <= 1.15d+55) then
        tmp = t_2
    else if (t <= 1.55d+90) then
        tmp = t_1
    else if (t <= 6.5d+112) then
        tmp = x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) + (j * (k * -27.0));
	double t_2 = t * ((18.0 * (x * (y * z))) - (4.0 * a));
	double tmp;
	if (t <= -3.7e-50) {
		tmp = t_2;
	} else if (t <= -6.2e-274) {
		tmp = t_1;
	} else if (t <= 4.7e-31) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if (t <= 1.15e+55) {
		tmp = t_2;
	} else if (t <= 1.55e+90) {
		tmp = t_1;
	} else if (t <= 6.5e+112) {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) + (j * (k * -27.0))
	t_2 = t * ((18.0 * (x * (y * z))) - (4.0 * a))
	tmp = 0
	if t <= -3.7e-50:
		tmp = t_2
	elif t <= -6.2e-274:
		tmp = t_1
	elif t <= 4.7e-31:
		tmp = (b * c) - (4.0 * (x * i))
	elif t <= 1.15e+55:
		tmp = t_2
	elif t <= 1.55e+90:
		tmp = t_1
	elif t <= 6.5e+112:
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i))
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) + Float64(j * Float64(k * -27.0)))
	t_2 = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(4.0 * a)))
	tmp = 0.0
	if (t <= -3.7e-50)
		tmp = t_2;
	elseif (t <= -6.2e-274)
		tmp = t_1;
	elseif (t <= 4.7e-31)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)));
	elseif (t <= 1.15e+55)
		tmp = t_2;
	elseif (t <= 1.55e+90)
		tmp = t_1;
	elseif (t <= 6.5e+112)
		tmp = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) + (j * (k * -27.0));
	t_2 = t * ((18.0 * (x * (y * z))) - (4.0 * a));
	tmp = 0.0;
	if (t <= -3.7e-50)
		tmp = t_2;
	elseif (t <= -6.2e-274)
		tmp = t_1;
	elseif (t <= 4.7e-31)
		tmp = (b * c) - (4.0 * (x * i));
	elseif (t <= 1.15e+55)
		tmp = t_2;
	elseif (t <= 1.55e+90)
		tmp = t_1;
	elseif (t <= 6.5e+112)
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.7e-50], t$95$2, If[LessEqual[t, -6.2e-274], t$95$1, If[LessEqual[t, 4.7e-31], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.15e+55], t$95$2, If[LessEqual[t, 1.55e+90], t$95$1, If[LessEqual[t, 6.5e+112], N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3.7000000000000001e-50 or 4.69999999999999987e-31 < t < 1.14999999999999994e55 or 6.4999999999999998e112 < t

   1. Initial program 90.2%

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

   3. Simplified 91.0%

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

   5. Taylor expanded in c around inf 78.5%

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

   6. Taylor expanded in t around -inf 68.3%

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

   if -3.7000000000000001e-50 < t < -6.19999999999999956e-274 or 1.14999999999999994e55 < t < 1.54999999999999994e90

   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 92.7%

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

   5. Taylor expanded in b around inf 72.8%

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

   if -6.19999999999999956e-274 < t < 4.69999999999999987e-31

   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 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 71.8%

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

   6. Taylor expanded in t around 0 62.8%

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

   if 1.54999999999999994e90 < t < 6.4999999999999998e112

   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 99.7%

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

   5. Taylor expanded in x around inf 81.2%

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

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.7 \cdot 10^{-50}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)\\ \mathbf{elif}\;t \leq -6.2 \cdot 10^{-274}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t \leq 4.7 \cdot 10^{-31}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+55}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{+90}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{+112}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 82.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)\\ t_2 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+84} \lor \neg \left(t\_2 \leq 2 \cdot 10^{+33}\right):\\ \;\;\;\;t\_1 - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 - 4 \cdot \left(x \cdot i\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (+ (* b c) (* t (- (* 18.0 (* x (* y z))) (* 4.0 a)))))
        (t_2 (* (* j 27.0) k)))
   (if (or (<= t_2 -5e+84) (not (<= t_2 2e+33)))
     (- t_1 (* 27.0 (* j k)))
     (- t_1 (* 4.0 (* x i))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) + (t * ((18.0 * (x * (y * z))) - (4.0 * a)));
	double t_2 = (j * 27.0) * k;
	double tmp;
	if ((t_2 <= -5e+84) || !(t_2 <= 2e+33)) {
		tmp = t_1 - (27.0 * (j * k));
	} else {
		tmp = t_1 - (4.0 * (x * i));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (b * c) + (t * ((18.0d0 * (x * (y * z))) - (4.0d0 * a)))
    t_2 = (j * 27.0d0) * k
    if ((t_2 <= (-5d+84)) .or. (.not. (t_2 <= 2d+33))) then
        tmp = t_1 - (27.0d0 * (j * k))
    else
        tmp = t_1 - (4.0d0 * (x * i))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) + (t * ((18.0 * (x * (y * z))) - (4.0 * a)));
	double t_2 = (j * 27.0) * k;
	double tmp;
	if ((t_2 <= -5e+84) || !(t_2 <= 2e+33)) {
		tmp = t_1 - (27.0 * (j * k));
	} else {
		tmp = t_1 - (4.0 * (x * i));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) + (t * ((18.0 * (x * (y * z))) - (4.0 * a)))
	t_2 = (j * 27.0) * k
	tmp = 0
	if (t_2 <= -5e+84) or not (t_2 <= 2e+33):
		tmp = t_1 - (27.0 * (j * k))
	else:
		tmp = t_1 - (4.0 * (x * i))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) + Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(4.0 * a))))
	t_2 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if ((t_2 <= -5e+84) || !(t_2 <= 2e+33))
		tmp = Float64(t_1 - Float64(27.0 * Float64(j * k)));
	else
		tmp = Float64(t_1 - Float64(4.0 * Float64(x * i)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) + (t * ((18.0 * (x * (y * z))) - (4.0 * a)));
	t_2 = (j * 27.0) * k;
	tmp = 0.0;
	if ((t_2 <= -5e+84) || ~((t_2 <= 2e+33)))
		tmp = t_1 - (27.0 * (j * k));
	else
		tmp = t_1 - (4.0 * (x * i));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[Or[LessEqual[t$95$2, -5e+84], N[Not[LessEqual[t$95$2, 2e+33]], $MachinePrecision]], N[(t$95$1 - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 - 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) < -5.0000000000000001e84 or 1.9999999999999999e33 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 84.2%

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

   3. Simplified 85.5%

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

   5. Taylor expanded in i around 0 85.2%

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

   if -5.0000000000000001e84 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 1.9999999999999999e33

   1. Initial program 89.4%

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

   3. Simplified 90.7%

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

   5. Taylor expanded in j around 0 89.5%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \leq -5 \cdot 10^{+84} \lor \neg \left(\left(j \cdot 27\right) \cdot k \leq 2 \cdot 10^{+33}\right):\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 79.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+35}:\\ \;\;\;\;\left(b \cdot c + 18 \cdot \left(t \cdot \left(z \cdot \left(y \cdot x\right)\right)\right)\right) - t\_1\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+33}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + y \cdot \left(z \cdot \left(t \cdot \left(18 \cdot x\right)\right)\right)\right) - t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)))
   (if (<= t_1 -5e+35)
     (- (+ (* b c) (* 18.0 (* t (* z (* y x))))) t_1)
     (if (<= t_1 2e+33)
       (-
        (+ (* b c) (* t (- (* 18.0 (* x (* y z))) (* 4.0 a))))
        (* 4.0 (* x i)))
       (- (+ (* b c) (* y (* z (* t (* 18.0 x))))) t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (t_1 <= -5e+35) {
		tmp = ((b * c) + (18.0 * (t * (z * (y * x))))) - t_1;
	} else if (t_1 <= 2e+33) {
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (4.0 * a)))) - (4.0 * (x * i));
	} else {
		tmp = ((b * c) + (y * (z * (t * (18.0 * x))))) - t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (j * 27.0d0) * k
    if (t_1 <= (-5d+35)) then
        tmp = ((b * c) + (18.0d0 * (t * (z * (y * x))))) - t_1
    else if (t_1 <= 2d+33) then
        tmp = ((b * c) + (t * ((18.0d0 * (x * (y * z))) - (4.0d0 * a)))) - (4.0d0 * (x * i))
    else
        tmp = ((b * c) + (y * (z * (t * (18.0d0 * x))))) - t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (t_1 <= -5e+35) {
		tmp = ((b * c) + (18.0 * (t * (z * (y * x))))) - t_1;
	} else if (t_1 <= 2e+33) {
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (4.0 * a)))) - (4.0 * (x * i));
	} else {
		tmp = ((b * c) + (y * (z * (t * (18.0 * x))))) - t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	tmp = 0
	if t_1 <= -5e+35:
		tmp = ((b * c) + (18.0 * (t * (z * (y * x))))) - t_1
	elif t_1 <= 2e+33:
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (4.0 * a)))) - (4.0 * (x * i))
	else:
		tmp = ((b * c) + (y * (z * (t * (18.0 * x))))) - t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_1 <= -5e+35)
		tmp = Float64(Float64(Float64(b * c) + Float64(18.0 * Float64(t * Float64(z * Float64(y * x))))) - t_1);
	elseif (t_1 <= 2e+33)
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(4.0 * a)))) - Float64(4.0 * Float64(x * i)));
	else
		tmp = Float64(Float64(Float64(b * c) + Float64(y * Float64(z * Float64(t * Float64(18.0 * x))))) - t_1);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * 27.0) * k;
	tmp = 0.0;
	if (t_1 <= -5e+35)
		tmp = ((b * c) + (18.0 * (t * (z * (y * x))))) - t_1;
	elseif (t_1 <= 2e+33)
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (4.0 * a)))) - (4.0 * (x * i));
	else
		tmp = ((b * c) + (y * (z * (t * (18.0 * x))))) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+35], N[(N[(N[(b * c), $MachinePrecision] + N[(18.0 * N[(t * N[(z * N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[t$95$1, 2e+33], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] + N[(y * N[(z * N[(t * N[(18.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -5.00000000000000021e35

   1. Initial program 92.1%

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

   3. Taylor expanded in x around 0 83.0%

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

   4. Taylor expanded in a around 0 79.6%

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

      1. pow1 79.6%

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

   6. Applied egg-rr 79.6%

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

      1. unpow1 79.6%

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

      2. associate-*r* 77.8%

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

   8. Simplified 77.8%

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

   9. Taylor expanded in t around inf 80.9%

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

       1. associate-*r* 84.5%

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

       2. *-commutative 84.5%

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

   11. Simplified 84.5%

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

   if -5.00000000000000021e35 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 1.9999999999999999e33

   1. Initial program 88.9%

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

   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 j around 0 89.6%

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

   if 1.9999999999999999e33 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 77.8%

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

   3. Taylor expanded in x around 0 82.4%

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

   4. Taylor expanded in a around 0 80.4%

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

      1. pow1 80.4%

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

   6. Applied egg-rr 80.4%

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

      1. unpow1 80.4%

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

      2. associate-*r* 84.6%

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

   8. Simplified 84.6%

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

   9. Taylor expanded in t around inf 77.9%

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

       1. associate-*r* 78.0%

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

       2. associate-*r* 78.0%

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

       3. *-commutative 78.0%

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

       4. associate-*r* 80.1%

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

       5. *-commutative 80.1%

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

       6. associate-*r* 80.1%

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

   11. Simplified 80.1%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \leq -5 \cdot 10^{+35}:\\ \;\;\;\;\left(b \cdot c + 18 \cdot \left(t \cdot \left(z \cdot \left(y \cdot x\right)\right)\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 2 \cdot 10^{+33}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + y \cdot \left(z \cdot \left(t \cdot \left(18 \cdot x\right)\right)\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 83.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)\\ t_2 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+84}:\\ \;\;\;\;t\_1 - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t\_2 \leq 200:\\ \;\;\;\;t\_1 - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) - 4 \cdot i\right)\right) - t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (+ (* b c) (* t (- (* 18.0 (* x (* y z))) (* 4.0 a)))))
        (t_2 (* (* j 27.0) k)))
   (if (<= t_2 -5e+84)
     (- t_1 (* 27.0 (* j k)))
     (if (<= t_2 200.0)
       (- t_1 (* 4.0 (* x i)))
       (- (+ (* b c) (* x (- (* 18.0 (* z (* y t))) (* 4.0 i)))) t_2)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) + (t * ((18.0 * (x * (y * z))) - (4.0 * a)));
	double t_2 = (j * 27.0) * k;
	double tmp;
	if (t_2 <= -5e+84) {
		tmp = t_1 - (27.0 * (j * k));
	} else if (t_2 <= 200.0) {
		tmp = t_1 - (4.0 * (x * i));
	} else {
		tmp = ((b * c) + (x * ((18.0 * (z * (y * t))) - (4.0 * i)))) - t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (b * c) + (t * ((18.0d0 * (x * (y * z))) - (4.0d0 * a)))
    t_2 = (j * 27.0d0) * k
    if (t_2 <= (-5d+84)) then
        tmp = t_1 - (27.0d0 * (j * k))
    else if (t_2 <= 200.0d0) then
        tmp = t_1 - (4.0d0 * (x * i))
    else
        tmp = ((b * c) + (x * ((18.0d0 * (z * (y * t))) - (4.0d0 * i)))) - t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) + (t * ((18.0 * (x * (y * z))) - (4.0 * a)));
	double t_2 = (j * 27.0) * k;
	double tmp;
	if (t_2 <= -5e+84) {
		tmp = t_1 - (27.0 * (j * k));
	} else if (t_2 <= 200.0) {
		tmp = t_1 - (4.0 * (x * i));
	} else {
		tmp = ((b * c) + (x * ((18.0 * (z * (y * t))) - (4.0 * i)))) - t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) + (t * ((18.0 * (x * (y * z))) - (4.0 * a)))
	t_2 = (j * 27.0) * k
	tmp = 0
	if t_2 <= -5e+84:
		tmp = t_1 - (27.0 * (j * k))
	elif t_2 <= 200.0:
		tmp = t_1 - (4.0 * (x * i))
	else:
		tmp = ((b * c) + (x * ((18.0 * (z * (y * t))) - (4.0 * i)))) - t_2
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) + Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(4.0 * a))))
	t_2 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_2 <= -5e+84)
		tmp = Float64(t_1 - Float64(27.0 * Float64(j * k)));
	elseif (t_2 <= 200.0)
		tmp = Float64(t_1 - Float64(4.0 * Float64(x * i)));
	else
		tmp = Float64(Float64(Float64(b * c) + Float64(x * Float64(Float64(18.0 * Float64(z * Float64(y * t))) - Float64(4.0 * i)))) - t_2);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) + (t * ((18.0 * (x * (y * z))) - (4.0 * a)));
	t_2 = (j * 27.0) * k;
	tmp = 0.0;
	if (t_2 <= -5e+84)
		tmp = t_1 - (27.0 * (j * k));
	elseif (t_2 <= 200.0)
		tmp = t_1 - (4.0 * (x * i));
	else
		tmp = ((b * c) + (x * ((18.0 * (z * (y * t))) - (4.0 * i)))) - t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+84], N[(t$95$1 - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 200.0], N[(t$95$1 - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] + N[(x * N[(N[(18.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -5.0000000000000001e84

   1. Initial program 90.6%

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

   3. Simplified 91.0%

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

   5. Taylor expanded in i around 0 88.2%

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

   if -5.0000000000000001e84 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 200

   1. Initial program 89.2%

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

   3. Simplified 90.4%

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

   5. Taylor expanded in j around 0 89.3%

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

   if 200 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 79.7%

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

   3. Taylor expanded in x around 0 83.9%

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

   4. Taylor expanded in a around 0 82.0%

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

      1. pow1 82.0%

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

   6. Applied egg-rr 82.0%

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

      1. unpow1 82.0%

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

      2. associate-*r* 85.9%

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

   8. Simplified 85.9%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \leq -5 \cdot 10^{+84}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 200:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) - 4 \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 55.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right) + \left(t \cdot a\right) \cdot -4\\ \mathbf{if}\;b \cdot c \leq -2 \cdot 10^{+132}:\\ \;\;\;\;c \cdot \left(b + -4 \cdot \frac{t \cdot a}{c}\right)\\ \mathbf{elif}\;b \cdot c \leq 2 \cdot 10^{-109}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq 5 \cdot 10^{+106}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right) + -4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 2 \cdot 10^{+148}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (+ (* j (* k -27.0)) (* (* t a) -4.0))))
   (if (<= (* b c) -2e+132)
     (* c (+ b (* -4.0 (/ (* t a) c))))
     (if (<= (* b c) 2e-109)
       t_1
       (if (<= (* b c) 5e+106)
         (+ (* -27.0 (* j k)) (* -4.0 (* x i)))
         (if (<= (* b c) 2e+148) t_1 (- (* b c) (* 4.0 (* x i)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * (k * -27.0)) + ((t * a) * -4.0);
	double tmp;
	if ((b * c) <= -2e+132) {
		tmp = c * (b + (-4.0 * ((t * a) / c)));
	} else if ((b * c) <= 2e-109) {
		tmp = t_1;
	} else if ((b * c) <= 5e+106) {
		tmp = (-27.0 * (j * k)) + (-4.0 * (x * i));
	} else if ((b * c) <= 2e+148) {
		tmp = t_1;
	} else {
		tmp = (b * c) - (4.0 * (x * i));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (j * (k * (-27.0d0))) + ((t * a) * (-4.0d0))
    if ((b * c) <= (-2d+132)) then
        tmp = c * (b + ((-4.0d0) * ((t * a) / c)))
    else if ((b * c) <= 2d-109) then
        tmp = t_1
    else if ((b * c) <= 5d+106) then
        tmp = ((-27.0d0) * (j * k)) + ((-4.0d0) * (x * i))
    else if ((b * c) <= 2d+148) then
        tmp = t_1
    else
        tmp = (b * c) - (4.0d0 * (x * i))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * (k * -27.0)) + ((t * a) * -4.0);
	double tmp;
	if ((b * c) <= -2e+132) {
		tmp = c * (b + (-4.0 * ((t * a) / c)));
	} else if ((b * c) <= 2e-109) {
		tmp = t_1;
	} else if ((b * c) <= 5e+106) {
		tmp = (-27.0 * (j * k)) + (-4.0 * (x * i));
	} else if ((b * c) <= 2e+148) {
		tmp = t_1;
	} else {
		tmp = (b * c) - (4.0 * (x * i));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * (k * -27.0)) + ((t * a) * -4.0)
	tmp = 0
	if (b * c) <= -2e+132:
		tmp = c * (b + (-4.0 * ((t * a) / c)))
	elif (b * c) <= 2e-109:
		tmp = t_1
	elif (b * c) <= 5e+106:
		tmp = (-27.0 * (j * k)) + (-4.0 * (x * i))
	elif (b * c) <= 2e+148:
		tmp = t_1
	else:
		tmp = (b * c) - (4.0 * (x * i))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * Float64(k * -27.0)) + Float64(Float64(t * a) * -4.0))
	tmp = 0.0
	if (Float64(b * c) <= -2e+132)
		tmp = Float64(c * Float64(b + Float64(-4.0 * Float64(Float64(t * a) / c))));
	elseif (Float64(b * c) <= 2e-109)
		tmp = t_1;
	elseif (Float64(b * c) <= 5e+106)
		tmp = Float64(Float64(-27.0 * Float64(j * k)) + Float64(-4.0 * Float64(x * i)));
	elseif (Float64(b * c) <= 2e+148)
		tmp = t_1;
	else
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * (k * -27.0)) + ((t * a) * -4.0);
	tmp = 0.0;
	if ((b * c) <= -2e+132)
		tmp = c * (b + (-4.0 * ((t * a) / c)));
	elseif ((b * c) <= 2e-109)
		tmp = t_1;
	elseif ((b * c) <= 5e+106)
		tmp = (-27.0 * (j * k)) + (-4.0 * (x * i));
	elseif ((b * c) <= 2e+148)
		tmp = t_1;
	else
		tmp = (b * c) - (4.0 * (x * i));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(N[(t * a), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -2e+132], N[(c * N[(b + N[(-4.0 * N[(N[(t * a), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 2e-109], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 5e+106], N[(N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 2e+148], t$95$1, N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 b c) < -1.99999999999999998e132

   1. Initial program 78.1%

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

   3. Simplified 76.1%

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

   5. Taylor expanded in c around inf 78.3%

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

   6. Taylor expanded in x around 0 80.2%

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

   7. Taylor expanded in j around 0 75.7%

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

   if -1.99999999999999998e132 < (*.f64 b c) < 2e-109 or 4.9999999999999998e106 < (*.f64 b c) < 2.0000000000000001e148

   1. Initial program 92.3%

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

   3. Simplified 95.4%

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

   5. Taylor expanded in a around inf 55.2%

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

      1. *-commutative 55.2%

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

   7. Simplified 55.2%

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

   if 2e-109 < (*.f64 b c) < 4.9999999999999998e106

   1. Initial program 83.9%

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

   3. Simplified 90.1%

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

   5. Taylor expanded in i around inf 45.8%

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

      1. associate-*r* 45.8%

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

      2. *-commutative 45.8%

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

      3. associate-*r* 45.8%

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

      4. *-commutative 45.8%

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

      5. *-commutative 45.8%

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

   7. Simplified 45.8%

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

   8. Taylor expanded in i around 0 45.8%

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

   if 2.0000000000000001e148 < (*.f64 b c)

   1. Initial program 86.8%

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

   3. Simplified 84.4%

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

   5. Taylor expanded in j around 0 87.0%

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

   6. Taylor expanded in t around 0 82.0%

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

4. Final simplification 60.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2 \cdot 10^{+132}:\\ \;\;\;\;c \cdot \left(b + -4 \cdot \frac{t \cdot a}{c}\right)\\ \mathbf{elif}\;b \cdot c \leq 2 \cdot 10^{-109}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + \left(t \cdot a\right) \cdot -4\\ \mathbf{elif}\;b \cdot c \leq 5 \cdot 10^{+106}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right) + -4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 2 \cdot 10^{+148}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + \left(t \cdot a\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 55.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2 \cdot 10^{+132}:\\ \;\;\;\;c \cdot \left(b + -4 \cdot \frac{t \cdot a}{c}\right)\\ \mathbf{elif}\;b \cdot c \leq 2 \cdot 10^{-109}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + \left(t \cdot a\right) \cdot -4\\ \mathbf{elif}\;b \cdot c \leq 5 \cdot 10^{+106}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right) + -4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 2 \cdot 10^{+148}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= (* b c) -2e+132)
   (* c (+ b (* -4.0 (/ (* t a) c))))
   (if (<= (* b c) 2e-109)
     (+ (* j (* k -27.0)) (* (* t a) -4.0))
     (if (<= (* b c) 5e+106)
       (+ (* -27.0 (* j k)) (* -4.0 (* x i)))
       (if (<= (* b c) 2e+148)
         (- (* t (* a -4.0)) (* (* j 27.0) k))
         (- (* b c) (* 4.0 (* x i))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b * c) <= -2e+132) {
		tmp = c * (b + (-4.0 * ((t * a) / c)));
	} else if ((b * c) <= 2e-109) {
		tmp = (j * (k * -27.0)) + ((t * a) * -4.0);
	} else if ((b * c) <= 5e+106) {
		tmp = (-27.0 * (j * k)) + (-4.0 * (x * i));
	} else if ((b * c) <= 2e+148) {
		tmp = (t * (a * -4.0)) - ((j * 27.0) * k);
	} else {
		tmp = (b * c) - (4.0 * (x * i));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((b * c) <= (-2d+132)) then
        tmp = c * (b + ((-4.0d0) * ((t * a) / c)))
    else if ((b * c) <= 2d-109) then
        tmp = (j * (k * (-27.0d0))) + ((t * a) * (-4.0d0))
    else if ((b * c) <= 5d+106) then
        tmp = ((-27.0d0) * (j * k)) + ((-4.0d0) * (x * i))
    else if ((b * c) <= 2d+148) then
        tmp = (t * (a * (-4.0d0))) - ((j * 27.0d0) * k)
    else
        tmp = (b * c) - (4.0d0 * (x * i))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b * c) <= -2e+132) {
		tmp = c * (b + (-4.0 * ((t * a) / c)));
	} else if ((b * c) <= 2e-109) {
		tmp = (j * (k * -27.0)) + ((t * a) * -4.0);
	} else if ((b * c) <= 5e+106) {
		tmp = (-27.0 * (j * k)) + (-4.0 * (x * i));
	} else if ((b * c) <= 2e+148) {
		tmp = (t * (a * -4.0)) - ((j * 27.0) * k);
	} else {
		tmp = (b * c) - (4.0 * (x * i));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (b * c) <= -2e+132:
		tmp = c * (b + (-4.0 * ((t * a) / c)))
	elif (b * c) <= 2e-109:
		tmp = (j * (k * -27.0)) + ((t * a) * -4.0)
	elif (b * c) <= 5e+106:
		tmp = (-27.0 * (j * k)) + (-4.0 * (x * i))
	elif (b * c) <= 2e+148:
		tmp = (t * (a * -4.0)) - ((j * 27.0) * k)
	else:
		tmp = (b * c) - (4.0 * (x * i))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (Float64(b * c) <= -2e+132)
		tmp = Float64(c * Float64(b + Float64(-4.0 * Float64(Float64(t * a) / c))));
	elseif (Float64(b * c) <= 2e-109)
		tmp = Float64(Float64(j * Float64(k * -27.0)) + Float64(Float64(t * a) * -4.0));
	elseif (Float64(b * c) <= 5e+106)
		tmp = Float64(Float64(-27.0 * Float64(j * k)) + Float64(-4.0 * Float64(x * i)));
	elseif (Float64(b * c) <= 2e+148)
		tmp = Float64(Float64(t * Float64(a * -4.0)) - Float64(Float64(j * 27.0) * k));
	else
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((b * c) <= -2e+132)
		tmp = c * (b + (-4.0 * ((t * a) / c)));
	elseif ((b * c) <= 2e-109)
		tmp = (j * (k * -27.0)) + ((t * a) * -4.0);
	elseif ((b * c) <= 5e+106)
		tmp = (-27.0 * (j * k)) + (-4.0 * (x * i));
	elseif ((b * c) <= 2e+148)
		tmp = (t * (a * -4.0)) - ((j * 27.0) * k);
	else
		tmp = (b * c) - (4.0 * (x * i));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[N[(b * c), $MachinePrecision], -2e+132], N[(c * N[(b + N[(-4.0 * N[(N[(t * a), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 2e-109], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(N[(t * a), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 5e+106], N[(N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 2e+148], N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 b c) < -1.99999999999999998e132

   1. Initial program 78.1%

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

   3. Simplified 76.1%

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

   5. Taylor expanded in c around inf 78.3%

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

   6. Taylor expanded in x around 0 80.2%

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

   7. Taylor expanded in j around 0 75.7%

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

   if -1.99999999999999998e132 < (*.f64 b c) < 2e-109

   1. Initial program 92.3%

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

   3. Simplified 95.7%

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

   5. Taylor expanded in a around inf 55.5%

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

      1. *-commutative 55.5%

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

   7. Simplified 55.5%

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

   if 2e-109 < (*.f64 b c) < 4.9999999999999998e106

   1. Initial program 83.9%

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

   3. Simplified 90.1%

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

   5. Taylor expanded in i around inf 45.8%

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

      1. associate-*r* 45.8%

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

      2. *-commutative 45.8%

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

      3. associate-*r* 45.8%

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

      4. *-commutative 45.8%

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

      5. *-commutative 45.8%

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

   7. Simplified 45.8%

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

   8. Taylor expanded in i around 0 45.8%

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

   if 4.9999999999999998e106 < (*.f64 b c) < 2.0000000000000001e148

   1. Initial program 91.6%

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

   3. Taylor expanded in x around 0 83.0%

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

   4. Taylor expanded in a around inf 52.1%

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

      1. associate-*r* 52.1%

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

   6. Simplified 52.1%

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

   if 2.0000000000000001e148 < (*.f64 b c)

   1. Initial program 86.8%

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

   3. Simplified 84.4%

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

   5. Taylor expanded in j around 0 87.0%

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

   6. Taylor expanded in t around 0 82.0%

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

4. Final simplification 60.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2 \cdot 10^{+132}:\\ \;\;\;\;c \cdot \left(b + -4 \cdot \frac{t \cdot a}{c}\right)\\ \mathbf{elif}\;b \cdot c \leq 2 \cdot 10^{-109}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + \left(t \cdot a\right) \cdot -4\\ \mathbf{elif}\;b \cdot c \leq 5 \cdot 10^{+106}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right) + -4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 2 \cdot 10^{+148}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 85.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -5 \cdot 10^{+144}:\\ \;\;\;\;\left(b \cdot c + y \cdot \left(z \cdot \left(t \cdot \left(18 \cdot x\right)\right)\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(y \cdot z\right) \cdot \left(18 \cdot x\right) - 4 \cdot a\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= (* b c) -5e+144)
   (- (+ (* b c) (* y (* z (* t (* 18.0 x))))) (* (* j 27.0) k))
   (-
    (+ (* b c) (* t (- (* (* y z) (* 18.0 x)) (* 4.0 a))))
    (+ (* x (* 4.0 i)) (* j (* 27.0 k))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b * c) <= -5e+144) {
		tmp = ((b * c) + (y * (z * (t * (18.0 * x))))) - ((j * 27.0) * k);
	} else {
		tmp = ((b * c) + (t * (((y * z) * (18.0 * x)) - (4.0 * a)))) - ((x * (4.0 * i)) + (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.
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) <= (-5d+144)) then
        tmp = ((b * c) + (y * (z * (t * (18.0d0 * x))))) - ((j * 27.0d0) * k)
    else
        tmp = ((b * c) + (t * (((y * z) * (18.0d0 * x)) - (4.0d0 * a)))) - ((x * (4.0d0 * i)) + (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;
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) <= -5e+144) {
		tmp = ((b * c) + (y * (z * (t * (18.0 * x))))) - ((j * 27.0) * k);
	} else {
		tmp = ((b * c) + (t * (((y * z) * (18.0 * x)) - (4.0 * a)))) - ((x * (4.0 * i)) + (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])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (b * c) <= -5e+144:
		tmp = ((b * c) + (y * (z * (t * (18.0 * x))))) - ((j * 27.0) * k)
	else:
		tmp = ((b * c) + (t * (((y * z) * (18.0 * x)) - (4.0 * a)))) - ((x * (4.0 * i)) + (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])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (Float64(b * c) <= -5e+144)
		tmp = Float64(Float64(Float64(b * c) + Float64(y * Float64(z * Float64(t * Float64(18.0 * x))))) - Float64(Float64(j * 27.0) * k));
	else
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(Float64(y * z) * Float64(18.0 * x)) - Float64(4.0 * a)))) - Float64(Float64(x * Float64(4.0 * i)) + Float64(j * Float64(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])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((b * c) <= -5e+144)
		tmp = ((b * c) + (y * (z * (t * (18.0 * x))))) - ((j * 27.0) * k);
	else
		tmp = ((b * c) + (t * (((y * z) * (18.0 * x)) - (4.0 * a)))) - ((x * (4.0 * i)) + (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.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[N[(b * c), $MachinePrecision], -5e+144], N[(N[(N[(b * c), $MachinePrecision] + N[(y * N[(z * N[(t * N[(18.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(N[(y * z), $MachinePrecision] * N[(18.0 * x), $MachinePrecision]), $MachinePrecision] - N[(4.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision] + N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -4.9999999999999999e144

   1. Initial program 79.2%

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

   3. Taylor expanded in x around 0 74.3%

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

   4. Taylor expanded in a around 0 76.9%

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

      1. pow1 76.9%

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

   6. Applied egg-rr 76.9%

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

      1. unpow1 76.9%

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

      2. associate-*r* 79.4%

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

   8. Simplified 79.4%

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

   9. Taylor expanded in t around inf 79.5%

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

       1. associate-*r* 79.5%

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

       2. associate-*r* 79.5%

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

       3. *-commutative 79.5%

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

       4. associate-*r* 89.4%

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

       5. *-commutative 89.4%

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

       6. associate-*r* 89.4%

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

   11. Simplified 89.4%

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

   if -4.9999999999999999e144 < (*.f64 b c)

   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 90.9%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -5 \cdot 10^{+144}:\\ \;\;\;\;\left(b \cdot c + y \cdot \left(z \cdot \left(t \cdot \left(18 \cdot x\right)\right)\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(y \cdot z\right) \cdot \left(18 \cdot x\right) - 4 \cdot a\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 47.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{if}\;t \leq -4.4 \cdot 10^{+176}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -8 \cdot 10^{+79}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;t \leq -2.7 \cdot 10^{-278}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{+88}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* 18.0 (* t (* x (* y z))))))
   (if (<= t -4.4e+176)
     t_1
     (if (<= t -8e+79)
       (* t (* a -4.0))
       (if (<= t -2.7e-278)
         (+ (* b c) (* j (* k -27.0)))
         (if (<= t 7.8e+88) (- (* b c) (* 4.0 (* x i))) t_1))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 18.0 * (t * (x * (y * z)));
	double tmp;
	if (t <= -4.4e+176) {
		tmp = t_1;
	} else if (t <= -8e+79) {
		tmp = t * (a * -4.0);
	} else if (t <= -2.7e-278) {
		tmp = (b * c) + (j * (k * -27.0));
	} else if (t <= 7.8e+88) {
		tmp = (b * c) - (4.0 * (x * 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.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 18.0d0 * (t * (x * (y * z)))
    if (t <= (-4.4d+176)) then
        tmp = t_1
    else if (t <= (-8d+79)) then
        tmp = t * (a * (-4.0d0))
    else if (t <= (-2.7d-278)) then
        tmp = (b * c) + (j * (k * (-27.0d0)))
    else if (t <= 7.8d+88) then
        tmp = (b * c) - (4.0d0 * (x * 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;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 18.0 * (t * (x * (y * z)));
	double tmp;
	if (t <= -4.4e+176) {
		tmp = t_1;
	} else if (t <= -8e+79) {
		tmp = t * (a * -4.0);
	} else if (t <= -2.7e-278) {
		tmp = (b * c) + (j * (k * -27.0));
	} else if (t <= 7.8e+88) {
		tmp = (b * c) - (4.0 * (x * 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])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = 18.0 * (t * (x * (y * z)))
	tmp = 0
	if t <= -4.4e+176:
		tmp = t_1
	elif t <= -8e+79:
		tmp = t * (a * -4.0)
	elif t <= -2.7e-278:
		tmp = (b * c) + (j * (k * -27.0))
	elif t <= 7.8e+88:
		tmp = (b * c) - (4.0 * (x * 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])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(18.0 * Float64(t * Float64(x * Float64(y * z))))
	tmp = 0.0
	if (t <= -4.4e+176)
		tmp = t_1;
	elseif (t <= -8e+79)
		tmp = Float64(t * Float64(a * -4.0));
	elseif (t <= -2.7e-278)
		tmp = Float64(Float64(b * c) + Float64(j * Float64(k * -27.0)));
	elseif (t <= 7.8e+88)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(x * 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])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = 18.0 * (t * (x * (y * z)));
	tmp = 0.0;
	if (t <= -4.4e+176)
		tmp = t_1;
	elseif (t <= -8e+79)
		tmp = t * (a * -4.0);
	elseif (t <= -2.7e-278)
		tmp = (b * c) + (j * (k * -27.0));
	elseif (t <= 7.8e+88)
		tmp = (b * c) - (4.0 * (x * 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.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.4e+176], t$95$1, If[LessEqual[t, -8e+79], N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.7e-278], N[(N[(b * c), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.8e+88], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -4.40000000000000015e176 or 7.8000000000000002e88 < t

   1. Initial program 84.9%

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

   3. Simplified 88.6%

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

   5. Taylor expanded in c around inf 74.7%

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

   6. Taylor expanded in y around inf 49.1%

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

   if -4.40000000000000015e176 < t < -7.99999999999999974e79

   1. Initial program 94.9%

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

   3. Simplified 95.0%

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

   5. Taylor expanded in c around inf 95.1%

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

   6. Taylor expanded in a around inf 51.8%

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

      1. *-commutative 51.8%

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

      2. *-commutative 51.8%

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

      3. associate-*r* 51.8%

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

   8. Simplified 51.8%

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

   if -7.99999999999999974e79 < t < -2.7000000000000001e-278

   1. Initial program 93.3%

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

   3. Simplified 93.3%

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

   5. Taylor expanded in b around inf 60.1%

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

   if -2.7000000000000001e-278 < t < 7.8000000000000002e88

   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 83.6%

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

   5. Taylor expanded in j around 0 73.0%

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

   6. Taylor expanded in t around 0 56.8%

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

4. Final simplification 54.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.4 \cdot 10^{+176}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq -8 \cdot 10^{+79}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;t \leq -2.7 \cdot 10^{-278}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{+88}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 81.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\\ \mathbf{if}\;t \leq -1.55 \cdot 10^{+82}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(t\_1 + a \cdot -4\right)\\ \mathbf{elif}\;t \leq 5.1 \cdot 10^{+90}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a + x \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + t \cdot \left(t\_1 - 4 \cdot a\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* 18.0 (* x (* y z)))))
   (if (<= t -1.55e+82)
     (+ (* j (* k -27.0)) (* t (+ t_1 (* a -4.0))))
     (if (<= t 5.1e+90)
       (- (- (* b c) (* 4.0 (+ (* t a) (* x i)))) (* (* j 27.0) k))
       (+ (* b c) (* t (- t_1 (* 4.0 a))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 18.0 * (x * (y * z));
	double tmp;
	if (t <= -1.55e+82) {
		tmp = (j * (k * -27.0)) + (t * (t_1 + (a * -4.0)));
	} else if (t <= 5.1e+90) {
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - ((j * 27.0) * k);
	} else {
		tmp = (b * c) + (t * (t_1 - (4.0 * 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.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 18.0d0 * (x * (y * z))
    if (t <= (-1.55d+82)) then
        tmp = (j * (k * (-27.0d0))) + (t * (t_1 + (a * (-4.0d0))))
    else if (t <= 5.1d+90) then
        tmp = ((b * c) - (4.0d0 * ((t * a) + (x * i)))) - ((j * 27.0d0) * k)
    else
        tmp = (b * c) + (t * (t_1 - (4.0d0 * 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;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 18.0 * (x * (y * z));
	double tmp;
	if (t <= -1.55e+82) {
		tmp = (j * (k * -27.0)) + (t * (t_1 + (a * -4.0)));
	} else if (t <= 5.1e+90) {
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - ((j * 27.0) * k);
	} else {
		tmp = (b * c) + (t * (t_1 - (4.0 * 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])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = 18.0 * (x * (y * z))
	tmp = 0
	if t <= -1.55e+82:
		tmp = (j * (k * -27.0)) + (t * (t_1 + (a * -4.0)))
	elif t <= 5.1e+90:
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - ((j * 27.0) * k)
	else:
		tmp = (b * c) + (t * (t_1 - (4.0 * 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])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(18.0 * Float64(x * Float64(y * z)))
	tmp = 0.0
	if (t <= -1.55e+82)
		tmp = Float64(Float64(j * Float64(k * -27.0)) + Float64(t * Float64(t_1 + Float64(a * -4.0))));
	elseif (t <= 5.1e+90)
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(Float64(t * a) + Float64(x * i)))) - Float64(Float64(j * 27.0) * k));
	else
		tmp = Float64(Float64(b * c) + Float64(t * Float64(t_1 - Float64(4.0 * 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])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = 18.0 * (x * (y * z));
	tmp = 0.0;
	if (t <= -1.55e+82)
		tmp = (j * (k * -27.0)) + (t * (t_1 + (a * -4.0)));
	elseif (t <= 5.1e+90)
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - ((j * 27.0) * k);
	else
		tmp = (b * c) + (t * (t_1 - (4.0 * 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.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.55e+82], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(t * N[(t$95$1 + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.1e+90], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] + N[(t * N[(t$95$1 - N[(4.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.55000000000000016e82

   1. Initial program 88.3%

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

   3. Simplified 92.2%

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

   5. Taylor expanded in t around inf 88.6%

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

   if -1.55000000000000016e82 < t < 5.09999999999999959e90

   1. Initial program 88.3%

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

   3. Taylor expanded in y around 0 82.7%

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

      1. distribute-lft-out 82.7%

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

      2. *-commutative 82.7%

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

   5. Simplified 82.7%

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

   if 5.09999999999999959e90 < t

   1. Initial program 84.3%

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

   3. Simplified 88.6%

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

   5. Taylor expanded in j around 0 84.4%

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

   6. Taylor expanded in i around 0 82.2%

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

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.55 \cdot 10^{+82}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{elif}\;t \leq 5.1 \cdot 10^{+90}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a + x \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 58.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)\\ \mathbf{if}\;t \leq -3.6 \cdot 10^{-50}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-277}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t \leq 9.8 \cdot 10^{-29}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* t (- (* 18.0 (* x (* y z))) (* 4.0 a)))))
   (if (<= t -3.6e-50)
     t_1
     (if (<= t -1e-277)
       (+ (* b c) (* j (* k -27.0)))
       (if (<= t 9.8e-29) (- (* b c) (* 4.0 (* x i))) t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * ((18.0 * (x * (y * z))) - (4.0 * a));
	double tmp;
	if (t <= -3.6e-50) {
		tmp = t_1;
	} else if (t <= -1e-277) {
		tmp = (b * c) + (j * (k * -27.0));
	} else if (t <= 9.8e-29) {
		tmp = (b * c) - (4.0 * (x * 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.
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))) - (4.0d0 * a))
    if (t <= (-3.6d-50)) then
        tmp = t_1
    else if (t <= (-1d-277)) then
        tmp = (b * c) + (j * (k * (-27.0d0)))
    else if (t <= 9.8d-29) then
        tmp = (b * c) - (4.0d0 * (x * 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;
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))) - (4.0 * a));
	double tmp;
	if (t <= -3.6e-50) {
		tmp = t_1;
	} else if (t <= -1e-277) {
		tmp = (b * c) + (j * (k * -27.0));
	} else if (t <= 9.8e-29) {
		tmp = (b * c) - (4.0 * (x * 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])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = t * ((18.0 * (x * (y * z))) - (4.0 * a))
	tmp = 0
	if t <= -3.6e-50:
		tmp = t_1
	elif t <= -1e-277:
		tmp = (b * c) + (j * (k * -27.0))
	elif t <= 9.8e-29:
		tmp = (b * c) - (4.0 * (x * 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])
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(4.0 * a)))
	tmp = 0.0
	if (t <= -3.6e-50)
		tmp = t_1;
	elseif (t <= -1e-277)
		tmp = Float64(Float64(b * c) + Float64(j * Float64(k * -27.0)));
	elseif (t <= 9.8e-29)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(x * 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])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = t * ((18.0 * (x * (y * z))) - (4.0 * a));
	tmp = 0.0;
	if (t <= -3.6e-50)
		tmp = t_1;
	elseif (t <= -1e-277)
		tmp = (b * c) + (j * (k * -27.0));
	elseif (t <= 9.8e-29)
		tmp = (b * c) - (4.0 * (x * 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.
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[(4.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.6e-50], t$95$1, If[LessEqual[t, -1e-277], N[(N[(b * c), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.8e-29], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.59999999999999979e-50 or 9.7999999999999997e-29 < t

   1. Initial program 88.3%

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

   3. Simplified 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 c around inf 76.3%

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

   6. Taylor expanded in t around -inf 65.7%

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

   if -3.59999999999999979e-50 < t < -9.99999999999999969e-278

   1. Initial program 91.8%

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

   3. Simplified 93.7%

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

   5. Taylor expanded in b around inf 72.9%

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

   if -9.99999999999999969e-278 < t < 9.7999999999999997e-29

   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 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 71.8%

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

   6. Taylor expanded in t around 0 62.8%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{-50}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-277}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t \leq 9.8 \cdot 10^{-29}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 28: 72.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{+66} \lor \neg \left(x \leq 1.7 \cdot 10^{+15}\right):\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + \left(t \cdot a\right) \cdot -4\right) - 27 \cdot \left(j \cdot k\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= x -2.3e+66) (not (<= x 1.7e+15)))
   (* x (- (* 18.0 (* t (* y z))) (* 4.0 i)))
   (- (+ (* b c) (* (* t a) -4.0)) (* 27.0 (* j k)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((x <= -2.3e+66) || !(x <= 1.7e+15)) {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	} else {
		tmp = ((b * c) + ((t * a) * -4.0)) - (27.0 * (j * k));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((x <= (-2.3d+66)) .or. (.not. (x <= 1.7d+15))) then
        tmp = x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i))
    else
        tmp = ((b * c) + ((t * a) * (-4.0d0))) - (27.0d0 * (j * k))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((x <= -2.3e+66) || !(x <= 1.7e+15)) {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	} else {
		tmp = ((b * c) + ((t * a) * -4.0)) - (27.0 * (j * k));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (x <= -2.3e+66) or not (x <= 1.7e+15):
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i))
	else:
		tmp = ((b * c) + ((t * a) * -4.0)) - (27.0 * (j * k))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((x <= -2.3e+66) || !(x <= 1.7e+15))
		tmp = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)));
	else
		tmp = Float64(Float64(Float64(b * c) + Float64(Float64(t * a) * -4.0)) - Float64(27.0 * Float64(j * k)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((x <= -2.3e+66) || ~((x <= 1.7e+15)))
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	else
		tmp = ((b * c) + ((t * a) * -4.0)) - (27.0 * (j * k));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[x, -2.3e+66], N[Not[LessEqual[x, 1.7e+15]], $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[(N[(t * a), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.3e66 or 1.7e15 < x

   1. Initial program 79.4%

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

   3. Simplified 86.2%

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

   5. Taylor expanded in x around inf 71.9%

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

   if -2.3e66 < x < 1.7e15

   1. Initial program 93.0%

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

   3. Simplified 90.6%

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

   5. Taylor expanded in x around 0 78.3%

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

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{+66} \lor \neg \left(x \leq 1.7 \cdot 10^{+15}\right):\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + \left(t \cdot a\right) \cdot -4\right) - 27 \cdot \left(j \cdot k\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 29: 49.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.95 \cdot 10^{+176}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq -8 \cdot 10^{+79}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+90}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\left(18 \cdot z\right) \cdot \left(y \cdot x\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= t -1.95e+176)
   (* 18.0 (* t (* x (* y z))))
   (if (<= t -8e+79)
     (* t (* a -4.0))
     (if (<= t 1.9e+90)
       (+ (* b c) (* j (* k -27.0)))
       (* t (* (* 18.0 z) (* y x)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (t <= -1.95e+176) {
		tmp = 18.0 * (t * (x * (y * z)));
	} else if (t <= -8e+79) {
		tmp = t * (a * -4.0);
	} else if (t <= 1.9e+90) {
		tmp = (b * c) + (j * (k * -27.0));
	} else {
		tmp = t * ((18.0 * z) * (y * x));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 <= (-1.95d+176)) then
        tmp = 18.0d0 * (t * (x * (y * z)))
    else if (t <= (-8d+79)) then
        tmp = t * (a * (-4.0d0))
    else if (t <= 1.9d+90) then
        tmp = (b * c) + (j * (k * (-27.0d0)))
    else
        tmp = t * ((18.0d0 * z) * (y * x))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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 <= -1.95e+176) {
		tmp = 18.0 * (t * (x * (y * z)));
	} else if (t <= -8e+79) {
		tmp = t * (a * -4.0);
	} else if (t <= 1.9e+90) {
		tmp = (b * c) + (j * (k * -27.0));
	} else {
		tmp = t * ((18.0 * z) * (y * x));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if t <= -1.95e+176:
		tmp = 18.0 * (t * (x * (y * z)))
	elif t <= -8e+79:
		tmp = t * (a * -4.0)
	elif t <= 1.9e+90:
		tmp = (b * c) + (j * (k * -27.0))
	else:
		tmp = t * ((18.0 * z) * (y * x))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (t <= -1.95e+176)
		tmp = Float64(18.0 * Float64(t * Float64(x * Float64(y * z))));
	elseif (t <= -8e+79)
		tmp = Float64(t * Float64(a * -4.0));
	elseif (t <= 1.9e+90)
		tmp = Float64(Float64(b * c) + Float64(j * Float64(k * -27.0)));
	else
		tmp = Float64(t * Float64(Float64(18.0 * z) * Float64(y * x)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (t <= -1.95e+176)
		tmp = 18.0 * (t * (x * (y * z)));
	elseif (t <= -8e+79)
		tmp = t * (a * -4.0);
	elseif (t <= 1.9e+90)
		tmp = (b * c) + (j * (k * -27.0));
	else
		tmp = t * ((18.0 * z) * (y * x));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[t, -1.95e+176], N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -8e+79], N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.9e+90], N[(N[(b * c), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(18.0 * z), $MachinePrecision] * N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.9500000000000001e176

   1. Initial program 85.2%

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

   3. Simplified 88.2%

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

   5. Taylor expanded in c around inf 74.7%

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

   6. Taylor expanded in y around inf 57.3%

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

   if -1.9500000000000001e176 < t < -7.99999999999999974e79

   1. Initial program 94.9%

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

   3. Simplified 95.0%

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

   5. Taylor expanded in c around inf 95.1%

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

   6. Taylor expanded in a around inf 51.8%

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

      1. *-commutative 51.8%

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

      2. *-commutative 51.8%

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

      3. associate-*r* 51.8%

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

   8. Simplified 51.8%

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

   if -7.99999999999999974e79 < t < 1.9000000000000001e90

   1. Initial program 88.2%

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

   3. Simplified 89.6%

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

   5. Taylor expanded in b around inf 52.6%

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

   if 1.9000000000000001e90 < t

   1. Initial program 84.3%

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

   3. Simplified 88.6%

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

   5. Taylor expanded in c around inf 76.4%

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

   6. Taylor expanded in y around inf 43.9%

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

      1. *-commutative 43.9%

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

      2. associate-*r* 44.0%

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

      3. associate-*r* 44.0%

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

      4. *-commutative 44.0%

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

      5. associate-*r* 43.9%

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

   8. Simplified 43.9%

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

4. Final simplification 51.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.95 \cdot 10^{+176}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq -8 \cdot 10^{+79}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+90}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\left(18 \cdot z\right) \cdot \left(y \cdot x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 30: 32.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := x \cdot \left(i \cdot -4\right)\\ \mathbf{if}\;i \leq -2.7 \cdot 10^{+137}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 9.5 \cdot 10^{-51}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;i \leq 2.5 \cdot 10^{+78}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* x (* i -4.0))))
   (if (<= i -2.7e+137)
     t_1
     (if (<= i 9.5e-51) (* b c) (if (<= i 2.5e+78) (* 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);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = x * (i * -4.0);
	double tmp;
	if (i <= -2.7e+137) {
		tmp = t_1;
	} else if (i <= 9.5e-51) {
		tmp = b * c;
	} else if (i <= 2.5e+78) {
		tmp = 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.
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 * (i * (-4.0d0))
    if (i <= (-2.7d+137)) then
        tmp = t_1
    else if (i <= 9.5d-51) then
        tmp = b * c
    else if (i <= 2.5d+78) then
        tmp = 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;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = x * (i * -4.0);
	double tmp;
	if (i <= -2.7e+137) {
		tmp = t_1;
	} else if (i <= 9.5e-51) {
		tmp = b * c;
	} else if (i <= 2.5e+78) {
		tmp = 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])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = x * (i * -4.0)
	tmp = 0
	if i <= -2.7e+137:
		tmp = t_1
	elif i <= 9.5e-51:
		tmp = b * c
	elif i <= 2.5e+78:
		tmp = 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])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(x * Float64(i * -4.0))
	tmp = 0.0
	if (i <= -2.7e+137)
		tmp = t_1;
	elseif (i <= 9.5e-51)
		tmp = Float64(b * c);
	elseif (i <= 2.5e+78)
		tmp = 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])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = x * (i * -4.0);
	tmp = 0.0;
	if (i <= -2.7e+137)
		tmp = t_1;
	elseif (i <= 9.5e-51)
		tmp = b * c;
	elseif (i <= 2.5e+78)
		tmp = 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.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -2.7e+137], t$95$1, If[LessEqual[i, 9.5e-51], N[(b * c), $MachinePrecision], If[LessEqual[i, 2.5e+78], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if i < -2.70000000000000017e137 or 2.49999999999999992e78 < i

   1. Initial program 79.4%

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

   3. Simplified 82.2%

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

   5. Taylor expanded in c around inf 70.9%

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

   6. Taylor expanded in i around inf 49.1%

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

      1. associate-*r* 49.1%

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

      2. metadata-eval 49.1%

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

      3. distribute-lft-neg-in 49.1%

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

      4. distribute-lft-neg-in 49.1%

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

      5. *-commutative 49.1%

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

      6. distribute-rgt-neg-in 49.1%

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

      7. distribute-lft-neg-in 49.1%

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

      8. metadata-eval 49.1%

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

      9. *-commutative 49.1%

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

   8. Simplified 49.1%

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

   if -2.70000000000000017e137 < i < 9.4999999999999998e-51

   1. Initial program 92.2%

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

   3. Simplified 92.8%

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

   5. Taylor expanded in c around inf 81.8%

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

   6. Taylor expanded in c around inf 34.2%

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

   if 9.4999999999999998e-51 < i < 2.49999999999999992e78

   1. Initial program 84.9%

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

   3. Simplified 85.1%

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

   5. Taylor expanded in y around inf 65.1%

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

   6. Taylor expanded in t around 0 39.3%

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

      1. associate-*r* 39.2%

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

      2. *-commutative 39.2%

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

      3. associate-*r* 39.3%

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

   8. Simplified 39.3%

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

4. Final simplification 39.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -2.7 \cdot 10^{+137}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;i \leq 9.5 \cdot 10^{-51}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;i \leq 2.5 \cdot 10^{+78}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 31: 38.7% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2.7 \cdot 10^{+78} \lor \neg \left(b \cdot c \leq 7.8 \cdot 10^{+133}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= (* b c) -2.7e+78) (not (<= (* b c) 7.8e+133)))
   (* b c)
   (* -27.0 (* j k))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (((b * c) <= -2.7e+78) || !((b * c) <= 7.8e+133)) {
		tmp = b * c;
	} else {
		tmp = -27.0 * (j * k);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (((b * c) <= (-2.7d+78)) .or. (.not. ((b * c) <= 7.8d+133))) then
        tmp = b * c
    else
        tmp = (-27.0d0) * (j * k)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (((b * c) <= -2.7e+78) || !((b * c) <= 7.8e+133)) {
		tmp = b * c;
	} else {
		tmp = -27.0 * (j * k);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if ((b * c) <= -2.7e+78) or not ((b * c) <= 7.8e+133):
		tmp = b * c
	else:
		tmp = -27.0 * (j * k)
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((Float64(b * c) <= -2.7e+78) || !(Float64(b * c) <= 7.8e+133))
		tmp = Float64(b * c);
	else
		tmp = Float64(-27.0 * Float64(j * k));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (((b * c) <= -2.7e+78) || ~(((b * c) <= 7.8e+133)))
		tmp = b * c;
	else
		tmp = -27.0 * (j * k);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[N[(b * c), $MachinePrecision], -2.7e+78], N[Not[LessEqual[N[(b * c), $MachinePrecision], 7.8e+133]], $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) < -2.70000000000000004e78 or 7.80000000000000028e133 < (*.f64 b c)

   1. Initial program 84.1%

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

   3. Simplified 82.1%

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

   5. Taylor expanded in c around inf 83.2%

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

   6. Taylor expanded in c around inf 62.2%

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

   if -2.70000000000000004e78 < (*.f64 b c) < 7.80000000000000028e133

   1. Initial program 89.4%

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

   3. Simplified 93.6%

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

   5. Taylor expanded in j around inf 26.2%

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

4. Final simplification 38.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2.7 \cdot 10^{+78} \lor \neg \left(b \cdot c \leq 7.8 \cdot 10^{+133}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 32: 25.3% accurate, 10.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.6%

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

3. Simplified 88.9%

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

5. Taylor expanded in c around inf 76.6%

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

6. Taylor expanded in c around inf 26.4%

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

7. Final simplification 26.4%

   \[\leadsto b \cdot c \]
8. Add Preprocessing

Developer target: 89.5% 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 2024082 
(FPCore (x y z t a b c i j k)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, E"
  :precision binary64

  :alt
  (if (< t -1.6210815397541398e-69) (- (- (* (* 18.0 t) (* (* x y) z)) (* (+ (* a t) (* i x)) 4.0)) (- (* (* k j) 27.0) (* c b))) (if (< t 165.68027943805222) (+ (- (* (* 18.0 y) (* x (* z t))) (* (+ (* a t) (* i x)) 4.0)) (- (* c b) (* 27.0 (* k j)))) (- (- (* (* 18.0 t) (* (* x y) z)) (* (+ (* a t) (* i x)) 4.0)) (- (* (* k j) 27.0) (* c b)))))

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