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

Percentage Accurate: 85.1% → 91.3%

Time: 36.8s

Alternatives: 23

Speedup: 0.8×

• 50.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 91.3% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (x * 4.0) * i
	t_2 = (j * 27.0) * k
	t_3 = t * (a * 4.0)
	tmp = 0
	if ((((((((x * 18.0) * y) * z) * t) - t_3) + (b * c)) - t_1) - t_2) <= math.inf:
		tmp = (((b * c) + ((t * (y * ((x * 18.0) * z))) - t_3)) - t_1) - t_2
	else:
		tmp = x * (((-27.0 * ((j * k) / x)) - (z * (y * (t * -18.0)))) - (i * 4.0))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(x * 4.0) * i)
	t_2 = Float64(Float64(j * 27.0) * k)
	t_3 = Float64(t * Float64(a * 4.0))
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 18.0) * y) * z) * t) - t_3) + Float64(b * c)) - t_1) - t_2) <= Inf)
		tmp = Float64(Float64(Float64(Float64(b * c) + Float64(Float64(t * Float64(y * Float64(Float64(x * 18.0) * z))) - t_3)) - t_1) - t_2);
	else
		tmp = Float64(x * Float64(Float64(Float64(-27.0 * Float64(Float64(j * k) / x)) - Float64(z * Float64(y * Float64(t * -18.0)))) - Float64(i * 4.0)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (x * 4.0) * i;
	t_2 = (j * 27.0) * k;
	t_3 = t * (a * 4.0);
	tmp = 0.0;
	if (((((((((x * 18.0) * y) * z) * t) - t_3) + (b * c)) - t_1) - t_2) <= Inf)
		tmp = (((b * c) + ((t * (y * ((x * 18.0) * z))) - t_3)) - t_1) - t_2;
	else
		tmp = x * (((-27.0 * ((j * k) / x)) - (z * (y * (t * -18.0)))) - (i * 4.0));
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 97.4%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

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

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

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

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

      5. *-lowering-*.f64 95.3%

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

   4. Applied egg-rr 95.3%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in x around -inf

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

   5. Simplified 48.0%

      \[\leadsto \color{blue}{\left(4 \cdot i + \left(\left(\left(t \cdot -18\right) \cdot y\right) \cdot z - \frac{b \cdot c + \left(j \cdot \left(k \cdot -27\right) + -4 \cdot \left(a \cdot t\right)\right)}{x}\right)\right) \cdot \left(0 - x\right)} \]

   6. Taylor expanded in j around inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(4, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(t, -18\right), y\right), z\right), \color{blue}{\left(-27 \cdot \frac{j \cdot k}{x}\right)}\right)\right), \mathsf{\_.f64}\left(0, x\right)\right) \]
   7. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(4, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(t, -18\right), y\right), z\right), \mathsf{*.f64}\left(-27, \left(\frac{j \cdot k}{x}\right)\right)\right)\right), \mathsf{\_.f64}\left(0, x\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(4, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(t, -18\right), y\right), z\right), \mathsf{*.f64}\left(-27, \mathsf{/.f64}\left(\left(j \cdot k\right), x\right)\right)\right)\right), \mathsf{\_.f64}\left(0, x\right)\right) \]

      3. *-lowering-*.f64 76.0%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(4, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(t, -18\right), y\right), z\right), \mathsf{*.f64}\left(-27, \mathsf{/.f64}\left(\mathsf{*.f64}\left(j, k\right), x\right)\right)\right)\right), \mathsf{\_.f64}\left(0, x\right)\right) \]

   8. Simplified 76.0%

      \[\leadsto \left(4 \cdot i + \left(\left(\left(t \cdot -18\right) \cdot y\right) \cdot z - \color{blue}{-27 \cdot \frac{j \cdot k}{x}}\right)\right) \cdot \left(0 - x\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 93.4%

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

Alternative 2: 49.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := x \cdot \left(t \cdot \left(18 \cdot \left(y \cdot z\right)\right) + i \cdot -4\right)\\ \mathbf{if}\;j \cdot 27 \leq -1 \cdot 10^{+157}:\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;j \cdot 27 \leq -1 \cdot 10^{-53}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \cdot 27 \leq 5 \cdot 10^{-196}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;j \cdot 27 \leq 10^{-78}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot -4 + \frac{j \cdot \left(k \cdot -27\right)}{t}\right)\\ \end{array} \end{array} \]

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 (+ (* t (* 18.0 (* y z))) (* i -4.0)))))
   (if (<= (* j 27.0) -1e+157)
     (- (* b c) (* (* j 27.0) k))
     (if (<= (* j 27.0) -1e-53)
       t_1
       (if (<= (* j 27.0) 5e-196)
         (+ (* b c) (* -4.0 (* t a)))
         (if (<= (* j 27.0) 1e-78)
           t_1
           (* t (+ (* a -4.0) (/ (* j (* k -27.0)) t)))))))))

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 * ((t * (18.0 * (y * z))) + (i * -4.0));
	double tmp;
	if ((j * 27.0) <= -1e+157) {
		tmp = (b * c) - ((j * 27.0) * k);
	} else if ((j * 27.0) <= -1e-53) {
		tmp = t_1;
	} else if ((j * 27.0) <= 5e-196) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else if ((j * 27.0) <= 1e-78) {
		tmp = t_1;
	} else {
		tmp = t * ((a * -4.0) + ((j * (k * -27.0)) / t));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 * ((t * (18.0d0 * (y * z))) + (i * (-4.0d0)))
    if ((j * 27.0d0) <= (-1d+157)) then
        tmp = (b * c) - ((j * 27.0d0) * k)
    else if ((j * 27.0d0) <= (-1d-53)) then
        tmp = t_1
    else if ((j * 27.0d0) <= 5d-196) then
        tmp = (b * c) + ((-4.0d0) * (t * a))
    else if ((j * 27.0d0) <= 1d-78) then
        tmp = t_1
    else
        tmp = t * ((a * (-4.0d0)) + ((j * (k * (-27.0d0))) / t))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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 * ((t * (18.0 * (y * z))) + (i * -4.0));
	double tmp;
	if ((j * 27.0) <= -1e+157) {
		tmp = (b * c) - ((j * 27.0) * k);
	} else if ((j * 27.0) <= -1e-53) {
		tmp = t_1;
	} else if ((j * 27.0) <= 5e-196) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else if ((j * 27.0) <= 1e-78) {
		tmp = t_1;
	} else {
		tmp = t * ((a * -4.0) + ((j * (k * -27.0)) / t));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = x * ((t * (18.0 * (y * z))) + (i * -4.0))
	tmp = 0
	if (j * 27.0) <= -1e+157:
		tmp = (b * c) - ((j * 27.0) * k)
	elif (j * 27.0) <= -1e-53:
		tmp = t_1
	elif (j * 27.0) <= 5e-196:
		tmp = (b * c) + (-4.0 * (t * a))
	elif (j * 27.0) <= 1e-78:
		tmp = t_1
	else:
		tmp = t * ((a * -4.0) + ((j * (k * -27.0)) / t))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(x * Float64(Float64(t * Float64(18.0 * Float64(y * z))) + Float64(i * -4.0)))
	tmp = 0.0
	if (Float64(j * 27.0) <= -1e+157)
		tmp = Float64(Float64(b * c) - Float64(Float64(j * 27.0) * k));
	elseif (Float64(j * 27.0) <= -1e-53)
		tmp = t_1;
	elseif (Float64(j * 27.0) <= 5e-196)
		tmp = Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a)));
	elseif (Float64(j * 27.0) <= 1e-78)
		tmp = t_1;
	else
		tmp = Float64(t * Float64(Float64(a * -4.0) + Float64(Float64(j * Float64(k * -27.0)) / t)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = x * ((t * (18.0 * (y * z))) + (i * -4.0));
	tmp = 0.0;
	if ((j * 27.0) <= -1e+157)
		tmp = (b * c) - ((j * 27.0) * k);
	elseif ((j * 27.0) <= -1e-53)
		tmp = t_1;
	elseif ((j * 27.0) <= 5e-196)
		tmp = (b * c) + (-4.0 * (t * a));
	elseif ((j * 27.0) <= 1e-78)
		tmp = t_1;
	else
		tmp = t * ((a * -4.0) + ((j * (k * -27.0)) / t));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(x * N[(N[(t * N[(18.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(j * 27.0), $MachinePrecision], -1e+157], N[(N[(b * c), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(j * 27.0), $MachinePrecision], -1e-53], t$95$1, If[LessEqual[N[(j * 27.0), $MachinePrecision], 5e-196], N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(j * 27.0), $MachinePrecision], 1e-78], t$95$1, N[(t * N[(N[(a * -4.0), $MachinePrecision] + N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 j #s(literal 27 binary64)) < -9.99999999999999983e156

   1. Initial program 74.9%

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

   3. Taylor expanded in 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 70.8%

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

   5. Simplified 70.8%

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

   if -9.99999999999999983e156 < (*.f64 j #s(literal 27 binary64)) < -1.00000000000000003e-53 or 5.0000000000000005e-196 < (*.f64 j #s(literal 27 binary64)) < 9.99999999999999999e-79

   1. Initial program 92.7%

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

   3. Taylor expanded in x around inf

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

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

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

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

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

      3. metadata-eval N/A

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

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

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

      5. *-commutative N/A

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

      6. associate-*l* N/A

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

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

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

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

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

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

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

      10. *-lowering-*.f64 50.3%

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

   5. Simplified 50.3%

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

   if -1.00000000000000003e-53 < (*.f64 j #s(literal 27 binary64)) < 5.0000000000000005e-196

   1. Initial program 89.7%

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

   3. Taylor expanded in x around 0

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

      1. sub-neg N/A

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

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

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

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

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

      4. +-commutative N/A

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

      5. distribute-neg-in N/A

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

      6. distribute-lft-neg-in N/A

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

      7. metadata-eval N/A

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

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

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

      9. *-commutative N/A

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

      10. associate-*l* N/A

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

      11. *-commutative N/A

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

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

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

      13. *-commutative N/A

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

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

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

      15. distribute-lft-neg-in N/A

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

      16. metadata-eval N/A

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

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

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

      18. *-lowering-*.f64 60.7%

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

   5. Simplified 60.7%

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

   6. Taylor expanded in j around 0

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

      1. +-commutative N/A

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

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

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

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

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

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

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 57.0%

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

   8. Simplified 57.0%

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

   if 9.99999999999999999e-79 < (*.f64 j #s(literal 27 binary64))

   1. Initial program 87.1%

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

   3. Taylor expanded in x around 0

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

      1. sub-neg N/A

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

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

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

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

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

      4. +-commutative N/A

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

      5. distribute-neg-in N/A

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

      6. distribute-lft-neg-in N/A

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

      7. metadata-eval N/A

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

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

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

      9. *-commutative N/A

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

      10. associate-*l* N/A

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

      11. *-commutative N/A

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

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

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

      13. *-commutative N/A

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

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

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

      15. distribute-lft-neg-in N/A

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

      16. metadata-eval N/A

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

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

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

      18. *-lowering-*.f64 71.4%

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

   5. Simplified 71.4%

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

   6. Taylor expanded in t around inf

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

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

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. metadata-eval N/A

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

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

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

      6. associate-*r/ N/A

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

      7. div-sub N/A

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

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

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

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

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

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

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

   8. Simplified 63.1%

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

   9. Taylor expanded in b around 0

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

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

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

       2. +-commutative N/A

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

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

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

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

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

       5. associate-*r/ N/A

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

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

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

       7. *-commutative N/A

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

       8. associate-*r* N/A

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

       9. *-commutative N/A

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

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

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

       11. *-commutative N/A

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

       12. *-lowering-*.f64 54.2%

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

   11. Simplified 54.2%

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

4. Final simplification 56.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \cdot 27 \leq -1 \cdot 10^{+157}:\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;j \cdot 27 \leq -1 \cdot 10^{-53}:\\ \;\;\;\;x \cdot \left(t \cdot \left(18 \cdot \left(y \cdot z\right)\right) + i \cdot -4\right)\\ \mathbf{elif}\;j \cdot 27 \leq 5 \cdot 10^{-196}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;j \cdot 27 \leq 10^{-78}:\\ \;\;\;\;x \cdot \left(t \cdot \left(18 \cdot \left(y \cdot z\right)\right) + i \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot -4 + \frac{j \cdot \left(k \cdot -27\right)}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 88.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := x \cdot \left(\left(-27 \cdot \frac{j \cdot k}{x} - z \cdot \left(y \cdot \left(t \cdot -18\right)\right)\right) - i \cdot 4\right)\\ \mathbf{if}\;x \leq -4 \cdot 10^{+82}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.32 \cdot 10^{+213}:\\ \;\;\;\;\left(t \cdot \left(z \cdot \left(x \cdot \left(18 \cdot y\right)\right) + a \cdot -4\right) + \left(b \cdot c + -4 \cdot \left(x \cdot i\right)\right)\right) - \left(j \cdot k\right) \cdot 27\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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
          (- (- (* -27.0 (/ (* j k) x)) (* z (* y (* t -18.0)))) (* i 4.0)))))
   (if (<= x -4e+82)
     t_1
     (if (<= x 1.32e+213)
       (-
        (+
         (* t (+ (* z (* x (* 18.0 y))) (* a -4.0)))
         (+ (* b c) (* -4.0 (* x i))))
        (* (* j k) 27.0))
       t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = x * (((-27.0 * ((j * k) / x)) - (z * (y * (t * -18.0)))) - (i * 4.0));
	double tmp;
	if (x <= -4e+82) {
		tmp = t_1;
	} else if (x <= 1.32e+213) {
		tmp = ((t * ((z * (x * (18.0 * y))) + (a * -4.0))) + ((b * c) + (-4.0 * (x * i)))) - ((j * k) * 27.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((((-27.0d0) * ((j * k) / x)) - (z * (y * (t * (-18.0d0))))) - (i * 4.0d0))
    if (x <= (-4d+82)) then
        tmp = t_1
    else if (x <= 1.32d+213) then
        tmp = ((t * ((z * (x * (18.0d0 * y))) + (a * (-4.0d0)))) + ((b * c) + ((-4.0d0) * (x * i)))) - ((j * k) * 27.0d0)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = x * (((-27.0 * ((j * k) / x)) - (z * (y * (t * -18.0)))) - (i * 4.0));
	double tmp;
	if (x <= -4e+82) {
		tmp = t_1;
	} else if (x <= 1.32e+213) {
		tmp = ((t * ((z * (x * (18.0 * y))) + (a * -4.0))) + ((b * c) + (-4.0 * (x * i)))) - ((j * k) * 27.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = x * (((-27.0 * ((j * k) / x)) - (z * (y * (t * -18.0)))) - (i * 4.0))
	tmp = 0
	if x <= -4e+82:
		tmp = t_1
	elif x <= 1.32e+213:
		tmp = ((t * ((z * (x * (18.0 * y))) + (a * -4.0))) + ((b * c) + (-4.0 * (x * i)))) - ((j * k) * 27.0)
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(x * Float64(Float64(Float64(-27.0 * Float64(Float64(j * k) / x)) - Float64(z * Float64(y * Float64(t * -18.0)))) - Float64(i * 4.0)))
	tmp = 0.0
	if (x <= -4e+82)
		tmp = t_1;
	elseif (x <= 1.32e+213)
		tmp = Float64(Float64(Float64(t * Float64(Float64(z * Float64(x * Float64(18.0 * y))) + Float64(a * -4.0))) + Float64(Float64(b * c) + Float64(-4.0 * Float64(x * i)))) - Float64(Float64(j * k) * 27.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = x * (((-27.0 * ((j * k) / x)) - (z * (y * (t * -18.0)))) - (i * 4.0));
	tmp = 0.0;
	if (x <= -4e+82)
		tmp = t_1;
	elseif (x <= 1.32e+213)
		tmp = ((t * ((z * (x * (18.0 * y))) + (a * -4.0))) + ((b * c) + (-4.0 * (x * i)))) - ((j * k) * 27.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(x * N[(N[(N[(-27.0 * N[(N[(j * k), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] - N[(z * N[(y * N[(t * -18.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4e+82], t$95$1, If[LessEqual[x, 1.32e+213], N[(N[(N[(t * N[(N[(z * N[(x * N[(18.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * k), $MachinePrecision] * 27.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -3.9999999999999999e82 or 1.32e213 < x

   1. Initial program 69.1%

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

   3. Taylor expanded in x around -inf

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

   5. Simplified 90.8%

      \[\leadsto \color{blue}{\left(4 \cdot i + \left(\left(\left(t \cdot -18\right) \cdot y\right) \cdot z - \frac{b \cdot c + \left(j \cdot \left(k \cdot -27\right) + -4 \cdot \left(a \cdot t\right)\right)}{x}\right)\right) \cdot \left(0 - x\right)} \]

   6. Taylor expanded in j around inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(4, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(t, -18\right), y\right), z\right), \color{blue}{\left(-27 \cdot \frac{j \cdot k}{x}\right)}\right)\right), \mathsf{\_.f64}\left(0, x\right)\right) \]
   7. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(4, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(t, -18\right), y\right), z\right), \mathsf{*.f64}\left(-27, \left(\frac{j \cdot k}{x}\right)\right)\right)\right), \mathsf{\_.f64}\left(0, x\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(4, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(t, -18\right), y\right), z\right), \mathsf{*.f64}\left(-27, \mathsf{/.f64}\left(\left(j \cdot k\right), x\right)\right)\right)\right), \mathsf{\_.f64}\left(0, x\right)\right) \]

      3. *-lowering-*.f64 90.2%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(4, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(t, -18\right), y\right), z\right), \mathsf{*.f64}\left(-27, \mathsf{/.f64}\left(\mathsf{*.f64}\left(j, k\right), x\right)\right)\right)\right), \mathsf{\_.f64}\left(0, x\right)\right) \]

   8. Simplified 90.2%

      \[\leadsto \left(4 \cdot i + \left(\left(\left(t \cdot -18\right) \cdot y\right) \cdot z - \color{blue}{-27 \cdot \frac{j \cdot k}{x}}\right)\right) \cdot \left(0 - x\right) \]

   if -3.9999999999999999e82 < x < 1.32e213

   1. Initial program 93.0%

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

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

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

   4. Applied egg-rr 94.0%

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

4. Final simplification 93.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+82}:\\ \;\;\;\;x \cdot \left(\left(-27 \cdot \frac{j \cdot k}{x} - z \cdot \left(y \cdot \left(t \cdot -18\right)\right)\right) - i \cdot 4\right)\\ \mathbf{elif}\;x \leq 1.32 \cdot 10^{+213}:\\ \;\;\;\;\left(t \cdot \left(z \cdot \left(x \cdot \left(18 \cdot y\right)\right) + a \cdot -4\right) + \left(b \cdot c + -4 \cdot \left(x \cdot i\right)\right)\right) - \left(j \cdot k\right) \cdot 27\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(-27 \cdot \frac{j \cdot k}{x} - z \cdot \left(y \cdot \left(t \cdot -18\right)\right)\right) - i \cdot 4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 54.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+141}:\\ \;\;\;\;c \cdot \left(b + \frac{k \cdot \left(j \cdot -27\right)}{c}\right)\\ \mathbf{elif}\;t\_1 \leq -1 \cdot 10^{+97}:\\ \;\;\;\;\left(18 \cdot \left(x \cdot z\right)\right) \cdot \left(y \cdot t\right)\\ \mathbf{elif}\;t\_1 \leq 10^{+93}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - \left(j \cdot k\right) \cdot 27\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)))
   (if (<= t_1 -2e+141)
     (* c (+ b (/ (* k (* j -27.0)) c)))
     (if (<= t_1 -1e+97)
       (* (* 18.0 (* x z)) (* y t))
       (if (<= t_1 1e+93)
         (+ (* b c) (* -4.0 (* t a)))
         (- (* b c) (* (* j k) 27.0)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (t_1 <= -2e+141) {
		tmp = c * (b + ((k * (j * -27.0)) / c));
	} else if (t_1 <= -1e+97) {
		tmp = (18.0 * (x * z)) * (y * t);
	} else if (t_1 <= 1e+93) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else {
		tmp = (b * c) - ((j * k) * 27.0);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (j * 27.0d0) * k
    if (t_1 <= (-2d+141)) then
        tmp = c * (b + ((k * (j * (-27.0d0))) / c))
    else if (t_1 <= (-1d+97)) then
        tmp = (18.0d0 * (x * z)) * (y * t)
    else if (t_1 <= 1d+93) then
        tmp = (b * c) + ((-4.0d0) * (t * a))
    else
        tmp = (b * c) - ((j * k) * 27.0d0)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (t_1 <= -2e+141) {
		tmp = c * (b + ((k * (j * -27.0)) / c));
	} else if (t_1 <= -1e+97) {
		tmp = (18.0 * (x * z)) * (y * t);
	} else if (t_1 <= 1e+93) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else {
		tmp = (b * c) - ((j * k) * 27.0);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	tmp = 0
	if t_1 <= -2e+141:
		tmp = c * (b + ((k * (j * -27.0)) / c))
	elif t_1 <= -1e+97:
		tmp = (18.0 * (x * z)) * (y * t)
	elif t_1 <= 1e+93:
		tmp = (b * c) + (-4.0 * (t * a))
	else:
		tmp = (b * c) - ((j * k) * 27.0)
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_1 <= -2e+141)
		tmp = Float64(c * Float64(b + Float64(Float64(k * Float64(j * -27.0)) / c)));
	elseif (t_1 <= -1e+97)
		tmp = Float64(Float64(18.0 * Float64(x * z)) * Float64(y * t));
	elseif (t_1 <= 1e+93)
		tmp = Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a)));
	else
		tmp = Float64(Float64(b * c) - Float64(Float64(j * k) * 27.0));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * 27.0) * k;
	tmp = 0.0;
	if (t_1 <= -2e+141)
		tmp = c * (b + ((k * (j * -27.0)) / c));
	elseif (t_1 <= -1e+97)
		tmp = (18.0 * (x * z)) * (y * t);
	elseif (t_1 <= 1e+93)
		tmp = (b * c) + (-4.0 * (t * a));
	else
		tmp = (b * c) - ((j * k) * 27.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+141], N[(c * N[(b + N[(N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -1e+97], N[(N[(18.0 * N[(x * z), $MachinePrecision]), $MachinePrecision] * N[(y * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+93], N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] - N[(N[(j * k), $MachinePrecision] * 27.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -2.00000000000000003e141

   1. Initial program 75.2%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   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 79.1%

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

   5. Simplified 79.1%

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

   6. Taylor expanded in c around inf

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

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

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

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

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

      3. associate-*r/ N/A

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

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

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

      5. associate-*r* N/A

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

      6. *-commutative N/A

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

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

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

      8. *-commutative N/A

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

      9. *-lowering-*.f64 76.5%

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

   8. Simplified 76.5%

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

   if -2.00000000000000003e141 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -1.0000000000000001e97

   1. Initial program 99.8%

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

   3. Taylor expanded in x around -inf

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

   5. Simplified 78.2%

      \[\leadsto \color{blue}{\left(4 \cdot i + \left(\left(\left(t \cdot -18\right) \cdot y\right) \cdot z - \frac{b \cdot c + \left(j \cdot \left(k \cdot -27\right) + -4 \cdot \left(a \cdot t\right)\right)}{x}\right)\right) \cdot \left(0 - x\right)} \]

   6. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

         \[\leadsto \left(\left(x \cdot \left(y \cdot z\right)\right) \cdot t\right) \cdot 18 \]

      3. associate-*l* N/A

         \[\leadsto \left(x \cdot \left(\left(y \cdot z\right) \cdot t\right)\right) \cdot 18 \]

      4. *-commutative N/A

         \[\leadsto \left(x \cdot \left(t \cdot \left(y \cdot z\right)\right)\right) \cdot 18 \]

      5. associate-*r* N/A

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

      6. *-commutative N/A

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

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

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

      8. *-commutative N/A

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

      9. associate-*r* N/A

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

      10. *-commutative N/A

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

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

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

      12. *-commutative N/A

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

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

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

      14. *-lowering-*.f64 59.7%

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

   8. Simplified 59.7%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. associate-*l* N/A

         \[\leadsto \left(\left(x \cdot \left(y \cdot z\right)\right) \cdot 18\right) \cdot t \]

      4. *-commutative N/A

         \[\leadsto \left(\left(x \cdot \left(z \cdot y\right)\right) \cdot 18\right) \cdot t \]

      5. associate-*l* N/A

         \[\leadsto \left(\left(\left(x \cdot z\right) \cdot y\right) \cdot 18\right) \cdot t \]

      6. *-commutative N/A

         \[\leadsto \left(18 \cdot \left(\left(x \cdot z\right) \cdot y\right)\right) \cdot t \]

      7. associate-*r* N/A

         \[\leadsto \left(\left(18 \cdot \left(x \cdot z\right)\right) \cdot y\right) \cdot t \]

      8. associate-*l* N/A

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

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

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

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

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

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

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

      12. *-lowering-*.f64 58.0%

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

   10. Applied egg-rr 58.0%

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

   if -1.0000000000000001e97 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 1.00000000000000004e93

   1. Initial program 90.7%

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

   3. Taylor expanded in x around 0

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

      1. sub-neg N/A

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

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

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

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

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

      4. +-commutative N/A

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

      5. distribute-neg-in N/A

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

      6. distribute-lft-neg-in N/A

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

      7. metadata-eval N/A

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

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

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

      9. *-commutative N/A

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

      10. associate-*l* N/A

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

      11. *-commutative N/A

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

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

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

      13. *-commutative N/A

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

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

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

      15. distribute-lft-neg-in N/A

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

      16. metadata-eval N/A

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

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

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

      18. *-lowering-*.f64 55.0%

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

   5. Simplified 55.0%

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

   6. Taylor expanded in j around 0

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

      1. +-commutative N/A

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

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

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

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

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

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

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 51.6%

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

   8. Simplified 51.6%

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

   if 1.00000000000000004e93 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 83.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   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 78.2%

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

   5. Simplified 78.2%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      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 78.2%

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

   7. Applied egg-rr 78.2%

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

Alternative 5: 55.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+141}:\\ \;\;\;\;b \cdot c - t\_1\\ \mathbf{elif}\;t\_1 \leq -1 \cdot 10^{+97}:\\ \;\;\;\;\left(18 \cdot \left(x \cdot z\right)\right) \cdot \left(y \cdot t\right)\\ \mathbf{elif}\;t\_1 \leq 10^{+93}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - \left(j \cdot k\right) \cdot 27\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)))
   (if (<= t_1 -2e+141)
     (- (* b c) t_1)
     (if (<= t_1 -1e+97)
       (* (* 18.0 (* x z)) (* y t))
       (if (<= t_1 1e+93)
         (+ (* b c) (* -4.0 (* t a)))
         (- (* b c) (* (* j k) 27.0)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (t_1 <= -2e+141) {
		tmp = (b * c) - t_1;
	} else if (t_1 <= -1e+97) {
		tmp = (18.0 * (x * z)) * (y * t);
	} else if (t_1 <= 1e+93) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else {
		tmp = (b * c) - ((j * k) * 27.0);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (j * 27.0d0) * k
    if (t_1 <= (-2d+141)) then
        tmp = (b * c) - t_1
    else if (t_1 <= (-1d+97)) then
        tmp = (18.0d0 * (x * z)) * (y * t)
    else if (t_1 <= 1d+93) then
        tmp = (b * c) + ((-4.0d0) * (t * a))
    else
        tmp = (b * c) - ((j * k) * 27.0d0)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (t_1 <= -2e+141) {
		tmp = (b * c) - t_1;
	} else if (t_1 <= -1e+97) {
		tmp = (18.0 * (x * z)) * (y * t);
	} else if (t_1 <= 1e+93) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else {
		tmp = (b * c) - ((j * k) * 27.0);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	tmp = 0
	if t_1 <= -2e+141:
		tmp = (b * c) - t_1
	elif t_1 <= -1e+97:
		tmp = (18.0 * (x * z)) * (y * t)
	elif t_1 <= 1e+93:
		tmp = (b * c) + (-4.0 * (t * a))
	else:
		tmp = (b * c) - ((j * k) * 27.0)
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_1 <= -2e+141)
		tmp = Float64(Float64(b * c) - t_1);
	elseif (t_1 <= -1e+97)
		tmp = Float64(Float64(18.0 * Float64(x * z)) * Float64(y * t));
	elseif (t_1 <= 1e+93)
		tmp = Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a)));
	else
		tmp = Float64(Float64(b * c) - Float64(Float64(j * k) * 27.0));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * 27.0) * k;
	tmp = 0.0;
	if (t_1 <= -2e+141)
		tmp = (b * c) - t_1;
	elseif (t_1 <= -1e+97)
		tmp = (18.0 * (x * z)) * (y * t);
	elseif (t_1 <= 1e+93)
		tmp = (b * c) + (-4.0 * (t * a));
	else
		tmp = (b * c) - ((j * k) * 27.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+141], N[(N[(b * c), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[t$95$1, -1e+97], N[(N[(18.0 * N[(x * z), $MachinePrecision]), $MachinePrecision] * N[(y * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+93], N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] - N[(N[(j * k), $MachinePrecision] * 27.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -2.00000000000000003e141

   1. Initial program 75.2%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   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 79.1%

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

   5. Simplified 79.1%

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

   if -2.00000000000000003e141 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -1.0000000000000001e97

   1. Initial program 99.8%

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

   3. Taylor expanded in x around -inf

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

   5. Simplified 78.2%

      \[\leadsto \color{blue}{\left(4 \cdot i + \left(\left(\left(t \cdot -18\right) \cdot y\right) \cdot z - \frac{b \cdot c + \left(j \cdot \left(k \cdot -27\right) + -4 \cdot \left(a \cdot t\right)\right)}{x}\right)\right) \cdot \left(0 - x\right)} \]

   6. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

         \[\leadsto \left(\left(x \cdot \left(y \cdot z\right)\right) \cdot t\right) \cdot 18 \]

      3. associate-*l* N/A

         \[\leadsto \left(x \cdot \left(\left(y \cdot z\right) \cdot t\right)\right) \cdot 18 \]

      4. *-commutative N/A

         \[\leadsto \left(x \cdot \left(t \cdot \left(y \cdot z\right)\right)\right) \cdot 18 \]

      5. associate-*r* N/A

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

      6. *-commutative N/A

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

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

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

      8. *-commutative N/A

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

      9. associate-*r* N/A

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

      10. *-commutative N/A

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

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

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

      12. *-commutative N/A

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

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

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

      14. *-lowering-*.f64 59.7%

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

   8. Simplified 59.7%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. associate-*l* N/A

         \[\leadsto \left(\left(x \cdot \left(y \cdot z\right)\right) \cdot 18\right) \cdot t \]

      4. *-commutative N/A

         \[\leadsto \left(\left(x \cdot \left(z \cdot y\right)\right) \cdot 18\right) \cdot t \]

      5. associate-*l* N/A

         \[\leadsto \left(\left(\left(x \cdot z\right) \cdot y\right) \cdot 18\right) \cdot t \]

      6. *-commutative N/A

         \[\leadsto \left(18 \cdot \left(\left(x \cdot z\right) \cdot y\right)\right) \cdot t \]

      7. associate-*r* N/A

         \[\leadsto \left(\left(18 \cdot \left(x \cdot z\right)\right) \cdot y\right) \cdot t \]

      8. associate-*l* N/A

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

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

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

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

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

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

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

      12. *-lowering-*.f64 58.0%

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

   10. Applied egg-rr 58.0%

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

   if -1.0000000000000001e97 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 1.00000000000000004e93

   1. Initial program 90.7%

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

   3. Taylor expanded in x around 0

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

      1. sub-neg N/A

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

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

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

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

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

      4. +-commutative N/A

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

      5. distribute-neg-in N/A

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

      6. distribute-lft-neg-in N/A

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

      7. metadata-eval N/A

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

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

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

      9. *-commutative N/A

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

      10. associate-*l* N/A

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

      11. *-commutative N/A

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

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

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

      13. *-commutative N/A

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

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

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

      15. distribute-lft-neg-in N/A

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

      16. metadata-eval N/A

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

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

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

      18. *-lowering-*.f64 55.0%

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

   5. Simplified 55.0%

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

   6. Taylor expanded in j around 0

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

      1. +-commutative N/A

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

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

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

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

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

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

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 51.6%

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

   8. Simplified 51.6%

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

   if 1.00000000000000004e93 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 83.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   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 78.2%

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

   5. Simplified 78.2%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      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 78.2%

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

   7. Applied egg-rr 78.2%

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

Alternative 6: 55.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ t_2 := b \cdot c - t\_1\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+141}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq -1 \cdot 10^{+97}:\\ \;\;\;\;\left(18 \cdot \left(x \cdot z\right)\right) \cdot \left(y \cdot t\right)\\ \mathbf{elif}\;t\_1 \leq 10^{+93}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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 (* (* j 27.0) k)) (t_2 (- (* b c) t_1)))
   (if (<= t_1 -2e+141)
     t_2
     (if (<= t_1 -1e+97)
       (* (* 18.0 (* x z)) (* y t))
       (if (<= t_1 1e+93) (+ (* b c) (* -4.0 (* t a))) t_2)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double t_2 = (b * c) - t_1;
	double tmp;
	if (t_1 <= -2e+141) {
		tmp = t_2;
	} else if (t_1 <= -1e+97) {
		tmp = (18.0 * (x * z)) * (y * t);
	} else if (t_1 <= 1e+93) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (j * 27.0d0) * k
    t_2 = (b * c) - t_1
    if (t_1 <= (-2d+141)) then
        tmp = t_2
    else if (t_1 <= (-1d+97)) then
        tmp = (18.0d0 * (x * z)) * (y * t)
    else if (t_1 <= 1d+93) then
        tmp = (b * c) + ((-4.0d0) * (t * a))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double t_2 = (b * c) - t_1;
	double tmp;
	if (t_1 <= -2e+141) {
		tmp = t_2;
	} else if (t_1 <= -1e+97) {
		tmp = (18.0 * (x * z)) * (y * t);
	} else if (t_1 <= 1e+93) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	t_2 = (b * c) - t_1
	tmp = 0
	if t_1 <= -2e+141:
		tmp = t_2
	elif t_1 <= -1e+97:
		tmp = (18.0 * (x * z)) * (y * t)
	elif t_1 <= 1e+93:
		tmp = (b * c) + (-4.0 * (t * a))
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	t_2 = Float64(Float64(b * c) - t_1)
	tmp = 0.0
	if (t_1 <= -2e+141)
		tmp = t_2;
	elseif (t_1 <= -1e+97)
		tmp = Float64(Float64(18.0 * Float64(x * z)) * Float64(y * t));
	elseif (t_1 <= 1e+93)
		tmp = Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * 27.0) * k;
	t_2 = (b * c) - t_1;
	tmp = 0.0;
	if (t_1 <= -2e+141)
		tmp = t_2;
	elseif (t_1 <= -1e+97)
		tmp = (18.0 * (x * z)) * (y * t);
	elseif (t_1 <= 1e+93)
		tmp = (b * c) + (-4.0 * (t * a));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] - t$95$1), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+141], t$95$2, If[LessEqual[t$95$1, -1e+97], N[(N[(18.0 * N[(x * z), $MachinePrecision]), $MachinePrecision] * N[(y * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+93], N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -2.00000000000000003e141 or 1.00000000000000004e93 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 80.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   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 78.5%

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

   5. Simplified 78.5%

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

   if -2.00000000000000003e141 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -1.0000000000000001e97

   1. Initial program 99.8%

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

   3. Taylor expanded in x around -inf

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

   5. Simplified 78.2%

      \[\leadsto \color{blue}{\left(4 \cdot i + \left(\left(\left(t \cdot -18\right) \cdot y\right) \cdot z - \frac{b \cdot c + \left(j \cdot \left(k \cdot -27\right) + -4 \cdot \left(a \cdot t\right)\right)}{x}\right)\right) \cdot \left(0 - x\right)} \]

   6. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

         \[\leadsto \left(\left(x \cdot \left(y \cdot z\right)\right) \cdot t\right) \cdot 18 \]

      3. associate-*l* N/A

         \[\leadsto \left(x \cdot \left(\left(y \cdot z\right) \cdot t\right)\right) \cdot 18 \]

      4. *-commutative N/A

         \[\leadsto \left(x \cdot \left(t \cdot \left(y \cdot z\right)\right)\right) \cdot 18 \]

      5. associate-*r* N/A

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

      6. *-commutative N/A

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

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

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

      8. *-commutative N/A

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

      9. associate-*r* N/A

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

      10. *-commutative N/A

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

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

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

      12. *-commutative N/A

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

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

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

      14. *-lowering-*.f64 59.7%

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

   8. Simplified 59.7%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. associate-*l* N/A

         \[\leadsto \left(\left(x \cdot \left(y \cdot z\right)\right) \cdot 18\right) \cdot t \]

      4. *-commutative N/A

         \[\leadsto \left(\left(x \cdot \left(z \cdot y\right)\right) \cdot 18\right) \cdot t \]

      5. associate-*l* N/A

         \[\leadsto \left(\left(\left(x \cdot z\right) \cdot y\right) \cdot 18\right) \cdot t \]

      6. *-commutative N/A

         \[\leadsto \left(18 \cdot \left(\left(x \cdot z\right) \cdot y\right)\right) \cdot t \]

      7. associate-*r* N/A

         \[\leadsto \left(\left(18 \cdot \left(x \cdot z\right)\right) \cdot y\right) \cdot t \]

      8. associate-*l* N/A

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

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

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

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

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

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

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

      12. *-lowering-*.f64 58.0%

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

   10. Applied egg-rr 58.0%

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

   if -1.0000000000000001e97 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 1.00000000000000004e93

   1. Initial program 90.7%

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

   3. Taylor expanded in x around 0

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

      1. sub-neg N/A

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

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

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

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

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

      4. +-commutative N/A

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

      5. distribute-neg-in N/A

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

      6. distribute-lft-neg-in N/A

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

      7. metadata-eval N/A

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

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

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

      9. *-commutative N/A

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

      10. associate-*l* N/A

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

      11. *-commutative N/A

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

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

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

      13. *-commutative N/A

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

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

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

      15. distribute-lft-neg-in N/A

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

      16. metadata-eval N/A

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

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

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

      18. *-lowering-*.f64 55.0%

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

   5. Simplified 55.0%

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

   6. Taylor expanded in j around 0

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

      1. +-commutative N/A

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

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

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

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

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

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

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 51.6%

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

   8. Simplified 51.6%

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

Alternative 7: 49.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;j \cdot 27 \leq -2 \cdot 10^{+140}:\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;j \cdot 27 \leq -1 \cdot 10^{-52}:\\ \;\;\;\;t \cdot \left(a \cdot -4 + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;j \cdot 27 \leq 10^{-78}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot -4 + \frac{j \cdot \left(k \cdot -27\right)}{t}\right)\\ \end{array} \end{array} \]

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 (<= (* j 27.0) -2e+140)
   (- (* b c) (* (* j 27.0) k))
   (if (<= (* j 27.0) -1e-52)
     (* t (+ (* a -4.0) (* 18.0 (* x (* y z)))))
     (if (<= (* j 27.0) 1e-78)
       (+ (* b c) (* -4.0 (* t a)))
       (* t (+ (* a -4.0) (/ (* j (* k -27.0)) t)))))))

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 ((j * 27.0) <= -2e+140) {
		tmp = (b * c) - ((j * 27.0) * k);
	} else if ((j * 27.0) <= -1e-52) {
		tmp = t * ((a * -4.0) + (18.0 * (x * (y * z))));
	} else if ((j * 27.0) <= 1e-78) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else {
		tmp = t * ((a * -4.0) + ((j * (k * -27.0)) / t));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 ((j * 27.0d0) <= (-2d+140)) then
        tmp = (b * c) - ((j * 27.0d0) * k)
    else if ((j * 27.0d0) <= (-1d-52)) then
        tmp = t * ((a * (-4.0d0)) + (18.0d0 * (x * (y * z))))
    else if ((j * 27.0d0) <= 1d-78) then
        tmp = (b * c) + ((-4.0d0) * (t * a))
    else
        tmp = t * ((a * (-4.0d0)) + ((j * (k * (-27.0d0))) / t))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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 ((j * 27.0) <= -2e+140) {
		tmp = (b * c) - ((j * 27.0) * k);
	} else if ((j * 27.0) <= -1e-52) {
		tmp = t * ((a * -4.0) + (18.0 * (x * (y * z))));
	} else if ((j * 27.0) <= 1e-78) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else {
		tmp = t * ((a * -4.0) + ((j * (k * -27.0)) / t));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (j * 27.0) <= -2e+140:
		tmp = (b * c) - ((j * 27.0) * k)
	elif (j * 27.0) <= -1e-52:
		tmp = t * ((a * -4.0) + (18.0 * (x * (y * z))))
	elif (j * 27.0) <= 1e-78:
		tmp = (b * c) + (-4.0 * (t * a))
	else:
		tmp = t * ((a * -4.0) + ((j * (k * -27.0)) / t))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (Float64(j * 27.0) <= -2e+140)
		tmp = Float64(Float64(b * c) - Float64(Float64(j * 27.0) * k));
	elseif (Float64(j * 27.0) <= -1e-52)
		tmp = Float64(t * Float64(Float64(a * -4.0) + Float64(18.0 * Float64(x * Float64(y * z)))));
	elseif (Float64(j * 27.0) <= 1e-78)
		tmp = Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a)));
	else
		tmp = Float64(t * Float64(Float64(a * -4.0) + Float64(Float64(j * Float64(k * -27.0)) / t)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((j * 27.0) <= -2e+140)
		tmp = (b * c) - ((j * 27.0) * k);
	elseif ((j * 27.0) <= -1e-52)
		tmp = t * ((a * -4.0) + (18.0 * (x * (y * z))));
	elseif ((j * 27.0) <= 1e-78)
		tmp = (b * c) + (-4.0 * (t * a));
	else
		tmp = t * ((a * -4.0) + ((j * (k * -27.0)) / t));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[N[(j * 27.0), $MachinePrecision], -2e+140], N[(N[(b * c), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(j * 27.0), $MachinePrecision], -1e-52], N[(t * N[(N[(a * -4.0), $MachinePrecision] + N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(j * 27.0), $MachinePrecision], 1e-78], N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(a * -4.0), $MachinePrecision] + N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 j #s(literal 27 binary64)) < -2.00000000000000012e140

   1. Initial program 75.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   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 68.8%

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

   5. Simplified 68.8%

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

   if -2.00000000000000012e140 < (*.f64 j #s(literal 27 binary64)) < -1e-52

   1. Initial program 94.6%

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

   3. Taylor expanded in t around inf

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

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

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

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

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

      3. metadata-eval N/A

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

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

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

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

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

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

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

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

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

      8. *-lowering-*.f64 44.6%

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

   5. Simplified 44.6%

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

   if -1e-52 < (*.f64 j #s(literal 27 binary64)) < 9.99999999999999999e-79

   1. Initial program 89.8%

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

   3. Taylor expanded in x around 0

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

      1. sub-neg N/A

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

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

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

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

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

      4. +-commutative N/A

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

      5. distribute-neg-in N/A

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

      6. distribute-lft-neg-in N/A

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

      7. metadata-eval N/A

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

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

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

      9. *-commutative N/A

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

      10. associate-*l* N/A

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

      11. *-commutative N/A

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

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

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

      13. *-commutative N/A

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

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

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

      15. distribute-lft-neg-in N/A

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

      16. metadata-eval N/A

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

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

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

      18. *-lowering-*.f64 54.5%

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

   5. Simplified 54.5%

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

   6. Taylor expanded in j around 0

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

      1. +-commutative N/A

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

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

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

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

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

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

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 51.0%

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

   8. Simplified 51.0%

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

   if 9.99999999999999999e-79 < (*.f64 j #s(literal 27 binary64))

   1. Initial program 87.1%

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

   3. Taylor expanded in x around 0

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

      1. sub-neg N/A

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

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

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

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

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

      4. +-commutative N/A

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

      5. distribute-neg-in N/A

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

      6. distribute-lft-neg-in N/A

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

      7. metadata-eval N/A

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

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

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

      9. *-commutative N/A

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

      10. associate-*l* N/A

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

      11. *-commutative N/A

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

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

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

      13. *-commutative N/A

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

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

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

      15. distribute-lft-neg-in N/A

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

      16. metadata-eval N/A

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

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

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

      18. *-lowering-*.f64 71.4%

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

   5. Simplified 71.4%

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

   6. Taylor expanded in t around inf

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

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

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. metadata-eval N/A

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

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

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

      6. associate-*r/ N/A

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

      7. div-sub N/A

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

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

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

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

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

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

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

   8. Simplified 63.1%

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

   9. Taylor expanded in b around 0

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

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

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

       2. +-commutative N/A

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

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

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

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

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

       5. associate-*r/ N/A

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

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

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

       7. *-commutative N/A

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

       8. associate-*r* N/A

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

       9. *-commutative N/A

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

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

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

       11. *-commutative N/A

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

       12. *-lowering-*.f64 54.2%

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

   11. Simplified 54.2%

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

4. Final simplification 53.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \cdot 27 \leq -2 \cdot 10^{+140}:\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;j \cdot 27 \leq -1 \cdot 10^{-52}:\\ \;\;\;\;t \cdot \left(a \cdot -4 + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;j \cdot 27 \leq 10^{-78}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot -4 + \frac{j \cdot \left(k \cdot -27\right)}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 82.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := x \cdot \left(\left(-27 \cdot \frac{j \cdot k}{x} - z \cdot \left(y \cdot \left(t \cdot -18\right)\right)\right) - i \cdot 4\right)\\ \mathbf{if}\;x \leq -2.6 \cdot 10^{+31}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+109}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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
         (*
          x
          (- (- (* -27.0 (/ (* j k) x)) (* z (* y (* t -18.0)))) (* i 4.0)))))
   (if (<= x -2.6e+31)
     t_1
     (if (<= x 1.3e+109)
       (-
        (+ (* b c) (* t (+ (* 18.0 (* y (* x z))) (* a -4.0))))
        (* (* 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 = x * (((-27.0 * ((j * k) / x)) - (z * (y * (t * -18.0)))) - (i * 4.0));
	double tmp;
	if (x <= -2.6e+31) {
		tmp = t_1;
	} else if (x <= 1.3e+109) {
		tmp = ((b * c) + (t * ((18.0 * (y * (x * z))) + (a * -4.0)))) - ((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 = x * ((((-27.0d0) * ((j * k) / x)) - (z * (y * (t * (-18.0d0))))) - (i * 4.0d0))
    if (x <= (-2.6d+31)) then
        tmp = t_1
    else if (x <= 1.3d+109) then
        tmp = ((b * c) + (t * ((18.0d0 * (y * (x * z))) + (a * (-4.0d0))))) - ((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 = x * (((-27.0 * ((j * k) / x)) - (z * (y * (t * -18.0)))) - (i * 4.0));
	double tmp;
	if (x <= -2.6e+31) {
		tmp = t_1;
	} else if (x <= 1.3e+109) {
		tmp = ((b * c) + (t * ((18.0 * (y * (x * z))) + (a * -4.0)))) - ((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 = x * (((-27.0 * ((j * k) / x)) - (z * (y * (t * -18.0)))) - (i * 4.0))
	tmp = 0
	if x <= -2.6e+31:
		tmp = t_1
	elif x <= 1.3e+109:
		tmp = ((b * c) + (t * ((18.0 * (y * (x * z))) + (a * -4.0)))) - ((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(x * Float64(Float64(Float64(-27.0 * Float64(Float64(j * k) / x)) - Float64(z * Float64(y * Float64(t * -18.0)))) - Float64(i * 4.0)))
	tmp = 0.0
	if (x <= -2.6e+31)
		tmp = t_1;
	elseif (x <= 1.3e+109)
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(18.0 * Float64(y * Float64(x * z))) + Float64(a * -4.0)))) - 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 = x * (((-27.0 * ((j * k) / x)) - (z * (y * (t * -18.0)))) - (i * 4.0));
	tmp = 0.0;
	if (x <= -2.6e+31)
		tmp = t_1;
	elseif (x <= 1.3e+109)
		tmp = ((b * c) + (t * ((18.0 * (y * (x * z))) + (a * -4.0)))) - ((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[(x * N[(N[(N[(-27.0 * N[(N[(j * k), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] - N[(z * N[(y * N[(t * -18.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.6e+31], t$95$1, If[LessEqual[x, 1.3e+109], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(18.0 * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.6e31 or 1.2999999999999999e109 < x

   1. Initial program 74.0%

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

   3. Taylor expanded in x around -inf

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

   5. Simplified 90.2%

      \[\leadsto \color{blue}{\left(4 \cdot i + \left(\left(\left(t \cdot -18\right) \cdot y\right) \cdot z - \frac{b \cdot c + \left(j \cdot \left(k \cdot -27\right) + -4 \cdot \left(a \cdot t\right)\right)}{x}\right)\right) \cdot \left(0 - x\right)} \]

   6. Taylor expanded in j around inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(4, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(t, -18\right), y\right), z\right), \color{blue}{\left(-27 \cdot \frac{j \cdot k}{x}\right)}\right)\right), \mathsf{\_.f64}\left(0, x\right)\right) \]
   7. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(4, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(t, -18\right), y\right), z\right), \mathsf{*.f64}\left(-27, \left(\frac{j \cdot k}{x}\right)\right)\right)\right), \mathsf{\_.f64}\left(0, x\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(4, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(t, -18\right), y\right), z\right), \mathsf{*.f64}\left(-27, \mathsf{/.f64}\left(\left(j \cdot k\right), x\right)\right)\right)\right), \mathsf{\_.f64}\left(0, x\right)\right) \]

      3. *-lowering-*.f64 83.3%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(4, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(t, -18\right), y\right), z\right), \mathsf{*.f64}\left(-27, \mathsf{/.f64}\left(\mathsf{*.f64}\left(j, k\right), x\right)\right)\right)\right), \mathsf{\_.f64}\left(0, x\right)\right) \]

   8. Simplified 83.3%

      \[\leadsto \left(4 \cdot i + \left(\left(\left(t \cdot -18\right) \cdot y\right) \cdot z - \color{blue}{-27 \cdot \frac{j \cdot k}{x}}\right)\right) \cdot \left(0 - x\right) \]

   if -2.6e31 < x < 1.2999999999999999e109

   1. Initial program 95.2%

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

   3. Taylor expanded in i around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

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

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

   5. Simplified 80.5%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

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

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

      4. *-lowering-*.f64 84.4%

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

   7. Applied egg-rr 84.4%

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

4. Final simplification 84.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{+31}:\\ \;\;\;\;x \cdot \left(\left(-27 \cdot \frac{j \cdot k}{x} - z \cdot \left(y \cdot \left(t \cdot -18\right)\right)\right) - i \cdot 4\right)\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+109}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(-27 \cdot \frac{j \cdot k}{x} - z \cdot \left(y \cdot \left(t \cdot -18\right)\right)\right) - i \cdot 4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 77.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := x \cdot \left(\left(-27 \cdot \frac{j \cdot k}{x} - z \cdot \left(y \cdot \left(t \cdot -18\right)\right)\right) - i \cdot 4\right)\\ \mathbf{if}\;i \leq -1 \cdot 10^{+152}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 1.16 \cdot 10^{+179}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(a \cdot -4 + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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
         (*
          x
          (- (- (* -27.0 (/ (* j k) x)) (* z (* y (* t -18.0)))) (* i 4.0)))))
   (if (<= i -1e+152)
     t_1
     (if (<= i 1.16e+179)
       (-
        (+ (* b c) (* t (+ (* a -4.0) (* 18.0 (* x (* y z))))))
        (* (* 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 = x * (((-27.0 * ((j * k) / x)) - (z * (y * (t * -18.0)))) - (i * 4.0));
	double tmp;
	if (i <= -1e+152) {
		tmp = t_1;
	} else if (i <= 1.16e+179) {
		tmp = ((b * c) + (t * ((a * -4.0) + (18.0 * (x * (y * z)))))) - ((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 = x * ((((-27.0d0) * ((j * k) / x)) - (z * (y * (t * (-18.0d0))))) - (i * 4.0d0))
    if (i <= (-1d+152)) then
        tmp = t_1
    else if (i <= 1.16d+179) then
        tmp = ((b * c) + (t * ((a * (-4.0d0)) + (18.0d0 * (x * (y * z)))))) - ((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 = x * (((-27.0 * ((j * k) / x)) - (z * (y * (t * -18.0)))) - (i * 4.0));
	double tmp;
	if (i <= -1e+152) {
		tmp = t_1;
	} else if (i <= 1.16e+179) {
		tmp = ((b * c) + (t * ((a * -4.0) + (18.0 * (x * (y * z)))))) - ((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 = x * (((-27.0 * ((j * k) / x)) - (z * (y * (t * -18.0)))) - (i * 4.0))
	tmp = 0
	if i <= -1e+152:
		tmp = t_1
	elif i <= 1.16e+179:
		tmp = ((b * c) + (t * ((a * -4.0) + (18.0 * (x * (y * z)))))) - ((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(x * Float64(Float64(Float64(-27.0 * Float64(Float64(j * k) / x)) - Float64(z * Float64(y * Float64(t * -18.0)))) - Float64(i * 4.0)))
	tmp = 0.0
	if (i <= -1e+152)
		tmp = t_1;
	elseif (i <= 1.16e+179)
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(a * -4.0) + Float64(18.0 * Float64(x * Float64(y * z)))))) - 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 = x * (((-27.0 * ((j * k) / x)) - (z * (y * (t * -18.0)))) - (i * 4.0));
	tmp = 0.0;
	if (i <= -1e+152)
		tmp = t_1;
	elseif (i <= 1.16e+179)
		tmp = ((b * c) + (t * ((a * -4.0) + (18.0 * (x * (y * z)))))) - ((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[(x * N[(N[(N[(-27.0 * N[(N[(j * k), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] - N[(z * N[(y * N[(t * -18.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1e+152], t$95$1, If[LessEqual[i, 1.16e+179], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(a * -4.0), $MachinePrecision] + N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if i < -1e152 or 1.16e179 < i

   1. Initial program 79.4%

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

   3. Taylor expanded in x around -inf

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

   5. Simplified 78.6%

      \[\leadsto \color{blue}{\left(4 \cdot i + \left(\left(\left(t \cdot -18\right) \cdot y\right) \cdot z - \frac{b \cdot c + \left(j \cdot \left(k \cdot -27\right) + -4 \cdot \left(a \cdot t\right)\right)}{x}\right)\right) \cdot \left(0 - x\right)} \]

   6. Taylor expanded in j around inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(4, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(t, -18\right), y\right), z\right), \color{blue}{\left(-27 \cdot \frac{j \cdot k}{x}\right)}\right)\right), \mathsf{\_.f64}\left(0, x\right)\right) \]
   7. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(4, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(t, -18\right), y\right), z\right), \mathsf{*.f64}\left(-27, \left(\frac{j \cdot k}{x}\right)\right)\right)\right), \mathsf{\_.f64}\left(0, x\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(4, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(t, -18\right), y\right), z\right), \mathsf{*.f64}\left(-27, \mathsf{/.f64}\left(\left(j \cdot k\right), x\right)\right)\right)\right), \mathsf{\_.f64}\left(0, x\right)\right) \]

      3. *-lowering-*.f64 78.9%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(4, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(t, -18\right), y\right), z\right), \mathsf{*.f64}\left(-27, \mathsf{/.f64}\left(\mathsf{*.f64}\left(j, k\right), x\right)\right)\right)\right), \mathsf{\_.f64}\left(0, x\right)\right) \]

   8. Simplified 78.9%

      \[\leadsto \left(4 \cdot i + \left(\left(\left(t \cdot -18\right) \cdot y\right) \cdot z - \color{blue}{-27 \cdot \frac{j \cdot k}{x}}\right)\right) \cdot \left(0 - x\right) \]

   if -1e152 < i < 1.16e179

   1. Initial program 90.7%

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

   3. Taylor expanded in i around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

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

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

   5. Simplified 83.3%

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

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1 \cdot 10^{+152}:\\ \;\;\;\;x \cdot \left(\left(-27 \cdot \frac{j \cdot k}{x} - z \cdot \left(y \cdot \left(t \cdot -18\right)\right)\right) - i \cdot 4\right)\\ \mathbf{elif}\;i \leq 1.16 \cdot 10^{+179}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(a \cdot -4 + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(-27 \cdot \frac{j \cdot k}{x} - z \cdot \left(y \cdot \left(t \cdot -18\right)\right)\right) - i \cdot 4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 74.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(x \cdot 4\right) \cdot i\\ t_2 := \left(j \cdot 27\right) \cdot k\\ t_3 := b \cdot c + t \cdot \left(a \cdot -4 + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{if}\;t \leq -1.95 \cdot 10^{+150}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq -1.45 \cdot 10^{-100}:\\ \;\;\;\;\left(-4 \cdot \left(t \cdot a\right) - t\_1\right) - t\_2\\ \mathbf{elif}\;t \leq 1760000000000:\\ \;\;\;\;\left(b \cdot c - t\_1\right) - t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* x 4.0) i))
        (t_2 (* (* j 27.0) k))
        (t_3 (+ (* b c) (* t (+ (* a -4.0) (* 18.0 (* x (* y z))))))))
   (if (<= t -1.95e+150)
     t_3
     (if (<= t -1.45e-100)
       (- (- (* -4.0 (* t a)) t_1) t_2)
       (if (<= t 1760000000000.0) (- (- (* b c) t_1) t_2) 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 * 4.0) * i;
	double t_2 = (j * 27.0) * k;
	double t_3 = (b * c) + (t * ((a * -4.0) + (18.0 * (x * (y * z)))));
	double tmp;
	if (t <= -1.95e+150) {
		tmp = t_3;
	} else if (t <= -1.45e-100) {
		tmp = ((-4.0 * (t * a)) - t_1) - t_2;
	} else if (t <= 1760000000000.0) {
		tmp = ((b * c) - t_1) - t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (x * 4.0d0) * i
    t_2 = (j * 27.0d0) * k
    t_3 = (b * c) + (t * ((a * (-4.0d0)) + (18.0d0 * (x * (y * z)))))
    if (t <= (-1.95d+150)) then
        tmp = t_3
    else if (t <= (-1.45d-100)) then
        tmp = (((-4.0d0) * (t * a)) - t_1) - t_2
    else if (t <= 1760000000000.0d0) then
        tmp = ((b * c) - t_1) - t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (x * 4.0) * i;
	double t_2 = (j * 27.0) * k;
	double t_3 = (b * c) + (t * ((a * -4.0) + (18.0 * (x * (y * z)))));
	double tmp;
	if (t <= -1.95e+150) {
		tmp = t_3;
	} else if (t <= -1.45e-100) {
		tmp = ((-4.0 * (t * a)) - t_1) - t_2;
	} else if (t <= 1760000000000.0) {
		tmp = ((b * c) - t_1) - t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (x * 4.0) * i
	t_2 = (j * 27.0) * k
	t_3 = (b * c) + (t * ((a * -4.0) + (18.0 * (x * (y * z)))))
	tmp = 0
	if t <= -1.95e+150:
		tmp = t_3
	elif t <= -1.45e-100:
		tmp = ((-4.0 * (t * a)) - t_1) - t_2
	elif t <= 1760000000000.0:
		tmp = ((b * c) - t_1) - t_2
	else:
		tmp = t_3
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(x * 4.0) * i)
	t_2 = Float64(Float64(j * 27.0) * k)
	t_3 = Float64(Float64(b * c) + Float64(t * Float64(Float64(a * -4.0) + Float64(18.0 * Float64(x * Float64(y * z))))))
	tmp = 0.0
	if (t <= -1.95e+150)
		tmp = t_3;
	elseif (t <= -1.45e-100)
		tmp = Float64(Float64(Float64(-4.0 * Float64(t * a)) - t_1) - t_2);
	elseif (t <= 1760000000000.0)
		tmp = Float64(Float64(Float64(b * c) - t_1) - t_2);
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (x * 4.0) * i;
	t_2 = (j * 27.0) * k;
	t_3 = (b * c) + (t * ((a * -4.0) + (18.0 * (x * (y * z)))));
	tmp = 0.0;
	if (t <= -1.95e+150)
		tmp = t_3;
	elseif (t <= -1.45e-100)
		tmp = ((-4.0 * (t * a)) - t_1) - t_2;
	elseif (t <= 1760000000000.0)
		tmp = ((b * c) - t_1) - t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, Block[{t$95$3 = N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(a * -4.0), $MachinePrecision] + N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.95e+150], t$95$3, If[LessEqual[t, -1.45e-100], N[(N[(N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision], If[LessEqual[t, 1760000000000.0], N[(N[(N[(b * c), $MachinePrecision] - t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision], t$95$3]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.94999999999999995e150 or 1.76e12 < t

   1. Initial program 86.0%

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

   3. Taylor expanded in i around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

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

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

   5. Simplified 88.7%

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

   6. Taylor expanded in j around 0

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

      8. *-lowering-*.f64 81.5%

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

   8. Simplified 81.5%

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

   if -1.94999999999999995e150 < t < -1.44999999999999988e-100

   1. Initial program 88.8%

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

   3. Taylor expanded in a around inf

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

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

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

      2. *-lowering-*.f64 69.9%

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

   5. Simplified 69.9%

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

   if -1.44999999999999988e-100 < t < 1.76e12

   1. Initial program 89.0%

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

   3. Taylor expanded in t around 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 79.2%

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

   5. Simplified 79.2%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.95 \cdot 10^{+150}:\\ \;\;\;\;b \cdot c + t \cdot \left(a \cdot -4 + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq -1.45 \cdot 10^{-100}:\\ \;\;\;\;\left(-4 \cdot \left(t \cdot a\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;t \leq 1760000000000:\\ \;\;\;\;\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + t \cdot \left(a \cdot -4 + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 77.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := x \cdot \left(\left(-27 \cdot \frac{j \cdot k}{x} - z \cdot \left(y \cdot \left(t \cdot -18\right)\right)\right) - i \cdot 4\right)\\ \mathbf{if}\;x \leq -650:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 5.9 \cdot 10^{-12}:\\ \;\;\;\;b \cdot c + \left(j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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
          (- (- (* -27.0 (/ (* j k) x)) (* z (* y (* t -18.0)))) (* i 4.0)))))
   (if (<= x -650.0)
     t_1
     (if (<= x 5.9e-12)
       (+ (* b c) (+ (* j (* k -27.0)) (* -4.0 (* t a))))
       t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = x * (((-27.0 * ((j * k) / x)) - (z * (y * (t * -18.0)))) - (i * 4.0));
	double tmp;
	if (x <= -650.0) {
		tmp = t_1;
	} else if (x <= 5.9e-12) {
		tmp = (b * c) + ((j * (k * -27.0)) + (-4.0 * (t * a)));
	} 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 * ((((-27.0d0) * ((j * k) / x)) - (z * (y * (t * (-18.0d0))))) - (i * 4.0d0))
    if (x <= (-650.0d0)) then
        tmp = t_1
    else if (x <= 5.9d-12) then
        tmp = (b * c) + ((j * (k * (-27.0d0))) + ((-4.0d0) * (t * a)))
    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 * (((-27.0 * ((j * k) / x)) - (z * (y * (t * -18.0)))) - (i * 4.0));
	double tmp;
	if (x <= -650.0) {
		tmp = t_1;
	} else if (x <= 5.9e-12) {
		tmp = (b * c) + ((j * (k * -27.0)) + (-4.0 * (t * a)));
	} 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 * (((-27.0 * ((j * k) / x)) - (z * (y * (t * -18.0)))) - (i * 4.0))
	tmp = 0
	if x <= -650.0:
		tmp = t_1
	elif x <= 5.9e-12:
		tmp = (b * c) + ((j * (k * -27.0)) + (-4.0 * (t * a)))
	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(Float64(-27.0 * Float64(Float64(j * k) / x)) - Float64(z * Float64(y * Float64(t * -18.0)))) - Float64(i * 4.0)))
	tmp = 0.0
	if (x <= -650.0)
		tmp = t_1;
	elseif (x <= 5.9e-12)
		tmp = Float64(Float64(b * c) + Float64(Float64(j * Float64(k * -27.0)) + Float64(-4.0 * Float64(t * a))));
	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 * (((-27.0 * ((j * k) / x)) - (z * (y * (t * -18.0)))) - (i * 4.0));
	tmp = 0.0;
	if (x <= -650.0)
		tmp = t_1;
	elseif (x <= 5.9e-12)
		tmp = (b * c) + ((j * (k * -27.0)) + (-4.0 * (t * a)));
	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[(N[(-27.0 * N[(N[(j * k), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] - N[(z * N[(y * N[(t * -18.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -650.0], t$95$1, If[LessEqual[x, 5.9e-12], N[(N[(b * c), $MachinePrecision] + N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -650 or 5.9e-12 < x

   1. Initial program 78.7%

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

   3. Taylor expanded in x around -inf

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

   5. Simplified 91.7%

      \[\leadsto \color{blue}{\left(4 \cdot i + \left(\left(\left(t \cdot -18\right) \cdot y\right) \cdot z - \frac{b \cdot c + \left(j \cdot \left(k \cdot -27\right) + -4 \cdot \left(a \cdot t\right)\right)}{x}\right)\right) \cdot \left(0 - x\right)} \]

   6. Taylor expanded in j around inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(4, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(t, -18\right), y\right), z\right), \color{blue}{\left(-27 \cdot \frac{j \cdot k}{x}\right)}\right)\right), \mathsf{\_.f64}\left(0, x\right)\right) \]
   7. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(4, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(t, -18\right), y\right), z\right), \mathsf{*.f64}\left(-27, \left(\frac{j \cdot k}{x}\right)\right)\right)\right), \mathsf{\_.f64}\left(0, x\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(4, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(t, -18\right), y\right), z\right), \mathsf{*.f64}\left(-27, \mathsf{/.f64}\left(\left(j \cdot k\right), x\right)\right)\right)\right), \mathsf{\_.f64}\left(0, x\right)\right) \]

      3. *-lowering-*.f64 79.2%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(4, i\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(t, -18\right), y\right), z\right), \mathsf{*.f64}\left(-27, \mathsf{/.f64}\left(\mathsf{*.f64}\left(j, k\right), x\right)\right)\right)\right), \mathsf{\_.f64}\left(0, x\right)\right) \]

   8. Simplified 79.2%

      \[\leadsto \left(4 \cdot i + \left(\left(\left(t \cdot -18\right) \cdot y\right) \cdot z - \color{blue}{-27 \cdot \frac{j \cdot k}{x}}\right)\right) \cdot \left(0 - x\right) \]

   if -650 < x < 5.9e-12

   1. Initial program 95.6%

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

   3. Taylor expanded in x around 0

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

      1. sub-neg N/A

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

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

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

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

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

      4. +-commutative N/A

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

      5. distribute-neg-in N/A

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

      6. distribute-lft-neg-in N/A

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

      7. metadata-eval N/A

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

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

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

      9. *-commutative N/A

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

      10. associate-*l* N/A

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

      11. *-commutative N/A

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

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

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

      13. *-commutative N/A

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

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

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

      15. distribute-lft-neg-in N/A

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

      16. metadata-eval N/A

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

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

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

      18. *-lowering-*.f64 74.8%

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

   5. Simplified 74.8%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -650:\\ \;\;\;\;x \cdot \left(\left(-27 \cdot \frac{j \cdot k}{x} - z \cdot \left(y \cdot \left(t \cdot -18\right)\right)\right) - i \cdot 4\right)\\ \mathbf{elif}\;x \leq 5.9 \cdot 10^{-12}:\\ \;\;\;\;b \cdot c + \left(j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(-27 \cdot \frac{j \cdot k}{x} - z \cdot \left(y \cdot \left(t \cdot -18\right)\right)\right) - i \cdot 4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 76.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c + t \cdot \left(a \cdot -4 + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{if}\;t \leq -90000000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+16}:\\ \;\;\;\;\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (+ (* b c) (* t (+ (* a -4.0) (* 18.0 (* x (* y z))))))))
   (if (<= t -90000000000000.0)
     t_1
     (if (<= t 8e+16) (- (- (* 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 = (b * c) + (t * ((a * -4.0) + (18.0 * (x * (y * z)))));
	double tmp;
	if (t <= -90000000000000.0) {
		tmp = t_1;
	} else if (t <= 8e+16) {
		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 = (b * c) + (t * ((a * (-4.0d0)) + (18.0d0 * (x * (y * z)))))
    if (t <= (-90000000000000.0d0)) then
        tmp = t_1
    else if (t <= 8d+16) 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 = (b * c) + (t * ((a * -4.0) + (18.0 * (x * (y * z)))));
	double tmp;
	if (t <= -90000000000000.0) {
		tmp = t_1;
	} else if (t <= 8e+16) {
		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 = (b * c) + (t * ((a * -4.0) + (18.0 * (x * (y * z)))))
	tmp = 0
	if t <= -90000000000000.0:
		tmp = t_1
	elif t <= 8e+16:
		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(Float64(b * c) + Float64(t * Float64(Float64(a * -4.0) + Float64(18.0 * Float64(x * Float64(y * z))))))
	tmp = 0.0
	if (t <= -90000000000000.0)
		tmp = t_1;
	elseif (t <= 8e+16)
		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 = (b * c) + (t * ((a * -4.0) + (18.0 * (x * (y * z)))));
	tmp = 0.0;
	if (t <= -90000000000000.0)
		tmp = t_1;
	elseif (t <= 8e+16)
		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[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(a * -4.0), $MachinePrecision] + N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -90000000000000.0], t$95$1, If[LessEqual[t, 8e+16], 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 < -9e13 or 8e16 < t

   1. Initial program 87.1%

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

   3. Taylor expanded in i around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

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

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

   5. Simplified 85.2%

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

   6. Taylor expanded in j around 0

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

      8. *-lowering-*.f64 76.7%

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

   8. Simplified 76.7%

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

   if -9e13 < t < 8e16

   1. Initial program 88.6%

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

   3. Taylor expanded in t around 0

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

      1. *-lowering-*.f64 75.5%

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

   5. Simplified 75.5%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -90000000000000:\\ \;\;\;\;b \cdot c + t \cdot \left(a \cdot -4 + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+16}:\\ \;\;\;\;\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + t \cdot \left(a \cdot -4 + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 32.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;j \leq -1.4 \cdot 10^{+139}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;j \leq -6.6 \cdot 10^{-56}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;j \leq 6.2 \cdot 10^{-95}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;j \leq 1.3 \cdot 10^{-31}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= j -1.4e+139)
   (* k (* j -27.0))
   (if (<= j -6.6e-56)
     (* -4.0 (* x i))
     (if (<= j 6.2e-95)
       (* b c)
       (if (<= j 1.3e-31) (* -4.0 (* t a)) (* j (* k -27.0)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (j <= -1.4e+139) {
		tmp = k * (j * -27.0);
	} else if (j <= -6.6e-56) {
		tmp = -4.0 * (x * i);
	} else if (j <= 6.2e-95) {
		tmp = b * c;
	} else if (j <= 1.3e-31) {
		tmp = -4.0 * (t * a);
	} else {
		tmp = j * (k * -27.0);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (j <= (-1.4d+139)) then
        tmp = k * (j * (-27.0d0))
    else if (j <= (-6.6d-56)) then
        tmp = (-4.0d0) * (x * i)
    else if (j <= 6.2d-95) then
        tmp = b * c
    else if (j <= 1.3d-31) then
        tmp = (-4.0d0) * (t * a)
    else
        tmp = j * (k * (-27.0d0))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (j <= -1.4e+139) {
		tmp = k * (j * -27.0);
	} else if (j <= -6.6e-56) {
		tmp = -4.0 * (x * i);
	} else if (j <= 6.2e-95) {
		tmp = b * c;
	} else if (j <= 1.3e-31) {
		tmp = -4.0 * (t * a);
	} else {
		tmp = j * (k * -27.0);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if j <= -1.4e+139:
		tmp = k * (j * -27.0)
	elif j <= -6.6e-56:
		tmp = -4.0 * (x * i)
	elif j <= 6.2e-95:
		tmp = b * c
	elif j <= 1.3e-31:
		tmp = -4.0 * (t * a)
	else:
		tmp = j * (k * -27.0)
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (j <= -1.4e+139)
		tmp = Float64(k * Float64(j * -27.0));
	elseif (j <= -6.6e-56)
		tmp = Float64(-4.0 * Float64(x * i));
	elseif (j <= 6.2e-95)
		tmp = Float64(b * c);
	elseif (j <= 1.3e-31)
		tmp = Float64(-4.0 * Float64(t * a));
	else
		tmp = Float64(j * Float64(k * -27.0));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (j <= -1.4e+139)
		tmp = k * (j * -27.0);
	elseif (j <= -6.6e-56)
		tmp = -4.0 * (x * i);
	elseif (j <= 6.2e-95)
		tmp = b * c;
	elseif (j <= 1.3e-31)
		tmp = -4.0 * (t * a);
	else
		tmp = j * (k * -27.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[j, -1.4e+139], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -6.6e-56], N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 6.2e-95], N[(b * c), $MachinePrecision], If[LessEqual[j, 1.3e-31], N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -1.3999999999999999e139

   1. Initial program 74.9%

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

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

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

   4. Applied egg-rr 74.8%

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

   5. Taylor expanded in j around inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

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

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

      4. *-commutative N/A

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

      5. *-lowering-*.f64 61.1%

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

   7. Simplified 61.1%

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

   if -1.3999999999999999e139 < j < -6.59999999999999967e-56

   1. Initial program 94.9%

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

   3. Taylor expanded in i around inf

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

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

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 26.7%

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

   5. Simplified 26.7%

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

   if -6.59999999999999967e-56 < j < 6.19999999999999983e-95

   1. Initial program 90.2%

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

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot c} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 31.0%

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

   5. Simplified 31.0%

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

   if 6.19999999999999983e-95 < j < 1.29999999999999998e-31

   1. Initial program 80.3%

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

   3. Taylor expanded in a around inf

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

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

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

      2. *-lowering-*.f64 41.9%

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

   5. Simplified 41.9%

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

   if 1.29999999999999998e-31 < j

   1. Initial program 88.0%

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

   3. Taylor expanded in j around inf

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

      1. *-commutative N/A

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

      2. associate-*l* 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 39.9%

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

   5. Simplified 39.9%

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

4. Final simplification 37.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.4 \cdot 10^{+139}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;j \leq -6.6 \cdot 10^{-56}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;j \leq 6.2 \cdot 10^{-95}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;j \leq 1.3 \cdot 10^{-31}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 32.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;j \leq -8.5 \cdot 10^{+139}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;j \leq -9.8 \cdot 10^{-56}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;j \leq 2 \cdot 10^{-97}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;j \leq 2.3 \cdot 10^{-31}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= j -8.5e+139)
   (* -27.0 (* j k))
   (if (<= j -9.8e-56)
     (* -4.0 (* x i))
     (if (<= j 2e-97)
       (* b c)
       (if (<= j 2.3e-31) (* -4.0 (* t a)) (* j (* k -27.0)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (j <= -8.5e+139) {
		tmp = -27.0 * (j * k);
	} else if (j <= -9.8e-56) {
		tmp = -4.0 * (x * i);
	} else if (j <= 2e-97) {
		tmp = b * c;
	} else if (j <= 2.3e-31) {
		tmp = -4.0 * (t * a);
	} else {
		tmp = j * (k * -27.0);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (j <= (-8.5d+139)) then
        tmp = (-27.0d0) * (j * k)
    else if (j <= (-9.8d-56)) then
        tmp = (-4.0d0) * (x * i)
    else if (j <= 2d-97) then
        tmp = b * c
    else if (j <= 2.3d-31) then
        tmp = (-4.0d0) * (t * a)
    else
        tmp = j * (k * (-27.0d0))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (j <= -8.5e+139) {
		tmp = -27.0 * (j * k);
	} else if (j <= -9.8e-56) {
		tmp = -4.0 * (x * i);
	} else if (j <= 2e-97) {
		tmp = b * c;
	} else if (j <= 2.3e-31) {
		tmp = -4.0 * (t * a);
	} else {
		tmp = j * (k * -27.0);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if j <= -8.5e+139:
		tmp = -27.0 * (j * k)
	elif j <= -9.8e-56:
		tmp = -4.0 * (x * i)
	elif j <= 2e-97:
		tmp = b * c
	elif j <= 2.3e-31:
		tmp = -4.0 * (t * a)
	else:
		tmp = j * (k * -27.0)
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (j <= -8.5e+139)
		tmp = Float64(-27.0 * Float64(j * k));
	elseif (j <= -9.8e-56)
		tmp = Float64(-4.0 * Float64(x * i));
	elseif (j <= 2e-97)
		tmp = Float64(b * c);
	elseif (j <= 2.3e-31)
		tmp = Float64(-4.0 * Float64(t * a));
	else
		tmp = Float64(j * Float64(k * -27.0));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (j <= -8.5e+139)
		tmp = -27.0 * (j * k);
	elseif (j <= -9.8e-56)
		tmp = -4.0 * (x * i);
	elseif (j <= 2e-97)
		tmp = b * c;
	elseif (j <= 2.3e-31)
		tmp = -4.0 * (t * a);
	else
		tmp = j * (k * -27.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[j, -8.5e+139], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -9.8e-56], N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2e-97], N[(b * c), $MachinePrecision], If[LessEqual[j, 2.3e-31], N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -8.5e139

   1. Initial program 74.9%

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

   3. Taylor expanded in x around -inf

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

   5. Simplified 70.7%

      \[\leadsto \color{blue}{\left(4 \cdot i + \left(\left(\left(t \cdot -18\right) \cdot y\right) \cdot z - \frac{b \cdot c + \left(j \cdot \left(k \cdot -27\right) + -4 \cdot \left(a \cdot t\right)\right)}{x}\right)\right) \cdot \left(0 - x\right)} \]

   6. Taylor expanded in j around inf

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

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

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

      2. *-lowering-*.f64 61.1%

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

   8. Simplified 61.1%

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

   if -8.5e139 < j < -9.8e-56

   1. Initial program 94.9%

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

   3. Taylor expanded in i around inf

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

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

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 26.7%

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

   5. Simplified 26.7%

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

   if -9.8e-56 < j < 2.00000000000000007e-97

   1. Initial program 90.2%

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

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot c} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 31.0%

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

   5. Simplified 31.0%

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

   if 2.00000000000000007e-97 < j < 2.2999999999999998e-31

   1. Initial program 80.3%

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

   3. Taylor expanded in a around inf

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

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

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

      2. *-lowering-*.f64 41.9%

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

   5. Simplified 41.9%

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

   if 2.2999999999999998e-31 < j

   1. Initial program 88.0%

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

   3. Taylor expanded in j around inf

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

      1. *-commutative N/A

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

      2. associate-*l* 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 39.9%

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

   5. Simplified 39.9%

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

4. Final simplification 37.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -8.5 \cdot 10^{+139}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;j \leq -9.8 \cdot 10^{-56}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;j \leq 2 \cdot 10^{-97}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;j \leq 2.3 \cdot 10^{-31}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 32.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := -27 \cdot \left(j \cdot k\right)\\ \mathbf{if}\;j \leq -4.6 \cdot 10^{+139}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -5.3 \cdot 10^{-55}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;j \leq 1.12 \cdot 10^{-96}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;j \leq 2.2 \cdot 10^{-31}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (* -27.0 (* j k))))
   (if (<= j -4.6e+139)
     t_1
     (if (<= j -5.3e-55)
       (* -4.0 (* x i))
       (if (<= j 1.12e-96)
         (* b c)
         (if (<= j 2.2e-31) (* -4.0 (* t a)) t_1))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -27.0 * (j * k);
	double tmp;
	if (j <= -4.6e+139) {
		tmp = t_1;
	} else if (j <= -5.3e-55) {
		tmp = -4.0 * (x * i);
	} else if (j <= 1.12e-96) {
		tmp = b * c;
	} else if (j <= 2.2e-31) {
		tmp = -4.0 * (t * a);
	} 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 = (-27.0d0) * (j * k)
    if (j <= (-4.6d+139)) then
        tmp = t_1
    else if (j <= (-5.3d-55)) then
        tmp = (-4.0d0) * (x * i)
    else if (j <= 1.12d-96) then
        tmp = b * c
    else if (j <= 2.2d-31) then
        tmp = (-4.0d0) * (t * a)
    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 = -27.0 * (j * k);
	double tmp;
	if (j <= -4.6e+139) {
		tmp = t_1;
	} else if (j <= -5.3e-55) {
		tmp = -4.0 * (x * i);
	} else if (j <= 1.12e-96) {
		tmp = b * c;
	} else if (j <= 2.2e-31) {
		tmp = -4.0 * (t * a);
	} 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 = -27.0 * (j * k)
	tmp = 0
	if j <= -4.6e+139:
		tmp = t_1
	elif j <= -5.3e-55:
		tmp = -4.0 * (x * i)
	elif j <= 1.12e-96:
		tmp = b * c
	elif j <= 2.2e-31:
		tmp = -4.0 * (t * a)
	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(-27.0 * Float64(j * k))
	tmp = 0.0
	if (j <= -4.6e+139)
		tmp = t_1;
	elseif (j <= -5.3e-55)
		tmp = Float64(-4.0 * Float64(x * i));
	elseif (j <= 1.12e-96)
		tmp = Float64(b * c);
	elseif (j <= 2.2e-31)
		tmp = Float64(-4.0 * Float64(t * a));
	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 = -27.0 * (j * k);
	tmp = 0.0;
	if (j <= -4.6e+139)
		tmp = t_1;
	elseif (j <= -5.3e-55)
		tmp = -4.0 * (x * i);
	elseif (j <= 1.12e-96)
		tmp = b * c;
	elseif (j <= 2.2e-31)
		tmp = -4.0 * (t * a);
	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[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -4.6e+139], t$95$1, If[LessEqual[j, -5.3e-55], N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.12e-96], N[(b * c), $MachinePrecision], If[LessEqual[j, 2.2e-31], N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -4.6e139 or 2.2000000000000001e-31 < j

   1. Initial program 83.8%

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

   3. Taylor expanded in x around -inf

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

   5. Simplified 78.8%

      \[\leadsto \color{blue}{\left(4 \cdot i + \left(\left(\left(t \cdot -18\right) \cdot y\right) \cdot z - \frac{b \cdot c + \left(j \cdot \left(k \cdot -27\right) + -4 \cdot \left(a \cdot t\right)\right)}{x}\right)\right) \cdot \left(0 - x\right)} \]

   6. Taylor expanded in j around inf

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

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

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

      2. *-lowering-*.f64 46.7%

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

   8. Simplified 46.7%

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

   if -4.6e139 < j < -5.3000000000000003e-55

   1. Initial program 94.9%

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

   3. Taylor expanded in i around inf

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

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

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 26.7%

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

   5. Simplified 26.7%

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

   if -5.3000000000000003e-55 < j < 1.1200000000000001e-96

   1. Initial program 90.2%

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

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot c} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 31.0%

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

   5. Simplified 31.0%

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

   if 1.1200000000000001e-96 < j < 2.2000000000000001e-31

   1. Initial program 80.3%

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

   3. Taylor expanded in a around inf

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

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

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

      2. *-lowering-*.f64 41.9%

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

   5. Simplified 41.9%

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

4. Final simplification 37.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -4.6 \cdot 10^{+139}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;j \leq -5.3 \cdot 10^{-55}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;j \leq 1.12 \cdot 10^{-96}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;j \leq 2.2 \cdot 10^{-31}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 70.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -2.05 \cdot 10^{-64}:\\ \;\;\;\;\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+27}:\\ \;\;\;\;b \cdot c + \left(j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t \cdot \left(18 \cdot \left(y \cdot z\right)\right) + i \cdot -4\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= x -2.05e-64)
   (- (- (* b c) (* (* x 4.0) i)) (* (* j 27.0) k))
   (if (<= x 3.2e+27)
     (+ (* b c) (+ (* j (* k -27.0)) (* -4.0 (* t a))))
     (* x (+ (* t (* 18.0 (* y z))) (* i -4.0))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (x <= -2.05e-64) {
		tmp = ((b * c) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	} else if (x <= 3.2e+27) {
		tmp = (b * c) + ((j * (k * -27.0)) + (-4.0 * (t * a)));
	} else {
		tmp = x * ((t * (18.0 * (y * z))) + (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 <= (-2.05d-64)) then
        tmp = ((b * c) - ((x * 4.0d0) * i)) - ((j * 27.0d0) * k)
    else if (x <= 3.2d+27) then
        tmp = (b * c) + ((j * (k * (-27.0d0))) + ((-4.0d0) * (t * a)))
    else
        tmp = x * ((t * (18.0d0 * (y * z))) + (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 <= -2.05e-64) {
		tmp = ((b * c) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	} else if (x <= 3.2e+27) {
		tmp = (b * c) + ((j * (k * -27.0)) + (-4.0 * (t * a)));
	} else {
		tmp = x * ((t * (18.0 * (y * z))) + (i * -4.0));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if x <= -2.05e-64:
		tmp = ((b * c) - ((x * 4.0) * i)) - ((j * 27.0) * k)
	elif x <= 3.2e+27:
		tmp = (b * c) + ((j * (k * -27.0)) + (-4.0 * (t * a)))
	else:
		tmp = x * ((t * (18.0 * (y * z))) + (i * -4.0))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (x <= -2.05e-64)
		tmp = Float64(Float64(Float64(b * c) - Float64(Float64(x * 4.0) * i)) - Float64(Float64(j * 27.0) * k));
	elseif (x <= 3.2e+27)
		tmp = Float64(Float64(b * c) + Float64(Float64(j * Float64(k * -27.0)) + Float64(-4.0 * Float64(t * a))));
	else
		tmp = Float64(x * Float64(Float64(t * Float64(18.0 * Float64(y * z))) + 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 <= -2.05e-64)
		tmp = ((b * c) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	elseif (x <= 3.2e+27)
		tmp = (b * c) + ((j * (k * -27.0)) + (-4.0 * (t * a)));
	else
		tmp = x * ((t * (18.0 * (y * z))) + (i * -4.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[x, -2.05e-64], N[(N[(N[(b * c), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.2e+27], N[(N[(b * c), $MachinePrecision] + N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(t * N[(18.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.05e-64

   1. Initial program 81.4%

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

   3. Taylor expanded in t around 0

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

      1. *-lowering-*.f64 71.1%

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

   5. Simplified 71.1%

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

   if -2.05e-64 < x < 3.20000000000000015e27

   1. Initial program 95.9%

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

   3. Taylor expanded in x around 0

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

      1. sub-neg N/A

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

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

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

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

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

      4. +-commutative N/A

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

      5. distribute-neg-in N/A

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

      6. distribute-lft-neg-in N/A

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

      7. metadata-eval N/A

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

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

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

      9. *-commutative N/A

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

      10. associate-*l* N/A

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

      11. *-commutative N/A

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

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

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

      13. *-commutative N/A

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

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

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

      15. distribute-lft-neg-in N/A

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

      16. metadata-eval N/A

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

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

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

      18. *-lowering-*.f64 76.5%

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

   5. Simplified 76.5%

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

   if 3.20000000000000015e27 < x

   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 x around inf

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

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

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

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

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

      3. metadata-eval N/A

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

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

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

      5. *-commutative N/A

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

      6. associate-*l* N/A

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

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

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

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

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

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

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

      10. *-lowering-*.f64 67.6%

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

   5. Simplified 67.6%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.05 \cdot 10^{-64}:\\ \;\;\;\;\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+27}:\\ \;\;\;\;b \cdot c + \left(j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t \cdot \left(18 \cdot \left(y \cdot z\right)\right) + i \cdot -4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 65.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := x \cdot \left(t \cdot \left(18 \cdot \left(y \cdot z\right)\right) + i \cdot -4\right)\\ \mathbf{if}\;i \leq -1.05 \cdot 10^{+146}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 1.2 \cdot 10^{+101}:\\ \;\;\;\;b \cdot c + \left(j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (+ (* t (* 18.0 (* y z))) (* i -4.0)))))
   (if (<= i -1.05e+146)
     t_1
     (if (<= i 1.2e+101)
       (+ (* b c) (+ (* j (* k -27.0)) (* -4.0 (* t a))))
       t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = x * ((t * (18.0 * (y * z))) + (i * -4.0));
	double tmp;
	if (i <= -1.05e+146) {
		tmp = t_1;
	} else if (i <= 1.2e+101) {
		tmp = (b * c) + ((j * (k * -27.0)) + (-4.0 * (t * a)));
	} 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 * ((t * (18.0d0 * (y * z))) + (i * (-4.0d0)))
    if (i <= (-1.05d+146)) then
        tmp = t_1
    else if (i <= 1.2d+101) then
        tmp = (b * c) + ((j * (k * (-27.0d0))) + ((-4.0d0) * (t * a)))
    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 * ((t * (18.0 * (y * z))) + (i * -4.0));
	double tmp;
	if (i <= -1.05e+146) {
		tmp = t_1;
	} else if (i <= 1.2e+101) {
		tmp = (b * c) + ((j * (k * -27.0)) + (-4.0 * (t * a)));
	} 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 * ((t * (18.0 * (y * z))) + (i * -4.0))
	tmp = 0
	if i <= -1.05e+146:
		tmp = t_1
	elif i <= 1.2e+101:
		tmp = (b * c) + ((j * (k * -27.0)) + (-4.0 * (t * a)))
	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(t * Float64(18.0 * Float64(y * z))) + Float64(i * -4.0)))
	tmp = 0.0
	if (i <= -1.05e+146)
		tmp = t_1;
	elseif (i <= 1.2e+101)
		tmp = Float64(Float64(b * c) + Float64(Float64(j * Float64(k * -27.0)) + Float64(-4.0 * Float64(t * a))));
	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 * ((t * (18.0 * (y * z))) + (i * -4.0));
	tmp = 0.0;
	if (i <= -1.05e+146)
		tmp = t_1;
	elseif (i <= 1.2e+101)
		tmp = (b * c) + ((j * (k * -27.0)) + (-4.0 * (t * a)));
	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[(t * N[(18.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1.05e+146], t$95$1, If[LessEqual[i, 1.2e+101], N[(N[(b * c), $MachinePrecision] + N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if i < -1.05e146 or 1.19999999999999994e101 < i

   1. Initial program 81.9%

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

   3. Taylor expanded in x around inf

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

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

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

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

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

      3. metadata-eval N/A

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

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

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

      5. *-commutative N/A

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

      6. associate-*l* N/A

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

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

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

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

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

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

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, z\right), 18\right)\right), \left(-4 \cdot i\right)\right)\right) \]

      10. *-lowering-*.f64 66.6%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, z\right), 18\right)\right), \mathsf{*.f64}\left(-4, \color{blue}{i}\right)\right)\right) \]

   5. Simplified 66.6%

      \[\leadsto \color{blue}{x \cdot \left(t \cdot \left(\left(y \cdot z\right) \cdot 18\right) + -4 \cdot i\right)} \]

   if -1.05e146 < i < 1.19999999999999994e101

   1. Initial program 90.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto b \cdot c + \color{blue}{\left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)} \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(b \cdot c\right), \color{blue}{\left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\mathsf{neg}\left(\color{blue}{\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)}\right)\right)\right) \]

      4. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\mathsf{neg}\left(\left(27 \cdot \left(j \cdot k\right) + 4 \cdot \left(a \cdot t\right)\right)\right)\right)\right) \]

      5. distribute-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)}\right)\right) \]

      6. distribute-lft-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right) + \left(\mathsf{neg}\left(\color{blue}{4 \cdot \left(a \cdot t\right)}\right)\right)\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(-27 \cdot \left(j \cdot k\right) + \left(\mathsf{neg}\left(\color{blue}{4} \cdot \left(a \cdot t\right)\right)\right)\right)\right) \]

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{+.f64}\left(\left(-27 \cdot \left(j \cdot k\right)\right), \color{blue}{\left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)}\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{+.f64}\left(\left(\left(j \cdot k\right) \cdot -27\right), \left(\mathsf{neg}\left(\color{blue}{4 \cdot \left(a \cdot t\right)}\right)\right)\right)\right) \]

      10. associate-*l* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{+.f64}\left(\left(j \cdot \left(k \cdot -27\right)\right), \left(\mathsf{neg}\left(\color{blue}{4 \cdot \left(a \cdot t\right)}\right)\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{+.f64}\left(\left(j \cdot \left(-27 \cdot k\right)\right), \left(\mathsf{neg}\left(4 \cdot \color{blue}{\left(a \cdot t\right)}\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(j, \left(-27 \cdot k\right)\right), \left(\mathsf{neg}\left(\color{blue}{4 \cdot \left(a \cdot t\right)}\right)\right)\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(j, \left(k \cdot -27\right)\right), \left(\mathsf{neg}\left(4 \cdot \color{blue}{\left(a \cdot t\right)}\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(j, \mathsf{*.f64}\left(k, -27\right)\right), \left(\mathsf{neg}\left(4 \cdot \color{blue}{\left(a \cdot t\right)}\right)\right)\right)\right) \]

      15. distribute-lft-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(j, \mathsf{*.f64}\left(k, -27\right)\right), \left(\left(\mathsf{neg}\left(4\right)\right) \cdot \color{blue}{\left(a \cdot t\right)}\right)\right)\right) \]

      16. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(j, \mathsf{*.f64}\left(k, -27\right)\right), \left(-4 \cdot \left(\color{blue}{a} \cdot t\right)\right)\right)\right) \]

      17. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(j, \mathsf{*.f64}\left(k, -27\right)\right), \mathsf{*.f64}\left(-4, \color{blue}{\left(a \cdot t\right)}\right)\right)\right) \]

      18. *-lowering-*.f64 73.1%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(j, \mathsf{*.f64}\left(k, -27\right)\right), \mathsf{*.f64}\left(-4, \mathsf{*.f64}\left(a, \color{blue}{t}\right)\right)\right)\right) \]

   5. Simplified 73.1%

      \[\leadsto \color{blue}{b \cdot c + \left(j \cdot \left(k \cdot -27\right) + -4 \cdot \left(a \cdot t\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.05 \cdot 10^{+146}:\\ \;\;\;\;x \cdot \left(t \cdot \left(18 \cdot \left(y \cdot z\right)\right) + i \cdot -4\right)\\ \mathbf{elif}\;i \leq 1.2 \cdot 10^{+101}:\\ \;\;\;\;b \cdot c + \left(j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t \cdot \left(18 \cdot \left(y \cdot z\right)\right) + i \cdot -4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 44.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;j \leq -4 \cdot 10^{+139}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;j \leq -8.6 \cdot 10^{-56}:\\ \;\;\;\;-4 \cdot \left(x \cdot i + t \cdot a\right)\\ \mathbf{elif}\;j \leq 2.3 \cdot 10^{-31}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{j \cdot \left(k \cdot -27\right)}{t}\\ \end{array} \end{array} \]

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 (<= j -4e+139)
   (* k (* j -27.0))
   (if (<= j -8.6e-56)
     (* -4.0 (+ (* x i) (* t a)))
     (if (<= j 2.3e-31)
       (+ (* b c) (* -4.0 (* t a)))
       (* t (/ (* j (* k -27.0)) t))))))

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 (j <= -4e+139) {
		tmp = k * (j * -27.0);
	} else if (j <= -8.6e-56) {
		tmp = -4.0 * ((x * i) + (t * a));
	} else if (j <= 2.3e-31) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else {
		tmp = t * ((j * (k * -27.0)) / t);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 (j <= (-4d+139)) then
        tmp = k * (j * (-27.0d0))
    else if (j <= (-8.6d-56)) then
        tmp = (-4.0d0) * ((x * i) + (t * a))
    else if (j <= 2.3d-31) then
        tmp = (b * c) + ((-4.0d0) * (t * a))
    else
        tmp = t * ((j * (k * (-27.0d0))) / t)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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 (j <= -4e+139) {
		tmp = k * (j * -27.0);
	} else if (j <= -8.6e-56) {
		tmp = -4.0 * ((x * i) + (t * a));
	} else if (j <= 2.3e-31) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else {
		tmp = t * ((j * (k * -27.0)) / t);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if j <= -4e+139:
		tmp = k * (j * -27.0)
	elif j <= -8.6e-56:
		tmp = -4.0 * ((x * i) + (t * a))
	elif j <= 2.3e-31:
		tmp = (b * c) + (-4.0 * (t * a))
	else:
		tmp = t * ((j * (k * -27.0)) / t)
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (j <= -4e+139)
		tmp = Float64(k * Float64(j * -27.0));
	elseif (j <= -8.6e-56)
		tmp = Float64(-4.0 * Float64(Float64(x * i) + Float64(t * a)));
	elseif (j <= 2.3e-31)
		tmp = Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a)));
	else
		tmp = Float64(t * Float64(Float64(j * Float64(k * -27.0)) / t));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (j <= -4e+139)
		tmp = k * (j * -27.0);
	elseif (j <= -8.6e-56)
		tmp = -4.0 * ((x * i) + (t * a));
	elseif (j <= 2.3e-31)
		tmp = (b * c) + (-4.0 * (t * a));
	else
		tmp = t * ((j * (k * -27.0)) / t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[j, -4e+139], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -8.6e-56], N[(-4.0 * N[(N[(x * i), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.3e-31], N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if j < -4.00000000000000013e139

   1. Initial program 74.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right), \color{blue}{\left(\left(j \cdot 27\right) \cdot k\right)}\right) \]

   4. Applied egg-rr 74.8%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot z + a \cdot -4\right) + \left(b \cdot c + -4 \cdot \left(x \cdot i\right)\right)\right) - 27 \cdot \left(j \cdot k\right)} \]

   5. Taylor expanded in j around inf

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]
   6. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(-27 \cdot j\right) \cdot \color{blue}{k} \]

      2. *-commutative N/A

         \[\leadsto k \cdot \color{blue}{\left(-27 \cdot j\right)} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(k, \color{blue}{\left(-27 \cdot j\right)}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(k, \left(j \cdot \color{blue}{-27}\right)\right) \]

      5. *-lowering-*.f64 61.1%

         \[\leadsto \mathsf{*.f64}\left(k, \mathsf{*.f64}\left(j, \color{blue}{-27}\right)\right) \]

   7. Simplified 61.1%

      \[\leadsto \color{blue}{k \cdot \left(j \cdot -27\right)} \]

   if -4.00000000000000013e139 < j < -8.6000000000000002e-56

   1. Initial program 94.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\color{blue}{\left(-4 \cdot \left(a \cdot t\right)\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(-4, \left(a \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

      2. *-lowering-*.f64 58.5%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(-4, \mathsf{*.f64}\left(a, t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

   5. Simplified 58.5%

      \[\leadsto \left(\color{blue}{-4 \cdot \left(a \cdot t\right)} - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   6. Taylor expanded in j around 0

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t\right) - 4 \cdot \left(i \cdot x\right)} \]
   7. Step-by-step derivation

      1. cancel-sign-sub-inv N/A

         \[\leadsto -4 \cdot \left(a \cdot t\right) + \color{blue}{\left(\mathsf{neg}\left(4\right)\right) \cdot \left(i \cdot x\right)} \]

      2. metadata-eval N/A

         \[\leadsto -4 \cdot \left(a \cdot t\right) + -4 \cdot \left(\color{blue}{i} \cdot x\right) \]

      3. distribute-lft-out N/A

         \[\leadsto -4 \cdot \color{blue}{\left(a \cdot t + i \cdot x\right)} \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-4, \color{blue}{\left(a \cdot t + i \cdot x\right)}\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-4, \mathsf{+.f64}\left(\left(a \cdot t\right), \color{blue}{\left(i \cdot x\right)}\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(-4, \mathsf{+.f64}\left(\left(t \cdot a\right), \left(\color{blue}{i} \cdot x\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, a\right), \left(\color{blue}{i} \cdot x\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(-4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, a\right), \left(x \cdot \color{blue}{i}\right)\right)\right) \]

      9. *-lowering-*.f64 46.4%

         \[\leadsto \mathsf{*.f64}\left(-4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, a\right), \mathsf{*.f64}\left(x, \color{blue}{i}\right)\right)\right) \]

   8. Simplified 46.4%

      \[\leadsto \color{blue}{-4 \cdot \left(t \cdot a + x \cdot i\right)} \]

   if -8.6000000000000002e-56 < j < 2.2999999999999998e-31

   1. Initial program 88.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto b \cdot c + \color{blue}{\left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)} \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(b \cdot c\right), \color{blue}{\left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\mathsf{neg}\left(\color{blue}{\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)}\right)\right)\right) \]

      4. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\mathsf{neg}\left(\left(27 \cdot \left(j \cdot k\right) + 4 \cdot \left(a \cdot t\right)\right)\right)\right)\right) \]

      5. distribute-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)}\right)\right) \]

      6. distribute-lft-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right) + \left(\mathsf{neg}\left(\color{blue}{4 \cdot \left(a \cdot t\right)}\right)\right)\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(-27 \cdot \left(j \cdot k\right) + \left(\mathsf{neg}\left(\color{blue}{4} \cdot \left(a \cdot t\right)\right)\right)\right)\right) \]

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{+.f64}\left(\left(-27 \cdot \left(j \cdot k\right)\right), \color{blue}{\left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)}\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{+.f64}\left(\left(\left(j \cdot k\right) \cdot -27\right), \left(\mathsf{neg}\left(\color{blue}{4 \cdot \left(a \cdot t\right)}\right)\right)\right)\right) \]

      10. associate-*l* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{+.f64}\left(\left(j \cdot \left(k \cdot -27\right)\right), \left(\mathsf{neg}\left(\color{blue}{4 \cdot \left(a \cdot t\right)}\right)\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{+.f64}\left(\left(j \cdot \left(-27 \cdot k\right)\right), \left(\mathsf{neg}\left(4 \cdot \color{blue}{\left(a \cdot t\right)}\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(j, \left(-27 \cdot k\right)\right), \left(\mathsf{neg}\left(\color{blue}{4 \cdot \left(a \cdot t\right)}\right)\right)\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(j, \left(k \cdot -27\right)\right), \left(\mathsf{neg}\left(4 \cdot \color{blue}{\left(a \cdot t\right)}\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(j, \mathsf{*.f64}\left(k, -27\right)\right), \left(\mathsf{neg}\left(4 \cdot \color{blue}{\left(a \cdot t\right)}\right)\right)\right)\right) \]

      15. distribute-lft-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(j, \mathsf{*.f64}\left(k, -27\right)\right), \left(\left(\mathsf{neg}\left(4\right)\right) \cdot \color{blue}{\left(a \cdot t\right)}\right)\right)\right) \]

      16. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(j, \mathsf{*.f64}\left(k, -27\right)\right), \left(-4 \cdot \left(\color{blue}{a} \cdot t\right)\right)\right)\right) \]

      17. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(j, \mathsf{*.f64}\left(k, -27\right)\right), \mathsf{*.f64}\left(-4, \color{blue}{\left(a \cdot t\right)}\right)\right)\right) \]

      18. *-lowering-*.f64 57.5%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(j, \mathsf{*.f64}\left(k, -27\right)\right), \mathsf{*.f64}\left(-4, \mathsf{*.f64}\left(a, \color{blue}{t}\right)\right)\right)\right) \]

   5. Simplified 57.5%

      \[\leadsto \color{blue}{b \cdot c + \left(j \cdot \left(k \cdot -27\right) + -4 \cdot \left(a \cdot t\right)\right)} \]

   6. Taylor expanded in j around 0

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t\right) + b \cdot c} \]
   7. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto b \cdot c + \color{blue}{-4 \cdot \left(a \cdot t\right)} \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(b \cdot c\right), \color{blue}{\left(-4 \cdot \left(a \cdot t\right)\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\color{blue}{-4} \cdot \left(a \cdot t\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(-4, \color{blue}{\left(a \cdot t\right)}\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(-4, \left(t \cdot \color{blue}{a}\right)\right)\right) \]

      6. *-lowering-*.f64 52.7%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(-4, \mathsf{*.f64}\left(t, \color{blue}{a}\right)\right)\right) \]

   8. Simplified 52.7%

      \[\leadsto \color{blue}{b \cdot c + -4 \cdot \left(t \cdot a\right)} \]

   if 2.2999999999999998e-31 < j

   1. Initial program 88.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto b \cdot c + \color{blue}{\left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)} \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(b \cdot c\right), \color{blue}{\left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\mathsf{neg}\left(\color{blue}{\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)}\right)\right)\right) \]

      4. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\mathsf{neg}\left(\left(27 \cdot \left(j \cdot k\right) + 4 \cdot \left(a \cdot t\right)\right)\right)\right)\right) \]

      5. distribute-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)}\right)\right) \]

      6. distribute-lft-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right) + \left(\mathsf{neg}\left(\color{blue}{4 \cdot \left(a \cdot t\right)}\right)\right)\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(-27 \cdot \left(j \cdot k\right) + \left(\mathsf{neg}\left(\color{blue}{4} \cdot \left(a \cdot t\right)\right)\right)\right)\right) \]

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{+.f64}\left(\left(-27 \cdot \left(j \cdot k\right)\right), \color{blue}{\left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)}\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{+.f64}\left(\left(\left(j \cdot k\right) \cdot -27\right), \left(\mathsf{neg}\left(\color{blue}{4 \cdot \left(a \cdot t\right)}\right)\right)\right)\right) \]

      10. associate-*l* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{+.f64}\left(\left(j \cdot \left(k \cdot -27\right)\right), \left(\mathsf{neg}\left(\color{blue}{4 \cdot \left(a \cdot t\right)}\right)\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{+.f64}\left(\left(j \cdot \left(-27 \cdot k\right)\right), \left(\mathsf{neg}\left(4 \cdot \color{blue}{\left(a \cdot t\right)}\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(j, \left(-27 \cdot k\right)\right), \left(\mathsf{neg}\left(\color{blue}{4 \cdot \left(a \cdot t\right)}\right)\right)\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(j, \left(k \cdot -27\right)\right), \left(\mathsf{neg}\left(4 \cdot \color{blue}{\left(a \cdot t\right)}\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(j, \mathsf{*.f64}\left(k, -27\right)\right), \left(\mathsf{neg}\left(4 \cdot \color{blue}{\left(a \cdot t\right)}\right)\right)\right)\right) \]

      15. distribute-lft-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(j, \mathsf{*.f64}\left(k, -27\right)\right), \left(\left(\mathsf{neg}\left(4\right)\right) \cdot \color{blue}{\left(a \cdot t\right)}\right)\right)\right) \]

      16. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(j, \mathsf{*.f64}\left(k, -27\right)\right), \left(-4 \cdot \left(\color{blue}{a} \cdot t\right)\right)\right)\right) \]

      17. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(j, \mathsf{*.f64}\left(k, -27\right)\right), \mathsf{*.f64}\left(-4, \color{blue}{\left(a \cdot t\right)}\right)\right)\right) \]

      18. *-lowering-*.f64 69.7%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(j, \mathsf{*.f64}\left(k, -27\right)\right), \mathsf{*.f64}\left(-4, \mathsf{*.f64}\left(a, \color{blue}{t}\right)\right)\right)\right) \]

   5. Simplified 69.7%

      \[\leadsto \color{blue}{b \cdot c + \left(j \cdot \left(k \cdot -27\right) + -4 \cdot \left(a \cdot t\right)\right)} \]

   6. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(-27 \cdot \frac{j \cdot k}{t} + \left(-4 \cdot a + \frac{b \cdot c}{t}\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(-27 \cdot \frac{j \cdot k}{t} + \left(-4 \cdot a + \frac{b \cdot c}{t}\right)\right)}\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(\left(-4 \cdot a + \frac{b \cdot c}{t}\right) + \color{blue}{-27 \cdot \frac{j \cdot k}{t}}\right)\right) \]

      3. associate-+l+ N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(-4 \cdot a + \color{blue}{\left(\frac{b \cdot c}{t} + -27 \cdot \frac{j \cdot k}{t}\right)}\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(-4 \cdot a + \left(\frac{b \cdot c}{t} + \left(\mathsf{neg}\left(27\right)\right) \cdot \frac{\color{blue}{j \cdot k}}{t}\right)\right)\right) \]

      5. cancel-sign-sub-inv N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(-4 \cdot a + \left(\frac{b \cdot c}{t} - \color{blue}{27 \cdot \frac{j \cdot k}{t}}\right)\right)\right) \]

      6. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(-4 \cdot a + \left(\frac{b \cdot c}{t} - \frac{27 \cdot \left(j \cdot k\right)}{\color{blue}{t}}\right)\right)\right) \]

      7. div-sub N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(-4 \cdot a + \frac{b \cdot c - 27 \cdot \left(j \cdot k\right)}{\color{blue}{t}}\right)\right) \]

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(-4 \cdot a\right), \color{blue}{\left(\frac{b \cdot c - 27 \cdot \left(j \cdot k\right)}{t}\right)}\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \left(\frac{\color{blue}{b \cdot c - 27 \cdot \left(j \cdot k\right)}}{t}\right)\right)\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \mathsf{/.f64}\left(\left(b \cdot c - 27 \cdot \left(j \cdot k\right)\right), \color{blue}{t}\right)\right)\right) \]

   8. Simplified 61.4%

      \[\leadsto \color{blue}{t \cdot \left(-4 \cdot a + \frac{b \cdot c + k \cdot \left(j \cdot -27\right)}{t}\right)} \]

   9. Taylor expanded in k around inf

      \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(-27 \cdot \frac{j \cdot k}{t}\right)}\right) \]
   10. Step-by-step derivation

       1. associate-*r/ N/A

          \[\leadsto \mathsf{*.f64}\left(t, \left(\frac{-27 \cdot \left(j \cdot k\right)}{\color{blue}{t}}\right)\right) \]

       2. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(\left(-27 \cdot \left(j \cdot k\right)\right), \color{blue}{t}\right)\right) \]

       3. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(\left(\left(j \cdot k\right) \cdot -27\right), t\right)\right) \]

       4. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(\left(j \cdot \left(k \cdot -27\right)\right), t\right)\right) \]

       5. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(\left(j \cdot \left(-27 \cdot k\right)\right), t\right)\right) \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(j, \left(-27 \cdot k\right)\right), t\right)\right) \]

       7. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(j, \left(k \cdot -27\right)\right), t\right)\right) \]

       8. *-lowering-*.f64 39.5%

          \[\leadsto \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(j, \mathsf{*.f64}\left(k, -27\right)\right), t\right)\right) \]

   11. Simplified 39.5%

       \[\leadsto t \cdot \color{blue}{\frac{j \cdot \left(k \cdot -27\right)}{t}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 49.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -4 \cdot 10^{+139}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;j \leq -8.6 \cdot 10^{-56}:\\ \;\;\;\;-4 \cdot \left(x \cdot i + t \cdot a\right)\\ \mathbf{elif}\;j \leq 2.3 \cdot 10^{-31}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{j \cdot \left(k \cdot -27\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 32.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := -27 \cdot \left(j \cdot k\right)\\ \mathbf{if}\;j \leq -1.52 \cdot 10^{+116}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 1.55 \cdot 10^{-99}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;j \leq 2.3 \cdot 10^{-31}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (* -27.0 (* j k))))
   (if (<= j -1.52e+116)
     t_1
     (if (<= j 1.55e-99) (* b c) (if (<= j 2.3e-31) (* -4.0 (* t a)) t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -27.0 * (j * k);
	double tmp;
	if (j <= -1.52e+116) {
		tmp = t_1;
	} else if (j <= 1.55e-99) {
		tmp = b * c;
	} else if (j <= 2.3e-31) {
		tmp = -4.0 * (t * a);
	} 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 = (-27.0d0) * (j * k)
    if (j <= (-1.52d+116)) then
        tmp = t_1
    else if (j <= 1.55d-99) then
        tmp = b * c
    else if (j <= 2.3d-31) then
        tmp = (-4.0d0) * (t * a)
    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 = -27.0 * (j * k);
	double tmp;
	if (j <= -1.52e+116) {
		tmp = t_1;
	} else if (j <= 1.55e-99) {
		tmp = b * c;
	} else if (j <= 2.3e-31) {
		tmp = -4.0 * (t * a);
	} 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 = -27.0 * (j * k)
	tmp = 0
	if j <= -1.52e+116:
		tmp = t_1
	elif j <= 1.55e-99:
		tmp = b * c
	elif j <= 2.3e-31:
		tmp = -4.0 * (t * a)
	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(-27.0 * Float64(j * k))
	tmp = 0.0
	if (j <= -1.52e+116)
		tmp = t_1;
	elseif (j <= 1.55e-99)
		tmp = Float64(b * c);
	elseif (j <= 2.3e-31)
		tmp = Float64(-4.0 * Float64(t * a));
	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 = -27.0 * (j * k);
	tmp = 0.0;
	if (j <= -1.52e+116)
		tmp = t_1;
	elseif (j <= 1.55e-99)
		tmp = b * c;
	elseif (j <= 2.3e-31)
		tmp = -4.0 * (t * a);
	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[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.52e+116], t$95$1, If[LessEqual[j, 1.55e-99], N[(b * c), $MachinePrecision], If[LessEqual[j, 2.3e-31], N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if j < -1.52e116 or 2.2999999999999998e-31 < j

   1. Initial program 83.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in x around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(\left(-18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + -1 \cdot \frac{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)}{x}\right) - -4 \cdot i\right)\right)} \]

   5. Simplified 78.2%

      \[\leadsto \color{blue}{\left(4 \cdot i + \left(\left(\left(t \cdot -18\right) \cdot y\right) \cdot z - \frac{b \cdot c + \left(j \cdot \left(k \cdot -27\right) + -4 \cdot \left(a \cdot t\right)\right)}{x}\right)\right) \cdot \left(0 - x\right)} \]

   6. Taylor expanded in j around inf

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-27, \color{blue}{\left(j \cdot k\right)}\right) \]

      2. *-lowering-*.f64 46.0%

         \[\leadsto \mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, \color{blue}{k}\right)\right) \]

   8. Simplified 46.0%

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]

   if -1.52e116 < j < 1.5499999999999999e-99

   1. Initial program 91.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot c} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 30.2%

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{c}\right) \]

   5. Simplified 30.2%

      \[\leadsto \color{blue}{b \cdot c} \]

   if 1.5499999999999999e-99 < j < 2.2999999999999998e-31

   1. Initial program 80.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-4, \color{blue}{\left(a \cdot t\right)}\right) \]

      2. *-lowering-*.f64 41.9%

         \[\leadsto \mathsf{*.f64}\left(-4, \mathsf{*.f64}\left(a, \color{blue}{t}\right)\right) \]

   5. Simplified 41.9%

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 37.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.52 \cdot 10^{+116}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;j \leq 1.55 \cdot 10^{-99}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;j \leq 2.3 \cdot 10^{-31}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 42.6% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;j \leq -1.95 \cdot 10^{+141}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;j \leq 2.3 \cdot 10^{-31}:\\ \;\;\;\;-4 \cdot \left(x \cdot i + t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{j \cdot \left(k \cdot -27\right)}{t}\\ \end{array} \end{array} \]

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 (<= j -1.95e+141)
   (* k (* j -27.0))
   (if (<= j 2.3e-31)
     (* -4.0 (+ (* x i) (* t a)))
     (* t (/ (* j (* k -27.0)) t)))))

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 (j <= -1.95e+141) {
		tmp = k * (j * -27.0);
	} else if (j <= 2.3e-31) {
		tmp = -4.0 * ((x * i) + (t * a));
	} else {
		tmp = t * ((j * (k * -27.0)) / t);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 (j <= (-1.95d+141)) then
        tmp = k * (j * (-27.0d0))
    else if (j <= 2.3d-31) then
        tmp = (-4.0d0) * ((x * i) + (t * a))
    else
        tmp = t * ((j * (k * (-27.0d0))) / t)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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 (j <= -1.95e+141) {
		tmp = k * (j * -27.0);
	} else if (j <= 2.3e-31) {
		tmp = -4.0 * ((x * i) + (t * a));
	} else {
		tmp = t * ((j * (k * -27.0)) / t);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if j <= -1.95e+141:
		tmp = k * (j * -27.0)
	elif j <= 2.3e-31:
		tmp = -4.0 * ((x * i) + (t * a))
	else:
		tmp = t * ((j * (k * -27.0)) / t)
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (j <= -1.95e+141)
		tmp = Float64(k * Float64(j * -27.0));
	elseif (j <= 2.3e-31)
		tmp = Float64(-4.0 * Float64(Float64(x * i) + Float64(t * a)));
	else
		tmp = Float64(t * Float64(Float64(j * Float64(k * -27.0)) / t));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (j <= -1.95e+141)
		tmp = k * (j * -27.0);
	elseif (j <= 2.3e-31)
		tmp = -4.0 * ((x * i) + (t * a));
	else
		tmp = t * ((j * (k * -27.0)) / t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[j, -1.95e+141], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.3e-31], N[(-4.0 * N[(N[(x * i), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if j < -1.94999999999999996e141

   1. Initial program 74.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right), \color{blue}{\left(\left(j \cdot 27\right) \cdot k\right)}\right) \]

   4. Applied egg-rr 74.8%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot z + a \cdot -4\right) + \left(b \cdot c + -4 \cdot \left(x \cdot i\right)\right)\right) - 27 \cdot \left(j \cdot k\right)} \]

   5. Taylor expanded in j around inf

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]
   6. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(-27 \cdot j\right) \cdot \color{blue}{k} \]

      2. *-commutative N/A

         \[\leadsto k \cdot \color{blue}{\left(-27 \cdot j\right)} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(k, \color{blue}{\left(-27 \cdot j\right)}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(k, \left(j \cdot \color{blue}{-27}\right)\right) \]

      5. *-lowering-*.f64 61.1%

         \[\leadsto \mathsf{*.f64}\left(k, \mathsf{*.f64}\left(j, \color{blue}{-27}\right)\right) \]

   7. Simplified 61.1%

      \[\leadsto \color{blue}{k \cdot \left(j \cdot -27\right)} \]

   if -1.94999999999999996e141 < j < 2.2999999999999998e-31

   1. Initial program 90.5%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\color{blue}{\left(-4 \cdot \left(a \cdot t\right)\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(-4, \left(a \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

      2. *-lowering-*.f64 55.2%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(-4, \mathsf{*.f64}\left(a, t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

   5. Simplified 55.2%

      \[\leadsto \left(\color{blue}{-4 \cdot \left(a \cdot t\right)} - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   6. Taylor expanded in j around 0

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t\right) - 4 \cdot \left(i \cdot x\right)} \]
   7. Step-by-step derivation

      1. cancel-sign-sub-inv N/A

         \[\leadsto -4 \cdot \left(a \cdot t\right) + \color{blue}{\left(\mathsf{neg}\left(4\right)\right) \cdot \left(i \cdot x\right)} \]

      2. metadata-eval N/A

         \[\leadsto -4 \cdot \left(a \cdot t\right) + -4 \cdot \left(\color{blue}{i} \cdot x\right) \]

      3. distribute-lft-out N/A

         \[\leadsto -4 \cdot \color{blue}{\left(a \cdot t + i \cdot x\right)} \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-4, \color{blue}{\left(a \cdot t + i \cdot x\right)}\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-4, \mathsf{+.f64}\left(\left(a \cdot t\right), \color{blue}{\left(i \cdot x\right)}\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(-4, \mathsf{+.f64}\left(\left(t \cdot a\right), \left(\color{blue}{i} \cdot x\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, a\right), \left(\color{blue}{i} \cdot x\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(-4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, a\right), \left(x \cdot \color{blue}{i}\right)\right)\right) \]

      9. *-lowering-*.f64 47.9%

         \[\leadsto \mathsf{*.f64}\left(-4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, a\right), \mathsf{*.f64}\left(x, \color{blue}{i}\right)\right)\right) \]

   8. Simplified 47.9%

      \[\leadsto \color{blue}{-4 \cdot \left(t \cdot a + x \cdot i\right)} \]

   if 2.2999999999999998e-31 < j

   1. Initial program 88.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto b \cdot c + \color{blue}{\left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)} \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(b \cdot c\right), \color{blue}{\left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\mathsf{neg}\left(\color{blue}{\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)}\right)\right)\right) \]

      4. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\mathsf{neg}\left(\left(27 \cdot \left(j \cdot k\right) + 4 \cdot \left(a \cdot t\right)\right)\right)\right)\right) \]

      5. distribute-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)}\right)\right) \]

      6. distribute-lft-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right) + \left(\mathsf{neg}\left(\color{blue}{4 \cdot \left(a \cdot t\right)}\right)\right)\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(-27 \cdot \left(j \cdot k\right) + \left(\mathsf{neg}\left(\color{blue}{4} \cdot \left(a \cdot t\right)\right)\right)\right)\right) \]

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{+.f64}\left(\left(-27 \cdot \left(j \cdot k\right)\right), \color{blue}{\left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)}\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{+.f64}\left(\left(\left(j \cdot k\right) \cdot -27\right), \left(\mathsf{neg}\left(\color{blue}{4 \cdot \left(a \cdot t\right)}\right)\right)\right)\right) \]

      10. associate-*l* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{+.f64}\left(\left(j \cdot \left(k \cdot -27\right)\right), \left(\mathsf{neg}\left(\color{blue}{4 \cdot \left(a \cdot t\right)}\right)\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{+.f64}\left(\left(j \cdot \left(-27 \cdot k\right)\right), \left(\mathsf{neg}\left(4 \cdot \color{blue}{\left(a \cdot t\right)}\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(j, \left(-27 \cdot k\right)\right), \left(\mathsf{neg}\left(\color{blue}{4 \cdot \left(a \cdot t\right)}\right)\right)\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(j, \left(k \cdot -27\right)\right), \left(\mathsf{neg}\left(4 \cdot \color{blue}{\left(a \cdot t\right)}\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(j, \mathsf{*.f64}\left(k, -27\right)\right), \left(\mathsf{neg}\left(4 \cdot \color{blue}{\left(a \cdot t\right)}\right)\right)\right)\right) \]

      15. distribute-lft-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(j, \mathsf{*.f64}\left(k, -27\right)\right), \left(\left(\mathsf{neg}\left(4\right)\right) \cdot \color{blue}{\left(a \cdot t\right)}\right)\right)\right) \]

      16. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(j, \mathsf{*.f64}\left(k, -27\right)\right), \left(-4 \cdot \left(\color{blue}{a} \cdot t\right)\right)\right)\right) \]

      17. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(j, \mathsf{*.f64}\left(k, -27\right)\right), \mathsf{*.f64}\left(-4, \color{blue}{\left(a \cdot t\right)}\right)\right)\right) \]

      18. *-lowering-*.f64 69.7%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(j, \mathsf{*.f64}\left(k, -27\right)\right), \mathsf{*.f64}\left(-4, \mathsf{*.f64}\left(a, \color{blue}{t}\right)\right)\right)\right) \]

   5. Simplified 69.7%

      \[\leadsto \color{blue}{b \cdot c + \left(j \cdot \left(k \cdot -27\right) + -4 \cdot \left(a \cdot t\right)\right)} \]

   6. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(-27 \cdot \frac{j \cdot k}{t} + \left(-4 \cdot a + \frac{b \cdot c}{t}\right)\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(-27 \cdot \frac{j \cdot k}{t} + \left(-4 \cdot a + \frac{b \cdot c}{t}\right)\right)}\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(\left(-4 \cdot a + \frac{b \cdot c}{t}\right) + \color{blue}{-27 \cdot \frac{j \cdot k}{t}}\right)\right) \]

      3. associate-+l+ N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(-4 \cdot a + \color{blue}{\left(\frac{b \cdot c}{t} + -27 \cdot \frac{j \cdot k}{t}\right)}\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(-4 \cdot a + \left(\frac{b \cdot c}{t} + \left(\mathsf{neg}\left(27\right)\right) \cdot \frac{\color{blue}{j \cdot k}}{t}\right)\right)\right) \]

      5. cancel-sign-sub-inv N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(-4 \cdot a + \left(\frac{b \cdot c}{t} - \color{blue}{27 \cdot \frac{j \cdot k}{t}}\right)\right)\right) \]

      6. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(-4 \cdot a + \left(\frac{b \cdot c}{t} - \frac{27 \cdot \left(j \cdot k\right)}{\color{blue}{t}}\right)\right)\right) \]

      7. div-sub N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(-4 \cdot a + \frac{b \cdot c - 27 \cdot \left(j \cdot k\right)}{\color{blue}{t}}\right)\right) \]

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(-4 \cdot a\right), \color{blue}{\left(\frac{b \cdot c - 27 \cdot \left(j \cdot k\right)}{t}\right)}\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \left(\frac{\color{blue}{b \cdot c - 27 \cdot \left(j \cdot k\right)}}{t}\right)\right)\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \mathsf{/.f64}\left(\left(b \cdot c - 27 \cdot \left(j \cdot k\right)\right), \color{blue}{t}\right)\right)\right) \]

   8. Simplified 61.4%

      \[\leadsto \color{blue}{t \cdot \left(-4 \cdot a + \frac{b \cdot c + k \cdot \left(j \cdot -27\right)}{t}\right)} \]

   9. Taylor expanded in k around inf

      \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(-27 \cdot \frac{j \cdot k}{t}\right)}\right) \]
   10. Step-by-step derivation

       1. associate-*r/ N/A

          \[\leadsto \mathsf{*.f64}\left(t, \left(\frac{-27 \cdot \left(j \cdot k\right)}{\color{blue}{t}}\right)\right) \]

       2. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(\left(-27 \cdot \left(j \cdot k\right)\right), \color{blue}{t}\right)\right) \]

       3. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(\left(\left(j \cdot k\right) \cdot -27\right), t\right)\right) \]

       4. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(\left(j \cdot \left(k \cdot -27\right)\right), t\right)\right) \]

       5. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(\left(j \cdot \left(-27 \cdot k\right)\right), t\right)\right) \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(j, \left(-27 \cdot k\right)\right), t\right)\right) \]

       7. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(j, \left(k \cdot -27\right)\right), t\right)\right) \]

       8. *-lowering-*.f64 39.5%

          \[\leadsto \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(j, \mathsf{*.f64}\left(k, -27\right)\right), t\right)\right) \]

   11. Simplified 39.5%

       \[\leadsto t \cdot \color{blue}{\frac{j \cdot \left(k \cdot -27\right)}{t}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 47.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.95 \cdot 10^{+141}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;j \leq 2.3 \cdot 10^{-31}:\\ \;\;\;\;-4 \cdot \left(x \cdot i + t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{j \cdot \left(k \cdot -27\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 43.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;j \leq -1.5 \cdot 10^{+139}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;j \leq 2.3 \cdot 10^{-31}:\\ \;\;\;\;-4 \cdot \left(x \cdot i + t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= j -1.5e+139)
   (* k (* j -27.0))
   (if (<= j 2.3e-31) (* -4.0 (+ (* x i) (* t a))) (* j (* k -27.0)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (j <= -1.5e+139) {
		tmp = k * (j * -27.0);
	} else if (j <= 2.3e-31) {
		tmp = -4.0 * ((x * i) + (t * a));
	} else {
		tmp = j * (k * -27.0);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (j <= (-1.5d+139)) then
        tmp = k * (j * (-27.0d0))
    else if (j <= 2.3d-31) then
        tmp = (-4.0d0) * ((x * i) + (t * a))
    else
        tmp = j * (k * (-27.0d0))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (j <= -1.5e+139) {
		tmp = k * (j * -27.0);
	} else if (j <= 2.3e-31) {
		tmp = -4.0 * ((x * i) + (t * a));
	} else {
		tmp = j * (k * -27.0);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if j <= -1.5e+139:
		tmp = k * (j * -27.0)
	elif j <= 2.3e-31:
		tmp = -4.0 * ((x * i) + (t * a))
	else:
		tmp = j * (k * -27.0)
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (j <= -1.5e+139)
		tmp = Float64(k * Float64(j * -27.0));
	elseif (j <= 2.3e-31)
		tmp = Float64(-4.0 * Float64(Float64(x * i) + Float64(t * a)));
	else
		tmp = Float64(j * Float64(k * -27.0));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (j <= -1.5e+139)
		tmp = k * (j * -27.0);
	elseif (j <= 2.3e-31)
		tmp = -4.0 * ((x * i) + (t * a));
	else
		tmp = j * (k * -27.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[j, -1.5e+139], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.3e-31], N[(-4.0 * N[(N[(x * i), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if j < -1.5e139

   1. Initial program 74.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right), \color{blue}{\left(\left(j \cdot 27\right) \cdot k\right)}\right) \]

   4. Applied egg-rr 74.8%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot z + a \cdot -4\right) + \left(b \cdot c + -4 \cdot \left(x \cdot i\right)\right)\right) - 27 \cdot \left(j \cdot k\right)} \]

   5. Taylor expanded in j around inf

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]
   6. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(-27 \cdot j\right) \cdot \color{blue}{k} \]

      2. *-commutative N/A

         \[\leadsto k \cdot \color{blue}{\left(-27 \cdot j\right)} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(k, \color{blue}{\left(-27 \cdot j\right)}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(k, \left(j \cdot \color{blue}{-27}\right)\right) \]

      5. *-lowering-*.f64 61.1%

         \[\leadsto \mathsf{*.f64}\left(k, \mathsf{*.f64}\left(j, \color{blue}{-27}\right)\right) \]

   7. Simplified 61.1%

      \[\leadsto \color{blue}{k \cdot \left(j \cdot -27\right)} \]

   if -1.5e139 < j < 2.2999999999999998e-31

   1. Initial program 90.5%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\color{blue}{\left(-4 \cdot \left(a \cdot t\right)\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(-4, \left(a \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

      2. *-lowering-*.f64 55.2%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(-4, \mathsf{*.f64}\left(a, t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

   5. Simplified 55.2%

      \[\leadsto \left(\color{blue}{-4 \cdot \left(a \cdot t\right)} - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   6. Taylor expanded in j around 0

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t\right) - 4 \cdot \left(i \cdot x\right)} \]
   7. Step-by-step derivation

      1. cancel-sign-sub-inv N/A

         \[\leadsto -4 \cdot \left(a \cdot t\right) + \color{blue}{\left(\mathsf{neg}\left(4\right)\right) \cdot \left(i \cdot x\right)} \]

      2. metadata-eval N/A

         \[\leadsto -4 \cdot \left(a \cdot t\right) + -4 \cdot \left(\color{blue}{i} \cdot x\right) \]

      3. distribute-lft-out N/A

         \[\leadsto -4 \cdot \color{blue}{\left(a \cdot t + i \cdot x\right)} \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-4, \color{blue}{\left(a \cdot t + i \cdot x\right)}\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-4, \mathsf{+.f64}\left(\left(a \cdot t\right), \color{blue}{\left(i \cdot x\right)}\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(-4, \mathsf{+.f64}\left(\left(t \cdot a\right), \left(\color{blue}{i} \cdot x\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, a\right), \left(\color{blue}{i} \cdot x\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(-4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, a\right), \left(x \cdot \color{blue}{i}\right)\right)\right) \]

      9. *-lowering-*.f64 47.9%

         \[\leadsto \mathsf{*.f64}\left(-4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, a\right), \mathsf{*.f64}\left(x, \color{blue}{i}\right)\right)\right) \]

   8. Simplified 47.9%

      \[\leadsto \color{blue}{-4 \cdot \left(t \cdot a + x \cdot i\right)} \]

   if 2.2999999999999998e-31 < j

   1. Initial program 88.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(j \cdot k\right) \cdot \color{blue}{-27} \]

      2. associate-*l* 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 39.9%

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(k, \color{blue}{-27}\right)\right) \]

   5. Simplified 39.9%

      \[\leadsto \color{blue}{j \cdot \left(k \cdot -27\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 47.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.5 \cdot 10^{+139}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;j \leq 2.3 \cdot 10^{-31}:\\ \;\;\;\;-4 \cdot \left(x \cdot i + t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 32.1% accurate, 2.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := -27 \cdot \left(j \cdot k\right)\\ \mathbf{if}\;j \leq -3.8 \cdot 10^{+113}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 2.15 \cdot 10^{-78}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* -27.0 (* j k))))
   (if (<= j -3.8e+113) t_1 (if (<= j 2.15e-78) (* 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 (j <= -3.8e+113) {
		tmp = t_1;
	} else if (j <= 2.15e-78) {
		tmp = b * c;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-27.0d0) * (j * k)
    if (j <= (-3.8d+113)) then
        tmp = t_1
    else if (j <= 2.15d-78) then
        tmp = b * c
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -27.0 * (j * k);
	double tmp;
	if (j <= -3.8e+113) {
		tmp = t_1;
	} else if (j <= 2.15e-78) {
		tmp = b * c;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = -27.0 * (j * k)
	tmp = 0
	if j <= -3.8e+113:
		tmp = t_1
	elif j <= 2.15e-78:
		tmp = b * c
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(-27.0 * Float64(j * k))
	tmp = 0.0
	if (j <= -3.8e+113)
		tmp = t_1;
	elseif (j <= 2.15e-78)
		tmp = Float64(b * c);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = -27.0 * (j * k);
	tmp = 0.0;
	if (j <= -3.8e+113)
		tmp = t_1;
	elseif (j <= 2.15e-78)
		tmp = b * c;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -3.8e+113], t$95$1, If[LessEqual[j, 2.15e-78], N[(b * c), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if j < -3.8000000000000003e113 or 2.14999999999999997e-78 < j

   1. Initial program 84.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in x around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(\left(-18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + -1 \cdot \frac{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)}{x}\right) - -4 \cdot i\right)\right)} \]

   5. Simplified 76.8%

      \[\leadsto \color{blue}{\left(4 \cdot i + \left(\left(\left(t \cdot -18\right) \cdot y\right) \cdot z - \frac{b \cdot c + \left(j \cdot \left(k \cdot -27\right) + -4 \cdot \left(a \cdot t\right)\right)}{x}\right)\right) \cdot \left(0 - x\right)} \]

   6. Taylor expanded in j around inf

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-27, \color{blue}{\left(j \cdot k\right)}\right) \]

      2. *-lowering-*.f64 44.0%

         \[\leadsto \mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, \color{blue}{k}\right)\right) \]

   8. Simplified 44.0%

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]

   if -3.8000000000000003e113 < j < 2.14999999999999997e-78

   1. Initial program 90.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot c} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 29.7%

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{c}\right) \]

   5. Simplified 29.7%

      \[\leadsto \color{blue}{b \cdot c} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 23: 23.9% accurate, 10.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ b \cdot c \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k) :precision binary64 (* b c))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	return b * c;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    code = b * c
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	return b * c;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	return b * c

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	return Float64(b * c)
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp = code(x, y, z, t, a, b, c, i, j, k)
	tmp = b * c;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := N[(b * c), $MachinePrecision]

Derivation

1. Initial program 87.9%

   \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
2. Add Preprocessing

3. Taylor expanded in b around inf

   \[\leadsto \color{blue}{b \cdot c} \]
4. Step-by-step derivation

   1. *-lowering-*.f64 24.1%

      \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{c}\right) \]

5. Simplified 24.1%

   \[\leadsto \color{blue}{b \cdot c} \]
6. Add Preprocessing

Developer Target 1: 89.0% 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 2024191 
(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)))