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

Percentage Accurate: 85.8% → 92.5%

Time: 23.3s

Alternatives: 21

Speedup: 0.8×

• 49.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.8% 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: 92.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(\left(x \cdot 18\right) \cdot y\right) \cdot z\\ t_2 := \left(j \cdot 27\right) \cdot k\\ t_3 := 18 \cdot \left(y \cdot z\right)\\ t_4 := \left(\left(t\_1 \cdot t - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\\ \mathbf{if}\;t\_4 \leq -\infty:\\ \;\;\;\;y \cdot \left(18 \cdot \left(x \cdot \left(z \cdot t\right)\right) + \frac{b \cdot c + -4 \cdot \left(t \cdot a + x \cdot i\right)}{y}\right) - t\_2\\ \mathbf{elif}\;t\_4 \leq 5 \cdot 10^{+306}:\\ \;\;\;\;t \cdot \left(t\_1 + a \cdot -4\right) + \left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right)\\ \mathbf{elif}\;t\_4 \leq \infty:\\ \;\;\;\;x \cdot \left(\left(i \cdot -4 + t \cdot t\_3\right) + \frac{b \cdot c + t \cdot \left(a \cdot -4\right)}{x}\right) - t\_2\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot -4 + x \cdot t\_3\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* (* x 18.0) y) z))
        (t_2 (* (* j 27.0) k))
        (t_3 (* 18.0 (* y z)))
        (t_4 (- (+ (- (* t_1 t) (* t (* a 4.0))) (* b c)) (* (* x 4.0) i))))
   (if (<= t_4 (- INFINITY))
     (-
      (*
       y
       (+
        (* 18.0 (* x (* z t)))
        (/ (+ (* b c) (* -4.0 (+ (* t a) (* x i)))) y)))
      t_2)
     (if (<= t_4 5e+306)
       (+
        (* t (+ t_1 (* a -4.0)))
        (+ (* -27.0 (* j k)) (+ (* b c) (* x (* i -4.0)))))
       (if (<= t_4 INFINITY)
         (-
          (* x (+ (+ (* i -4.0) (* t t_3)) (/ (+ (* b c) (* t (* a -4.0))) x)))
          t_2)
         (* t (+ (* a -4.0) (* 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 = ((x * 18.0) * y) * z;
	double t_2 = (j * 27.0) * k;
	double t_3 = 18.0 * (y * z);
	double t_4 = (((t_1 * t) - (t * (a * 4.0))) + (b * c)) - ((x * 4.0) * i);
	double tmp;
	if (t_4 <= -((double) INFINITY)) {
		tmp = (y * ((18.0 * (x * (z * t))) + (((b * c) + (-4.0 * ((t * a) + (x * i)))) / y))) - t_2;
	} else if (t_4 <= 5e+306) {
		tmp = (t * (t_1 + (a * -4.0))) + ((-27.0 * (j * k)) + ((b * c) + (x * (i * -4.0))));
	} else if (t_4 <= ((double) INFINITY)) {
		tmp = (x * (((i * -4.0) + (t * t_3)) + (((b * c) + (t * (a * -4.0))) / x))) - t_2;
	} else {
		tmp = t * ((a * -4.0) + (x * t_3));
	}
	return tmp;
}

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((x * 18.0) * y) * z;
	double t_2 = (j * 27.0) * k;
	double t_3 = 18.0 * (y * z);
	double t_4 = (((t_1 * t) - (t * (a * 4.0))) + (b * c)) - ((x * 4.0) * i);
	double tmp;
	if (t_4 <= -Double.POSITIVE_INFINITY) {
		tmp = (y * ((18.0 * (x * (z * t))) + (((b * c) + (-4.0 * ((t * a) + (x * i)))) / y))) - t_2;
	} else if (t_4 <= 5e+306) {
		tmp = (t * (t_1 + (a * -4.0))) + ((-27.0 * (j * k)) + ((b * c) + (x * (i * -4.0))));
	} else if (t_4 <= Double.POSITIVE_INFINITY) {
		tmp = (x * (((i * -4.0) + (t * t_3)) + (((b * c) + (t * (a * -4.0))) / x))) - t_2;
	} else {
		tmp = t * ((a * -4.0) + (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 = ((x * 18.0) * y) * z
	t_2 = (j * 27.0) * k
	t_3 = 18.0 * (y * z)
	t_4 = (((t_1 * t) - (t * (a * 4.0))) + (b * c)) - ((x * 4.0) * i)
	tmp = 0
	if t_4 <= -math.inf:
		tmp = (y * ((18.0 * (x * (z * t))) + (((b * c) + (-4.0 * ((t * a) + (x * i)))) / y))) - t_2
	elif t_4 <= 5e+306:
		tmp = (t * (t_1 + (a * -4.0))) + ((-27.0 * (j * k)) + ((b * c) + (x * (i * -4.0))))
	elif t_4 <= math.inf:
		tmp = (x * (((i * -4.0) + (t * t_3)) + (((b * c) + (t * (a * -4.0))) / x))) - t_2
	else:
		tmp = t * ((a * -4.0) + (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(Float64(Float64(x * 18.0) * y) * z)
	t_2 = Float64(Float64(j * 27.0) * k)
	t_3 = Float64(18.0 * Float64(y * z))
	t_4 = Float64(Float64(Float64(Float64(t_1 * t) - Float64(t * Float64(a * 4.0))) + Float64(b * c)) - Float64(Float64(x * 4.0) * i))
	tmp = 0.0
	if (t_4 <= Float64(-Inf))
		tmp = Float64(Float64(y * Float64(Float64(18.0 * Float64(x * Float64(z * t))) + Float64(Float64(Float64(b * c) + Float64(-4.0 * Float64(Float64(t * a) + Float64(x * i)))) / y))) - t_2);
	elseif (t_4 <= 5e+306)
		tmp = Float64(Float64(t * Float64(t_1 + Float64(a * -4.0))) + Float64(Float64(-27.0 * Float64(j * k)) + Float64(Float64(b * c) + Float64(x * Float64(i * -4.0)))));
	elseif (t_4 <= Inf)
		tmp = Float64(Float64(x * Float64(Float64(Float64(i * -4.0) + Float64(t * t_3)) + Float64(Float64(Float64(b * c) + Float64(t * Float64(a * -4.0))) / x))) - t_2);
	else
		tmp = Float64(t * Float64(Float64(a * -4.0) + Float64(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 = ((x * 18.0) * y) * z;
	t_2 = (j * 27.0) * k;
	t_3 = 18.0 * (y * z);
	t_4 = (((t_1 * t) - (t * (a * 4.0))) + (b * c)) - ((x * 4.0) * i);
	tmp = 0.0;
	if (t_4 <= -Inf)
		tmp = (y * ((18.0 * (x * (z * t))) + (((b * c) + (-4.0 * ((t * a) + (x * i)))) / y))) - t_2;
	elseif (t_4 <= 5e+306)
		tmp = (t * (t_1 + (a * -4.0))) + ((-27.0 * (j * k)) + ((b * c) + (x * (i * -4.0))));
	elseif (t_4 <= Inf)
		tmp = (x * (((i * -4.0) + (t * t_3)) + (((b * c) + (t * (a * -4.0))) / x))) - t_2;
	else
		tmp = t * ((a * -4.0) + (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[(N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, Block[{t$95$3 = N[(18.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(N[(t$95$1 * t), $MachinePrecision] - N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$4, (-Infinity)], N[(N[(y * N[(N[(18.0 * N[(x * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], If[LessEqual[t$95$4, 5e+306], N[(N[(t * N[(t$95$1 + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision] + N[(N[(b * c), $MachinePrecision] + N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, Infinity], N[(N[(x * N[(N[(N[(i * -4.0), $MachinePrecision] + N[(t * t$95$3), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], N[(t * N[(N[(a * -4.0), $MachinePrecision] + N[(x * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

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 80.7%

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

   3. Taylor expanded in y around inf

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(y \cdot \left(\left(18 \cdot \left(t \cdot \left(x \cdot z\right)\right) + \frac{b \cdot c}{y}\right) - \left(4 \cdot \frac{a \cdot t}{y} + 4 \cdot \frac{i \cdot x}{y}\right)\right)\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \left(\left(18 \cdot \left(t \cdot \left(x \cdot z\right)\right) + \frac{b \cdot c}{y}\right) - \left(4 \cdot \frac{a \cdot t}{y} + 4 \cdot \frac{i \cdot x}{y}\right)\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \left(18 \cdot \left(t \cdot \left(x \cdot z\right)\right) + \left(\frac{b \cdot c}{y} - \left(4 \cdot \frac{a \cdot t}{y} + 4 \cdot \frac{i \cdot x}{y}\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, \color{blue}{27}\right), k\right)\right) \]

      3. associate--r+ N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \left(18 \cdot \left(t \cdot \left(x \cdot z\right)\right) + \left(\left(\frac{b \cdot c}{y} - 4 \cdot \frac{a \cdot t}{y}\right) - 4 \cdot \frac{i \cdot x}{y}\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      4. associate-*r/ N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \left(18 \cdot \left(t \cdot \left(x \cdot z\right)\right) + \left(\left(\frac{b \cdot c}{y} - \frac{4 \cdot \left(a \cdot t\right)}{y}\right) - 4 \cdot \frac{i \cdot x}{y}\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      5. div-sub N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \left(18 \cdot \left(t \cdot \left(x \cdot z\right)\right) + \left(\frac{b \cdot c - 4 \cdot \left(a \cdot t\right)}{y} - 4 \cdot \frac{i \cdot x}{y}\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      6. associate-*r/ N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \left(18 \cdot \left(t \cdot \left(x \cdot z\right)\right) + \left(\frac{b \cdot c - 4 \cdot \left(a \cdot t\right)}{y} - \frac{4 \cdot \left(i \cdot x\right)}{y}\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      7. div-sub N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \left(18 \cdot \left(t \cdot \left(x \cdot z\right)\right) + \frac{\left(b \cdot c - 4 \cdot \left(a \cdot t\right)\right) - 4 \cdot \left(i \cdot x\right)}{y}\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      8. associate--r+ N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \left(18 \cdot \left(t \cdot \left(x \cdot z\right)\right) + \frac{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)}{y}\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\left(18 \cdot \left(t \cdot \left(x \cdot z\right)\right)\right), \left(\frac{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)}{y}\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, \color{blue}{27}\right), k\right)\right) \]

   5. Simplified 89.1%

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

   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)) < 4.99999999999999993e306

   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. Step-by-step derivation

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 99.8%

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

   if 4.99999999999999993e306 < (-.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 72.9%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(x \cdot \left(\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \frac{b \cdot c}{x}\right) - \left(4 \cdot i + 4 \cdot \frac{a \cdot t}{x}\right)\right)\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

   5. Simplified 90.6%

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

   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))

   1. Initial program 0.0%

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

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 25.0%

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

   5. Taylor expanded in t around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(-4 \cdot a\right), \color{blue}{\left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \left(\color{blue}{18} \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \left(\left(x \cdot \left(y \cdot z\right)\right) \cdot \color{blue}{18}\right)\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \left(x \cdot \color{blue}{\left(\left(y \cdot z\right) \cdot 18\right)}\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \left(x \cdot \left(18 \cdot \color{blue}{\left(y \cdot z\right)}\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \mathsf{*.f64}\left(x, \color{blue}{\left(18 \cdot \left(y \cdot z\right)\right)}\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(18, \color{blue}{\left(y \cdot z\right)}\right)\right)\right)\right) \]

      9. *-lowering-*.f64 67.1%

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(y, \color{blue}{z}\right)\right)\right)\right)\right) \]

   7. Simplified 67.1%

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

4. Final simplification 92.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i \leq -\infty:\\ \;\;\;\;y \cdot \left(18 \cdot \left(x \cdot \left(z \cdot t\right)\right) + \frac{b \cdot c + -4 \cdot \left(t \cdot a + x \cdot i\right)}{y}\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i \leq 5 \cdot 10^{+306}:\\ \;\;\;\;t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right) + \left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right)\\ \mathbf{elif}\;\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i \leq \infty:\\ \;\;\;\;x \cdot \left(\left(i \cdot -4 + t \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right) + \frac{b \cdot c + t \cdot \left(a \cdot -4\right)}{x}\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot -4 + x \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 92.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := x \cdot \left(\left(i \cdot -4 + t \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right) + \frac{b \cdot c + t \cdot \left(a \cdot -4\right)}{x}\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;x \leq -2.5 \cdot 10^{+106}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{+39}:\\ \;\;\;\;t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right) + \left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1
         (-
          (*
           x
           (+
            (+ (* i -4.0) (* t (* 18.0 (* y z))))
            (/ (+ (* b c) (* t (* a -4.0))) x)))
          (* (* j 27.0) k))))
   (if (<= x -2.5e+106)
     t_1
     (if (<= x 1.2e+39)
       (+
        (* t (+ (* (* (* x 18.0) y) z) (* a -4.0)))
        (+ (* -27.0 (* j k)) (+ (* b c) (* x (* i -4.0)))))
       t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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) + (t * (18.0 * (y * z)))) + (((b * c) + (t * (a * -4.0))) / x))) - ((j * 27.0) * k);
	double tmp;
	if (x <= -2.5e+106) {
		tmp = t_1;
	} else if (x <= 1.2e+39) {
		tmp = (t * ((((x * 18.0) * y) * z) + (a * -4.0))) + ((-27.0 * (j * k)) + ((b * c) + (x * (i * -4.0))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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)) + (t * (18.0d0 * (y * z)))) + (((b * c) + (t * (a * (-4.0d0)))) / x))) - ((j * 27.0d0) * k)
    if (x <= (-2.5d+106)) then
        tmp = t_1
    else if (x <= 1.2d+39) then
        tmp = (t * ((((x * 18.0d0) * y) * z) + (a * (-4.0d0)))) + (((-27.0d0) * (j * k)) + ((b * c) + (x * (i * (-4.0d0)))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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) + (t * (18.0 * (y * z)))) + (((b * c) + (t * (a * -4.0))) / x))) - ((j * 27.0) * k);
	double tmp;
	if (x <= -2.5e+106) {
		tmp = t_1;
	} else if (x <= 1.2e+39) {
		tmp = (t * ((((x * 18.0) * y) * z) + (a * -4.0))) + ((-27.0 * (j * k)) + ((b * c) + (x * (i * -4.0))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (x * (((i * -4.0) + (t * (18.0 * (y * z)))) + (((b * c) + (t * (a * -4.0))) / x))) - ((j * 27.0) * k)
	tmp = 0
	if x <= -2.5e+106:
		tmp = t_1
	elif x <= 1.2e+39:
		tmp = (t * ((((x * 18.0) * y) * z) + (a * -4.0))) + ((-27.0 * (j * k)) + ((b * c) + (x * (i * -4.0))))
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(x * Float64(Float64(Float64(i * -4.0) + Float64(t * Float64(18.0 * Float64(y * z)))) + Float64(Float64(Float64(b * c) + Float64(t * Float64(a * -4.0))) / x))) - Float64(Float64(j * 27.0) * k))
	tmp = 0.0
	if (x <= -2.5e+106)
		tmp = t_1;
	elseif (x <= 1.2e+39)
		tmp = Float64(Float64(t * Float64(Float64(Float64(Float64(x * 18.0) * y) * z) + Float64(a * -4.0))) + Float64(Float64(-27.0 * Float64(j * k)) + Float64(Float64(b * c) + Float64(x * Float64(i * -4.0)))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (x * (((i * -4.0) + (t * (18.0 * (y * z)))) + (((b * c) + (t * (a * -4.0))) / x))) - ((j * 27.0) * k);
	tmp = 0.0;
	if (x <= -2.5e+106)
		tmp = t_1;
	elseif (x <= 1.2e+39)
		tmp = (t * ((((x * 18.0) * y) * z) + (a * -4.0))) + ((-27.0 * (j * k)) + ((b * c) + (x * (i * -4.0))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(x * N[(N[(N[(i * -4.0), $MachinePrecision] + N[(t * N[(18.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.5e+106], t$95$1, If[LessEqual[x, 1.2e+39], N[(N[(t * N[(N[(N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision] + N[(N[(b * c), $MachinePrecision] + N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.4999999999999999e106 or 1.2e39 < x

   1. Initial program 66.2%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(x \cdot \left(\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \frac{b \cdot c}{x}\right) - \left(4 \cdot i + 4 \cdot \frac{a \cdot t}{x}\right)\right)\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

   5. Simplified 87.8%

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

   if -2.4999999999999999e106 < x < 1.2e39

   1. Initial program 91.1%

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

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 92.4%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+106}:\\ \;\;\;\;x \cdot \left(\left(i \cdot -4 + t \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right) + \frac{b \cdot c + t \cdot \left(a \cdot -4\right)}{x}\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{+39}:\\ \;\;\;\;t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right) + \left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(i \cdot -4 + t \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right) + \frac{b \cdot c + t \cdot \left(a \cdot -4\right)}{x}\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 67.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+140}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t\_1 \leq -2 \cdot 10^{+100}:\\ \;\;\;\;\left(z \cdot \left(18 \cdot y\right)\right) \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;t\_1 \leq 10^{+149}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)))
   (if (<= t_1 -1e+140)
     (+ (* t (* a -4.0)) (* j (* k -27.0)))
     (if (<= t_1 -2e+100)
       (* (* z (* 18.0 y)) (* x t))
       (if (<= t_1 1e+149)
         (+ (* b c) (* -4.0 (+ (* t a) (* x i))))
         (- (* b c) t_1))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (t_1 <= -1e+140) {
		tmp = (t * (a * -4.0)) + (j * (k * -27.0));
	} else if (t_1 <= -2e+100) {
		tmp = (z * (18.0 * y)) * (x * t);
	} else if (t_1 <= 1e+149) {
		tmp = (b * c) + (-4.0 * ((t * a) + (x * i)));
	} else {
		tmp = (b * c) - t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 <= (-1d+140)) then
        tmp = (t * (a * (-4.0d0))) + (j * (k * (-27.0d0)))
    else if (t_1 <= (-2d+100)) then
        tmp = (z * (18.0d0 * y)) * (x * t)
    else if (t_1 <= 1d+149) then
        tmp = (b * c) + ((-4.0d0) * ((t * a) + (x * i)))
    else
        tmp = (b * c) - t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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 <= -1e+140) {
		tmp = (t * (a * -4.0)) + (j * (k * -27.0));
	} else if (t_1 <= -2e+100) {
		tmp = (z * (18.0 * y)) * (x * t);
	} else if (t_1 <= 1e+149) {
		tmp = (b * c) + (-4.0 * ((t * a) + (x * i)));
	} else {
		tmp = (b * c) - t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	tmp = 0
	if t_1 <= -1e+140:
		tmp = (t * (a * -4.0)) + (j * (k * -27.0))
	elif t_1 <= -2e+100:
		tmp = (z * (18.0 * y)) * (x * t)
	elif t_1 <= 1e+149:
		tmp = (b * c) + (-4.0 * ((t * a) + (x * i)))
	else:
		tmp = (b * c) - t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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 <= -1e+140)
		tmp = Float64(Float64(t * Float64(a * -4.0)) + Float64(j * Float64(k * -27.0)));
	elseif (t_1 <= -2e+100)
		tmp = Float64(Float64(z * Float64(18.0 * y)) * Float64(x * t));
	elseif (t_1 <= 1e+149)
		tmp = Float64(Float64(b * c) + Float64(-4.0 * Float64(Float64(t * a) + Float64(x * i))));
	else
		tmp = Float64(Float64(b * c) - t_1);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
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 <= -1e+140)
		tmp = (t * (a * -4.0)) + (j * (k * -27.0));
	elseif (t_1 <= -2e+100)
		tmp = (z * (18.0 * y)) * (x * t);
	elseif (t_1 <= 1e+149)
		tmp = (b * c) + (-4.0 * ((t * a) + (x * i)));
	else
		tmp = (b * c) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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, -1e+140], N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -2e+100], N[(N[(z * N[(18.0 * y), $MachinePrecision]), $MachinePrecision] * N[(x * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+149], N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] - t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -1.00000000000000006e140

   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. Step-by-step derivation

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 79.3%

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

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(-4 \cdot \left(a \cdot t\right)\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, k\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(-4 \cdot \left(t \cdot a\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(-27, \color{blue}{\mathsf{*.f64}\left(j, k\right)}\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

      2. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(-4 \cdot t\right) \cdot a\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, k\right)\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(t \cdot -4\right) \cdot a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\color{blue}{-27}, \mathsf{*.f64}\left(j, k\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(-4 \cdot a\right)\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, k\right)\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(-4 \cdot a\right)\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, k\right)\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 81.8%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(-4, a\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(-27, \color{blue}{\mathsf{*.f64}\left(j, k\right)}\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

   7. Simplified 81.8%

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

   8. Taylor expanded in j around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(-4, a\right)\right), \color{blue}{\left(-27 \cdot \left(j \cdot k\right)\right)}\right) \]
   9. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(-4, a\right)\right), \left(\left(j \cdot k\right) \cdot \color{blue}{-27}\right)\right) \]

      2. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(-4, a\right)\right), \left(j \cdot \color{blue}{\left(k \cdot -27\right)}\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(-4, a\right)\right), \left(j \cdot \left(-27 \cdot \color{blue}{k}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(-4, a\right)\right), \mathsf{*.f64}\left(j, \color{blue}{\left(-27 \cdot k\right)}\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(-4, a\right)\right), \mathsf{*.f64}\left(j, \left(k \cdot \color{blue}{-27}\right)\right)\right) \]

      6. *-lowering-*.f64 69.7%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(-4, a\right)\right), \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(k, \color{blue}{-27}\right)\right)\right) \]

   10. Simplified 69.7%

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

   if -1.00000000000000006e140 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -2.00000000000000003e100

   1. Initial program 66.3%

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

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 66.3%

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

   5. Taylor expanded in y around inf

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

      1. associate-*r* N/A

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

      2. associate-*r* N/A

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

      3. associate-*l* N/A

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

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(18 \cdot \left(t \cdot \left(x \cdot y\right)\right)\right), \color{blue}{z}\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(18, \left(t \cdot \left(x \cdot y\right)\right)\right), z\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(18, \left(\left(x \cdot y\right) \cdot t\right)\right), z\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(18, \left(\left(y \cdot x\right) \cdot t\right)\right), z\right) \]

      8. associate-*l* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(18, \left(y \cdot \left(x \cdot t\right)\right)\right), z\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(18, \mathsf{*.f64}\left(y, \left(x \cdot t\right)\right)\right), z\right) \]

      10. *-lowering-*.f64 99.7%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(18, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, t\right)\right)\right), z\right) \]

   7. Simplified 99.7%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(18 \cdot \left(y \cdot z\right)\right), \color{blue}{\left(x \cdot t\right)}\right) \]

      7. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\left(18 \cdot y\right) \cdot z\right), \left(\color{blue}{x} \cdot t\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\left(z \cdot \left(18 \cdot y\right)\right), \left(\color{blue}{x} \cdot t\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, \left(18 \cdot y\right)\right), \left(\color{blue}{x} \cdot t\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(18, y\right)\right), \left(x \cdot t\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(18, y\right)\right), \left(t \cdot \color{blue}{x}\right)\right) \]

      12. *-lowering-*.f64 100.0%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(18, y\right)\right), \mathsf{*.f64}\left(t, \color{blue}{x}\right)\right) \]

   9. Applied egg-rr 100.0%

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

   if -2.00000000000000003e100 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 1.00000000000000005e149

   1. Initial program 84.8%

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

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 86.5%

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

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(-4 \cdot \left(a \cdot t\right)\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, k\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(-4 \cdot \left(t \cdot a\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(-27, \color{blue}{\mathsf{*.f64}\left(j, k\right)}\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

      2. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(-4 \cdot t\right) \cdot a\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, k\right)\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(t \cdot -4\right) \cdot a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\color{blue}{-27}, \mathsf{*.f64}\left(j, k\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(-4 \cdot a\right)\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, k\right)\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(-4 \cdot a\right)\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, k\right)\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 73.8%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(-4, a\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(-27, \color{blue}{\mathsf{*.f64}\left(j, k\right)}\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

   7. Simplified 73.8%

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

   8. Taylor expanded in j around 0

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

      1. +-commutative N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. +-commutative N/A

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

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(b \cdot c\right), \color{blue}{\left(-4 \cdot \left(a \cdot t\right) + -4 \cdot \left(i \cdot x\right)\right)}\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\color{blue}{-4 \cdot \left(a \cdot t\right)} + -4 \cdot \left(i \cdot x\right)\right)\right) \]

      7. distribute-lft-out N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(-4 \cdot \color{blue}{\left(a \cdot t + i \cdot x\right)}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(-4, \color{blue}{\left(a \cdot t + i \cdot x\right)}\right)\right) \]

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(-4, \mathsf{+.f64}\left(\left(a \cdot t\right), \color{blue}{\left(i \cdot x\right)}\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(-4, \mathsf{+.f64}\left(\left(t \cdot a\right), \left(\color{blue}{i} \cdot x\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(-4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, a\right), \left(\color{blue}{i} \cdot x\right)\right)\right)\right) \]

      12. *-lowering-*.f64 66.9%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(-4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, a\right), \mathsf{*.f64}\left(i, \color{blue}{x}\right)\right)\right)\right) \]

   10. Simplified 66.9%

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

   if 1.00000000000000005e149 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 76.3%

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

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(b \cdot c\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 71.4%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

   5. Simplified 71.4%

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

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \leq -1 \cdot 10^{+140}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq -2 \cdot 10^{+100}:\\ \;\;\;\;\left(z \cdot \left(18 \cdot y\right)\right) \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 10^{+149}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 88.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := x \cdot \left(i \cdot -4 + y \cdot \left(z \cdot \left(18 \cdot t\right)\right)\right)\\ \mathbf{if}\;x \leq -9.2 \cdot 10^{+167}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.22 \cdot 10^{+151}:\\ \;\;\;\;t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right) + \left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* x (+ (* i -4.0) (* y (* z (* 18.0 t)))))))
   (if (<= x -9.2e+167)
     t_1
     (if (<= x 1.22e+151)
       (+
        (* t (+ (* (* (* x 18.0) y) z) (* a -4.0)))
        (+ (* -27.0 (* j k)) (+ (* b c) (* x (* i -4.0)))))
       t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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) + (y * (z * (18.0 * t))));
	double tmp;
	if (x <= -9.2e+167) {
		tmp = t_1;
	} else if (x <= 1.22e+151) {
		tmp = (t * ((((x * 18.0) * y) * z) + (a * -4.0))) + ((-27.0 * (j * k)) + ((b * c) + (x * (i * -4.0))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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)) + (y * (z * (18.0d0 * t))))
    if (x <= (-9.2d+167)) then
        tmp = t_1
    else if (x <= 1.22d+151) then
        tmp = (t * ((((x * 18.0d0) * y) * z) + (a * (-4.0d0)))) + (((-27.0d0) * (j * k)) + ((b * c) + (x * (i * (-4.0d0)))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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) + (y * (z * (18.0 * t))));
	double tmp;
	if (x <= -9.2e+167) {
		tmp = t_1;
	} else if (x <= 1.22e+151) {
		tmp = (t * ((((x * 18.0) * y) * z) + (a * -4.0))) + ((-27.0 * (j * k)) + ((b * c) + (x * (i * -4.0))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = x * ((i * -4.0) + (y * (z * (18.0 * t))))
	tmp = 0
	if x <= -9.2e+167:
		tmp = t_1
	elif x <= 1.22e+151:
		tmp = (t * ((((x * 18.0) * y) * z) + (a * -4.0))) + ((-27.0 * (j * k)) + ((b * c) + (x * (i * -4.0))))
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(x * Float64(Float64(i * -4.0) + Float64(y * Float64(z * Float64(18.0 * t)))))
	tmp = 0.0
	if (x <= -9.2e+167)
		tmp = t_1;
	elseif (x <= 1.22e+151)
		tmp = Float64(Float64(t * Float64(Float64(Float64(Float64(x * 18.0) * y) * z) + Float64(a * -4.0))) + Float64(Float64(-27.0 * Float64(j * k)) + Float64(Float64(b * c) + Float64(x * Float64(i * -4.0)))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = x * ((i * -4.0) + (y * (z * (18.0 * t))));
	tmp = 0.0;
	if (x <= -9.2e+167)
		tmp = t_1;
	elseif (x <= 1.22e+151)
		tmp = (t * ((((x * 18.0) * y) * z) + (a * -4.0))) + ((-27.0 * (j * k)) + ((b * c) + (x * (i * -4.0))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(x * N[(N[(i * -4.0), $MachinePrecision] + N[(y * N[(z * N[(18.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -9.2e+167], t$95$1, If[LessEqual[x, 1.22e+151], N[(N[(t * N[(N[(N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision] + N[(N[(b * c), $MachinePrecision] + N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -9.19999999999999952e167 or 1.22000000000000005e151 < x

   1. Initial program 59.5%

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

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 61.2%

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

   5. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(-4 \cdot i\right), \color{blue}{\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \left(\color{blue}{18} \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \left(\left(t \cdot \left(y \cdot z\right)\right) \cdot \color{blue}{18}\right)\right)\right) \]

      5. associate-*l* N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \left(t \cdot \color{blue}{\left(\left(y \cdot z\right) \cdot 18\right)}\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \left(t \cdot \left(18 \cdot \color{blue}{\left(y \cdot z\right)}\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \mathsf{*.f64}\left(t, \color{blue}{\left(18 \cdot \left(y \cdot z\right)\right)}\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(18, \color{blue}{\left(y \cdot z\right)}\right)\right)\right)\right) \]

      9. *-lowering-*.f64 79.7%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(y, \color{blue}{z}\right)\right)\right)\right)\right) \]

   7. Simplified 79.7%

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

      1. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \left(\left(t \cdot 18\right) \cdot \color{blue}{\left(y \cdot z\right)}\right)\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \left(\left(t \cdot 18\right) \cdot \left(z \cdot \color{blue}{y}\right)\right)\right)\right) \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \left(\left(\left(t \cdot 18\right) \cdot z\right) \cdot \color{blue}{y}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \mathsf{*.f64}\left(\left(\left(t \cdot 18\right) \cdot z\right), \color{blue}{y}\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(t \cdot 18\right), z\right), y\right)\right)\right) \]

      6. *-lowering-*.f64 84.9%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(t, 18\right), z\right), y\right)\right)\right) \]

   9. Applied egg-rr 84.9%

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

   if -9.19999999999999952e167 < x < 1.22000000000000005e151

   1. Initial program 87.9%

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

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 90.4%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.2 \cdot 10^{+167}:\\ \;\;\;\;x \cdot \left(i \cdot -4 + y \cdot \left(z \cdot \left(18 \cdot t\right)\right)\right)\\ \mathbf{elif}\;x \leq 1.22 \cdot 10^{+151}:\\ \;\;\;\;t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right) + \left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(i \cdot -4 + y \cdot \left(z \cdot \left(18 \cdot t\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 53.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c - \left(j \cdot 27\right) \cdot k\\ t_2 := -4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{if}\;b \cdot c \leq -1.25 \cdot 10^{+138}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq -1.45 \cdot 10^{-41}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \cdot c \leq 8.5 \cdot 10^{-140}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 8.5 \cdot 10^{+123}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (- (* b c) (* (* j 27.0) k))) (t_2 (* -4.0 (+ (* t a) (* x i)))))
   (if (<= (* b c) -1.25e+138)
     t_1
     (if (<= (* b c) -1.45e-41)
       t_2
       (if (<= (* b c) 8.5e-140)
         (+ (* t (* a -4.0)) (* j (* k -27.0)))
         (if (<= (* b c) 8.5e+123) t_2 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 = (b * c) - ((j * 27.0) * k);
	double t_2 = -4.0 * ((t * a) + (x * i));
	double tmp;
	if ((b * c) <= -1.25e+138) {
		tmp = t_1;
	} else if ((b * c) <= -1.45e-41) {
		tmp = t_2;
	} else if ((b * c) <= 8.5e-140) {
		tmp = (t * (a * -4.0)) + (j * (k * -27.0));
	} else if ((b * c) <= 8.5e+123) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = (b * c) - ((j * 27.0d0) * k)
    t_2 = (-4.0d0) * ((t * a) + (x * i))
    if ((b * c) <= (-1.25d+138)) then
        tmp = t_1
    else if ((b * c) <= (-1.45d-41)) then
        tmp = t_2
    else if ((b * c) <= 8.5d-140) then
        tmp = (t * (a * (-4.0d0))) + (j * (k * (-27.0d0)))
    else if ((b * c) <= 8.5d+123) then
        tmp = t_2
    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 = (b * c) - ((j * 27.0) * k);
	double t_2 = -4.0 * ((t * a) + (x * i));
	double tmp;
	if ((b * c) <= -1.25e+138) {
		tmp = t_1;
	} else if ((b * c) <= -1.45e-41) {
		tmp = t_2;
	} else if ((b * c) <= 8.5e-140) {
		tmp = (t * (a * -4.0)) + (j * (k * -27.0));
	} else if ((b * c) <= 8.5e+123) {
		tmp = t_2;
	} 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 = (b * c) - ((j * 27.0) * k)
	t_2 = -4.0 * ((t * a) + (x * i))
	tmp = 0
	if (b * c) <= -1.25e+138:
		tmp = t_1
	elif (b * c) <= -1.45e-41:
		tmp = t_2
	elif (b * c) <= 8.5e-140:
		tmp = (t * (a * -4.0)) + (j * (k * -27.0))
	elif (b * c) <= 8.5e+123:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) - Float64(Float64(j * 27.0) * k))
	t_2 = Float64(-4.0 * Float64(Float64(t * a) + Float64(x * i)))
	tmp = 0.0
	if (Float64(b * c) <= -1.25e+138)
		tmp = t_1;
	elseif (Float64(b * c) <= -1.45e-41)
		tmp = t_2;
	elseif (Float64(b * c) <= 8.5e-140)
		tmp = Float64(Float64(t * Float64(a * -4.0)) + Float64(j * Float64(k * -27.0)));
	elseif (Float64(b * c) <= 8.5e+123)
		tmp = t_2;
	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 = (b * c) - ((j * 27.0) * k);
	t_2 = -4.0 * ((t * a) + (x * i));
	tmp = 0.0;
	if ((b * c) <= -1.25e+138)
		tmp = t_1;
	elseif ((b * c) <= -1.45e-41)
		tmp = t_2;
	elseif ((b * c) <= 8.5e-140)
		tmp = (t * (a * -4.0)) + (j * (k * -27.0));
	elseif ((b * c) <= 8.5e+123)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -1.25e+138], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], -1.45e-41], t$95$2, If[LessEqual[N[(b * c), $MachinePrecision], 8.5e-140], N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 8.5e+123], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -1.25000000000000004e138 or 8.5e123 < (*.f64 b c)

   1. Initial program 78.2%

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

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(b \cdot c\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 75.2%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

   5. Simplified 75.2%

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

   if -1.25000000000000004e138 < (*.f64 b c) < -1.44999999999999989e-41 or 8.49999999999999997e-140 < (*.f64 b c) < 8.5e123

   1. Initial program 80.2%

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

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 84.4%

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

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(-4 \cdot \left(a \cdot t\right)\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, k\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(-4 \cdot \left(t \cdot a\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(-27, \color{blue}{\mathsf{*.f64}\left(j, k\right)}\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

      2. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(-4 \cdot t\right) \cdot a\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, k\right)\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(t \cdot -4\right) \cdot a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\color{blue}{-27}, \mathsf{*.f64}\left(j, k\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(-4 \cdot a\right)\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, k\right)\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(-4 \cdot a\right)\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, k\right)\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 73.6%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(-4, a\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(-27, \color{blue}{\mathsf{*.f64}\left(j, k\right)}\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

   7. Simplified 73.6%

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

   8. Taylor expanded in j around 0

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

      1. +-commutative N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. +-commutative N/A

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

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(b \cdot c\right), \color{blue}{\left(-4 \cdot \left(a \cdot t\right) + -4 \cdot \left(i \cdot x\right)\right)}\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\color{blue}{-4 \cdot \left(a \cdot t\right)} + -4 \cdot \left(i \cdot x\right)\right)\right) \]

      7. distribute-lft-out N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(-4 \cdot \color{blue}{\left(a \cdot t + i \cdot x\right)}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(-4, \color{blue}{\left(a \cdot t + i \cdot x\right)}\right)\right) \]

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(-4, \mathsf{+.f64}\left(\left(a \cdot t\right), \color{blue}{\left(i \cdot x\right)}\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(-4, \mathsf{+.f64}\left(\left(t \cdot a\right), \left(\color{blue}{i} \cdot x\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(-4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, a\right), \left(\color{blue}{i} \cdot x\right)\right)\right)\right) \]

      12. *-lowering-*.f64 57.6%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(-4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, a\right), \mathsf{*.f64}\left(i, \color{blue}{x}\right)\right)\right)\right) \]

   10. Simplified 57.6%

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

   11. Taylor expanded in b around 0

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

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(-4, \color{blue}{\left(a \cdot t + i \cdot x\right)}\right) \]

       2. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(-4, \mathsf{+.f64}\left(\left(a \cdot t\right), \color{blue}{\left(i \cdot x\right)}\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(-4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, t\right), \left(\color{blue}{i} \cdot x\right)\right)\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(-4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, t\right), \left(x \cdot \color{blue}{i}\right)\right)\right) \]

       5. *-lowering-*.f64 52.0%

          \[\leadsto \mathsf{*.f64}\left(-4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, t\right), \mathsf{*.f64}\left(x, \color{blue}{i}\right)\right)\right) \]

   13. Simplified 52.0%

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

   if -1.44999999999999989e-41 < (*.f64 b c) < 8.49999999999999997e-140

   1. Initial program 86.8%

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

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 86.8%

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

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(-4 \cdot \left(a \cdot t\right)\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, k\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(-4 \cdot \left(t \cdot a\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(-27, \color{blue}{\mathsf{*.f64}\left(j, k\right)}\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

      2. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(-4 \cdot t\right) \cdot a\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, k\right)\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(t \cdot -4\right) \cdot a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\color{blue}{-27}, \mathsf{*.f64}\left(j, k\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(-4 \cdot a\right)\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, k\right)\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(-4 \cdot a\right)\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, k\right)\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 75.1%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(-4, a\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(-27, \color{blue}{\mathsf{*.f64}\left(j, k\right)}\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

   7. Simplified 75.1%

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

   8. Taylor expanded in j around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(-4, a\right)\right), \color{blue}{\left(-27 \cdot \left(j \cdot k\right)\right)}\right) \]
   9. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(-4, a\right)\right), \left(\left(j \cdot k\right) \cdot \color{blue}{-27}\right)\right) \]

      2. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(-4, a\right)\right), \left(j \cdot \color{blue}{\left(k \cdot -27\right)}\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(-4, a\right)\right), \left(j \cdot \left(-27 \cdot \color{blue}{k}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(-4, a\right)\right), \mathsf{*.f64}\left(j, \color{blue}{\left(-27 \cdot k\right)}\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(-4, a\right)\right), \mathsf{*.f64}\left(j, \left(k \cdot \color{blue}{-27}\right)\right)\right) \]

      6. *-lowering-*.f64 59.0%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(-4, a\right)\right), \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(k, \color{blue}{-27}\right)\right)\right) \]

   10. Simplified 59.0%

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

4. Final simplification 61.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.25 \cdot 10^{+138}:\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;b \cdot c \leq -1.45 \cdot 10^{-41}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 8.5 \cdot 10^{-140}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 8.5 \cdot 10^{+123}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 57.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ t_2 := x \cdot \left(i \cdot -4 + y \cdot \left(z \cdot \left(18 \cdot t\right)\right)\right)\\ \mathbf{if}\;x \leq -2.8 \cdot 10^{+56}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -7.2 \cdot 10^{-99}:\\ \;\;\;\;b \cdot c + t\_1\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{-156}:\\ \;\;\;\;t\_1 + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq 6.9 \cdot 10^{+100}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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 (* t (* a -4.0)))
        (t_2 (* x (+ (* i -4.0) (* y (* z (* 18.0 t)))))))
   (if (<= x -2.8e+56)
     t_2
     (if (<= x -7.2e-99)
       (+ (* b c) t_1)
       (if (<= x 4.1e-156)
         (+ t_1 (* j (* k -27.0)))
         (if (<= x 6.9e+100) (- (* b c) (* 27.0 (* j k))) 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 = t * (a * -4.0);
	double t_2 = x * ((i * -4.0) + (y * (z * (18.0 * t))));
	double tmp;
	if (x <= -2.8e+56) {
		tmp = t_2;
	} else if (x <= -7.2e-99) {
		tmp = (b * c) + t_1;
	} else if (x <= 4.1e-156) {
		tmp = t_1 + (j * (k * -27.0));
	} else if (x <= 6.9e+100) {
		tmp = (b * c) - (27.0 * (j * k));
	} 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 = t * (a * (-4.0d0))
    t_2 = x * ((i * (-4.0d0)) + (y * (z * (18.0d0 * t))))
    if (x <= (-2.8d+56)) then
        tmp = t_2
    else if (x <= (-7.2d-99)) then
        tmp = (b * c) + t_1
    else if (x <= 4.1d-156) then
        tmp = t_1 + (j * (k * (-27.0d0)))
    else if (x <= 6.9d+100) then
        tmp = (b * c) - (27.0d0 * (j * k))
    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 = t * (a * -4.0);
	double t_2 = x * ((i * -4.0) + (y * (z * (18.0 * t))));
	double tmp;
	if (x <= -2.8e+56) {
		tmp = t_2;
	} else if (x <= -7.2e-99) {
		tmp = (b * c) + t_1;
	} else if (x <= 4.1e-156) {
		tmp = t_1 + (j * (k * -27.0));
	} else if (x <= 6.9e+100) {
		tmp = (b * c) - (27.0 * (j * k));
	} 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 = t * (a * -4.0)
	t_2 = x * ((i * -4.0) + (y * (z * (18.0 * t))))
	tmp = 0
	if x <= -2.8e+56:
		tmp = t_2
	elif x <= -7.2e-99:
		tmp = (b * c) + t_1
	elif x <= 4.1e-156:
		tmp = t_1 + (j * (k * -27.0))
	elif x <= 6.9e+100:
		tmp = (b * c) - (27.0 * (j * k))
	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(t * Float64(a * -4.0))
	t_2 = Float64(x * Float64(Float64(i * -4.0) + Float64(y * Float64(z * Float64(18.0 * t)))))
	tmp = 0.0
	if (x <= -2.8e+56)
		tmp = t_2;
	elseif (x <= -7.2e-99)
		tmp = Float64(Float64(b * c) + t_1);
	elseif (x <= 4.1e-156)
		tmp = Float64(t_1 + Float64(j * Float64(k * -27.0)));
	elseif (x <= 6.9e+100)
		tmp = Float64(Float64(b * c) - Float64(27.0 * Float64(j * k)));
	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 = t * (a * -4.0);
	t_2 = x * ((i * -4.0) + (y * (z * (18.0 * t))));
	tmp = 0.0;
	if (x <= -2.8e+56)
		tmp = t_2;
	elseif (x <= -7.2e-99)
		tmp = (b * c) + t_1;
	elseif (x <= 4.1e-156)
		tmp = t_1 + (j * (k * -27.0));
	elseif (x <= 6.9e+100)
		tmp = (b * c) - (27.0 * (j * k));
	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[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(i * -4.0), $MachinePrecision] + N[(y * N[(z * N[(18.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.8e+56], t$95$2, If[LessEqual[x, -7.2e-99], N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[x, 4.1e-156], N[(t$95$1 + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.9e+100], N[(N[(b * c), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.80000000000000008e56 or 6.9000000000000001e100 < x

   1. Initial program 65.5%

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

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 70.1%

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

   5. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(-4 \cdot i\right), \color{blue}{\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \left(\color{blue}{18} \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \left(\left(t \cdot \left(y \cdot z\right)\right) \cdot \color{blue}{18}\right)\right)\right) \]

      5. associate-*l* N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \left(t \cdot \color{blue}{\left(\left(y \cdot z\right) \cdot 18\right)}\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \left(t \cdot \left(18 \cdot \color{blue}{\left(y \cdot z\right)}\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \mathsf{*.f64}\left(t, \color{blue}{\left(18 \cdot \left(y \cdot z\right)\right)}\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(18, \color{blue}{\left(y \cdot z\right)}\right)\right)\right)\right) \]

      9. *-lowering-*.f64 72.2%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(y, \color{blue}{z}\right)\right)\right)\right)\right) \]

   7. Simplified 72.2%

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

      1. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \left(\left(t \cdot 18\right) \cdot \color{blue}{\left(y \cdot z\right)}\right)\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \left(\left(t \cdot 18\right) \cdot \left(z \cdot \color{blue}{y}\right)\right)\right)\right) \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \left(\left(\left(t \cdot 18\right) \cdot z\right) \cdot \color{blue}{y}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \mathsf{*.f64}\left(\left(\left(t \cdot 18\right) \cdot z\right), \color{blue}{y}\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(t \cdot 18\right), z\right), y\right)\right)\right) \]

      6. *-lowering-*.f64 75.6%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(t, 18\right), z\right), y\right)\right)\right) \]

   9. Applied egg-rr 75.6%

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

   if -2.80000000000000008e56 < x < -7.2000000000000001e-99

   1. Initial program 94.1%

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

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 97.1%

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

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(-4 \cdot \left(a \cdot t\right)\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, k\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(-4 \cdot \left(t \cdot a\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(-27, \color{blue}{\mathsf{*.f64}\left(j, k\right)}\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

      2. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(-4 \cdot t\right) \cdot a\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, k\right)\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(t \cdot -4\right) \cdot a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\color{blue}{-27}, \mathsf{*.f64}\left(j, k\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(-4 \cdot a\right)\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, k\right)\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(-4 \cdot a\right)\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, k\right)\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 82.6%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(-4, a\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(-27, \color{blue}{\mathsf{*.f64}\left(j, k\right)}\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

   7. Simplified 82.6%

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

   8. Taylor expanded in b around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(-4, a\right)\right), \color{blue}{\left(b \cdot c\right)}\right) \]
   9. Step-by-step derivation

      1. *-lowering-*.f64 69.3%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(-4, a\right)\right), \mathsf{*.f64}\left(b, \color{blue}{c}\right)\right) \]

   10. Simplified 69.3%

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

   if -7.2000000000000001e-99 < x < 4.1000000000000002e-156

   1. Initial program 92.9%

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

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 92.8%

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

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(-4 \cdot \left(a \cdot t\right)\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, k\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(-4 \cdot \left(t \cdot a\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(-27, \color{blue}{\mathsf{*.f64}\left(j, k\right)}\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

      2. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(-4 \cdot t\right) \cdot a\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, k\right)\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(t \cdot -4\right) \cdot a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\color{blue}{-27}, \mathsf{*.f64}\left(j, k\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(-4 \cdot a\right)\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, k\right)\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(-4 \cdot a\right)\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, k\right)\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 80.5%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(-4, a\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(-27, \color{blue}{\mathsf{*.f64}\left(j, k\right)}\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

   7. Simplified 80.5%

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

   8. Taylor expanded in j around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(-4, a\right)\right), \color{blue}{\left(-27 \cdot \left(j \cdot k\right)\right)}\right) \]
   9. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(-4, a\right)\right), \left(\left(j \cdot k\right) \cdot \color{blue}{-27}\right)\right) \]

      2. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(-4, a\right)\right), \left(j \cdot \color{blue}{\left(k \cdot -27\right)}\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(-4, a\right)\right), \left(j \cdot \left(-27 \cdot \color{blue}{k}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(-4, a\right)\right), \mathsf{*.f64}\left(j, \color{blue}{\left(-27 \cdot k\right)}\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(-4, a\right)\right), \mathsf{*.f64}\left(j, \left(k \cdot \color{blue}{-27}\right)\right)\right) \]

      6. *-lowering-*.f64 64.0%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(-4, a\right)\right), \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(k, \color{blue}{-27}\right)\right)\right) \]

   10. Simplified 64.0%

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

   if 4.1000000000000002e-156 < x < 6.9000000000000001e100

   1. Initial program 81.6%

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

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(b \cdot c\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 58.2%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

   5. Simplified 58.2%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(k \cdot \color{blue}{\left(j \cdot 27\right)}\right)\right) \]

      2. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\left(k \cdot j\right) \cdot \color{blue}{27}\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\left(j \cdot k\right) \cdot 27\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\left(j \cdot k\right), \color{blue}{27}\right)\right) \]

      5. *-lowering-*.f64 58.3%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, k\right), 27\right)\right) \]

   7. Applied egg-rr 58.3%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{+56}:\\ \;\;\;\;x \cdot \left(i \cdot -4 + y \cdot \left(z \cdot \left(18 \cdot t\right)\right)\right)\\ \mathbf{elif}\;x \leq -7.2 \cdot 10^{-99}:\\ \;\;\;\;b \cdot c + t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{-156}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq 6.9 \cdot 10^{+100}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(i \cdot -4 + y \cdot \left(z \cdot \left(18 \cdot t\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 82.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := -27 \cdot \left(j \cdot k\right)\\ \mathbf{if}\;t \leq -6 \cdot 10^{+60}:\\ \;\;\;\;t \cdot \left(a \cdot -4 + x \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right) - \left(\left(x \cdot 4\right) \cdot i + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{-116}:\\ \;\;\;\;\left(t\_1 + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right) + t \cdot \left(a \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right) + \left(b \cdot c + t\_1\right)\\ \end{array} \end{array} \]

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 (* -27.0 (* j k))))
   (if (<= t -6e+60)
     (-
      (* t (+ (* a -4.0) (* x (* 18.0 (* y z)))))
      (+ (* (* x 4.0) i) (* j (* 27.0 k))))
     (if (<= t 4.4e-116)
       (+ (+ t_1 (+ (* b c) (* x (* i -4.0)))) (* t (* a -4.0)))
       (+ (* t (+ (* (* (* x 18.0) y) z) (* a -4.0))) (+ (* b c) t_1))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -27.0 * (j * k);
	double tmp;
	if (t <= -6e+60) {
		tmp = (t * ((a * -4.0) + (x * (18.0 * (y * z))))) - (((x * 4.0) * i) + (j * (27.0 * k)));
	} else if (t <= 4.4e-116) {
		tmp = (t_1 + ((b * c) + (x * (i * -4.0)))) + (t * (a * -4.0));
	} else {
		tmp = (t * ((((x * 18.0) * y) * z) + (a * -4.0))) + ((b * c) + t_1);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-27.0d0) * (j * k)
    if (t <= (-6d+60)) then
        tmp = (t * ((a * (-4.0d0)) + (x * (18.0d0 * (y * z))))) - (((x * 4.0d0) * i) + (j * (27.0d0 * k)))
    else if (t <= 4.4d-116) then
        tmp = (t_1 + ((b * c) + (x * (i * (-4.0d0))))) + (t * (a * (-4.0d0)))
    else
        tmp = (t * ((((x * 18.0d0) * y) * z) + (a * (-4.0d0)))) + ((b * c) + t_1)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -27.0 * (j * k);
	double tmp;
	if (t <= -6e+60) {
		tmp = (t * ((a * -4.0) + (x * (18.0 * (y * z))))) - (((x * 4.0) * i) + (j * (27.0 * k)));
	} else if (t <= 4.4e-116) {
		tmp = (t_1 + ((b * c) + (x * (i * -4.0)))) + (t * (a * -4.0));
	} else {
		tmp = (t * ((((x * 18.0) * y) * z) + (a * -4.0))) + ((b * c) + t_1);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = -27.0 * (j * k)
	tmp = 0
	if t <= -6e+60:
		tmp = (t * ((a * -4.0) + (x * (18.0 * (y * z))))) - (((x * 4.0) * i) + (j * (27.0 * k)))
	elif t <= 4.4e-116:
		tmp = (t_1 + ((b * c) + (x * (i * -4.0)))) + (t * (a * -4.0))
	else:
		tmp = (t * ((((x * 18.0) * y) * z) + (a * -4.0))) + ((b * c) + t_1)
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(-27.0 * Float64(j * k))
	tmp = 0.0
	if (t <= -6e+60)
		tmp = Float64(Float64(t * Float64(Float64(a * -4.0) + Float64(x * Float64(18.0 * Float64(y * z))))) - Float64(Float64(Float64(x * 4.0) * i) + Float64(j * Float64(27.0 * k))));
	elseif (t <= 4.4e-116)
		tmp = Float64(Float64(t_1 + Float64(Float64(b * c) + Float64(x * Float64(i * -4.0)))) + Float64(t * Float64(a * -4.0)));
	else
		tmp = Float64(Float64(t * Float64(Float64(Float64(Float64(x * 18.0) * y) * z) + Float64(a * -4.0))) + Float64(Float64(b * c) + t_1));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = -27.0 * (j * k);
	tmp = 0.0;
	if (t <= -6e+60)
		tmp = (t * ((a * -4.0) + (x * (18.0 * (y * z))))) - (((x * 4.0) * i) + (j * (27.0 * k)));
	elseif (t <= 4.4e-116)
		tmp = (t_1 + ((b * c) + (x * (i * -4.0)))) + (t * (a * -4.0));
	else
		tmp = (t * ((((x * 18.0) * y) * z) + (a * -4.0))) + ((b * c) + t_1);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6e+60], N[(N[(t * N[(N[(a * -4.0), $MachinePrecision] + N[(x * N[(18.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision] + N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.4e-116], N[(N[(t$95$1 + N[(N[(b * c), $MachinePrecision] + N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t * N[(N[(N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.9999999999999997e60

   1. Initial program 77.7%

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

   3. Taylor expanded in b around 0

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

      1. associate--r+ N/A

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

      2. cancel-sign-sub-inv N/A

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

      5. associate--l+ N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. *-commutative N/A

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

      9. associate-*r* N/A

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

      10. *-commutative N/A

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

      11. associate-*r* N/A

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

      12. *-commutative N/A

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

   5. Simplified 83.7%

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

   if -5.9999999999999997e60 < t < 4.4000000000000002e-116

   1. Initial program 80.9%

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

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 80.9%

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

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(-4 \cdot \left(a \cdot t\right)\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, k\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(-4 \cdot \left(t \cdot a\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(-27, \color{blue}{\mathsf{*.f64}\left(j, k\right)}\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

      2. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(-4 \cdot t\right) \cdot a\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, k\right)\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(t \cdot -4\right) \cdot a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\color{blue}{-27}, \mathsf{*.f64}\left(j, k\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(-4 \cdot a\right)\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, k\right)\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(-4 \cdot a\right)\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, k\right)\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 85.6%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(-4, a\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(-27, \color{blue}{\mathsf{*.f64}\left(j, k\right)}\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

   7. Simplified 85.6%

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

   if 4.4000000000000002e-116 < t

   1. Initial program 84.4%

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

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 87.8%

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

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, k\right)\right), \color{blue}{\left(b \cdot c\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 88.4%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, k\right)\right), \mathsf{*.f64}\left(b, \color{blue}{c}\right)\right)\right) \]

   7. Simplified 88.4%

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

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{+60}:\\ \;\;\;\;t \cdot \left(a \cdot -4 + x \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right) - \left(\left(x \cdot 4\right) \cdot i + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{-116}:\\ \;\;\;\;\left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right) + t \cdot \left(a \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right) + \left(b \cdot c + -27 \cdot \left(j \cdot k\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 84.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := -27 \cdot \left(j \cdot k\right)\\ t_2 := t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right) + \left(b \cdot c + t\_1\right)\\ \mathbf{if}\;t \leq -4400:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-115}:\\ \;\;\;\;\left(t\_1 + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right) + t \cdot \left(a \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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 (* -27.0 (* j k)))
        (t_2 (+ (* t (+ (* (* (* x 18.0) y) z) (* a -4.0))) (+ (* b c) t_1))))
   (if (<= t -4400.0)
     t_2
     (if (<= t 6.5e-115)
       (+ (+ t_1 (+ (* b c) (* x (* i -4.0)))) (* t (* a -4.0)))
       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 = -27.0 * (j * k);
	double t_2 = (t * ((((x * 18.0) * y) * z) + (a * -4.0))) + ((b * c) + t_1);
	double tmp;
	if (t <= -4400.0) {
		tmp = t_2;
	} else if (t <= 6.5e-115) {
		tmp = (t_1 + ((b * c) + (x * (i * -4.0)))) + (t * (a * -4.0));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 = (-27.0d0) * (j * k)
    t_2 = (t * ((((x * 18.0d0) * y) * z) + (a * (-4.0d0)))) + ((b * c) + t_1)
    if (t <= (-4400.0d0)) then
        tmp = t_2
    else if (t <= 6.5d-115) then
        tmp = (t_1 + ((b * c) + (x * (i * (-4.0d0))))) + (t * (a * (-4.0d0)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -27.0 * (j * k);
	double t_2 = (t * ((((x * 18.0) * y) * z) + (a * -4.0))) + ((b * c) + t_1);
	double tmp;
	if (t <= -4400.0) {
		tmp = t_2;
	} else if (t <= 6.5e-115) {
		tmp = (t_1 + ((b * c) + (x * (i * -4.0)))) + (t * (a * -4.0));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = -27.0 * (j * k)
	t_2 = (t * ((((x * 18.0) * y) * z) + (a * -4.0))) + ((b * c) + t_1)
	tmp = 0
	if t <= -4400.0:
		tmp = t_2
	elif t <= 6.5e-115:
		tmp = (t_1 + ((b * c) + (x * (i * -4.0)))) + (t * (a * -4.0))
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(-27.0 * Float64(j * k))
	t_2 = Float64(Float64(t * Float64(Float64(Float64(Float64(x * 18.0) * y) * z) + Float64(a * -4.0))) + Float64(Float64(b * c) + t_1))
	tmp = 0.0
	if (t <= -4400.0)
		tmp = t_2;
	elseif (t <= 6.5e-115)
		tmp = Float64(Float64(t_1 + Float64(Float64(b * c) + Float64(x * Float64(i * -4.0)))) + Float64(t * Float64(a * -4.0)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = -27.0 * (j * k);
	t_2 = (t * ((((x * 18.0) * y) * z) + (a * -4.0))) + ((b * c) + t_1);
	tmp = 0.0;
	if (t <= -4400.0)
		tmp = t_2;
	elseif (t <= 6.5e-115)
		tmp = (t_1 + ((b * c) + (x * (i * -4.0)))) + (t * (a * -4.0));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t * N[(N[(N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4400.0], t$95$2, If[LessEqual[t, 6.5e-115], N[(N[(t$95$1 + N[(N[(b * c), $MachinePrecision] + N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if t < -4400 or 6.50000000000000033e-115 < t

   1. Initial program 82.6%

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

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 86.4%

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

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, k\right)\right), \color{blue}{\left(b \cdot c\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 86.2%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, k\right)\right), \mathsf{*.f64}\left(b, \color{blue}{c}\right)\right)\right) \]

   7. Simplified 86.2%

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

   if -4400 < t < 6.50000000000000033e-115

   1. Initial program 79.8%

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

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 79.8%

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

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(-4 \cdot \left(a \cdot t\right)\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, k\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(-4 \cdot \left(t \cdot a\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(-27, \color{blue}{\mathsf{*.f64}\left(j, k\right)}\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

      2. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(-4 \cdot t\right) \cdot a\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, k\right)\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(t \cdot -4\right) \cdot a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\color{blue}{-27}, \mathsf{*.f64}\left(j, k\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(-4 \cdot a\right)\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, k\right)\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(-4 \cdot a\right)\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, k\right)\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 85.9%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(-4, a\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(-27, \color{blue}{\mathsf{*.f64}\left(j, k\right)}\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

   7. Simplified 85.9%

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

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4400:\\ \;\;\;\;t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right) + \left(b \cdot c + -27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-115}:\\ \;\;\;\;\left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right) + t \cdot \left(a \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right) + \left(b \cdot c + -27 \cdot \left(j \cdot k\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 79.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(z \cdot \left(18 \cdot \left(y \cdot \left(x \cdot t\right)\right)\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;z \leq -3.5 \cdot 10^{-63}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+186}:\\ \;\;\;\;\left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right) + t \cdot \left(a \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1
         (-
          (- (* z (* 18.0 (* y (* x t)))) (* (* x 4.0) i))
          (* (* j 27.0) k))))
   (if (<= z -3.5e-63)
     t_1
     (if (<= z 1.75e+186)
       (+ (+ (* -27.0 (* j k)) (+ (* b c) (* x (* i -4.0)))) (* t (* a -4.0)))
       t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((z * (18.0 * (y * (x * t)))) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	double tmp;
	if (z <= -3.5e-63) {
		tmp = t_1;
	} else if (z <= 1.75e+186) {
		tmp = ((-27.0 * (j * k)) + ((b * c) + (x * (i * -4.0)))) + (t * (a * -4.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((z * (18.0d0 * (y * (x * t)))) - ((x * 4.0d0) * i)) - ((j * 27.0d0) * k)
    if (z <= (-3.5d-63)) then
        tmp = t_1
    else if (z <= 1.75d+186) then
        tmp = (((-27.0d0) * (j * k)) + ((b * c) + (x * (i * (-4.0d0))))) + (t * (a * (-4.0d0)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((z * (18.0 * (y * (x * t)))) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	double tmp;
	if (z <= -3.5e-63) {
		tmp = t_1;
	} else if (z <= 1.75e+186) {
		tmp = ((-27.0 * (j * k)) + ((b * c) + (x * (i * -4.0)))) + (t * (a * -4.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = ((z * (18.0 * (y * (x * t)))) - ((x * 4.0) * i)) - ((j * 27.0) * k)
	tmp = 0
	if z <= -3.5e-63:
		tmp = t_1
	elif z <= 1.75e+186:
		tmp = ((-27.0 * (j * k)) + ((b * c) + (x * (i * -4.0)))) + (t * (a * -4.0))
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(Float64(z * Float64(18.0 * Float64(y * Float64(x * t)))) - Float64(Float64(x * 4.0) * i)) - Float64(Float64(j * 27.0) * k))
	tmp = 0.0
	if (z <= -3.5e-63)
		tmp = t_1;
	elseif (z <= 1.75e+186)
		tmp = Float64(Float64(Float64(-27.0 * Float64(j * k)) + Float64(Float64(b * c) + Float64(x * Float64(i * -4.0)))) + Float64(t * Float64(a * -4.0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = ((z * (18.0 * (y * (x * t)))) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	tmp = 0.0;
	if (z <= -3.5e-63)
		tmp = t_1;
	elseif (z <= 1.75e+186)
		tmp = ((-27.0 * (j * k)) + ((b * c) + (x * (i * -4.0)))) + (t * (a * -4.0));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(N[(z * N[(18.0 * N[(y * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.5e-63], t$95$1, If[LessEqual[z, 1.75e+186], N[(N[(N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision] + N[(N[(b * c), $MachinePrecision] + N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.50000000000000003e-63 or 1.74999999999999993e186 < z

   1. Initial program 72.4%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\color{blue}{\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   4. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\left(18 \cdot \left(t \cdot \left(\left(x \cdot y\right) \cdot z\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      2. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\left(18 \cdot \left(\left(t \cdot \left(x \cdot y\right)\right) \cdot z\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      3. associate-*l* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\left(\left(18 \cdot \left(t \cdot \left(x \cdot y\right)\right)\right) \cdot z\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\left(18 \cdot \left(t \cdot \left(x \cdot y\right)\right)\right), z\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(18, \left(t \cdot \left(x \cdot y\right)\right)\right), z\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(18, \left(\left(x \cdot y\right) \cdot t\right)\right), z\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(18, \left(\left(y \cdot x\right) \cdot t\right)\right), z\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      8. associate-*l* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(18, \left(y \cdot \left(x \cdot t\right)\right)\right), z\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(18, \mathsf{*.f64}\left(y, \left(x \cdot t\right)\right)\right), z\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      10. *-lowering-*.f64 65.3%

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(18, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, t\right)\right)\right), z\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

   5. Simplified 65.3%

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

   if -3.50000000000000003e-63 < z < 1.74999999999999993e186

   1. Initial program 87.7%

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

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 88.3%

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

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(-4 \cdot \left(a \cdot t\right)\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, k\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(-4 \cdot \left(t \cdot a\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(-27, \color{blue}{\mathsf{*.f64}\left(j, k\right)}\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

      2. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(-4 \cdot t\right) \cdot a\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, k\right)\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(t \cdot -4\right) \cdot a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\color{blue}{-27}, \mathsf{*.f64}\left(j, k\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(-4 \cdot a\right)\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, k\right)\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(-4 \cdot a\right)\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, k\right)\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 84.7%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(-4, a\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(-27, \color{blue}{\mathsf{*.f64}\left(j, k\right)}\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

   7. Simplified 84.7%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-63}:\\ \;\;\;\;\left(z \cdot \left(18 \cdot \left(y \cdot \left(x \cdot t\right)\right)\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+186}:\\ \;\;\;\;\left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right) + t \cdot \left(a \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot \left(18 \cdot \left(y \cdot \left(x \cdot t\right)\right)\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 79.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := x \cdot \left(i \cdot -4 + y \cdot \left(z \cdot \left(18 \cdot t\right)\right)\right)\\ \mathbf{if}\;x \leq -2.5 \cdot 10^{+165}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{+146}:\\ \;\;\;\;\left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right) + t \cdot \left(a \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* x (+ (* i -4.0) (* y (* z (* 18.0 t)))))))
   (if (<= x -2.5e+165)
     t_1
     (if (<= x 4.4e+146)
       (+ (+ (* -27.0 (* j k)) (+ (* b c) (* x (* i -4.0)))) (* t (* a -4.0)))
       t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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) + (y * (z * (18.0 * t))));
	double tmp;
	if (x <= -2.5e+165) {
		tmp = t_1;
	} else if (x <= 4.4e+146) {
		tmp = ((-27.0 * (j * k)) + ((b * c) + (x * (i * -4.0)))) + (t * (a * -4.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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)) + (y * (z * (18.0d0 * t))))
    if (x <= (-2.5d+165)) then
        tmp = t_1
    else if (x <= 4.4d+146) then
        tmp = (((-27.0d0) * (j * k)) + ((b * c) + (x * (i * (-4.0d0))))) + (t * (a * (-4.0d0)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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) + (y * (z * (18.0 * t))));
	double tmp;
	if (x <= -2.5e+165) {
		tmp = t_1;
	} else if (x <= 4.4e+146) {
		tmp = ((-27.0 * (j * k)) + ((b * c) + (x * (i * -4.0)))) + (t * (a * -4.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = x * ((i * -4.0) + (y * (z * (18.0 * t))))
	tmp = 0
	if x <= -2.5e+165:
		tmp = t_1
	elif x <= 4.4e+146:
		tmp = ((-27.0 * (j * k)) + ((b * c) + (x * (i * -4.0)))) + (t * (a * -4.0))
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(x * Float64(Float64(i * -4.0) + Float64(y * Float64(z * Float64(18.0 * t)))))
	tmp = 0.0
	if (x <= -2.5e+165)
		tmp = t_1;
	elseif (x <= 4.4e+146)
		tmp = Float64(Float64(Float64(-27.0 * Float64(j * k)) + Float64(Float64(b * c) + Float64(x * Float64(i * -4.0)))) + Float64(t * Float64(a * -4.0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = x * ((i * -4.0) + (y * (z * (18.0 * t))));
	tmp = 0.0;
	if (x <= -2.5e+165)
		tmp = t_1;
	elseif (x <= 4.4e+146)
		tmp = ((-27.0 * (j * k)) + ((b * c) + (x * (i * -4.0)))) + (t * (a * -4.0));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(x * N[(N[(i * -4.0), $MachinePrecision] + N[(y * N[(z * N[(18.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.5e+165], t$95$1, If[LessEqual[x, 4.4e+146], N[(N[(N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision] + N[(N[(b * c), $MachinePrecision] + N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.49999999999999985e165 or 4.3999999999999996e146 < x

   1. Initial program 58.5%

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

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 61.9%

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

   5. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(-4 \cdot i\right), \color{blue}{\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \left(\color{blue}{18} \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \left(\left(t \cdot \left(y \cdot z\right)\right) \cdot \color{blue}{18}\right)\right)\right) \]

      5. associate-*l* N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \left(t \cdot \color{blue}{\left(\left(y \cdot z\right) \cdot 18\right)}\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \left(t \cdot \left(18 \cdot \color{blue}{\left(y \cdot z\right)}\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \mathsf{*.f64}\left(t, \color{blue}{\left(18 \cdot \left(y \cdot z\right)\right)}\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(18, \color{blue}{\left(y \cdot z\right)}\right)\right)\right)\right) \]

      9. *-lowering-*.f64 80.1%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(y, \color{blue}{z}\right)\right)\right)\right)\right) \]

   7. Simplified 80.1%

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

      1. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \left(\left(t \cdot 18\right) \cdot \color{blue}{\left(y \cdot z\right)}\right)\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \left(\left(t \cdot 18\right) \cdot \left(z \cdot \color{blue}{y}\right)\right)\right)\right) \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \left(\left(\left(t \cdot 18\right) \cdot z\right) \cdot \color{blue}{y}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \mathsf{*.f64}\left(\left(\left(t \cdot 18\right) \cdot z\right), \color{blue}{y}\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(t \cdot 18\right), z\right), y\right)\right)\right) \]

      6. *-lowering-*.f64 85.1%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(t, 18\right), z\right), y\right)\right)\right) \]

   9. Applied egg-rr 85.1%

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

   if -2.49999999999999985e165 < x < 4.3999999999999996e146

   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. Step-by-step derivation

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 90.4%

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

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(-4 \cdot \left(a \cdot t\right)\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, k\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(-4 \cdot \left(t \cdot a\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(-27, \color{blue}{\mathsf{*.f64}\left(j, k\right)}\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

      2. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(-4 \cdot t\right) \cdot a\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, k\right)\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(t \cdot -4\right) \cdot a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\color{blue}{-27}, \mathsf{*.f64}\left(j, k\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(-4 \cdot a\right)\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, k\right)\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(-4 \cdot a\right)\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, k\right)\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 78.8%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(-4, a\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(-27, \color{blue}{\mathsf{*.f64}\left(j, k\right)}\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

   7. Simplified 78.8%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+165}:\\ \;\;\;\;x \cdot \left(i \cdot -4 + y \cdot \left(z \cdot \left(18 \cdot t\right)\right)\right)\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{+146}:\\ \;\;\;\;\left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right) + t \cdot \left(a \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(i \cdot -4 + y \cdot \left(z \cdot \left(18 \cdot t\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 36.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -4.1 \cdot 10^{+130}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -3.6 \cdot 10^{-42}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 4.4 \cdot 10^{+155}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

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
 (if (<= (* b c) -4.1e+130)
   (* b c)
   (if (<= (* b c) -3.6e-42)
     (* -4.0 (* x i))
     (if (<= (* b c) 4.4e+155) (* k (* j -27.0)) (* 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 tmp;
	if ((b * c) <= -4.1e+130) {
		tmp = b * c;
	} else if ((b * c) <= -3.6e-42) {
		tmp = -4.0 * (x * i);
	} else if ((b * c) <= 4.4e+155) {
		tmp = k * (j * -27.0);
	} 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) :: tmp
    if ((b * c) <= (-4.1d+130)) then
        tmp = b * c
    else if ((b * c) <= (-3.6d-42)) then
        tmp = (-4.0d0) * (x * i)
    else if ((b * c) <= 4.4d+155) then
        tmp = k * (j * (-27.0d0))
    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 tmp;
	if ((b * c) <= -4.1e+130) {
		tmp = b * c;
	} else if ((b * c) <= -3.6e-42) {
		tmp = -4.0 * (x * i);
	} else if ((b * c) <= 4.4e+155) {
		tmp = k * (j * -27.0);
	} 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):
	tmp = 0
	if (b * c) <= -4.1e+130:
		tmp = b * c
	elif (b * c) <= -3.6e-42:
		tmp = -4.0 * (x * i)
	elif (b * c) <= 4.4e+155:
		tmp = k * (j * -27.0)
	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)
	tmp = 0.0
	if (Float64(b * c) <= -4.1e+130)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -3.6e-42)
		tmp = Float64(-4.0 * Float64(x * i));
	elseif (Float64(b * c) <= 4.4e+155)
		tmp = Float64(k * Float64(j * -27.0));
	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)
	tmp = 0.0;
	if ((b * c) <= -4.1e+130)
		tmp = b * c;
	elseif ((b * c) <= -3.6e-42)
		tmp = -4.0 * (x * i);
	elseif ((b * c) <= 4.4e+155)
		tmp = k * (j * -27.0);
	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_] := If[LessEqual[N[(b * c), $MachinePrecision], -4.1e+130], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -3.6e-42], N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 4.4e+155], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -4.09999999999999978e130 or 4.4000000000000005e155 < (*.f64 b c)

   1. Initial program 78.2%

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

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 80.6%

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

   5. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot c} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 64.7%

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{c}\right) \]

   7. Simplified 64.7%

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

   if -4.09999999999999978e130 < (*.f64 b c) < -3.6000000000000002e-42

   1. Initial program 79.5%

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

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 82.2%

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

   5. Taylor expanded in i around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-4, \color{blue}{\left(i \cdot x\right)}\right) \]

      2. *-lowering-*.f64 34.3%

         \[\leadsto \mathsf{*.f64}\left(-4, \mathsf{*.f64}\left(i, \color{blue}{x}\right)\right) \]

   7. Simplified 34.3%

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

   if -3.6000000000000002e-42 < (*.f64 b c) < 4.4000000000000005e155

   1. Initial program 84.0%

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

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 86.2%

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

   5. Taylor expanded in j around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

         \[\leadsto \left(k \cdot -27\right) \cdot j \]

      4. associate-*r* N/A

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

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(k, \color{blue}{\left(-27 \cdot j\right)}\right) \]

      6. *-lowering-*.f64 31.1%

         \[\leadsto \mathsf{*.f64}\left(k, \mathsf{*.f64}\left(-27, \color{blue}{j}\right)\right) \]

   7. Simplified 31.1%

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

4. Final simplification 42.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -4.1 \cdot 10^{+130}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -3.6 \cdot 10^{-42}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 4.4 \cdot 10^{+155}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 36.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -4.1 \cdot 10^{+130}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -2.2 \cdot 10^{-41}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 1.15 \cdot 10^{+156}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

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
 (if (<= (* b c) -4.1e+130)
   (* b c)
   (if (<= (* b c) -2.2e-41)
     (* -4.0 (* x i))
     (if (<= (* b c) 1.15e+156) (* j (* k -27.0)) (* b c)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b * c) <= -4.1e+130) {
		tmp = b * c;
	} else if ((b * c) <= -2.2e-41) {
		tmp = -4.0 * (x * i);
	} else if ((b * c) <= 1.15e+156) {
		tmp = j * (k * -27.0);
	} 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) :: tmp
    if ((b * c) <= (-4.1d+130)) then
        tmp = b * c
    else if ((b * c) <= (-2.2d-41)) then
        tmp = (-4.0d0) * (x * i)
    else if ((b * c) <= 1.15d+156) then
        tmp = j * (k * (-27.0d0))
    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 tmp;
	if ((b * c) <= -4.1e+130) {
		tmp = b * c;
	} else if ((b * c) <= -2.2e-41) {
		tmp = -4.0 * (x * i);
	} else if ((b * c) <= 1.15e+156) {
		tmp = j * (k * -27.0);
	} 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):
	tmp = 0
	if (b * c) <= -4.1e+130:
		tmp = b * c
	elif (b * c) <= -2.2e-41:
		tmp = -4.0 * (x * i)
	elif (b * c) <= 1.15e+156:
		tmp = j * (k * -27.0)
	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)
	tmp = 0.0
	if (Float64(b * c) <= -4.1e+130)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -2.2e-41)
		tmp = Float64(-4.0 * Float64(x * i));
	elseif (Float64(b * c) <= 1.15e+156)
		tmp = Float64(j * Float64(k * -27.0));
	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)
	tmp = 0.0;
	if ((b * c) <= -4.1e+130)
		tmp = b * c;
	elseif ((b * c) <= -2.2e-41)
		tmp = -4.0 * (x * i);
	elseif ((b * c) <= 1.15e+156)
		tmp = j * (k * -27.0);
	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_] := If[LessEqual[N[(b * c), $MachinePrecision], -4.1e+130], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -2.2e-41], N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1.15e+156], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -4.09999999999999978e130 or 1.1499999999999999e156 < (*.f64 b c)

   1. Initial program 78.2%

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

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 80.6%

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

   5. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot c} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 64.7%

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{c}\right) \]

   7. Simplified 64.7%

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

   if -4.09999999999999978e130 < (*.f64 b c) < -2.2e-41

   1. Initial program 79.5%

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

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 82.2%

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

   5. Taylor expanded in i around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-4, \color{blue}{\left(i \cdot x\right)}\right) \]

      2. *-lowering-*.f64 34.3%

         \[\leadsto \mathsf{*.f64}\left(-4, \mathsf{*.f64}\left(i, \color{blue}{x}\right)\right) \]

   7. Simplified 34.3%

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

   if -2.2e-41 < (*.f64 b c) < 1.1499999999999999e156

   1. Initial program 84.0%

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

   3. Taylor expanded in t around inf

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\color{blue}{\left(t \cdot \left(\left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + \frac{b \cdot c}{t}\right) - 4 \cdot a\right)\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \left(\left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + \frac{b \cdot c}{t}\right) - 4 \cdot a\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

      2. cancel-sign-sub-inv N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \left(\left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + \frac{b \cdot c}{t}\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot a\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      3. metadata-eval N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \left(\left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + \frac{b \cdot c}{t}\right) + -4 \cdot a\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + \frac{b \cdot c}{t}\right), \left(-4 \cdot a\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{+.f64}\left(\left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right), \left(\frac{b \cdot c}{t}\right)\right), \left(-4 \cdot a\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{+.f64}\left(\left(\left(x \cdot \left(y \cdot z\right)\right) \cdot 18\right), \left(\frac{b \cdot c}{t}\right)\right), \left(-4 \cdot a\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      7. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{+.f64}\left(\left(x \cdot \left(\left(y \cdot z\right) \cdot 18\right)\right), \left(\frac{b \cdot c}{t}\right)\right), \left(-4 \cdot a\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{+.f64}\left(\left(x \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right), \left(\frac{b \cdot c}{t}\right)\right), \left(-4 \cdot a\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \left(18 \cdot \left(y \cdot z\right)\right)\right), \left(\frac{b \cdot c}{t}\right)\right), \left(-4 \cdot a\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(18, \left(y \cdot z\right)\right)\right), \left(\frac{b \cdot c}{t}\right)\right), \left(-4 \cdot a\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(y, z\right)\right)\right), \left(\frac{b \cdot c}{t}\right)\right), \left(-4 \cdot a\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      12. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(y, z\right)\right)\right), \mathsf{/.f64}\left(\left(b \cdot c\right), t\right)\right), \left(-4 \cdot a\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(y, z\right)\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(b, c\right), t\right)\right), \left(-4 \cdot a\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      14. *-lowering-*.f64 84.0%

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(y, z\right)\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(b, c\right), t\right)\right), \mathsf{*.f64}\left(-4, a\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

   5. Simplified 84.0%

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

   6. Taylor expanded in j around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \color{blue}{\left(-27 \cdot k\right)}\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(j, \left(k \cdot \color{blue}{-27}\right)\right) \]

      6. *-lowering-*.f64 31.1%

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(k, \color{blue}{-27}\right)\right) \]

   8. Simplified 31.1%

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

4. Final simplification 42.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -4.1 \cdot 10^{+130}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -2.2 \cdot 10^{-41}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 1.15 \cdot 10^{+156}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 72.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := t \cdot \left(a \cdot -4 + x \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{if}\;t \leq -7.2 \cdot 10^{+107}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+75}:\\ \;\;\;\;\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (+ (* a -4.0) (* x (* 18.0 (* y z)))))))
   (if (<= t -7.2e+107)
     t_1
     (if (<= t 8.5e+75)
       (- (- (* b c) (* (* x 4.0) i)) (* (* j 27.0) k))
       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 * ((a * -4.0) + (x * (18.0 * (y * z))));
	double tmp;
	if (t <= -7.2e+107) {
		tmp = t_1;
	} else if (t <= 8.5e+75) {
		tmp = ((b * c) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	} 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 * ((a * (-4.0d0)) + (x * (18.0d0 * (y * z))))
    if (t <= (-7.2d+107)) then
        tmp = t_1
    else if (t <= 8.5d+75) then
        tmp = ((b * c) - ((x * 4.0d0) * i)) - ((j * 27.0d0) * k)
    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 * ((a * -4.0) + (x * (18.0 * (y * z))));
	double tmp;
	if (t <= -7.2e+107) {
		tmp = t_1;
	} else if (t <= 8.5e+75) {
		tmp = ((b * c) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	} 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 * ((a * -4.0) + (x * (18.0 * (y * z))))
	tmp = 0
	if t <= -7.2e+107:
		tmp = t_1
	elif t <= 8.5e+75:
		tmp = ((b * c) - ((x * 4.0) * i)) - ((j * 27.0) * k)
	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(a * -4.0) + Float64(x * Float64(18.0 * Float64(y * z)))))
	tmp = 0.0
	if (t <= -7.2e+107)
		tmp = t_1;
	elseif (t <= 8.5e+75)
		tmp = Float64(Float64(Float64(b * c) - Float64(Float64(x * 4.0) * i)) - Float64(Float64(j * 27.0) * k));
	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 * ((a * -4.0) + (x * (18.0 * (y * z))));
	tmp = 0.0;
	if (t <= -7.2e+107)
		tmp = t_1;
	elseif (t <= 8.5e+75)
		tmp = ((b * c) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	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[(a * -4.0), $MachinePrecision] + N[(x * N[(18.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.2e+107], t$95$1, If[LessEqual[t, 8.5e+75], N[(N[(N[(b * c), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -7.1999999999999995e107 or 8.4999999999999993e75 < t

   1. Initial program 81.8%

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

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 86.6%

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

   5. Taylor expanded in t around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(-4 \cdot a\right), \color{blue}{\left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \left(\color{blue}{18} \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \left(\left(x \cdot \left(y \cdot z\right)\right) \cdot \color{blue}{18}\right)\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \left(x \cdot \color{blue}{\left(\left(y \cdot z\right) \cdot 18\right)}\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \left(x \cdot \left(18 \cdot \color{blue}{\left(y \cdot z\right)}\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \mathsf{*.f64}\left(x, \color{blue}{\left(18 \cdot \left(y \cdot z\right)\right)}\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(18, \color{blue}{\left(y \cdot z\right)}\right)\right)\right)\right) \]

      9. *-lowering-*.f64 72.9%

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(y, \color{blue}{z}\right)\right)\right)\right)\right) \]

   7. Simplified 72.9%

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

   if -7.1999999999999995e107 < t < 8.4999999999999993e75

   1. Initial program 81.2%

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

   3. Taylor expanded in t around 0

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\color{blue}{\left(b \cdot c\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 77.0%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

   5. Simplified 77.0%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{+107}:\\ \;\;\;\;t \cdot \left(a \cdot -4 + x \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+75}:\\ \;\;\;\;\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot -4 + x \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 71.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := x \cdot \left(i \cdot -4 + y \cdot \left(z \cdot \left(18 \cdot t\right)\right)\right)\\ \mathbf{if}\;x \leq -5.3 \cdot 10^{+147}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{+102}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right) + \left(b \cdot c + -27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* x (+ (* i -4.0) (* y (* z (* 18.0 t)))))))
   (if (<= x -5.3e+147)
     t_1
     (if (<= x 1.25e+102)
       (+ (* t (* a -4.0)) (+ (* b c) (* -27.0 (* j k))))
       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) + (y * (z * (18.0 * t))));
	double tmp;
	if (x <= -5.3e+147) {
		tmp = t_1;
	} else if (x <= 1.25e+102) {
		tmp = (t * (a * -4.0)) + ((b * c) + (-27.0 * (j * k)));
	} 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)) + (y * (z * (18.0d0 * t))))
    if (x <= (-5.3d+147)) then
        tmp = t_1
    else if (x <= 1.25d+102) then
        tmp = (t * (a * (-4.0d0))) + ((b * c) + ((-27.0d0) * (j * k)))
    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) + (y * (z * (18.0 * t))));
	double tmp;
	if (x <= -5.3e+147) {
		tmp = t_1;
	} else if (x <= 1.25e+102) {
		tmp = (t * (a * -4.0)) + ((b * c) + (-27.0 * (j * k)));
	} 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) + (y * (z * (18.0 * t))))
	tmp = 0
	if x <= -5.3e+147:
		tmp = t_1
	elif x <= 1.25e+102:
		tmp = (t * (a * -4.0)) + ((b * c) + (-27.0 * (j * k)))
	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(i * -4.0) + Float64(y * Float64(z * Float64(18.0 * t)))))
	tmp = 0.0
	if (x <= -5.3e+147)
		tmp = t_1;
	elseif (x <= 1.25e+102)
		tmp = Float64(Float64(t * Float64(a * -4.0)) + Float64(Float64(b * c) + Float64(-27.0 * Float64(j * k))));
	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) + (y * (z * (18.0 * t))));
	tmp = 0.0;
	if (x <= -5.3e+147)
		tmp = t_1;
	elseif (x <= 1.25e+102)
		tmp = (t * (a * -4.0)) + ((b * c) + (-27.0 * (j * k)));
	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[(i * -4.0), $MachinePrecision] + N[(y * N[(z * N[(18.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5.3e+147], t$95$1, If[LessEqual[x, 1.25e+102], N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + N[(N[(b * c), $MachinePrecision] + N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -5.3000000000000002e147 or 1.25e102 < x

   1. Initial program 63.6%

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

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 66.4%

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

   5. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(-4 \cdot i\right), \color{blue}{\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \left(\color{blue}{18} \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \left(\left(t \cdot \left(y \cdot z\right)\right) \cdot \color{blue}{18}\right)\right)\right) \]

      5. associate-*l* N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \left(t \cdot \color{blue}{\left(\left(y \cdot z\right) \cdot 18\right)}\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \left(t \cdot \left(18 \cdot \color{blue}{\left(y \cdot z\right)}\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \mathsf{*.f64}\left(t, \color{blue}{\left(18 \cdot \left(y \cdot z\right)\right)}\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(18, \color{blue}{\left(y \cdot z\right)}\right)\right)\right)\right) \]

      9. *-lowering-*.f64 77.8%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(y, \color{blue}{z}\right)\right)\right)\right)\right) \]

   7. Simplified 77.8%

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

      1. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \left(\left(t \cdot 18\right) \cdot \color{blue}{\left(y \cdot z\right)}\right)\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \left(\left(t \cdot 18\right) \cdot \left(z \cdot \color{blue}{y}\right)\right)\right)\right) \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \left(\left(\left(t \cdot 18\right) \cdot z\right) \cdot \color{blue}{y}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \mathsf{*.f64}\left(\left(\left(t \cdot 18\right) \cdot z\right), \color{blue}{y}\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(t \cdot 18\right), z\right), y\right)\right)\right) \]

      6. *-lowering-*.f64 82.1%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(t, 18\right), z\right), y\right)\right)\right) \]

   9. Applied egg-rr 82.1%

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

   if -5.3000000000000002e147 < x < 1.25e102

   1. Initial program 88.2%

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

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 90.4%

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

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(-4 \cdot \left(a \cdot t\right)\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, k\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(-4 \cdot \left(t \cdot a\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(-27, \color{blue}{\mathsf{*.f64}\left(j, k\right)}\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

      2. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(-4 \cdot t\right) \cdot a\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, k\right)\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(t \cdot -4\right) \cdot a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\color{blue}{-27}, \mathsf{*.f64}\left(j, k\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(-4 \cdot a\right)\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, k\right)\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(-4 \cdot a\right)\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, k\right)\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 78.0%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(-4, a\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(-27, \color{blue}{\mathsf{*.f64}\left(j, k\right)}\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

   7. Simplified 78.0%

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

   8. Taylor expanded in b around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(-4, a\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, k\right)\right), \color{blue}{\left(b \cdot c\right)}\right)\right) \]
   9. Step-by-step derivation

      1. *-lowering-*.f64 71.4%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(-4, a\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, k\right)\right), \mathsf{*.f64}\left(b, \color{blue}{c}\right)\right)\right) \]

   10. Simplified 71.4%

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

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.3 \cdot 10^{+147}:\\ \;\;\;\;x \cdot \left(i \cdot -4 + y \cdot \left(z \cdot \left(18 \cdot t\right)\right)\right)\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{+102}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right) + \left(b \cdot c + -27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(i \cdot -4 + y \cdot \left(z \cdot \left(18 \cdot t\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 43.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;k \leq -2 \cdot 10^{+28}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;k \leq 7.5 \cdot 10^{+98}:\\ \;\;\;\;b \cdot c + x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;k \leq 2.4 \cdot 10^{+233}:\\ \;\;\;\;z \cdot \left(18 \cdot \left(y \cdot \left(x \cdot t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0))))
   (if (<= k -2e+28)
     t_1
     (if (<= k 7.5e+98)
       (+ (* b c) (* x (* i -4.0)))
       (if (<= k 2.4e+233) (* z (* 18.0 (* y (* x t)))) t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double tmp;
	if (k <= -2e+28) {
		tmp = t_1;
	} else if (k <= 7.5e+98) {
		tmp = (b * c) + (x * (i * -4.0));
	} else if (k <= 2.4e+233) {
		tmp = z * (18.0 * (y * (x * t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * (k * (-27.0d0))
    if (k <= (-2d+28)) then
        tmp = t_1
    else if (k <= 7.5d+98) then
        tmp = (b * c) + (x * (i * (-4.0d0)))
    else if (k <= 2.4d+233) then
        tmp = z * (18.0d0 * (y * (x * t)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double tmp;
	if (k <= -2e+28) {
		tmp = t_1;
	} else if (k <= 7.5e+98) {
		tmp = (b * c) + (x * (i * -4.0));
	} else if (k <= 2.4e+233) {
		tmp = z * (18.0 * (y * (x * t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	tmp = 0
	if k <= -2e+28:
		tmp = t_1
	elif k <= 7.5e+98:
		tmp = (b * c) + (x * (i * -4.0))
	elif k <= 2.4e+233:
		tmp = z * (18.0 * (y * (x * t)))
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * -27.0))
	tmp = 0.0
	if (k <= -2e+28)
		tmp = t_1;
	elseif (k <= 7.5e+98)
		tmp = Float64(Float64(b * c) + Float64(x * Float64(i * -4.0)));
	elseif (k <= 2.4e+233)
		tmp = Float64(z * Float64(18.0 * Float64(y * Float64(x * t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * -27.0);
	tmp = 0.0;
	if (k <= -2e+28)
		tmp = t_1;
	elseif (k <= 7.5e+98)
		tmp = (b * c) + (x * (i * -4.0));
	elseif (k <= 2.4e+233)
		tmp = z * (18.0 * (y * (x * t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[k, -2e+28], t$95$1, If[LessEqual[k, 7.5e+98], N[(N[(b * c), $MachinePrecision] + N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 2.4e+233], N[(z * N[(18.0 * N[(y * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if k < -1.99999999999999992e28 or 2.40000000000000003e233 < k

   1. Initial program 78.9%

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

   3. Taylor expanded in t around inf

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\color{blue}{\left(t \cdot \left(\left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + \frac{b \cdot c}{t}\right) - 4 \cdot a\right)\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \left(\left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + \frac{b \cdot c}{t}\right) - 4 \cdot a\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

      2. cancel-sign-sub-inv N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \left(\left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + \frac{b \cdot c}{t}\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot a\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      3. metadata-eval N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \left(\left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + \frac{b \cdot c}{t}\right) + -4 \cdot a\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + \frac{b \cdot c}{t}\right), \left(-4 \cdot a\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{+.f64}\left(\left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right), \left(\frac{b \cdot c}{t}\right)\right), \left(-4 \cdot a\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{+.f64}\left(\left(\left(x \cdot \left(y \cdot z\right)\right) \cdot 18\right), \left(\frac{b \cdot c}{t}\right)\right), \left(-4 \cdot a\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      7. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{+.f64}\left(\left(x \cdot \left(\left(y \cdot z\right) \cdot 18\right)\right), \left(\frac{b \cdot c}{t}\right)\right), \left(-4 \cdot a\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{+.f64}\left(\left(x \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right), \left(\frac{b \cdot c}{t}\right)\right), \left(-4 \cdot a\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \left(18 \cdot \left(y \cdot z\right)\right)\right), \left(\frac{b \cdot c}{t}\right)\right), \left(-4 \cdot a\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(18, \left(y \cdot z\right)\right)\right), \left(\frac{b \cdot c}{t}\right)\right), \left(-4 \cdot a\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(y, z\right)\right)\right), \left(\frac{b \cdot c}{t}\right)\right), \left(-4 \cdot a\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      12. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(y, z\right)\right)\right), \mathsf{/.f64}\left(\left(b \cdot c\right), t\right)\right), \left(-4 \cdot a\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(y, z\right)\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(b, c\right), t\right)\right), \left(-4 \cdot a\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      14. *-lowering-*.f64 73.9%

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(y, z\right)\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(b, c\right), t\right)\right), \mathsf{*.f64}\left(-4, a\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

   5. Simplified 73.9%

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

   6. Taylor expanded in j around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \color{blue}{\left(-27 \cdot k\right)}\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(j, \left(k \cdot \color{blue}{-27}\right)\right) \]

      6. *-lowering-*.f64 50.5%

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(k, \color{blue}{-27}\right)\right) \]

   8. Simplified 50.5%

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

   if -1.99999999999999992e28 < k < 7.50000000000000036e98

   1. Initial program 82.6%

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

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 83.9%

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

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(-4 \cdot \left(a \cdot t\right)\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, k\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(-4 \cdot \left(t \cdot a\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(-27, \color{blue}{\mathsf{*.f64}\left(j, k\right)}\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

      2. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(-4 \cdot t\right) \cdot a\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, k\right)\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(t \cdot -4\right) \cdot a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\color{blue}{-27}, \mathsf{*.f64}\left(j, k\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(-4 \cdot a\right)\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, k\right)\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(-4 \cdot a\right)\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, k\right)\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 69.9%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(-4, a\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(-27, \color{blue}{\mathsf{*.f64}\left(j, k\right)}\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

   7. Simplified 69.9%

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

   8. Taylor expanded in j around 0

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

      1. +-commutative N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. +-commutative N/A

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

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(b \cdot c\right), \color{blue}{\left(-4 \cdot \left(a \cdot t\right) + -4 \cdot \left(i \cdot x\right)\right)}\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\color{blue}{-4 \cdot \left(a \cdot t\right)} + -4 \cdot \left(i \cdot x\right)\right)\right) \]

      7. distribute-lft-out N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(-4 \cdot \color{blue}{\left(a \cdot t + i \cdot x\right)}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(-4, \color{blue}{\left(a \cdot t + i \cdot x\right)}\right)\right) \]

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(-4, \mathsf{+.f64}\left(\left(a \cdot t\right), \color{blue}{\left(i \cdot x\right)}\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(-4, \mathsf{+.f64}\left(\left(t \cdot a\right), \left(\color{blue}{i} \cdot x\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(-4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, a\right), \left(\color{blue}{i} \cdot x\right)\right)\right)\right) \]

      12. *-lowering-*.f64 61.1%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(-4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, a\right), \mathsf{*.f64}\left(i, \color{blue}{x}\right)\right)\right)\right) \]

   10. Simplified 61.1%

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

   11. Taylor expanded in t around 0

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

       1. +-commutative N/A

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

       2. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\left(b \cdot c\right), \color{blue}{\left(-4 \cdot \left(i \cdot x\right)\right)}\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\color{blue}{-4} \cdot \left(i \cdot x\right)\right)\right) \]

       4. associate-*r* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\left(-4 \cdot i\right) \cdot \color{blue}{x}\right)\right) \]

       5. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(x \cdot \color{blue}{\left(-4 \cdot i\right)}\right)\right) \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \color{blue}{\left(-4 \cdot i\right)}\right)\right) \]

       7. *-lowering-*.f64 46.2%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(-4, \color{blue}{i}\right)\right)\right) \]

   13. Simplified 46.2%

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

   if 7.50000000000000036e98 < k < 2.40000000000000003e233

   1. Initial program 82.1%

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

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 89.2%

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

   5. Taylor expanded in y around inf

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

      1. associate-*r* N/A

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

      2. associate-*r* N/A

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

      3. associate-*l* N/A

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

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(18 \cdot \left(t \cdot \left(x \cdot y\right)\right)\right), \color{blue}{z}\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(18, \left(t \cdot \left(x \cdot y\right)\right)\right), z\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(18, \left(\left(x \cdot y\right) \cdot t\right)\right), z\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(18, \left(\left(y \cdot x\right) \cdot t\right)\right), z\right) \]

      8. associate-*l* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(18, \left(y \cdot \left(x \cdot t\right)\right)\right), z\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(18, \mathsf{*.f64}\left(y, \left(x \cdot t\right)\right)\right), z\right) \]

      10. *-lowering-*.f64 40.2%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(18, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, t\right)\right)\right), z\right) \]

   7. Simplified 40.2%

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

4. Final simplification 46.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -2 \cdot 10^{+28}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;k \leq 7.5 \cdot 10^{+98}:\\ \;\;\;\;b \cdot c + x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;k \leq 2.4 \cdot 10^{+233}:\\ \;\;\;\;z \cdot \left(18 \cdot \left(y \cdot \left(x \cdot t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 60.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := t \cdot \left(a \cdot -4 + x \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{if}\;t \leq -2 \cdot 10^{+58}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+74}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (+ (* a -4.0) (* x (* 18.0 (* y z)))))))
   (if (<= t -2e+58)
     t_1
     (if (<= t 1.15e+74) (- (* b c) (* 27.0 (* j k))) 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 * ((a * -4.0) + (x * (18.0 * (y * z))));
	double tmp;
	if (t <= -2e+58) {
		tmp = t_1;
	} else if (t <= 1.15e+74) {
		tmp = (b * c) - (27.0 * (j * k));
	} 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 * ((a * (-4.0d0)) + (x * (18.0d0 * (y * z))))
    if (t <= (-2d+58)) then
        tmp = t_1
    else if (t <= 1.15d+74) then
        tmp = (b * c) - (27.0d0 * (j * k))
    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 * ((a * -4.0) + (x * (18.0 * (y * z))));
	double tmp;
	if (t <= -2e+58) {
		tmp = t_1;
	} else if (t <= 1.15e+74) {
		tmp = (b * c) - (27.0 * (j * k));
	} 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 * ((a * -4.0) + (x * (18.0 * (y * z))))
	tmp = 0
	if t <= -2e+58:
		tmp = t_1
	elif t <= 1.15e+74:
		tmp = (b * c) - (27.0 * (j * k))
	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(a * -4.0) + Float64(x * Float64(18.0 * Float64(y * z)))))
	tmp = 0.0
	if (t <= -2e+58)
		tmp = t_1;
	elseif (t <= 1.15e+74)
		tmp = Float64(Float64(b * c) - Float64(27.0 * Float64(j * k)));
	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 * ((a * -4.0) + (x * (18.0 * (y * z))));
	tmp = 0.0;
	if (t <= -2e+58)
		tmp = t_1;
	elseif (t <= 1.15e+74)
		tmp = (b * c) - (27.0 * (j * k));
	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[(a * -4.0), $MachinePrecision] + N[(x * N[(18.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2e+58], t$95$1, If[LessEqual[t, 1.15e+74], N[(N[(b * c), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.99999999999999989e58 or 1.1499999999999999e74 < t

   1. Initial program 80.1%

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

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 85.5%

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

   5. Taylor expanded in t around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(-4 \cdot a\right), \color{blue}{\left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \left(\color{blue}{18} \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \left(\left(x \cdot \left(y \cdot z\right)\right) \cdot \color{blue}{18}\right)\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \left(x \cdot \color{blue}{\left(\left(y \cdot z\right) \cdot 18\right)}\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \left(x \cdot \left(18 \cdot \color{blue}{\left(y \cdot z\right)}\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \mathsf{*.f64}\left(x, \color{blue}{\left(18 \cdot \left(y \cdot z\right)\right)}\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(18, \color{blue}{\left(y \cdot z\right)}\right)\right)\right)\right) \]

      9. *-lowering-*.f64 72.6%

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(y, \color{blue}{z}\right)\right)\right)\right)\right) \]

   7. Simplified 72.6%

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

   if -1.99999999999999989e58 < t < 1.1499999999999999e74

   1. Initial program 82.5%

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

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(b \cdot c\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 56.2%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

   5. Simplified 56.2%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(k \cdot \color{blue}{\left(j \cdot 27\right)}\right)\right) \]

      2. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\left(k \cdot j\right) \cdot \color{blue}{27}\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\left(j \cdot k\right) \cdot 27\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\left(j \cdot k\right), \color{blue}{27}\right)\right) \]

      5. *-lowering-*.f64 56.2%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, k\right), 27\right)\right) \]

   7. Applied egg-rr 56.2%

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

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{+58}:\\ \;\;\;\;t \cdot \left(a \cdot -4 + x \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+74}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot -4 + x \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 53.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c - \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;b \cdot c \leq -9 \cdot 10^{+137}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq 4 \cdot 10^{+123}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (- (* b c) (* (* j 27.0) k))))
   (if (<= (* b c) -9e+137)
     t_1
     (if (<= (* b c) 4e+123) (* -4.0 (+ (* t a) (* 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 = (b * c) - ((j * 27.0) * k);
	double tmp;
	if ((b * c) <= -9e+137) {
		tmp = t_1;
	} else if ((b * c) <= 4e+123) {
		tmp = -4.0 * ((t * a) + (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 = (b * c) - ((j * 27.0d0) * k)
    if ((b * c) <= (-9d+137)) then
        tmp = t_1
    else if ((b * c) <= 4d+123) then
        tmp = (-4.0d0) * ((t * a) + (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 = (b * c) - ((j * 27.0) * k);
	double tmp;
	if ((b * c) <= -9e+137) {
		tmp = t_1;
	} else if ((b * c) <= 4e+123) {
		tmp = -4.0 * ((t * a) + (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 = (b * c) - ((j * 27.0) * k)
	tmp = 0
	if (b * c) <= -9e+137:
		tmp = t_1
	elif (b * c) <= 4e+123:
		tmp = -4.0 * ((t * a) + (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(Float64(b * c) - Float64(Float64(j * 27.0) * k))
	tmp = 0.0
	if (Float64(b * c) <= -9e+137)
		tmp = t_1;
	elseif (Float64(b * c) <= 4e+123)
		tmp = Float64(-4.0 * Float64(Float64(t * a) + 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 = (b * c) - ((j * 27.0) * k);
	tmp = 0.0;
	if ((b * c) <= -9e+137)
		tmp = t_1;
	elseif ((b * c) <= 4e+123)
		tmp = -4.0 * ((t * a) + (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[(N[(b * c), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -9e+137], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 4e+123], N[(-4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -9.0000000000000003e137 or 3.99999999999999991e123 < (*.f64 b c)

   1. Initial program 78.2%

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

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(b \cdot c\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 75.2%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

   5. Simplified 75.2%

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

   if -9.0000000000000003e137 < (*.f64 b c) < 3.99999999999999991e123

   1. Initial program 83.1%

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

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 85.5%

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

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(-4 \cdot \left(a \cdot t\right)\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, k\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(-4 \cdot \left(t \cdot a\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(-27, \color{blue}{\mathsf{*.f64}\left(j, k\right)}\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

      2. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(-4 \cdot t\right) \cdot a\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, k\right)\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(t \cdot -4\right) \cdot a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\color{blue}{-27}, \mathsf{*.f64}\left(j, k\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(-4 \cdot a\right)\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, k\right)\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(-4 \cdot a\right)\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, k\right)\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 74.3%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(-4, a\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(-27, \color{blue}{\mathsf{*.f64}\left(j, k\right)}\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

   7. Simplified 74.3%

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

   8. Taylor expanded in j around 0

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

      1. +-commutative N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. +-commutative N/A

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

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(b \cdot c\right), \color{blue}{\left(-4 \cdot \left(a \cdot t\right) + -4 \cdot \left(i \cdot x\right)\right)}\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\color{blue}{-4 \cdot \left(a \cdot t\right)} + -4 \cdot \left(i \cdot x\right)\right)\right) \]

      7. distribute-lft-out N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(-4 \cdot \color{blue}{\left(a \cdot t + i \cdot x\right)}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(-4, \color{blue}{\left(a \cdot t + i \cdot x\right)}\right)\right) \]

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(-4, \mathsf{+.f64}\left(\left(a \cdot t\right), \color{blue}{\left(i \cdot x\right)}\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(-4, \mathsf{+.f64}\left(\left(t \cdot a\right), \left(\color{blue}{i} \cdot x\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(-4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, a\right), \left(\color{blue}{i} \cdot x\right)\right)\right)\right) \]

      12. *-lowering-*.f64 50.6%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(-4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, a\right), \mathsf{*.f64}\left(i, \color{blue}{x}\right)\right)\right)\right) \]

   10. Simplified 50.6%

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

   11. Taylor expanded in b around 0

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

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(-4, \color{blue}{\left(a \cdot t + i \cdot x\right)}\right) \]

       2. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(-4, \mathsf{+.f64}\left(\left(a \cdot t\right), \color{blue}{\left(i \cdot x\right)}\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(-4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, t\right), \left(\color{blue}{i} \cdot x\right)\right)\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(-4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, t\right), \left(x \cdot \color{blue}{i}\right)\right)\right) \]

       5. *-lowering-*.f64 46.9%

          \[\leadsto \mathsf{*.f64}\left(-4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, t\right), \mathsf{*.f64}\left(x, \color{blue}{i}\right)\right)\right) \]

   13. Simplified 46.9%

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

4. Final simplification 56.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -9 \cdot 10^{+137}:\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;b \cdot c \leq 4 \cdot 10^{+123}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 50.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2.1 \cdot 10^{+139}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq 9.5 \cdot 10^{+126}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

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
 (if (<= (* b c) -2.1e+139)
   (* b c)
   (if (<= (* b c) 9.5e+126) (* -4.0 (+ (* t a) (* x i))) (* 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 tmp;
	if ((b * c) <= -2.1e+139) {
		tmp = b * c;
	} else if ((b * c) <= 9.5e+126) {
		tmp = -4.0 * ((t * a) + (x * i));
	} 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) :: tmp
    if ((b * c) <= (-2.1d+139)) then
        tmp = b * c
    else if ((b * c) <= 9.5d+126) then
        tmp = (-4.0d0) * ((t * a) + (x * i))
    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 tmp;
	if ((b * c) <= -2.1e+139) {
		tmp = b * c;
	} else if ((b * c) <= 9.5e+126) {
		tmp = -4.0 * ((t * a) + (x * i));
	} 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):
	tmp = 0
	if (b * c) <= -2.1e+139:
		tmp = b * c
	elif (b * c) <= 9.5e+126:
		tmp = -4.0 * ((t * a) + (x * i))
	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)
	tmp = 0.0
	if (Float64(b * c) <= -2.1e+139)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= 9.5e+126)
		tmp = Float64(-4.0 * Float64(Float64(t * a) + Float64(x * i)));
	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)
	tmp = 0.0;
	if ((b * c) <= -2.1e+139)
		tmp = b * c;
	elseif ((b * c) <= 9.5e+126)
		tmp = -4.0 * ((t * a) + (x * i));
	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_] := If[LessEqual[N[(b * c), $MachinePrecision], -2.1e+139], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 9.5e+126], N[(-4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -2.0999999999999999e139 or 9.49999999999999951e126 < (*.f64 b c)

   1. Initial program 78.2%

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

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 80.5%

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

   5. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot c} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 62.8%

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{c}\right) \]

   7. Simplified 62.8%

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

   if -2.0999999999999999e139 < (*.f64 b c) < 9.49999999999999951e126

   1. Initial program 83.1%

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

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 85.5%

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

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(-4 \cdot \left(a \cdot t\right)\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, k\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(-4 \cdot \left(t \cdot a\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(-27, \color{blue}{\mathsf{*.f64}\left(j, k\right)}\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

      2. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(-4 \cdot t\right) \cdot a\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, k\right)\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(t \cdot -4\right) \cdot a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\color{blue}{-27}, \mathsf{*.f64}\left(j, k\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(-4 \cdot a\right)\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, k\right)\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(-4 \cdot a\right)\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, k\right)\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 74.3%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(-4, a\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(-27, \color{blue}{\mathsf{*.f64}\left(j, k\right)}\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

   7. Simplified 74.3%

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

   8. Taylor expanded in j around 0

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

      1. +-commutative N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. +-commutative N/A

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

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(b \cdot c\right), \color{blue}{\left(-4 \cdot \left(a \cdot t\right) + -4 \cdot \left(i \cdot x\right)\right)}\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\color{blue}{-4 \cdot \left(a \cdot t\right)} + -4 \cdot \left(i \cdot x\right)\right)\right) \]

      7. distribute-lft-out N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(-4 \cdot \color{blue}{\left(a \cdot t + i \cdot x\right)}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(-4, \color{blue}{\left(a \cdot t + i \cdot x\right)}\right)\right) \]

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(-4, \mathsf{+.f64}\left(\left(a \cdot t\right), \color{blue}{\left(i \cdot x\right)}\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(-4, \mathsf{+.f64}\left(\left(t \cdot a\right), \left(\color{blue}{i} \cdot x\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(-4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, a\right), \left(\color{blue}{i} \cdot x\right)\right)\right)\right) \]

      12. *-lowering-*.f64 50.6%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(-4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, a\right), \mathsf{*.f64}\left(i, \color{blue}{x}\right)\right)\right)\right) \]

   10. Simplified 50.6%

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

   11. Taylor expanded in b around 0

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

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(-4, \color{blue}{\left(a \cdot t + i \cdot x\right)}\right) \]

       2. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(-4, \mathsf{+.f64}\left(\left(a \cdot t\right), \color{blue}{\left(i \cdot x\right)}\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(-4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, t\right), \left(\color{blue}{i} \cdot x\right)\right)\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(-4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, t\right), \left(x \cdot \color{blue}{i}\right)\right)\right) \]

       5. *-lowering-*.f64 46.9%

          \[\leadsto \mathsf{*.f64}\left(-4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, t\right), \mathsf{*.f64}\left(x, \color{blue}{i}\right)\right)\right) \]

   13. Simplified 46.9%

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

4. Final simplification 52.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2.1 \cdot 10^{+139}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq 9.5 \cdot 10^{+126}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 48.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{+57}:\\ \;\;\;\;z \cdot \left(18 \cdot \left(y \cdot \left(x \cdot t\right)\right)\right)\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-120}:\\ \;\;\;\;b \cdot c + t \cdot \left(a \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + x \cdot \left(i \cdot -4\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= x -5.2e+57)
   (* z (* 18.0 (* y (* x t))))
   (if (<= x 1.25e-120)
     (+ (* b c) (* t (* a -4.0)))
     (+ (* b c) (* x (* i -4.0))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (x <= -5.2e+57) {
		tmp = z * (18.0 * (y * (x * t)));
	} else if (x <= 1.25e-120) {
		tmp = (b * c) + (t * (a * -4.0));
	} else {
		tmp = (b * c) + (x * (i * -4.0));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 <= (-5.2d+57)) then
        tmp = z * (18.0d0 * (y * (x * t)))
    else if (x <= 1.25d-120) then
        tmp = (b * c) + (t * (a * (-4.0d0)))
    else
        tmp = (b * c) + (x * (i * (-4.0d0)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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 <= -5.2e+57) {
		tmp = z * (18.0 * (y * (x * t)));
	} else if (x <= 1.25e-120) {
		tmp = (b * c) + (t * (a * -4.0));
	} else {
		tmp = (b * c) + (x * (i * -4.0));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if x <= -5.2e+57:
		tmp = z * (18.0 * (y * (x * t)))
	elif x <= 1.25e-120:
		tmp = (b * c) + (t * (a * -4.0))
	else:
		tmp = (b * c) + (x * (i * -4.0))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (x <= -5.2e+57)
		tmp = Float64(z * Float64(18.0 * Float64(y * Float64(x * t))));
	elseif (x <= 1.25e-120)
		tmp = Float64(Float64(b * c) + Float64(t * Float64(a * -4.0)));
	else
		tmp = Float64(Float64(b * c) + Float64(x * Float64(i * -4.0)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (x <= -5.2e+57)
		tmp = z * (18.0 * (y * (x * t)));
	elseif (x <= 1.25e-120)
		tmp = (b * c) + (t * (a * -4.0));
	else
		tmp = (b * c) + (x * (i * -4.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[x, -5.2e+57], N[(z * N[(18.0 * N[(y * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.25e-120], N[(N[(b * c), $MachinePrecision] + N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] + N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.2e57

   1. Initial program 66.6%

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

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 72.3%

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

   5. Taylor expanded in y around inf

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

      1. associate-*r* N/A

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

      2. associate-*r* N/A

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

      3. associate-*l* N/A

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

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(18 \cdot \left(t \cdot \left(x \cdot y\right)\right)\right), \color{blue}{z}\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(18, \left(t \cdot \left(x \cdot y\right)\right)\right), z\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(18, \left(\left(x \cdot y\right) \cdot t\right)\right), z\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(18, \left(\left(y \cdot x\right) \cdot t\right)\right), z\right) \]

      8. associate-*l* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(18, \left(y \cdot \left(x \cdot t\right)\right)\right), z\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(18, \mathsf{*.f64}\left(y, \left(x \cdot t\right)\right)\right), z\right) \]

      10. *-lowering-*.f64 53.2%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(18, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, t\right)\right)\right), z\right) \]

   7. Simplified 53.2%

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

   if -5.2e57 < x < 1.25000000000000002e-120

   1. Initial program 93.6%

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

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 94.4%

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

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(-4 \cdot \left(a \cdot t\right)\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, k\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(-4 \cdot \left(t \cdot a\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(-27, \color{blue}{\mathsf{*.f64}\left(j, k\right)}\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

      2. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(-4 \cdot t\right) \cdot a\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, k\right)\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(t \cdot -4\right) \cdot a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\color{blue}{-27}, \mathsf{*.f64}\left(j, k\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(-4 \cdot a\right)\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, k\right)\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(-4 \cdot a\right)\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, k\right)\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 82.3%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(-4, a\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(-27, \color{blue}{\mathsf{*.f64}\left(j, k\right)}\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

   7. Simplified 82.3%

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

   8. Taylor expanded in b around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(-4, a\right)\right), \color{blue}{\left(b \cdot c\right)}\right) \]
   9. Step-by-step derivation

      1. *-lowering-*.f64 54.1%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(-4, a\right)\right), \mathsf{*.f64}\left(b, \color{blue}{c}\right)\right) \]

   10. Simplified 54.1%

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

   if 1.25000000000000002e-120 < x

   1. Initial program 71.5%

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

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 74.1%

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

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(-4 \cdot \left(a \cdot t\right)\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, k\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(-4 \cdot \left(t \cdot a\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(-27, \color{blue}{\mathsf{*.f64}\left(j, k\right)}\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

      2. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(-4 \cdot t\right) \cdot a\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, k\right)\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(t \cdot -4\right) \cdot a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\color{blue}{-27}, \mathsf{*.f64}\left(j, k\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(-4 \cdot a\right)\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, k\right)\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(-4 \cdot a\right)\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, k\right)\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 69.9%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(-4, a\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(-27, \color{blue}{\mathsf{*.f64}\left(j, k\right)}\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

   7. Simplified 69.9%

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

   8. Taylor expanded in j around 0

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

      1. +-commutative N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. +-commutative N/A

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

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(b \cdot c\right), \color{blue}{\left(-4 \cdot \left(a \cdot t\right) + -4 \cdot \left(i \cdot x\right)\right)}\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\color{blue}{-4 \cdot \left(a \cdot t\right)} + -4 \cdot \left(i \cdot x\right)\right)\right) \]

      7. distribute-lft-out N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(-4 \cdot \color{blue}{\left(a \cdot t + i \cdot x\right)}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(-4, \color{blue}{\left(a \cdot t + i \cdot x\right)}\right)\right) \]

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(-4, \mathsf{+.f64}\left(\left(a \cdot t\right), \color{blue}{\left(i \cdot x\right)}\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(-4, \mathsf{+.f64}\left(\left(t \cdot a\right), \left(\color{blue}{i} \cdot x\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(-4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, a\right), \left(\color{blue}{i} \cdot x\right)\right)\right)\right) \]

      12. *-lowering-*.f64 53.7%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(-4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, a\right), \mathsf{*.f64}\left(i, \color{blue}{x}\right)\right)\right)\right) \]

   10. Simplified 53.7%

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

   11. Taylor expanded in t around 0

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

       1. +-commutative N/A

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

       2. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\left(b \cdot c\right), \color{blue}{\left(-4 \cdot \left(i \cdot x\right)\right)}\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\color{blue}{-4} \cdot \left(i \cdot x\right)\right)\right) \]

       4. associate-*r* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\left(-4 \cdot i\right) \cdot \color{blue}{x}\right)\right) \]

       5. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(x \cdot \color{blue}{\left(-4 \cdot i\right)}\right)\right) \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \color{blue}{\left(-4 \cdot i\right)}\right)\right) \]

       7. *-lowering-*.f64 52.5%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(-4, \color{blue}{i}\right)\right)\right) \]

   13. Simplified 52.5%

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

4. Final simplification 53.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{+57}:\\ \;\;\;\;z \cdot \left(18 \cdot \left(y \cdot \left(x \cdot t\right)\right)\right)\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-120}:\\ \;\;\;\;b \cdot c + t \cdot \left(a \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + x \cdot \left(i \cdot -4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 35.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -3.95 \cdot 10^{+130}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq 1.85 \cdot 10^{+97}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

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
 (if (<= (* b c) -3.95e+130)
   (* b c)
   (if (<= (* b c) 1.85e+97) (* -4.0 (* x i)) (* 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 tmp;
	if ((b * c) <= -3.95e+130) {
		tmp = b * c;
	} else if ((b * c) <= 1.85e+97) {
		tmp = -4.0 * (x * i);
	} 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) :: tmp
    if ((b * c) <= (-3.95d+130)) then
        tmp = b * c
    else if ((b * c) <= 1.85d+97) then
        tmp = (-4.0d0) * (x * i)
    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 tmp;
	if ((b * c) <= -3.95e+130) {
		tmp = b * c;
	} else if ((b * c) <= 1.85e+97) {
		tmp = -4.0 * (x * i);
	} 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):
	tmp = 0
	if (b * c) <= -3.95e+130:
		tmp = b * c
	elif (b * c) <= 1.85e+97:
		tmp = -4.0 * (x * i)
	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)
	tmp = 0.0
	if (Float64(b * c) <= -3.95e+130)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= 1.85e+97)
		tmp = Float64(-4.0 * Float64(x * i));
	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)
	tmp = 0.0;
	if ((b * c) <= -3.95e+130)
		tmp = b * c;
	elseif ((b * c) <= 1.85e+97)
		tmp = -4.0 * (x * i);
	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_] := If[LessEqual[N[(b * c), $MachinePrecision], -3.95e+130], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1.85e+97], N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -3.9500000000000002e130 or 1.85e97 < (*.f64 b c)

   1. Initial program 78.1%

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

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 81.3%

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

   5. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot c} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 58.2%

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{c}\right) \]

   7. Simplified 58.2%

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

   if -3.9500000000000002e130 < (*.f64 b c) < 1.85e97

   1. Initial program 83.4%

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

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 85.3%

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

   5. Taylor expanded in i around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-4, \color{blue}{\left(i \cdot x\right)}\right) \]

      2. *-lowering-*.f64 26.6%

         \[\leadsto \mathsf{*.f64}\left(-4, \mathsf{*.f64}\left(i, \color{blue}{x}\right)\right) \]

   7. Simplified 26.6%

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

4. Final simplification 38.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -3.95 \cdot 10^{+130}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq 1.85 \cdot 10^{+97}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 23.3% 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 81.5%

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

   1. associate--l+ N/A

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

   2. associate--l+ N/A

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

   3. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

   4. distribute-rgt-out-- N/A

      \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

   5. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

   6. sub-neg N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   7. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   8. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   9. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   10. *-lowering-*.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   11. distribute-rgt-neg-in N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   12. *-lowering-*.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   13. metadata-eval N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

3. Simplified 83.8%

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

5. Taylor expanded in b around inf

   \[\leadsto \color{blue}{b \cdot c} \]
6. Step-by-step derivation

   1. *-lowering-*.f64 24.8%

      \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{c}\right) \]

7. Simplified 24.8%

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

Developer Target 1: 89.4% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024163 
(FPCore (x y z t a b c i j k)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, E"
  :precision binary64

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

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