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

Percentage Accurate: 85.4% → 89.5%

Time: 36.7s

Alternatives: 32

Speedup: 0.8×

• 50.1% 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: 85.4% 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: 89.5% accurate, 0.5× speedup

Math

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

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
 (let* ((t_1 (* (* (* x 18.0) y) z)))
   (if (<=
        (- (+ (- (* t_1 t) (* t (* a 4.0))) (* b c)) (* (* x 4.0) i))
        2e+305)
     (+
      (* t (+ t_1 (* a -4.0)))
      (+ (* -27.0 (* j k)) (+ (* b c) (* x (* i -4.0)))))
     (-
      (* b (+ c (* x (+ (/ (* i -4.0) b) (/ (* t (* 18.0 (* y z))) b)))))
      (* k (* j 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 = ((x * 18.0) * y) * z;
	double tmp;
	if (((((t_1 * t) - (t * (a * 4.0))) + (b * c)) - ((x * 4.0) * i)) <= 2e+305) {
		tmp = (t * (t_1 + (a * -4.0))) + ((-27.0 * (j * k)) + ((b * c) + (x * (i * -4.0))));
	} else {
		tmp = (b * (c + (x * (((i * -4.0) / b) + ((t * (18.0 * (y * z))) / b))))) - (k * (j * 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 = ((x * 18.0d0) * y) * z
    if (((((t_1 * t) - (t * (a * 4.0d0))) + (b * c)) - ((x * 4.0d0) * i)) <= 2d+305) then
        tmp = (t * (t_1 + (a * (-4.0d0)))) + (((-27.0d0) * (j * k)) + ((b * c) + (x * (i * (-4.0d0)))))
    else
        tmp = (b * (c + (x * (((i * (-4.0d0)) / b) + ((t * (18.0d0 * (y * z))) / b))))) - (k * (j * 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 = ((x * 18.0) * y) * z;
	double tmp;
	if (((((t_1 * t) - (t * (a * 4.0))) + (b * c)) - ((x * 4.0) * i)) <= 2e+305) {
		tmp = (t * (t_1 + (a * -4.0))) + ((-27.0 * (j * k)) + ((b * c) + (x * (i * -4.0))));
	} else {
		tmp = (b * (c + (x * (((i * -4.0) / b) + ((t * (18.0 * (y * z))) / b))))) - (k * (j * 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 = ((x * 18.0) * y) * z
	tmp = 0
	if ((((t_1 * t) - (t * (a * 4.0))) + (b * c)) - ((x * 4.0) * i)) <= 2e+305:
		tmp = (t * (t_1 + (a * -4.0))) + ((-27.0 * (j * k)) + ((b * c) + (x * (i * -4.0))))
	else:
		tmp = (b * (c + (x * (((i * -4.0) / b) + ((t * (18.0 * (y * z))) / b))))) - (k * (j * 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(Float64(x * 18.0) * y) * z)
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(t_1 * t) - Float64(t * Float64(a * 4.0))) + Float64(b * c)) - Float64(Float64(x * 4.0) * i)) <= 2e+305)
		tmp = Float64(Float64(t * Float64(t_1 + Float64(a * -4.0))) + Float64(Float64(-27.0 * Float64(j * k)) + Float64(Float64(b * c) + Float64(x * Float64(i * -4.0)))));
	else
		tmp = Float64(Float64(b * Float64(c + Float64(x * Float64(Float64(Float64(i * -4.0) / b) + Float64(Float64(t * Float64(18.0 * Float64(y * z))) / b))))) - Float64(k * Float64(j * 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 = ((x * 18.0) * y) * z;
	tmp = 0.0;
	if (((((t_1 * t) - (t * (a * 4.0))) + (b * c)) - ((x * 4.0) * i)) <= 2e+305)
		tmp = (t * (t_1 + (a * -4.0))) + ((-27.0 * (j * k)) + ((b * c) + (x * (i * -4.0))));
	else
		tmp = (b * (c + (x * (((i * -4.0) / b) + ((t * (18.0 * (y * z))) / b))))) - (k * (j * 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[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[N[(N[(N[(N[(t$95$1 * t), $MachinePrecision] - N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision], 2e+305], N[(N[(t * N[(t$95$1 + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision] + N[(N[(b * c), $MachinePrecision] + N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * N[(c + N[(x * N[(N[(N[(i * -4.0), $MachinePrecision] / b), $MachinePrecision] + N[(N[(t * N[(18.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x #s(literal 18 binary64)) y) z) t) (*.f64 (*.f64 a #s(literal 4 binary64)) t)) (*.f64 b c)) (*.f64 (*.f64 x #s(literal 4 binary64)) i)) < 1.9999999999999999e305

   1. Initial program 97.6%

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

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

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

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

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

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

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

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

      6. sub-neg N/A

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

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

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

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

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

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

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

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

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

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

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

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

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

      13. metadata-eval N/A

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

   3. Simplified 97.7%

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

   if 1.9999999999999999e305 < (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x #s(literal 18 binary64)) y) z) t) (*.f64 (*.f64 a #s(literal 4 binary64)) t)) (*.f64 b c)) (*.f64 (*.f64 x #s(literal 4 binary64)) i))

   1. Initial program 61.0%

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

   3. Taylor expanded in b around inf

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

   5. Simplified 78.0%

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

   6. Taylor expanded in a around 0

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

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

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

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

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

      3. associate-*r/ N/A

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

      4. associate-*r* N/A

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

      5. associate-*l/ N/A

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

      6. associate-*r/ N/A

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

      7. associate-*r/ N/A

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

      8. *-commutative N/A

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

      9. associate-*r* N/A

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

      10. associate-*l* N/A

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

      11. associate-*l/ N/A

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

      12. associate-*r/ N/A

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

      13. distribute-rgt-in N/A

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

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

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

   8. Simplified 81.9%

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

4. Final simplification 93.0%

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

Alternative 2: 66.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right)\\ t_2 := k \cdot \left(j \cdot 27\right)\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+20}:\\ \;\;\;\;t\_1 + -27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{-158}:\\ \;\;\;\;b \cdot \left(c + \frac{-4 \cdot \left(t \cdot a + x \cdot i\right)}{b}\right)\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{-51}:\\ \;\;\;\;b \cdot c + t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* t (+ (* (* (* x 18.0) y) z) (* a -4.0))))
        (t_2 (* k (* j 27.0))))
   (if (<= t_2 -1e+20)
     (+ t_1 (* -27.0 (* j k)))
     (if (<= t_2 5e-158)
       (* b (+ c (/ (* -4.0 (+ (* t a) (* x i))) b)))
       (if (<= t_2 5e-51)
         (+ (* b c) t_1)
         (- (- (* b c) (* (* x 4.0) i)) t_2))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * ((((x * 18.0) * y) * z) + (a * -4.0));
	double t_2 = k * (j * 27.0);
	double tmp;
	if (t_2 <= -1e+20) {
		tmp = t_1 + (-27.0 * (j * k));
	} else if (t_2 <= 5e-158) {
		tmp = b * (c + ((-4.0 * ((t * a) + (x * i))) / b));
	} else if (t_2 <= 5e-51) {
		tmp = (b * c) + t_1;
	} else {
		tmp = ((b * c) - ((x * 4.0) * i)) - t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * ((((x * 18.0d0) * y) * z) + (a * (-4.0d0)))
    t_2 = k * (j * 27.0d0)
    if (t_2 <= (-1d+20)) then
        tmp = t_1 + ((-27.0d0) * (j * k))
    else if (t_2 <= 5d-158) then
        tmp = b * (c + (((-4.0d0) * ((t * a) + (x * i))) / b))
    else if (t_2 <= 5d-51) then
        tmp = (b * c) + t_1
    else
        tmp = ((b * c) - ((x * 4.0d0) * i)) - t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * ((((x * 18.0) * y) * z) + (a * -4.0));
	double t_2 = k * (j * 27.0);
	double tmp;
	if (t_2 <= -1e+20) {
		tmp = t_1 + (-27.0 * (j * k));
	} else if (t_2 <= 5e-158) {
		tmp = b * (c + ((-4.0 * ((t * a) + (x * i))) / b));
	} else if (t_2 <= 5e-51) {
		tmp = (b * c) + t_1;
	} else {
		tmp = ((b * c) - ((x * 4.0) * i)) - t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = t * ((((x * 18.0) * y) * z) + (a * -4.0))
	t_2 = k * (j * 27.0)
	tmp = 0
	if t_2 <= -1e+20:
		tmp = t_1 + (-27.0 * (j * k))
	elif t_2 <= 5e-158:
		tmp = b * (c + ((-4.0 * ((t * a) + (x * i))) / b))
	elif t_2 <= 5e-51:
		tmp = (b * c) + t_1
	else:
		tmp = ((b * c) - ((x * 4.0) * i)) - t_2
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(t * Float64(Float64(Float64(Float64(x * 18.0) * y) * z) + Float64(a * -4.0)))
	t_2 = Float64(k * Float64(j * 27.0))
	tmp = 0.0
	if (t_2 <= -1e+20)
		tmp = Float64(t_1 + Float64(-27.0 * Float64(j * k)));
	elseif (t_2 <= 5e-158)
		tmp = Float64(b * Float64(c + Float64(Float64(-4.0 * Float64(Float64(t * a) + Float64(x * i))) / b)));
	elseif (t_2 <= 5e-51)
		tmp = Float64(Float64(b * c) + t_1);
	else
		tmp = Float64(Float64(Float64(b * c) - Float64(Float64(x * 4.0) * i)) - t_2);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = t * ((((x * 18.0) * y) * z) + (a * -4.0));
	t_2 = k * (j * 27.0);
	tmp = 0.0;
	if (t_2 <= -1e+20)
		tmp = t_1 + (-27.0 * (j * k));
	elseif (t_2 <= 5e-158)
		tmp = b * (c + ((-4.0 * ((t * a) + (x * i))) / b));
	elseif (t_2 <= 5e-51)
		tmp = (b * c) + t_1;
	else
		tmp = ((b * c) - ((x * 4.0) * i)) - t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(t * N[(N[(N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+20], N[(t$95$1 + N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e-158], N[(b * N[(c + N[(N[(-4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e-51], N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -1e20

   1. Initial program 86.4%

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

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

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

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

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

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

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

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

      6. sub-neg N/A

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

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

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

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

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

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

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

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

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

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

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

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

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

      13. metadata-eval N/A

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

   3. Simplified 88.4%

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

   5. Taylor expanded in j around inf

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

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

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

      2. *-lowering-*.f64 85.8%

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

   7. Simplified 85.8%

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

   if -1e20 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 4.99999999999999972e-158

   1. Initial program 91.1%

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

   3. Taylor expanded in b around inf

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

   5. Simplified 86.9%

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

   6. Taylor expanded in y around 0

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

      1. distribute-lft-out N/A

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

      2. associate-/l* N/A

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

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

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

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

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

      5. +-commutative N/A

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

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

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

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

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

      8. *-commutative N/A

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

      9. *-lowering-*.f64 76.5%

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

   8. Simplified 76.5%

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

   9. Taylor expanded in j around 0

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

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

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

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

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

       3. associate-*r/ N/A

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

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

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

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

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

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

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

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

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

       8. *-lowering-*.f64 76.5%

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

   11. Simplified 76.5%

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

   if 4.99999999999999972e-158 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 5.00000000000000004e-51

   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. Step-by-step derivation

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

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

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

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

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

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

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

      6. sub-neg N/A

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

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

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

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

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

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

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

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

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

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

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

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

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

      13. metadata-eval N/A

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

   3. Simplified 88.9%

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

   5. Taylor expanded in b around inf

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

      1. *-lowering-*.f64 81.7%

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

   7. Simplified 81.7%

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

   if 5.00000000000000004e-51 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 79.1%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   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 73.3%

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

   5. Simplified 73.3%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \cdot \left(j \cdot 27\right) \leq -1 \cdot 10^{+20}:\\ \;\;\;\;t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right) + -27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 5 \cdot 10^{-158}:\\ \;\;\;\;b \cdot \left(c + \frac{-4 \cdot \left(t \cdot a + x \cdot i\right)}{b}\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 5 \cdot 10^{-51}:\\ \;\;\;\;b \cdot c + t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 82.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := 18 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;b \cdot c \leq -1000:\\ \;\;\;\;b \cdot \left(c + x \cdot \left(\frac{i \cdot -4}{b} + \frac{t \cdot t\_1}{b}\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;b \cdot c \leq 5 \cdot 10^{+130}:\\ \;\;\;\;t \cdot \left(a \cdot -4 + x \cdot t\_1\right) - \left(\left(x \cdot 4\right) \cdot i + j \cdot \left(k \cdot 27\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(c + \frac{-4 \cdot \left(t \cdot a + x \cdot i\right) + j \cdot \left(-27 \cdot k\right)}{b}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* 18.0 (* y z))))
   (if (<= (* b c) -1000.0)
     (-
      (* b (+ c (* x (+ (/ (* i -4.0) b) (/ (* t t_1) b)))))
      (* k (* j 27.0)))
     (if (<= (* b c) 5e+130)
       (- (* t (+ (* a -4.0) (* x t_1))) (+ (* (* x 4.0) i) (* j (* k 27.0))))
       (* b (+ c (/ (+ (* -4.0 (+ (* t a) (* x i))) (* j (* -27.0 k))) b)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 18.0 * (y * z);
	double tmp;
	if ((b * c) <= -1000.0) {
		tmp = (b * (c + (x * (((i * -4.0) / b) + ((t * t_1) / b))))) - (k * (j * 27.0));
	} else if ((b * c) <= 5e+130) {
		tmp = (t * ((a * -4.0) + (x * t_1))) - (((x * 4.0) * i) + (j * (k * 27.0)));
	} else {
		tmp = b * (c + (((-4.0 * ((t * a) + (x * i))) + (j * (-27.0 * k))) / b));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 18.0d0 * (y * z)
    if ((b * c) <= (-1000.0d0)) then
        tmp = (b * (c + (x * (((i * (-4.0d0)) / b) + ((t * t_1) / b))))) - (k * (j * 27.0d0))
    else if ((b * c) <= 5d+130) then
        tmp = (t * ((a * (-4.0d0)) + (x * t_1))) - (((x * 4.0d0) * i) + (j * (k * 27.0d0)))
    else
        tmp = b * (c + ((((-4.0d0) * ((t * a) + (x * i))) + (j * ((-27.0d0) * k))) / b))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 18.0 * (y * z);
	double tmp;
	if ((b * c) <= -1000.0) {
		tmp = (b * (c + (x * (((i * -4.0) / b) + ((t * t_1) / b))))) - (k * (j * 27.0));
	} else if ((b * c) <= 5e+130) {
		tmp = (t * ((a * -4.0) + (x * t_1))) - (((x * 4.0) * i) + (j * (k * 27.0)));
	} else {
		tmp = b * (c + (((-4.0 * ((t * a) + (x * i))) + (j * (-27.0 * k))) / b));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = 18.0 * (y * z)
	tmp = 0
	if (b * c) <= -1000.0:
		tmp = (b * (c + (x * (((i * -4.0) / b) + ((t * t_1) / b))))) - (k * (j * 27.0))
	elif (b * c) <= 5e+130:
		tmp = (t * ((a * -4.0) + (x * t_1))) - (((x * 4.0) * i) + (j * (k * 27.0)))
	else:
		tmp = b * (c + (((-4.0 * ((t * a) + (x * i))) + (j * (-27.0 * k))) / b))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(18.0 * Float64(y * z))
	tmp = 0.0
	if (Float64(b * c) <= -1000.0)
		tmp = Float64(Float64(b * Float64(c + Float64(x * Float64(Float64(Float64(i * -4.0) / b) + Float64(Float64(t * t_1) / b))))) - Float64(k * Float64(j * 27.0)));
	elseif (Float64(b * c) <= 5e+130)
		tmp = Float64(Float64(t * Float64(Float64(a * -4.0) + Float64(x * t_1))) - Float64(Float64(Float64(x * 4.0) * i) + Float64(j * Float64(k * 27.0))));
	else
		tmp = Float64(b * Float64(c + Float64(Float64(Float64(-4.0 * Float64(Float64(t * a) + Float64(x * i))) + Float64(j * Float64(-27.0 * k))) / b)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = 18.0 * (y * z);
	tmp = 0.0;
	if ((b * c) <= -1000.0)
		tmp = (b * (c + (x * (((i * -4.0) / b) + ((t * t_1) / b))))) - (k * (j * 27.0));
	elseif ((b * c) <= 5e+130)
		tmp = (t * ((a * -4.0) + (x * t_1))) - (((x * 4.0) * i) + (j * (k * 27.0)));
	else
		tmp = b * (c + (((-4.0 * ((t * a) + (x * i))) + (j * (-27.0 * k))) / b));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(18.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -1000.0], N[(N[(b * N[(c + N[(x * N[(N[(N[(i * -4.0), $MachinePrecision] / b), $MachinePrecision] + N[(N[(t * t$95$1), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 5e+130], N[(N[(t * N[(N[(a * -4.0), $MachinePrecision] + N[(x * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision] + N[(j * N[(k * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(c + N[(N[(N[(-4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(-27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -1e3

   1. Initial program 85.4%

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

   3. Taylor expanded in b around inf

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

   5. Simplified 87.2%

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

   6. Taylor expanded in a around 0

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

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

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

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

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

      3. associate-*r/ N/A

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

      4. associate-*r* N/A

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

      5. associate-*l/ N/A

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

      6. associate-*r/ N/A

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

      7. associate-*r/ N/A

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

      8. *-commutative N/A

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

      9. associate-*r* N/A

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

      10. associate-*l* N/A

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

      11. associate-*l/ N/A

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

      12. associate-*r/ N/A

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

      13. distribute-rgt-in N/A

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

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

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

   8. Simplified 85.8%

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

   if -1e3 < (*.f64 b c) < 4.9999999999999996e130

   1. Initial program 90.0%

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

   3. Taylor expanded in b around 0

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

      1. associate--r+ N/A

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

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

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

      5. associate--l+ N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. associate--l+ N/A

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

   5. Simplified 86.4%

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

   if 4.9999999999999996e130 < (*.f64 b c)

   1. Initial program 78.2%

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

   3. Taylor expanded in b around inf

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

   5. Simplified 87.1%

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

   6. Taylor expanded in y around 0

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

      1. distribute-lft-out N/A

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

      2. associate-/l* N/A

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

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

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

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

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

      5. +-commutative N/A

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

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

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

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

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

      8. *-commutative N/A

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

      9. *-lowering-*.f64 87.3%

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

   8. Simplified 87.3%

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

   9. Taylor expanded in b around inf

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

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

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

       2. associate--l+ N/A

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

       3. associate-*r/ N/A

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

       4. associate-*r/ N/A

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

       5. div-sub N/A

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

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

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

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

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

   11. Simplified 89.4%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1000:\\ \;\;\;\;b \cdot \left(c + x \cdot \left(\frac{i \cdot -4}{b} + \frac{t \cdot \left(18 \cdot \left(y \cdot z\right)\right)}{b}\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;b \cdot c \leq 5 \cdot 10^{+130}:\\ \;\;\;\;t \cdot \left(a \cdot -4 + x \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right) - \left(\left(x \cdot 4\right) \cdot i + j \cdot \left(k \cdot 27\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(c + \frac{-4 \cdot \left(t \cdot a + x \cdot i\right) + j \cdot \left(-27 \cdot k\right)}{b}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 82.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := b \cdot \left(c + \frac{-4 \cdot \left(t \cdot a + x \cdot i\right) + j \cdot \left(-27 \cdot k\right)}{b}\right)\\ \mathbf{if}\;b \cdot c \leq -2 \cdot 10^{+22}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq 5 \cdot 10^{+130}:\\ \;\;\;\;t \cdot \left(a \cdot -4 + x \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right) - \left(\left(x \cdot 4\right) \cdot i + j \cdot \left(k \cdot 27\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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
         (* b (+ c (/ (+ (* -4.0 (+ (* t a) (* x i))) (* j (* -27.0 k))) b)))))
   (if (<= (* b c) -2e+22)
     t_1
     (if (<= (* b c) 5e+130)
       (-
        (* t (+ (* a -4.0) (* x (* 18.0 (* y z)))))
        (+ (* (* x 4.0) 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 = b * (c + (((-4.0 * ((t * a) + (x * i))) + (j * (-27.0 * k))) / b));
	double tmp;
	if ((b * c) <= -2e+22) {
		tmp = t_1;
	} else if ((b * c) <= 5e+130) {
		tmp = (t * ((a * -4.0) + (x * (18.0 * (y * z))))) - (((x * 4.0) * 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 = b * (c + ((((-4.0d0) * ((t * a) + (x * i))) + (j * ((-27.0d0) * k))) / b))
    if ((b * c) <= (-2d+22)) then
        tmp = t_1
    else if ((b * c) <= 5d+130) then
        tmp = (t * ((a * (-4.0d0)) + (x * (18.0d0 * (y * z))))) - (((x * 4.0d0) * 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 = b * (c + (((-4.0 * ((t * a) + (x * i))) + (j * (-27.0 * k))) / b));
	double tmp;
	if ((b * c) <= -2e+22) {
		tmp = t_1;
	} else if ((b * c) <= 5e+130) {
		tmp = (t * ((a * -4.0) + (x * (18.0 * (y * z))))) - (((x * 4.0) * 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 = b * (c + (((-4.0 * ((t * a) + (x * i))) + (j * (-27.0 * k))) / b))
	tmp = 0
	if (b * c) <= -2e+22:
		tmp = t_1
	elif (b * c) <= 5e+130:
		tmp = (t * ((a * -4.0) + (x * (18.0 * (y * z))))) - (((x * 4.0) * 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(b * Float64(c + Float64(Float64(Float64(-4.0 * Float64(Float64(t * a) + Float64(x * i))) + Float64(j * Float64(-27.0 * k))) / b)))
	tmp = 0.0
	if (Float64(b * c) <= -2e+22)
		tmp = t_1;
	elseif (Float64(b * c) <= 5e+130)
		tmp = Float64(Float64(t * Float64(Float64(a * -4.0) + Float64(x * Float64(18.0 * Float64(y * z))))) - Float64(Float64(Float64(x * 4.0) * i) + Float64(j * Float64(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 = b * (c + (((-4.0 * ((t * a) + (x * i))) + (j * (-27.0 * k))) / b));
	tmp = 0.0;
	if ((b * c) <= -2e+22)
		tmp = t_1;
	elseif ((b * c) <= 5e+130)
		tmp = (t * ((a * -4.0) + (x * (18.0 * (y * z))))) - (((x * 4.0) * 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[(b * N[(c + N[(N[(N[(-4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(-27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -2e+22], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 5e+130], N[(N[(t * N[(N[(a * -4.0), $MachinePrecision] + N[(x * N[(18.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision] + N[(j * N[(k * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -2e22 or 4.9999999999999996e130 < (*.f64 b c)

   1. Initial program 82.5%

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

   3. Taylor expanded in b around inf

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

   5. Simplified 88.4%

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

   6. Taylor expanded in y around 0

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

      1. distribute-lft-out N/A

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

      2. associate-/l* N/A

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

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

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

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

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

      5. +-commutative N/A

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

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

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

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

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

      8. *-commutative N/A

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

      9. *-lowering-*.f64 85.8%

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

   8. Simplified 85.8%

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

   9. Taylor expanded in b around inf

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

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

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

       2. associate--l+ N/A

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

       3. associate-*r/ N/A

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

       4. associate-*r/ N/A

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

       5. div-sub N/A

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

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

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

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

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

   11. Simplified 86.8%

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

   if -2e22 < (*.f64 b c) < 4.9999999999999996e130

   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 b around 0

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

      1. associate--r+ N/A

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

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

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

      5. associate--l+ N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. associate--l+ N/A

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

   5. Simplified 85.6%

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

4. Final simplification 86.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2 \cdot 10^{+22}:\\ \;\;\;\;b \cdot \left(c + \frac{-4 \cdot \left(t \cdot a + x \cdot i\right) + j \cdot \left(-27 \cdot k\right)}{b}\right)\\ \mathbf{elif}\;b \cdot c \leq 5 \cdot 10^{+130}:\\ \;\;\;\;t \cdot \left(a \cdot -4 + x \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right) - \left(\left(x \cdot 4\right) \cdot i + j \cdot \left(k \cdot 27\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(c + \frac{-4 \cdot \left(t \cdot a + x \cdot i\right) + j \cdot \left(-27 \cdot k\right)}{b}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 88.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := -27 \cdot \left(j \cdot k\right)\\ \mathbf{if}\;k \cdot \left(j \cdot 27\right) \leq 5 \cdot 10^{+296}:\\ \;\;\;\;\left(t\_1 + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right) + t \cdot \left(z \cdot \left(x \cdot \left(18 \cdot y\right)\right) + a \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* -27.0 (* j k))))
   (if (<= (* k (* j 27.0)) 5e+296)
     (+
      (+ t_1 (+ (* b c) (* x (* i -4.0))))
      (* t (+ (* z (* x (* 18.0 y))) (* a -4.0))))
     t_1)))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -27.0 * (j * k);
	double tmp;
	if ((k * (j * 27.0)) <= 5e+296) {
		tmp = (t_1 + ((b * c) + (x * (i * -4.0)))) + (t * ((z * (x * (18.0 * y))) + (a * -4.0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-27.0d0) * (j * k)
    if ((k * (j * 27.0d0)) <= 5d+296) then
        tmp = (t_1 + ((b * c) + (x * (i * (-4.0d0))))) + (t * ((z * (x * (18.0d0 * y))) + (a * (-4.0d0))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -27.0 * (j * k);
	double tmp;
	if ((k * (j * 27.0)) <= 5e+296) {
		tmp = (t_1 + ((b * c) + (x * (i * -4.0)))) + (t * ((z * (x * (18.0 * y))) + (a * -4.0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = -27.0 * (j * k)
	tmp = 0
	if (k * (j * 27.0)) <= 5e+296:
		tmp = (t_1 + ((b * c) + (x * (i * -4.0)))) + (t * ((z * (x * (18.0 * y))) + (a * -4.0)))
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(-27.0 * Float64(j * k))
	tmp = 0.0
	if (Float64(k * Float64(j * 27.0)) <= 5e+296)
		tmp = Float64(Float64(t_1 + Float64(Float64(b * c) + Float64(x * Float64(i * -4.0)))) + Float64(t * Float64(Float64(z * Float64(x * Float64(18.0 * y))) + Float64(a * -4.0))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = -27.0 * (j * k);
	tmp = 0.0;
	if ((k * (j * 27.0)) <= 5e+296)
		tmp = (t_1 + ((b * c) + (x * (i * -4.0)))) + (t * ((z * (x * (18.0 * y))) + (a * -4.0)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision], 5e+296], N[(N[(t$95$1 + N[(N[(b * c), $MachinePrecision] + N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(z * N[(x * N[(18.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 5.0000000000000001e296

   1. Initial program 88.4%

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

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

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

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

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

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

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

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

      6. sub-neg N/A

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

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

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

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

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

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

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

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

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

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

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

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

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

      13. metadata-eval N/A

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

   3. Simplified 90.5%

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

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

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

      2. associate-*l* N/A

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

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

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

      4. *-lowering-*.f64 90.1%

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

   6. Applied egg-rr 90.1%

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

   if 5.0000000000000001e296 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 60.0%

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

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

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

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

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

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

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

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

      6. sub-neg N/A

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

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

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

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

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

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

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

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

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

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

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

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

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

      13. metadata-eval N/A

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

   3. Simplified 60.0%

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

   5. Taylor expanded in j around inf

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]
   6. 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 100.0%

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

   7. Simplified 100.0%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \cdot \left(j \cdot 27\right) \leq 5 \cdot 10^{+296}:\\ \;\;\;\;\left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right) + t \cdot \left(z \cdot \left(x \cdot \left(18 \cdot y\right)\right) + a \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 64.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := k \cdot \left(j \cdot 27\right)\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+20}:\\ \;\;\;\;z \cdot \left(t \cdot \left(x \cdot \left(18 \cdot y\right)\right)\right) - t\_1\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+100}:\\ \;\;\;\;b \cdot \left(c + \frac{-4 \cdot \left(t \cdot a + x \cdot i\right)}{b}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot \left(\left(x \cdot 18\right) \cdot t\right)\right) - t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* k (* j 27.0))))
   (if (<= t_1 -1e+20)
     (- (* z (* t (* x (* 18.0 y)))) t_1)
     (if (<= t_1 2e+100)
       (* b (+ c (/ (* -4.0 (+ (* t a) (* x i))) b)))
       (- (* y (* z (* (* x 18.0) t))) t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = k * (j * 27.0);
	double tmp;
	if (t_1 <= -1e+20) {
		tmp = (z * (t * (x * (18.0 * y)))) - t_1;
	} else if (t_1 <= 2e+100) {
		tmp = b * (c + ((-4.0 * ((t * a) + (x * i))) / b));
	} else {
		tmp = (y * (z * ((x * 18.0) * t))) - t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = k * (j * 27.0d0)
    if (t_1 <= (-1d+20)) then
        tmp = (z * (t * (x * (18.0d0 * y)))) - t_1
    else if (t_1 <= 2d+100) then
        tmp = b * (c + (((-4.0d0) * ((t * a) + (x * i))) / b))
    else
        tmp = (y * (z * ((x * 18.0d0) * t))) - t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = k * (j * 27.0);
	double tmp;
	if (t_1 <= -1e+20) {
		tmp = (z * (t * (x * (18.0 * y)))) - t_1;
	} else if (t_1 <= 2e+100) {
		tmp = b * (c + ((-4.0 * ((t * a) + (x * i))) / b));
	} else {
		tmp = (y * (z * ((x * 18.0) * t))) - t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = k * (j * 27.0)
	tmp = 0
	if t_1 <= -1e+20:
		tmp = (z * (t * (x * (18.0 * y)))) - t_1
	elif t_1 <= 2e+100:
		tmp = b * (c + ((-4.0 * ((t * a) + (x * i))) / b))
	else:
		tmp = (y * (z * ((x * 18.0) * t))) - t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(k * Float64(j * 27.0))
	tmp = 0.0
	if (t_1 <= -1e+20)
		tmp = Float64(Float64(z * Float64(t * Float64(x * Float64(18.0 * y)))) - t_1);
	elseif (t_1 <= 2e+100)
		tmp = Float64(b * Float64(c + Float64(Float64(-4.0 * Float64(Float64(t * a) + Float64(x * i))) / b)));
	else
		tmp = Float64(Float64(y * Float64(z * Float64(Float64(x * 18.0) * t))) - t_1);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = k * (j * 27.0);
	tmp = 0.0;
	if (t_1 <= -1e+20)
		tmp = (z * (t * (x * (18.0 * y)))) - t_1;
	elseif (t_1 <= 2e+100)
		tmp = b * (c + ((-4.0 * ((t * a) + (x * i))) / b));
	else
		tmp = (y * (z * ((x * 18.0) * t))) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+20], N[(N[(z * N[(t * N[(x * N[(18.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[t$95$1, 2e+100], N[(b * N[(c + N[(N[(-4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * N[(z * N[(N[(x * 18.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -1e20

   1. Initial program 86.4%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. associate-*r* N/A

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

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

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

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

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

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

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

      9. *-lowering-*.f64 72.7%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(18, x\right)\right), \mathsf{*.f64}\left(y, z\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, \color{blue}{27}\right), k\right)\right) \]

   5. Simplified 72.7%

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

      1. associate-*r* N/A

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

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

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

      3. associate-*l* N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

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

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

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

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

      8. *-lowering-*.f64 74.7%

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

   7. Applied egg-rr 74.7%

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

   if -1e20 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 2.00000000000000003e100

   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 b around inf

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

   5. Simplified 81.4%

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

   6. Taylor expanded in y around 0

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

      1. distribute-lft-out N/A

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

      2. associate-/l* N/A

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

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

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

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

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

      5. +-commutative N/A

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

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

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

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

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

      8. *-commutative N/A

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

      9. *-lowering-*.f64 71.3%

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

   8. Simplified 71.3%

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

   9. Taylor expanded in j around 0

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

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

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

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

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

       3. associate-*r/ N/A

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

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

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

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

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

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

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

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

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

       8. *-lowering-*.f64 70.1%

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

   11. Simplified 70.1%

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

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

   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 y around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. associate-*r* N/A

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

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

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

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

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

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

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

      9. *-lowering-*.f64 75.3%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(18, x\right)\right), \mathsf{*.f64}\left(y, z\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, \color{blue}{27}\right), k\right)\right) \]

   5. Simplified 75.3%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

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

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

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

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

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

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

      6. *-commutative N/A

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

      7. *-lowering-*.f64 78.0%

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

   7. Applied egg-rr 78.0%

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

4. Final simplification 72.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \cdot \left(j \cdot 27\right) \leq -1 \cdot 10^{+20}:\\ \;\;\;\;z \cdot \left(t \cdot \left(x \cdot \left(18 \cdot y\right)\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 2 \cdot 10^{+100}:\\ \;\;\;\;b \cdot \left(c + \frac{-4 \cdot \left(t \cdot a + x \cdot i\right)}{b}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot \left(\left(x \cdot 18\right) \cdot t\right)\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 62.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := k \cdot \left(j \cdot 27\right)\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+20}:\\ \;\;\;\;z \cdot \left(t \cdot \left(x \cdot \left(18 \cdot y\right)\right)\right) - t\_1\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+138}:\\ \;\;\;\;b \cdot \left(c + \frac{-4 \cdot \left(t \cdot a + x \cdot i\right)}{b}\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right) - t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* k (* j 27.0))))
   (if (<= t_1 -1e+20)
     (- (* z (* t (* x (* 18.0 y)))) t_1)
     (if (<= t_1 5e+138)
       (* b (+ c (/ (* -4.0 (+ (* t a) (* x i))) b)))
       (- (* -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 = k * (j * 27.0);
	double tmp;
	if (t_1 <= -1e+20) {
		tmp = (z * (t * (x * (18.0 * y)))) - t_1;
	} else if (t_1 <= 5e+138) {
		tmp = b * (c + ((-4.0 * ((t * a) + (x * i))) / b));
	} else {
		tmp = (-4.0 * (t * a)) - t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = k * (j * 27.0d0)
    if (t_1 <= (-1d+20)) then
        tmp = (z * (t * (x * (18.0d0 * y)))) - t_1
    else if (t_1 <= 5d+138) then
        tmp = b * (c + (((-4.0d0) * ((t * a) + (x * i))) / b))
    else
        tmp = ((-4.0d0) * (t * a)) - t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = k * (j * 27.0);
	double tmp;
	if (t_1 <= -1e+20) {
		tmp = (z * (t * (x * (18.0 * y)))) - t_1;
	} else if (t_1 <= 5e+138) {
		tmp = b * (c + ((-4.0 * ((t * a) + (x * i))) / b));
	} else {
		tmp = (-4.0 * (t * a)) - t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = k * (j * 27.0)
	tmp = 0
	if t_1 <= -1e+20:
		tmp = (z * (t * (x * (18.0 * y)))) - t_1
	elif t_1 <= 5e+138:
		tmp = b * (c + ((-4.0 * ((t * a) + (x * i))) / b))
	else:
		tmp = (-4.0 * (t * a)) - t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(k * Float64(j * 27.0))
	tmp = 0.0
	if (t_1 <= -1e+20)
		tmp = Float64(Float64(z * Float64(t * Float64(x * Float64(18.0 * y)))) - t_1);
	elseif (t_1 <= 5e+138)
		tmp = Float64(b * Float64(c + Float64(Float64(-4.0 * Float64(Float64(t * a) + Float64(x * i))) / b)));
	else
		tmp = Float64(Float64(-4.0 * Float64(t * a)) - t_1);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = k * (j * 27.0);
	tmp = 0.0;
	if (t_1 <= -1e+20)
		tmp = (z * (t * (x * (18.0 * y)))) - t_1;
	elseif (t_1 <= 5e+138)
		tmp = b * (c + ((-4.0 * ((t * a) + (x * i))) / b));
	else
		tmp = (-4.0 * (t * a)) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+20], N[(N[(z * N[(t * N[(x * N[(18.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[t$95$1, 5e+138], N[(b * N[(c + N[(N[(-4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -1e20

   1. Initial program 86.4%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. associate-*r* N/A

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

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

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

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

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

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

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

      9. *-lowering-*.f64 72.7%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(18, x\right)\right), \mathsf{*.f64}\left(y, z\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, \color{blue}{27}\right), k\right)\right) \]

   5. Simplified 72.7%

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

      1. associate-*r* N/A

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

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

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

      3. associate-*l* N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

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

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

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

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

      8. *-lowering-*.f64 74.7%

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

   7. Applied egg-rr 74.7%

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

   if -1e20 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 5.00000000000000016e138

   1. Initial program 89.5%

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

   3. Taylor expanded in b around inf

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

   5. Simplified 81.9%

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

   6. Taylor expanded in y around 0

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

      1. distribute-lft-out N/A

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

      2. associate-/l* N/A

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

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

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

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

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

      5. +-commutative N/A

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

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

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

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

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

      8. *-commutative N/A

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

      9. *-lowering-*.f64 71.6%

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

   8. Simplified 71.6%

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

   9. Taylor expanded in j around 0

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

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

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

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

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

       3. associate-*r/ N/A

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

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

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

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

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

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

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

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

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

       8. *-lowering-*.f64 69.9%

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

   11. Simplified 69.9%

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

   if 5.00000000000000016e138 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 74.2%

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

   3. Taylor expanded in a around inf

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

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

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 79.6%

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

   5. Simplified 79.6%

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

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \cdot \left(j \cdot 27\right) \leq -1 \cdot 10^{+20}:\\ \;\;\;\;z \cdot \left(t \cdot \left(x \cdot \left(18 \cdot y\right)\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 5 \cdot 10^{+138}:\\ \;\;\;\;b \cdot \left(c + \frac{-4 \cdot \left(t \cdot a + x \cdot i\right)}{b}\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 64.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := -4 \cdot \left(t \cdot a + x \cdot i\right)\\ t_2 := k \cdot \left(j \cdot 27\right)\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+28}:\\ \;\;\;\;t\_1 - t\_2\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+138}:\\ \;\;\;\;b \cdot \left(c + \frac{t\_1}{b}\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right) - t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* -4.0 (+ (* t a) (* x i)))) (t_2 (* k (* j 27.0))))
   (if (<= t_2 -1e+28)
     (- t_1 t_2)
     (if (<= t_2 5e+138) (* b (+ c (/ t_1 b))) (- (* -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 = -4.0 * ((t * a) + (x * i));
	double t_2 = k * (j * 27.0);
	double tmp;
	if (t_2 <= -1e+28) {
		tmp = t_1 - t_2;
	} else if (t_2 <= 5e+138) {
		tmp = b * (c + (t_1 / b));
	} else {
		tmp = (-4.0 * (t * a)) - t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (-4.0d0) * ((t * a) + (x * i))
    t_2 = k * (j * 27.0d0)
    if (t_2 <= (-1d+28)) then
        tmp = t_1 - t_2
    else if (t_2 <= 5d+138) then
        tmp = b * (c + (t_1 / b))
    else
        tmp = ((-4.0d0) * (t * a)) - t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -4.0 * ((t * a) + (x * i));
	double t_2 = k * (j * 27.0);
	double tmp;
	if (t_2 <= -1e+28) {
		tmp = t_1 - t_2;
	} else if (t_2 <= 5e+138) {
		tmp = b * (c + (t_1 / b));
	} else {
		tmp = (-4.0 * (t * a)) - t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = -4.0 * ((t * a) + (x * i))
	t_2 = k * (j * 27.0)
	tmp = 0
	if t_2 <= -1e+28:
		tmp = t_1 - t_2
	elif t_2 <= 5e+138:
		tmp = b * (c + (t_1 / b))
	else:
		tmp = (-4.0 * (t * a)) - t_2
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(-4.0 * Float64(Float64(t * a) + Float64(x * i)))
	t_2 = Float64(k * Float64(j * 27.0))
	tmp = 0.0
	if (t_2 <= -1e+28)
		tmp = Float64(t_1 - t_2);
	elseif (t_2 <= 5e+138)
		tmp = Float64(b * Float64(c + Float64(t_1 / b)));
	else
		tmp = Float64(Float64(-4.0 * Float64(t * a)) - t_2);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = -4.0 * ((t * a) + (x * i));
	t_2 = k * (j * 27.0);
	tmp = 0.0;
	if (t_2 <= -1e+28)
		tmp = t_1 - t_2;
	elseif (t_2 <= 5e+138)
		tmp = b * (c + (t_1 / b));
	else
		tmp = (-4.0 * (t * a)) - t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(-4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+28], N[(t$95$1 - t$95$2), $MachinePrecision], If[LessEqual[t$95$2, 5e+138], N[(b * N[(c + N[(t$95$1 / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -9.99999999999999958e27

   1. Initial program 88.1%

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

   3. Taylor expanded in b around inf

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

   5. Simplified 82.7%

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

   6. Taylor expanded in y around 0

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

      1. distribute-lft-out N/A

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

      2. associate-/l* N/A

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

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

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

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

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

      5. +-commutative N/A

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

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

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

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

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

      8. *-commutative N/A

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

      9. *-lowering-*.f64 80.8%

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

   8. Simplified 80.8%

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

   9. Taylor expanded in b around 0

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

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

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

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

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

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

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

       4. *-lowering-*.f64 76.0%

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

   11. Simplified 76.0%

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

   if -9.99999999999999958e27 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 5.00000000000000016e138

   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 b around inf

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

   5. Simplified 82.0%

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

   6. Taylor expanded in y around 0

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

      1. distribute-lft-out N/A

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

      2. associate-/l* N/A

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

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

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

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

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

      5. +-commutative N/A

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

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

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

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

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

      8. *-commutative N/A

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

      9. *-lowering-*.f64 71.1%

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

   8. Simplified 71.1%

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

   9. Taylor expanded in j around 0

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

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

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

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

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

       3. associate-*r/ N/A

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

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

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

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

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

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

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

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

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

       8. *-lowering-*.f64 69.5%

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

   11. Simplified 69.5%

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

   if 5.00000000000000016e138 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 74.2%

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

   3. Taylor expanded in a around inf

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

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

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 79.6%

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

   5. Simplified 79.6%

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

4. Final simplification 72.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \cdot \left(j \cdot 27\right) \leq -1 \cdot 10^{+28}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 5 \cdot 10^{+138}:\\ \;\;\;\;b \cdot \left(c + \frac{-4 \cdot \left(t \cdot a + x \cdot i\right)}{b}\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 62.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := k \cdot \left(j \cdot 27\right)\\ t_2 := -4 \cdot \left(t \cdot a\right) - t\_1\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+28}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+138}:\\ \;\;\;\;b \cdot \left(c + \frac{-4 \cdot \left(t \cdot a + x \cdot i\right)}{b}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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 (* k (* j 27.0))) (t_2 (- (* -4.0 (* t a)) t_1)))
   (if (<= t_1 -1e+28)
     t_2
     (if (<= t_1 5e+138) (* b (+ c (/ (* -4.0 (+ (* t a) (* x i))) b))) 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 = k * (j * 27.0);
	double t_2 = (-4.0 * (t * a)) - t_1;
	double tmp;
	if (t_1 <= -1e+28) {
		tmp = t_2;
	} else if (t_1 <= 5e+138) {
		tmp = b * (c + ((-4.0 * ((t * a) + (x * i))) / b));
	} 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 = k * (j * 27.0d0)
    t_2 = ((-4.0d0) * (t * a)) - t_1
    if (t_1 <= (-1d+28)) then
        tmp = t_2
    else if (t_1 <= 5d+138) then
        tmp = b * (c + (((-4.0d0) * ((t * a) + (x * i))) / b))
    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 = k * (j * 27.0);
	double t_2 = (-4.0 * (t * a)) - t_1;
	double tmp;
	if (t_1 <= -1e+28) {
		tmp = t_2;
	} else if (t_1 <= 5e+138) {
		tmp = b * (c + ((-4.0 * ((t * a) + (x * i))) / b));
	} 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 = k * (j * 27.0)
	t_2 = (-4.0 * (t * a)) - t_1
	tmp = 0
	if t_1 <= -1e+28:
		tmp = t_2
	elif t_1 <= 5e+138:
		tmp = b * (c + ((-4.0 * ((t * a) + (x * i))) / b))
	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(k * Float64(j * 27.0))
	t_2 = Float64(Float64(-4.0 * Float64(t * a)) - t_1)
	tmp = 0.0
	if (t_1 <= -1e+28)
		tmp = t_2;
	elseif (t_1 <= 5e+138)
		tmp = Float64(b * Float64(c + Float64(Float64(-4.0 * Float64(Float64(t * a) + Float64(x * i))) / b)));
	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 = k * (j * 27.0);
	t_2 = (-4.0 * (t * a)) - t_1;
	tmp = 0.0;
	if (t_1 <= -1e+28)
		tmp = t_2;
	elseif (t_1 <= 5e+138)
		tmp = b * (c + ((-4.0 * ((t * a) + (x * i))) / b));
	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[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+28], t$95$2, If[LessEqual[t$95$1, 5e+138], N[(b * N[(c + N[(N[(-4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -9.99999999999999958e27 or 5.00000000000000016e138 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 82.4%

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

   3. Taylor expanded in a around inf

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

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

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 75.2%

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

   5. Simplified 75.2%

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

   if -9.99999999999999958e27 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 5.00000000000000016e138

   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 b around inf

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

   5. Simplified 82.0%

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

   6. Taylor expanded in y around 0

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

      1. distribute-lft-out N/A

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

      2. associate-/l* N/A

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

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

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

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

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

      5. +-commutative N/A

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

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

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

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

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

      8. *-commutative N/A

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

      9. *-lowering-*.f64 71.1%

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

   8. Simplified 71.1%

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

   9. Taylor expanded in j around 0

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

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

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

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

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

       3. associate-*r/ N/A

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

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

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

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

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

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

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

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

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

       8. *-lowering-*.f64 69.5%

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

   11. Simplified 69.5%

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

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \cdot \left(j \cdot 27\right) \leq -1 \cdot 10^{+28}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 5 \cdot 10^{+138}:\\ \;\;\;\;b \cdot \left(c + \frac{-4 \cdot \left(t \cdot a + x \cdot i\right)}{b}\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 73.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right)\\ \mathbf{if}\;y \leq -1.35 \cdot 10^{+162}:\\ \;\;\;\;b \cdot c + t\_1\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-34}:\\ \;\;\;\;b \cdot \left(c + -4 \cdot \frac{t \cdot a + x \cdot i}{b}\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 + -27 \cdot \left(j \cdot k\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* t (+ (* (* (* x 18.0) y) z) (* a -4.0)))))
   (if (<= y -1.35e+162)
     (+ (* b c) t_1)
     (if (<= y 5e-34)
       (- (* b (+ c (* -4.0 (/ (+ (* t a) (* x i)) b)))) (* k (* j 27.0)))
       (+ t_1 (* -27.0 (* j k)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * ((((x * 18.0) * y) * z) + (a * -4.0));
	double tmp;
	if (y <= -1.35e+162) {
		tmp = (b * c) + t_1;
	} else if (y <= 5e-34) {
		tmp = (b * (c + (-4.0 * (((t * a) + (x * i)) / b)))) - (k * (j * 27.0));
	} else {
		tmp = t_1 + (-27.0 * (j * k));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((((x * 18.0d0) * y) * z) + (a * (-4.0d0)))
    if (y <= (-1.35d+162)) then
        tmp = (b * c) + t_1
    else if (y <= 5d-34) then
        tmp = (b * (c + ((-4.0d0) * (((t * a) + (x * i)) / b)))) - (k * (j * 27.0d0))
    else
        tmp = t_1 + ((-27.0d0) * (j * k))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * ((((x * 18.0) * y) * z) + (a * -4.0));
	double tmp;
	if (y <= -1.35e+162) {
		tmp = (b * c) + t_1;
	} else if (y <= 5e-34) {
		tmp = (b * (c + (-4.0 * (((t * a) + (x * i)) / b)))) - (k * (j * 27.0));
	} else {
		tmp = t_1 + (-27.0 * (j * k));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = t * ((((x * 18.0) * y) * z) + (a * -4.0))
	tmp = 0
	if y <= -1.35e+162:
		tmp = (b * c) + t_1
	elif y <= 5e-34:
		tmp = (b * (c + (-4.0 * (((t * a) + (x * i)) / b)))) - (k * (j * 27.0))
	else:
		tmp = t_1 + (-27.0 * (j * k))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(t * Float64(Float64(Float64(Float64(x * 18.0) * y) * z) + Float64(a * -4.0)))
	tmp = 0.0
	if (y <= -1.35e+162)
		tmp = Float64(Float64(b * c) + t_1);
	elseif (y <= 5e-34)
		tmp = Float64(Float64(b * Float64(c + Float64(-4.0 * Float64(Float64(Float64(t * a) + Float64(x * i)) / b)))) - Float64(k * Float64(j * 27.0)));
	else
		tmp = Float64(t_1 + Float64(-27.0 * Float64(j * k)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = t * ((((x * 18.0) * y) * z) + (a * -4.0));
	tmp = 0.0;
	if (y <= -1.35e+162)
		tmp = (b * c) + t_1;
	elseif (y <= 5e-34)
		tmp = (b * (c + (-4.0 * (((t * a) + (x * i)) / b)))) - (k * (j * 27.0));
	else
		tmp = t_1 + (-27.0 * (j * k));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(t * N[(N[(N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.35e+162], N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[y, 5e-34], N[(N[(b * N[(c + N[(-4.0 * N[(N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.3500000000000001e162

   1. Initial program 91.0%

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

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

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

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

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

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

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

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

      6. sub-neg N/A

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

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

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

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

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

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

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

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

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

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

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

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

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

      13. metadata-eval N/A

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

   3. Simplified 94.0%

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

   5. Taylor expanded in b around inf

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

      1. *-lowering-*.f64 80.6%

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

   7. Simplified 80.6%

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

   if -1.3500000000000001e162 < y < 5.0000000000000003e-34

   1. Initial program 90.0%

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

   3. Taylor expanded in b around inf

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

   5. Simplified 84.0%

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

   6. Taylor expanded in y around 0

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

      1. distribute-lft-out N/A

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

      2. associate-/l* N/A

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

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

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

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

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

      5. +-commutative N/A

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

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

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

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

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

      8. *-commutative N/A

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

      9. *-lowering-*.f64 81.0%

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

   8. Simplified 81.0%

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

   if 5.0000000000000003e-34 < y

   1. Initial program 77.7%

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

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

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

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

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

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

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

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

      6. sub-neg N/A

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

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

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

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

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

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

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

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

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

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

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

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

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

      13. metadata-eval N/A

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

   3. Simplified 79.2%

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

   5. Taylor expanded in j around inf

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

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

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

      2. *-lowering-*.f64 58.9%

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

   7. Simplified 58.9%

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

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{+162}:\\ \;\;\;\;b \cdot c + t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right)\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-34}:\\ \;\;\;\;b \cdot \left(c + -4 \cdot \frac{t \cdot a + x \cdot i}{b}\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right) + -27 \cdot \left(j \cdot k\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 72.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right)\\ \mathbf{if}\;y \leq -2.65 \cdot 10^{+135}:\\ \;\;\;\;b \cdot c + t\_1\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{-35}:\\ \;\;\;\;b \cdot \left(c + \frac{-4 \cdot \left(t \cdot a + x \cdot i\right) + j \cdot \left(-27 \cdot k\right)}{b}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 + -27 \cdot \left(j \cdot k\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* t (+ (* (* (* x 18.0) y) z) (* a -4.0)))))
   (if (<= y -2.65e+135)
     (+ (* b c) t_1)
     (if (<= y 8.8e-35)
       (* b (+ c (/ (+ (* -4.0 (+ (* t a) (* x i))) (* j (* -27.0 k))) b)))
       (+ t_1 (* -27.0 (* j k)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * ((((x * 18.0) * y) * z) + (a * -4.0));
	double tmp;
	if (y <= -2.65e+135) {
		tmp = (b * c) + t_1;
	} else if (y <= 8.8e-35) {
		tmp = b * (c + (((-4.0 * ((t * a) + (x * i))) + (j * (-27.0 * k))) / b));
	} else {
		tmp = t_1 + (-27.0 * (j * k));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((((x * 18.0d0) * y) * z) + (a * (-4.0d0)))
    if (y <= (-2.65d+135)) then
        tmp = (b * c) + t_1
    else if (y <= 8.8d-35) then
        tmp = b * (c + ((((-4.0d0) * ((t * a) + (x * i))) + (j * ((-27.0d0) * k))) / b))
    else
        tmp = t_1 + ((-27.0d0) * (j * k))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * ((((x * 18.0) * y) * z) + (a * -4.0));
	double tmp;
	if (y <= -2.65e+135) {
		tmp = (b * c) + t_1;
	} else if (y <= 8.8e-35) {
		tmp = b * (c + (((-4.0 * ((t * a) + (x * i))) + (j * (-27.0 * k))) / b));
	} else {
		tmp = t_1 + (-27.0 * (j * k));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = t * ((((x * 18.0) * y) * z) + (a * -4.0))
	tmp = 0
	if y <= -2.65e+135:
		tmp = (b * c) + t_1
	elif y <= 8.8e-35:
		tmp = b * (c + (((-4.0 * ((t * a) + (x * i))) + (j * (-27.0 * k))) / b))
	else:
		tmp = t_1 + (-27.0 * (j * k))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(t * Float64(Float64(Float64(Float64(x * 18.0) * y) * z) + Float64(a * -4.0)))
	tmp = 0.0
	if (y <= -2.65e+135)
		tmp = Float64(Float64(b * c) + t_1);
	elseif (y <= 8.8e-35)
		tmp = Float64(b * Float64(c + Float64(Float64(Float64(-4.0 * Float64(Float64(t * a) + Float64(x * i))) + Float64(j * Float64(-27.0 * k))) / b)));
	else
		tmp = Float64(t_1 + Float64(-27.0 * Float64(j * k)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = t * ((((x * 18.0) * y) * z) + (a * -4.0));
	tmp = 0.0;
	if (y <= -2.65e+135)
		tmp = (b * c) + t_1;
	elseif (y <= 8.8e-35)
		tmp = b * (c + (((-4.0 * ((t * a) + (x * i))) + (j * (-27.0 * k))) / b));
	else
		tmp = t_1 + (-27.0 * (j * k));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(t * N[(N[(N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.65e+135], N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[y, 8.8e-35], N[(b * N[(c + N[(N[(N[(-4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(-27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.65000000000000008e135

   1. Initial program 90.1%

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

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

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

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

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

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

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

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

      6. sub-neg N/A

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

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

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

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

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

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

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

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

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

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

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

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

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

      13. metadata-eval N/A

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

   3. Simplified 92.6%

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

   5. Taylor expanded in b around inf

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

      1. *-lowering-*.f64 78.8%

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

   7. Simplified 78.8%

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

   if -2.65000000000000008e135 < y < 8.79999999999999975e-35

   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

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

   5. Simplified 84.5%

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

   6. Taylor expanded in y around 0

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

      1. distribute-lft-out N/A

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

      2. associate-/l* N/A

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

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

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

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

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

      5. +-commutative N/A

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

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

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

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

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

      8. *-commutative N/A

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

      9. *-lowering-*.f64 81.4%

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

   8. Simplified 81.4%

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

   9. Taylor expanded in b around inf

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

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

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

       2. associate--l+ N/A

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

       3. associate-*r/ N/A

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

       4. associate-*r/ N/A

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

       5. div-sub N/A

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

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

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

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

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

   11. Simplified 78.9%

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

   if 8.79999999999999975e-35 < y

   1. Initial program 78.0%

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

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

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

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

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

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

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

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

      6. sub-neg N/A

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

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

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

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

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

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

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

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

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

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

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

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

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

      13. metadata-eval N/A

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

   3. Simplified 79.4%

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

   5. Taylor expanded in j around inf

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

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

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

      2. *-lowering-*.f64 58.1%

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

   7. Simplified 58.1%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.65 \cdot 10^{+135}:\\ \;\;\;\;b \cdot c + t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right)\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{-35}:\\ \;\;\;\;b \cdot \left(c + \frac{-4 \cdot \left(t \cdot a + x \cdot i\right) + j \cdot \left(-27 \cdot k\right)}{b}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right) + -27 \cdot \left(j \cdot k\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 51.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := -4 \cdot \left(t \cdot a\right)\\ t_2 := k \cdot \left(j \cdot 27\right)\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+20}:\\ \;\;\;\;t\_1 - t\_2\\ \mathbf{elif}\;t\_2 \leq 3 \cdot 10^{-123}:\\ \;\;\;\;b \cdot c + t\_1\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(x \cdot -4 + \frac{j \cdot \left(-27 \cdot k\right)}{i}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* -4.0 (* t a))) (t_2 (* k (* j 27.0))))
   (if (<= t_2 -1e+20)
     (- t_1 t_2)
     (if (<= t_2 3e-123)
       (+ (* b c) t_1)
       (* i (+ (* x -4.0) (/ (* j (* -27.0 k)) i)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -4.0 * (t * a);
	double t_2 = k * (j * 27.0);
	double tmp;
	if (t_2 <= -1e+20) {
		tmp = t_1 - t_2;
	} else if (t_2 <= 3e-123) {
		tmp = (b * c) + t_1;
	} else {
		tmp = i * ((x * -4.0) + ((j * (-27.0 * k)) / i));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (-4.0d0) * (t * a)
    t_2 = k * (j * 27.0d0)
    if (t_2 <= (-1d+20)) then
        tmp = t_1 - t_2
    else if (t_2 <= 3d-123) then
        tmp = (b * c) + t_1
    else
        tmp = i * ((x * (-4.0d0)) + ((j * ((-27.0d0) * k)) / i))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -4.0 * (t * a);
	double t_2 = k * (j * 27.0);
	double tmp;
	if (t_2 <= -1e+20) {
		tmp = t_1 - t_2;
	} else if (t_2 <= 3e-123) {
		tmp = (b * c) + t_1;
	} else {
		tmp = i * ((x * -4.0) + ((j * (-27.0 * k)) / i));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = -4.0 * (t * a)
	t_2 = k * (j * 27.0)
	tmp = 0
	if t_2 <= -1e+20:
		tmp = t_1 - t_2
	elif t_2 <= 3e-123:
		tmp = (b * c) + t_1
	else:
		tmp = i * ((x * -4.0) + ((j * (-27.0 * k)) / i))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(-4.0 * Float64(t * a))
	t_2 = Float64(k * Float64(j * 27.0))
	tmp = 0.0
	if (t_2 <= -1e+20)
		tmp = Float64(t_1 - t_2);
	elseif (t_2 <= 3e-123)
		tmp = Float64(Float64(b * c) + t_1);
	else
		tmp = Float64(i * Float64(Float64(x * -4.0) + Float64(Float64(j * Float64(-27.0 * k)) / i)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = -4.0 * (t * a);
	t_2 = k * (j * 27.0);
	tmp = 0.0;
	if (t_2 <= -1e+20)
		tmp = t_1 - t_2;
	elseif (t_2 <= 3e-123)
		tmp = (b * c) + t_1;
	else
		tmp = i * ((x * -4.0) + ((j * (-27.0 * k)) / i));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+20], N[(t$95$1 - t$95$2), $MachinePrecision], If[LessEqual[t$95$2, 3e-123], N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision], N[(i * N[(N[(x * -4.0), $MachinePrecision] + N[(N[(j * N[(-27.0 * k), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -1e20

   1. Initial program 86.4%

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

   3. Taylor expanded in a around inf

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

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

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 70.9%

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

   5. Simplified 70.9%

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

   if -1e20 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 2.99999999999999984e-123

   1. Initial program 90.1%

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

   3. Taylor expanded in x around 0

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

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

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

      2. metadata-eval N/A

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

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

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

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

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

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

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

      6. *-commutative N/A

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

      7. *-lowering-*.f64 56.0%

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

   5. Simplified 56.0%

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

   6. Taylor expanded in j around 0

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t\right) + b \cdot c} \]
   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. *-lowering-*.f64 55.9%

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

   8. Simplified 55.9%

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

   if 2.99999999999999984e-123 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 82.3%

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

   3. Taylor expanded in i around inf

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

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

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

      2. *-lowering-*.f64 55.8%

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

   5. Simplified 55.8%

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

   6. Taylor expanded in i around inf

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

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

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

      2. +-commutative N/A

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

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

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

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

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

      5. associate-*r/ N/A

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

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

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. *-commutative N/A

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

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

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

      11. *-commutative N/A

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

      12. *-lowering-*.f64 57.0%

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

   8. Simplified 57.0%

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

4. Final simplification 59.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \cdot \left(j \cdot 27\right) \leq -1 \cdot 10^{+20}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 3 \cdot 10^{-123}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(x \cdot -4 + \frac{j \cdot \left(-27 \cdot k\right)}{i}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 69.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := k \cdot \left(j \cdot 27\right)\\ t_2 := x \cdot \left(i \cdot -4 + 18 \cdot \left(z \cdot \left(y \cdot t\right)\right)\right)\\ \mathbf{if}\;x \leq -8.5 \cdot 10^{-28}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-190}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - t\_1\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{+226}:\\ \;\;\;\;\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* k (* j 27.0)))
        (t_2 (* x (+ (* i -4.0) (* 18.0 (* z (* y t)))))))
   (if (<= x -8.5e-28)
     t_2
     (if (<= x 3.5e-190)
       (- (+ (* b c) (* -4.0 (* t a))) t_1)
       (if (<= x 5.8e+226) (- (- (* b c) (* (* x 4.0) i)) t_1) t_2)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = k * (j * 27.0);
	double t_2 = x * ((i * -4.0) + (18.0 * (z * (y * t))));
	double tmp;
	if (x <= -8.5e-28) {
		tmp = t_2;
	} else if (x <= 3.5e-190) {
		tmp = ((b * c) + (-4.0 * (t * a))) - t_1;
	} else if (x <= 5.8e+226) {
		tmp = ((b * c) - ((x * 4.0) * i)) - t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = k * (j * 27.0d0)
    t_2 = x * ((i * (-4.0d0)) + (18.0d0 * (z * (y * t))))
    if (x <= (-8.5d-28)) then
        tmp = t_2
    else if (x <= 3.5d-190) then
        tmp = ((b * c) + ((-4.0d0) * (t * a))) - t_1
    else if (x <= 5.8d+226) then
        tmp = ((b * c) - ((x * 4.0d0) * i)) - t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = k * (j * 27.0);
	double t_2 = x * ((i * -4.0) + (18.0 * (z * (y * t))));
	double tmp;
	if (x <= -8.5e-28) {
		tmp = t_2;
	} else if (x <= 3.5e-190) {
		tmp = ((b * c) + (-4.0 * (t * a))) - t_1;
	} else if (x <= 5.8e+226) {
		tmp = ((b * c) - ((x * 4.0) * i)) - t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = k * (j * 27.0)
	t_2 = x * ((i * -4.0) + (18.0 * (z * (y * t))))
	tmp = 0
	if x <= -8.5e-28:
		tmp = t_2
	elif x <= 3.5e-190:
		tmp = ((b * c) + (-4.0 * (t * a))) - t_1
	elif x <= 5.8e+226:
		tmp = ((b * c) - ((x * 4.0) * i)) - t_1
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(k * Float64(j * 27.0))
	t_2 = Float64(x * Float64(Float64(i * -4.0) + Float64(18.0 * Float64(z * Float64(y * t)))))
	tmp = 0.0
	if (x <= -8.5e-28)
		tmp = t_2;
	elseif (x <= 3.5e-190)
		tmp = Float64(Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a))) - t_1);
	elseif (x <= 5.8e+226)
		tmp = Float64(Float64(Float64(b * c) - Float64(Float64(x * 4.0) * i)) - t_1);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = k * (j * 27.0);
	t_2 = x * ((i * -4.0) + (18.0 * (z * (y * t))));
	tmp = 0.0;
	if (x <= -8.5e-28)
		tmp = t_2;
	elseif (x <= 3.5e-190)
		tmp = ((b * c) + (-4.0 * (t * a))) - t_1;
	elseif (x <= 5.8e+226)
		tmp = ((b * c) - ((x * 4.0) * i)) - t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(i * -4.0), $MachinePrecision] + N[(18.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -8.5e-28], t$95$2, If[LessEqual[x, 3.5e-190], N[(N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[x, 5.8e+226], N[(N[(N[(b * c), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -8.49999999999999925e-28 or 5.79999999999999949e226 < x

   1. Initial program 74.4%

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

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

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

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

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

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

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

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

      6. sub-neg N/A

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

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

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

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

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

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

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

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

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

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

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

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

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

      13. metadata-eval N/A

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

   3. Simplified 79.0%

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

   5. Taylor expanded in x around inf

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

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

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

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

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

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

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

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

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

      5. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \mathsf{*.f64}\left(18, \left(\left(t \cdot y\right) \cdot \color{blue}{z}\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(\left(t \cdot y\right), \color{blue}{z}\right)\right)\right)\right) \]

      7. *-lowering-*.f64 74.9%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, y\right), z\right)\right)\right)\right) \]

   7. Simplified 74.9%

      \[\leadsto \color{blue}{x \cdot \left(-4 \cdot i + 18 \cdot \left(\left(t \cdot y\right) \cdot z\right)\right)} \]

   if -8.49999999999999925e-28 < x < 3.4999999999999999e-190

   1. Initial program 97.6%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(b \cdot c - 4 \cdot \left(a \cdot t\right)\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   4. Step-by-step derivation

      1. cancel-sign-sub-inv N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(a \cdot t\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + -4 \cdot \left(a \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(b \cdot c\right), \left(-4 \cdot \left(a \cdot t\right)\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(-4 \cdot \left(a \cdot t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(-4, \left(a \cdot t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, \color{blue}{27}\right), k\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(-4, \left(t \cdot a\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      7. *-lowering-*.f64 84.4%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(-4, \mathsf{*.f64}\left(t, a\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

   5. Simplified 84.4%

      \[\leadsto \color{blue}{\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   if 3.4999999999999999e-190 < x < 5.79999999999999949e226

   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 72.5%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

   5. Simplified 72.5%

      \[\leadsto \left(\color{blue}{b \cdot c} - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
3. Recombined 3 regimes into one program.

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{-28}:\\ \;\;\;\;x \cdot \left(i \cdot -4 + 18 \cdot \left(z \cdot \left(y \cdot t\right)\right)\right)\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-190}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{+226}:\\ \;\;\;\;\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(i \cdot -4 + 18 \cdot \left(z \cdot \left(y \cdot t\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 69.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := x \cdot \left(i \cdot -4 + 18 \cdot \left(z \cdot \left(y \cdot t\right)\right)\right)\\ \mathbf{if}\;x \leq -8.5 \cdot 10^{-28}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{+75}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{+228}:\\ \;\;\;\;b \cdot \left(c + \frac{-4 \cdot \left(t \cdot a + x \cdot i\right)}{b}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* x (+ (* i -4.0) (* 18.0 (* z (* y t)))))))
   (if (<= x -8.5e-28)
     t_1
     (if (<= x 4.8e+75)
       (- (+ (* b c) (* -4.0 (* t a))) (* k (* j 27.0)))
       (if (<= x 4.5e+228)
         (* b (+ c (/ (* -4.0 (+ (* t a) (* x i))) b)))
         t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = x * ((i * -4.0) + (18.0 * (z * (y * t))));
	double tmp;
	if (x <= -8.5e-28) {
		tmp = t_1;
	} else if (x <= 4.8e+75) {
		tmp = ((b * c) + (-4.0 * (t * a))) - (k * (j * 27.0));
	} else if (x <= 4.5e+228) {
		tmp = b * (c + ((-4.0 * ((t * a) + (x * i))) / b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((i * (-4.0d0)) + (18.0d0 * (z * (y * t))))
    if (x <= (-8.5d-28)) then
        tmp = t_1
    else if (x <= 4.8d+75) then
        tmp = ((b * c) + ((-4.0d0) * (t * a))) - (k * (j * 27.0d0))
    else if (x <= 4.5d+228) then
        tmp = b * (c + (((-4.0d0) * ((t * a) + (x * i))) / b))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = x * ((i * -4.0) + (18.0 * (z * (y * t))));
	double tmp;
	if (x <= -8.5e-28) {
		tmp = t_1;
	} else if (x <= 4.8e+75) {
		tmp = ((b * c) + (-4.0 * (t * a))) - (k * (j * 27.0));
	} else if (x <= 4.5e+228) {
		tmp = b * (c + ((-4.0 * ((t * a) + (x * i))) / b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = x * ((i * -4.0) + (18.0 * (z * (y * t))))
	tmp = 0
	if x <= -8.5e-28:
		tmp = t_1
	elif x <= 4.8e+75:
		tmp = ((b * c) + (-4.0 * (t * a))) - (k * (j * 27.0))
	elif x <= 4.5e+228:
		tmp = b * (c + ((-4.0 * ((t * a) + (x * i))) / b))
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(x * Float64(Float64(i * -4.0) + Float64(18.0 * Float64(z * Float64(y * t)))))
	tmp = 0.0
	if (x <= -8.5e-28)
		tmp = t_1;
	elseif (x <= 4.8e+75)
		tmp = Float64(Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a))) - Float64(k * Float64(j * 27.0)));
	elseif (x <= 4.5e+228)
		tmp = Float64(b * Float64(c + Float64(Float64(-4.0 * Float64(Float64(t * a) + Float64(x * i))) / b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = x * ((i * -4.0) + (18.0 * (z * (y * t))));
	tmp = 0.0;
	if (x <= -8.5e-28)
		tmp = t_1;
	elseif (x <= 4.8e+75)
		tmp = ((b * c) + (-4.0 * (t * a))) - (k * (j * 27.0));
	elseif (x <= 4.5e+228)
		tmp = b * (c + ((-4.0 * ((t * a) + (x * i))) / b));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(x * N[(N[(i * -4.0), $MachinePrecision] + N[(18.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -8.5e-28], t$95$1, If[LessEqual[x, 4.8e+75], N[(N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.5e+228], N[(b * N[(c + N[(N[(-4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -8.49999999999999925e-28 or 4.49999999999999983e228 < x

   1. Initial program 74.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \color{blue}{\left(j \cdot 27\right)} \cdot k \]

      2. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)} \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 79.0%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right) + \left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(-4 \cdot i\right), \color{blue}{\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \left(\color{blue}{18} \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \mathsf{*.f64}\left(18, \color{blue}{\left(t \cdot \left(y \cdot z\right)\right)}\right)\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \mathsf{*.f64}\left(18, \left(\left(t \cdot y\right) \cdot \color{blue}{z}\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(\left(t \cdot y\right), \color{blue}{z}\right)\right)\right)\right) \]

      7. *-lowering-*.f64 74.9%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, y\right), z\right)\right)\right)\right) \]

   7. Simplified 74.9%

      \[\leadsto \color{blue}{x \cdot \left(-4 \cdot i + 18 \cdot \left(\left(t \cdot y\right) \cdot z\right)\right)} \]

   if -8.49999999999999925e-28 < x < 4.8e75

   1. Initial program 96.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(b \cdot c - 4 \cdot \left(a \cdot t\right)\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   4. Step-by-step derivation

      1. cancel-sign-sub-inv N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(a \cdot t\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + -4 \cdot \left(a \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(b \cdot c\right), \left(-4 \cdot \left(a \cdot t\right)\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(-4 \cdot \left(a \cdot t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(-4, \left(a \cdot t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, \color{blue}{27}\right), k\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(-4, \left(t \cdot a\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      7. *-lowering-*.f64 78.2%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(-4, \mathsf{*.f64}\left(t, a\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

   5. Simplified 78.2%

      \[\leadsto \color{blue}{\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   if 4.8e75 < x < 4.49999999999999983e228

   1. Initial program 78.5%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(b \cdot \left(\left(c + 18 \cdot \frac{t \cdot \left(x \cdot \left(y \cdot z\right)\right)}{b}\right) - \left(4 \cdot \frac{a \cdot t}{b} + 4 \cdot \frac{i \cdot x}{b}\right)\right)\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

   5. Simplified 82.6%

      \[\leadsto \color{blue}{b \cdot \left(c + \frac{-4 \cdot \left(i \cdot x\right) + t \cdot \left(-4 \cdot a + x \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right)}{b}\right)} - \left(j \cdot 27\right) \cdot k \]

   6. Taylor expanded in y around 0

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(c, \color{blue}{\left(\frac{-4 \cdot \left(a \cdot t\right) + -4 \cdot \left(i \cdot x\right)}{b}\right)}\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   7. Step-by-step derivation

      1. distribute-lft-out N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(c, \left(\frac{-4 \cdot \left(a \cdot t + i \cdot x\right)}{b}\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(c, \left(-4 \cdot \frac{a \cdot t + i \cdot x}{b}\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(c, \mathsf{*.f64}\left(-4, \left(\frac{a \cdot t + i \cdot x}{b}\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(c, \mathsf{*.f64}\left(-4, \mathsf{/.f64}\left(\left(a \cdot t + i \cdot x\right), b\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(c, \mathsf{*.f64}\left(-4, \mathsf{/.f64}\left(\left(i \cdot x + a \cdot t\right), b\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(c, \mathsf{*.f64}\left(-4, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(i \cdot x\right), \left(a \cdot t\right)\right), b\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(c, \mathsf{*.f64}\left(-4, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(i, x\right), \left(a \cdot t\right)\right), b\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(c, \mathsf{*.f64}\left(-4, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(i, x\right), \left(t \cdot a\right)\right), b\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      9. *-lowering-*.f64 75.6%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(c, \mathsf{*.f64}\left(-4, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(i, x\right), \mathsf{*.f64}\left(t, a\right)\right), b\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

   8. Simplified 75.6%

      \[\leadsto b \cdot \left(c + \color{blue}{-4 \cdot \frac{i \cdot x + t \cdot a}{b}}\right) - \left(j \cdot 27\right) \cdot k \]

   9. Taylor expanded in j around 0

      \[\leadsto \color{blue}{b \cdot \left(c + -4 \cdot \frac{a \cdot t + i \cdot x}{b}\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(c + -4 \cdot \frac{a \cdot t + i \cdot x}{b}\right)}\right) \]

       2. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(c, \color{blue}{\left(-4 \cdot \frac{a \cdot t + i \cdot x}{b}\right)}\right)\right) \]

       3. associate-*r/ N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(c, \left(\frac{-4 \cdot \left(a \cdot t + i \cdot x\right)}{\color{blue}{b}}\right)\right)\right) \]

       4. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(c, \mathsf{/.f64}\left(\left(-4 \cdot \left(a \cdot t + i \cdot x\right)\right), \color{blue}{b}\right)\right)\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(c, \mathsf{/.f64}\left(\mathsf{*.f64}\left(-4, \left(a \cdot t + i \cdot x\right)\right), b\right)\right)\right) \]

       6. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(c, \mathsf{/.f64}\left(\mathsf{*.f64}\left(-4, \mathsf{+.f64}\left(\left(a \cdot t\right), \left(i \cdot x\right)\right)\right), b\right)\right)\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(c, \mathsf{/.f64}\left(\mathsf{*.f64}\left(-4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, t\right), \left(i \cdot x\right)\right)\right), b\right)\right)\right) \]

       8. *-lowering-*.f64 65.6%

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(c, \mathsf{/.f64}\left(\mathsf{*.f64}\left(-4, \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, t\right), \mathsf{*.f64}\left(i, x\right)\right)\right), b\right)\right)\right) \]

   11. Simplified 65.6%

       \[\leadsto \color{blue}{b \cdot \left(c + \frac{-4 \cdot \left(a \cdot t + i \cdot x\right)}{b}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{-28}:\\ \;\;\;\;x \cdot \left(i \cdot -4 + 18 \cdot \left(z \cdot \left(y \cdot t\right)\right)\right)\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{+75}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{+228}:\\ \;\;\;\;b \cdot \left(c + \frac{-4 \cdot \left(t \cdot a + x \cdot i\right)}{b}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(i \cdot -4 + 18 \cdot \left(z \cdot \left(y \cdot t\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 34.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+130}:\\ \;\;\;\;z \cdot \left(\left(18 \cdot t\right) \cdot \left(x \cdot y\right)\right)\\ \mathbf{elif}\;y \leq -5.6 \cdot 10^{+70}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-184}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;y \leq 3.15 \cdot 10^{-167}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t\\ \end{array} \end{array} \]

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 (<= y -3.6e+130)
   (* z (* (* 18.0 t) (* x y)))
   (if (<= y -5.6e+70)
     (* -27.0 (* j k))
     (if (<= y -1.9e-184)
       (* b c)
       (if (<= y 3.15e-167) (* -4.0 (* x i)) (* (* (* (* x 18.0) y) z) 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 (y <= -3.6e+130) {
		tmp = z * ((18.0 * t) * (x * y));
	} else if (y <= -5.6e+70) {
		tmp = -27.0 * (j * k);
	} else if (y <= -1.9e-184) {
		tmp = b * c;
	} else if (y <= 3.15e-167) {
		tmp = -4.0 * (x * i);
	} else {
		tmp = (((x * 18.0) * y) * z) * 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 (y <= (-3.6d+130)) then
        tmp = z * ((18.0d0 * t) * (x * y))
    else if (y <= (-5.6d+70)) then
        tmp = (-27.0d0) * (j * k)
    else if (y <= (-1.9d-184)) then
        tmp = b * c
    else if (y <= 3.15d-167) then
        tmp = (-4.0d0) * (x * i)
    else
        tmp = (((x * 18.0d0) * y) * z) * 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 (y <= -3.6e+130) {
		tmp = z * ((18.0 * t) * (x * y));
	} else if (y <= -5.6e+70) {
		tmp = -27.0 * (j * k);
	} else if (y <= -1.9e-184) {
		tmp = b * c;
	} else if (y <= 3.15e-167) {
		tmp = -4.0 * (x * i);
	} else {
		tmp = (((x * 18.0) * y) * z) * 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 y <= -3.6e+130:
		tmp = z * ((18.0 * t) * (x * y))
	elif y <= -5.6e+70:
		tmp = -27.0 * (j * k)
	elif y <= -1.9e-184:
		tmp = b * c
	elif y <= 3.15e-167:
		tmp = -4.0 * (x * i)
	else:
		tmp = (((x * 18.0) * y) * z) * 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 (y <= -3.6e+130)
		tmp = Float64(z * Float64(Float64(18.0 * t) * Float64(x * y)));
	elseif (y <= -5.6e+70)
		tmp = Float64(-27.0 * Float64(j * k));
	elseif (y <= -1.9e-184)
		tmp = Float64(b * c);
	elseif (y <= 3.15e-167)
		tmp = Float64(-4.0 * Float64(x * i));
	else
		tmp = Float64(Float64(Float64(Float64(x * 18.0) * y) * z) * 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 (y <= -3.6e+130)
		tmp = z * ((18.0 * t) * (x * y));
	elseif (y <= -5.6e+70)
		tmp = -27.0 * (j * k);
	elseif (y <= -1.9e-184)
		tmp = b * c;
	elseif (y <= 3.15e-167)
		tmp = -4.0 * (x * i);
	else
		tmp = (((x * 18.0) * y) * z) * 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[y, -3.6e+130], N[(z * N[(N[(18.0 * t), $MachinePrecision] * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -5.6e+70], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.9e-184], N[(b * c), $MachinePrecision], If[LessEqual[y, 3.15e-167], N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -3.6000000000000001e130

   1. Initial program 88.5%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(b \cdot \left(\left(c + 18 \cdot \frac{t \cdot \left(x \cdot \left(y \cdot z\right)\right)}{b}\right) - \left(4 \cdot \frac{a \cdot t}{b} + 4 \cdot \frac{i \cdot x}{b}\right)\right)\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

   5. Simplified 77.6%

      \[\leadsto \color{blue}{b \cdot \left(c + \frac{-4 \cdot \left(i \cdot x\right) + t \cdot \left(-4 \cdot a + x \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right)}{b}\right)} - \left(j \cdot 27\right) \cdot k \]

   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. associate-*r* N/A

         \[\leadsto t \cdot \color{blue}{\left(\left(x \cdot \left(y \cdot z\right)\right) \cdot 18\right)} \]

      3. *-commutative N/A

         \[\leadsto t \cdot \left(18 \cdot \color{blue}{\left(x \cdot \left(y \cdot z\right)\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)}\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(18, \color{blue}{\left(x \cdot \left(y \cdot z\right)\right)}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(x, \color{blue}{\left(y \cdot z\right)}\right)\right)\right) \]

      7. *-lowering-*.f64 48.0%

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{z}\right)\right)\right)\right) \]

   8. Simplified 48.0%

      \[\leadsto \color{blue}{t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(t \cdot 18\right) \cdot \color{blue}{\left(x \cdot \left(y \cdot z\right)\right)} \]

      2. associate-*r* N/A

         \[\leadsto \left(t \cdot 18\right) \cdot \left(\left(x \cdot y\right) \cdot \color{blue}{z}\right) \]

      3. associate-*r* N/A

         \[\leadsto \left(\left(t \cdot 18\right) \cdot \left(x \cdot y\right)\right) \cdot \color{blue}{z} \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\left(t \cdot 18\right) \cdot \left(x \cdot y\right)\right), \color{blue}{z}\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(t \cdot 18\right), \left(x \cdot y\right)\right), z\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(t, 18\right), \left(x \cdot y\right)\right), z\right) \]

      7. *-lowering-*.f64 50.4%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(t, 18\right), \mathsf{*.f64}\left(x, y\right)\right), z\right) \]

   10. Applied egg-rr 50.4%

       \[\leadsto \color{blue}{\left(\left(t \cdot 18\right) \cdot \left(x \cdot y\right)\right) \cdot z} \]

   if -3.6000000000000001e130 < y < -5.59999999999999979e70

   1. Initial program 93.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \color{blue}{\left(j \cdot 27\right)} \cdot k \]

      2. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)} \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 93.9%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right) + \left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in j around inf

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]
   6. 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 57.7%

         \[\leadsto \mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, \color{blue}{k}\right)\right) \]

   7. Simplified 57.7%

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]

   if -5.59999999999999979e70 < y < -1.90000000000000008e-184

   1. Initial program 85.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \color{blue}{\left(j \cdot 27\right)} \cdot k \]

      2. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)} \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 89.3%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right) + \left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot c} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 38.4%

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{c}\right) \]

   7. Simplified 38.4%

      \[\leadsto \color{blue}{b \cdot c} \]

   if -1.90000000000000008e-184 < y < 3.1500000000000001e-167

   1. Initial program 91.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \color{blue}{\left(j \cdot 27\right)} \cdot k \]

      2. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)} \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 93.6%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right) + \left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around inf

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right)} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-4, \color{blue}{\left(i \cdot x\right)}\right) \]

      2. *-lowering-*.f64 31.7%

         \[\leadsto \mathsf{*.f64}\left(-4, \mathsf{*.f64}\left(i, \color{blue}{x}\right)\right) \]

   7. Simplified 31.7%

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right)} \]

   if 3.1500000000000001e-167 < y

   1. Initial program 83.6%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(b \cdot \left(\left(c + 18 \cdot \frac{t \cdot \left(x \cdot \left(y \cdot z\right)\right)}{b}\right) - \left(4 \cdot \frac{a \cdot t}{b} + 4 \cdot \frac{i \cdot x}{b}\right)\right)\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

   5. Simplified 77.5%

      \[\leadsto \color{blue}{b \cdot \left(c + \frac{-4 \cdot \left(i \cdot x\right) + t \cdot \left(-4 \cdot a + x \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right)}{b}\right)} - \left(j \cdot 27\right) \cdot k \]

   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. associate-*r* N/A

         \[\leadsto t \cdot \color{blue}{\left(\left(x \cdot \left(y \cdot z\right)\right) \cdot 18\right)} \]

      3. *-commutative N/A

         \[\leadsto t \cdot \left(18 \cdot \color{blue}{\left(x \cdot \left(y \cdot z\right)\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)}\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(18, \color{blue}{\left(x \cdot \left(y \cdot z\right)\right)}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(x, \color{blue}{\left(y \cdot z\right)}\right)\right)\right) \]

      7. *-lowering-*.f64 33.2%

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{z}\right)\right)\right)\right) \]

   8. Simplified 33.2%

      \[\leadsto \color{blue}{t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(\left(18 \cdot x\right) \cdot \color{blue}{\left(y \cdot z\right)}\right)\right) \]

      2. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(\left(\left(18 \cdot x\right) \cdot y\right) \cdot \color{blue}{z}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(\left(\left(18 \cdot x\right) \cdot y\right), \color{blue}{z}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(18 \cdot x\right), y\right), z\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right)\right) \]

      6. *-lowering-*.f64 35.1%

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right)\right) \]

   10. Applied egg-rr 35.1%

       \[\leadsto t \cdot \color{blue}{\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 39.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+130}:\\ \;\;\;\;z \cdot \left(\left(18 \cdot t\right) \cdot \left(x \cdot y\right)\right)\\ \mathbf{elif}\;y \leq -5.6 \cdot 10^{+70}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-184}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;y \leq 3.15 \cdot 10^{-167}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 34.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(x \cdot 18\right) \cdot y\\ \mathbf{if}\;y \leq -2.8 \cdot 10^{+130}:\\ \;\;\;\;z \cdot \left(t\_1 \cdot t\right)\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{+68}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{-184}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;y \leq 3.15 \cdot 10^{-167}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t\_1 \cdot z\right) \cdot t\\ \end{array} \end{array} \]

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
 (let* ((t_1 (* (* x 18.0) y)))
   (if (<= y -2.8e+130)
     (* z (* t_1 t))
     (if (<= y -2.7e+68)
       (* -27.0 (* j k))
       (if (<= y -1.25e-184)
         (* b c)
         (if (<= y 3.15e-167) (* -4.0 (* x i)) (* (* t_1 z) 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 * 18.0) * y;
	double tmp;
	if (y <= -2.8e+130) {
		tmp = z * (t_1 * t);
	} else if (y <= -2.7e+68) {
		tmp = -27.0 * (j * k);
	} else if (y <= -1.25e-184) {
		tmp = b * c;
	} else if (y <= 3.15e-167) {
		tmp = -4.0 * (x * i);
	} else {
		tmp = (t_1 * z) * 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 * 18.0d0) * y
    if (y <= (-2.8d+130)) then
        tmp = z * (t_1 * t)
    else if (y <= (-2.7d+68)) then
        tmp = (-27.0d0) * (j * k)
    else if (y <= (-1.25d-184)) then
        tmp = b * c
    else if (y <= 3.15d-167) then
        tmp = (-4.0d0) * (x * i)
    else
        tmp = (t_1 * z) * 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 * 18.0) * y;
	double tmp;
	if (y <= -2.8e+130) {
		tmp = z * (t_1 * t);
	} else if (y <= -2.7e+68) {
		tmp = -27.0 * (j * k);
	} else if (y <= -1.25e-184) {
		tmp = b * c;
	} else if (y <= 3.15e-167) {
		tmp = -4.0 * (x * i);
	} else {
		tmp = (t_1 * z) * 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 * 18.0) * y
	tmp = 0
	if y <= -2.8e+130:
		tmp = z * (t_1 * t)
	elif y <= -2.7e+68:
		tmp = -27.0 * (j * k)
	elif y <= -1.25e-184:
		tmp = b * c
	elif y <= 3.15e-167:
		tmp = -4.0 * (x * i)
	else:
		tmp = (t_1 * z) * 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(Float64(x * 18.0) * y)
	tmp = 0.0
	if (y <= -2.8e+130)
		tmp = Float64(z * Float64(t_1 * t));
	elseif (y <= -2.7e+68)
		tmp = Float64(-27.0 * Float64(j * k));
	elseif (y <= -1.25e-184)
		tmp = Float64(b * c);
	elseif (y <= 3.15e-167)
		tmp = Float64(-4.0 * Float64(x * i));
	else
		tmp = Float64(Float64(t_1 * z) * 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 * 18.0) * y;
	tmp = 0.0;
	if (y <= -2.8e+130)
		tmp = z * (t_1 * t);
	elseif (y <= -2.7e+68)
		tmp = -27.0 * (j * k);
	elseif (y <= -1.25e-184)
		tmp = b * c;
	elseif (y <= 3.15e-167)
		tmp = -4.0 * (x * i);
	else
		tmp = (t_1 * z) * 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[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -2.8e+130], N[(z * N[(t$95$1 * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.7e+68], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.25e-184], N[(b * c), $MachinePrecision], If[LessEqual[y, 3.15e-167], N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision], N[(N[(t$95$1 * z), $MachinePrecision] * t), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -2.7999999999999999e130

   1. Initial program 88.5%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \color{blue}{\left(j \cdot 27\right)} \cdot k \]

      2. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)} \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 90.8%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right) + \left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf

      \[\leadsto \color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) \cdot \color{blue}{18} \]

      2. associate-*r* N/A

         \[\leadsto t \cdot \color{blue}{\left(\left(x \cdot \left(y \cdot z\right)\right) \cdot 18\right)} \]

      3. *-commutative N/A

         \[\leadsto t \cdot \left(18 \cdot \color{blue}{\left(x \cdot \left(y \cdot z\right)\right)}\right) \]

      4. associate-*r* N/A

         \[\leadsto t \cdot \left(\left(18 \cdot x\right) \cdot \color{blue}{\left(y \cdot z\right)}\right) \]

      5. associate-*r* N/A

         \[\leadsto \left(t \cdot \left(18 \cdot x\right)\right) \cdot \color{blue}{\left(y \cdot z\right)} \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(t \cdot \left(18 \cdot x\right)\right), \color{blue}{\left(y \cdot z\right)}\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \left(18 \cdot x\right)\right), \left(\color{blue}{y} \cdot z\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(18, x\right)\right), \left(y \cdot z\right)\right) \]

      9. *-lowering-*.f64 45.2%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(18, x\right)\right), \mathsf{*.f64}\left(y, \color{blue}{z}\right)\right) \]

   7. Simplified 45.2%

      \[\leadsto \color{blue}{\left(t \cdot \left(18 \cdot x\right)\right) \cdot \left(y \cdot z\right)} \]
   8. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(\left(t \cdot \left(18 \cdot x\right)\right) \cdot y\right) \cdot \color{blue}{z} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\left(t \cdot \left(18 \cdot x\right)\right) \cdot y\right), \color{blue}{z}\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\left(t \cdot \left(x \cdot 18\right)\right) \cdot y\right), z\right) \]

      4. associate-*l* N/A

         \[\leadsto \mathsf{*.f64}\left(\left(t \cdot \left(\left(x \cdot 18\right) \cdot y\right)\right), z\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \left(\left(x \cdot 18\right) \cdot y\right)\right), z\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(\left(x \cdot 18\right), y\right)\right), z\right) \]

      7. *-lowering-*.f64 50.4%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right)\right), z\right) \]

   9. Applied egg-rr 50.4%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot y\right)\right) \cdot z} \]

   if -2.7999999999999999e130 < y < -2.69999999999999991e68

   1. Initial program 93.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \color{blue}{\left(j \cdot 27\right)} \cdot k \]

      2. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)} \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 93.9%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right) + \left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in j around inf

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]
   6. 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 57.7%

         \[\leadsto \mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, \color{blue}{k}\right)\right) \]

   7. Simplified 57.7%

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]

   if -2.69999999999999991e68 < y < -1.25000000000000001e-184

   1. Initial program 85.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \color{blue}{\left(j \cdot 27\right)} \cdot k \]

      2. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)} \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 89.3%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right) + \left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot c} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 38.4%

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{c}\right) \]

   7. Simplified 38.4%

      \[\leadsto \color{blue}{b \cdot c} \]

   if -1.25000000000000001e-184 < y < 3.1500000000000001e-167

   1. Initial program 91.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \color{blue}{\left(j \cdot 27\right)} \cdot k \]

      2. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)} \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 93.6%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right) + \left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around inf

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right)} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-4, \color{blue}{\left(i \cdot x\right)}\right) \]

      2. *-lowering-*.f64 31.7%

         \[\leadsto \mathsf{*.f64}\left(-4, \mathsf{*.f64}\left(i, \color{blue}{x}\right)\right) \]

   7. Simplified 31.7%

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right)} \]

   if 3.1500000000000001e-167 < y

   1. Initial program 83.6%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(b \cdot \left(\left(c + 18 \cdot \frac{t \cdot \left(x \cdot \left(y \cdot z\right)\right)}{b}\right) - \left(4 \cdot \frac{a \cdot t}{b} + 4 \cdot \frac{i \cdot x}{b}\right)\right)\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

   5. Simplified 77.5%

      \[\leadsto \color{blue}{b \cdot \left(c + \frac{-4 \cdot \left(i \cdot x\right) + t \cdot \left(-4 \cdot a + x \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right)}{b}\right)} - \left(j \cdot 27\right) \cdot k \]

   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. associate-*r* N/A

         \[\leadsto t \cdot \color{blue}{\left(\left(x \cdot \left(y \cdot z\right)\right) \cdot 18\right)} \]

      3. *-commutative N/A

         \[\leadsto t \cdot \left(18 \cdot \color{blue}{\left(x \cdot \left(y \cdot z\right)\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)}\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(18, \color{blue}{\left(x \cdot \left(y \cdot z\right)\right)}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(x, \color{blue}{\left(y \cdot z\right)}\right)\right)\right) \]

      7. *-lowering-*.f64 33.2%

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{z}\right)\right)\right)\right) \]

   8. Simplified 33.2%

      \[\leadsto \color{blue}{t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(\left(18 \cdot x\right) \cdot \color{blue}{\left(y \cdot z\right)}\right)\right) \]

      2. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(\left(\left(18 \cdot x\right) \cdot y\right) \cdot \color{blue}{z}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(\left(\left(18 \cdot x\right) \cdot y\right), \color{blue}{z}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(18 \cdot x\right), y\right), z\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right)\right) \]

      6. *-lowering-*.f64 35.1%

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right)\right) \]

   10. Applied egg-rr 35.1%

       \[\leadsto t \cdot \color{blue}{\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 39.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+130}:\\ \;\;\;\;z \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot t\right)\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{+68}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{-184}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;y \leq 3.15 \cdot 10^{-167}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 34.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{-124}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-120}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-82}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;z \leq 1.46 \cdot 10^{+43}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= z -4.5e-124)
   (* t (* 18.0 (* x (* y z))))
   (if (<= z 2.9e-120)
     (* b c)
     (if (<= z 2.9e-82)
       (* -27.0 (* j k))
       (if (<= z 1.46e+43) (* -4.0 (* x i)) (* t (* 18.0 (* y (* x z)))))))))

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 (z <= -4.5e-124) {
		tmp = t * (18.0 * (x * (y * z)));
	} else if (z <= 2.9e-120) {
		tmp = b * c;
	} else if (z <= 2.9e-82) {
		tmp = -27.0 * (j * k);
	} else if (z <= 1.46e+43) {
		tmp = -4.0 * (x * i);
	} else {
		tmp = t * (18.0 * (y * (x * z)));
	}
	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 (z <= (-4.5d-124)) then
        tmp = t * (18.0d0 * (x * (y * z)))
    else if (z <= 2.9d-120) then
        tmp = b * c
    else if (z <= 2.9d-82) then
        tmp = (-27.0d0) * (j * k)
    else if (z <= 1.46d+43) then
        tmp = (-4.0d0) * (x * i)
    else
        tmp = t * (18.0d0 * (y * (x * z)))
    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 (z <= -4.5e-124) {
		tmp = t * (18.0 * (x * (y * z)));
	} else if (z <= 2.9e-120) {
		tmp = b * c;
	} else if (z <= 2.9e-82) {
		tmp = -27.0 * (j * k);
	} else if (z <= 1.46e+43) {
		tmp = -4.0 * (x * i);
	} else {
		tmp = t * (18.0 * (y * (x * z)));
	}
	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 z <= -4.5e-124:
		tmp = t * (18.0 * (x * (y * z)))
	elif z <= 2.9e-120:
		tmp = b * c
	elif z <= 2.9e-82:
		tmp = -27.0 * (j * k)
	elif z <= 1.46e+43:
		tmp = -4.0 * (x * i)
	else:
		tmp = t * (18.0 * (y * (x * z)))
	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 (z <= -4.5e-124)
		tmp = Float64(t * Float64(18.0 * Float64(x * Float64(y * z))));
	elseif (z <= 2.9e-120)
		tmp = Float64(b * c);
	elseif (z <= 2.9e-82)
		tmp = Float64(-27.0 * Float64(j * k));
	elseif (z <= 1.46e+43)
		tmp = Float64(-4.0 * Float64(x * i));
	else
		tmp = Float64(t * Float64(18.0 * Float64(y * Float64(x * z))));
	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 (z <= -4.5e-124)
		tmp = t * (18.0 * (x * (y * z)));
	elseif (z <= 2.9e-120)
		tmp = b * c;
	elseif (z <= 2.9e-82)
		tmp = -27.0 * (j * k);
	elseif (z <= 1.46e+43)
		tmp = -4.0 * (x * i);
	else
		tmp = t * (18.0 * (y * (x * z)));
	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[z, -4.5e-124], N[(t * N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.9e-120], N[(b * c), $MachinePrecision], If[LessEqual[z, 2.9e-82], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.46e+43], N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision], N[(t * N[(18.0 * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -4.4999999999999996e-124

   1. Initial program 79.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(b \cdot \left(\left(c + 18 \cdot \frac{t \cdot \left(x \cdot \left(y \cdot z\right)\right)}{b}\right) - \left(4 \cdot \frac{a \cdot t}{b} + 4 \cdot \frac{i \cdot x}{b}\right)\right)\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

   5. Simplified 76.3%

      \[\leadsto \color{blue}{b \cdot \left(c + \frac{-4 \cdot \left(i \cdot x\right) + t \cdot \left(-4 \cdot a + x \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right)}{b}\right)} - \left(j \cdot 27\right) \cdot k \]

   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. associate-*r* N/A

         \[\leadsto t \cdot \color{blue}{\left(\left(x \cdot \left(y \cdot z\right)\right) \cdot 18\right)} \]

      3. *-commutative N/A

         \[\leadsto t \cdot \left(18 \cdot \color{blue}{\left(x \cdot \left(y \cdot z\right)\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)}\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(18, \color{blue}{\left(x \cdot \left(y \cdot z\right)\right)}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(x, \color{blue}{\left(y \cdot z\right)}\right)\right)\right) \]

      7. *-lowering-*.f64 39.3%

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{z}\right)\right)\right)\right) \]

   8. Simplified 39.3%

      \[\leadsto \color{blue}{t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]

   if -4.4999999999999996e-124 < z < 2.9e-120

   1. Initial program 94.5%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \color{blue}{\left(j \cdot 27\right)} \cdot k \]

      2. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)} \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 94.6%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right) + \left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot c} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 29.9%

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{c}\right) \]

   7. Simplified 29.9%

      \[\leadsto \color{blue}{b \cdot c} \]

   if 2.9e-120 < z < 2.89999999999999977e-82

   1. Initial program 79.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \color{blue}{\left(j \cdot 27\right)} \cdot k \]

      2. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)} \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 80.0%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right) + \left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in j around inf

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]
   6. 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 100.0%

         \[\leadsto \mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, \color{blue}{k}\right)\right) \]

   7. Simplified 100.0%

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]

   if 2.89999999999999977e-82 < z < 1.45999999999999989e43

   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. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \color{blue}{\left(j \cdot 27\right)} \cdot k \]

      2. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)} \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 83.4%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right) + \left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around inf

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right)} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-4, \color{blue}{\left(i \cdot x\right)}\right) \]

      2. *-lowering-*.f64 26.2%

         \[\leadsto \mathsf{*.f64}\left(-4, \mathsf{*.f64}\left(i, \color{blue}{x}\right)\right) \]

   7. Simplified 26.2%

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right)} \]

   if 1.45999999999999989e43 < z

   1. Initial program 85.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(b \cdot \left(\left(c + 18 \cdot \frac{t \cdot \left(x \cdot \left(y \cdot z\right)\right)}{b}\right) - \left(4 \cdot \frac{a \cdot t}{b} + 4 \cdot \frac{i \cdot x}{b}\right)\right)\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

   5. Simplified 77.9%

      \[\leadsto \color{blue}{b \cdot \left(c + \frac{-4 \cdot \left(i \cdot x\right) + t \cdot \left(-4 \cdot a + x \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right)}{b}\right)} - \left(j \cdot 27\right) \cdot k \]

   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. associate-*r* N/A

         \[\leadsto t \cdot \color{blue}{\left(\left(x \cdot \left(y \cdot z\right)\right) \cdot 18\right)} \]

      3. *-commutative N/A

         \[\leadsto t \cdot \left(18 \cdot \color{blue}{\left(x \cdot \left(y \cdot z\right)\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)}\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(18, \color{blue}{\left(x \cdot \left(y \cdot z\right)\right)}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(x, \color{blue}{\left(y \cdot z\right)}\right)\right)\right) \]

      7. *-lowering-*.f64 41.1%

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{z}\right)\right)\right)\right) \]

   8. Simplified 41.1%

      \[\leadsto \color{blue}{t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(18, \left(x \cdot \left(z \cdot \color{blue}{y}\right)\right)\right)\right) \]

      2. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(18, \left(\left(x \cdot z\right) \cdot \color{blue}{y}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(\left(x \cdot z\right), \color{blue}{y}\right)\right)\right) \]

      4. *-lowering-*.f64 48.0%

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, z\right), y\right)\right)\right) \]

   10. Applied egg-rr 48.0%

       \[\leadsto t \cdot \left(18 \cdot \color{blue}{\left(\left(x \cdot z\right) \cdot y\right)}\right) \]
3. Recombined 5 regimes into one program.

4. Final simplification 37.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{-124}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-120}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-82}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;z \leq 1.46 \cdot 10^{+43}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 33.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{if}\;y \leq -4.8 \cdot 10^{+130}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{+73}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{-185}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-167}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* t (* 18.0 (* x (* y z))))))
   (if (<= y -4.8e+130)
     t_1
     (if (<= y -1.15e+73)
       (* -27.0 (* j k))
       (if (<= y -3.8e-185)
         (* b c)
         (if (<= y 3.1e-167) (* -4.0 (* x i)) t_1))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * (18.0 * (x * (y * z)));
	double tmp;
	if (y <= -4.8e+130) {
		tmp = t_1;
	} else if (y <= -1.15e+73) {
		tmp = -27.0 * (j * k);
	} else if (y <= -3.8e-185) {
		tmp = b * c;
	} else if (y <= 3.1e-167) {
		tmp = -4.0 * (x * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (18.0d0 * (x * (y * z)))
    if (y <= (-4.8d+130)) then
        tmp = t_1
    else if (y <= (-1.15d+73)) then
        tmp = (-27.0d0) * (j * k)
    else if (y <= (-3.8d-185)) then
        tmp = b * c
    else if (y <= 3.1d-167) then
        tmp = (-4.0d0) * (x * i)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * (18.0 * (x * (y * z)));
	double tmp;
	if (y <= -4.8e+130) {
		tmp = t_1;
	} else if (y <= -1.15e+73) {
		tmp = -27.0 * (j * k);
	} else if (y <= -3.8e-185) {
		tmp = b * c;
	} else if (y <= 3.1e-167) {
		tmp = -4.0 * (x * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = t * (18.0 * (x * (y * z)))
	tmp = 0
	if y <= -4.8e+130:
		tmp = t_1
	elif y <= -1.15e+73:
		tmp = -27.0 * (j * k)
	elif y <= -3.8e-185:
		tmp = b * c
	elif y <= 3.1e-167:
		tmp = -4.0 * (x * i)
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(t * Float64(18.0 * Float64(x * Float64(y * z))))
	tmp = 0.0
	if (y <= -4.8e+130)
		tmp = t_1;
	elseif (y <= -1.15e+73)
		tmp = Float64(-27.0 * Float64(j * k));
	elseif (y <= -3.8e-185)
		tmp = Float64(b * c);
	elseif (y <= 3.1e-167)
		tmp = Float64(-4.0 * Float64(x * i));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = t * (18.0 * (x * (y * z)));
	tmp = 0.0;
	if (y <= -4.8e+130)
		tmp = t_1;
	elseif (y <= -1.15e+73)
		tmp = -27.0 * (j * k);
	elseif (y <= -3.8e-185)
		tmp = b * c;
	elseif (y <= 3.1e-167)
		tmp = -4.0 * (x * i);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(t * N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.8e+130], t$95$1, If[LessEqual[y, -1.15e+73], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.8e-185], N[(b * c), $MachinePrecision], If[LessEqual[y, 3.1e-167], N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.80000000000000048e130 or 3.1e-167 < y

   1. Initial program 85.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(b \cdot \left(\left(c + 18 \cdot \frac{t \cdot \left(x \cdot \left(y \cdot z\right)\right)}{b}\right) - \left(4 \cdot \frac{a \cdot t}{b} + 4 \cdot \frac{i \cdot x}{b}\right)\right)\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

   5. Simplified 77.5%

      \[\leadsto \color{blue}{b \cdot \left(c + \frac{-4 \cdot \left(i \cdot x\right) + t \cdot \left(-4 \cdot a + x \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right)}{b}\right)} - \left(j \cdot 27\right) \cdot k \]

   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. associate-*r* N/A

         \[\leadsto t \cdot \color{blue}{\left(\left(x \cdot \left(y \cdot z\right)\right) \cdot 18\right)} \]

      3. *-commutative N/A

         \[\leadsto t \cdot \left(18 \cdot \color{blue}{\left(x \cdot \left(y \cdot z\right)\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)}\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(18, \color{blue}{\left(x \cdot \left(y \cdot z\right)\right)}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(x, \color{blue}{\left(y \cdot z\right)}\right)\right)\right) \]

      7. *-lowering-*.f64 37.5%

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{z}\right)\right)\right)\right) \]

   8. Simplified 37.5%

      \[\leadsto \color{blue}{t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]

   if -4.80000000000000048e130 < y < -1.15e73

   1. Initial program 93.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \color{blue}{\left(j \cdot 27\right)} \cdot k \]

      2. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)} \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 93.9%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right) + \left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in j around inf

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]
   6. 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 57.7%

         \[\leadsto \mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, \color{blue}{k}\right)\right) \]

   7. Simplified 57.7%

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]

   if -1.15e73 < y < -3.7999999999999999e-185

   1. Initial program 85.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \color{blue}{\left(j \cdot 27\right)} \cdot k \]

      2. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)} \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 89.6%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right) + \left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot c} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 37.6%

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{c}\right) \]

   7. Simplified 37.6%

      \[\leadsto \color{blue}{b \cdot c} \]

   if -3.7999999999999999e-185 < y < 3.1e-167

   1. Initial program 91.2%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \color{blue}{\left(j \cdot 27\right)} \cdot k \]

      2. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)} \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 93.4%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right) + \left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around inf

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right)} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-4, \color{blue}{\left(i \cdot x\right)}\right) \]

      2. *-lowering-*.f64 32.3%

         \[\leadsto \mathsf{*.f64}\left(-4, \mathsf{*.f64}\left(i, \color{blue}{x}\right)\right) \]

   7. Simplified 32.3%

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 37.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+130}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{+73}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{-185}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-167}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 51.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := -4 \cdot \left(t \cdot a\right)\\ t_2 := k \cdot \left(j \cdot 27\right)\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+20}:\\ \;\;\;\;t\_1 - t\_2\\ \mathbf{elif}\;t\_2 \leq 3 \cdot 10^{-123}:\\ \;\;\;\;b \cdot c + t\_1\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right) - t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* -4.0 (* t a))) (t_2 (* k (* j 27.0))))
   (if (<= t_2 -1e+20)
     (- t_1 t_2)
     (if (<= t_2 3e-123) (+ (* b c) t_1) (- (* -4.0 (* x i)) t_2)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -4.0 * (t * a);
	double t_2 = k * (j * 27.0);
	double tmp;
	if (t_2 <= -1e+20) {
		tmp = t_1 - t_2;
	} else if (t_2 <= 3e-123) {
		tmp = (b * c) + t_1;
	} else {
		tmp = (-4.0 * (x * i)) - t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (-4.0d0) * (t * a)
    t_2 = k * (j * 27.0d0)
    if (t_2 <= (-1d+20)) then
        tmp = t_1 - t_2
    else if (t_2 <= 3d-123) then
        tmp = (b * c) + t_1
    else
        tmp = ((-4.0d0) * (x * i)) - t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -4.0 * (t * a);
	double t_2 = k * (j * 27.0);
	double tmp;
	if (t_2 <= -1e+20) {
		tmp = t_1 - t_2;
	} else if (t_2 <= 3e-123) {
		tmp = (b * c) + t_1;
	} else {
		tmp = (-4.0 * (x * i)) - t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = -4.0 * (t * a)
	t_2 = k * (j * 27.0)
	tmp = 0
	if t_2 <= -1e+20:
		tmp = t_1 - t_2
	elif t_2 <= 3e-123:
		tmp = (b * c) + t_1
	else:
		tmp = (-4.0 * (x * i)) - t_2
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(-4.0 * Float64(t * a))
	t_2 = Float64(k * Float64(j * 27.0))
	tmp = 0.0
	if (t_2 <= -1e+20)
		tmp = Float64(t_1 - t_2);
	elseif (t_2 <= 3e-123)
		tmp = Float64(Float64(b * c) + t_1);
	else
		tmp = Float64(Float64(-4.0 * Float64(x * i)) - t_2);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = -4.0 * (t * a);
	t_2 = k * (j * 27.0);
	tmp = 0.0;
	if (t_2 <= -1e+20)
		tmp = t_1 - t_2;
	elseif (t_2 <= 3e-123)
		tmp = (b * c) + t_1;
	else
		tmp = (-4.0 * (x * i)) - t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+20], N[(t$95$1 - t$95$2), $MachinePrecision], If[LessEqual[t$95$2, 3e-123], N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision], N[(N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -1e20

   1. Initial program 86.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(-4 \cdot \left(a \cdot t\right)\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(-4, \left(a \cdot t\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(-4, \left(t \cdot a\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, \color{blue}{27}\right), k\right)\right) \]

      3. *-lowering-*.f64 70.9%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(-4, \mathsf{*.f64}\left(t, a\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, \color{blue}{27}\right), k\right)\right) \]

   5. Simplified 70.9%

      \[\leadsto \color{blue}{-4 \cdot \left(t \cdot a\right)} - \left(j \cdot 27\right) \cdot k \]

   if -1e20 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 2.99999999999999984e-123

   1. Initial program 90.1%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(b \cdot c - 4 \cdot \left(a \cdot t\right)\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   4. Step-by-step derivation

      1. cancel-sign-sub-inv N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(a \cdot t\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + -4 \cdot \left(a \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(b \cdot c\right), \left(-4 \cdot \left(a \cdot t\right)\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(-4 \cdot \left(a \cdot t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(-4, \left(a \cdot t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, \color{blue}{27}\right), k\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(-4, \left(t \cdot a\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      7. *-lowering-*.f64 56.0%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(-4, \mathsf{*.f64}\left(t, a\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

   5. Simplified 56.0%

      \[\leadsto \color{blue}{\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   6. Taylor expanded in j around 0

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t\right) + b \cdot c} \]
   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. *-lowering-*.f64 55.9%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(-4, \mathsf{*.f64}\left(a, \color{blue}{t}\right)\right)\right) \]

   8. Simplified 55.9%

      \[\leadsto \color{blue}{b \cdot c + -4 \cdot \left(a \cdot t\right)} \]

   if 2.99999999999999984e-123 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 82.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(-4 \cdot \left(i \cdot x\right)\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(-4, \left(i \cdot x\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

      2. *-lowering-*.f64 55.8%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(-4, \mathsf{*.f64}\left(i, x\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, \color{blue}{27}\right), k\right)\right) \]

   5. Simplified 55.8%

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right)} - \left(j \cdot 27\right) \cdot k \]
3. Recombined 3 regimes into one program.

4. Final simplification 58.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \cdot \left(j \cdot 27\right) \leq -1 \cdot 10^{+20}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 3 \cdot 10^{-123}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 58.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -3.05 \cdot 10^{+68}:\\ \;\;\;\;t \cdot \left(a \cdot -4 + x \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{-163}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+52}:\\ \;\;\;\;b \cdot c - j \cdot \left(k \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot -4 + \left(18 \cdot y\right) \cdot \left(x \cdot z\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= t -3.05e+68)
   (* t (+ (* a -4.0) (* x (* 18.0 (* y z)))))
   (if (<= t 7.2e-163)
     (- (* -4.0 (* x i)) (* k (* j 27.0)))
     (if (<= t 3.2e+52)
       (- (* b c) (* j (* k 27.0)))
       (* t (+ (* a -4.0) (* (* 18.0 y) (* x z))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (t <= -3.05e+68) {
		tmp = t * ((a * -4.0) + (x * (18.0 * (y * z))));
	} else if (t <= 7.2e-163) {
		tmp = (-4.0 * (x * i)) - (k * (j * 27.0));
	} else if (t <= 3.2e+52) {
		tmp = (b * c) - (j * (k * 27.0));
	} else {
		tmp = t * ((a * -4.0) + ((18.0 * y) * (x * z)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (t <= (-3.05d+68)) then
        tmp = t * ((a * (-4.0d0)) + (x * (18.0d0 * (y * z))))
    else if (t <= 7.2d-163) then
        tmp = ((-4.0d0) * (x * i)) - (k * (j * 27.0d0))
    else if (t <= 3.2d+52) then
        tmp = (b * c) - (j * (k * 27.0d0))
    else
        tmp = t * ((a * (-4.0d0)) + ((18.0d0 * y) * (x * z)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (t <= -3.05e+68) {
		tmp = t * ((a * -4.0) + (x * (18.0 * (y * z))));
	} else if (t <= 7.2e-163) {
		tmp = (-4.0 * (x * i)) - (k * (j * 27.0));
	} else if (t <= 3.2e+52) {
		tmp = (b * c) - (j * (k * 27.0));
	} else {
		tmp = t * ((a * -4.0) + ((18.0 * y) * (x * z)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if t <= -3.05e+68:
		tmp = t * ((a * -4.0) + (x * (18.0 * (y * z))))
	elif t <= 7.2e-163:
		tmp = (-4.0 * (x * i)) - (k * (j * 27.0))
	elif t <= 3.2e+52:
		tmp = (b * c) - (j * (k * 27.0))
	else:
		tmp = t * ((a * -4.0) + ((18.0 * y) * (x * z)))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (t <= -3.05e+68)
		tmp = Float64(t * Float64(Float64(a * -4.0) + Float64(x * Float64(18.0 * Float64(y * z)))));
	elseif (t <= 7.2e-163)
		tmp = Float64(Float64(-4.0 * Float64(x * i)) - Float64(k * Float64(j * 27.0)));
	elseif (t <= 3.2e+52)
		tmp = Float64(Float64(b * c) - Float64(j * Float64(k * 27.0)));
	else
		tmp = Float64(t * Float64(Float64(a * -4.0) + Float64(Float64(18.0 * y) * Float64(x * z))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (t <= -3.05e+68)
		tmp = t * ((a * -4.0) + (x * (18.0 * (y * z))));
	elseif (t <= 7.2e-163)
		tmp = (-4.0 * (x * i)) - (k * (j * 27.0));
	elseif (t <= 3.2e+52)
		tmp = (b * c) - (j * (k * 27.0));
	else
		tmp = t * ((a * -4.0) + ((18.0 * y) * (x * z)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[t, -3.05e+68], N[(t * N[(N[(a * -4.0), $MachinePrecision] + N[(x * N[(18.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.2e-163], N[(N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.2e+52], N[(N[(b * c), $MachinePrecision] - N[(j * N[(k * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(a * -4.0), $MachinePrecision] + N[(N[(18.0 * y), $MachinePrecision] * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3.05e68

   1. Initial program 80.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \color{blue}{\left(j \cdot 27\right)} \cdot k \]

      2. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)} \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 89.3%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right) + \left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(-4 \cdot a\right), \color{blue}{\left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \left(\color{blue}{18} \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \left(\left(x \cdot \left(y \cdot z\right)\right) \cdot \color{blue}{18}\right)\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \left(x \cdot \color{blue}{\left(\left(y \cdot z\right) \cdot 18\right)}\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \left(x \cdot \left(18 \cdot \color{blue}{\left(y \cdot z\right)}\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \mathsf{*.f64}\left(x, \color{blue}{\left(18 \cdot \left(y \cdot z\right)\right)}\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(18, \color{blue}{\left(y \cdot z\right)}\right)\right)\right)\right) \]

      9. *-lowering-*.f64 62.5%

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(y, \color{blue}{z}\right)\right)\right)\right)\right) \]

   7. Simplified 62.5%

      \[\leadsto \color{blue}{t \cdot \left(-4 \cdot a + x \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right)} \]

   if -3.05e68 < t < 7.1999999999999996e-163

   1. Initial program 87.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(-4 \cdot \left(i \cdot x\right)\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(-4, \left(i \cdot x\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

      2. *-lowering-*.f64 58.4%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(-4, \mathsf{*.f64}\left(i, x\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, \color{blue}{27}\right), k\right)\right) \]

   5. Simplified 58.4%

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right)} - \left(j \cdot 27\right) \cdot k \]

   if 7.1999999999999996e-163 < t < 3.2e52

   1. Initial program 92.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   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 59.0%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

   5. Simplified 59.0%

      \[\leadsto \color{blue}{b \cdot c} - \left(j \cdot 27\right) \cdot k \]
   6. Step-by-step derivation

      1. associate-*l* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(j \cdot \color{blue}{\left(27 \cdot k\right)}\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\left(27 \cdot k\right) \cdot \color{blue}{j}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\left(27 \cdot k\right), \color{blue}{j}\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\left(k \cdot 27\right), j\right)\right) \]

      5. *-lowering-*.f64 59.0%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(k, 27\right), j\right)\right) \]

   7. Applied egg-rr 59.0%

      \[\leadsto b \cdot c - \color{blue}{\left(k \cdot 27\right) \cdot j} \]

   if 3.2e52 < t

   1. Initial program 85.5%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \color{blue}{\left(j \cdot 27\right)} \cdot k \]

      2. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)} \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 87.6%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right) + \left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(-4 \cdot a\right), \color{blue}{\left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \left(\color{blue}{18} \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \left(\left(x \cdot \left(y \cdot z\right)\right) \cdot \color{blue}{18}\right)\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \left(x \cdot \color{blue}{\left(\left(y \cdot z\right) \cdot 18\right)}\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \left(x \cdot \left(18 \cdot \color{blue}{\left(y \cdot z\right)}\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \mathsf{*.f64}\left(x, \color{blue}{\left(18 \cdot \left(y \cdot z\right)\right)}\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(18, \color{blue}{\left(y \cdot z\right)}\right)\right)\right)\right) \]

      9. *-lowering-*.f64 69.5%

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(y, \color{blue}{z}\right)\right)\right)\right)\right) \]

   7. Simplified 69.5%

      \[\leadsto \color{blue}{t \cdot \left(-4 \cdot a + x \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \left(\left(18 \cdot \left(y \cdot z\right)\right) \cdot \color{blue}{x}\right)\right)\right) \]

      2. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \left(\left(\left(18 \cdot y\right) \cdot z\right) \cdot x\right)\right)\right) \]

      3. associate-*l* N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \left(\left(18 \cdot y\right) \cdot \color{blue}{\left(z \cdot x\right)}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \mathsf{*.f64}\left(\left(18 \cdot y\right), \color{blue}{\left(z \cdot x\right)}\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(18, y\right), \left(\color{blue}{z} \cdot x\right)\right)\right)\right) \]

      6. *-lowering-*.f64 71.4%

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(18, y\right), \mathsf{*.f64}\left(z, \color{blue}{x}\right)\right)\right)\right) \]

   9. Applied egg-rr 71.4%

      \[\leadsto t \cdot \left(-4 \cdot a + \color{blue}{\left(18 \cdot y\right) \cdot \left(z \cdot x\right)}\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 61.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.05 \cdot 10^{+68}:\\ \;\;\;\;t \cdot \left(a \cdot -4 + x \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{-163}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+52}:\\ \;\;\;\;b \cdot c - j \cdot \left(k \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot -4 + \left(18 \cdot y\right) \cdot \left(x \cdot z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 58.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := t \cdot \left(a \cdot -4 + x \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{if}\;t \leq -6.6 \cdot 10^{+68}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{-163}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+44}:\\ \;\;\;\;b \cdot c - j \cdot \left(k \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* t (+ (* a -4.0) (* x (* 18.0 (* y z)))))))
   (if (<= t -6.6e+68)
     t_1
     (if (<= t 1.45e-163)
       (- (* -4.0 (* x i)) (* k (* j 27.0)))
       (if (<= t 2.6e+44) (- (* b c) (* j (* k 27.0))) t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * ((a * -4.0) + (x * (18.0 * (y * z))));
	double tmp;
	if (t <= -6.6e+68) {
		tmp = t_1;
	} else if (t <= 1.45e-163) {
		tmp = (-4.0 * (x * i)) - (k * (j * 27.0));
	} else if (t <= 2.6e+44) {
		tmp = (b * c) - (j * (k * 27.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((a * (-4.0d0)) + (x * (18.0d0 * (y * z))))
    if (t <= (-6.6d+68)) then
        tmp = t_1
    else if (t <= 1.45d-163) then
        tmp = ((-4.0d0) * (x * i)) - (k * (j * 27.0d0))
    else if (t <= 2.6d+44) then
        tmp = (b * c) - (j * (k * 27.0d0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * ((a * -4.0) + (x * (18.0 * (y * z))));
	double tmp;
	if (t <= -6.6e+68) {
		tmp = t_1;
	} else if (t <= 1.45e-163) {
		tmp = (-4.0 * (x * i)) - (k * (j * 27.0));
	} else if (t <= 2.6e+44) {
		tmp = (b * c) - (j * (k * 27.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = t * ((a * -4.0) + (x * (18.0 * (y * z))))
	tmp = 0
	if t <= -6.6e+68:
		tmp = t_1
	elif t <= 1.45e-163:
		tmp = (-4.0 * (x * i)) - (k * (j * 27.0))
	elif t <= 2.6e+44:
		tmp = (b * c) - (j * (k * 27.0))
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(t * Float64(Float64(a * -4.0) + Float64(x * Float64(18.0 * Float64(y * z)))))
	tmp = 0.0
	if (t <= -6.6e+68)
		tmp = t_1;
	elseif (t <= 1.45e-163)
		tmp = Float64(Float64(-4.0 * Float64(x * i)) - Float64(k * Float64(j * 27.0)));
	elseif (t <= 2.6e+44)
		tmp = Float64(Float64(b * c) - Float64(j * Float64(k * 27.0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = t * ((a * -4.0) + (x * (18.0 * (y * z))));
	tmp = 0.0;
	if (t <= -6.6e+68)
		tmp = t_1;
	elseif (t <= 1.45e-163)
		tmp = (-4.0 * (x * i)) - (k * (j * 27.0));
	elseif (t <= 2.6e+44)
		tmp = (b * c) - (j * (k * 27.0));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(t * N[(N[(a * -4.0), $MachinePrecision] + N[(x * N[(18.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.6e+68], t$95$1, If[LessEqual[t, 1.45e-163], N[(N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.6e+44], N[(N[(b * c), $MachinePrecision] - N[(j * N[(k * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.6000000000000001e68 or 2.5999999999999999e44 < t

   1. Initial program 83.2%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \color{blue}{\left(j \cdot 27\right)} \cdot k \]

      2. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)} \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 88.4%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right) + \left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(-4 \cdot a\right), \color{blue}{\left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \left(\color{blue}{18} \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \left(\left(x \cdot \left(y \cdot z\right)\right) \cdot \color{blue}{18}\right)\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \left(x \cdot \color{blue}{\left(\left(y \cdot z\right) \cdot 18\right)}\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \left(x \cdot \left(18 \cdot \color{blue}{\left(y \cdot z\right)}\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \mathsf{*.f64}\left(x, \color{blue}{\left(18 \cdot \left(y \cdot z\right)\right)}\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(18, \color{blue}{\left(y \cdot z\right)}\right)\right)\right)\right) \]

      9. *-lowering-*.f64 66.0%

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(y, \color{blue}{z}\right)\right)\right)\right)\right) \]

   7. Simplified 66.0%

      \[\leadsto \color{blue}{t \cdot \left(-4 \cdot a + x \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right)} \]

   if -6.6000000000000001e68 < t < 1.4500000000000001e-163

   1. Initial program 87.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(-4 \cdot \left(i \cdot x\right)\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(-4, \left(i \cdot x\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

      2. *-lowering-*.f64 58.4%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(-4, \mathsf{*.f64}\left(i, x\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, \color{blue}{27}\right), k\right)\right) \]

   5. Simplified 58.4%

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right)} - \left(j \cdot 27\right) \cdot k \]

   if 1.4500000000000001e-163 < t < 2.5999999999999999e44

   1. Initial program 92.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   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 59.0%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

   5. Simplified 59.0%

      \[\leadsto \color{blue}{b \cdot c} - \left(j \cdot 27\right) \cdot k \]
   6. Step-by-step derivation

      1. associate-*l* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(j \cdot \color{blue}{\left(27 \cdot k\right)}\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\left(27 \cdot k\right) \cdot \color{blue}{j}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\left(27 \cdot k\right), \color{blue}{j}\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\left(k \cdot 27\right), j\right)\right) \]

      5. *-lowering-*.f64 59.0%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(k, 27\right), j\right)\right) \]

   7. Applied egg-rr 59.0%

      \[\leadsto b \cdot c - \color{blue}{\left(k \cdot 27\right) \cdot j} \]
3. Recombined 3 regimes into one program.

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.6 \cdot 10^{+68}:\\ \;\;\;\;t \cdot \left(a \cdot -4 + x \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{-163}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+44}:\\ \;\;\;\;b \cdot c - j \cdot \left(k \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot -4 + x \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 75.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c + t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right)\\ \mathbf{if}\;t \leq -4.3 \cdot 10^{+68}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.46 \cdot 10^{+43}:\\ \;\;\;\;\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (+ (* b c) (* t (+ (* (* (* x 18.0) y) z) (* a -4.0))))))
   (if (<= t -4.3e+68)
     t_1
     (if (<= t 1.46e+43)
       (- (- (* b c) (* (* x 4.0) i)) (* k (* j 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 = (b * c) + (t * ((((x * 18.0) * y) * z) + (a * -4.0)));
	double tmp;
	if (t <= -4.3e+68) {
		tmp = t_1;
	} else if (t <= 1.46e+43) {
		tmp = ((b * c) - ((x * 4.0) * i)) - (k * (j * 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 = (b * c) + (t * ((((x * 18.0d0) * y) * z) + (a * (-4.0d0))))
    if (t <= (-4.3d+68)) then
        tmp = t_1
    else if (t <= 1.46d+43) then
        tmp = ((b * c) - ((x * 4.0d0) * i)) - (k * (j * 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 = (b * c) + (t * ((((x * 18.0) * y) * z) + (a * -4.0)));
	double tmp;
	if (t <= -4.3e+68) {
		tmp = t_1;
	} else if (t <= 1.46e+43) {
		tmp = ((b * c) - ((x * 4.0) * i)) - (k * (j * 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 = (b * c) + (t * ((((x * 18.0) * y) * z) + (a * -4.0)))
	tmp = 0
	if t <= -4.3e+68:
		tmp = t_1
	elif t <= 1.46e+43:
		tmp = ((b * c) - ((x * 4.0) * i)) - (k * (j * 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(Float64(b * c) + Float64(t * Float64(Float64(Float64(Float64(x * 18.0) * y) * z) + Float64(a * -4.0))))
	tmp = 0.0
	if (t <= -4.3e+68)
		tmp = t_1;
	elseif (t <= 1.46e+43)
		tmp = Float64(Float64(Float64(b * c) - Float64(Float64(x * 4.0) * i)) - Float64(k * Float64(j * 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 = (b * c) + (t * ((((x * 18.0) * y) * z) + (a * -4.0)));
	tmp = 0.0;
	if (t <= -4.3e+68)
		tmp = t_1;
	elseif (t <= 1.46e+43)
		tmp = ((b * c) - ((x * 4.0) * i)) - (k * (j * 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[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.3e+68], t$95$1, If[LessEqual[t, 1.46e+43], N[(N[(N[(b * c), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -4.3000000000000001e68 or 1.45999999999999989e43 < t

   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. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \color{blue}{\left(j \cdot 27\right)} \cdot k \]

      2. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)} \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 88.5%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right) + \left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \color{blue}{\left(b \cdot c\right)}\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 79.4%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \mathsf{*.f64}\left(b, \color{blue}{c}\right)\right) \]

   7. Simplified 79.4%

      \[\leadsto t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right) + \color{blue}{b \cdot c} \]

   if -4.3000000000000001e68 < t < 1.45999999999999989e43

   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 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 75.4%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

   5. Simplified 75.4%

      \[\leadsto \left(\color{blue}{b \cdot c} - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
3. Recombined 2 regimes into one program.

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.3 \cdot 10^{+68}:\\ \;\;\;\;b \cdot c + t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right)\\ \mathbf{elif}\;t \leq 1.46 \cdot 10^{+43}:\\ \;\;\;\;\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 54.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := k \cdot \left(j \cdot 27\right)\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+17}:\\ \;\;\;\;b \cdot c - j \cdot \left(k \cdot 27\right)\\ \mathbf{elif}\;t\_1 \leq 10^{+122}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* k (* j 27.0))))
   (if (<= t_1 -2e+17)
     (- (* b c) (* j (* k 27.0)))
     (if (<= t_1 1e+122) (+ (* b c) (* -4.0 (* t a))) (- (* 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 = k * (j * 27.0);
	double tmp;
	if (t_1 <= -2e+17) {
		tmp = (b * c) - (j * (k * 27.0));
	} else if (t_1 <= 1e+122) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else {
		tmp = (b * c) - t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = k * (j * 27.0d0)
    if (t_1 <= (-2d+17)) then
        tmp = (b * c) - (j * (k * 27.0d0))
    else if (t_1 <= 1d+122) then
        tmp = (b * c) + ((-4.0d0) * (t * a))
    else
        tmp = (b * c) - t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = k * (j * 27.0);
	double tmp;
	if (t_1 <= -2e+17) {
		tmp = (b * c) - (j * (k * 27.0));
	} else if (t_1 <= 1e+122) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else {
		tmp = (b * c) - t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = k * (j * 27.0)
	tmp = 0
	if t_1 <= -2e+17:
		tmp = (b * c) - (j * (k * 27.0))
	elif t_1 <= 1e+122:
		tmp = (b * c) + (-4.0 * (t * a))
	else:
		tmp = (b * c) - t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(k * Float64(j * 27.0))
	tmp = 0.0
	if (t_1 <= -2e+17)
		tmp = Float64(Float64(b * c) - Float64(j * Float64(k * 27.0)));
	elseif (t_1 <= 1e+122)
		tmp = Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a)));
	else
		tmp = Float64(Float64(b * c) - t_1);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = k * (j * 27.0);
	tmp = 0.0;
	if (t_1 <= -2e+17)
		tmp = (b * c) - (j * (k * 27.0));
	elseif (t_1 <= 1e+122)
		tmp = (b * c) + (-4.0 * (t * a));
	else
		tmp = (b * c) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+17], N[(N[(b * c), $MachinePrecision] - N[(j * N[(k * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+122], N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] - t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -2e17

   1. Initial program 85.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   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 62.5%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

   5. Simplified 62.5%

      \[\leadsto \color{blue}{b \cdot c} - \left(j \cdot 27\right) \cdot k \]
   6. Step-by-step derivation

      1. associate-*l* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(j \cdot \color{blue}{\left(27 \cdot k\right)}\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\left(27 \cdot k\right) \cdot \color{blue}{j}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\left(27 \cdot k\right), \color{blue}{j}\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\left(k \cdot 27\right), j\right)\right) \]

      5. *-lowering-*.f64 62.5%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(k, 27\right), j\right)\right) \]

   7. Applied egg-rr 62.5%

      \[\leadsto b \cdot c - \color{blue}{\left(k \cdot 27\right) \cdot j} \]

   if -2e17 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 1.00000000000000001e122

   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

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(b \cdot c - 4 \cdot \left(a \cdot t\right)\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   4. Step-by-step derivation

      1. cancel-sign-sub-inv N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(a \cdot t\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + -4 \cdot \left(a \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(b \cdot c\right), \left(-4 \cdot \left(a \cdot t\right)\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(-4 \cdot \left(a \cdot t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(-4, \left(a \cdot t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, \color{blue}{27}\right), k\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(-4, \left(t \cdot a\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      7. *-lowering-*.f64 51.1%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(-4, \mathsf{*.f64}\left(t, a\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

   5. Simplified 51.1%

      \[\leadsto \color{blue}{\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   6. Taylor expanded in j around 0

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t\right) + b \cdot c} \]
   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. *-lowering-*.f64 50.4%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(-4, \mathsf{*.f64}\left(a, \color{blue}{t}\right)\right)\right) \]

   8. Simplified 50.4%

      \[\leadsto \color{blue}{b \cdot c + -4 \cdot \left(a \cdot t\right)} \]

   if 1.00000000000000001e122 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 75.5%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(b \cdot c\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 73.1%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

   5. Simplified 73.1%

      \[\leadsto \color{blue}{b \cdot c} - \left(j \cdot 27\right) \cdot k \]
3. Recombined 3 regimes into one program.

4. Final simplification 56.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \cdot \left(j \cdot 27\right) \leq -2 \cdot 10^{+17}:\\ \;\;\;\;b \cdot c - j \cdot \left(k \cdot 27\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 10^{+122}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - k \cdot \left(j \cdot 27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 54.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := k \cdot \left(j \cdot 27\right)\\ t_2 := b \cdot c - t\_1\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+17}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 10^{+122}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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 (* k (* j 27.0))) (t_2 (- (* b c) t_1)))
   (if (<= t_1 -2e+17)
     t_2
     (if (<= t_1 1e+122) (+ (* 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 = k * (j * 27.0);
	double t_2 = (b * c) - t_1;
	double tmp;
	if (t_1 <= -2e+17) {
		tmp = t_2;
	} else if (t_1 <= 1e+122) {
		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 = k * (j * 27.0d0)
    t_2 = (b * c) - t_1
    if (t_1 <= (-2d+17)) then
        tmp = t_2
    else if (t_1 <= 1d+122) 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 = k * (j * 27.0);
	double t_2 = (b * c) - t_1;
	double tmp;
	if (t_1 <= -2e+17) {
		tmp = t_2;
	} else if (t_1 <= 1e+122) {
		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 = k * (j * 27.0)
	t_2 = (b * c) - t_1
	tmp = 0
	if t_1 <= -2e+17:
		tmp = t_2
	elif t_1 <= 1e+122:
		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(k * Float64(j * 27.0))
	t_2 = Float64(Float64(b * c) - t_1)
	tmp = 0.0
	if (t_1 <= -2e+17)
		tmp = t_2;
	elseif (t_1 <= 1e+122)
		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 = k * (j * 27.0);
	t_2 = (b * c) - t_1;
	tmp = 0.0;
	if (t_1 <= -2e+17)
		tmp = t_2;
	elseif (t_1 <= 1e+122)
		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[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] - t$95$1), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+17], t$95$2, If[LessEqual[t$95$1, 1e+122], N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -2e17 or 1.00000000000000001e122 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   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 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 66.8%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

   5. Simplified 66.8%

      \[\leadsto \color{blue}{b \cdot c} - \left(j \cdot 27\right) \cdot k \]

   if -2e17 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 1.00000000000000001e122

   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

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(b \cdot c - 4 \cdot \left(a \cdot t\right)\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   4. Step-by-step derivation

      1. cancel-sign-sub-inv N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(a \cdot t\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + -4 \cdot \left(a \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(b \cdot c\right), \left(-4 \cdot \left(a \cdot t\right)\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(-4 \cdot \left(a \cdot t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(-4, \left(a \cdot t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, \color{blue}{27}\right), k\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(-4, \left(t \cdot a\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      7. *-lowering-*.f64 51.1%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(-4, \mathsf{*.f64}\left(t, a\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

   5. Simplified 51.1%

      \[\leadsto \color{blue}{\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   6. Taylor expanded in j around 0

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t\right) + b \cdot c} \]
   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. *-lowering-*.f64 50.4%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(-4, \mathsf{*.f64}\left(a, \color{blue}{t}\right)\right)\right) \]

   8. Simplified 50.4%

      \[\leadsto \color{blue}{b \cdot c + -4 \cdot \left(a \cdot t\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 56.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \cdot \left(j \cdot 27\right) \leq -2 \cdot 10^{+17}:\\ \;\;\;\;b \cdot c - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 10^{+122}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - k \cdot \left(j \cdot 27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 37.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.35 \cdot 10^{+154}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -3.5 \cdot 10^{-139}:\\ \;\;\;\;18 \cdot \left(x \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 6 \cdot 10^{+124}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= (* b c) -1.35e+154)
   (* b c)
   (if (<= (* b c) -3.5e-139)
     (* 18.0 (* x (* t (* y z))))
     (if (<= (* b c) 6e+124) (* -27.0 (* j k)) (* b c)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b * c) <= -1.35e+154) {
		tmp = b * c;
	} else if ((b * c) <= -3.5e-139) {
		tmp = 18.0 * (x * (t * (y * z)));
	} else if ((b * c) <= 6e+124) {
		tmp = -27.0 * (j * k);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((b * c) <= (-1.35d+154)) then
        tmp = b * c
    else if ((b * c) <= (-3.5d-139)) then
        tmp = 18.0d0 * (x * (t * (y * z)))
    else if ((b * c) <= 6d+124) then
        tmp = (-27.0d0) * (j * k)
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b * c) <= -1.35e+154) {
		tmp = b * c;
	} else if ((b * c) <= -3.5e-139) {
		tmp = 18.0 * (x * (t * (y * z)));
	} else if ((b * c) <= 6e+124) {
		tmp = -27.0 * (j * k);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (b * c) <= -1.35e+154:
		tmp = b * c
	elif (b * c) <= -3.5e-139:
		tmp = 18.0 * (x * (t * (y * z)))
	elif (b * c) <= 6e+124:
		tmp = -27.0 * (j * k)
	else:
		tmp = b * c
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (Float64(b * c) <= -1.35e+154)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -3.5e-139)
		tmp = Float64(18.0 * Float64(x * Float64(t * Float64(y * z))));
	elseif (Float64(b * c) <= 6e+124)
		tmp = Float64(-27.0 * Float64(j * k));
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((b * c) <= -1.35e+154)
		tmp = b * c;
	elseif ((b * c) <= -3.5e-139)
		tmp = 18.0 * (x * (t * (y * z)));
	elseif ((b * c) <= 6e+124)
		tmp = -27.0 * (j * k);
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[N[(b * c), $MachinePrecision], -1.35e+154], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -3.5e-139], N[(18.0 * N[(x * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 6e+124], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -1.35000000000000003e154 or 5.9999999999999999e124 < (*.f64 b c)

   1. Initial program 80.2%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \color{blue}{\left(j \cdot 27\right)} \cdot k \]

      2. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)} \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 82.5%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right) + \left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot c} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 55.9%

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{c}\right) \]

   7. Simplified 55.9%

      \[\leadsto \color{blue}{b \cdot c} \]

   if -1.35000000000000003e154 < (*.f64 b c) < -3.50000000000000001e-139

   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. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \color{blue}{\left(j \cdot 27\right)} \cdot k \]

      2. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)} \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 90.8%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right) + \left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(\color{blue}{j}, k\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

      2. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(x \cdot \left(18 \cdot y\right)\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, k\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \left(18 \cdot y\right)\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, k\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

      4. *-lowering-*.f64 90.7%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(18, y\right)\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, k\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

   6. Applied egg-rr 90.7%

      \[\leadsto t \cdot \left(\color{blue}{\left(x \cdot \left(18 \cdot y\right)\right) \cdot z} + a \cdot -4\right) + \left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right) \]

   7. Taylor expanded in y around inf

      \[\leadsto \color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]
   8. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(18, \color{blue}{\left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(18, \left(\left(x \cdot \left(y \cdot z\right)\right) \cdot \color{blue}{t}\right)\right) \]

      3. associate-*l* N/A

         \[\leadsto \mathsf{*.f64}\left(18, \left(x \cdot \color{blue}{\left(\left(y \cdot z\right) \cdot t\right)}\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(18, \left(x \cdot \left(t \cdot \color{blue}{\left(y \cdot z\right)}\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(x, \color{blue}{\left(t \cdot \left(y \cdot z\right)\right)}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(t, \color{blue}{\left(y \cdot z\right)}\right)\right)\right) \]

      7. *-lowering-*.f64 37.9%

         \[\leadsto \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, \color{blue}{z}\right)\right)\right)\right) \]

   9. Simplified 37.9%

      \[\leadsto \color{blue}{18 \cdot \left(x \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} \]

   if -3.50000000000000001e-139 < (*.f64 b c) < 5.9999999999999999e124

   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. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \color{blue}{\left(j \cdot 27\right)} \cdot k \]

      2. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)} \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 92.4%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right) + \left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in j around inf

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]
   6. 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 31.2%

         \[\leadsto \mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, \color{blue}{k}\right)\right) \]

   7. Simplified 31.2%

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 26: 54.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := k \cdot \left(j \cdot 27\right)\\ \mathbf{if}\;b \cdot c \leq -1.52 \cdot 10^{+156}:\\ \;\;\;\;b \cdot c - t\_1\\ \mathbf{elif}\;b \cdot c \leq 1.55 \cdot 10^{+152}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* k (* j 27.0))))
   (if (<= (* b c) -1.52e+156)
     (- (* b c) t_1)
     (if (<= (* b c) 1.55e+152)
       (- (* -4.0 (* x i)) t_1)
       (+ (* b c) (* -4.0 (* t a)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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 = k * (j * 27.0);
	double tmp;
	if ((b * c) <= -1.52e+156) {
		tmp = (b * c) - t_1;
	} else if ((b * c) <= 1.55e+152) {
		tmp = (-4.0 * (x * i)) - t_1;
	} else {
		tmp = (b * c) + (-4.0 * (t * a));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 = k * (j * 27.0d0)
    if ((b * c) <= (-1.52d+156)) then
        tmp = (b * c) - t_1
    else if ((b * c) <= 1.55d+152) then
        tmp = ((-4.0d0) * (x * i)) - t_1
    else
        tmp = (b * c) + ((-4.0d0) * (t * a))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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 = k * (j * 27.0);
	double tmp;
	if ((b * c) <= -1.52e+156) {
		tmp = (b * c) - t_1;
	} else if ((b * c) <= 1.55e+152) {
		tmp = (-4.0 * (x * i)) - t_1;
	} else {
		tmp = (b * c) + (-4.0 * (t * a));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = k * (j * 27.0)
	tmp = 0
	if (b * c) <= -1.52e+156:
		tmp = (b * c) - t_1
	elif (b * c) <= 1.55e+152:
		tmp = (-4.0 * (x * i)) - t_1
	else:
		tmp = (b * c) + (-4.0 * (t * a))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(k * Float64(j * 27.0))
	tmp = 0.0
	if (Float64(b * c) <= -1.52e+156)
		tmp = Float64(Float64(b * c) - t_1);
	elseif (Float64(b * c) <= 1.55e+152)
		tmp = Float64(Float64(-4.0 * Float64(x * i)) - t_1);
	else
		tmp = Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = k * (j * 27.0);
	tmp = 0.0;
	if ((b * c) <= -1.52e+156)
		tmp = (b * c) - t_1;
	elseif ((b * c) <= 1.55e+152)
		tmp = (-4.0 * (x * i)) - t_1;
	else
		tmp = (b * c) + (-4.0 * (t * a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -1.52e+156], N[(N[(b * c), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1.55e+152], N[(N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -1.52e156

   1. Initial program 80.5%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(b \cdot c\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 80.9%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

   5. Simplified 80.9%

      \[\leadsto \color{blue}{b \cdot c} - \left(j \cdot 27\right) \cdot k \]

   if -1.52e156 < (*.f64 b c) < 1.55e152

   1. Initial program 90.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(-4 \cdot \left(i \cdot x\right)\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(-4, \left(i \cdot x\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

      2. *-lowering-*.f64 51.0%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(-4, \mathsf{*.f64}\left(i, x\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, \color{blue}{27}\right), k\right)\right) \]

   5. Simplified 51.0%

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right)} - \left(j \cdot 27\right) \cdot k \]

   if 1.55e152 < (*.f64 b c)

   1. Initial program 78.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(b \cdot c - 4 \cdot \left(a \cdot t\right)\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   4. Step-by-step derivation

      1. cancel-sign-sub-inv N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(a \cdot t\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + -4 \cdot \left(a \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(b \cdot c\right), \left(-4 \cdot \left(a \cdot t\right)\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(-4 \cdot \left(a \cdot t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(-4, \left(a \cdot t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, \color{blue}{27}\right), k\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(-4, \left(t \cdot a\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      7. *-lowering-*.f64 73.6%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(-4, \mathsf{*.f64}\left(t, a\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

   5. Simplified 73.6%

      \[\leadsto \color{blue}{\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   6. Taylor expanded in j around 0

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t\right) + b \cdot c} \]
   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. *-lowering-*.f64 64.3%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(-4, \mathsf{*.f64}\left(a, \color{blue}{t}\right)\right)\right) \]

   8. Simplified 64.3%

      \[\leadsto \color{blue}{b \cdot c + -4 \cdot \left(a \cdot t\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 57.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.52 \cdot 10^{+156}:\\ \;\;\;\;b \cdot c - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;b \cdot c \leq 1.55 \cdot 10^{+152}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 59.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := x \cdot \left(i \cdot -4 + 18 \cdot \left(z \cdot \left(y \cdot t\right)\right)\right)\\ \mathbf{if}\;x \leq -3.4 \cdot 10^{-37}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{+81}:\\ \;\;\;\;b \cdot c - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* x (+ (* i -4.0) (* 18.0 (* z (* y t)))))))
   (if (<= x -3.4e-37)
     t_1
     (if (<= x 1.15e+81) (- (* b c) (* k (* j 27.0))) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = x * ((i * -4.0) + (18.0 * (z * (y * t))));
	double tmp;
	if (x <= -3.4e-37) {
		tmp = t_1;
	} else if (x <= 1.15e+81) {
		tmp = (b * c) - (k * (j * 27.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((i * (-4.0d0)) + (18.0d0 * (z * (y * t))))
    if (x <= (-3.4d-37)) then
        tmp = t_1
    else if (x <= 1.15d+81) then
        tmp = (b * c) - (k * (j * 27.0d0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = x * ((i * -4.0) + (18.0 * (z * (y * t))));
	double tmp;
	if (x <= -3.4e-37) {
		tmp = t_1;
	} else if (x <= 1.15e+81) {
		tmp = (b * c) - (k * (j * 27.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = x * ((i * -4.0) + (18.0 * (z * (y * t))))
	tmp = 0
	if x <= -3.4e-37:
		tmp = t_1
	elif x <= 1.15e+81:
		tmp = (b * c) - (k * (j * 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(i * -4.0) + Float64(18.0 * Float64(z * Float64(y * t)))))
	tmp = 0.0
	if (x <= -3.4e-37)
		tmp = t_1;
	elseif (x <= 1.15e+81)
		tmp = Float64(Float64(b * c) - Float64(k * Float64(j * 27.0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = x * ((i * -4.0) + (18.0 * (z * (y * t))));
	tmp = 0.0;
	if (x <= -3.4e-37)
		tmp = t_1;
	elseif (x <= 1.15e+81)
		tmp = (b * c) - (k * (j * 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[(i * -4.0), $MachinePrecision] + N[(18.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.4e-37], t$95$1, If[LessEqual[x, 1.15e+81], N[(N[(b * c), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -3.40000000000000018e-37 or 1.1499999999999999e81 < x

   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. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \color{blue}{\left(j \cdot 27\right)} \cdot k \]

      2. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)} \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 78.7%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right) + \left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(-4 \cdot i\right), \color{blue}{\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \left(\color{blue}{18} \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \mathsf{*.f64}\left(18, \color{blue}{\left(t \cdot \left(y \cdot z\right)\right)}\right)\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \mathsf{*.f64}\left(18, \left(\left(t \cdot y\right) \cdot \color{blue}{z}\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(\left(t \cdot y\right), \color{blue}{z}\right)\right)\right)\right) \]

      7. *-lowering-*.f64 69.8%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, y\right), z\right)\right)\right)\right) \]

   7. Simplified 69.8%

      \[\leadsto \color{blue}{x \cdot \left(-4 \cdot i + 18 \cdot \left(\left(t \cdot y\right) \cdot z\right)\right)} \]

   if -3.40000000000000018e-37 < x < 1.1499999999999999e81

   1. Initial program 96.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   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 59.2%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

   5. Simplified 59.2%

      \[\leadsto \color{blue}{b \cdot c} - \left(j \cdot 27\right) \cdot k \]
3. Recombined 2 regimes into one program.

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{-37}:\\ \;\;\;\;x \cdot \left(i \cdot -4 + 18 \cdot \left(z \cdot \left(y \cdot t\right)\right)\right)\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{+81}:\\ \;\;\;\;b \cdot c - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(i \cdot -4 + 18 \cdot \left(z \cdot \left(y \cdot t\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 28: 32.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;k \leq -0.54:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;k \leq 3.2 \cdot 10^{-281}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;k \leq 7.5 \cdot 10^{+114}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(-27 \cdot k\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= k -0.54)
   (* -27.0 (* j k))
   (if (<= k 3.2e-281)
     (* -4.0 (* x i))
     (if (<= k 7.5e+114) (* b c) (* j (* -27.0 k))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (k <= -0.54) {
		tmp = -27.0 * (j * k);
	} else if (k <= 3.2e-281) {
		tmp = -4.0 * (x * i);
	} else if (k <= 7.5e+114) {
		tmp = b * c;
	} else {
		tmp = j * (-27.0 * k);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (k <= (-0.54d0)) then
        tmp = (-27.0d0) * (j * k)
    else if (k <= 3.2d-281) then
        tmp = (-4.0d0) * (x * i)
    else if (k <= 7.5d+114) then
        tmp = b * c
    else
        tmp = j * ((-27.0d0) * k)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (k <= -0.54) {
		tmp = -27.0 * (j * k);
	} else if (k <= 3.2e-281) {
		tmp = -4.0 * (x * i);
	} else if (k <= 7.5e+114) {
		tmp = b * c;
	} else {
		tmp = j * (-27.0 * k);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if k <= -0.54:
		tmp = -27.0 * (j * k)
	elif k <= 3.2e-281:
		tmp = -4.0 * (x * i)
	elif k <= 7.5e+114:
		tmp = b * c
	else:
		tmp = j * (-27.0 * k)
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (k <= -0.54)
		tmp = Float64(-27.0 * Float64(j * k));
	elseif (k <= 3.2e-281)
		tmp = Float64(-4.0 * Float64(x * i));
	elseif (k <= 7.5e+114)
		tmp = Float64(b * c);
	else
		tmp = Float64(j * Float64(-27.0 * k));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (k <= -0.54)
		tmp = -27.0 * (j * k);
	elseif (k <= 3.2e-281)
		tmp = -4.0 * (x * i);
	elseif (k <= 7.5e+114)
		tmp = b * c;
	else
		tmp = j * (-27.0 * k);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[k, -0.54], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 3.2e-281], N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 7.5e+114], N[(b * c), $MachinePrecision], N[(j * N[(-27.0 * k), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if k < -0.54000000000000004

   1. Initial program 80.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \color{blue}{\left(j \cdot 27\right)} \cdot k \]

      2. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)} \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 88.3%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right) + \left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in j around inf

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]
   6. 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 40.8%

         \[\leadsto \mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, \color{blue}{k}\right)\right) \]

   7. Simplified 40.8%

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]

   if -0.54000000000000004 < k < 3.2000000000000001e-281

   1. Initial program 92.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \color{blue}{\left(j \cdot 27\right)} \cdot k \]

      2. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)} \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 92.0%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right) + \left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around inf

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right)} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-4, \color{blue}{\left(i \cdot x\right)}\right) \]

      2. *-lowering-*.f64 36.2%

         \[\leadsto \mathsf{*.f64}\left(-4, \mathsf{*.f64}\left(i, \color{blue}{x}\right)\right) \]

   7. Simplified 36.2%

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right)} \]

   if 3.2000000000000001e-281 < k < 7.5000000000000001e114

   1. Initial program 88.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \color{blue}{\left(j \cdot 27\right)} \cdot k \]

      2. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)} \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 89.6%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right) + \left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot c} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 28.6%

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{c}\right) \]

   7. Simplified 28.6%

      \[\leadsto \color{blue}{b \cdot c} \]

   if 7.5000000000000001e114 < k

   1. Initial program 82.2%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \color{blue}{\left(j \cdot 27\right)} \cdot k \]

      2. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)} \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 82.2%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right) + \left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in j around inf

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]
   6. 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 58.0%

         \[\leadsto \mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, \color{blue}{k}\right)\right) \]

   7. Simplified 58.0%

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]
   8. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto -27 \cdot \left(k \cdot \color{blue}{j}\right) \]

      2. associate-*r* N/A

         \[\leadsto \left(-27 \cdot k\right) \cdot \color{blue}{j} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-27 \cdot k\right), \color{blue}{j}\right) \]

      4. *-lowering-*.f64 58.0%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-27, k\right), j\right) \]

   9. Applied egg-rr 58.0%

      \[\leadsto \color{blue}{\left(-27 \cdot k\right) \cdot j} \]
3. Recombined 4 regimes into one program.

4. Final simplification 38.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -0.54:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;k \leq 3.2 \cdot 10^{-281}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;k \leq 7.5 \cdot 10^{+114}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(-27 \cdot k\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 29: 32.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := -27 \cdot \left(j \cdot k\right)\\ \mathbf{if}\;k \leq -0.5:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;k \leq 9.2 \cdot 10^{-282}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;k \leq 6.2 \cdot 10^{+115}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (<= k -0.5)
     t_1
     (if (<= k 9.2e-282) (* -4.0 (* x i)) (if (<= k 6.2e+115) (* 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 (k <= -0.5) {
		tmp = t_1;
	} else if (k <= 9.2e-282) {
		tmp = -4.0 * (x * i);
	} else if (k <= 6.2e+115) {
		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 (k <= (-0.5d0)) then
        tmp = t_1
    else if (k <= 9.2d-282) then
        tmp = (-4.0d0) * (x * i)
    else if (k <= 6.2d+115) 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 (k <= -0.5) {
		tmp = t_1;
	} else if (k <= 9.2e-282) {
		tmp = -4.0 * (x * i);
	} else if (k <= 6.2e+115) {
		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 k <= -0.5:
		tmp = t_1
	elif k <= 9.2e-282:
		tmp = -4.0 * (x * i)
	elif k <= 6.2e+115:
		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 (k <= -0.5)
		tmp = t_1;
	elseif (k <= 9.2e-282)
		tmp = Float64(-4.0 * Float64(x * i));
	elseif (k <= 6.2e+115)
		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 (k <= -0.5)
		tmp = t_1;
	elseif (k <= 9.2e-282)
		tmp = -4.0 * (x * i);
	elseif (k <= 6.2e+115)
		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[k, -0.5], t$95$1, If[LessEqual[k, 9.2e-282], N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 6.2e+115], N[(b * c), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if k < -0.5 or 6.2000000000000001e115 < k

   1. Initial program 81.2%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \color{blue}{\left(j \cdot 27\right)} \cdot k \]

      2. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)} \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 85.4%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right) + \left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in j around inf

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]
   6. 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 48.8%

         \[\leadsto \mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, \color{blue}{k}\right)\right) \]

   7. Simplified 48.8%

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]

   if -0.5 < k < 9.1999999999999996e-282

   1. Initial program 92.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \color{blue}{\left(j \cdot 27\right)} \cdot k \]

      2. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)} \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 92.0%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right) + \left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around inf

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right)} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-4, \color{blue}{\left(i \cdot x\right)}\right) \]

      2. *-lowering-*.f64 36.2%

         \[\leadsto \mathsf{*.f64}\left(-4, \mathsf{*.f64}\left(i, \color{blue}{x}\right)\right) \]

   7. Simplified 36.2%

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right)} \]

   if 9.1999999999999996e-282 < k < 6.2000000000000001e115

   1. Initial program 88.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \color{blue}{\left(j \cdot 27\right)} \cdot k \]

      2. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)} \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 89.6%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right) + \left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot c} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 28.6%

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{c}\right) \]

   7. Simplified 28.6%

      \[\leadsto \color{blue}{b \cdot c} \]
3. Recombined 3 regimes into one program.

4. Final simplification 38.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -0.5:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;k \leq 9.2 \cdot 10^{-282}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;k \leq 6.2 \cdot 10^{+115}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 30: 45.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := -27 \cdot \left(j \cdot k\right)\\ \mathbf{if}\;j \leq -6.2 \cdot 10^{+126}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 6 \cdot 10^{+110}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 -6.2e+126)
     t_1
     (if (<= j 6e+110) (+ (* b c) (* -4.0 (* t a))) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -27.0 * (j * k);
	double tmp;
	if (j <= -6.2e+126) {
		tmp = t_1;
	} else if (j <= 6e+110) {
		tmp = (b * c) + (-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 <= (-6.2d+126)) then
        tmp = t_1
    else if (j <= 6d+110) then
        tmp = (b * c) + ((-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 <= -6.2e+126) {
		tmp = t_1;
	} else if (j <= 6e+110) {
		tmp = (b * c) + (-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 <= -6.2e+126:
		tmp = t_1
	elif j <= 6e+110:
		tmp = (b * c) + (-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 <= -6.2e+126)
		tmp = t_1;
	elseif (j <= 6e+110)
		tmp = Float64(Float64(b * c) + 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 <= -6.2e+126)
		tmp = t_1;
	elseif (j <= 6e+110)
		tmp = (b * c) + (-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, -6.2e+126], t$95$1, If[LessEqual[j, 6e+110], N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if j < -6.2e126 or 6.00000000000000014e110 < j

   1. Initial program 84.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \color{blue}{\left(j \cdot 27\right)} \cdot k \]

      2. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)} \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 85.7%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right) + \left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in j around inf

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-27, \color{blue}{\left(j \cdot k\right)}\right) \]

      2. *-lowering-*.f64 53.9%

         \[\leadsto \mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, \color{blue}{k}\right)\right) \]

   7. Simplified 53.9%

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]

   if -6.2e126 < j < 6.00000000000000014e110

   1. Initial program 87.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(b \cdot c - 4 \cdot \left(a \cdot t\right)\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   4. Step-by-step derivation

      1. cancel-sign-sub-inv N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(a \cdot t\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + -4 \cdot \left(a \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(b \cdot c\right), \left(-4 \cdot \left(a \cdot t\right)\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(-4 \cdot \left(a \cdot t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(-4, \left(a \cdot t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, \color{blue}{27}\right), k\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(-4, \left(t \cdot a\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      7. *-lowering-*.f64 54.4%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(-4, \mathsf{*.f64}\left(t, a\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

   5. Simplified 54.4%

      \[\leadsto \color{blue}{\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   6. Taylor expanded in j around 0

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t\right) + b \cdot c} \]
   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. *-lowering-*.f64 46.4%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(-4, \mathsf{*.f64}\left(a, \color{blue}{t}\right)\right)\right) \]

   8. Simplified 46.4%

      \[\leadsto \color{blue}{b \cdot c + -4 \cdot \left(a \cdot t\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 48.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -6.2 \cdot 10^{+126}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;j \leq 6 \cdot 10^{+110}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 31: 32.3% accurate, 2.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := -27 \cdot \left(j \cdot k\right)\\ \mathbf{if}\;j \leq -6.5 \cdot 10^{+126}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 8.2 \cdot 10^{-43}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 -6.5e+126) t_1 (if (<= j 8.2e-43) (* 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 <= -6.5e+126) {
		tmp = t_1;
	} else if (j <= 8.2e-43) {
		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 <= (-6.5d+126)) then
        tmp = t_1
    else if (j <= 8.2d-43) 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 <= -6.5e+126) {
		tmp = t_1;
	} else if (j <= 8.2e-43) {
		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 <= -6.5e+126:
		tmp = t_1
	elif j <= 8.2e-43:
		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 <= -6.5e+126)
		tmp = t_1;
	elseif (j <= 8.2e-43)
		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 <= -6.5e+126)
		tmp = t_1;
	elseif (j <= 8.2e-43)
		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, -6.5e+126], t$95$1, If[LessEqual[j, 8.2e-43], N[(b * c), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if j < -6.5000000000000005e126 or 8.1999999999999996e-43 < j

   1. Initial program 88.1%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \color{blue}{\left(j \cdot 27\right)} \cdot k \]

      2. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)} \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 89.0%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right) + \left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in j around inf

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]
   6. 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 42.8%

         \[\leadsto \mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, \color{blue}{k}\right)\right) \]

   7. Simplified 42.8%

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]

   if -6.5000000000000005e126 < j < 8.1999999999999996e-43

   1. Initial program 85.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \color{blue}{\left(j \cdot 27\right)} \cdot k \]

      2. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)} \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 88.5%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right) + \left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot c} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 30.1%

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{c}\right) \]

   7. Simplified 30.1%

      \[\leadsto \color{blue}{b \cdot c} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 32: 24.1% 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 86.8%

   \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
2. Step-by-step derivation

   1. associate--l+ N/A

      \[\leadsto \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \color{blue}{\left(j \cdot 27\right)} \cdot k \]

   2. associate--l+ N/A

      \[\leadsto \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)} \]

   3. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

   4. distribute-rgt-out-- N/A

      \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

   5. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

   6. sub-neg N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   7. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   8. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   9. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   10. *-lowering-*.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   11. distribute-rgt-neg-in N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   12. *-lowering-*.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   13. metadata-eval N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

3. Simplified 88.7%

   \[\leadsto \color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right) + \left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right)} \]
4. Add Preprocessing

5. Taylor expanded in b around inf

   \[\leadsto \color{blue}{b \cdot c} \]
6. Step-by-step derivation

   1. *-lowering-*.f64 24.0%

      \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{c}\right) \]

7. Simplified 24.0%

   \[\leadsto \color{blue}{b \cdot c} \]
8. Add Preprocessing

Developer Target 1: 89.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a \cdot t + i \cdot x\right) \cdot 4\\ t_2 := \left(\left(18 \cdot t\right) \cdot \left(\left(x \cdot y\right) \cdot z\right) - t\_1\right) - \left(\left(k \cdot j\right) \cdot 27 - c \cdot b\right)\\ \mathbf{if}\;t < -1.6210815397541398 \cdot 10^{-69}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t < 165.68027943805222:\\ \;\;\;\;\left(\left(18 \cdot y\right) \cdot \left(x \cdot \left(z \cdot t\right)\right) - t\_1\right) + \left(c \cdot b - 27 \cdot \left(k \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (+ (* a t) (* i x)) 4.0))
        (t_2
         (-
          (- (* (* 18.0 t) (* (* x y) z)) t_1)
          (- (* (* k j) 27.0) (* c b)))))
   (if (< t -1.6210815397541398e-69)
     t_2
     (if (< t 165.68027943805222)
       (+ (- (* (* 18.0 y) (* x (* z t))) t_1) (- (* c b) (* 27.0 (* k j))))
       t_2))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((a * t) + (i * x)) * 4.0;
	double t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b));
	double tmp;
	if (t < -1.6210815397541398e-69) {
		tmp = t_2;
	} else if (t < 165.68027943805222) {
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((a * t) + (i * x)) * 4.0d0
    t_2 = (((18.0d0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0d0) - (c * b))
    if (t < (-1.6210815397541398d-69)) then
        tmp = t_2
    else if (t < 165.68027943805222d0) then
        tmp = (((18.0d0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0d0 * (k * j)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((a * t) + (i * x)) * 4.0;
	double t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b));
	double tmp;
	if (t < -1.6210815397541398e-69) {
		tmp = t_2;
	} else if (t < 165.68027943805222) {
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = ((a * t) + (i * x)) * 4.0
	t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b))
	tmp = 0
	if t < -1.6210815397541398e-69:
		tmp = t_2
	elif t < 165.68027943805222:
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(Float64(a * t) + Float64(i * x)) * 4.0)
	t_2 = Float64(Float64(Float64(Float64(18.0 * t) * Float64(Float64(x * y) * z)) - t_1) - Float64(Float64(Float64(k * j) * 27.0) - Float64(c * b)))
	tmp = 0.0
	if (t < -1.6210815397541398e-69)
		tmp = t_2;
	elseif (t < 165.68027943805222)
		tmp = Float64(Float64(Float64(Float64(18.0 * y) * Float64(x * Float64(z * t))) - t_1) + Float64(Float64(c * b) - Float64(27.0 * Float64(k * j))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = ((a * t) + (i * x)) * 4.0;
	t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b));
	tmp = 0.0;
	if (t < -1.6210815397541398e-69)
		tmp = t_2;
	elseif (t < 165.68027943805222)
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(N[(a * t), $MachinePrecision] + N[(i * x), $MachinePrecision]), $MachinePrecision] * 4.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(18.0 * t), $MachinePrecision] * N[(N[(x * y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] - N[(N[(N[(k * j), $MachinePrecision] * 27.0), $MachinePrecision] - N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -1.6210815397541398e-69], t$95$2, If[Less[t, 165.68027943805222], N[(N[(N[(N[(18.0 * y), $MachinePrecision] * N[(x * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] + N[(N[(c * b), $MachinePrecision] - N[(27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2024145 
(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)))