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

Percentage Accurate: 84.6% → 91.9%

Time: 19.6s

Alternatives: 26

Speedup: 0.9×

• 50.8% 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: 84.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 91.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 53000000:\\ \;\;\;\;\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(z \cdot y\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(-4 \cdot i\right)\right)\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \mathsf{fma}\left(-27, j \cdot \frac{k}{z}, \mathsf{fma}\left(-4, a \cdot \frac{t}{z}, \mathsf{fma}\left(-4, i \cdot \frac{x}{z}, \mathsf{fma}\left(18, t \cdot \left(x \cdot y\right), b \cdot \frac{c}{z}\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 (<= z 53000000.0)
   (+
    (fma t (fma x (* 18.0 (* z y)) (* a -4.0)) (fma b c (* x (* -4.0 i))))
    (* j (* k -27.0)))
   (*
    z
    (fma
     -27.0
     (* j (/ k z))
     (fma
      -4.0
      (* a (/ t z))
      (fma -4.0 (* i (/ x z)) (fma 18.0 (* t (* x y)) (* b (/ c z)))))))))

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);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (z <= 53000000.0) {
		tmp = fma(t, fma(x, (18.0 * (z * y)), (a * -4.0)), fma(b, c, (x * (-4.0 * i)))) + (j * (k * -27.0));
	} else {
		tmp = z * fma(-27.0, (j * (k / z)), fma(-4.0, (a * (t / z)), fma(-4.0, (i * (x / z)), fma(18.0, (t * (x * y)), (b * (c / z))))));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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 (z <= 53000000.0)
		tmp = Float64(fma(t, fma(x, Float64(18.0 * Float64(z * y)), Float64(a * -4.0)), fma(b, c, Float64(x * Float64(-4.0 * i)))) + Float64(j * Float64(k * -27.0)));
	else
		tmp = Float64(z * fma(-27.0, Float64(j * Float64(k / z)), fma(-4.0, Float64(a * Float64(t / z)), fma(-4.0, Float64(i * Float64(x / z)), fma(18.0, Float64(t * Float64(x * y)), Float64(b * Float64(c / z)))))));
	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.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[z, 53000000.0], N[(N[(t * N[(x * N[(18.0 * N[(z * y), $MachinePrecision]), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + N[(b * c + N[(x * N[(-4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(-27.0 * N[(j * N[(k / z), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * N[(a * N[(t / z), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * N[(i * N[(x / z), $MachinePrecision]), $MachinePrecision] + N[(18.0 * N[(t * N[(x * y), $MachinePrecision]), $MachinePrecision] + N[(b * N[(c / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 5.3e7

   1. Initial program 86.6%

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

   3. Simplified 91.7%

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

   if 5.3e7 < z

   1. Initial program 88.9%

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

   3. Simplified 79.9%

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

   5. Taylor expanded in z around inf 90.4%

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

      1. fma-define 90.3%

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

      2. associate-/l* 89.7%

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

      3. fma-define 89.7%

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

      4. associate-/l* 89.7%

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

      5. fma-define 89.7%

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

      6. associate-/l* 89.9%

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

      7. fma-define 89.9%

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

      8. *-commutative 89.9%

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

      9. associate-/l* 88.3%

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

   7. Simplified 88.3%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 53000000:\\ \;\;\;\;\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(z \cdot y\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(-4 \cdot i\right)\right)\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \mathsf{fma}\left(-27, j \cdot \frac{k}{z}, \mathsf{fma}\left(-4, a \cdot \frac{t}{z}, \mathsf{fma}\left(-4, i \cdot \frac{x}{z}, \mathsf{fma}\left(18, t \cdot \left(x \cdot y\right), b \cdot \frac{c}{z}\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 53.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := k \cdot \left(j \cdot 27\right)\\ t_2 := t \cdot \left(18 \cdot \left(x \cdot \left(z \cdot y\right)\right) - a \cdot 4\right)\\ \mathbf{if}\;t\_1 \leq -10:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \mathbf{elif}\;t\_1 \leq -1 \cdot 10^{-83}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-318}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-147}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-109}:\\ \;\;\;\;x \cdot \left(-4 \cdot i + b \cdot \frac{c}{x}\right)\\ \mathbf{elif}\;t\_1 \leq 10^{-13}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(z \cdot y\right)\right) - i \cdot 4\right)\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+74}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(\frac{b \cdot c}{k} - j \cdot 27\right)\\ \end{array} \end{array} \]

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.
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 (* t (- (* 18.0 (* x (* z y))) (* a 4.0)))))
   (if (<= t_1 -10.0)
     (+ (* j (* k -27.0)) (* b c))
     (if (<= t_1 -1e-83)
       t_2
       (if (<= t_1 2e-318)
         (- (* b c) (* 4.0 (* x i)))
         (if (<= t_1 2e-147)
           t_2
           (if (<= t_1 5e-109)
             (* x (+ (* -4.0 i) (* b (/ c x))))
             (if (<= t_1 1e-13)
               (* x (- (* 18.0 (* t (* z y))) (* i 4.0)))
               (if (<= t_1 2e+74)
                 t_2
                 (* k (- (/ (* b c) 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);
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 = t * ((18.0 * (x * (z * y))) - (a * 4.0));
	double tmp;
	if (t_1 <= -10.0) {
		tmp = (j * (k * -27.0)) + (b * c);
	} else if (t_1 <= -1e-83) {
		tmp = t_2;
	} else if (t_1 <= 2e-318) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if (t_1 <= 2e-147) {
		tmp = t_2;
	} else if (t_1 <= 5e-109) {
		tmp = x * ((-4.0 * i) + (b * (c / x)));
	} else if (t_1 <= 1e-13) {
		tmp = x * ((18.0 * (t * (z * y))) - (i * 4.0));
	} else if (t_1 <= 2e+74) {
		tmp = t_2;
	} else {
		tmp = k * (((b * c) / 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.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = k * (j * 27.0d0)
    t_2 = t * ((18.0d0 * (x * (z * y))) - (a * 4.0d0))
    if (t_1 <= (-10.0d0)) then
        tmp = (j * (k * (-27.0d0))) + (b * c)
    else if (t_1 <= (-1d-83)) then
        tmp = t_2
    else if (t_1 <= 2d-318) then
        tmp = (b * c) - (4.0d0 * (x * i))
    else if (t_1 <= 2d-147) then
        tmp = t_2
    else if (t_1 <= 5d-109) then
        tmp = x * (((-4.0d0) * i) + (b * (c / x)))
    else if (t_1 <= 1d-13) then
        tmp = x * ((18.0d0 * (t * (z * y))) - (i * 4.0d0))
    else if (t_1 <= 2d+74) then
        tmp = t_2
    else
        tmp = k * (((b * c) / 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;
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 = t * ((18.0 * (x * (z * y))) - (a * 4.0));
	double tmp;
	if (t_1 <= -10.0) {
		tmp = (j * (k * -27.0)) + (b * c);
	} else if (t_1 <= -1e-83) {
		tmp = t_2;
	} else if (t_1 <= 2e-318) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if (t_1 <= 2e-147) {
		tmp = t_2;
	} else if (t_1 <= 5e-109) {
		tmp = x * ((-4.0 * i) + (b * (c / x)));
	} else if (t_1 <= 1e-13) {
		tmp = x * ((18.0 * (t * (z * y))) - (i * 4.0));
	} else if (t_1 <= 2e+74) {
		tmp = t_2;
	} else {
		tmp = k * (((b * c) / 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])
[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 = t * ((18.0 * (x * (z * y))) - (a * 4.0))
	tmp = 0
	if t_1 <= -10.0:
		tmp = (j * (k * -27.0)) + (b * c)
	elif t_1 <= -1e-83:
		tmp = t_2
	elif t_1 <= 2e-318:
		tmp = (b * c) - (4.0 * (x * i))
	elif t_1 <= 2e-147:
		tmp = t_2
	elif t_1 <= 5e-109:
		tmp = x * ((-4.0 * i) + (b * (c / x)))
	elif t_1 <= 1e-13:
		tmp = x * ((18.0 * (t * (z * y))) - (i * 4.0))
	elif t_1 <= 2e+74:
		tmp = t_2
	else:
		tmp = k * (((b * c) / 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])
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(t * Float64(Float64(18.0 * Float64(x * Float64(z * y))) - Float64(a * 4.0)))
	tmp = 0.0
	if (t_1 <= -10.0)
		tmp = Float64(Float64(j * Float64(k * -27.0)) + Float64(b * c));
	elseif (t_1 <= -1e-83)
		tmp = t_2;
	elseif (t_1 <= 2e-318)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)));
	elseif (t_1 <= 2e-147)
		tmp = t_2;
	elseif (t_1 <= 5e-109)
		tmp = Float64(x * Float64(Float64(-4.0 * i) + Float64(b * Float64(c / x))));
	elseif (t_1 <= 1e-13)
		tmp = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(z * y))) - Float64(i * 4.0)));
	elseif (t_1 <= 2e+74)
		tmp = t_2;
	else
		tmp = Float64(k * Float64(Float64(Float64(b * c) / 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])){:}
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 = t * ((18.0 * (x * (z * y))) - (a * 4.0));
	tmp = 0.0;
	if (t_1 <= -10.0)
		tmp = (j * (k * -27.0)) + (b * c);
	elseif (t_1 <= -1e-83)
		tmp = t_2;
	elseif (t_1 <= 2e-318)
		tmp = (b * c) - (4.0 * (x * i));
	elseif (t_1 <= 2e-147)
		tmp = t_2;
	elseif (t_1 <= 5e-109)
		tmp = x * ((-4.0 * i) + (b * (c / x)));
	elseif (t_1 <= 1e-13)
		tmp = x * ((18.0 * (t * (z * y))) - (i * 4.0));
	elseif (t_1 <= 2e+74)
		tmp = t_2;
	else
		tmp = k * (((b * c) / 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.
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[(t * N[(N[(18.0 * N[(x * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -10.0], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -1e-83], t$95$2, If[LessEqual[t$95$1, 2e-318], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e-147], t$95$2, If[LessEqual[t$95$1, 5e-109], N[(x * N[(N[(-4.0 * i), $MachinePrecision] + N[(b * N[(c / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e-13], 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$1, 2e+74], t$95$2, N[(k * N[(N[(N[(b * c), $MachinePrecision] / k), $MachinePrecision] - N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -10

   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 87.3%

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

   5. Taylor expanded in b around inf 72.5%

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

   if -10 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -1e-83 or 2.0000024e-318 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 1.9999999999999999e-147 or 1e-13 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 1.9999999999999999e74

   1. Initial program 89.8%

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

   3. Simplified 95.8%

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

   5. Taylor expanded in t around inf 72.7%

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

   if -1e-83 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 2.0000024e-318

   1. Initial program 90.6%

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

   3. Taylor expanded in t around 0 71.3%

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

   4. Taylor expanded in j around 0 71.3%

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

   if 1.9999999999999999e-147 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 5.0000000000000002e-109

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 72.7%

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

   4. Taylor expanded in j around 0 72.7%

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

   5. Taylor expanded in x around inf 86.4%

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

      1. cancel-sign-sub-inv 86.4%

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

      2. associate-/l* 86.4%

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

      3. metadata-eval 86.4%

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

   7. Simplified 86.4%

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

   if 5.0000000000000002e-109 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 1e-13

   1. Initial program 73.6%

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

   3. Simplified 66.7%

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

   5. Taylor expanded in x around inf 61.6%

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

   if 1.9999999999999999e74 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 85.6%

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

   3. Taylor expanded in a around inf 80.9%

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

   4. Taylor expanded in y around inf 78.4%

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

   5. Taylor expanded in b around inf 64.2%

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

   6. Taylor expanded in k around inf 66.6%

      \[\leadsto \color{blue}{k \cdot \left(\frac{b \cdot c}{k} - 27 \cdot j\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \cdot \left(j \cdot 27\right) \leq -10:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq -1 \cdot 10^{-83}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(z \cdot y\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 2 \cdot 10^{-318}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 2 \cdot 10^{-147}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(z \cdot y\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 5 \cdot 10^{-109}:\\ \;\;\;\;x \cdot \left(-4 \cdot i + b \cdot \frac{c}{x}\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 10^{-13}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(z \cdot y\right)\right) - i \cdot 4\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 2 \cdot 10^{+74}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(z \cdot y\right)\right) - a \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(\frac{b \cdot c}{k} - j \cdot 27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 90.8% accurate, 0.5× speedup

Math

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

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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
         (-
          (-
           (+ (- (* t (* z (* y (* x 18.0)))) (* t (* a 4.0))) (* b c))
           (* i (* x 4.0)))
          (* k (* j 27.0)))))
   (if (<= t_1 INFINITY) t_1 (* t (- (* 18.0 (* x (* z y))) (* a 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);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((((t * (z * (y * (x * 18.0)))) - (t * (a * 4.0))) + (b * c)) - (i * (x * 4.0))) - (k * (j * 27.0));
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = t * ((18.0 * (x * (z * y))) - (a * 4.0));
	}
	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;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((((t * (z * (y * (x * 18.0)))) - (t * (a * 4.0))) + (b * c)) - (i * (x * 4.0))) - (k * (j * 27.0));
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = t * ((18.0 * (x * (z * y))) - (a * 4.0));
	}
	return tmp;
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 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

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

   1. Initial program 0.0%

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

   3. Simplified 30.4%

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

   5. Taylor expanded in t around inf 65.4%

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

4. Final simplification 93.1%

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

Alternative 4: 51.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := k \cdot \left(j \cdot 27\right)\\ \mathbf{if}\;t\_2 \leq -10:\\ \;\;\;\;t\_1 + b \cdot c\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{-83}:\\ \;\;\;\;t\_1 + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;t\_2 \leq 10^{-25}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+74}:\\ \;\;\;\;t \cdot \left(-27 \cdot \frac{j \cdot k}{t} + a \cdot -4\right)\\ \mathbf{elif}\;t\_2 \leq 10^{+125}:\\ \;\;\;\;c \cdot \left(b + -27 \cdot \left(j \cdot \frac{k}{c}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 + x \cdot \left(-4 \cdot i\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 (* k -27.0))) (t_2 (* k (* j 27.0))))
   (if (<= t_2 -10.0)
     (+ t_1 (* b c))
     (if (<= t_2 -1e-83)
       (+ t_1 (* -4.0 (* t a)))
       (if (<= t_2 1e-25)
         (- (* b c) (* 4.0 (* x i)))
         (if (<= t_2 5e+74)
           (* t (+ (* -27.0 (/ (* j k) t)) (* a -4.0)))
           (if (<= t_2 1e+125)
             (* c (+ b (* -27.0 (* j (/ k c)))))
             (+ t_1 (* x (* -4.0 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);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = k * (j * 27.0);
	double tmp;
	if (t_2 <= -10.0) {
		tmp = t_1 + (b * c);
	} else if (t_2 <= -1e-83) {
		tmp = t_1 + (-4.0 * (t * a));
	} else if (t_2 <= 1e-25) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if (t_2 <= 5e+74) {
		tmp = t * ((-27.0 * ((j * k) / t)) + (a * -4.0));
	} else if (t_2 <= 1e+125) {
		tmp = c * (b + (-27.0 * (j * (k / c))));
	} else {
		tmp = t_1 + (x * (-4.0 * 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.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * (k * (-27.0d0))
    t_2 = k * (j * 27.0d0)
    if (t_2 <= (-10.0d0)) then
        tmp = t_1 + (b * c)
    else if (t_2 <= (-1d-83)) then
        tmp = t_1 + ((-4.0d0) * (t * a))
    else if (t_2 <= 1d-25) then
        tmp = (b * c) - (4.0d0 * (x * i))
    else if (t_2 <= 5d+74) then
        tmp = t * (((-27.0d0) * ((j * k) / t)) + (a * (-4.0d0)))
    else if (t_2 <= 1d+125) then
        tmp = c * (b + ((-27.0d0) * (j * (k / c))))
    else
        tmp = t_1 + (x * ((-4.0d0) * 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;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = k * (j * 27.0);
	double tmp;
	if (t_2 <= -10.0) {
		tmp = t_1 + (b * c);
	} else if (t_2 <= -1e-83) {
		tmp = t_1 + (-4.0 * (t * a));
	} else if (t_2 <= 1e-25) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if (t_2 <= 5e+74) {
		tmp = t * ((-27.0 * ((j * k) / t)) + (a * -4.0));
	} else if (t_2 <= 1e+125) {
		tmp = c * (b + (-27.0 * (j * (k / c))));
	} else {
		tmp = t_1 + (x * (-4.0 * i));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[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 * (k * -27.0)
	t_2 = k * (j * 27.0)
	tmp = 0
	if t_2 <= -10.0:
		tmp = t_1 + (b * c)
	elif t_2 <= -1e-83:
		tmp = t_1 + (-4.0 * (t * a))
	elif t_2 <= 1e-25:
		tmp = (b * c) - (4.0 * (x * i))
	elif t_2 <= 5e+74:
		tmp = t * ((-27.0 * ((j * k) / t)) + (a * -4.0))
	elif t_2 <= 1e+125:
		tmp = c * (b + (-27.0 * (j * (k / c))))
	else:
		tmp = t_1 + (x * (-4.0 * i))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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(k * -27.0))
	t_2 = Float64(k * Float64(j * 27.0))
	tmp = 0.0
	if (t_2 <= -10.0)
		tmp = Float64(t_1 + Float64(b * c));
	elseif (t_2 <= -1e-83)
		tmp = Float64(t_1 + Float64(-4.0 * Float64(t * a)));
	elseif (t_2 <= 1e-25)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)));
	elseif (t_2 <= 5e+74)
		tmp = Float64(t * Float64(Float64(-27.0 * Float64(Float64(j * k) / t)) + Float64(a * -4.0)));
	elseif (t_2 <= 1e+125)
		tmp = Float64(c * Float64(b + Float64(-27.0 * Float64(j * Float64(k / c)))));
	else
		tmp = Float64(t_1 + Float64(x * Float64(-4.0 * i)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
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 * (k * -27.0);
	t_2 = k * (j * 27.0);
	tmp = 0.0;
	if (t_2 <= -10.0)
		tmp = t_1 + (b * c);
	elseif (t_2 <= -1e-83)
		tmp = t_1 + (-4.0 * (t * a));
	elseif (t_2 <= 1e-25)
		tmp = (b * c) - (4.0 * (x * i));
	elseif (t_2 <= 5e+74)
		tmp = t * ((-27.0 * ((j * k) / t)) + (a * -4.0));
	elseif (t_2 <= 1e+125)
		tmp = c * (b + (-27.0 * (j * (k / c))));
	else
		tmp = t_1 + (x * (-4.0 * i));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -10.0], N[(t$95$1 + N[(b * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -1e-83], N[(t$95$1 + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e-25], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+74], N[(t * N[(N[(-27.0 * N[(N[(j * k), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+125], N[(c * N[(b + N[(-27.0 * N[(j * N[(k / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(x * N[(-4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -10

   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 87.3%

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

   5. Taylor expanded in b around inf 72.5%

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

   if -10 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -1e-83

   1. Initial program 93.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in a around inf 57.1%

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

   if -1e-83 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 1.00000000000000004e-25

   1. Initial program 88.1%

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

   3. Taylor expanded in t around 0 62.7%

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

   4. Taylor expanded in j around 0 61.0%

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

   if 1.00000000000000004e-25 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 4.99999999999999963e74

   1. Initial program 92.5%

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

   3. Simplified 92.7%

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

   5. Taylor expanded in a around inf 58.3%

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

   6. Taylor expanded in t around inf 58.3%

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

   if 4.99999999999999963e74 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 9.9999999999999992e124

   1. Initial program 88.0%

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

   3. Taylor expanded in a around inf 88.0%

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

   4. Taylor expanded in y around inf 87.3%

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

   5. Taylor expanded in b around inf 51.6%

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

   6. Taylor expanded in c around inf 51.6%

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

      1. *-commutative 51.6%

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

      2. associate-/l* 63.6%

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

   8. Simplified 63.6%

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

   if 9.9999999999999992e124 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 84.5%

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

   3. Simplified 78.6%

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

   5. Taylor expanded in i around inf 75.4%

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

      1. associate-*r* 75.4%

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

      2. *-commutative 75.4%

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

   7. Simplified 75.4%

      \[\leadsto \color{blue}{x \cdot \left(-4 \cdot i\right)} + j \cdot \left(k \cdot -27\right) \]
3. Recombined 6 regimes into one program.

4. Final simplification 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \cdot \left(j \cdot 27\right) \leq -10:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq -1 \cdot 10^{-83}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 10^{-25}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 5 \cdot 10^{+74}:\\ \;\;\;\;t \cdot \left(-27 \cdot \frac{j \cdot k}{t} + a \cdot -4\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 10^{+125}:\\ \;\;\;\;c \cdot \left(b + -27 \cdot \left(j \cdot \frac{k}{c}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + x \cdot \left(-4 \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 51.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := k \cdot \left(j \cdot 27\right)\\ t_3 := t\_1 + -4 \cdot \left(t \cdot a\right)\\ \mathbf{if}\;t\_2 \leq -10:\\ \;\;\;\;t\_1 + b \cdot c\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{-83}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 10^{-25}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+74}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 10^{+125}:\\ \;\;\;\;c \cdot \left(b + -27 \cdot \left(j \cdot \frac{k}{c}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 + x \cdot \left(-4 \cdot i\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 (* k -27.0)))
        (t_2 (* k (* j 27.0)))
        (t_3 (+ t_1 (* -4.0 (* t a)))))
   (if (<= t_2 -10.0)
     (+ t_1 (* b c))
     (if (<= t_2 -1e-83)
       t_3
       (if (<= t_2 1e-25)
         (- (* b c) (* 4.0 (* x i)))
         (if (<= t_2 5e+74)
           t_3
           (if (<= t_2 1e+125)
             (* c (+ b (* -27.0 (* j (/ k c)))))
             (+ t_1 (* x (* -4.0 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);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = k * (j * 27.0);
	double t_3 = t_1 + (-4.0 * (t * a));
	double tmp;
	if (t_2 <= -10.0) {
		tmp = t_1 + (b * c);
	} else if (t_2 <= -1e-83) {
		tmp = t_3;
	} else if (t_2 <= 1e-25) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if (t_2 <= 5e+74) {
		tmp = t_3;
	} else if (t_2 <= 1e+125) {
		tmp = c * (b + (-27.0 * (j * (k / c))));
	} else {
		tmp = t_1 + (x * (-4.0 * 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.
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 = j * (k * (-27.0d0))
    t_2 = k * (j * 27.0d0)
    t_3 = t_1 + ((-4.0d0) * (t * a))
    if (t_2 <= (-10.0d0)) then
        tmp = t_1 + (b * c)
    else if (t_2 <= (-1d-83)) then
        tmp = t_3
    else if (t_2 <= 1d-25) then
        tmp = (b * c) - (4.0d0 * (x * i))
    else if (t_2 <= 5d+74) then
        tmp = t_3
    else if (t_2 <= 1d+125) then
        tmp = c * (b + ((-27.0d0) * (j * (k / c))))
    else
        tmp = t_1 + (x * ((-4.0d0) * 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;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = k * (j * 27.0);
	double t_3 = t_1 + (-4.0 * (t * a));
	double tmp;
	if (t_2 <= -10.0) {
		tmp = t_1 + (b * c);
	} else if (t_2 <= -1e-83) {
		tmp = t_3;
	} else if (t_2 <= 1e-25) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if (t_2 <= 5e+74) {
		tmp = t_3;
	} else if (t_2 <= 1e+125) {
		tmp = c * (b + (-27.0 * (j * (k / c))));
	} else {
		tmp = t_1 + (x * (-4.0 * i));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[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 * (k * -27.0)
	t_2 = k * (j * 27.0)
	t_3 = t_1 + (-4.0 * (t * a))
	tmp = 0
	if t_2 <= -10.0:
		tmp = t_1 + (b * c)
	elif t_2 <= -1e-83:
		tmp = t_3
	elif t_2 <= 1e-25:
		tmp = (b * c) - (4.0 * (x * i))
	elif t_2 <= 5e+74:
		tmp = t_3
	elif t_2 <= 1e+125:
		tmp = c * (b + (-27.0 * (j * (k / c))))
	else:
		tmp = t_1 + (x * (-4.0 * i))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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(k * -27.0))
	t_2 = Float64(k * Float64(j * 27.0))
	t_3 = Float64(t_1 + Float64(-4.0 * Float64(t * a)))
	tmp = 0.0
	if (t_2 <= -10.0)
		tmp = Float64(t_1 + Float64(b * c));
	elseif (t_2 <= -1e-83)
		tmp = t_3;
	elseif (t_2 <= 1e-25)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)));
	elseif (t_2 <= 5e+74)
		tmp = t_3;
	elseif (t_2 <= 1e+125)
		tmp = Float64(c * Float64(b + Float64(-27.0 * Float64(j * Float64(k / c)))));
	else
		tmp = Float64(t_1 + Float64(x * Float64(-4.0 * i)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
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 * (k * -27.0);
	t_2 = k * (j * 27.0);
	t_3 = t_1 + (-4.0 * (t * a));
	tmp = 0.0;
	if (t_2 <= -10.0)
		tmp = t_1 + (b * c);
	elseif (t_2 <= -1e-83)
		tmp = t_3;
	elseif (t_2 <= 1e-25)
		tmp = (b * c) - (4.0 * (x * i));
	elseif (t_2 <= 5e+74)
		tmp = t_3;
	elseif (t_2 <= 1e+125)
		tmp = c * (b + (-27.0 * (j * (k / c))));
	else
		tmp = t_1 + (x * (-4.0 * i));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$1 + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -10.0], N[(t$95$1 + N[(b * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -1e-83], t$95$3, If[LessEqual[t$95$2, 1e-25], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+74], t$95$3, If[LessEqual[t$95$2, 1e+125], N[(c * N[(b + N[(-27.0 * N[(j * N[(k / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(x * N[(-4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -10

   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 87.3%

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

   5. Taylor expanded in b around inf 72.5%

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

   if -10 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -1e-83 or 1.00000000000000004e-25 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 4.99999999999999963e74

   1. Initial program 93.1%

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

   3. Simplified 96.5%

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

   5. Taylor expanded in a around inf 57.7%

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

   if -1e-83 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 1.00000000000000004e-25

   1. Initial program 88.1%

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

   3. Taylor expanded in t around 0 62.7%

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

   4. Taylor expanded in j around 0 61.0%

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

   if 4.99999999999999963e74 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 9.9999999999999992e124

   1. Initial program 88.0%

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

   3. Taylor expanded in a around inf 88.0%

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

   4. Taylor expanded in y around inf 87.3%

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

   5. Taylor expanded in b around inf 51.6%

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

   6. Taylor expanded in c around inf 51.6%

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

      1. *-commutative 51.6%

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

      2. associate-/l* 63.6%

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

   8. Simplified 63.6%

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

   if 9.9999999999999992e124 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 84.5%

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

   3. Simplified 78.6%

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

   5. Taylor expanded in i around inf 75.4%

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

      1. associate-*r* 75.4%

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

      2. *-commutative 75.4%

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

   7. Simplified 75.4%

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

4. Final simplification 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \cdot \left(j \cdot 27\right) \leq -10:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq -1 \cdot 10^{-83}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 10^{-25}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 5 \cdot 10^{+74}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 10^{+125}:\\ \;\;\;\;c \cdot \left(b + -27 \cdot \left(j \cdot \frac{k}{c}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + x \cdot \left(-4 \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 53.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := k \cdot \left(j \cdot 27\right)\\ t_2 := t \cdot \left(18 \cdot \left(x \cdot \left(z \cdot y\right)\right) - a \cdot 4\right)\\ \mathbf{if}\;t\_1 \leq -10:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \mathbf{elif}\;t\_1 \leq -1 \cdot 10^{-83}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-318}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+74}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(\frac{b \cdot c}{k} - j \cdot 27\right)\\ \end{array} \end{array} \]

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.
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 (* t (- (* 18.0 (* x (* z y))) (* a 4.0)))))
   (if (<= t_1 -10.0)
     (+ (* j (* k -27.0)) (* b c))
     (if (<= t_1 -1e-83)
       t_2
       (if (<= t_1 2e-318)
         (- (* b c) (* 4.0 (* x i)))
         (if (<= t_1 2e+74) t_2 (* k (- (/ (* b c) 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);
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 = t * ((18.0 * (x * (z * y))) - (a * 4.0));
	double tmp;
	if (t_1 <= -10.0) {
		tmp = (j * (k * -27.0)) + (b * c);
	} else if (t_1 <= -1e-83) {
		tmp = t_2;
	} else if (t_1 <= 2e-318) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if (t_1 <= 2e+74) {
		tmp = t_2;
	} else {
		tmp = k * (((b * c) / 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.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = k * (j * 27.0d0)
    t_2 = t * ((18.0d0 * (x * (z * y))) - (a * 4.0d0))
    if (t_1 <= (-10.0d0)) then
        tmp = (j * (k * (-27.0d0))) + (b * c)
    else if (t_1 <= (-1d-83)) then
        tmp = t_2
    else if (t_1 <= 2d-318) then
        tmp = (b * c) - (4.0d0 * (x * i))
    else if (t_1 <= 2d+74) then
        tmp = t_2
    else
        tmp = k * (((b * c) / 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;
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 = t * ((18.0 * (x * (z * y))) - (a * 4.0));
	double tmp;
	if (t_1 <= -10.0) {
		tmp = (j * (k * -27.0)) + (b * c);
	} else if (t_1 <= -1e-83) {
		tmp = t_2;
	} else if (t_1 <= 2e-318) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if (t_1 <= 2e+74) {
		tmp = t_2;
	} else {
		tmp = k * (((b * c) / 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])
[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 = t * ((18.0 * (x * (z * y))) - (a * 4.0))
	tmp = 0
	if t_1 <= -10.0:
		tmp = (j * (k * -27.0)) + (b * c)
	elif t_1 <= -1e-83:
		tmp = t_2
	elif t_1 <= 2e-318:
		tmp = (b * c) - (4.0 * (x * i))
	elif t_1 <= 2e+74:
		tmp = t_2
	else:
		tmp = k * (((b * c) / 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])
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(t * Float64(Float64(18.0 * Float64(x * Float64(z * y))) - Float64(a * 4.0)))
	tmp = 0.0
	if (t_1 <= -10.0)
		tmp = Float64(Float64(j * Float64(k * -27.0)) + Float64(b * c));
	elseif (t_1 <= -1e-83)
		tmp = t_2;
	elseif (t_1 <= 2e-318)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)));
	elseif (t_1 <= 2e+74)
		tmp = t_2;
	else
		tmp = Float64(k * Float64(Float64(Float64(b * c) / 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])){:}
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 = t * ((18.0 * (x * (z * y))) - (a * 4.0));
	tmp = 0.0;
	if (t_1 <= -10.0)
		tmp = (j * (k * -27.0)) + (b * c);
	elseif (t_1 <= -1e-83)
		tmp = t_2;
	elseif (t_1 <= 2e-318)
		tmp = (b * c) - (4.0 * (x * i));
	elseif (t_1 <= 2e+74)
		tmp = t_2;
	else
		tmp = k * (((b * c) / 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.
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[(t * N[(N[(18.0 * N[(x * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -10.0], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -1e-83], t$95$2, If[LessEqual[t$95$1, 2e-318], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+74], t$95$2, N[(k * N[(N[(N[(b * c), $MachinePrecision] / k), $MachinePrecision] - N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -10

   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 87.3%

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

   5. Taylor expanded in b around inf 72.5%

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

   if -10 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -1e-83 or 2.0000024e-318 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 1.9999999999999999e74

   1. Initial program 87.4%

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

   3. Simplified 88.7%

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

   5. Taylor expanded in t around inf 64.7%

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

   if -1e-83 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 2.0000024e-318

   1. Initial program 90.6%

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

   3. Taylor expanded in t around 0 71.3%

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

   4. Taylor expanded in j around 0 71.3%

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

   if 1.9999999999999999e74 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 85.6%

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

   3. Taylor expanded in a around inf 80.9%

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

   4. Taylor expanded in y around inf 78.4%

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

   5. Taylor expanded in b around inf 64.2%

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

   6. Taylor expanded in k around inf 66.6%

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

4. Final simplification 69.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \cdot \left(j \cdot 27\right) \leq -10:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq -1 \cdot 10^{-83}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(z \cdot y\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 2 \cdot 10^{-318}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 2 \cdot 10^{+74}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(z \cdot y\right)\right) - a \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(\frac{b \cdot c}{k} - j \cdot 27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 87.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := k \cdot \left(j \cdot 27\right)\\ \mathbf{if}\;y \leq -1.42 \cdot 10^{+166}:\\ \;\;\;\;\left(b \cdot c + y \cdot \left(-4 \cdot \frac{t \cdot a}{y} + 18 \cdot \left(t \cdot \left(z \cdot x\right)\right)\right)\right) - t\_1\\ \mathbf{elif}\;y \leq 10^{+24}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(z \cdot y\right) \cdot \left(x \cdot 18\right) - a \cdot 4\right)\right) - \left(x \cdot \left(i \cdot 4\right) + j \cdot \left(k \cdot 27\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b \cdot c + t \cdot \left(y \cdot \left(-4 \cdot \frac{a}{y} + 18 \cdot \left(z \cdot x\right)\right)\right)\right) - i \cdot \left(x \cdot 4\right)\right) - t\_1\\ \end{array} \end{array} \]

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.
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 (<= y -1.42e+166)
     (-
      (+ (* b c) (* y (+ (* -4.0 (/ (* t a) y)) (* 18.0 (* t (* z x))))))
      t_1)
     (if (<= y 1e+24)
       (-
        (+ (* b c) (* t (- (* (* z y) (* x 18.0)) (* a 4.0))))
        (+ (* x (* i 4.0)) (* j (* k 27.0))))
       (-
        (-
         (+ (* b c) (* t (* y (+ (* -4.0 (/ a y)) (* 18.0 (* z x))))))
         (* i (* x 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);
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 (y <= -1.42e+166) {
		tmp = ((b * c) + (y * ((-4.0 * ((t * a) / y)) + (18.0 * (t * (z * x)))))) - t_1;
	} else if (y <= 1e+24) {
		tmp = ((b * c) + (t * (((z * y) * (x * 18.0)) - (a * 4.0)))) - ((x * (i * 4.0)) + (j * (k * 27.0)));
	} else {
		tmp = (((b * c) + (t * (y * ((-4.0 * (a / y)) + (18.0 * (z * x)))))) - (i * (x * 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.
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 (y <= (-1.42d+166)) then
        tmp = ((b * c) + (y * (((-4.0d0) * ((t * a) / y)) + (18.0d0 * (t * (z * x)))))) - t_1
    else if (y <= 1d+24) then
        tmp = ((b * c) + (t * (((z * y) * (x * 18.0d0)) - (a * 4.0d0)))) - ((x * (i * 4.0d0)) + (j * (k * 27.0d0)))
    else
        tmp = (((b * c) + (t * (y * (((-4.0d0) * (a / y)) + (18.0d0 * (z * x)))))) - (i * (x * 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;
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 (y <= -1.42e+166) {
		tmp = ((b * c) + (y * ((-4.0 * ((t * a) / y)) + (18.0 * (t * (z * x)))))) - t_1;
	} else if (y <= 1e+24) {
		tmp = ((b * c) + (t * (((z * y) * (x * 18.0)) - (a * 4.0)))) - ((x * (i * 4.0)) + (j * (k * 27.0)));
	} else {
		tmp = (((b * c) + (t * (y * ((-4.0 * (a / y)) + (18.0 * (z * x)))))) - (i * (x * 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])
[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 y <= -1.42e+166:
		tmp = ((b * c) + (y * ((-4.0 * ((t * a) / y)) + (18.0 * (t * (z * x)))))) - t_1
	elif y <= 1e+24:
		tmp = ((b * c) + (t * (((z * y) * (x * 18.0)) - (a * 4.0)))) - ((x * (i * 4.0)) + (j * (k * 27.0)))
	else:
		tmp = (((b * c) + (t * (y * ((-4.0 * (a / y)) + (18.0 * (z * x)))))) - (i * (x * 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])
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 (y <= -1.42e+166)
		tmp = Float64(Float64(Float64(b * c) + Float64(y * Float64(Float64(-4.0 * Float64(Float64(t * a) / y)) + Float64(18.0 * Float64(t * Float64(z * x)))))) - t_1);
	elseif (y <= 1e+24)
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(Float64(z * y) * Float64(x * 18.0)) - Float64(a * 4.0)))) - Float64(Float64(x * Float64(i * 4.0)) + Float64(j * Float64(k * 27.0))));
	else
		tmp = Float64(Float64(Float64(Float64(b * c) + Float64(t * Float64(y * Float64(Float64(-4.0 * Float64(a / y)) + Float64(18.0 * Float64(z * x)))))) - Float64(i * Float64(x * 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])){:}
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 (y <= -1.42e+166)
		tmp = ((b * c) + (y * ((-4.0 * ((t * a) / y)) + (18.0 * (t * (z * x)))))) - t_1;
	elseif (y <= 1e+24)
		tmp = ((b * c) + (t * (((z * y) * (x * 18.0)) - (a * 4.0)))) - ((x * (i * 4.0)) + (j * (k * 27.0)));
	else
		tmp = (((b * c) + (t * (y * ((-4.0 * (a / y)) + (18.0 * (z * x)))))) - (i * (x * 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.
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[y, -1.42e+166], N[(N[(N[(b * c), $MachinePrecision] + N[(y * N[(N[(-4.0 * N[(N[(t * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] + N[(18.0 * N[(t * N[(z * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[y, 1e+24], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(N[(z * y), $MachinePrecision] * N[(x * 18.0), $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], N[(N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(y * N[(N[(-4.0 * N[(a / y), $MachinePrecision]), $MachinePrecision] + N[(18.0 * N[(z * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * N[(x * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.41999999999999995e166

   1. Initial program 81.3%

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

   3. Taylor expanded in a around inf 73.7%

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

   4. Taylor expanded in y around inf 89.0%

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

   5. Taylor expanded in i around 0 86.6%

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

   if -1.41999999999999995e166 < y < 9.9999999999999998e23

   1. Initial program 90.1%

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

   3. Simplified 93.0%

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

   if 9.9999999999999998e23 < y

   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 a around inf 75.2%

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

   4. Taylor expanded in y around inf 87.3%

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

   5. Taylor expanded in t around 0 87.4%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.42 \cdot 10^{+166}:\\ \;\;\;\;\left(b \cdot c + y \cdot \left(-4 \cdot \frac{t \cdot a}{y} + 18 \cdot \left(t \cdot \left(z \cdot x\right)\right)\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;y \leq 10^{+24}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(z \cdot y\right) \cdot \left(x \cdot 18\right) - a \cdot 4\right)\right) - \left(x \cdot \left(i \cdot 4\right) + j \cdot \left(k \cdot 27\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b \cdot c + t \cdot \left(y \cdot \left(-4 \cdot \frac{a}{y} + 18 \cdot \left(z \cdot x\right)\right)\right)\right) - i \cdot \left(x \cdot 4\right)\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 51.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := k \cdot \left(j \cdot 27\right)\\ \mathbf{if}\;t\_2 \leq -10:\\ \;\;\;\;t\_1 + b \cdot c\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{-83} \lor \neg \left(t\_2 \leq 10^{-25}\right):\\ \;\;\;\;t\_1 + -4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 (* k -27.0))) (t_2 (* k (* j 27.0))))
   (if (<= t_2 -10.0)
     (+ t_1 (* b c))
     (if (or (<= t_2 -1e-83) (not (<= t_2 1e-25)))
       (+ t_1 (* -4.0 (* t a)))
       (- (* b c) (* 4.0 (* x i)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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 * (k * -27.0);
	double t_2 = k * (j * 27.0);
	double tmp;
	if (t_2 <= -10.0) {
		tmp = t_1 + (b * c);
	} else if ((t_2 <= -1e-83) || !(t_2 <= 1e-25)) {
		tmp = t_1 + (-4.0 * (t * a));
	} else {
		tmp = (b * c) - (4.0 * (x * i));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 = j * (k * (-27.0d0))
    t_2 = k * (j * 27.0d0)
    if (t_2 <= (-10.0d0)) then
        tmp = t_1 + (b * c)
    else if ((t_2 <= (-1d-83)) .or. (.not. (t_2 <= 1d-25))) then
        tmp = t_1 + ((-4.0d0) * (t * a))
    else
        tmp = (b * c) - (4.0d0 * (x * i))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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 * (k * -27.0);
	double t_2 = k * (j * 27.0);
	double tmp;
	if (t_2 <= -10.0) {
		tmp = t_1 + (b * c);
	} else if ((t_2 <= -1e-83) || !(t_2 <= 1e-25)) {
		tmp = t_1 + (-4.0 * (t * a));
	} else {
		tmp = (b * c) - (4.0 * (x * i));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[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 * (k * -27.0)
	t_2 = k * (j * 27.0)
	tmp = 0
	if t_2 <= -10.0:
		tmp = t_1 + (b * c)
	elif (t_2 <= -1e-83) or not (t_2 <= 1e-25):
		tmp = t_1 + (-4.0 * (t * a))
	else:
		tmp = (b * c) - (4.0 * (x * i))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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(k * -27.0))
	t_2 = Float64(k * Float64(j * 27.0))
	tmp = 0.0
	if (t_2 <= -10.0)
		tmp = Float64(t_1 + Float64(b * c));
	elseif ((t_2 <= -1e-83) || !(t_2 <= 1e-25))
		tmp = Float64(t_1 + Float64(-4.0 * Float64(t * a)));
	else
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
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 * (k * -27.0);
	t_2 = k * (j * 27.0);
	tmp = 0.0;
	if (t_2 <= -10.0)
		tmp = t_1 + (b * c);
	elseif ((t_2 <= -1e-83) || ~((t_2 <= 1e-25)))
		tmp = t_1 + (-4.0 * (t * a));
	else
		tmp = (b * c) - (4.0 * (x * i));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -10.0], N[(t$95$1 + N[(b * c), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t$95$2, -1e-83], N[Not[LessEqual[t$95$2, 1e-25]], $MachinePrecision]], N[(t$95$1 + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -10

   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 87.3%

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

   5. Taylor expanded in b around inf 72.5%

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

   if -10 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -1e-83 or 1.00000000000000004e-25 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 88.6%

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

   3. Simplified 87.3%

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

   5. Taylor expanded in a around inf 58.2%

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

   if -1e-83 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 1.00000000000000004e-25

   1. Initial program 88.1%

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

   3. Taylor expanded in t around 0 62.7%

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

   4. Taylor expanded in j around 0 61.0%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \cdot \left(j \cdot 27\right) \leq -10:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq -1 \cdot 10^{-83} \lor \neg \left(k \cdot \left(j \cdot 27\right) \leq 10^{-25}\right):\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 71.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := k \cdot \left(j \cdot 27\right)\\ t_2 := \left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - t\_1\\ t_3 := t \cdot \left(18 \cdot \left(x \cdot \left(z \cdot y\right)\right) - a \cdot 4\right)\\ \mathbf{if}\;t \leq -2.2 \cdot 10^{+134}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq -45000000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{-36}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(z \cdot y\right)\right) - i \cdot 4\right) - t\_1\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+111}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

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.
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) (* 4.0 (* x i))) t_1))
        (t_3 (* t (- (* 18.0 (* x (* z y))) (* a 4.0)))))
   (if (<= t -2.2e+134)
     t_3
     (if (<= t -45000000000.0)
       t_2
       (if (<= t -1.9e-36)
         (- (* x (- (* 18.0 (* t (* z y))) (* i 4.0))) t_1)
         (if (<= t 2.6e+111) 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);
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) - (4.0 * (x * i))) - t_1;
	double t_3 = t * ((18.0 * (x * (z * y))) - (a * 4.0));
	double tmp;
	if (t <= -2.2e+134) {
		tmp = t_3;
	} else if (t <= -45000000000.0) {
		tmp = t_2;
	} else if (t <= -1.9e-36) {
		tmp = (x * ((18.0 * (t * (z * y))) - (i * 4.0))) - t_1;
	} else if (t <= 2.6e+111) {
		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.
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) - (4.0d0 * (x * i))) - t_1
    t_3 = t * ((18.0d0 * (x * (z * y))) - (a * 4.0d0))
    if (t <= (-2.2d+134)) then
        tmp = t_3
    else if (t <= (-45000000000.0d0)) then
        tmp = t_2
    else if (t <= (-1.9d-36)) then
        tmp = (x * ((18.0d0 * (t * (z * y))) - (i * 4.0d0))) - t_1
    else if (t <= 2.6d+111) 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;
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) - (4.0 * (x * i))) - t_1;
	double t_3 = t * ((18.0 * (x * (z * y))) - (a * 4.0));
	double tmp;
	if (t <= -2.2e+134) {
		tmp = t_3;
	} else if (t <= -45000000000.0) {
		tmp = t_2;
	} else if (t <= -1.9e-36) {
		tmp = (x * ((18.0 * (t * (z * y))) - (i * 4.0))) - t_1;
	} else if (t <= 2.6e+111) {
		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])
[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) - (4.0 * (x * i))) - t_1
	t_3 = t * ((18.0 * (x * (z * y))) - (a * 4.0))
	tmp = 0
	if t <= -2.2e+134:
		tmp = t_3
	elif t <= -45000000000.0:
		tmp = t_2
	elif t <= -1.9e-36:
		tmp = (x * ((18.0 * (t * (z * y))) - (i * 4.0))) - t_1
	elif t <= 2.6e+111:
		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])
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(4.0 * Float64(x * i))) - t_1)
	t_3 = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(z * y))) - Float64(a * 4.0)))
	tmp = 0.0
	if (t <= -2.2e+134)
		tmp = t_3;
	elseif (t <= -45000000000.0)
		tmp = t_2;
	elseif (t <= -1.9e-36)
		tmp = Float64(Float64(x * Float64(Float64(18.0 * Float64(t * Float64(z * y))) - Float64(i * 4.0))) - t_1);
	elseif (t <= 2.6e+111)
		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])){:}
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) - (4.0 * (x * i))) - t_1;
	t_3 = t * ((18.0 * (x * (z * y))) - (a * 4.0));
	tmp = 0.0;
	if (t <= -2.2e+134)
		tmp = t_3;
	elseif (t <= -45000000000.0)
		tmp = t_2;
	elseif (t <= -1.9e-36)
		tmp = (x * ((18.0 * (t * (z * y))) - (i * 4.0))) - t_1;
	elseif (t <= 2.6e+111)
		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.
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[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $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]}, If[LessEqual[t, -2.2e+134], t$95$3, If[LessEqual[t, -45000000000.0], t$95$2, If[LessEqual[t, -1.9e-36], N[(N[(x * N[(N[(18.0 * N[(t * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[t, 2.6e+111], t$95$2, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.2e134 or 2.5999999999999999e111 < t

   1. Initial program 77.9%

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

   3. Simplified 83.8%

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

   5. Taylor expanded in t around inf 80.6%

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

   if -2.2e134 < t < -4.5e10 or -1.89999999999999985e-36 < t < 2.5999999999999999e111

   1. Initial program 90.8%

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

   3. Taylor expanded in t around 0 80.1%

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

   if -4.5e10 < t < -1.89999999999999985e-36

   1. Initial program 88.1%

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

   3. Taylor expanded in a around inf 88.1%

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

   4. Taylor expanded in y around inf 76.5%

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

   5. Taylor expanded in x around inf 87.8%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{+134}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(z \cdot y\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq -45000000000:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{-36}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(z \cdot y\right)\right) - i \cdot 4\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+111}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(z \cdot y\right)\right) - a \cdot 4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 71.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - k \cdot \left(j \cdot 27\right)\\ t_2 := t \cdot \left(18 \cdot \left(x \cdot \left(z \cdot y\right)\right) - a \cdot 4\right)\\ \mathbf{if}\;t \leq -9.5 \cdot 10^{+134}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -35000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{-36}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + x \cdot \left(-4 \cdot i + 18 \cdot \left(t \cdot \left(z \cdot y\right)\right)\right)\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+111}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (- (- (* b c) (* 4.0 (* x i))) (* k (* j 27.0))))
        (t_2 (* t (- (* 18.0 (* x (* z y))) (* a 4.0)))))
   (if (<= t -9.5e+134)
     t_2
     (if (<= t -35000000000.0)
       t_1
       (if (<= t -2.5e-36)
         (+ (* j (* k -27.0)) (* x (+ (* -4.0 i) (* 18.0 (* t (* z y))))))
         (if (<= t 8e+111) 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);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((b * c) - (4.0 * (x * i))) - (k * (j * 27.0));
	double t_2 = t * ((18.0 * (x * (z * y))) - (a * 4.0));
	double tmp;
	if (t <= -9.5e+134) {
		tmp = t_2;
	} else if (t <= -35000000000.0) {
		tmp = t_1;
	} else if (t <= -2.5e-36) {
		tmp = (j * (k * -27.0)) + (x * ((-4.0 * i) + (18.0 * (t * (z * y)))));
	} else if (t <= 8e+111) {
		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.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((b * c) - (4.0d0 * (x * i))) - (k * (j * 27.0d0))
    t_2 = t * ((18.0d0 * (x * (z * y))) - (a * 4.0d0))
    if (t <= (-9.5d+134)) then
        tmp = t_2
    else if (t <= (-35000000000.0d0)) then
        tmp = t_1
    else if (t <= (-2.5d-36)) then
        tmp = (j * (k * (-27.0d0))) + (x * (((-4.0d0) * i) + (18.0d0 * (t * (z * y)))))
    else if (t <= 8d+111) 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;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((b * c) - (4.0 * (x * i))) - (k * (j * 27.0));
	double t_2 = t * ((18.0 * (x * (z * y))) - (a * 4.0));
	double tmp;
	if (t <= -9.5e+134) {
		tmp = t_2;
	} else if (t <= -35000000000.0) {
		tmp = t_1;
	} else if (t <= -2.5e-36) {
		tmp = (j * (k * -27.0)) + (x * ((-4.0 * i) + (18.0 * (t * (z * y)))));
	} else if (t <= 8e+111) {
		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])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = ((b * c) - (4.0 * (x * i))) - (k * (j * 27.0))
	t_2 = t * ((18.0 * (x * (z * y))) - (a * 4.0))
	tmp = 0
	if t <= -9.5e+134:
		tmp = t_2
	elif t <= -35000000000.0:
		tmp = t_1
	elif t <= -2.5e-36:
		tmp = (j * (k * -27.0)) + (x * ((-4.0 * i) + (18.0 * (t * (z * y)))))
	elif t <= 8e+111:
		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])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(x * i))) - Float64(k * Float64(j * 27.0)))
	t_2 = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(z * y))) - Float64(a * 4.0)))
	tmp = 0.0
	if (t <= -9.5e+134)
		tmp = t_2;
	elseif (t <= -35000000000.0)
		tmp = t_1;
	elseif (t <= -2.5e-36)
		tmp = Float64(Float64(j * Float64(k * -27.0)) + Float64(x * Float64(Float64(-4.0 * i) + Float64(18.0 * Float64(t * Float64(z * y))))));
	elseif (t <= 8e+111)
		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])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = ((b * c) - (4.0 * (x * i))) - (k * (j * 27.0));
	t_2 = t * ((18.0 * (x * (z * y))) - (a * 4.0));
	tmp = 0.0;
	if (t <= -9.5e+134)
		tmp = t_2;
	elseif (t <= -35000000000.0)
		tmp = t_1;
	elseif (t <= -2.5e-36)
		tmp = (j * (k * -27.0)) + (x * ((-4.0 * i) + (18.0 * (t * (z * y)))));
	elseif (t <= 8e+111)
		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.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(18.0 * N[(x * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -9.5e+134], t$95$2, If[LessEqual[t, -35000000000.0], t$95$1, If[LessEqual[t, -2.5e-36], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(-4.0 * i), $MachinePrecision] + N[(18.0 * N[(t * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8e+111], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.5000000000000004e134 or 7.99999999999999965e111 < t

   1. Initial program 77.9%

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

   3. Simplified 83.8%

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

   5. Taylor expanded in t around inf 80.6%

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

   if -9.5000000000000004e134 < t < -3.5e10 or -2.50000000000000002e-36 < t < 7.99999999999999965e111

   1. Initial program 90.8%

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

   3. Taylor expanded in t around 0 80.1%

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

   if -3.5e10 < t < -2.50000000000000002e-36

   1. Initial program 88.1%

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

   3. Simplified 88.1%

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

   5. Taylor expanded in x around inf 87.8%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{+134}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(z \cdot y\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq -35000000000:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{-36}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + x \cdot \left(-4 \cdot i + 18 \cdot \left(t \cdot \left(z \cdot y\right)\right)\right)\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+111}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(z \cdot y\right)\right) - a \cdot 4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 86.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{+166}:\\ \;\;\;\;\left(b \cdot c + y \cdot \left(-4 \cdot \frac{t \cdot a}{y} + 18 \cdot \left(t \cdot \left(z \cdot x\right)\right)\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(z \cdot y\right) \cdot \left(x \cdot 18\right) - a \cdot 4\right)\right) - \left(x \cdot \left(i \cdot 4\right) + j \cdot \left(k \cdot 27\right)\right)\\ \end{array} \end{array} \]

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.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= y -1.65e+166)
   (-
    (+ (* b c) (* y (+ (* -4.0 (/ (* t a) y)) (* 18.0 (* t (* z x))))))
    (* k (* j 27.0)))
   (-
    (+ (* b c) (* t (- (* (* z y) (* x 18.0)) (* 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);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (y <= -1.65e+166) {
		tmp = ((b * c) + (y * ((-4.0 * ((t * a) / y)) + (18.0 * (t * (z * x)))))) - (k * (j * 27.0));
	} else {
		tmp = ((b * c) + (t * (((z * y) * (x * 18.0)) - (a * 4.0)))) - ((x * (i * 4.0)) + (j * (k * 27.0)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 (y <= (-1.65d+166)) then
        tmp = ((b * c) + (y * (((-4.0d0) * ((t * a) / y)) + (18.0d0 * (t * (z * x)))))) - (k * (j * 27.0d0))
    else
        tmp = ((b * c) + (t * (((z * y) * (x * 18.0d0)) - (a * 4.0d0)))) - ((x * (i * 4.0d0)) + (j * (k * 27.0d0)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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 (y <= -1.65e+166) {
		tmp = ((b * c) + (y * ((-4.0 * ((t * a) / y)) + (18.0 * (t * (z * x)))))) - (k * (j * 27.0));
	} else {
		tmp = ((b * c) + (t * (((z * y) * (x * 18.0)) - (a * 4.0)))) - ((x * (i * 4.0)) + (j * (k * 27.0)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[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 y <= -1.65e+166:
		tmp = ((b * c) + (y * ((-4.0 * ((t * a) / y)) + (18.0 * (t * (z * x)))))) - (k * (j * 27.0))
	else:
		tmp = ((b * c) + (t * (((z * y) * (x * 18.0)) - (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])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (y <= -1.65e+166)
		tmp = Float64(Float64(Float64(b * c) + Float64(y * Float64(Float64(-4.0 * Float64(Float64(t * a) / y)) + Float64(18.0 * Float64(t * Float64(z * x)))))) - Float64(k * Float64(j * 27.0)));
	else
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(Float64(z * y) * Float64(x * 18.0)) - Float64(a * 4.0)))) - Float64(Float64(x * Float64(i * 4.0)) + Float64(j * Float64(k * 27.0))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
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 (y <= -1.65e+166)
		tmp = ((b * c) + (y * ((-4.0 * ((t * a) / y)) + (18.0 * (t * (z * x)))))) - (k * (j * 27.0));
	else
		tmp = ((b * c) + (t * (((z * y) * (x * 18.0)) - (a * 4.0)))) - ((x * (i * 4.0)) + (j * (k * 27.0)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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[LessEqual[y, -1.65e+166], N[(N[(N[(b * c), $MachinePrecision] + N[(y * N[(N[(-4.0 * N[(N[(t * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] + N[(18.0 * N[(t * N[(z * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(N[(z * y), $MachinePrecision] * N[(x * 18.0), $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]]

Derivation

1. Split input into 2 regimes

2. if y < -1.6500000000000001e166

   1. Initial program 81.3%

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

   3. Taylor expanded in a around inf 73.7%

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

   4. Taylor expanded in y around inf 89.0%

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

   5. Taylor expanded in i around 0 86.6%

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

   if -1.6500000000000001e166 < y

   1. Initial program 88.2%

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

   3. Simplified 89.6%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{+166}:\\ \;\;\;\;\left(b \cdot c + y \cdot \left(-4 \cdot \frac{t \cdot a}{y} + 18 \cdot \left(t \cdot \left(z \cdot x\right)\right)\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(z \cdot y\right) \cdot \left(x \cdot 18\right) - a \cdot 4\right)\right) - \left(x \cdot \left(i \cdot 4\right) + j \cdot \left(k \cdot 27\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 81.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := k \cdot \left(j \cdot 27\right)\\ \mathbf{if}\;y \leq -9 \cdot 10^{+79}:\\ \;\;\;\;\left(b \cdot c + y \cdot \left(-4 \cdot \frac{t \cdot a}{y} + 18 \cdot \left(t \cdot \left(z \cdot x\right)\right)\right)\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a + x \cdot i\right)\right) - t\_1\\ \end{array} \end{array} \]

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.
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 (<= y -9e+79)
     (-
      (+ (* b c) (* y (+ (* -4.0 (/ (* t a) y)) (* 18.0 (* t (* z x))))))
      t_1)
     (- (- (* b c) (* 4.0 (+ (* t a) (* x i)))) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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 (y <= -9e+79) {
		tmp = ((b * c) + (y * ((-4.0 * ((t * a) / y)) + (18.0 * (t * (z * x)))))) - t_1;
	} else {
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - 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.
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 (y <= (-9d+79)) then
        tmp = ((b * c) + (y * (((-4.0d0) * ((t * a) / y)) + (18.0d0 * (t * (z * x)))))) - t_1
    else
        tmp = ((b * c) - (4.0d0 * ((t * a) + (x * i)))) - 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;
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 (y <= -9e+79) {
		tmp = ((b * c) + (y * ((-4.0 * ((t * a) / y)) + (18.0 * (t * (z * x)))))) - t_1;
	} else {
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - 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])
[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 y <= -9e+79:
		tmp = ((b * c) + (y * ((-4.0 * ((t * a) / y)) + (18.0 * (t * (z * x)))))) - t_1
	else:
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - 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])
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 (y <= -9e+79)
		tmp = Float64(Float64(Float64(b * c) + Float64(y * Float64(Float64(-4.0 * Float64(Float64(t * a) / y)) + Float64(18.0 * Float64(t * Float64(z * x)))))) - t_1);
	else
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(Float64(t * a) + Float64(x * i)))) - 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])){:}
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 (y <= -9e+79)
		tmp = ((b * c) + (y * ((-4.0 * ((t * a) / y)) + (18.0 * (t * (z * x)))))) - t_1;
	else
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - 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.
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[y, -9e+79], N[(N[(N[(b * c), $MachinePrecision] + N[(y * N[(N[(-4.0 * N[(N[(t * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] + N[(18.0 * N[(t * N[(z * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -8.99999999999999987e79

   1. Initial program 77.8%

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

   3. Taylor expanded in a around inf 74.1%

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

   4. Taylor expanded in y around inf 87.6%

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

   5. Taylor expanded in i around 0 87.8%

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

   if -8.99999999999999987e79 < y

   1. Initial program 89.4%

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

   3. Taylor expanded in y around 0 83.8%

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

      1. distribute-lft-out 83.8%

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

      2. *-commutative 83.8%

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

   5. Simplified 83.8%

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

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+79}:\\ \;\;\;\;\left(b \cdot c + y \cdot \left(-4 \cdot \frac{t \cdot a}{y} + 18 \cdot \left(t \cdot \left(z \cdot x\right)\right)\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a + x \cdot i\right)\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 68.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := k \cdot \left(j \cdot 27\right)\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+149}:\\ \;\;\;\;t\_1 + b \cdot c\\ \mathbf{elif}\;t\_2 \leq 10^{+125}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 + x \cdot \left(-4 \cdot i\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 (* k -27.0))) (t_2 (* k (* j 27.0))))
   (if (<= t_2 -1e+149)
     (+ t_1 (* b c))
     (if (<= t_2 1e+125)
       (- (* b c) (* 4.0 (+ (* t a) (* x i))))
       (+ t_1 (* x (* -4.0 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);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = k * (j * 27.0);
	double tmp;
	if (t_2 <= -1e+149) {
		tmp = t_1 + (b * c);
	} else if (t_2 <= 1e+125) {
		tmp = (b * c) - (4.0 * ((t * a) + (x * i)));
	} else {
		tmp = t_1 + (x * (-4.0 * 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.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * (k * (-27.0d0))
    t_2 = k * (j * 27.0d0)
    if (t_2 <= (-1d+149)) then
        tmp = t_1 + (b * c)
    else if (t_2 <= 1d+125) then
        tmp = (b * c) - (4.0d0 * ((t * a) + (x * i)))
    else
        tmp = t_1 + (x * ((-4.0d0) * 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;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = k * (j * 27.0);
	double tmp;
	if (t_2 <= -1e+149) {
		tmp = t_1 + (b * c);
	} else if (t_2 <= 1e+125) {
		tmp = (b * c) - (4.0 * ((t * a) + (x * i)));
	} else {
		tmp = t_1 + (x * (-4.0 * i));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[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 * (k * -27.0)
	t_2 = k * (j * 27.0)
	tmp = 0
	if t_2 <= -1e+149:
		tmp = t_1 + (b * c)
	elif t_2 <= 1e+125:
		tmp = (b * c) - (4.0 * ((t * a) + (x * i)))
	else:
		tmp = t_1 + (x * (-4.0 * i))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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(k * -27.0))
	t_2 = Float64(k * Float64(j * 27.0))
	tmp = 0.0
	if (t_2 <= -1e+149)
		tmp = Float64(t_1 + Float64(b * c));
	elseif (t_2 <= 1e+125)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(Float64(t * a) + Float64(x * i))));
	else
		tmp = Float64(t_1 + Float64(x * Float64(-4.0 * i)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
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 * (k * -27.0);
	t_2 = k * (j * 27.0);
	tmp = 0.0;
	if (t_2 <= -1e+149)
		tmp = t_1 + (b * c);
	elseif (t_2 <= 1e+125)
		tmp = (b * c) - (4.0 * ((t * a) + (x * i)));
	else
		tmp = t_1 + (x * (-4.0 * i));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+149], N[(t$95$1 + N[(b * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+125], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(x * N[(-4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 81.9%

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

   3. Simplified 87.3%

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

   5. Taylor expanded in b around inf 85.4%

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

   if -1.00000000000000005e149 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 9.9999999999999992e124

   1. Initial program 88.8%

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

   3. Taylor expanded in y around 0 76.8%

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

      1. distribute-lft-out 76.8%

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

      2. *-commutative 76.8%

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

   5. Simplified 76.8%

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

   6. Taylor expanded in j around 0 70.1%

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

   if 9.9999999999999992e124 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 84.5%

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

   3. Simplified 78.6%

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

   5. Taylor expanded in i around inf 75.4%

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

      1. associate-*r* 75.4%

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

      2. *-commutative 75.4%

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

   7. Simplified 75.4%

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

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \cdot \left(j \cdot 27\right) \leq -1 \cdot 10^{+149}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 10^{+125}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + x \cdot \left(-4 \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 78.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := k \cdot \left(j \cdot 27\right)\\ \mathbf{if}\;z \leq -5.2 \cdot 10^{-50}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + x \cdot \left(-4 \cdot i + 18 \cdot \left(t \cdot \left(z \cdot y\right)\right)\right)\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{+178}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a + x \cdot i\right)\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(-x\right) \cdot \left(i \cdot 4 + -18 \cdot \left(z \cdot \left(t \cdot y\right)\right)\right) - t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 (<= z -5.2e-50)
     (+ (* j (* k -27.0)) (* x (+ (* -4.0 i) (* 18.0 (* t (* z y))))))
     (if (<= z 5.1e+178)
       (- (- (* b c) (* 4.0 (+ (* t a) (* x i)))) t_1)
       (- (* (- x) (+ (* i 4.0) (* -18.0 (* z (* t y))))) 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);
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 (z <= -5.2e-50) {
		tmp = (j * (k * -27.0)) + (x * ((-4.0 * i) + (18.0 * (t * (z * y)))));
	} else if (z <= 5.1e+178) {
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - t_1;
	} else {
		tmp = (-x * ((i * 4.0) + (-18.0 * (z * (t * y))))) - 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.
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 (z <= (-5.2d-50)) then
        tmp = (j * (k * (-27.0d0))) + (x * (((-4.0d0) * i) + (18.0d0 * (t * (z * y)))))
    else if (z <= 5.1d+178) then
        tmp = ((b * c) - (4.0d0 * ((t * a) + (x * i)))) - t_1
    else
        tmp = (-x * ((i * 4.0d0) + ((-18.0d0) * (z * (t * y))))) - 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;
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 (z <= -5.2e-50) {
		tmp = (j * (k * -27.0)) + (x * ((-4.0 * i) + (18.0 * (t * (z * y)))));
	} else if (z <= 5.1e+178) {
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - t_1;
	} else {
		tmp = (-x * ((i * 4.0) + (-18.0 * (z * (t * y))))) - 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])
[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 z <= -5.2e-50:
		tmp = (j * (k * -27.0)) + (x * ((-4.0 * i) + (18.0 * (t * (z * y)))))
	elif z <= 5.1e+178:
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - t_1
	else:
		tmp = (-x * ((i * 4.0) + (-18.0 * (z * (t * y))))) - 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])
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 (z <= -5.2e-50)
		tmp = Float64(Float64(j * Float64(k * -27.0)) + Float64(x * Float64(Float64(-4.0 * i) + Float64(18.0 * Float64(t * Float64(z * y))))));
	elseif (z <= 5.1e+178)
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(Float64(t * a) + Float64(x * i)))) - t_1);
	else
		tmp = Float64(Float64(Float64(-x) * Float64(Float64(i * 4.0) + Float64(-18.0 * Float64(z * Float64(t * y))))) - 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])){:}
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 (z <= -5.2e-50)
		tmp = (j * (k * -27.0)) + (x * ((-4.0 * i) + (18.0 * (t * (z * y)))));
	elseif (z <= 5.1e+178)
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - t_1;
	else
		tmp = (-x * ((i * 4.0) + (-18.0 * (z * (t * y))))) - 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.
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[z, -5.2e-50], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(-4.0 * i), $MachinePrecision] + N[(18.0 * N[(t * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.1e+178], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[((-x) * N[(N[(i * 4.0), $MachinePrecision] + N[(-18.0 * N[(z * N[(t * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.2000000000000003e-50

   1. Initial program 79.3%

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

   3. Simplified 84.1%

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

   5. Taylor expanded in x around inf 67.4%

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

   if -5.2000000000000003e-50 < z < 5.0999999999999997e178

   1. Initial program 92.6%

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

   3. Taylor expanded in y around 0 88.3%

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

      1. distribute-lft-out 88.3%

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

      2. *-commutative 88.3%

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

   5. Simplified 88.3%

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

   if 5.0999999999999997e178 < z

   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 a around inf 66.1%

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

   4. Taylor expanded in y around inf 62.3%

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

   5. Taylor expanded in x around -inf 66.5%

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

      1. associate-*r* 66.5%

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

      2. mul-1-neg 66.5%

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

      3. cancel-sign-sub-inv 66.5%

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

      4. associate-*r* 77.5%

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

      5. metadata-eval 77.5%

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

   7. Simplified 77.5%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{-50}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + x \cdot \left(-4 \cdot i + 18 \cdot \left(t \cdot \left(z \cdot y\right)\right)\right)\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{+178}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a + x \cdot i\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-x\right) \cdot \left(i \cdot 4 + -18 \cdot \left(z \cdot \left(t \cdot y\right)\right)\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 53.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := k \cdot \left(j \cdot 27\right)\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{-57}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+73}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(\frac{b \cdot c}{k} - j \cdot 27\right)\\ \end{array} \end{array} \]

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.
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 -4e-57)
     (+ (* j (* k -27.0)) (* b c))
     (if (<= t_1 5e+73)
       (- (* b c) (* 4.0 (* x i)))
       (* k (- (/ (* b c) 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);
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 <= -4e-57) {
		tmp = (j * (k * -27.0)) + (b * c);
	} else if (t_1 <= 5e+73) {
		tmp = (b * c) - (4.0 * (x * i));
	} else {
		tmp = k * (((b * c) / 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.
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 <= (-4d-57)) then
        tmp = (j * (k * (-27.0d0))) + (b * c)
    else if (t_1 <= 5d+73) then
        tmp = (b * c) - (4.0d0 * (x * i))
    else
        tmp = k * (((b * c) / 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;
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 <= -4e-57) {
		tmp = (j * (k * -27.0)) + (b * c);
	} else if (t_1 <= 5e+73) {
		tmp = (b * c) - (4.0 * (x * i));
	} else {
		tmp = k * (((b * c) / 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])
[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 <= -4e-57:
		tmp = (j * (k * -27.0)) + (b * c)
	elif t_1 <= 5e+73:
		tmp = (b * c) - (4.0 * (x * i))
	else:
		tmp = k * (((b * c) / 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])
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 <= -4e-57)
		tmp = Float64(Float64(j * Float64(k * -27.0)) + Float64(b * c));
	elseif (t_1 <= 5e+73)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)));
	else
		tmp = Float64(k * Float64(Float64(Float64(b * c) / 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])){:}
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 <= -4e-57)
		tmp = (j * (k * -27.0)) + (b * c);
	elseif (t_1 <= 5e+73)
		tmp = (b * c) - (4.0 * (x * i));
	else
		tmp = k * (((b * c) / 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.
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, -4e-57], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+73], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(k * N[(N[(N[(b * c), $MachinePrecision] / k), $MachinePrecision] - N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -3.99999999999999982e-57

   1. Initial program 86.1%

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

   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 b around inf 65.8%

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

   if -3.99999999999999982e-57 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 4.99999999999999976e73

   1. Initial program 88.3%

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

   3. Taylor expanded in t around 0 58.2%

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

   4. Taylor expanded in j around 0 55.7%

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

   if 4.99999999999999976e73 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 85.9%

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

   3. Taylor expanded in a around inf 81.4%

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

   4. Taylor expanded in y around inf 78.9%

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

   5. Taylor expanded in b around inf 62.7%

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

   6. Taylor expanded in k around inf 65.1%

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

4. Final simplification 60.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \cdot \left(j \cdot 27\right) \leq -4 \cdot 10^{-57}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 5 \cdot 10^{+73}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(\frac{b \cdot c}{k} - j \cdot 27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 53.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := k \cdot \left(j \cdot 27\right)\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{-57}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+73}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(\frac{b \cdot c}{j} - k \cdot 27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 -4e-57)
     (+ (* j (* k -27.0)) (* b c))
     (if (<= t_1 5e+73)
       (- (* b c) (* 4.0 (* x i)))
       (* j (- (/ (* b c) j) (* k 27.0)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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 <= -4e-57) {
		tmp = (j * (k * -27.0)) + (b * c);
	} else if (t_1 <= 5e+73) {
		tmp = (b * c) - (4.0 * (x * i));
	} else {
		tmp = j * (((b * c) / j) - (k * 27.0));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 <= (-4d-57)) then
        tmp = (j * (k * (-27.0d0))) + (b * c)
    else if (t_1 <= 5d+73) then
        tmp = (b * c) - (4.0d0 * (x * i))
    else
        tmp = j * (((b * c) / j) - (k * 27.0d0))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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 <= -4e-57) {
		tmp = (j * (k * -27.0)) + (b * c);
	} else if (t_1 <= 5e+73) {
		tmp = (b * c) - (4.0 * (x * i));
	} else {
		tmp = j * (((b * c) / j) - (k * 27.0));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[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 <= -4e-57:
		tmp = (j * (k * -27.0)) + (b * c)
	elif t_1 <= 5e+73:
		tmp = (b * c) - (4.0 * (x * i))
	else:
		tmp = j * (((b * c) / j) - (k * 27.0))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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 <= -4e-57)
		tmp = Float64(Float64(j * Float64(k * -27.0)) + Float64(b * c));
	elseif (t_1 <= 5e+73)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)));
	else
		tmp = Float64(j * Float64(Float64(Float64(b * c) / j) - Float64(k * 27.0)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
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 <= -4e-57)
		tmp = (j * (k * -27.0)) + (b * c);
	elseif (t_1 <= 5e+73)
		tmp = (b * c) - (4.0 * (x * i));
	else
		tmp = j * (((b * c) / j) - (k * 27.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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, -4e-57], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+73], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(j * N[(N[(N[(b * c), $MachinePrecision] / j), $MachinePrecision] - N[(k * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -3.99999999999999982e-57

   1. Initial program 86.1%

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

   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 b around inf 65.8%

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

   if -3.99999999999999982e-57 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 4.99999999999999976e73

   1. Initial program 88.3%

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

   3. Taylor expanded in t around 0 58.2%

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

   4. Taylor expanded in j around 0 55.7%

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

   if 4.99999999999999976e73 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 85.9%

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

   3. Taylor expanded in a around inf 81.4%

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

   4. Taylor expanded in y around inf 78.9%

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

   5. Taylor expanded in b around inf 62.7%

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

   6. Taylor expanded in j around inf 65.2%

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

4. Final simplification 60.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \cdot \left(j \cdot 27\right) \leq -4 \cdot 10^{-57}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 5 \cdot 10^{+73}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(\frac{b \cdot c}{j} - k \cdot 27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 79.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+80}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(z \cdot y\right) \cdot \left(x \cdot 18\right) - a \cdot 4\right)\right) - j \cdot \left(k \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a + x \cdot i\right)\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \end{array} \]

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.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= y -1.1e+80)
   (- (+ (* b c) (* t (- (* (* z y) (* x 18.0)) (* a 4.0)))) (* j (* k 27.0)))
   (- (- (* b c) (* 4.0 (+ (* t a) (* x i)))) (* 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);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (y <= -1.1e+80) {
		tmp = ((b * c) + (t * (((z * y) * (x * 18.0)) - (a * 4.0)))) - (j * (k * 27.0));
	} else {
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - (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.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (y <= (-1.1d+80)) then
        tmp = ((b * c) + (t * (((z * y) * (x * 18.0d0)) - (a * 4.0d0)))) - (j * (k * 27.0d0))
    else
        tmp = ((b * c) - (4.0d0 * ((t * a) + (x * i)))) - (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;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (y <= -1.1e+80) {
		tmp = ((b * c) + (t * (((z * y) * (x * 18.0)) - (a * 4.0)))) - (j * (k * 27.0));
	} else {
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - (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])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if y <= -1.1e+80:
		tmp = ((b * c) + (t * (((z * y) * (x * 18.0)) - (a * 4.0)))) - (j * (k * 27.0))
	else:
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - (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])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (y <= -1.1e+80)
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(Float64(z * y) * Float64(x * 18.0)) - Float64(a * 4.0)))) - Float64(j * Float64(k * 27.0)));
	else
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(Float64(t * a) + Float64(x * i)))) - 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])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (y <= -1.1e+80)
		tmp = ((b * c) + (t * (((z * y) * (x * 18.0)) - (a * 4.0)))) - (j * (k * 27.0));
	else
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - (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.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[y, -1.1e+80], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(N[(z * y), $MachinePrecision] * N[(x * 18.0), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(j * N[(k * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.10000000000000001e80

   1. Initial program 77.8%

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

   3. Simplified 81.7%

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

   5. Taylor expanded in x around 0 82.0%

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

      1. *-commutative 82.0%

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

      2. associate-*r* 82.0%

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

   7. Simplified 82.0%

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

   if -1.10000000000000001e80 < y

   1. Initial program 89.4%

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

   3. Taylor expanded in y around 0 83.8%

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

      1. distribute-lft-out 83.8%

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

      2. *-commutative 83.8%

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

   5. Simplified 83.8%

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

4. Final simplification 83.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+80}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(z \cdot y\right) \cdot \left(x \cdot 18\right) - a \cdot 4\right)\right) - j \cdot \left(k \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a + x \cdot i\right)\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 53.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := k \cdot \left(j \cdot 27\right)\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{-57} \lor \neg \left(t\_1 \leq 5 \cdot 10^{+73}\right):\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 (<= t_1 -4e-57) (not (<= t_1 5e+73)))
     (+ (* j (* k -27.0)) (* b c))
     (- (* b c) (* 4.0 (* x i))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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 <= -4e-57) || !(t_1 <= 5e+73)) {
		tmp = (j * (k * -27.0)) + (b * c);
	} else {
		tmp = (b * c) - (4.0 * (x * i));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 <= (-4d-57)) .or. (.not. (t_1 <= 5d+73))) then
        tmp = (j * (k * (-27.0d0))) + (b * c)
    else
        tmp = (b * c) - (4.0d0 * (x * i))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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 <= -4e-57) || !(t_1 <= 5e+73)) {
		tmp = (j * (k * -27.0)) + (b * c);
	} else {
		tmp = (b * c) - (4.0 * (x * i));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[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 <= -4e-57) or not (t_1 <= 5e+73):
		tmp = (j * (k * -27.0)) + (b * c)
	else:
		tmp = (b * c) - (4.0 * (x * i))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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 <= -4e-57) || !(t_1 <= 5e+73))
		tmp = Float64(Float64(j * Float64(k * -27.0)) + Float64(b * c));
	else
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
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 <= -4e-57) || ~((t_1 <= 5e+73)))
		tmp = (j * (k * -27.0)) + (b * c);
	else
		tmp = (b * c) - (4.0 * (x * i));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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[t$95$1, -4e-57], N[Not[LessEqual[t$95$1, 5e+73]], $MachinePrecision]], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -3.99999999999999982e-57 or 4.99999999999999976e73 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 86.0%

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

   3. Simplified 86.2%

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

   5. Taylor expanded in b around inf 64.8%

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

   if -3.99999999999999982e-57 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 4.99999999999999976e73

   1. Initial program 88.3%

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

   3. Taylor expanded in t around 0 58.2%

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

   4. Taylor expanded in j around 0 55.7%

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

4. Final simplification 60.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \cdot \left(j \cdot 27\right) \leq -4 \cdot 10^{-57} \lor \neg \left(k \cdot \left(j \cdot 27\right) \leq 5 \cdot 10^{+73}\right):\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 33.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;c \leq -3.6 \cdot 10^{-109}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;c \leq 4.5 \cdot 10^{-264}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;c \leq 1.15 \cdot 10^{-176}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;c \leq 2.3 \cdot 10^{+93}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 (<= c -3.6e-109)
   (* b c)
   (if (<= c 4.5e-264)
     (* j (* k -27.0))
     (if (<= c 1.15e-176)
       (* -4.0 (* x i))
       (if (<= c 2.3e+93) (* k (* j -27.0)) (* b c))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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 (c <= -3.6e-109) {
		tmp = b * c;
	} else if (c <= 4.5e-264) {
		tmp = j * (k * -27.0);
	} else if (c <= 1.15e-176) {
		tmp = -4.0 * (x * i);
	} else if (c <= 2.3e+93) {
		tmp = k * (j * -27.0);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 (c <= (-3.6d-109)) then
        tmp = b * c
    else if (c <= 4.5d-264) then
        tmp = j * (k * (-27.0d0))
    else if (c <= 1.15d-176) then
        tmp = (-4.0d0) * (x * i)
    else if (c <= 2.3d+93) then
        tmp = k * (j * (-27.0d0))
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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 (c <= -3.6e-109) {
		tmp = b * c;
	} else if (c <= 4.5e-264) {
		tmp = j * (k * -27.0);
	} else if (c <= 1.15e-176) {
		tmp = -4.0 * (x * i);
	} else if (c <= 2.3e+93) {
		tmp = k * (j * -27.0);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[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 c <= -3.6e-109:
		tmp = b * c
	elif c <= 4.5e-264:
		tmp = j * (k * -27.0)
	elif c <= 1.15e-176:
		tmp = -4.0 * (x * i)
	elif c <= 2.3e+93:
		tmp = k * (j * -27.0)
	else:
		tmp = b * c
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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 (c <= -3.6e-109)
		tmp = Float64(b * c);
	elseif (c <= 4.5e-264)
		tmp = Float64(j * Float64(k * -27.0));
	elseif (c <= 1.15e-176)
		tmp = Float64(-4.0 * Float64(x * i));
	elseif (c <= 2.3e+93)
		tmp = Float64(k * Float64(j * -27.0));
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
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 (c <= -3.6e-109)
		tmp = b * c;
	elseif (c <= 4.5e-264)
		tmp = j * (k * -27.0);
	elseif (c <= 1.15e-176)
		tmp = -4.0 * (x * i);
	elseif (c <= 2.3e+93)
		tmp = k * (j * -27.0);
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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[LessEqual[c, -3.6e-109], N[(b * c), $MachinePrecision], If[LessEqual[c, 4.5e-264], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.15e-176], N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.3e+93], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -3.6000000000000001e-109 or 2.3000000000000002e93 < c

   1. Initial program 86.3%

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

   3. Taylor expanded in t around 0 71.6%

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

   4. Taylor expanded in b around inf 42.7%

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

   if -3.6000000000000001e-109 < c < 4.5000000000000001e-264

   1. Initial program 90.5%

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

   3. Simplified 94.2%

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

   5. Taylor expanded in j around inf 32.1%

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

      1. *-commutative 32.1%

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

      2. associate-*r* 32.2%

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

      3. *-commutative 32.2%

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

   7. Simplified 32.2%

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

   if 4.5000000000000001e-264 < c < 1.1500000000000001e-176

   1. Initial program 76.5%

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

   3. Simplified 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 i around inf 51.4%

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

      1. associate-*r* 51.4%

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

      2. *-commutative 51.4%

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

   7. Simplified 51.4%

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

   8. Taylor expanded in x around inf 30.1%

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

      1. *-commutative 30.1%

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

   10. Simplified 30.1%

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

   if 1.1500000000000001e-176 < c < 2.3000000000000002e93

   1. Initial program 89.9%

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

   3. Simplified 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 52.4%

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

      1. associate-*r* 52.4%

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

      2. *-commutative 52.4%

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

   7. Simplified 52.4%

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

   8. Taylor expanded in x around 0 26.4%

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

      1. *-commutative 26.4%

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

      2. *-commutative 26.4%

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

      3. associate-*r* 26.3%

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

      4. *-commutative 26.3%

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

   10. Simplified 26.3%

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

4. Final simplification 35.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.6 \cdot 10^{-109}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;c \leq 4.5 \cdot 10^{-264}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;c \leq 1.15 \cdot 10^{-176}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;c \leq 2.3 \cdot 10^{+93}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 33.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;c \leq -1 \cdot 10^{-109}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;c \leq 2.6 \cdot 10^{-264}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 1.3 \cdot 10^{-174}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;c \leq 1.8 \cdot 10^{+93}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

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.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0))))
   (if (<= c -1e-109)
     (* b c)
     (if (<= c 2.6e-264)
       t_1
       (if (<= c 1.3e-174)
         (* -4.0 (* x i))
         (if (<= c 1.8e+93) 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);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double tmp;
	if (c <= -1e-109) {
		tmp = b * c;
	} else if (c <= 2.6e-264) {
		tmp = t_1;
	} else if (c <= 1.3e-174) {
		tmp = -4.0 * (x * i);
	} else if (c <= 1.8e+93) {
		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.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * (k * (-27.0d0))
    if (c <= (-1d-109)) then
        tmp = b * c
    else if (c <= 2.6d-264) then
        tmp = t_1
    else if (c <= 1.3d-174) then
        tmp = (-4.0d0) * (x * i)
    else if (c <= 1.8d+93) 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;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double tmp;
	if (c <= -1e-109) {
		tmp = b * c;
	} else if (c <= 2.6e-264) {
		tmp = t_1;
	} else if (c <= 1.3e-174) {
		tmp = -4.0 * (x * i);
	} else if (c <= 1.8e+93) {
		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])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	tmp = 0
	if c <= -1e-109:
		tmp = b * c
	elif c <= 2.6e-264:
		tmp = t_1
	elif c <= 1.3e-174:
		tmp = -4.0 * (x * i)
	elif c <= 1.8e+93:
		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])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * -27.0))
	tmp = 0.0
	if (c <= -1e-109)
		tmp = Float64(b * c);
	elseif (c <= 2.6e-264)
		tmp = t_1;
	elseif (c <= 1.3e-174)
		tmp = Float64(-4.0 * Float64(x * i));
	elseif (c <= 1.8e+93)
		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])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * -27.0);
	tmp = 0.0;
	if (c <= -1e-109)
		tmp = b * c;
	elseif (c <= 2.6e-264)
		tmp = t_1;
	elseif (c <= 1.3e-174)
		tmp = -4.0 * (x * i);
	elseif (c <= 1.8e+93)
		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.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1e-109], N[(b * c), $MachinePrecision], If[LessEqual[c, 2.6e-264], t$95$1, If[LessEqual[c, 1.3e-174], N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.8e+93], t$95$1, N[(b * c), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -9.9999999999999999e-110 or 1.8e93 < c

   1. Initial program 86.3%

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

   3. Taylor expanded in t around 0 71.6%

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

   4. Taylor expanded in b around inf 42.7%

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

   if -9.9999999999999999e-110 < c < 2.6000000000000002e-264 or 1.3000000000000001e-174 < c < 1.8e93

   1. Initial program 90.2%

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

   3. Simplified 91.2%

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

   5. Taylor expanded in j around inf 29.0%

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

      1. *-commutative 29.0%

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

      2. associate-*r* 29.1%

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

      3. *-commutative 29.1%

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

   7. Simplified 29.1%

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

   if 2.6000000000000002e-264 < c < 1.3000000000000001e-174

   1. Initial program 76.5%

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

   3. Simplified 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 i around inf 51.4%

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

      1. associate-*r* 51.4%

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

      2. *-commutative 51.4%

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

   7. Simplified 51.4%

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

   8. Taylor expanded in x around inf 30.1%

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

      1. *-commutative 30.1%

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

   10. Simplified 30.1%

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

4. Final simplification 35.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1 \cdot 10^{-109}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;c \leq 2.6 \cdot 10^{-264}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;c \leq 1.3 \cdot 10^{-174}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;c \leq 1.8 \cdot 10^{+93}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 33.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := -27 \cdot \left(j \cdot k\right)\\ \mathbf{if}\;c \leq -4.8 \cdot 10^{-118}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;c \leq 1.6 \cdot 10^{-262}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 9.2 \cdot 10^{-177}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;c \leq 1.95 \cdot 10^{+95}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

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.
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 (<= c -4.8e-118)
     (* b c)
     (if (<= c 1.6e-262)
       t_1
       (if (<= c 9.2e-177)
         (* -4.0 (* x i))
         (if (<= c 1.95e+95) 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);
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 (c <= -4.8e-118) {
		tmp = b * c;
	} else if (c <= 1.6e-262) {
		tmp = t_1;
	} else if (c <= 9.2e-177) {
		tmp = -4.0 * (x * i);
	} else if (c <= 1.95e+95) {
		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.
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 (c <= (-4.8d-118)) then
        tmp = b * c
    else if (c <= 1.6d-262) then
        tmp = t_1
    else if (c <= 9.2d-177) then
        tmp = (-4.0d0) * (x * i)
    else if (c <= 1.95d+95) 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;
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 (c <= -4.8e-118) {
		tmp = b * c;
	} else if (c <= 1.6e-262) {
		tmp = t_1;
	} else if (c <= 9.2e-177) {
		tmp = -4.0 * (x * i);
	} else if (c <= 1.95e+95) {
		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])
[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 c <= -4.8e-118:
		tmp = b * c
	elif c <= 1.6e-262:
		tmp = t_1
	elif c <= 9.2e-177:
		tmp = -4.0 * (x * i)
	elif c <= 1.95e+95:
		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])
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 (c <= -4.8e-118)
		tmp = Float64(b * c);
	elseif (c <= 1.6e-262)
		tmp = t_1;
	elseif (c <= 9.2e-177)
		tmp = Float64(-4.0 * Float64(x * i));
	elseif (c <= 1.95e+95)
		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])){:}
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 (c <= -4.8e-118)
		tmp = b * c;
	elseif (c <= 1.6e-262)
		tmp = t_1;
	elseif (c <= 9.2e-177)
		tmp = -4.0 * (x * i);
	elseif (c <= 1.95e+95)
		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.
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[c, -4.8e-118], N[(b * c), $MachinePrecision], If[LessEqual[c, 1.6e-262], t$95$1, If[LessEqual[c, 9.2e-177], N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.95e+95], t$95$1, N[(b * c), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -4.8000000000000003e-118 or 1.9499999999999999e95 < c

   1. Initial program 86.7%

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

   3. Taylor expanded in t around 0 70.7%

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

   4. Taylor expanded in b around inf 41.8%

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

   if -4.8000000000000003e-118 < c < 1.6e-262 or 9.20000000000000087e-177 < c < 1.9499999999999999e95

   1. Initial program 90.0%

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

   3. Simplified 91.0%

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

   5. Taylor expanded in j around inf 28.7%

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

   if 1.6e-262 < c < 9.20000000000000087e-177

   1. Initial program 75.3%

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

   3. Simplified 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 i around inf 53.7%

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

      1. associate-*r* 53.7%

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

      2. *-commutative 53.7%

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

   7. Simplified 53.7%

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

   8. Taylor expanded in x around inf 31.5%

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

      1. *-commutative 31.5%

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

   10. Simplified 31.5%

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

Alternative 22: 71.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{+135} \lor \neg \left(t \leq 9 \cdot 10^{+110}\right):\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(z \cdot y\right)\right) - a \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \end{array} \]

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.
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 -1.3e+135) (not (<= t 9e+110)))
   (* t (- (* 18.0 (* x (* z y))) (* a 4.0)))
   (- (- (* b c) (* 4.0 (* x i))) (* 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);
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 <= -1.3e+135) || !(t <= 9e+110)) {
		tmp = t * ((18.0 * (x * (z * y))) - (a * 4.0));
	} else {
		tmp = ((b * c) - (4.0 * (x * i))) - (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.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((t <= (-1.3d+135)) .or. (.not. (t <= 9d+110))) then
        tmp = t * ((18.0d0 * (x * (z * y))) - (a * 4.0d0))
    else
        tmp = ((b * c) - (4.0d0 * (x * i))) - (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;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((t <= -1.3e+135) || !(t <= 9e+110)) {
		tmp = t * ((18.0 * (x * (z * y))) - (a * 4.0));
	} else {
		tmp = ((b * c) - (4.0 * (x * i))) - (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])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (t <= -1.3e+135) or not (t <= 9e+110):
		tmp = t * ((18.0 * (x * (z * y))) - (a * 4.0))
	else:
		tmp = ((b * c) - (4.0 * (x * i))) - (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])
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 <= -1.3e+135) || !(t <= 9e+110))
		tmp = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(z * y))) - Float64(a * 4.0)));
	else
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(x * i))) - 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])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((t <= -1.3e+135) || ~((t <= 9e+110)))
		tmp = t * ((18.0 * (x * (z * y))) - (a * 4.0));
	else
		tmp = ((b * c) - (4.0 * (x * i))) - (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.
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, -1.3e+135], N[Not[LessEqual[t, 9e+110]], $MachinePrecision]], N[(t * N[(N[(18.0 * N[(x * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.3e135 or 9.0000000000000005e110 < t

   1. Initial program 77.9%

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

   3. Simplified 83.8%

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

   5. Taylor expanded in t around inf 80.6%

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

   if -1.3e135 < t < 9.0000000000000005e110

   1. Initial program 90.6%

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

   3. Taylor expanded in t around 0 78.3%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{+135} \lor \neg \left(t \leq 9 \cdot 10^{+110}\right):\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(z \cdot y\right)\right) - a \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 76.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+166}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + x \cdot \left(-4 \cdot i + 18 \cdot \left(t \cdot \left(z \cdot y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a + x \cdot i\right)\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \end{array} \]

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.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= y -6.2e+166)
   (+ (* j (* k -27.0)) (* x (+ (* -4.0 i) (* 18.0 (* t (* z y))))))
   (- (- (* b c) (* 4.0 (+ (* t a) (* x i)))) (* 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);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (y <= -6.2e+166) {
		tmp = (j * (k * -27.0)) + (x * ((-4.0 * i) + (18.0 * (t * (z * y)))));
	} else {
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - (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.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (y <= (-6.2d+166)) then
        tmp = (j * (k * (-27.0d0))) + (x * (((-4.0d0) * i) + (18.0d0 * (t * (z * y)))))
    else
        tmp = ((b * c) - (4.0d0 * ((t * a) + (x * i)))) - (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;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (y <= -6.2e+166) {
		tmp = (j * (k * -27.0)) + (x * ((-4.0 * i) + (18.0 * (t * (z * y)))));
	} else {
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - (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])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if y <= -6.2e+166:
		tmp = (j * (k * -27.0)) + (x * ((-4.0 * i) + (18.0 * (t * (z * y)))))
	else:
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - (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])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (y <= -6.2e+166)
		tmp = Float64(Float64(j * Float64(k * -27.0)) + Float64(x * Float64(Float64(-4.0 * i) + Float64(18.0 * Float64(t * Float64(z * y))))));
	else
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(Float64(t * a) + Float64(x * i)))) - 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])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (y <= -6.2e+166)
		tmp = (j * (k * -27.0)) + (x * ((-4.0 * i) + (18.0 * (t * (z * y)))));
	else
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - (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.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[y, -6.2e+166], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(-4.0 * i), $MachinePrecision] + N[(18.0 * N[(t * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.19999999999999966e166

   1. Initial program 80.8%

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

   3. Simplified 80.7%

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

   5. Taylor expanded in x around inf 81.1%

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

   if -6.19999999999999966e166 < y

   1. Initial program 88.2%

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

   3. Taylor expanded in y around 0 82.5%

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

      1. distribute-lft-out 82.5%

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

      2. *-commutative 82.5%

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

   5. Simplified 82.5%

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

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+166}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + x \cdot \left(-4 \cdot i + 18 \cdot \left(t \cdot \left(z \cdot y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a + x \cdot i\right)\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 34.0% accurate, 2.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;c \leq -1.3 \cdot 10^{-113} \lor \neg \left(c \leq 3.5 \cdot 10^{+93}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \end{array} \]

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.
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 (<= c -1.3e-113) (not (<= c 3.5e+93))) (* 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);
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 ((c <= -1.3e-113) || !(c <= 3.5e+93)) {
		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.
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 ((c <= (-1.3d-113)) .or. (.not. (c <= 3.5d+93))) 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;
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 ((c <= -1.3e-113) || !(c <= 3.5e+93)) {
		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])
[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 (c <= -1.3e-113) or not (c <= 3.5e+93):
		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])
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 ((c <= -1.3e-113) || !(c <= 3.5e+93))
		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])){:}
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 ((c <= -1.3e-113) || ~((c <= 3.5e+93)))
		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.
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[c, -1.3e-113], N[Not[LessEqual[c, 3.5e+93]], $MachinePrecision]], N[(b * c), $MachinePrecision], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -1.3e-113 or 3.49999999999999998e93 < c

   1. Initial program 86.7%

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

   3. Taylor expanded in t around 0 70.7%

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

   4. Taylor expanded in b around inf 41.8%

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

   if -1.3e-113 < c < 3.49999999999999998e93

   1. Initial program 87.7%

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

   3. Simplified 90.1%

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

   5. Taylor expanded in j around inf 27.9%

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

4. Final simplification 34.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.3 \cdot 10^{-113} \lor \neg \left(c \leq 3.5 \cdot 10^{+93}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 45.3% accurate, 2.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq 4.2 \cdot 10^{+115}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \end{array} \end{array} \]

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.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= x 4.2e+115) (+ (* j (* k -27.0)) (* b c)) (* -4.0 (* x i))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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 <= 4.2e+115) {
		tmp = (j * (k * -27.0)) + (b * c);
	} else {
		tmp = -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.
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 <= 4.2d+115) then
        tmp = (j * (k * (-27.0d0))) + (b * c)
    else
        tmp = (-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;
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 <= 4.2e+115) {
		tmp = (j * (k * -27.0)) + (b * c);
	} else {
		tmp = -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])
[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 <= 4.2e+115:
		tmp = (j * (k * -27.0)) + (b * c)
	else:
		tmp = -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])
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 <= 4.2e+115)
		tmp = Float64(Float64(j * Float64(k * -27.0)) + Float64(b * c));
	else
		tmp = 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])){:}
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 <= 4.2e+115)
		tmp = (j * (k * -27.0)) + (b * c);
	else
		tmp = -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.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[x, 4.2e+115], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 4.20000000000000007e115

   1. Initial program 89.8%

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

   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 b around inf 51.3%

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

   if 4.20000000000000007e115 < x

   1. Initial program 69.0%

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

   3. Simplified 81.3%

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

   5. Taylor expanded in i around inf 61.2%

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

      1. associate-*r* 61.2%

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

      2. *-commutative 61.2%

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

   7. Simplified 61.2%

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

   8. Taylor expanded in x around inf 51.6%

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

      1. *-commutative 51.6%

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

   10. Simplified 51.6%

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

4. Final simplification 51.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 4.2 \cdot 10^{+115}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + b \cdot c\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 24.0% accurate, 10.3× speedup

Math

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

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

Derivation

1. Initial program 87.2%

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

3. Taylor expanded in t around 0 64.6%

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

4. Taylor expanded in b around inf 24.6%

   \[\leadsto \color{blue}{b \cdot c} \]
5. Add Preprocessing

Developer target: 88.7% 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 2024096 
(FPCore (x y z t a b c i j k)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, E"
  :precision binary64

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

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