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

Percentage Accurate: 85.4% → 92.3%

Time: 34.5s

Alternatives: 25

Speedup: 0.8×

• 49.1% 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: 92.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -920 \lor \neg \left(t \leq 1.02 \cdot 10^{-83}\right):\\ \;\;\;\;\mathsf{fma}\left(t, \mathsf{fma}\left(-4, a, 18 \cdot \left(z \cdot \left(x \cdot y\right)\right)\right), \mathsf{fma}\left(-27, j \cdot k, \mathsf{fma}\left(-4, x \cdot i, b \cdot c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + \mathsf{fma}\left(y, \left(t \cdot z\right) \cdot \left(18 \cdot x\right), t \cdot \left(a \cdot \left(-4\right)\right)\right)\right) - \left(x \cdot \left(i \cdot 4\right) + j \cdot \left(k \cdot 27\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= t -920.0) (not (<= t 1.02e-83)))
   (fma
    t
    (fma -4.0 a (* 18.0 (* z (* x y))))
    (fma -27.0 (* j k) (fma -4.0 (* x i) (* b c))))
   (-
    (+ (* b c) (fma y (* (* t z) (* 18.0 x)) (* t (* a (- 4.0)))))
    (+ (* x (* i 4.0)) (* j (* k 27.0))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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 <= -920.0) || !(t <= 1.02e-83)) {
		tmp = fma(t, fma(-4.0, a, (18.0 * (z * (x * y)))), fma(-27.0, (j * k), fma(-4.0, (x * i), (b * c))));
	} else {
		tmp = ((b * c) + fma(y, ((t * z) * (18.0 * x)), (t * (a * -4.0)))) - ((x * (i * 4.0)) + (j * (k * 27.0)));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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 <= -920.0) || !(t <= 1.02e-83))
		tmp = fma(t, fma(-4.0, a, Float64(18.0 * Float64(z * Float64(x * y)))), fma(-27.0, Float64(j * k), fma(-4.0, Float64(x * i), Float64(b * c))));
	else
		tmp = Float64(Float64(Float64(b * c) + fma(y, Float64(Float64(t * z) * Float64(18.0 * x)), Float64(t * Float64(a * Float64(-4.0))))) - Float64(Float64(x * Float64(i * 4.0)) + Float64(j * Float64(k * 27.0))));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[t, -920.0], N[Not[LessEqual[t, 1.02e-83]], $MachinePrecision]], N[(t * N[(-4.0 * a + N[(18.0 * N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-27.0 * N[(j * k), $MachinePrecision] + N[(-4.0 * N[(x * i), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] + N[(y * N[(N[(t * z), $MachinePrecision] * N[(18.0 * x), $MachinePrecision]), $MachinePrecision] + N[(t * N[(a * (-4.0)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * N[(i * 4.0), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -920 or 1.0199999999999999e-83 < t

   1. Initial program 83.3%

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

   3. Simplified 89.8%

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

   5. Taylor expanded in t around 0 86.3%

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

   7. Simplified 92.9%

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

   if -920 < t < 1.0199999999999999e-83

   1. Initial program 82.8%

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

   3. Simplified 81.0%

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

      1. associate-*r* 82.7%

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

      2. distribute-rgt-out-- 82.7%

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

      3. associate-*l* 90.2%

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

      4. *-commutative 90.2%

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

      5. *-commutative 90.2%

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

   6. Applied egg-rr 90.2%

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

      1. cancel-sign-sub-inv 90.2%

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

      2. associate-*l* 94.6%

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

      3. fma-def 94.6%

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

      4. *-commutative 94.6%

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

      5. *-commutative 94.6%

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

   8. Applied egg-rr 94.6%

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

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -920 \lor \neg \left(t \leq 1.02 \cdot 10^{-83}\right):\\ \;\;\;\;\mathsf{fma}\left(t, \mathsf{fma}\left(-4, a, 18 \cdot \left(z \cdot \left(x \cdot y\right)\right)\right), \mathsf{fma}\left(-27, j \cdot k, \mathsf{fma}\left(-4, x \cdot i, b \cdot c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + \mathsf{fma}\left(y, \left(t \cdot z\right) \cdot \left(18 \cdot x\right), t \cdot \left(a \cdot \left(-4\right)\right)\right)\right) - \left(x \cdot \left(i \cdot 4\right) + j \cdot \left(k \cdot 27\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 92.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.55 \cdot 10^{+17} \lor \neg \left(t \leq 4.2 \cdot 10^{-83}\right):\\ \;\;\;\;\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(z \cdot y\right), -4 \cdot a\right), \mathsf{fma}\left(b, c, x \cdot \left(-4 \cdot i\right)\right)\right) + j \cdot \left(-27 \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + \mathsf{fma}\left(y, \left(t \cdot z\right) \cdot \left(18 \cdot x\right), t \cdot \left(a \cdot \left(-4\right)\right)\right)\right) - \left(x \cdot \left(i \cdot 4\right) + j \cdot \left(k \cdot 27\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= t -1.55e+17) (not (<= t 4.2e-83)))
   (+
    (fma t (fma x (* 18.0 (* z y)) (* -4.0 a)) (fma b c (* x (* -4.0 i))))
    (* j (* -27.0 k)))
   (-
    (+ (* b c) (fma y (* (* t z) (* 18.0 x)) (* t (* a (- 4.0)))))
    (+ (* x (* i 4.0)) (* j (* k 27.0))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((t <= -1.55e+17) || !(t <= 4.2e-83)) {
		tmp = fma(t, fma(x, (18.0 * (z * y)), (-4.0 * a)), fma(b, c, (x * (-4.0 * i)))) + (j * (-27.0 * k));
	} else {
		tmp = ((b * c) + fma(y, ((t * z) * (18.0 * x)), (t * (a * -4.0)))) - ((x * (i * 4.0)) + (j * (k * 27.0)));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((t <= -1.55e+17) || !(t <= 4.2e-83))
		tmp = Float64(fma(t, fma(x, Float64(18.0 * Float64(z * y)), Float64(-4.0 * a)), fma(b, c, Float64(x * Float64(-4.0 * i)))) + Float64(j * Float64(-27.0 * k)));
	else
		tmp = Float64(Float64(Float64(b * c) + fma(y, Float64(Float64(t * z) * Float64(18.0 * x)), Float64(t * Float64(a * Float64(-4.0))))) - Float64(Float64(x * Float64(i * 4.0)) + Float64(j * Float64(k * 27.0))));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[t, -1.55e+17], N[Not[LessEqual[t, 4.2e-83]], $MachinePrecision]], N[(N[(t * N[(x * N[(18.0 * N[(z * y), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] + N[(b * c + N[(x * N[(-4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(-27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] + N[(y * N[(N[(t * z), $MachinePrecision] * N[(18.0 * x), $MachinePrecision]), $MachinePrecision] + N[(t * N[(a * (-4.0)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * N[(i * 4.0), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.55e17 or 4.1999999999999998e-83 < t

   1. Initial program 82.9%

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

   3. Simplified 90.2%

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

   if -1.55e17 < t < 4.1999999999999998e-83

   1. Initial program 83.2%

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

   3. Simplified 80.8%

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

      1. associate-*r* 83.2%

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

      2. distribute-rgt-out-- 83.2%

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

      3. associate-*l* 89.8%

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

      4. *-commutative 89.8%

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

      5. *-commutative 89.8%

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

   6. Applied egg-rr 89.8%

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

      1. cancel-sign-sub-inv 89.8%

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

      2. associate-*l* 94.1%

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

      3. fma-def 94.1%

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

      4. *-commutative 94.1%

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

      5. *-commutative 94.1%

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

   8. Applied egg-rr 94.1%

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

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.55 \cdot 10^{+17} \lor \neg \left(t \leq 4.2 \cdot 10^{-83}\right):\\ \;\;\;\;\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(z \cdot y\right), -4 \cdot a\right), \mathsf{fma}\left(b, c, x \cdot \left(-4 \cdot i\right)\right)\right) + j \cdot \left(-27 \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + \mathsf{fma}\left(y, \left(t \cdot z\right) \cdot \left(18 \cdot x\right), t \cdot \left(a \cdot \left(-4\right)\right)\right)\right) - \left(x \cdot \left(i \cdot 4\right) + j \cdot \left(k \cdot 27\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 92.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(\left(b \cdot c + \left(t \cdot \left(z \cdot \left(y \cdot \left(18 \cdot x\right)\right)\right) - t \cdot \left(a \cdot 4\right)\right)\right) - i \cdot \left(x \cdot 4\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{if}\;t\_1 \leq 4 \cdot 10^{+299}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;\left(b \cdot c + \mathsf{fma}\left(y, \left(t \cdot z\right) \cdot \left(18 \cdot x\right), t \cdot \left(a \cdot \left(-4\right)\right)\right)\right) - \left(x \cdot \left(i \cdot 4\right) + j \cdot \left(k \cdot 27\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(z \cdot y\right)\right) - i \cdot 4\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 (* z (* y (* 18.0 x)))) (* t (* a 4.0))))
           (* i (* x 4.0)))
          (* k (* j 27.0)))))
   (if (<= t_1 4e+299)
     t_1
     (if (<= t_1 INFINITY)
       (-
        (+ (* b c) (fma y (* (* t z) (* 18.0 x)) (* t (* a (- 4.0)))))
        (+ (* x (* i 4.0)) (* j (* k 27.0))))
       (* x (- (* 18.0 (* t (* z y))) (* i 4.0)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (((b * c) + ((t * (z * (y * (18.0 * x)))) - (t * (a * 4.0)))) - (i * (x * 4.0))) - (k * (j * 27.0));
	double tmp;
	if (t_1 <= 4e+299) {
		tmp = t_1;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = ((b * c) + fma(y, ((t * z) * (18.0 * x)), (t * (a * -4.0)))) - ((x * (i * 4.0)) + (j * (k * 27.0)));
	} else {
		tmp = x * ((18.0 * (t * (z * y))) - (i * 4.0));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(Float64(Float64(b * c) + Float64(Float64(t * Float64(z * Float64(y * Float64(18.0 * x)))) - Float64(t * Float64(a * 4.0)))) - Float64(i * Float64(x * 4.0))) - Float64(k * Float64(j * 27.0)))
	tmp = 0.0
	if (t_1 <= 4e+299)
		tmp = t_1;
	elseif (t_1 <= Inf)
		tmp = Float64(Float64(Float64(b * c) + fma(y, Float64(Float64(t * z) * Float64(18.0 * x)), Float64(t * Float64(a * Float64(-4.0))))) - Float64(Float64(x * Float64(i * 4.0)) + Float64(j * Float64(k * 27.0))));
	else
		tmp = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(z * y))) - Float64(i * 4.0)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(N[(N[(b * c), $MachinePrecision] + N[(N[(t * N[(z * N[(y * N[(18.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * N[(x * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 4e+299], t$95$1, If[LessEqual[t$95$1, Infinity], N[(N[(N[(b * c), $MachinePrecision] + N[(y * N[(N[(t * z), $MachinePrecision] * N[(18.0 * x), $MachinePrecision]), $MachinePrecision] + N[(t * N[(a * (-4.0)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * N[(i * 4.0), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(18.0 * N[(t * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t) (*.f64 (*.f64 a 4) t)) (*.f64 b c)) (*.f64 (*.f64 x 4) i)) (*.f64 (*.f64 j 27) k)) < 4.0000000000000002e299

   1. Initial program 97.4%

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

   if 4.0000000000000002e299 < (-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t) (*.f64 (*.f64 a 4) t)) (*.f64 b c)) (*.f64 (*.f64 x 4) i)) (*.f64 (*.f64 j 27) k)) < +inf.0

   1. Initial program 81.0%

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

   3. Simplified 87.9%

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

      1. associate-*r* 82.3%

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

      2. distribute-rgt-out-- 82.3%

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

      3. associate-*l* 88.7%

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

      4. *-commutative 88.7%

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

      5. *-commutative 88.7%

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

   6. Applied egg-rr 88.7%

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

      1. cancel-sign-sub-inv 88.7%

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

      2. associate-*l* 95.9%

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

      3. fma-def 95.9%

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

      4. *-commutative 95.9%

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

      5. *-commutative 95.9%

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

   8. Applied egg-rr 95.9%

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

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

   1. Initial program 0.0%

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

   3. Simplified 30.8%

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

   5. Taylor expanded in x around inf 62.1%

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

4. Final simplification 93.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(b \cdot c + \left(t \cdot \left(z \cdot \left(y \cdot \left(18 \cdot x\right)\right)\right) - t \cdot \left(a \cdot 4\right)\right)\right) - i \cdot \left(x \cdot 4\right)\right) - k \cdot \left(j \cdot 27\right) \leq 4 \cdot 10^{+299}:\\ \;\;\;\;\left(\left(b \cdot c + \left(t \cdot \left(z \cdot \left(y \cdot \left(18 \cdot x\right)\right)\right) - t \cdot \left(a \cdot 4\right)\right)\right) - i \cdot \left(x \cdot 4\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;\left(\left(b \cdot c + \left(t \cdot \left(z \cdot \left(y \cdot \left(18 \cdot x\right)\right)\right) - t \cdot \left(a \cdot 4\right)\right)\right) - i \cdot \left(x \cdot 4\right)\right) - k \cdot \left(j \cdot 27\right) \leq \infty:\\ \;\;\;\;\left(b \cdot c + \mathsf{fma}\left(y, \left(t \cdot z\right) \cdot \left(18 \cdot x\right), t \cdot \left(a \cdot \left(-4\right)\right)\right)\right) - \left(x \cdot \left(i \cdot 4\right) + j \cdot \left(k \cdot 27\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(z \cdot y\right)\right) - i \cdot 4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 92.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := k \cdot \left(j \cdot 27\right)\\ t_2 := \left(\left(b \cdot c + \left(t \cdot \left(z \cdot \left(y \cdot \left(18 \cdot x\right)\right)\right) - t \cdot \left(a \cdot 4\right)\right)\right) - i \cdot \left(x \cdot 4\right)\right) - t\_1\\ t_3 := x \cdot \left(18 \cdot \left(t \cdot \left(z \cdot y\right)\right) - i \cdot 4\right)\\ \mathbf{if}\;t\_2 \leq 4 \cdot 10^{+299}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;\left(\left(b \cdot c + t\_3\right) - 4 \cdot \left(t \cdot a\right)\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* k (* j 27.0)))
        (t_2
         (-
          (-
           (+ (* b c) (- (* t (* z (* y (* 18.0 x)))) (* t (* a 4.0))))
           (* i (* x 4.0)))
          t_1))
        (t_3 (* x (- (* 18.0 (* t (* z y))) (* i 4.0)))))
   (if (<= t_2 4e+299)
     t_2
     (if (<= t_2 INFINITY) (- (- (+ (* b c) t_3) (* 4.0 (* t a))) t_1) t_3))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = k * (j * 27.0);
	double t_2 = (((b * c) + ((t * (z * (y * (18.0 * x)))) - (t * (a * 4.0)))) - (i * (x * 4.0))) - t_1;
	double t_3 = x * ((18.0 * (t * (z * y))) - (i * 4.0));
	double tmp;
	if (t_2 <= 4e+299) {
		tmp = t_2;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = (((b * c) + t_3) - (4.0 * (t * a))) - t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = k * (j * 27.0);
	double t_2 = (((b * c) + ((t * (z * (y * (18.0 * x)))) - (t * (a * 4.0)))) - (i * (x * 4.0))) - t_1;
	double t_3 = x * ((18.0 * (t * (z * y))) - (i * 4.0));
	double tmp;
	if (t_2 <= 4e+299) {
		tmp = t_2;
	} else if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = (((b * c) + t_3) - (4.0 * (t * a))) - t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = k * (j * 27.0)
	t_2 = (((b * c) + ((t * (z * (y * (18.0 * x)))) - (t * (a * 4.0)))) - (i * (x * 4.0))) - t_1
	t_3 = x * ((18.0 * (t * (z * y))) - (i * 4.0))
	tmp = 0
	if t_2 <= 4e+299:
		tmp = t_2
	elif t_2 <= math.inf:
		tmp = (((b * c) + t_3) - (4.0 * (t * a))) - t_1
	else:
		tmp = t_3
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(k * Float64(j * 27.0))
	t_2 = Float64(Float64(Float64(Float64(b * c) + Float64(Float64(t * Float64(z * Float64(y * Float64(18.0 * x)))) - Float64(t * Float64(a * 4.0)))) - Float64(i * Float64(x * 4.0))) - t_1)
	t_3 = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(z * y))) - Float64(i * 4.0)))
	tmp = 0.0
	if (t_2 <= 4e+299)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = Float64(Float64(Float64(Float64(b * c) + t_3) - Float64(4.0 * Float64(t * a))) - t_1);
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = k * (j * 27.0);
	t_2 = (((b * c) + ((t * (z * (y * (18.0 * x)))) - (t * (a * 4.0)))) - (i * (x * 4.0))) - t_1;
	t_3 = x * ((18.0 * (t * (z * y))) - (i * 4.0));
	tmp = 0.0;
	if (t_2 <= 4e+299)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = (((b * c) + t_3) - (4.0 * (t * a))) - t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(b * c), $MachinePrecision] + N[(N[(t * N[(z * N[(y * N[(18.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * N[(x * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(N[(18.0 * N[(t * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, 4e+299], t$95$2, If[LessEqual[t$95$2, Infinity], N[(N[(N[(N[(b * c), $MachinePrecision] + t$95$3), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], t$95$3]]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t) (*.f64 (*.f64 a 4) t)) (*.f64 b c)) (*.f64 (*.f64 x 4) i)) (*.f64 (*.f64 j 27) k)) < 4.0000000000000002e299

   1. Initial program 97.4%

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

   if 4.0000000000000002e299 < (-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t) (*.f64 (*.f64 a 4) t)) (*.f64 b c)) (*.f64 (*.f64 x 4) i)) (*.f64 (*.f64 j 27) k)) < +inf.0

   1. Initial program 81.0%

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

   3. Taylor expanded in x around 0 93.3%

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

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

   1. Initial program 0.0%

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

   3. Simplified 30.8%

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

   5. Taylor expanded in x around inf 62.1%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(b \cdot c + \left(t \cdot \left(z \cdot \left(y \cdot \left(18 \cdot x\right)\right)\right) - t \cdot \left(a \cdot 4\right)\right)\right) - i \cdot \left(x \cdot 4\right)\right) - k \cdot \left(j \cdot 27\right) \leq 4 \cdot 10^{+299}:\\ \;\;\;\;\left(\left(b \cdot c + \left(t \cdot \left(z \cdot \left(y \cdot \left(18 \cdot x\right)\right)\right) - t \cdot \left(a \cdot 4\right)\right)\right) - i \cdot \left(x \cdot 4\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;\left(\left(b \cdot c + \left(t \cdot \left(z \cdot \left(y \cdot \left(18 \cdot x\right)\right)\right) - t \cdot \left(a \cdot 4\right)\right)\right) - i \cdot \left(x \cdot 4\right)\right) - k \cdot \left(j \cdot 27\right) \leq \infty:\\ \;\;\;\;\left(\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(z \cdot y\right)\right) - i \cdot 4\right)\right) - 4 \cdot \left(t \cdot a\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(z \cdot y\right)\right) - i \cdot 4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 36.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := a \cdot \left(t \cdot -4\right)\\ t_2 := k \cdot \left(-27 \cdot j\right)\\ \mathbf{if}\;b \cdot c \leq -1.05 \cdot 10^{+124}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -1.75 \cdot 10^{-45}:\\ \;\;\;\;i \cdot \left(-4 \cdot x\right)\\ \mathbf{elif}\;b \cdot c \leq -1.4 \cdot 10^{-199}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq -7.2 \cdot 10^{-239}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(z \cdot y\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq -9.2 \cdot 10^{-255}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \cdot c \leq 1.75 \cdot 10^{-249}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq 1.1 \cdot 10^{-130}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \cdot c \leq 3.8 \cdot 10^{-74}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq 7.4 \cdot 10^{+83}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 (* a (* t -4.0))) (t_2 (* k (* -27.0 j))))
   (if (<= (* b c) -1.05e+124)
     (* b c)
     (if (<= (* b c) -1.75e-45)
       (* i (* -4.0 x))
       (if (<= (* b c) -1.4e-199)
         (* -27.0 (* j k))
         (if (<= (* b c) -7.2e-239)
           (* 18.0 (* t (* x (* z y))))
           (if (<= (* b c) -9.2e-255)
             t_2
             (if (<= (* b c) 1.75e-249)
               t_1
               (if (<= (* b c) 1.1e-130)
                 t_2
                 (if (<= (* b c) 3.8e-74)
                   t_1
                   (if (<= (* b c) 7.4e+83) t_2 (* b c))))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = a * (t * -4.0);
	double t_2 = k * (-27.0 * j);
	double tmp;
	if ((b * c) <= -1.05e+124) {
		tmp = b * c;
	} else if ((b * c) <= -1.75e-45) {
		tmp = i * (-4.0 * x);
	} else if ((b * c) <= -1.4e-199) {
		tmp = -27.0 * (j * k);
	} else if ((b * c) <= -7.2e-239) {
		tmp = 18.0 * (t * (x * (z * y)));
	} else if ((b * c) <= -9.2e-255) {
		tmp = t_2;
	} else if ((b * c) <= 1.75e-249) {
		tmp = t_1;
	} else if ((b * c) <= 1.1e-130) {
		tmp = t_2;
	} else if ((b * c) <= 3.8e-74) {
		tmp = t_1;
	} else if ((b * c) <= 7.4e+83) {
		tmp = t_2;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 = a * (t * (-4.0d0))
    t_2 = k * ((-27.0d0) * j)
    if ((b * c) <= (-1.05d+124)) then
        tmp = b * c
    else if ((b * c) <= (-1.75d-45)) then
        tmp = i * ((-4.0d0) * x)
    else if ((b * c) <= (-1.4d-199)) then
        tmp = (-27.0d0) * (j * k)
    else if ((b * c) <= (-7.2d-239)) then
        tmp = 18.0d0 * (t * (x * (z * y)))
    else if ((b * c) <= (-9.2d-255)) then
        tmp = t_2
    else if ((b * c) <= 1.75d-249) then
        tmp = t_1
    else if ((b * c) <= 1.1d-130) then
        tmp = t_2
    else if ((b * c) <= 3.8d-74) then
        tmp = t_1
    else if ((b * c) <= 7.4d+83) then
        tmp = t_2
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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 = a * (t * -4.0);
	double t_2 = k * (-27.0 * j);
	double tmp;
	if ((b * c) <= -1.05e+124) {
		tmp = b * c;
	} else if ((b * c) <= -1.75e-45) {
		tmp = i * (-4.0 * x);
	} else if ((b * c) <= -1.4e-199) {
		tmp = -27.0 * (j * k);
	} else if ((b * c) <= -7.2e-239) {
		tmp = 18.0 * (t * (x * (z * y)));
	} else if ((b * c) <= -9.2e-255) {
		tmp = t_2;
	} else if ((b * c) <= 1.75e-249) {
		tmp = t_1;
	} else if ((b * c) <= 1.1e-130) {
		tmp = t_2;
	} else if ((b * c) <= 3.8e-74) {
		tmp = t_1;
	} else if ((b * c) <= 7.4e+83) {
		tmp = t_2;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[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 = a * (t * -4.0)
	t_2 = k * (-27.0 * j)
	tmp = 0
	if (b * c) <= -1.05e+124:
		tmp = b * c
	elif (b * c) <= -1.75e-45:
		tmp = i * (-4.0 * x)
	elif (b * c) <= -1.4e-199:
		tmp = -27.0 * (j * k)
	elif (b * c) <= -7.2e-239:
		tmp = 18.0 * (t * (x * (z * y)))
	elif (b * c) <= -9.2e-255:
		tmp = t_2
	elif (b * c) <= 1.75e-249:
		tmp = t_1
	elif (b * c) <= 1.1e-130:
		tmp = t_2
	elif (b * c) <= 3.8e-74:
		tmp = t_1
	elif (b * c) <= 7.4e+83:
		tmp = t_2
	else:
		tmp = b * c
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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(a * Float64(t * -4.0))
	t_2 = Float64(k * Float64(-27.0 * j))
	tmp = 0.0
	if (Float64(b * c) <= -1.05e+124)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -1.75e-45)
		tmp = Float64(i * Float64(-4.0 * x));
	elseif (Float64(b * c) <= -1.4e-199)
		tmp = Float64(-27.0 * Float64(j * k));
	elseif (Float64(b * c) <= -7.2e-239)
		tmp = Float64(18.0 * Float64(t * Float64(x * Float64(z * y))));
	elseif (Float64(b * c) <= -9.2e-255)
		tmp = t_2;
	elseif (Float64(b * c) <= 1.75e-249)
		tmp = t_1;
	elseif (Float64(b * c) <= 1.1e-130)
		tmp = t_2;
	elseif (Float64(b * c) <= 3.8e-74)
		tmp = t_1;
	elseif (Float64(b * c) <= 7.4e+83)
		tmp = t_2;
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
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 = a * (t * -4.0);
	t_2 = k * (-27.0 * j);
	tmp = 0.0;
	if ((b * c) <= -1.05e+124)
		tmp = b * c;
	elseif ((b * c) <= -1.75e-45)
		tmp = i * (-4.0 * x);
	elseif ((b * c) <= -1.4e-199)
		tmp = -27.0 * (j * k);
	elseif ((b * c) <= -7.2e-239)
		tmp = 18.0 * (t * (x * (z * y)));
	elseif ((b * c) <= -9.2e-255)
		tmp = t_2;
	elseif ((b * c) <= 1.75e-249)
		tmp = t_1;
	elseif ((b * c) <= 1.1e-130)
		tmp = t_2;
	elseif ((b * c) <= 3.8e-74)
		tmp = t_1;
	elseif ((b * c) <= 7.4e+83)
		tmp = t_2;
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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[(a * N[(t * -4.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(k * N[(-27.0 * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -1.05e+124], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -1.75e-45], N[(i * N[(-4.0 * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -1.4e-199], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -7.2e-239], N[(18.0 * N[(t * N[(x * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -9.2e-255], t$95$2, If[LessEqual[N[(b * c), $MachinePrecision], 1.75e-249], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 1.1e-130], t$95$2, If[LessEqual[N[(b * c), $MachinePrecision], 3.8e-74], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 7.4e+83], t$95$2, N[(b * c), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if (*.f64 b c) < -1.05000000000000006e124 or 7.4000000000000005e83 < (*.f64 b c)

   1. Initial program 73.1%

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

   3. Simplified 84.7%

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

   5. Taylor expanded in t around 0 78.8%

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

   7. Simplified 84.8%

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

   8. Taylor expanded in b around inf 55.7%

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

   if -1.05000000000000006e124 < (*.f64 b c) < -1.75e-45

   1. Initial program 87.9%

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

   3. Simplified 82.7%

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

   5. Taylor expanded in t around 0 79.8%

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

   7. Simplified 91.0%

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

   8. Taylor expanded in i around inf 35.5%

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

      1. *-commutative 35.5%

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

      2. associate-*r* 35.5%

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

   10. Simplified 35.5%

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

   if -1.75e-45 < (*.f64 b c) < -1.40000000000000009e-199

   1. Initial program 87.1%

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

   3. Simplified 80.6%

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

   5. Taylor expanded in j around inf 53.9%

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

   if -1.40000000000000009e-199 < (*.f64 b c) < -7.2000000000000002e-239

   1. Initial program 87.1%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in t around 0 99.6%

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

   7. Simplified 99.6%

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

   8. Taylor expanded in z around inf 75.9%

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

   if -7.2000000000000002e-239 < (*.f64 b c) < -9.1999999999999995e-255 or 1.75000000000000006e-249 < (*.f64 b c) < 1.0999999999999999e-130 or 3.7999999999999996e-74 < (*.f64 b c) < 7.4000000000000005e83

   1. Initial program 90.8%

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

   3. Simplified 88.7%

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

   5. Taylor expanded in j around inf 45.0%

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

      1. *-commutative 45.0%

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

      2. associate-*r* 45.0%

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

      3. *-commutative 45.0%

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

      4. associate-*l* 45.1%

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

   7. Simplified 45.1%

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

   if -9.1999999999999995e-255 < (*.f64 b c) < 1.75000000000000006e-249 or 1.0999999999999999e-130 < (*.f64 b c) < 3.7999999999999996e-74

   1. Initial program 86.3%

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

   3. Simplified 88.4%

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

   5. Taylor expanded in t around 0 88.3%

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

   7. Simplified 89.8%

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

   8. Taylor expanded in a around inf 38.5%

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

      1. associate-*r* 38.5%

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

      2. *-commutative 38.5%

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

      3. associate-*l* 38.5%

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

   10. Simplified 38.5%

       \[\leadsto \color{blue}{a \cdot \left(-4 \cdot t\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 47.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.05 \cdot 10^{+124}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -1.75 \cdot 10^{-45}:\\ \;\;\;\;i \cdot \left(-4 \cdot x\right)\\ \mathbf{elif}\;b \cdot c \leq -1.4 \cdot 10^{-199}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq -7.2 \cdot 10^{-239}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(z \cdot y\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq -9.2 \cdot 10^{-255}:\\ \;\;\;\;k \cdot \left(-27 \cdot j\right)\\ \mathbf{elif}\;b \cdot c \leq 1.75 \cdot 10^{-249}:\\ \;\;\;\;a \cdot \left(t \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 1.1 \cdot 10^{-130}:\\ \;\;\;\;k \cdot \left(-27 \cdot j\right)\\ \mathbf{elif}\;b \cdot c \leq 3.8 \cdot 10^{-74}:\\ \;\;\;\;a \cdot \left(t \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 7.4 \cdot 10^{+83}:\\ \;\;\;\;k \cdot \left(-27 \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 53.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(-27 \cdot k\right)\\ t_2 := b \cdot c + t\_1\\ t_3 := t \cdot \left(18 \cdot \left(x \cdot \left(z \cdot y\right)\right) - a \cdot 4\right)\\ t_4 := -4 \cdot \left(x \cdot i\right)\\ t_5 := -27 \cdot \left(j \cdot k\right) + t\_4\\ \mathbf{if}\;b \cdot c \leq -4.2 \cdot 10^{+122}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \cdot c \leq -4 \cdot 10^{-200}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;b \cdot c \leq 1.55 \cdot 10^{-260}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \cdot c \leq 3.25 \cdot 10^{-118}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;b \cdot c \leq 0.005:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;b \cdot c \leq 3.05 \cdot 10^{+32}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;b \cdot c \leq 3.5 \cdot 10^{+97}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \cdot c \leq 9.5 \cdot 10^{+133}:\\ \;\;\;\;t\_1 + t\_4\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* -27.0 k)))
        (t_2 (+ (* b c) t_1))
        (t_3 (* t (- (* 18.0 (* x (* z y))) (* a 4.0))))
        (t_4 (* -4.0 (* x i)))
        (t_5 (+ (* -27.0 (* j k)) t_4)))
   (if (<= (* b c) -4.2e+122)
     t_2
     (if (<= (* b c) -4e-200)
       t_5
       (if (<= (* b c) 1.55e-260)
         t_3
         (if (<= (* b c) 3.25e-118)
           t_5
           (if (<= (* b c) 0.005)
             (- (* -4.0 (* t a)) (* k (* j 27.0)))
             (if (<= (* b c) 3.05e+32)
               t_5
               (if (<= (* b c) 3.5e+97)
                 t_3
                 (if (<= (* b c) 9.5e+133) (+ t_1 t_4) t_2))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (-27.0 * k);
	double t_2 = (b * c) + t_1;
	double t_3 = t * ((18.0 * (x * (z * y))) - (a * 4.0));
	double t_4 = -4.0 * (x * i);
	double t_5 = (-27.0 * (j * k)) + t_4;
	double tmp;
	if ((b * c) <= -4.2e+122) {
		tmp = t_2;
	} else if ((b * c) <= -4e-200) {
		tmp = t_5;
	} else if ((b * c) <= 1.55e-260) {
		tmp = t_3;
	} else if ((b * c) <= 3.25e-118) {
		tmp = t_5;
	} else if ((b * c) <= 0.005) {
		tmp = (-4.0 * (t * a)) - (k * (j * 27.0));
	} else if ((b * c) <= 3.05e+32) {
		tmp = t_5;
	} else if ((b * c) <= 3.5e+97) {
		tmp = t_3;
	} else if ((b * c) <= 9.5e+133) {
		tmp = t_1 + t_4;
	} 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.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_1 = j * ((-27.0d0) * k)
    t_2 = (b * c) + t_1
    t_3 = t * ((18.0d0 * (x * (z * y))) - (a * 4.0d0))
    t_4 = (-4.0d0) * (x * i)
    t_5 = ((-27.0d0) * (j * k)) + t_4
    if ((b * c) <= (-4.2d+122)) then
        tmp = t_2
    else if ((b * c) <= (-4d-200)) then
        tmp = t_5
    else if ((b * c) <= 1.55d-260) then
        tmp = t_3
    else if ((b * c) <= 3.25d-118) then
        tmp = t_5
    else if ((b * c) <= 0.005d0) then
        tmp = ((-4.0d0) * (t * a)) - (k * (j * 27.0d0))
    else if ((b * c) <= 3.05d+32) then
        tmp = t_5
    else if ((b * c) <= 3.5d+97) then
        tmp = t_3
    else if ((b * c) <= 9.5d+133) then
        tmp = t_1 + t_4
    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;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (-27.0 * k);
	double t_2 = (b * c) + t_1;
	double t_3 = t * ((18.0 * (x * (z * y))) - (a * 4.0));
	double t_4 = -4.0 * (x * i);
	double t_5 = (-27.0 * (j * k)) + t_4;
	double tmp;
	if ((b * c) <= -4.2e+122) {
		tmp = t_2;
	} else if ((b * c) <= -4e-200) {
		tmp = t_5;
	} else if ((b * c) <= 1.55e-260) {
		tmp = t_3;
	} else if ((b * c) <= 3.25e-118) {
		tmp = t_5;
	} else if ((b * c) <= 0.005) {
		tmp = (-4.0 * (t * a)) - (k * (j * 27.0));
	} else if ((b * c) <= 3.05e+32) {
		tmp = t_5;
	} else if ((b * c) <= 3.5e+97) {
		tmp = t_3;
	} else if ((b * c) <= 9.5e+133) {
		tmp = t_1 + t_4;
	} 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])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (-27.0 * k)
	t_2 = (b * c) + t_1
	t_3 = t * ((18.0 * (x * (z * y))) - (a * 4.0))
	t_4 = -4.0 * (x * i)
	t_5 = (-27.0 * (j * k)) + t_4
	tmp = 0
	if (b * c) <= -4.2e+122:
		tmp = t_2
	elif (b * c) <= -4e-200:
		tmp = t_5
	elif (b * c) <= 1.55e-260:
		tmp = t_3
	elif (b * c) <= 3.25e-118:
		tmp = t_5
	elif (b * c) <= 0.005:
		tmp = (-4.0 * (t * a)) - (k * (j * 27.0))
	elif (b * c) <= 3.05e+32:
		tmp = t_5
	elif (b * c) <= 3.5e+97:
		tmp = t_3
	elif (b * c) <= 9.5e+133:
		tmp = t_1 + t_4
	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])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(-27.0 * k))
	t_2 = Float64(Float64(b * c) + t_1)
	t_3 = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(z * y))) - Float64(a * 4.0)))
	t_4 = Float64(-4.0 * Float64(x * i))
	t_5 = Float64(Float64(-27.0 * Float64(j * k)) + t_4)
	tmp = 0.0
	if (Float64(b * c) <= -4.2e+122)
		tmp = t_2;
	elseif (Float64(b * c) <= -4e-200)
		tmp = t_5;
	elseif (Float64(b * c) <= 1.55e-260)
		tmp = t_3;
	elseif (Float64(b * c) <= 3.25e-118)
		tmp = t_5;
	elseif (Float64(b * c) <= 0.005)
		tmp = Float64(Float64(-4.0 * Float64(t * a)) - Float64(k * Float64(j * 27.0)));
	elseif (Float64(b * c) <= 3.05e+32)
		tmp = t_5;
	elseif (Float64(b * c) <= 3.5e+97)
		tmp = t_3;
	elseif (Float64(b * c) <= 9.5e+133)
		tmp = Float64(t_1 + t_4);
	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])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (-27.0 * k);
	t_2 = (b * c) + t_1;
	t_3 = t * ((18.0 * (x * (z * y))) - (a * 4.0));
	t_4 = -4.0 * (x * i);
	t_5 = (-27.0 * (j * k)) + t_4;
	tmp = 0.0;
	if ((b * c) <= -4.2e+122)
		tmp = t_2;
	elseif ((b * c) <= -4e-200)
		tmp = t_5;
	elseif ((b * c) <= 1.55e-260)
		tmp = t_3;
	elseif ((b * c) <= 3.25e-118)
		tmp = t_5;
	elseif ((b * c) <= 0.005)
		tmp = (-4.0 * (t * a)) - (k * (j * 27.0));
	elseif ((b * c) <= 3.05e+32)
		tmp = t_5;
	elseif ((b * c) <= 3.5e+97)
		tmp = t_3;
	elseif ((b * c) <= 9.5e+133)
		tmp = t_1 + t_4;
	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.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(-27.0 * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(N[(18.0 * N[(x * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision] + t$95$4), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -4.2e+122], t$95$2, If[LessEqual[N[(b * c), $MachinePrecision], -4e-200], t$95$5, If[LessEqual[N[(b * c), $MachinePrecision], 1.55e-260], t$95$3, If[LessEqual[N[(b * c), $MachinePrecision], 3.25e-118], t$95$5, If[LessEqual[N[(b * c), $MachinePrecision], 0.005], N[(N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 3.05e+32], t$95$5, If[LessEqual[N[(b * c), $MachinePrecision], 3.5e+97], t$95$3, If[LessEqual[N[(b * c), $MachinePrecision], 9.5e+133], N[(t$95$1 + t$95$4), $MachinePrecision], t$95$2]]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 b c) < -4.20000000000000032e122 or 9.49999999999999996e133 < (*.f64 b c)

   1. Initial program 76.0%

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

   3. Simplified 86.7%

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

   5. Taylor expanded in b around inf 69.4%

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

   if -4.20000000000000032e122 < (*.f64 b c) < -3.9999999999999999e-200 or 1.54999999999999991e-260 < (*.f64 b c) < 3.24999999999999979e-118 or 0.0050000000000000001 < (*.f64 b c) < 3.05000000000000014e32

   1. Initial program 87.3%

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

   3. Simplified 81.2%

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

   5. Taylor expanded in i around inf 63.7%

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

   6. Taylor expanded in i around 0 65.9%

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

   if -3.9999999999999999e-200 < (*.f64 b c) < 1.54999999999999991e-260 or 3.05000000000000014e32 < (*.f64 b c) < 3.5000000000000001e97

   1. Initial program 85.9%

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

   3. Simplified 92.5%

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

      1. associate-*r* 89.1%

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

      2. distribute-rgt-out-- 86.0%

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

      3. associate-*l* 83.0%

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

      4. *-commutative 83.0%

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

      5. *-commutative 83.0%

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

   6. Applied egg-rr 83.0%

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

   7. Taylor expanded in t around inf 59.3%

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

   if 3.24999999999999979e-118 < (*.f64 b c) < 0.0050000000000000001

   1. Initial program 94.4%

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

   3. Taylor expanded in x around 0 88.7%

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

   4. Taylor expanded in a around inf 67.7%

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

      1. *-commutative 67.7%

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

   6. Simplified 67.7%

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

   if 3.5000000000000001e97 < (*.f64 b c) < 9.49999999999999996e133

   1. Initial program 52.0%

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

   3. Simplified 63.3%

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

   5. Taylor expanded in i around inf 64.2%

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

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -4.2 \cdot 10^{+122}:\\ \;\;\;\;b \cdot c + j \cdot \left(-27 \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq -4 \cdot 10^{-200}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right) + -4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 1.55 \cdot 10^{-260}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(z \cdot y\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;b \cdot c \leq 3.25 \cdot 10^{-118}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right) + -4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 0.005:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;b \cdot c \leq 3.05 \cdot 10^{+32}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right) + -4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 3.5 \cdot 10^{+97}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(z \cdot y\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;b \cdot c \leq 9.5 \cdot 10^{+133}:\\ \;\;\;\;j \cdot \left(-27 \cdot k\right) + -4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + j \cdot \left(-27 \cdot k\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 36.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := a \cdot \left(t \cdot -4\right)\\ t_2 := k \cdot \left(-27 \cdot j\right)\\ \mathbf{if}\;b \cdot c \leq -9 \cdot 10^{+122}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -1.5 \cdot 10^{-46}:\\ \;\;\;\;i \cdot \left(-4 \cdot x\right)\\ \mathbf{elif}\;b \cdot c \leq -1.26 \cdot 10^{-253}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq 9.2 \cdot 10^{-250}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq 1.32 \cdot 10^{-130}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \cdot c \leq 2.6 \cdot 10^{-75}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq 4.05 \cdot 10^{+93}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 (* a (* t -4.0))) (t_2 (* k (* -27.0 j))))
   (if (<= (* b c) -9e+122)
     (* b c)
     (if (<= (* b c) -1.5e-46)
       (* i (* -4.0 x))
       (if (<= (* b c) -1.26e-253)
         (* -27.0 (* j k))
         (if (<= (* b c) 9.2e-250)
           t_1
           (if (<= (* b c) 1.32e-130)
             t_2
             (if (<= (* b c) 2.6e-75)
               t_1
               (if (<= (* b c) 4.05e+93) t_2 (* b c))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = a * (t * -4.0);
	double t_2 = k * (-27.0 * j);
	double tmp;
	if ((b * c) <= -9e+122) {
		tmp = b * c;
	} else if ((b * c) <= -1.5e-46) {
		tmp = i * (-4.0 * x);
	} else if ((b * c) <= -1.26e-253) {
		tmp = -27.0 * (j * k);
	} else if ((b * c) <= 9.2e-250) {
		tmp = t_1;
	} else if ((b * c) <= 1.32e-130) {
		tmp = t_2;
	} else if ((b * c) <= 2.6e-75) {
		tmp = t_1;
	} else if ((b * c) <= 4.05e+93) {
		tmp = t_2;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 = a * (t * (-4.0d0))
    t_2 = k * ((-27.0d0) * j)
    if ((b * c) <= (-9d+122)) then
        tmp = b * c
    else if ((b * c) <= (-1.5d-46)) then
        tmp = i * ((-4.0d0) * x)
    else if ((b * c) <= (-1.26d-253)) then
        tmp = (-27.0d0) * (j * k)
    else if ((b * c) <= 9.2d-250) then
        tmp = t_1
    else if ((b * c) <= 1.32d-130) then
        tmp = t_2
    else if ((b * c) <= 2.6d-75) then
        tmp = t_1
    else if ((b * c) <= 4.05d+93) then
        tmp = t_2
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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 = a * (t * -4.0);
	double t_2 = k * (-27.0 * j);
	double tmp;
	if ((b * c) <= -9e+122) {
		tmp = b * c;
	} else if ((b * c) <= -1.5e-46) {
		tmp = i * (-4.0 * x);
	} else if ((b * c) <= -1.26e-253) {
		tmp = -27.0 * (j * k);
	} else if ((b * c) <= 9.2e-250) {
		tmp = t_1;
	} else if ((b * c) <= 1.32e-130) {
		tmp = t_2;
	} else if ((b * c) <= 2.6e-75) {
		tmp = t_1;
	} else if ((b * c) <= 4.05e+93) {
		tmp = t_2;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[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 = a * (t * -4.0)
	t_2 = k * (-27.0 * j)
	tmp = 0
	if (b * c) <= -9e+122:
		tmp = b * c
	elif (b * c) <= -1.5e-46:
		tmp = i * (-4.0 * x)
	elif (b * c) <= -1.26e-253:
		tmp = -27.0 * (j * k)
	elif (b * c) <= 9.2e-250:
		tmp = t_1
	elif (b * c) <= 1.32e-130:
		tmp = t_2
	elif (b * c) <= 2.6e-75:
		tmp = t_1
	elif (b * c) <= 4.05e+93:
		tmp = t_2
	else:
		tmp = b * c
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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(a * Float64(t * -4.0))
	t_2 = Float64(k * Float64(-27.0 * j))
	tmp = 0.0
	if (Float64(b * c) <= -9e+122)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -1.5e-46)
		tmp = Float64(i * Float64(-4.0 * x));
	elseif (Float64(b * c) <= -1.26e-253)
		tmp = Float64(-27.0 * Float64(j * k));
	elseif (Float64(b * c) <= 9.2e-250)
		tmp = t_1;
	elseif (Float64(b * c) <= 1.32e-130)
		tmp = t_2;
	elseif (Float64(b * c) <= 2.6e-75)
		tmp = t_1;
	elseif (Float64(b * c) <= 4.05e+93)
		tmp = t_2;
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
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 = a * (t * -4.0);
	t_2 = k * (-27.0 * j);
	tmp = 0.0;
	if ((b * c) <= -9e+122)
		tmp = b * c;
	elseif ((b * c) <= -1.5e-46)
		tmp = i * (-4.0 * x);
	elseif ((b * c) <= -1.26e-253)
		tmp = -27.0 * (j * k);
	elseif ((b * c) <= 9.2e-250)
		tmp = t_1;
	elseif ((b * c) <= 1.32e-130)
		tmp = t_2;
	elseif ((b * c) <= 2.6e-75)
		tmp = t_1;
	elseif ((b * c) <= 4.05e+93)
		tmp = t_2;
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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[(a * N[(t * -4.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(k * N[(-27.0 * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -9e+122], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -1.5e-46], N[(i * N[(-4.0 * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -1.26e-253], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 9.2e-250], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 1.32e-130], t$95$2, If[LessEqual[N[(b * c), $MachinePrecision], 2.6e-75], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 4.05e+93], t$95$2, N[(b * c), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 b c) < -8.99999999999999995e122 or 4.04999999999999992e93 < (*.f64 b c)

   1. Initial program 73.1%

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

   3. Simplified 84.7%

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

   5. Taylor expanded in t around 0 78.8%

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

   7. Simplified 84.8%

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

   8. Taylor expanded in b around inf 55.7%

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

   if -8.99999999999999995e122 < (*.f64 b c) < -1.49999999999999994e-46

   1. Initial program 87.9%

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

   3. Simplified 82.7%

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

   5. Taylor expanded in t around 0 79.8%

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

   7. Simplified 91.0%

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

   8. Taylor expanded in i around inf 35.5%

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

      1. *-commutative 35.5%

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

      2. associate-*r* 35.5%

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

   10. Simplified 35.5%

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

   if -1.49999999999999994e-46 < (*.f64 b c) < -1.2600000000000001e-253

   1. Initial program 88.0%

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

   3. Simplified 85.7%

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

   5. Taylor expanded in j around inf 48.5%

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

   if -1.2600000000000001e-253 < (*.f64 b c) < 9.1999999999999998e-250 or 1.3200000000000001e-130 < (*.f64 b c) < 2.6e-75

   1. Initial program 86.3%

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

   3. Simplified 88.4%

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

   5. Taylor expanded in t around 0 88.3%

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

   7. Simplified 89.8%

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

   8. Taylor expanded in a around inf 38.5%

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

      1. associate-*r* 38.5%

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

      2. *-commutative 38.5%

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

      3. associate-*l* 38.5%

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

   10. Simplified 38.5%

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

   if 9.1999999999999998e-250 < (*.f64 b c) < 1.3200000000000001e-130 or 2.6e-75 < (*.f64 b c) < 4.04999999999999992e93

   1. Initial program 90.2%

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

   3. Simplified 87.9%

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

   5. Taylor expanded in j around inf 42.2%

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

      1. *-commutative 42.2%

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

      2. associate-*r* 42.2%

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

      3. *-commutative 42.2%

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

      4. associate-*l* 42.3%

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

   7. Simplified 42.3%

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

4. Final simplification 46.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -9 \cdot 10^{+122}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -1.5 \cdot 10^{-46}:\\ \;\;\;\;i \cdot \left(-4 \cdot x\right)\\ \mathbf{elif}\;b \cdot c \leq -1.26 \cdot 10^{-253}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq 9.2 \cdot 10^{-250}:\\ \;\;\;\;a \cdot \left(t \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 1.32 \cdot 10^{-130}:\\ \;\;\;\;k \cdot \left(-27 \cdot j\right)\\ \mathbf{elif}\;b \cdot c \leq 2.6 \cdot 10^{-75}:\\ \;\;\;\;a \cdot \left(t \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 4.05 \cdot 10^{+93}:\\ \;\;\;\;k \cdot \left(-27 \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 54.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(-27 \cdot k\right)\\ t_2 := b \cdot c + t\_1\\ t_3 := t\_1 + -4 \cdot \left(t \cdot a\right)\\ t_4 := -4 \cdot \left(x \cdot i\right)\\ t_5 := -27 \cdot \left(j \cdot k\right) + t\_4\\ \mathbf{if}\;b \cdot c \leq -7 \cdot 10^{+122}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \cdot c \leq -7.2 \cdot 10^{-157}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;b \cdot c \leq 5.1 \cdot 10^{-281}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \cdot c \leq 3.4 \cdot 10^{-118}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;b \cdot c \leq 2.9 \cdot 10^{-12}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \cdot c \leq 2.7 \cdot 10^{+134}:\\ \;\;\;\;t\_1 + t\_4\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* -27.0 k)))
        (t_2 (+ (* b c) t_1))
        (t_3 (+ t_1 (* -4.0 (* t a))))
        (t_4 (* -4.0 (* x i)))
        (t_5 (+ (* -27.0 (* j k)) t_4)))
   (if (<= (* b c) -7e+122)
     t_2
     (if (<= (* b c) -7.2e-157)
       t_5
       (if (<= (* b c) 5.1e-281)
         t_3
         (if (<= (* b c) 3.4e-118)
           t_5
           (if (<= (* b c) 2.9e-12)
             t_3
             (if (<= (* b c) 2.7e+134) (+ t_1 t_4) t_2))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (-27.0 * k);
	double t_2 = (b * c) + t_1;
	double t_3 = t_1 + (-4.0 * (t * a));
	double t_4 = -4.0 * (x * i);
	double t_5 = (-27.0 * (j * k)) + t_4;
	double tmp;
	if ((b * c) <= -7e+122) {
		tmp = t_2;
	} else if ((b * c) <= -7.2e-157) {
		tmp = t_5;
	} else if ((b * c) <= 5.1e-281) {
		tmp = t_3;
	} else if ((b * c) <= 3.4e-118) {
		tmp = t_5;
	} else if ((b * c) <= 2.9e-12) {
		tmp = t_3;
	} else if ((b * c) <= 2.7e+134) {
		tmp = t_1 + t_4;
	} 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.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_1 = j * ((-27.0d0) * k)
    t_2 = (b * c) + t_1
    t_3 = t_1 + ((-4.0d0) * (t * a))
    t_4 = (-4.0d0) * (x * i)
    t_5 = ((-27.0d0) * (j * k)) + t_4
    if ((b * c) <= (-7d+122)) then
        tmp = t_2
    else if ((b * c) <= (-7.2d-157)) then
        tmp = t_5
    else if ((b * c) <= 5.1d-281) then
        tmp = t_3
    else if ((b * c) <= 3.4d-118) then
        tmp = t_5
    else if ((b * c) <= 2.9d-12) then
        tmp = t_3
    else if ((b * c) <= 2.7d+134) then
        tmp = t_1 + t_4
    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;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (-27.0 * k);
	double t_2 = (b * c) + t_1;
	double t_3 = t_1 + (-4.0 * (t * a));
	double t_4 = -4.0 * (x * i);
	double t_5 = (-27.0 * (j * k)) + t_4;
	double tmp;
	if ((b * c) <= -7e+122) {
		tmp = t_2;
	} else if ((b * c) <= -7.2e-157) {
		tmp = t_5;
	} else if ((b * c) <= 5.1e-281) {
		tmp = t_3;
	} else if ((b * c) <= 3.4e-118) {
		tmp = t_5;
	} else if ((b * c) <= 2.9e-12) {
		tmp = t_3;
	} else if ((b * c) <= 2.7e+134) {
		tmp = t_1 + t_4;
	} 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])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (-27.0 * k)
	t_2 = (b * c) + t_1
	t_3 = t_1 + (-4.0 * (t * a))
	t_4 = -4.0 * (x * i)
	t_5 = (-27.0 * (j * k)) + t_4
	tmp = 0
	if (b * c) <= -7e+122:
		tmp = t_2
	elif (b * c) <= -7.2e-157:
		tmp = t_5
	elif (b * c) <= 5.1e-281:
		tmp = t_3
	elif (b * c) <= 3.4e-118:
		tmp = t_5
	elif (b * c) <= 2.9e-12:
		tmp = t_3
	elif (b * c) <= 2.7e+134:
		tmp = t_1 + t_4
	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])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(-27.0 * k))
	t_2 = Float64(Float64(b * c) + t_1)
	t_3 = Float64(t_1 + Float64(-4.0 * Float64(t * a)))
	t_4 = Float64(-4.0 * Float64(x * i))
	t_5 = Float64(Float64(-27.0 * Float64(j * k)) + t_4)
	tmp = 0.0
	if (Float64(b * c) <= -7e+122)
		tmp = t_2;
	elseif (Float64(b * c) <= -7.2e-157)
		tmp = t_5;
	elseif (Float64(b * c) <= 5.1e-281)
		tmp = t_3;
	elseif (Float64(b * c) <= 3.4e-118)
		tmp = t_5;
	elseif (Float64(b * c) <= 2.9e-12)
		tmp = t_3;
	elseif (Float64(b * c) <= 2.7e+134)
		tmp = Float64(t_1 + t_4);
	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])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (-27.0 * k);
	t_2 = (b * c) + t_1;
	t_3 = t_1 + (-4.0 * (t * a));
	t_4 = -4.0 * (x * i);
	t_5 = (-27.0 * (j * k)) + t_4;
	tmp = 0.0;
	if ((b * c) <= -7e+122)
		tmp = t_2;
	elseif ((b * c) <= -7.2e-157)
		tmp = t_5;
	elseif ((b * c) <= 5.1e-281)
		tmp = t_3;
	elseif ((b * c) <= 3.4e-118)
		tmp = t_5;
	elseif ((b * c) <= 2.9e-12)
		tmp = t_3;
	elseif ((b * c) <= 2.7e+134)
		tmp = t_1 + t_4;
	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.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(-27.0 * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$1 + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision] + t$95$4), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -7e+122], t$95$2, If[LessEqual[N[(b * c), $MachinePrecision], -7.2e-157], t$95$5, If[LessEqual[N[(b * c), $MachinePrecision], 5.1e-281], t$95$3, If[LessEqual[N[(b * c), $MachinePrecision], 3.4e-118], t$95$5, If[LessEqual[N[(b * c), $MachinePrecision], 2.9e-12], t$95$3, If[LessEqual[N[(b * c), $MachinePrecision], 2.7e+134], N[(t$95$1 + t$95$4), $MachinePrecision], t$95$2]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 b c) < -7.00000000000000028e122 or 2.7e134 < (*.f64 b c)

   1. Initial program 76.0%

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

   3. Simplified 86.7%

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

   5. Taylor expanded in b around inf 69.4%

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

   if -7.00000000000000028e122 < (*.f64 b c) < -7.2e-157 or 5.10000000000000025e-281 < (*.f64 b c) < 3.39999999999999991e-118

   1. Initial program 84.7%

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

   3. Simplified 81.5%

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

   5. Taylor expanded in i around inf 62.2%

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

   6. Taylor expanded in i around 0 64.7%

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

   if -7.2e-157 < (*.f64 b c) < 5.10000000000000025e-281 or 3.39999999999999991e-118 < (*.f64 b c) < 2.9000000000000002e-12

   1. Initial program 90.4%

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

   3. Simplified 90.8%

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

   5. Taylor expanded in a around inf 57.2%

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

      1. *-commutative 57.2%

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

   7. Simplified 57.2%

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

   if 2.9000000000000002e-12 < (*.f64 b c) < 2.7e134

   1. Initial program 76.7%

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

   3. Simplified 84.3%

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

   5. Taylor expanded in i around inf 49.4%

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

4. Final simplification 62.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -7 \cdot 10^{+122}:\\ \;\;\;\;b \cdot c + j \cdot \left(-27 \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq -7.2 \cdot 10^{-157}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right) + -4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 5.1 \cdot 10^{-281}:\\ \;\;\;\;j \cdot \left(-27 \cdot k\right) + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;b \cdot c \leq 3.4 \cdot 10^{-118}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right) + -4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 2.9 \cdot 10^{-12}:\\ \;\;\;\;j \cdot \left(-27 \cdot k\right) + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;b \cdot c \leq 2.7 \cdot 10^{+134}:\\ \;\;\;\;j \cdot \left(-27 \cdot k\right) + -4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + j \cdot \left(-27 \cdot k\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 54.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(-27 \cdot k\right)\\ t_2 := b \cdot c + t\_1\\ t_3 := -4 \cdot \left(t \cdot a\right) - k \cdot \left(j \cdot 27\right)\\ t_4 := -4 \cdot \left(x \cdot i\right)\\ t_5 := -27 \cdot \left(j \cdot k\right) + t\_4\\ \mathbf{if}\;b \cdot c \leq -3.8 \cdot 10^{+123}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \cdot c \leq -4.5 \cdot 10^{-156}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;b \cdot c \leq 1.65 \cdot 10^{-286}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \cdot c \leq 3.8 \cdot 10^{-118}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;b \cdot c \leq 7 \cdot 10^{-11}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \cdot c \leq 1.62 \cdot 10^{+133}:\\ \;\;\;\;t\_1 + t\_4\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* -27.0 k)))
        (t_2 (+ (* b c) t_1))
        (t_3 (- (* -4.0 (* t a)) (* k (* j 27.0))))
        (t_4 (* -4.0 (* x i)))
        (t_5 (+ (* -27.0 (* j k)) t_4)))
   (if (<= (* b c) -3.8e+123)
     t_2
     (if (<= (* b c) -4.5e-156)
       t_5
       (if (<= (* b c) 1.65e-286)
         t_3
         (if (<= (* b c) 3.8e-118)
           t_5
           (if (<= (* b c) 7e-11)
             t_3
             (if (<= (* b c) 1.62e+133) (+ t_1 t_4) t_2))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (-27.0 * k);
	double t_2 = (b * c) + t_1;
	double t_3 = (-4.0 * (t * a)) - (k * (j * 27.0));
	double t_4 = -4.0 * (x * i);
	double t_5 = (-27.0 * (j * k)) + t_4;
	double tmp;
	if ((b * c) <= -3.8e+123) {
		tmp = t_2;
	} else if ((b * c) <= -4.5e-156) {
		tmp = t_5;
	} else if ((b * c) <= 1.65e-286) {
		tmp = t_3;
	} else if ((b * c) <= 3.8e-118) {
		tmp = t_5;
	} else if ((b * c) <= 7e-11) {
		tmp = t_3;
	} else if ((b * c) <= 1.62e+133) {
		tmp = t_1 + t_4;
	} 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.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_1 = j * ((-27.0d0) * k)
    t_2 = (b * c) + t_1
    t_3 = ((-4.0d0) * (t * a)) - (k * (j * 27.0d0))
    t_4 = (-4.0d0) * (x * i)
    t_5 = ((-27.0d0) * (j * k)) + t_4
    if ((b * c) <= (-3.8d+123)) then
        tmp = t_2
    else if ((b * c) <= (-4.5d-156)) then
        tmp = t_5
    else if ((b * c) <= 1.65d-286) then
        tmp = t_3
    else if ((b * c) <= 3.8d-118) then
        tmp = t_5
    else if ((b * c) <= 7d-11) then
        tmp = t_3
    else if ((b * c) <= 1.62d+133) then
        tmp = t_1 + t_4
    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;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (-27.0 * k);
	double t_2 = (b * c) + t_1;
	double t_3 = (-4.0 * (t * a)) - (k * (j * 27.0));
	double t_4 = -4.0 * (x * i);
	double t_5 = (-27.0 * (j * k)) + t_4;
	double tmp;
	if ((b * c) <= -3.8e+123) {
		tmp = t_2;
	} else if ((b * c) <= -4.5e-156) {
		tmp = t_5;
	} else if ((b * c) <= 1.65e-286) {
		tmp = t_3;
	} else if ((b * c) <= 3.8e-118) {
		tmp = t_5;
	} else if ((b * c) <= 7e-11) {
		tmp = t_3;
	} else if ((b * c) <= 1.62e+133) {
		tmp = t_1 + t_4;
	} 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])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (-27.0 * k)
	t_2 = (b * c) + t_1
	t_3 = (-4.0 * (t * a)) - (k * (j * 27.0))
	t_4 = -4.0 * (x * i)
	t_5 = (-27.0 * (j * k)) + t_4
	tmp = 0
	if (b * c) <= -3.8e+123:
		tmp = t_2
	elif (b * c) <= -4.5e-156:
		tmp = t_5
	elif (b * c) <= 1.65e-286:
		tmp = t_3
	elif (b * c) <= 3.8e-118:
		tmp = t_5
	elif (b * c) <= 7e-11:
		tmp = t_3
	elif (b * c) <= 1.62e+133:
		tmp = t_1 + t_4
	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])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(-27.0 * k))
	t_2 = Float64(Float64(b * c) + t_1)
	t_3 = Float64(Float64(-4.0 * Float64(t * a)) - Float64(k * Float64(j * 27.0)))
	t_4 = Float64(-4.0 * Float64(x * i))
	t_5 = Float64(Float64(-27.0 * Float64(j * k)) + t_4)
	tmp = 0.0
	if (Float64(b * c) <= -3.8e+123)
		tmp = t_2;
	elseif (Float64(b * c) <= -4.5e-156)
		tmp = t_5;
	elseif (Float64(b * c) <= 1.65e-286)
		tmp = t_3;
	elseif (Float64(b * c) <= 3.8e-118)
		tmp = t_5;
	elseif (Float64(b * c) <= 7e-11)
		tmp = t_3;
	elseif (Float64(b * c) <= 1.62e+133)
		tmp = Float64(t_1 + t_4);
	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])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (-27.0 * k);
	t_2 = (b * c) + t_1;
	t_3 = (-4.0 * (t * a)) - (k * (j * 27.0));
	t_4 = -4.0 * (x * i);
	t_5 = (-27.0 * (j * k)) + t_4;
	tmp = 0.0;
	if ((b * c) <= -3.8e+123)
		tmp = t_2;
	elseif ((b * c) <= -4.5e-156)
		tmp = t_5;
	elseif ((b * c) <= 1.65e-286)
		tmp = t_3;
	elseif ((b * c) <= 3.8e-118)
		tmp = t_5;
	elseif ((b * c) <= 7e-11)
		tmp = t_3;
	elseif ((b * c) <= 1.62e+133)
		tmp = t_1 + t_4;
	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.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(-27.0 * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision] + t$95$4), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -3.8e+123], t$95$2, If[LessEqual[N[(b * c), $MachinePrecision], -4.5e-156], t$95$5, If[LessEqual[N[(b * c), $MachinePrecision], 1.65e-286], t$95$3, If[LessEqual[N[(b * c), $MachinePrecision], 3.8e-118], t$95$5, If[LessEqual[N[(b * c), $MachinePrecision], 7e-11], t$95$3, If[LessEqual[N[(b * c), $MachinePrecision], 1.62e+133], N[(t$95$1 + t$95$4), $MachinePrecision], t$95$2]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 b c) < -3.79999999999999994e123 or 1.61999999999999998e133 < (*.f64 b c)

   1. Initial program 76.0%

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

   3. Simplified 86.7%

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

   5. Taylor expanded in b around inf 69.4%

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

   if -3.79999999999999994e123 < (*.f64 b c) < -4.49999999999999986e-156 or 1.6499999999999999e-286 < (*.f64 b c) < 3.8000000000000001e-118

   1. Initial program 84.7%

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

   3. Simplified 81.5%

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

   5. Taylor expanded in i around inf 62.2%

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

   6. Taylor expanded in i around 0 64.7%

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

   if -4.49999999999999986e-156 < (*.f64 b c) < 1.6499999999999999e-286 or 3.8000000000000001e-118 < (*.f64 b c) < 7.00000000000000038e-11

   1. Initial program 90.4%

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

   3. Taylor expanded in x around 0 90.6%

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

   4. Taylor expanded in a around inf 58.4%

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

      1. *-commutative 58.4%

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

   6. Simplified 58.4%

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

   if 7.00000000000000038e-11 < (*.f64 b c) < 1.61999999999999998e133

   1. Initial program 76.7%

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

   3. Simplified 84.3%

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

   5. Taylor expanded in i around inf 49.4%

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

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -3.8 \cdot 10^{+123}:\\ \;\;\;\;b \cdot c + j \cdot \left(-27 \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq -4.5 \cdot 10^{-156}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right) + -4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 1.65 \cdot 10^{-286}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;b \cdot c \leq 3.8 \cdot 10^{-118}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right) + -4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 7 \cdot 10^{-11}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;b \cdot c \leq 1.62 \cdot 10^{+133}:\\ \;\;\;\;j \cdot \left(-27 \cdot k\right) + -4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + j \cdot \left(-27 \cdot k\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 36.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := -27 \cdot \left(j \cdot k\right)\\ t_2 := a \cdot \left(t \cdot -4\right)\\ \mathbf{if}\;b \cdot c \leq -3.8 \cdot 10^{+178}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -3.7 \cdot 10^{-255}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq 1.05 \cdot 10^{-249}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \cdot c \leq 1.3 \cdot 10^{-130}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq 2.1 \cdot 10^{-74}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \cdot c \leq 4.9 \cdot 10^{+92}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* -27.0 (* j k))) (t_2 (* a (* t -4.0))))
   (if (<= (* b c) -3.8e+178)
     (* b c)
     (if (<= (* b c) -3.7e-255)
       t_1
       (if (<= (* b c) 1.05e-249)
         t_2
         (if (<= (* b c) 1.3e-130)
           t_1
           (if (<= (* b c) 2.1e-74)
             t_2
             (if (<= (* b c) 4.9e+92) t_1 (* b c)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -27.0 * (j * k);
	double t_2 = a * (t * -4.0);
	double tmp;
	if ((b * c) <= -3.8e+178) {
		tmp = b * c;
	} else if ((b * c) <= -3.7e-255) {
		tmp = t_1;
	} else if ((b * c) <= 1.05e-249) {
		tmp = t_2;
	} else if ((b * c) <= 1.3e-130) {
		tmp = t_1;
	} else if ((b * c) <= 2.1e-74) {
		tmp = t_2;
	} else if ((b * c) <= 4.9e+92) {
		tmp = t_1;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (-27.0d0) * (j * k)
    t_2 = a * (t * (-4.0d0))
    if ((b * c) <= (-3.8d+178)) then
        tmp = b * c
    else if ((b * c) <= (-3.7d-255)) then
        tmp = t_1
    else if ((b * c) <= 1.05d-249) then
        tmp = t_2
    else if ((b * c) <= 1.3d-130) then
        tmp = t_1
    else if ((b * c) <= 2.1d-74) then
        tmp = t_2
    else if ((b * c) <= 4.9d+92) then
        tmp = t_1
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -27.0 * (j * k);
	double t_2 = a * (t * -4.0);
	double tmp;
	if ((b * c) <= -3.8e+178) {
		tmp = b * c;
	} else if ((b * c) <= -3.7e-255) {
		tmp = t_1;
	} else if ((b * c) <= 1.05e-249) {
		tmp = t_2;
	} else if ((b * c) <= 1.3e-130) {
		tmp = t_1;
	} else if ((b * c) <= 2.1e-74) {
		tmp = t_2;
	} else if ((b * c) <= 4.9e+92) {
		tmp = t_1;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = -27.0 * (j * k)
	t_2 = a * (t * -4.0)
	tmp = 0
	if (b * c) <= -3.8e+178:
		tmp = b * c
	elif (b * c) <= -3.7e-255:
		tmp = t_1
	elif (b * c) <= 1.05e-249:
		tmp = t_2
	elif (b * c) <= 1.3e-130:
		tmp = t_1
	elif (b * c) <= 2.1e-74:
		tmp = t_2
	elif (b * c) <= 4.9e+92:
		tmp = t_1
	else:
		tmp = b * c
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(-27.0 * Float64(j * k))
	t_2 = Float64(a * Float64(t * -4.0))
	tmp = 0.0
	if (Float64(b * c) <= -3.8e+178)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -3.7e-255)
		tmp = t_1;
	elseif (Float64(b * c) <= 1.05e-249)
		tmp = t_2;
	elseif (Float64(b * c) <= 1.3e-130)
		tmp = t_1;
	elseif (Float64(b * c) <= 2.1e-74)
		tmp = t_2;
	elseif (Float64(b * c) <= 4.9e+92)
		tmp = t_1;
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = -27.0 * (j * k);
	t_2 = a * (t * -4.0);
	tmp = 0.0;
	if ((b * c) <= -3.8e+178)
		tmp = b * c;
	elseif ((b * c) <= -3.7e-255)
		tmp = t_1;
	elseif ((b * c) <= 1.05e-249)
		tmp = t_2;
	elseif ((b * c) <= 1.3e-130)
		tmp = t_1;
	elseif ((b * c) <= 2.1e-74)
		tmp = t_2;
	elseif ((b * c) <= 4.9e+92)
		tmp = t_1;
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(t * -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -3.8e+178], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -3.7e-255], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 1.05e-249], t$95$2, If[LessEqual[N[(b * c), $MachinePrecision], 1.3e-130], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 2.1e-74], t$95$2, If[LessEqual[N[(b * c), $MachinePrecision], 4.9e+92], t$95$1, N[(b * c), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -3.79999999999999998e178 or 4.9000000000000002e92 < (*.f64 b c)

   1. Initial program 74.5%

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

   3. Simplified 85.9%

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

   5. Taylor expanded in t around 0 79.4%

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

   7. Simplified 85.9%

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

   8. Taylor expanded in b around inf 58.1%

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

   if -3.79999999999999998e178 < (*.f64 b c) < -3.7000000000000002e-255 or 1.04999999999999996e-249 < (*.f64 b c) < 1.3e-130 or 2.1e-74 < (*.f64 b c) < 4.9000000000000002e92

   1. Initial program 87.0%

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

   3. Simplified 84.8%

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

   5. Taylor expanded in j around inf 38.3%

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

   if -3.7000000000000002e-255 < (*.f64 b c) < 1.04999999999999996e-249 or 1.3e-130 < (*.f64 b c) < 2.1e-74

   1. Initial program 86.3%

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

   3. Simplified 88.4%

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

   5. Taylor expanded in t around 0 88.3%

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

   7. Simplified 89.8%

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

   8. Taylor expanded in a around inf 38.5%

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

      1. associate-*r* 38.5%

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

      2. *-commutative 38.5%

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

      3. associate-*l* 38.5%

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

   10. Simplified 38.5%

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

4. Final simplification 44.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -3.8 \cdot 10^{+178}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -3.7 \cdot 10^{-255}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq 1.05 \cdot 10^{-249}:\\ \;\;\;\;a \cdot \left(t \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 1.3 \cdot 10^{-130}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq 2.1 \cdot 10^{-74}:\\ \;\;\;\;a \cdot \left(t \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 4.9 \cdot 10^{+92}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 36.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := k \cdot \left(-27 \cdot j\right)\\ t_2 := a \cdot \left(t \cdot -4\right)\\ \mathbf{if}\;b \cdot c \leq -8.8 \cdot 10^{+178}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -3.8 \cdot 10^{-253}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq 9.2 \cdot 10^{-250}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \cdot c \leq 1.2 \cdot 10^{-130}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq 3.8 \cdot 10^{-74}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \cdot c \leq 1.26 \cdot 10^{+91}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* k (* -27.0 j))) (t_2 (* a (* t -4.0))))
   (if (<= (* b c) -8.8e+178)
     (* b c)
     (if (<= (* b c) -3.8e-253)
       (* -27.0 (* j k))
       (if (<= (* b c) 9.2e-250)
         t_2
         (if (<= (* b c) 1.2e-130)
           t_1
           (if (<= (* b c) 3.8e-74)
             t_2
             (if (<= (* b c) 1.26e+91) t_1 (* b c)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = k * (-27.0 * j);
	double t_2 = a * (t * -4.0);
	double tmp;
	if ((b * c) <= -8.8e+178) {
		tmp = b * c;
	} else if ((b * c) <= -3.8e-253) {
		tmp = -27.0 * (j * k);
	} else if ((b * c) <= 9.2e-250) {
		tmp = t_2;
	} else if ((b * c) <= 1.2e-130) {
		tmp = t_1;
	} else if ((b * c) <= 3.8e-74) {
		tmp = t_2;
	} else if ((b * c) <= 1.26e+91) {
		tmp = t_1;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = k * ((-27.0d0) * j)
    t_2 = a * (t * (-4.0d0))
    if ((b * c) <= (-8.8d+178)) then
        tmp = b * c
    else if ((b * c) <= (-3.8d-253)) then
        tmp = (-27.0d0) * (j * k)
    else if ((b * c) <= 9.2d-250) then
        tmp = t_2
    else if ((b * c) <= 1.2d-130) then
        tmp = t_1
    else if ((b * c) <= 3.8d-74) then
        tmp = t_2
    else if ((b * c) <= 1.26d+91) then
        tmp = t_1
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = k * (-27.0 * j);
	double t_2 = a * (t * -4.0);
	double tmp;
	if ((b * c) <= -8.8e+178) {
		tmp = b * c;
	} else if ((b * c) <= -3.8e-253) {
		tmp = -27.0 * (j * k);
	} else if ((b * c) <= 9.2e-250) {
		tmp = t_2;
	} else if ((b * c) <= 1.2e-130) {
		tmp = t_1;
	} else if ((b * c) <= 3.8e-74) {
		tmp = t_2;
	} else if ((b * c) <= 1.26e+91) {
		tmp = t_1;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = k * (-27.0 * j)
	t_2 = a * (t * -4.0)
	tmp = 0
	if (b * c) <= -8.8e+178:
		tmp = b * c
	elif (b * c) <= -3.8e-253:
		tmp = -27.0 * (j * k)
	elif (b * c) <= 9.2e-250:
		tmp = t_2
	elif (b * c) <= 1.2e-130:
		tmp = t_1
	elif (b * c) <= 3.8e-74:
		tmp = t_2
	elif (b * c) <= 1.26e+91:
		tmp = t_1
	else:
		tmp = b * c
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(k * Float64(-27.0 * j))
	t_2 = Float64(a * Float64(t * -4.0))
	tmp = 0.0
	if (Float64(b * c) <= -8.8e+178)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -3.8e-253)
		tmp = Float64(-27.0 * Float64(j * k));
	elseif (Float64(b * c) <= 9.2e-250)
		tmp = t_2;
	elseif (Float64(b * c) <= 1.2e-130)
		tmp = t_1;
	elseif (Float64(b * c) <= 3.8e-74)
		tmp = t_2;
	elseif (Float64(b * c) <= 1.26e+91)
		tmp = t_1;
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = k * (-27.0 * j);
	t_2 = a * (t * -4.0);
	tmp = 0.0;
	if ((b * c) <= -8.8e+178)
		tmp = b * c;
	elseif ((b * c) <= -3.8e-253)
		tmp = -27.0 * (j * k);
	elseif ((b * c) <= 9.2e-250)
		tmp = t_2;
	elseif ((b * c) <= 1.2e-130)
		tmp = t_1;
	elseif ((b * c) <= 3.8e-74)
		tmp = t_2;
	elseif ((b * c) <= 1.26e+91)
		tmp = t_1;
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(k * N[(-27.0 * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(t * -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -8.8e+178], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -3.8e-253], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 9.2e-250], t$95$2, If[LessEqual[N[(b * c), $MachinePrecision], 1.2e-130], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 3.8e-74], t$95$2, If[LessEqual[N[(b * c), $MachinePrecision], 1.26e+91], t$95$1, N[(b * c), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 b c) < -8.79999999999999989e178 or 1.26e91 < (*.f64 b c)

   1. Initial program 74.5%

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

   3. Simplified 85.9%

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

   5. Taylor expanded in t around 0 79.4%

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

   7. Simplified 85.9%

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

   8. Taylor expanded in b around inf 58.1%

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

   if -8.79999999999999989e178 < (*.f64 b c) < -3.80000000000000012e-253

   1. Initial program 85.4%

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

   3. Simplified 83.3%

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

   5. Taylor expanded in j around inf 36.3%

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

   if -3.80000000000000012e-253 < (*.f64 b c) < 9.1999999999999998e-250 or 1.19999999999999998e-130 < (*.f64 b c) < 3.7999999999999996e-74

   1. Initial program 86.3%

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

   3. Simplified 88.4%

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

   5. Taylor expanded in t around 0 88.3%

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

   7. Simplified 89.8%

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

   8. Taylor expanded in a around inf 38.5%

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

      1. associate-*r* 38.5%

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

      2. *-commutative 38.5%

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

      3. associate-*l* 38.5%

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

   10. Simplified 38.5%

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

   if 9.1999999999999998e-250 < (*.f64 b c) < 1.19999999999999998e-130 or 3.7999999999999996e-74 < (*.f64 b c) < 1.26e91

   1. Initial program 90.2%

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

   3. Simplified 87.9%

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

   5. Taylor expanded in j around inf 42.2%

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

      1. *-commutative 42.2%

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

      2. associate-*r* 42.2%

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

      3. *-commutative 42.2%

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

      4. associate-*l* 42.3%

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

   7. Simplified 42.3%

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

4. Final simplification 44.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -8.8 \cdot 10^{+178}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -3.8 \cdot 10^{-253}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq 9.2 \cdot 10^{-250}:\\ \;\;\;\;a \cdot \left(t \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 1.2 \cdot 10^{-130}:\\ \;\;\;\;k \cdot \left(-27 \cdot j\right)\\ \mathbf{elif}\;b \cdot c \leq 3.8 \cdot 10^{-74}:\\ \;\;\;\;a \cdot \left(t \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 1.26 \cdot 10^{+91}:\\ \;\;\;\;k \cdot \left(-27 \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 52.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := k \cdot \left(j \cdot 27\right)\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-68}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right) + -4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+14}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(z \cdot \left(x \cdot y\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t\_1 \leq 10^{+146} \lor \neg \left(t\_1 \leq 2 \cdot 10^{+249}\right):\\ \;\;\;\;b \cdot c + j \cdot \left(-27 \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right) - t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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-68)
     (+ (* -27.0 (* j k)) (* -4.0 (* x i)))
     (if (<= t_1 4e+14)
       (* t (- (* 18.0 (* z (* x y))) (* a 4.0)))
       (if (or (<= t_1 1e+146) (not (<= t_1 2e+249)))
         (+ (* b c) (* j (* -27.0 k)))
         (- (* -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);
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-68) {
		tmp = (-27.0 * (j * k)) + (-4.0 * (x * i));
	} else if (t_1 <= 4e+14) {
		tmp = t * ((18.0 * (z * (x * y))) - (a * 4.0));
	} else if ((t_1 <= 1e+146) || !(t_1 <= 2e+249)) {
		tmp = (b * c) + (j * (-27.0 * k));
	} 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.
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-68)) then
        tmp = ((-27.0d0) * (j * k)) + ((-4.0d0) * (x * i))
    else if (t_1 <= 4d+14) then
        tmp = t * ((18.0d0 * (z * (x * y))) - (a * 4.0d0))
    else if ((t_1 <= 1d+146) .or. (.not. (t_1 <= 2d+249))) then
        tmp = (b * c) + (j * ((-27.0d0) * k))
    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;
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-68) {
		tmp = (-27.0 * (j * k)) + (-4.0 * (x * i));
	} else if (t_1 <= 4e+14) {
		tmp = t * ((18.0 * (z * (x * y))) - (a * 4.0));
	} else if ((t_1 <= 1e+146) || !(t_1 <= 2e+249)) {
		tmp = (b * c) + (j * (-27.0 * k));
	} 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])
[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-68:
		tmp = (-27.0 * (j * k)) + (-4.0 * (x * i))
	elif t_1 <= 4e+14:
		tmp = t * ((18.0 * (z * (x * y))) - (a * 4.0))
	elif (t_1 <= 1e+146) or not (t_1 <= 2e+249):
		tmp = (b * c) + (j * (-27.0 * k))
	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])
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-68)
		tmp = Float64(Float64(-27.0 * Float64(j * k)) + Float64(-4.0 * Float64(x * i)));
	elseif (t_1 <= 4e+14)
		tmp = Float64(t * Float64(Float64(18.0 * Float64(z * Float64(x * y))) - Float64(a * 4.0)));
	elseif ((t_1 <= 1e+146) || !(t_1 <= 2e+249))
		tmp = Float64(Float64(b * c) + Float64(j * Float64(-27.0 * k)));
	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])){:}
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-68)
		tmp = (-27.0 * (j * k)) + (-4.0 * (x * i));
	elseif (t_1 <= 4e+14)
		tmp = t * ((18.0 * (z * (x * y))) - (a * 4.0));
	elseif ((t_1 <= 1e+146) || ~((t_1 <= 2e+249)))
		tmp = (b * c) + (j * (-27.0 * k));
	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.
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-68], N[(N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 4e+14], N[(t * N[(N[(18.0 * N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t$95$1, 1e+146], N[Not[LessEqual[t$95$1, 2e+249]], $MachinePrecision]], N[(N[(b * c), $MachinePrecision] + N[(j * N[(-27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 j 27) k) < -1.00000000000000007e-68

   1. Initial program 84.3%

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

   3. Simplified 88.5%

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

   5. Taylor expanded in i around inf 69.3%

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

   6. Taylor expanded in i around 0 70.8%

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

   if -1.00000000000000007e-68 < (*.f64 (*.f64 j 27) k) < 4e14

   1. Initial program 81.2%

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

   3. Simplified 83.2%

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

      1. associate-*r* 86.4%

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

      2. distribute-rgt-out-- 81.2%

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

      3. associate-*l* 81.9%

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

      4. *-commutative 81.9%

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

      5. *-commutative 81.9%

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

   6. Applied egg-rr 81.9%

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

   7. Taylor expanded in t around inf 48.8%

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

      1. expm1-log1p-u 32.2%

         \[\leadsto t \cdot \left(18 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(x \cdot \left(y \cdot z\right)\right)\right)} - 4 \cdot a\right) \]

      2. expm1-udef 31.3%

         \[\leadsto t \cdot \left(18 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(x \cdot \left(y \cdot z\right)\right)} - 1\right)} - 4 \cdot a\right) \]

   9. Applied egg-rr 31.3%

      \[\leadsto t \cdot \left(18 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(x \cdot \left(y \cdot z\right)\right)} - 1\right)} - 4 \cdot a\right) \]
   10. Step-by-step derivation

       1. expm1-def 32.2%

          \[\leadsto t \cdot \left(18 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(x \cdot \left(y \cdot z\right)\right)\right)} - 4 \cdot a\right) \]

       2. expm1-log1p 48.8%

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

       3. associate-*r* 51.9%

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

   11. Simplified 51.9%

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

   if 4e14 < (*.f64 (*.f64 j 27) k) < 9.99999999999999934e145 or 1.9999999999999998e249 < (*.f64 (*.f64 j 27) k)

   1. Initial program 83.5%

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

   3. Simplified 82.0%

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

   5. Taylor expanded in b around inf 57.3%

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

   if 9.99999999999999934e145 < (*.f64 (*.f64 j 27) k) < 1.9999999999999998e249

   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. Add Preprocessing

   3. Taylor expanded in x around 0 75.5%

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

   4. Taylor expanded in a around inf 90.8%

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

      1. *-commutative 90.8%

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

   6. Simplified 90.8%

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

4. Final simplification 60.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \cdot \left(j \cdot 27\right) \leq -1 \cdot 10^{-68}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right) + -4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 4 \cdot 10^{+14}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(z \cdot \left(x \cdot y\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 10^{+146} \lor \neg \left(k \cdot \left(j \cdot 27\right) \leq 2 \cdot 10^{+249}\right):\\ \;\;\;\;b \cdot c + j \cdot \left(-27 \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 88.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := 4 \cdot \left(t \cdot a\right)\\ t_2 := k \cdot \left(j \cdot 27\right)\\ \mathbf{if}\;x \leq -2.1 \cdot 10^{-40} \lor \neg \left(x \leq 1.05 \cdot 10^{-122}\right):\\ \;\;\;\;\left(\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(z \cdot y\right)\right) - i \cdot 4\right)\right) - t\_1\right) - t\_2\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b \cdot c + \left(t \cdot 18\right) \cdot \left(z \cdot \left(x \cdot y\right)\right)\right) - t\_1\right) - t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 (or (<= x -2.1e-40) (not (<= x 1.05e-122)))
     (- (- (+ (* b c) (* x (- (* 18.0 (* t (* z y))) (* i 4.0)))) t_1) t_2)
     (- (- (+ (* b c) (* (* t 18.0) (* z (* x y)))) t_1) t_2))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 4.0 * (t * a);
	double t_2 = k * (j * 27.0);
	double tmp;
	if ((x <= -2.1e-40) || !(x <= 1.05e-122)) {
		tmp = (((b * c) + (x * ((18.0 * (t * (z * y))) - (i * 4.0)))) - t_1) - t_2;
	} else {
		tmp = (((b * c) + ((t * 18.0) * (z * (x * y)))) - t_1) - 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.
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 ((x <= (-2.1d-40)) .or. (.not. (x <= 1.05d-122))) then
        tmp = (((b * c) + (x * ((18.0d0 * (t * (z * y))) - (i * 4.0d0)))) - t_1) - t_2
    else
        tmp = (((b * c) + ((t * 18.0d0) * (z * (x * y)))) - t_1) - 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;
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 ((x <= -2.1e-40) || !(x <= 1.05e-122)) {
		tmp = (((b * c) + (x * ((18.0 * (t * (z * y))) - (i * 4.0)))) - t_1) - t_2;
	} else {
		tmp = (((b * c) + ((t * 18.0) * (z * (x * y)))) - t_1) - 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])
[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 (x <= -2.1e-40) or not (x <= 1.05e-122):
		tmp = (((b * c) + (x * ((18.0 * (t * (z * y))) - (i * 4.0)))) - t_1) - t_2
	else:
		tmp = (((b * c) + ((t * 18.0) * (z * (x * y)))) - t_1) - 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])
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 ((x <= -2.1e-40) || !(x <= 1.05e-122))
		tmp = Float64(Float64(Float64(Float64(b * c) + Float64(x * Float64(Float64(18.0 * Float64(t * Float64(z * y))) - Float64(i * 4.0)))) - t_1) - t_2);
	else
		tmp = Float64(Float64(Float64(Float64(b * c) + Float64(Float64(t * 18.0) * Float64(z * Float64(x * y)))) - t_1) - 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])){:}
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 ((x <= -2.1e-40) || ~((x <= 1.05e-122)))
		tmp = (((b * c) + (x * ((18.0 * (t * (z * y))) - (i * 4.0)))) - t_1) - t_2;
	else
		tmp = (((b * c) + ((t * 18.0) * (z * (x * y)))) - t_1) - 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.
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[Or[LessEqual[x, -2.1e-40], N[Not[LessEqual[x, 1.05e-122]], $MachinePrecision]], N[(N[(N[(N[(b * c), $MachinePrecision] + N[(x * N[(N[(18.0 * N[(t * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision], N[(N[(N[(N[(b * c), $MachinePrecision] + N[(N[(t * 18.0), $MachinePrecision] * N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.10000000000000018e-40 or 1.04999999999999996e-122 < x

   1. Initial program 75.9%

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

   3. Taylor expanded in x around 0 85.8%

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

   if -2.10000000000000018e-40 < x < 1.04999999999999996e-122

   1. Initial program 96.5%

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

   3. Taylor expanded in x around 0 79.4%

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

   4. Taylor expanded in t around inf 84.9%

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

      1. associate-*r* 83.8%

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

   6. Simplified 83.8%

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

      1. expm1-log1p-u 27.8%

         \[\leadsto t \cdot \left(18 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(x \cdot \left(y \cdot z\right)\right)\right)} - 4 \cdot a\right) \]

      2. expm1-udef 25.7%

         \[\leadsto t \cdot \left(18 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(x \cdot \left(y \cdot z\right)\right)} - 1\right)} - 4 \cdot a\right) \]

   8. Applied egg-rr 74.5%

      \[\leadsto \left(\left(b \cdot c + \left(18 \cdot t\right) \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(x \cdot \left(y \cdot z\right)\right)} - 1\right)}\right) - 4 \cdot \left(a \cdot t\right)\right) - \left(j \cdot 27\right) \cdot k \]
   9. Step-by-step derivation

      1. expm1-def 27.8%

         \[\leadsto t \cdot \left(18 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(x \cdot \left(y \cdot z\right)\right)\right)} - 4 \cdot a\right) \]

      2. expm1-log1p 33.8%

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

      3. associate-*r* 39.8%

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

   10. Simplified 94.4%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{-40} \lor \neg \left(x \leq 1.05 \cdot 10^{-122}\right):\\ \;\;\;\;\left(\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(z \cdot y\right)\right) - i \cdot 4\right)\right) - 4 \cdot \left(t \cdot a\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b \cdot c + \left(t \cdot 18\right) \cdot \left(z \cdot \left(x \cdot y\right)\right)\right) - 4 \cdot \left(t \cdot a\right)\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 71.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := k \cdot \left(j \cdot 27\right)\\ t_2 := \left(b \cdot c - \left(x \cdot i\right) \cdot 4\right) - t\_1\\ t_3 := x \cdot \left(18 \cdot \left(t \cdot \left(z \cdot y\right)\right) - i \cdot 4\right)\\ \mathbf{if}\;x \leq -7.5 \cdot 10^{+201}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq -2.9 \cdot 10^{-10}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 5.4 \cdot 10^{-52}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - t\_1\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+114}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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) (* (* x i) 4.0)) t_1))
        (t_3 (* x (- (* 18.0 (* t (* z y))) (* i 4.0)))))
   (if (<= x -7.5e+201)
     t_3
     (if (<= x -2.9e-10)
       t_2
       (if (<= x 5.4e-52)
         (- (- (* b c) (* 4.0 (* t a))) t_1)
         (if (<= x 4e+114) t_2 t_3))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = k * (j * 27.0);
	double t_2 = ((b * c) - ((x * i) * 4.0)) - t_1;
	double t_3 = x * ((18.0 * (t * (z * y))) - (i * 4.0));
	double tmp;
	if (x <= -7.5e+201) {
		tmp = t_3;
	} else if (x <= -2.9e-10) {
		tmp = t_2;
	} else if (x <= 5.4e-52) {
		tmp = ((b * c) - (4.0 * (t * a))) - t_1;
	} else if (x <= 4e+114) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = k * (j * 27.0d0)
    t_2 = ((b * c) - ((x * i) * 4.0d0)) - t_1
    t_3 = x * ((18.0d0 * (t * (z * y))) - (i * 4.0d0))
    if (x <= (-7.5d+201)) then
        tmp = t_3
    else if (x <= (-2.9d-10)) then
        tmp = t_2
    else if (x <= 5.4d-52) then
        tmp = ((b * c) - (4.0d0 * (t * a))) - t_1
    else if (x <= 4d+114) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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) - ((x * i) * 4.0)) - t_1;
	double t_3 = x * ((18.0 * (t * (z * y))) - (i * 4.0));
	double tmp;
	if (x <= -7.5e+201) {
		tmp = t_3;
	} else if (x <= -2.9e-10) {
		tmp = t_2;
	} else if (x <= 5.4e-52) {
		tmp = ((b * c) - (4.0 * (t * a))) - t_1;
	} else if (x <= 4e+114) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[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) - ((x * i) * 4.0)) - t_1
	t_3 = x * ((18.0 * (t * (z * y))) - (i * 4.0))
	tmp = 0
	if x <= -7.5e+201:
		tmp = t_3
	elif x <= -2.9e-10:
		tmp = t_2
	elif x <= 5.4e-52:
		tmp = ((b * c) - (4.0 * (t * a))) - t_1
	elif x <= 4e+114:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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(Float64(b * c) - Float64(Float64(x * i) * 4.0)) - t_1)
	t_3 = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(z * y))) - Float64(i * 4.0)))
	tmp = 0.0
	if (x <= -7.5e+201)
		tmp = t_3;
	elseif (x <= -2.9e-10)
		tmp = t_2;
	elseif (x <= 5.4e-52)
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(t * a))) - t_1);
	elseif (x <= 4e+114)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
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) - ((x * i) * 4.0)) - t_1;
	t_3 = x * ((18.0 * (t * (z * y))) - (i * 4.0));
	tmp = 0.0;
	if (x <= -7.5e+201)
		tmp = t_3;
	elseif (x <= -2.9e-10)
		tmp = t_2;
	elseif (x <= 5.4e-52)
		tmp = ((b * c) - (4.0 * (t * a))) - t_1;
	elseif (x <= 4e+114)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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[(N[(b * c), $MachinePrecision] - N[(N[(x * i), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(N[(18.0 * N[(t * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -7.5e+201], t$95$3, If[LessEqual[x, -2.9e-10], t$95$2, If[LessEqual[x, 5.4e-52], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[x, 4e+114], t$95$2, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.5000000000000004e201 or 4e114 < x

   1. Initial program 66.1%

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

   3. Simplified 75.2%

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

   5. Taylor expanded in x around inf 73.2%

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

   if -7.5000000000000004e201 < x < -2.89999999999999981e-10 or 5.40000000000000019e-52 < x < 4e114

   1. Initial program 82.9%

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

   3. Taylor expanded in t around 0 72.5%

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

   if -2.89999999999999981e-10 < x < 5.40000000000000019e-52

   1. Initial program 95.1%

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

   3. Taylor expanded in x around 0 82.4%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{+201}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(z \cdot y\right)\right) - i \cdot 4\right)\\ \mathbf{elif}\;x \leq -2.9 \cdot 10^{-10}:\\ \;\;\;\;\left(b \cdot c - \left(x \cdot i\right) \cdot 4\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;x \leq 5.4 \cdot 10^{-52}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+114}:\\ \;\;\;\;\left(b \cdot c - \left(x \cdot i\right) \cdot 4\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(z \cdot y\right)\right) - i \cdot 4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 84.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := k \cdot \left(j \cdot 27\right)\\ \mathbf{if}\;x \leq -8.4 \cdot 10^{-67} \lor \neg \left(x \leq 1.05 \cdot 10^{-111}\right):\\ \;\;\;\;\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(z \cdot y\right)\right) - i \cdot 4\right)\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b \cdot c + \left(t \cdot 18\right) \cdot \left(z \cdot \left(x \cdot y\right)\right)\right) - 4 \cdot \left(t \cdot a\right)\right) - t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* k (* j 27.0))))
   (if (or (<= x -8.4e-67) (not (<= x 1.05e-111)))
     (- (+ (* b c) (* x (- (* 18.0 (* t (* z y))) (* i 4.0)))) t_1)
     (- (- (+ (* b c) (* (* t 18.0) (* z (* x y)))) (* 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);
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 ((x <= -8.4e-67) || !(x <= 1.05e-111)) {
		tmp = ((b * c) + (x * ((18.0 * (t * (z * y))) - (i * 4.0)))) - t_1;
	} else {
		tmp = (((b * c) + ((t * 18.0) * (z * (x * y)))) - (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.
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 ((x <= (-8.4d-67)) .or. (.not. (x <= 1.05d-111))) then
        tmp = ((b * c) + (x * ((18.0d0 * (t * (z * y))) - (i * 4.0d0)))) - t_1
    else
        tmp = (((b * c) + ((t * 18.0d0) * (z * (x * y)))) - (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;
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 ((x <= -8.4e-67) || !(x <= 1.05e-111)) {
		tmp = ((b * c) + (x * ((18.0 * (t * (z * y))) - (i * 4.0)))) - t_1;
	} else {
		tmp = (((b * c) + ((t * 18.0) * (z * (x * y)))) - (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])
[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 (x <= -8.4e-67) or not (x <= 1.05e-111):
		tmp = ((b * c) + (x * ((18.0 * (t * (z * y))) - (i * 4.0)))) - t_1
	else:
		tmp = (((b * c) + ((t * 18.0) * (z * (x * y)))) - (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])
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 ((x <= -8.4e-67) || !(x <= 1.05e-111))
		tmp = Float64(Float64(Float64(b * c) + Float64(x * Float64(Float64(18.0 * Float64(t * Float64(z * y))) - Float64(i * 4.0)))) - t_1);
	else
		tmp = Float64(Float64(Float64(Float64(b * c) + Float64(Float64(t * 18.0) * Float64(z * Float64(x * y)))) - 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])){:}
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 ((x <= -8.4e-67) || ~((x <= 1.05e-111)))
		tmp = ((b * c) + (x * ((18.0 * (t * (z * y))) - (i * 4.0)))) - t_1;
	else
		tmp = (((b * c) + ((t * 18.0) * (z * (x * y)))) - (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.
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[Or[LessEqual[x, -8.4e-67], N[Not[LessEqual[x, 1.05e-111]], $MachinePrecision]], N[(N[(N[(b * c), $MachinePrecision] + N[(x * N[(N[(18.0 * N[(t * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(N[(N[(b * c), $MachinePrecision] + N[(N[(t * 18.0), $MachinePrecision] * N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -8.4000000000000006e-67 or 1.0499999999999999e-111 < x

   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 x around 0 85.2%

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

   4. Taylor expanded in a around 0 82.6%

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

   if -8.4000000000000006e-67 < x < 1.0499999999999999e-111

   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 80.3%

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

   4. Taylor expanded in t around inf 85.8%

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

      1. associate-*r* 84.8%

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

   6. Simplified 84.8%

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

      1. expm1-log1p-u 29.3%

         \[\leadsto t \cdot \left(18 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(x \cdot \left(y \cdot z\right)\right)\right)} - 4 \cdot a\right) \]

      2. expm1-udef 27.1%

         \[\leadsto t \cdot \left(18 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(x \cdot \left(y \cdot z\right)\right)} - 1\right)} - 4 \cdot a\right) \]

   8. Applied egg-rr 76.5%

      \[\leadsto \left(\left(b \cdot c + \left(18 \cdot t\right) \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(x \cdot \left(y \cdot z\right)\right)} - 1\right)}\right) - 4 \cdot \left(a \cdot t\right)\right) - \left(j \cdot 27\right) \cdot k \]
   9. Step-by-step derivation

      1. expm1-def 29.3%

         \[\leadsto t \cdot \left(18 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(x \cdot \left(y \cdot z\right)\right)\right)} - 4 \cdot a\right) \]

      2. expm1-log1p 34.2%

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

      3. associate-*r* 40.2%

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

   10. Simplified 95.5%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.4 \cdot 10^{-67} \lor \neg \left(x \leq 1.05 \cdot 10^{-111}\right):\\ \;\;\;\;\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(z \cdot y\right)\right) - i \cdot 4\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b \cdot c + \left(t \cdot 18\right) \cdot \left(z \cdot \left(x \cdot y\right)\right)\right) - 4 \cdot \left(t \cdot a\right)\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 85.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := k \cdot \left(j \cdot 27\right)\\ \mathbf{if}\;x \leq -2 \cdot 10^{-150}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(z \cdot y\right) \cdot \left(18 \cdot x\right) - a \cdot 4\right)\right) - \left(x \cdot \left(i \cdot 4\right) + j \cdot \left(k \cdot 27\right)\right)\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{-112}:\\ \;\;\;\;\left(\left(b \cdot c + \left(t \cdot 18\right) \cdot \left(z \cdot \left(x \cdot y\right)\right)\right) - 4 \cdot \left(t \cdot a\right)\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(z \cdot y\right)\right) - i \cdot 4\right)\right) - t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* k (* j 27.0))))
   (if (<= x -2e-150)
     (-
      (+ (* b c) (* t (- (* (* z y) (* 18.0 x)) (* a 4.0))))
      (+ (* x (* i 4.0)) (* j (* k 27.0))))
     (if (<= x 1.75e-112)
       (- (- (+ (* b c) (* (* t 18.0) (* z (* x y)))) (* 4.0 (* t a))) t_1)
       (- (+ (* b c) (* x (- (* 18.0 (* t (* z y))) (* i 4.0)))) t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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 (x <= -2e-150) {
		tmp = ((b * c) + (t * (((z * y) * (18.0 * x)) - (a * 4.0)))) - ((x * (i * 4.0)) + (j * (k * 27.0)));
	} else if (x <= 1.75e-112) {
		tmp = (((b * c) + ((t * 18.0) * (z * (x * y)))) - (4.0 * (t * a))) - t_1;
	} else {
		tmp = ((b * c) + (x * ((18.0 * (t * (z * y))) - (i * 4.0)))) - t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = k * (j * 27.0d0)
    if (x <= (-2d-150)) then
        tmp = ((b * c) + (t * (((z * y) * (18.0d0 * x)) - (a * 4.0d0)))) - ((x * (i * 4.0d0)) + (j * (k * 27.0d0)))
    else if (x <= 1.75d-112) then
        tmp = (((b * c) + ((t * 18.0d0) * (z * (x * y)))) - (4.0d0 * (t * a))) - t_1
    else
        tmp = ((b * c) + (x * ((18.0d0 * (t * (z * y))) - (i * 4.0d0)))) - t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = k * (j * 27.0);
	double tmp;
	if (x <= -2e-150) {
		tmp = ((b * c) + (t * (((z * y) * (18.0 * x)) - (a * 4.0)))) - ((x * (i * 4.0)) + (j * (k * 27.0)));
	} else if (x <= 1.75e-112) {
		tmp = (((b * c) + ((t * 18.0) * (z * (x * y)))) - (4.0 * (t * a))) - t_1;
	} else {
		tmp = ((b * c) + (x * ((18.0 * (t * (z * y))) - (i * 4.0)))) - t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = k * (j * 27.0)
	tmp = 0
	if x <= -2e-150:
		tmp = ((b * c) + (t * (((z * y) * (18.0 * x)) - (a * 4.0)))) - ((x * (i * 4.0)) + (j * (k * 27.0)))
	elif x <= 1.75e-112:
		tmp = (((b * c) + ((t * 18.0) * (z * (x * y)))) - (4.0 * (t * a))) - t_1
	else:
		tmp = ((b * c) + (x * ((18.0 * (t * (z * y))) - (i * 4.0)))) - t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(k * Float64(j * 27.0))
	tmp = 0.0
	if (x <= -2e-150)
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(Float64(z * y) * Float64(18.0 * x)) - Float64(a * 4.0)))) - Float64(Float64(x * Float64(i * 4.0)) + Float64(j * Float64(k * 27.0))));
	elseif (x <= 1.75e-112)
		tmp = Float64(Float64(Float64(Float64(b * c) + Float64(Float64(t * 18.0) * Float64(z * Float64(x * y)))) - Float64(4.0 * Float64(t * a))) - t_1);
	else
		tmp = Float64(Float64(Float64(b * c) + Float64(x * Float64(Float64(18.0 * Float64(t * Float64(z * y))) - Float64(i * 4.0)))) - t_1);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = k * (j * 27.0);
	tmp = 0.0;
	if (x <= -2e-150)
		tmp = ((b * c) + (t * (((z * y) * (18.0 * x)) - (a * 4.0)))) - ((x * (i * 4.0)) + (j * (k * 27.0)));
	elseif (x <= 1.75e-112)
		tmp = (((b * c) + ((t * 18.0) * (z * (x * y)))) - (4.0 * (t * a))) - t_1;
	else
		tmp = ((b * c) + (x * ((18.0 * (t * (z * y))) - (i * 4.0)))) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2e-150], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(N[(z * y), $MachinePrecision] * N[(18.0 * x), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * N[(i * 4.0), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.75e-112], N[(N[(N[(N[(b * c), $MachinePrecision] + N[(N[(t * 18.0), $MachinePrecision] * N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] + N[(x * N[(N[(18.0 * N[(t * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.00000000000000001e-150

   1. Initial program 76.3%

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

   3. Simplified 81.1%

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

   if -2.00000000000000001e-150 < x < 1.74999999999999997e-112

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0 78.7%

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

   4. Taylor expanded in t around inf 85.9%

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

      1. associate-*r* 84.6%

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

   6. Simplified 84.6%

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

      1. expm1-log1p-u 28.7%

         \[\leadsto t \cdot \left(18 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(x \cdot \left(y \cdot z\right)\right)\right)} - 4 \cdot a\right) \]

      2. expm1-udef 25.8%

         \[\leadsto t \cdot \left(18 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(x \cdot \left(y \cdot z\right)\right)} - 1\right)} - 4 \cdot a\right) \]

   8. Applied egg-rr 77.0%

      \[\leadsto \left(\left(b \cdot c + \left(18 \cdot t\right) \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(x \cdot \left(y \cdot z\right)\right)} - 1\right)}\right) - 4 \cdot \left(a \cdot t\right)\right) - \left(j \cdot 27\right) \cdot k \]
   9. Step-by-step derivation

      1. expm1-def 28.7%

         \[\leadsto t \cdot \left(18 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(x \cdot \left(y \cdot z\right)\right)\right)} - 4 \cdot a\right) \]

      2. expm1-log1p 33.4%

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

      3. associate-*r* 41.2%

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

   10. Simplified 97.1%

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

   if 1.74999999999999997e-112 < x

   1. Initial program 77.7%

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

   3. Taylor expanded in x around 0 86.8%

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

   4. Taylor expanded in a around 0 85.0%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{-150}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(z \cdot y\right) \cdot \left(18 \cdot x\right) - a \cdot 4\right)\right) - \left(x \cdot \left(i \cdot 4\right) + j \cdot \left(k \cdot 27\right)\right)\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{-112}:\\ \;\;\;\;\left(\left(b \cdot c + \left(t \cdot 18\right) \cdot \left(z \cdot \left(x \cdot y\right)\right)\right) - 4 \cdot \left(t \cdot a\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(z \cdot y\right)\right) - i \cdot 4\right)\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 57.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c + j \cdot \left(-27 \cdot k\right)\\ t_2 := x \cdot \left(18 \cdot \left(t \cdot \left(z \cdot y\right)\right) - i \cdot 4\right)\\ \mathbf{if}\;x \leq -1.92 \cdot 10^{-66}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{-212}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-89}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;x \leq 1.42 \cdot 10^{+91}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (+ (* b c) (* j (* -27.0 k))))
        (t_2 (* x (- (* 18.0 (* t (* z y))) (* i 4.0)))))
   (if (<= x -1.92e-66)
     t_2
     (if (<= x 2.9e-212)
       t_1
       (if (<= x 5e-89)
         (- (* -4.0 (* t a)) (* k (* j 27.0)))
         (if (<= x 1.42e+91) t_1 t_2))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) + (j * (-27.0 * k));
	double t_2 = x * ((18.0 * (t * (z * y))) - (i * 4.0));
	double tmp;
	if (x <= -1.92e-66) {
		tmp = t_2;
	} else if (x <= 2.9e-212) {
		tmp = t_1;
	} else if (x <= 5e-89) {
		tmp = (-4.0 * (t * a)) - (k * (j * 27.0));
	} else if (x <= 1.42e+91) {
		tmp = 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.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (b * c) + (j * ((-27.0d0) * k))
    t_2 = x * ((18.0d0 * (t * (z * y))) - (i * 4.0d0))
    if (x <= (-1.92d-66)) then
        tmp = t_2
    else if (x <= 2.9d-212) then
        tmp = t_1
    else if (x <= 5d-89) then
        tmp = ((-4.0d0) * (t * a)) - (k * (j * 27.0d0))
    else if (x <= 1.42d+91) then
        tmp = 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;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) + (j * (-27.0 * k));
	double t_2 = x * ((18.0 * (t * (z * y))) - (i * 4.0));
	double tmp;
	if (x <= -1.92e-66) {
		tmp = t_2;
	} else if (x <= 2.9e-212) {
		tmp = t_1;
	} else if (x <= 5e-89) {
		tmp = (-4.0 * (t * a)) - (k * (j * 27.0));
	} else if (x <= 1.42e+91) {
		tmp = 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])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) + (j * (-27.0 * k))
	t_2 = x * ((18.0 * (t * (z * y))) - (i * 4.0))
	tmp = 0
	if x <= -1.92e-66:
		tmp = t_2
	elif x <= 2.9e-212:
		tmp = t_1
	elif x <= 5e-89:
		tmp = (-4.0 * (t * a)) - (k * (j * 27.0))
	elif x <= 1.42e+91:
		tmp = 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])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) + Float64(j * Float64(-27.0 * k)))
	t_2 = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(z * y))) - Float64(i * 4.0)))
	tmp = 0.0
	if (x <= -1.92e-66)
		tmp = t_2;
	elseif (x <= 2.9e-212)
		tmp = t_1;
	elseif (x <= 5e-89)
		tmp = Float64(Float64(-4.0 * Float64(t * a)) - Float64(k * Float64(j * 27.0)));
	elseif (x <= 1.42e+91)
		tmp = 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])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) + (j * (-27.0 * k));
	t_2 = x * ((18.0 * (t * (z * y))) - (i * 4.0));
	tmp = 0.0;
	if (x <= -1.92e-66)
		tmp = t_2;
	elseif (x <= 2.9e-212)
		tmp = t_1;
	elseif (x <= 5e-89)
		tmp = (-4.0 * (t * a)) - (k * (j * 27.0));
	elseif (x <= 1.42e+91)
		tmp = 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.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] + N[(j * N[(-27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(18.0 * N[(t * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.92e-66], t$95$2, If[LessEqual[x, 2.9e-212], t$95$1, If[LessEqual[x, 5e-89], N[(N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.42e+91], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.92e-66 or 1.41999999999999995e91 < x

   1. Initial program 70.1%

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

   3. Simplified 79.8%

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

   5. Taylor expanded in x around inf 65.1%

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

   if -1.92e-66 < x < 2.8999999999999999e-212 or 4.99999999999999967e-89 < x < 1.41999999999999995e91

   1. Initial program 94.4%

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

   3. Simplified 87.4%

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

   5. Taylor expanded in b around inf 61.4%

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

   if 2.8999999999999999e-212 < x < 4.99999999999999967e-89

   1. Initial program 95.9%

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

   3. Taylor expanded in x around 0 78.3%

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

   4. Taylor expanded in a around inf 78.5%

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

      1. *-commutative 78.5%

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

   6. Simplified 78.5%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.92 \cdot 10^{-66}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(z \cdot y\right)\right) - i \cdot 4\right)\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{-212}:\\ \;\;\;\;b \cdot c + j \cdot \left(-27 \cdot k\right)\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-89}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;x \leq 1.42 \cdot 10^{+91}:\\ \;\;\;\;b \cdot c + j \cdot \left(-27 \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(z \cdot y\right)\right) - i \cdot 4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 81.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := k \cdot \left(j \cdot 27\right)\\ \mathbf{if}\;x \leq -9.8 \cdot 10^{-67} \lor \neg \left(x \leq 1.95 \cdot 10^{-53}\right):\\ \;\;\;\;\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(z \cdot y\right)\right) - i \cdot 4\right)\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* k (* j 27.0))))
   (if (or (<= x -9.8e-67) (not (<= x 1.95e-53)))
     (- (+ (* b c) (* x (- (* 18.0 (* t (* z y))) (* i 4.0)))) t_1)
     (- (- (* 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);
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 ((x <= -9.8e-67) || !(x <= 1.95e-53)) {
		tmp = ((b * c) + (x * ((18.0 * (t * (z * y))) - (i * 4.0)))) - t_1;
	} else {
		tmp = ((b * c) - (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.
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 ((x <= (-9.8d-67)) .or. (.not. (x <= 1.95d-53))) then
        tmp = ((b * c) + (x * ((18.0d0 * (t * (z * y))) - (i * 4.0d0)))) - t_1
    else
        tmp = ((b * c) - (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;
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 ((x <= -9.8e-67) || !(x <= 1.95e-53)) {
		tmp = ((b * c) + (x * ((18.0 * (t * (z * y))) - (i * 4.0)))) - t_1;
	} else {
		tmp = ((b * c) - (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])
[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 (x <= -9.8e-67) or not (x <= 1.95e-53):
		tmp = ((b * c) + (x * ((18.0 * (t * (z * y))) - (i * 4.0)))) - t_1
	else:
		tmp = ((b * c) - (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])
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 ((x <= -9.8e-67) || !(x <= 1.95e-53))
		tmp = Float64(Float64(Float64(b * c) + Float64(x * Float64(Float64(18.0 * Float64(t * Float64(z * y))) - Float64(i * 4.0)))) - t_1);
	else
		tmp = Float64(Float64(Float64(b * c) - 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])){:}
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 ((x <= -9.8e-67) || ~((x <= 1.95e-53)))
		tmp = ((b * c) + (x * ((18.0 * (t * (z * y))) - (i * 4.0)))) - t_1;
	else
		tmp = ((b * c) - (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.
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[Or[LessEqual[x, -9.8e-67], N[Not[LessEqual[x, 1.95e-53]], $MachinePrecision]], N[(N[(N[(b * c), $MachinePrecision] + N[(x * N[(N[(18.0 * N[(t * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -9.79999999999999987e-67 or 1.9500000000000001e-53 < 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. Add Preprocessing

   3. Taylor expanded in x around 0 85.6%

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

   4. Taylor expanded in a around 0 84.0%

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

   if -9.79999999999999987e-67 < x < 1.9500000000000001e-53

   1. Initial program 95.8%

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

   3. Taylor expanded in x around 0 86.0%

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

4. Final simplification 84.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.8 \cdot 10^{-67} \lor \neg \left(x \leq 1.95 \cdot 10^{-53}\right):\\ \;\;\;\;\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(z \cdot y\right)\right) - i \cdot 4\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 34.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := -27 \cdot \left(j \cdot k\right)\\ \mathbf{if}\;k \leq -3.5 \cdot 10^{+30}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;k \leq 3.6 \cdot 10^{-257}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(y \cdot \left(z \cdot x\right)\right)\right)\\ \mathbf{elif}\;k \leq 9 \cdot 10^{-47}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 1.8 \cdot 10^{-13}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(z \cdot y\right)\right)\right)\\ \mathbf{elif}\;k \leq 6.5 \cdot 10^{+92}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 -3.5e+30)
     t_1
     (if (<= k 3.6e-257)
       (* 18.0 (* t (* y (* z x))))
       (if (<= k 9e-47)
         (* b c)
         (if (<= k 1.8e-13)
           (* 18.0 (* t (* x (* z y))))
           (if (<= k 6.5e+92) (* b c) t_1)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -27.0 * (j * k);
	double tmp;
	if (k <= -3.5e+30) {
		tmp = t_1;
	} else if (k <= 3.6e-257) {
		tmp = 18.0 * (t * (y * (z * x)));
	} else if (k <= 9e-47) {
		tmp = b * c;
	} else if (k <= 1.8e-13) {
		tmp = 18.0 * (t * (x * (z * y)));
	} else if (k <= 6.5e+92) {
		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.
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 <= (-3.5d+30)) then
        tmp = t_1
    else if (k <= 3.6d-257) then
        tmp = 18.0d0 * (t * (y * (z * x)))
    else if (k <= 9d-47) then
        tmp = b * c
    else if (k <= 1.8d-13) then
        tmp = 18.0d0 * (t * (x * (z * y)))
    else if (k <= 6.5d+92) 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;
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 <= -3.5e+30) {
		tmp = t_1;
	} else if (k <= 3.6e-257) {
		tmp = 18.0 * (t * (y * (z * x)));
	} else if (k <= 9e-47) {
		tmp = b * c;
	} else if (k <= 1.8e-13) {
		tmp = 18.0 * (t * (x * (z * y)));
	} else if (k <= 6.5e+92) {
		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])
[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 <= -3.5e+30:
		tmp = t_1
	elif k <= 3.6e-257:
		tmp = 18.0 * (t * (y * (z * x)))
	elif k <= 9e-47:
		tmp = b * c
	elif k <= 1.8e-13:
		tmp = 18.0 * (t * (x * (z * y)))
	elif k <= 6.5e+92:
		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])
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 <= -3.5e+30)
		tmp = t_1;
	elseif (k <= 3.6e-257)
		tmp = Float64(18.0 * Float64(t * Float64(y * Float64(z * x))));
	elseif (k <= 9e-47)
		tmp = Float64(b * c);
	elseif (k <= 1.8e-13)
		tmp = Float64(18.0 * Float64(t * Float64(x * Float64(z * y))));
	elseif (k <= 6.5e+92)
		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])){:}
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 <= -3.5e+30)
		tmp = t_1;
	elseif (k <= 3.6e-257)
		tmp = 18.0 * (t * (y * (z * x)));
	elseif (k <= 9e-47)
		tmp = b * c;
	elseif (k <= 1.8e-13)
		tmp = 18.0 * (t * (x * (z * y)));
	elseif (k <= 6.5e+92)
		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.
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, -3.5e+30], t$95$1, If[LessEqual[k, 3.6e-257], N[(18.0 * N[(t * N[(y * N[(z * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 9e-47], N[(b * c), $MachinePrecision], If[LessEqual[k, 1.8e-13], N[(18.0 * N[(t * N[(x * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 6.5e+92], N[(b * c), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if k < -3.50000000000000021e30 or 6.49999999999999999e92 < k

   1. Initial program 87.0%

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

   3. Simplified 83.2%

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

   5. Taylor expanded in j around inf 52.7%

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

   if -3.50000000000000021e30 < k < 3.60000000000000007e-257

   1. Initial program 78.3%

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

   3. Simplified 89.9%

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

   5. Taylor expanded in t around 0 84.7%

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

   7. Simplified 87.3%

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

   8. Taylor expanded in z around inf 28.2%

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

      1. associate-*r* 29.4%

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

      2. *-commutative 29.4%

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

   10. Simplified 29.4%

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

   11. Taylor expanded in z around 0 28.2%

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

       1. *-commutative 28.2%

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

       2. associate-*l* 29.4%

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

   13. Simplified 29.4%

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

   if 3.60000000000000007e-257 < k < 9e-47 or 1.7999999999999999e-13 < k < 6.49999999999999999e92

   1. Initial program 84.9%

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

   3. Simplified 85.3%

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

   5. Taylor expanded in t around 0 83.7%

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

   7. Simplified 89.5%

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

   8. Taylor expanded in b around inf 35.6%

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

   if 9e-47 < k < 1.7999999999999999e-13

   1. Initial program 73.1%

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

   3. Simplified 86.6%

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

   5. Taylor expanded in t around 0 86.5%

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

   7. Simplified 86.5%

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

   8. Taylor expanded in z around inf 31.0%

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

4. Final simplification 40.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -3.5 \cdot 10^{+30}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;k \leq 3.6 \cdot 10^{-257}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(y \cdot \left(z \cdot x\right)\right)\right)\\ \mathbf{elif}\;k \leq 9 \cdot 10^{-47}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 1.8 \cdot 10^{-13}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(z \cdot y\right)\right)\right)\\ \mathbf{elif}\;k \leq 6.5 \cdot 10^{+92}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 33.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := -27 \cdot \left(j \cdot k\right)\\ \mathbf{if}\;k \leq -2.3 \cdot 10^{+30}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;k \leq 7 \cdot 10^{-248}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(z \cdot \left(x \cdot y\right)\right)\right)\\ \mathbf{elif}\;k \leq 3.8 \cdot 10^{-47}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 3.9 \cdot 10^{-17}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(z \cdot y\right)\right)\right)\\ \mathbf{elif}\;k \leq 1.75 \cdot 10^{+88}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 -2.3e+30)
     t_1
     (if (<= k 7e-248)
       (* 18.0 (* t (* z (* x y))))
       (if (<= k 3.8e-47)
         (* b c)
         (if (<= k 3.9e-17)
           (* 18.0 (* t (* x (* z y))))
           (if (<= k 1.75e+88) (* b c) t_1)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -27.0 * (j * k);
	double tmp;
	if (k <= -2.3e+30) {
		tmp = t_1;
	} else if (k <= 7e-248) {
		tmp = 18.0 * (t * (z * (x * y)));
	} else if (k <= 3.8e-47) {
		tmp = b * c;
	} else if (k <= 3.9e-17) {
		tmp = 18.0 * (t * (x * (z * y)));
	} else if (k <= 1.75e+88) {
		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.
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 <= (-2.3d+30)) then
        tmp = t_1
    else if (k <= 7d-248) then
        tmp = 18.0d0 * (t * (z * (x * y)))
    else if (k <= 3.8d-47) then
        tmp = b * c
    else if (k <= 3.9d-17) then
        tmp = 18.0d0 * (t * (x * (z * y)))
    else if (k <= 1.75d+88) 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;
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 <= -2.3e+30) {
		tmp = t_1;
	} else if (k <= 7e-248) {
		tmp = 18.0 * (t * (z * (x * y)));
	} else if (k <= 3.8e-47) {
		tmp = b * c;
	} else if (k <= 3.9e-17) {
		tmp = 18.0 * (t * (x * (z * y)));
	} else if (k <= 1.75e+88) {
		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])
[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 <= -2.3e+30:
		tmp = t_1
	elif k <= 7e-248:
		tmp = 18.0 * (t * (z * (x * y)))
	elif k <= 3.8e-47:
		tmp = b * c
	elif k <= 3.9e-17:
		tmp = 18.0 * (t * (x * (z * y)))
	elif k <= 1.75e+88:
		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])
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 <= -2.3e+30)
		tmp = t_1;
	elseif (k <= 7e-248)
		tmp = Float64(18.0 * Float64(t * Float64(z * Float64(x * y))));
	elseif (k <= 3.8e-47)
		tmp = Float64(b * c);
	elseif (k <= 3.9e-17)
		tmp = Float64(18.0 * Float64(t * Float64(x * Float64(z * y))));
	elseif (k <= 1.75e+88)
		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])){:}
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 <= -2.3e+30)
		tmp = t_1;
	elseif (k <= 7e-248)
		tmp = 18.0 * (t * (z * (x * y)));
	elseif (k <= 3.8e-47)
		tmp = b * c;
	elseif (k <= 3.9e-17)
		tmp = 18.0 * (t * (x * (z * y)));
	elseif (k <= 1.75e+88)
		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.
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, -2.3e+30], t$95$1, If[LessEqual[k, 7e-248], N[(18.0 * N[(t * N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 3.8e-47], N[(b * c), $MachinePrecision], If[LessEqual[k, 3.9e-17], N[(18.0 * N[(t * N[(x * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 1.75e+88], N[(b * c), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if k < -2.3e30 or 1.7499999999999999e88 < k

   1. Initial program 87.0%

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

   3. Simplified 83.2%

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

   5. Taylor expanded in j around inf 52.7%

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

   if -2.3e30 < k < 6.99999999999999966e-248

   1. Initial program 77.6%

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

   3. Simplified 88.9%

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

   5. Taylor expanded in t around 0 83.9%

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

   7. Simplified 86.4%

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

   8. Taylor expanded in z around inf 27.6%

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

      1. associate-*r* 28.8%

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

      2. *-commutative 28.8%

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

   10. Simplified 28.8%

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

   if 6.99999999999999966e-248 < k < 3.80000000000000015e-47 or 3.89999999999999989e-17 < k < 1.7499999999999999e88

   1. Initial program 84.0%

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

   3. Simplified 84.3%

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

   5. Taylor expanded in t around 0 82.8%

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

   7. Simplified 88.4%

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

   8. Taylor expanded in b around inf 36.0%

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

   if 3.80000000000000015e-47 < k < 3.89999999999999989e-17

   1. Initial program 80.9%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around 0 99.7%

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

   7. Simplified 99.7%

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

   8. Taylor expanded in z around inf 41.8%

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

4. Final simplification 40.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -2.3 \cdot 10^{+30}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;k \leq 7 \cdot 10^{-248}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(z \cdot \left(x \cdot y\right)\right)\right)\\ \mathbf{elif}\;k \leq 3.8 \cdot 10^{-47}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 3.9 \cdot 10^{-17}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(z \cdot y\right)\right)\right)\\ \mathbf{elif}\;k \leq 1.75 \cdot 10^{+88}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 54.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -3 \cdot 10^{+123} \lor \neg \left(b \cdot c \leq 3.5 \cdot 10^{+134}\right):\\ \;\;\;\;b \cdot c + j \cdot \left(-27 \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right) + -4 \cdot \left(x \cdot i\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= (* b c) -3e+123) (not (<= (* b c) 3.5e+134)))
   (+ (* b c) (* j (* -27.0 k)))
   (+ (* -27.0 (* j k)) (* -4.0 (* x i)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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) <= -3e+123) || !((b * c) <= 3.5e+134)) {
		tmp = (b * c) + (j * (-27.0 * k));
	} else {
		tmp = (-27.0 * (j * k)) + (-4.0 * (x * i));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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) <= (-3d+123)) .or. (.not. ((b * c) <= 3.5d+134))) then
        tmp = (b * c) + (j * ((-27.0d0) * k))
    else
        tmp = ((-27.0d0) * (j * k)) + ((-4.0d0) * (x * i))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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) <= -3e+123) || !((b * c) <= 3.5e+134)) {
		tmp = (b * c) + (j * (-27.0 * k));
	} else {
		tmp = (-27.0 * (j * k)) + (-4.0 * (x * i));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[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) <= -3e+123) or not ((b * c) <= 3.5e+134):
		tmp = (b * c) + (j * (-27.0 * k))
	else:
		tmp = (-27.0 * (j * k)) + (-4.0 * (x * i))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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) <= -3e+123) || !(Float64(b * c) <= 3.5e+134))
		tmp = Float64(Float64(b * c) + Float64(j * Float64(-27.0 * k)));
	else
		tmp = Float64(Float64(-27.0 * Float64(j * k)) + Float64(-4.0 * Float64(x * i)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
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) <= -3e+123) || ~(((b * c) <= 3.5e+134)))
		tmp = (b * c) + (j * (-27.0 * k));
	else
		tmp = (-27.0 * (j * k)) + (-4.0 * (x * i));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[N[(b * c), $MachinePrecision], -3e+123], N[Not[LessEqual[N[(b * c), $MachinePrecision], 3.5e+134]], $MachinePrecision]], N[(N[(b * c), $MachinePrecision] + N[(j * N[(-27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -3.00000000000000008e123 or 3.50000000000000003e134 < (*.f64 b c)

   1. Initial program 76.0%

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

   3. Simplified 86.7%

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

   5. Taylor expanded in b around inf 69.4%

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

   if -3.00000000000000008e123 < (*.f64 b c) < 3.50000000000000003e134

   1. Initial program 85.9%

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

   3. Simplified 85.7%

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

   5. Taylor expanded in i around inf 53.0%

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

   6. Taylor expanded in i around 0 54.1%

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

4. Final simplification 58.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -3 \cdot 10^{+123} \lor \neg \left(b \cdot c \leq 3.5 \cdot 10^{+134}\right):\\ \;\;\;\;b \cdot c + j \cdot \left(-27 \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right) + -4 \cdot \left(x \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 69.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{-66} \lor \neg \left(x \leq 2.1 \cdot 10^{+99}\right):\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(z \cdot y\right)\right) - i \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= x -2e-66) (not (<= x 2.1e+99)))
   (* x (- (* 18.0 (* t (* z y))) (* i 4.0)))
   (- (- (* b c) (* 4.0 (* t a))) (* k (* j 27.0)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((x <= -2e-66) || !(x <= 2.1e+99)) {
		tmp = x * ((18.0 * (t * (z * y))) - (i * 4.0));
	} else {
		tmp = ((b * c) - (4.0 * (t * a))) - (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.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((x <= (-2d-66)) .or. (.not. (x <= 2.1d+99))) then
        tmp = x * ((18.0d0 * (t * (z * y))) - (i * 4.0d0))
    else
        tmp = ((b * c) - (4.0d0 * (t * a))) - (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;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((x <= -2e-66) || !(x <= 2.1e+99)) {
		tmp = x * ((18.0 * (t * (z * y))) - (i * 4.0));
	} else {
		tmp = ((b * c) - (4.0 * (t * a))) - (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])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (x <= -2e-66) or not (x <= 2.1e+99):
		tmp = x * ((18.0 * (t * (z * y))) - (i * 4.0))
	else:
		tmp = ((b * c) - (4.0 * (t * a))) - (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])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((x <= -2e-66) || !(x <= 2.1e+99))
		tmp = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(z * y))) - Float64(i * 4.0)));
	else
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(t * a))) - 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])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((x <= -2e-66) || ~((x <= 2.1e+99)))
		tmp = x * ((18.0 * (t * (z * y))) - (i * 4.0));
	else
		tmp = ((b * c) - (4.0 * (t * a))) - (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.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[x, -2e-66], N[Not[LessEqual[x, 2.1e+99]], $MachinePrecision]], N[(x * N[(N[(18.0 * N[(t * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2e-66 or 2.1000000000000001e99 < x

   1. Initial program 70.4%

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

   3. Simplified 80.2%

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

   5. Taylor expanded in x around inf 66.2%

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

   if -2e-66 < x < 2.1000000000000001e99

   1. Initial program 94.1%

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

   3. Taylor expanded in x around 0 78.8%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{-66} \lor \neg \left(x \leq 2.1 \cdot 10^{+99}\right):\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(z \cdot y\right)\right) - i \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 47.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := 18 \cdot \left(\left(z \cdot y\right) \cdot \left(t \cdot x\right)\right)\\ \mathbf{if}\;x \leq -1.35 \cdot 10^{+188}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{+96}:\\ \;\;\;\;b \cdot c + j \cdot \left(-27 \cdot k\right)\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{+234}:\\ \;\;\;\;i \cdot \left(-4 \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* 18.0 (* (* z y) (* t x)))))
   (if (<= x -1.35e+188)
     t_1
     (if (<= x 2.1e+96)
       (+ (* b c) (* j (* -27.0 k)))
       (if (<= x 6.5e+234) (* i (* -4.0 x)) t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 18.0 * ((z * y) * (t * x));
	double tmp;
	if (x <= -1.35e+188) {
		tmp = t_1;
	} else if (x <= 2.1e+96) {
		tmp = (b * c) + (j * (-27.0 * k));
	} else if (x <= 6.5e+234) {
		tmp = i * (-4.0 * x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 18.0d0 * ((z * y) * (t * x))
    if (x <= (-1.35d+188)) then
        tmp = t_1
    else if (x <= 2.1d+96) then
        tmp = (b * c) + (j * ((-27.0d0) * k))
    else if (x <= 6.5d+234) then
        tmp = i * ((-4.0d0) * x)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 18.0 * ((z * y) * (t * x));
	double tmp;
	if (x <= -1.35e+188) {
		tmp = t_1;
	} else if (x <= 2.1e+96) {
		tmp = (b * c) + (j * (-27.0 * k));
	} else if (x <= 6.5e+234) {
		tmp = i * (-4.0 * x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = 18.0 * ((z * y) * (t * x))
	tmp = 0
	if x <= -1.35e+188:
		tmp = t_1
	elif x <= 2.1e+96:
		tmp = (b * c) + (j * (-27.0 * k))
	elif x <= 6.5e+234:
		tmp = i * (-4.0 * x)
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(18.0 * Float64(Float64(z * y) * Float64(t * x)))
	tmp = 0.0
	if (x <= -1.35e+188)
		tmp = t_1;
	elseif (x <= 2.1e+96)
		tmp = Float64(Float64(b * c) + Float64(j * Float64(-27.0 * k)));
	elseif (x <= 6.5e+234)
		tmp = Float64(i * Float64(-4.0 * x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = 18.0 * ((z * y) * (t * x));
	tmp = 0.0;
	if (x <= -1.35e+188)
		tmp = t_1;
	elseif (x <= 2.1e+96)
		tmp = (b * c) + (j * (-27.0 * k));
	elseif (x <= 6.5e+234)
		tmp = i * (-4.0 * x);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(18.0 * N[(N[(z * y), $MachinePrecision] * N[(t * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.35e+188], t$95$1, If[LessEqual[x, 2.1e+96], N[(N[(b * c), $MachinePrecision] + N[(j * N[(-27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.5e+234], N[(i * N[(-4.0 * x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.35e188 or 6.4999999999999995e234 < x

   1. Initial program 59.4%

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

   3. Simplified 72.3%

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

   5. Taylor expanded in t around 0 70.1%

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

   7. Simplified 65.8%

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

   8. Taylor expanded in z around inf 49.7%

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

      1. associate-*r* 55.8%

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

      2. *-commutative 55.8%

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

   10. Simplified 55.8%

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

   11. Taylor expanded in t around 0 49.7%

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

       1. associate-*r* 61.4%

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

   13. Simplified 61.4%

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

   if -1.35e188 < x < 2.1000000000000001e96

   1. Initial program 91.4%

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

   3. Simplified 88.8%

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

   5. Taylor expanded in b around inf 54.9%

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

   if 2.1000000000000001e96 < x < 6.4999999999999995e234

   1. Initial program 73.0%

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

   3. Simplified 89.5%

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

   5. Taylor expanded in t around 0 81.1%

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

   7. Simplified 81.3%

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

   8. Taylor expanded in i around inf 51.3%

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

      1. *-commutative 51.3%

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

      2. associate-*r* 51.3%

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

   10. Simplified 51.3%

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

4. Final simplification 55.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{+188}:\\ \;\;\;\;18 \cdot \left(\left(z \cdot y\right) \cdot \left(t \cdot x\right)\right)\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{+96}:\\ \;\;\;\;b \cdot c + j \cdot \left(-27 \cdot k\right)\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{+234}:\\ \;\;\;\;i \cdot \left(-4 \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;18 \cdot \left(\left(z \cdot y\right) \cdot \left(t \cdot x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 36.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.02 \cdot 10^{+177} \lor \neg \left(b \cdot c \leq 9.5 \cdot 10^{+87}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= (* b c) -1.02e+177) (not (<= (* b c) 9.5e+87)))
   (* b c)
   (* -27.0 (* j k))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (((b * c) <= -1.02e+177) || !((b * c) <= 9.5e+87)) {
		tmp = b * c;
	} else {
		tmp = -27.0 * (j * k);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (((b * c) <= (-1.02d+177)) .or. (.not. ((b * c) <= 9.5d+87))) then
        tmp = b * c
    else
        tmp = (-27.0d0) * (j * k)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (((b * c) <= -1.02e+177) || !((b * c) <= 9.5e+87)) {
		tmp = b * c;
	} else {
		tmp = -27.0 * (j * k);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if ((b * c) <= -1.02e+177) or not ((b * c) <= 9.5e+87):
		tmp = b * c
	else:
		tmp = -27.0 * (j * k)
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((Float64(b * c) <= -1.02e+177) || !(Float64(b * c) <= 9.5e+87))
		tmp = Float64(b * c);
	else
		tmp = Float64(-27.0 * Float64(j * k));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (((b * c) <= -1.02e+177) || ~(((b * c) <= 9.5e+87)))
		tmp = b * c;
	else
		tmp = -27.0 * (j * k);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[N[(b * c), $MachinePrecision], -1.02e+177], N[Not[LessEqual[N[(b * c), $MachinePrecision], 9.5e+87]], $MachinePrecision]], N[(b * c), $MachinePrecision], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -1.02e177 or 9.4999999999999992e87 < (*.f64 b c)

   1. Initial program 74.5%

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

   3. Simplified 85.9%

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

   5. Taylor expanded in t around 0 79.4%

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

   7. Simplified 85.9%

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

   8. Taylor expanded in b around inf 58.1%

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

   if -1.02e177 < (*.f64 b c) < 9.4999999999999992e87

   1. Initial program 86.7%

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

   3. Simplified 86.0%

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

   5. Taylor expanded in j around inf 32.5%

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

4. Final simplification 40.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.02 \cdot 10^{+177} \lor \neg \left(b \cdot c \leq 9.5 \cdot 10^{+87}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 23.7% accurate, 10.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ b \cdot c \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k) :precision binary64 (* b c))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	return b * c;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    code = b * c
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	return b * c;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	return b * c

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	return Float64(b * c)
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp = code(x, y, z, t, a, b, c, i, j, k)
	tmp = b * c;
end

Wolfram

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

Derivation

1. Initial program 83.1%

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

3. Simplified 85.9%

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

5. Taylor expanded in t around 0 84.4%

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

7. Simplified 88.9%

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

8. Taylor expanded in b around inf 21.6%

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

9. Final simplification 21.6%

   \[\leadsto b \cdot c \]
10. Add Preprocessing

Developer target: 89.3% 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 2024031 
(FPCore (x y z t a b c i j k)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, E"
  :precision binary64

  :herbie-target
  (if (< t -1.6210815397541398e-69) (- (- (* (* 18.0 t) (* (* x y) z)) (* (+ (* a t) (* i x)) 4.0)) (- (* (* k j) 27.0) (* c b))) (if (< t 165.68027943805222) (+ (- (* (* 18.0 y) (* x (* z t))) (* (+ (* a t) (* i x)) 4.0)) (- (* c b) (* 27.0 (* k j)))) (- (- (* (* 18.0 t) (* (* x y) z)) (* (+ (* a t) (* i x)) 4.0)) (- (* (* k j) 27.0) (* c b)))))

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