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

Percentage Accurate: 84.8% → 90.5%

Time: 20.9s

Alternatives: 23

Speedup: 0.9×

• 50.6% 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: 84.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 90.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;y \leq -6.3 \cdot 10^{+162}:\\ \;\;\;\;y \cdot \left(\left(-4 \cdot \frac{a \cdot t}{y} + \left(18 \cdot \left(t \cdot \left(x \cdot z\right)\right) + \frac{b \cdot c}{y}\right)\right) - \left(4 \cdot \frac{x \cdot i}{y} + 27 \cdot \frac{j \cdot k}{y}\right)\right)\\ \mathbf{elif}\;y \leq 2.45 \cdot 10^{+33}:\\ \;\;\;\;\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), -4 \cdot a\right), \mathsf{fma}\left(b, c, x \cdot \left(-4 \cdot i\right)\right)\right) + t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_1 + z \cdot \left(\left(-4 \cdot \left(i \cdot \frac{x}{z}\right) + \left(t \cdot 18\right) \cdot \left(y \cdot x\right)\right) + \frac{\mathsf{fma}\left(-4, a \cdot t, b \cdot c\right)}{z}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0))))
   (if (<= y -6.3e+162)
     (*
      y
      (-
       (+ (* -4.0 (/ (* a t) y)) (+ (* 18.0 (* t (* x z))) (/ (* b c) y)))
       (+ (* 4.0 (/ (* x i) y)) (* 27.0 (/ (* j k) y)))))
     (if (<= y 2.45e+33)
       (+
        (fma t (fma x (* 18.0 (* y z)) (* -4.0 a)) (fma b c (* x (* -4.0 i))))
        t_1)
       (+
        t_1
        (*
         z
         (+
          (+ (* -4.0 (* i (/ x z))) (* (* t 18.0) (* y x)))
          (/ (fma -4.0 (* a t) (* b c)) z))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double tmp;
	if (y <= -6.3e+162) {
		tmp = y * (((-4.0 * ((a * t) / y)) + ((18.0 * (t * (x * z))) + ((b * c) / y))) - ((4.0 * ((x * i) / y)) + (27.0 * ((j * k) / y))));
	} else if (y <= 2.45e+33) {
		tmp = fma(t, fma(x, (18.0 * (y * z)), (-4.0 * a)), fma(b, c, (x * (-4.0 * i)))) + t_1;
	} else {
		tmp = t_1 + (z * (((-4.0 * (i * (x / z))) + ((t * 18.0) * (y * x))) + (fma(-4.0, (a * t), (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])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * -27.0))
	tmp = 0.0
	if (y <= -6.3e+162)
		tmp = Float64(y * Float64(Float64(Float64(-4.0 * Float64(Float64(a * t) / y)) + Float64(Float64(18.0 * Float64(t * Float64(x * z))) + Float64(Float64(b * c) / y))) - Float64(Float64(4.0 * Float64(Float64(x * i) / y)) + Float64(27.0 * Float64(Float64(j * k) / y)))));
	elseif (y <= 2.45e+33)
		tmp = Float64(fma(t, fma(x, Float64(18.0 * Float64(y * z)), Float64(-4.0 * a)), fma(b, c, Float64(x * Float64(-4.0 * i)))) + t_1);
	else
		tmp = Float64(t_1 + Float64(z * Float64(Float64(Float64(-4.0 * Float64(i * Float64(x / z))) + Float64(Float64(t * 18.0) * Float64(y * x))) + Float64(fma(-4.0, Float64(a * t), Float64(b * 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.
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[y, -6.3e+162], N[(y * N[(N[(N[(-4.0 * N[(N[(a * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] + N[(N[(18.0 * N[(t * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(b * c), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(4.0 * N[(N[(x * i), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] + N[(27.0 * N[(N[(j * k), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.45e+33], N[(N[(t * N[(x * N[(18.0 * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] + N[(b * c + N[(x * N[(-4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(t$95$1 + N[(z * N[(N[(N[(-4.0 * N[(i * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t * 18.0), $MachinePrecision] * N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(-4.0 * N[(a * t), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.3000000000000001e162

   1. Initial program 64.2%

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

   3. Simplified 64.2%

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

   5. Taylor expanded in y around inf 96.3%

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

   if -6.3000000000000001e162 < y < 2.45000000000000007e33

   1. Initial program 91.7%

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

   3. Simplified 94.5%

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

   if 2.45000000000000007e33 < y

   1. Initial program 89.5%

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

   3. Simplified 85.2%

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

   5. Taylor expanded in z around inf 72.5%

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

      1. +-commutative 72.5%

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

      2. associate-+r+ 72.5%

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

      3. associate-+l+ 72.5%

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

      4. associate-/l* 68.1%

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

      5. associate-*r* 68.1%

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

      6. metadata-eval 68.1%

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

      7. cancel-sign-sub-inv 68.1%

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

      8. associate-*r/ 68.1%

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

      9. div-sub 68.4%

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

   7. Simplified 68.4%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.3 \cdot 10^{+162}:\\ \;\;\;\;y \cdot \left(\left(-4 \cdot \frac{a \cdot t}{y} + \left(18 \cdot \left(t \cdot \left(x \cdot z\right)\right) + \frac{b \cdot c}{y}\right)\right) - \left(4 \cdot \frac{x \cdot i}{y} + 27 \cdot \frac{j \cdot k}{y}\right)\right)\\ \mathbf{elif}\;y \leq 2.45 \cdot 10^{+33}:\\ \;\;\;\;\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), -4 \cdot a\right), \mathsf{fma}\left(b, c, x \cdot \left(-4 \cdot i\right)\right)\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + z \cdot \left(\left(-4 \cdot \left(i \cdot \frac{x}{z}\right) + \left(t \cdot 18\right) \cdot \left(y \cdot x\right)\right) + \frac{\mathsf{fma}\left(-4, a \cdot t, b \cdot c\right)}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 92.1% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = i * (x * 4.0);
	double t_2 = k * (27.0 * j);
	double tmp;
	if (((((b * c) + ((t * (z * (y * (18.0 * x)))) - (t * (a * 4.0)))) - t_1) - t_2) <= Double.POSITIVE_INFINITY) {
		tmp = (((b * c) + (t * ((z * (x * (y * 18.0))) - (a * 4.0)))) - t_1) - t_2;
	} else {
		tmp = x * ((18.0 * (t * (y * z))) - (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])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = i * (x * 4.0)
	t_2 = k * (27.0 * j)
	tmp = 0
	if ((((b * c) + ((t * (z * (y * (18.0 * x)))) - (t * (a * 4.0)))) - t_1) - t_2) <= math.inf:
		tmp = (((b * c) + (t * ((z * (x * (y * 18.0))) - (a * 4.0)))) - t_1) - t_2
	else:
		tmp = x * ((18.0 * (t * (y * z))) - (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])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(i * Float64(x * 4.0))
	t_2 = Float64(k * Float64(27.0 * j))
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(b * c) + Float64(Float64(t * Float64(z * Float64(y * Float64(18.0 * x)))) - Float64(t * Float64(a * 4.0)))) - t_1) - t_2) <= Inf)
		tmp = Float64(Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(z * Float64(x * Float64(y * 18.0))) - Float64(a * 4.0)))) - t_1) - t_2);
	else
		tmp = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - 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])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = i * (x * 4.0);
	t_2 = k * (27.0 * j);
	tmp = 0.0;
	if (((((b * c) + ((t * (z * (y * (18.0 * x)))) - (t * (a * 4.0)))) - t_1) - t_2) <= Inf)
		tmp = (((b * c) + (t * ((z * (x * (y * 18.0))) - (a * 4.0)))) - t_1) - t_2;
	else
		tmp = x * ((18.0 * (t * (y * z))) - (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.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(i * N[(x * 4.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(k * N[(27.0 * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(N[(N[(b * c), $MachinePrecision] + N[(N[(t * N[(z * N[(y * N[(18.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision], Infinity], N[(N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(z * N[(x * N[(y * 18.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision], N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $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 94.3%

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

      1. distribute-rgt-out-- 94.3%

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

      2. associate-*r* 93.1%

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

      3. *-commutative 93.1%

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

      4. associate-*r* 94.3%

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

      5. *-commutative 94.3%

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

      6. associate-*l* 94.3%

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

   4. Applied egg-rr 94.3%

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

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

   1. Initial program 0.0%

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

   3. Simplified 25.0%

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

   5. Taylor expanded in x around inf 81.4%

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

4. Final simplification 93.5%

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

Alternative 3: 89.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+73}:\\ \;\;\;\;y \cdot \left(\left(-4 \cdot \frac{a \cdot t}{y} + \left(18 \cdot \left(t \cdot \left(x \cdot z\right)\right) + \frac{b \cdot c}{y}\right)\right) - \left(4 \cdot \frac{x \cdot i}{y} + 27 \cdot \frac{j \cdot k}{y}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b \cdot c + t \cdot \left(z \cdot \left(x \cdot \left(y \cdot 18\right)\right) - a \cdot 4\right)\right) - i \cdot \left(x \cdot 4\right)\right) - k \cdot \left(27 \cdot j\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= y -3.2e+73)
   (*
    y
    (-
     (+ (* -4.0 (/ (* a t) y)) (+ (* 18.0 (* t (* x z))) (/ (* b c) y)))
     (+ (* 4.0 (/ (* x i) y)) (* 27.0 (/ (* j k) y)))))
   (-
    (- (+ (* b c) (* t (- (* z (* x (* y 18.0))) (* a 4.0)))) (* i (* x 4.0)))
    (* k (* 27.0 j)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (y <= -3.2e+73) {
		tmp = y * (((-4.0 * ((a * t) / y)) + ((18.0 * (t * (x * z))) + ((b * c) / y))) - ((4.0 * ((x * i) / y)) + (27.0 * ((j * k) / y))));
	} else {
		tmp = (((b * c) + (t * ((z * (x * (y * 18.0))) - (a * 4.0)))) - (i * (x * 4.0))) - (k * (27.0 * j));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (y <= (-3.2d+73)) then
        tmp = y * ((((-4.0d0) * ((a * t) / y)) + ((18.0d0 * (t * (x * z))) + ((b * c) / y))) - ((4.0d0 * ((x * i) / y)) + (27.0d0 * ((j * k) / y))))
    else
        tmp = (((b * c) + (t * ((z * (x * (y * 18.0d0))) - (a * 4.0d0)))) - (i * (x * 4.0d0))) - (k * (27.0d0 * j))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (y <= -3.2e+73) {
		tmp = y * (((-4.0 * ((a * t) / y)) + ((18.0 * (t * (x * z))) + ((b * c) / y))) - ((4.0 * ((x * i) / y)) + (27.0 * ((j * k) / y))));
	} else {
		tmp = (((b * c) + (t * ((z * (x * (y * 18.0))) - (a * 4.0)))) - (i * (x * 4.0))) - (k * (27.0 * j));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if y <= -3.2e+73:
		tmp = y * (((-4.0 * ((a * t) / y)) + ((18.0 * (t * (x * z))) + ((b * c) / y))) - ((4.0 * ((x * i) / y)) + (27.0 * ((j * k) / y))))
	else:
		tmp = (((b * c) + (t * ((z * (x * (y * 18.0))) - (a * 4.0)))) - (i * (x * 4.0))) - (k * (27.0 * j))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (y <= -3.2e+73)
		tmp = Float64(y * Float64(Float64(Float64(-4.0 * Float64(Float64(a * t) / y)) + Float64(Float64(18.0 * Float64(t * Float64(x * z))) + Float64(Float64(b * c) / y))) - Float64(Float64(4.0 * Float64(Float64(x * i) / y)) + Float64(27.0 * Float64(Float64(j * k) / y)))));
	else
		tmp = Float64(Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(z * Float64(x * Float64(y * 18.0))) - Float64(a * 4.0)))) - Float64(i * Float64(x * 4.0))) - Float64(k * Float64(27.0 * j)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (y <= -3.2e+73)
		tmp = y * (((-4.0 * ((a * t) / y)) + ((18.0 * (t * (x * z))) + ((b * c) / y))) - ((4.0 * ((x * i) / y)) + (27.0 * ((j * k) / y))));
	else
		tmp = (((b * c) + (t * ((z * (x * (y * 18.0))) - (a * 4.0)))) - (i * (x * 4.0))) - (k * (27.0 * j));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[y, -3.2e+73], N[(y * N[(N[(N[(-4.0 * N[(N[(a * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] + N[(N[(18.0 * N[(t * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(b * c), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(4.0 * N[(N[(x * i), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] + N[(27.0 * N[(N[(j * k), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(z * N[(x * N[(y * 18.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * N[(x * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(27.0 * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.19999999999999982e73

   1. Initial program 72.0%

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

   3. Simplified 72.0%

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

   5. Taylor expanded in y around inf 94.7%

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

   if -3.19999999999999982e73 < y

   1. Initial program 91.3%

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

      1. distribute-rgt-out-- 92.7%

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

      2. associate-*r* 91.8%

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

      3. *-commutative 91.8%

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

      4. associate-*r* 92.7%

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

      5. *-commutative 92.7%

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

      6. associate-*l* 92.7%

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

   4. Applied egg-rr 92.7%

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

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+73}:\\ \;\;\;\;y \cdot \left(\left(-4 \cdot \frac{a \cdot t}{y} + \left(18 \cdot \left(t \cdot \left(x \cdot z\right)\right) + \frac{b \cdot c}{y}\right)\right) - \left(4 \cdot \frac{x \cdot i}{y} + 27 \cdot \frac{j \cdot k}{y}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b \cdot c + t \cdot \left(z \cdot \left(x \cdot \left(y \cdot 18\right)\right) - a \cdot 4\right)\right) - i \cdot \left(x \cdot 4\right)\right) - k \cdot \left(27 \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 59.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := b \cdot c + t\_1\\ \mathbf{if}\;t \leq -2.25 \cdot 10^{+95}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + -4 \cdot a\right)\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{-24}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{-190}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-303}:\\ \;\;\;\;t\_1 + i \cdot \left(-4 \cdot x\right)\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{-58}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot \left(-4 \cdot \frac{a}{y} + 18 \cdot \left(x \cdot z\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0))) (t_2 (+ (* b c) t_1)))
   (if (<= t -2.25e+95)
     (* t (+ (* 18.0 (* x (* y z))) (* -4.0 a)))
     (if (<= t -1.8e-24)
       (* x (- (* 18.0 (* t (* y z))) (* 4.0 i)))
       (if (<= t -6.5e-190)
         t_2
         (if (<= t -2e-303)
           (+ t_1 (* i (* -4.0 x)))
           (if (<= t 4.3e-58)
             t_2
             (* t (* y (+ (* -4.0 (/ a y)) (* 18.0 (* x z))))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = (b * c) + t_1;
	double tmp;
	if (t <= -2.25e+95) {
		tmp = t * ((18.0 * (x * (y * z))) + (-4.0 * a));
	} else if (t <= -1.8e-24) {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	} else if (t <= -6.5e-190) {
		tmp = t_2;
	} else if (t <= -2e-303) {
		tmp = t_1 + (i * (-4.0 * x));
	} else if (t <= 4.3e-58) {
		tmp = t_2;
	} else {
		tmp = t * (y * ((-4.0 * (a / y)) + (18.0 * (x * z))));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * (k * (-27.0d0))
    t_2 = (b * c) + t_1
    if (t <= (-2.25d+95)) then
        tmp = t * ((18.0d0 * (x * (y * z))) + ((-4.0d0) * a))
    else if (t <= (-1.8d-24)) then
        tmp = x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i))
    else if (t <= (-6.5d-190)) then
        tmp = t_2
    else if (t <= (-2d-303)) then
        tmp = t_1 + (i * ((-4.0d0) * x))
    else if (t <= 4.3d-58) then
        tmp = t_2
    else
        tmp = t * (y * (((-4.0d0) * (a / y)) + (18.0d0 * (x * z))))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = (b * c) + t_1;
	double tmp;
	if (t <= -2.25e+95) {
		tmp = t * ((18.0 * (x * (y * z))) + (-4.0 * a));
	} else if (t <= -1.8e-24) {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	} else if (t <= -6.5e-190) {
		tmp = t_2;
	} else if (t <= -2e-303) {
		tmp = t_1 + (i * (-4.0 * x));
	} else if (t <= 4.3e-58) {
		tmp = t_2;
	} else {
		tmp = t * (y * ((-4.0 * (a / y)) + (18.0 * (x * z))));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	t_2 = (b * c) + t_1
	tmp = 0
	if t <= -2.25e+95:
		tmp = t * ((18.0 * (x * (y * z))) + (-4.0 * a))
	elif t <= -1.8e-24:
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i))
	elif t <= -6.5e-190:
		tmp = t_2
	elif t <= -2e-303:
		tmp = t_1 + (i * (-4.0 * x))
	elif t <= 4.3e-58:
		tmp = t_2
	else:
		tmp = t * (y * ((-4.0 * (a / y)) + (18.0 * (x * z))))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * -27.0))
	t_2 = Float64(Float64(b * c) + t_1)
	tmp = 0.0
	if (t <= -2.25e+95)
		tmp = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) + Float64(-4.0 * a)));
	elseif (t <= -1.8e-24)
		tmp = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)));
	elseif (t <= -6.5e-190)
		tmp = t_2;
	elseif (t <= -2e-303)
		tmp = Float64(t_1 + Float64(i * Float64(-4.0 * x)));
	elseif (t <= 4.3e-58)
		tmp = t_2;
	else
		tmp = Float64(t * Float64(y * Float64(Float64(-4.0 * Float64(a / y)) + Float64(18.0 * Float64(x * z)))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * -27.0);
	t_2 = (b * c) + t_1;
	tmp = 0.0;
	if (t <= -2.25e+95)
		tmp = t * ((18.0 * (x * (y * z))) + (-4.0 * a));
	elseif (t <= -1.8e-24)
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	elseif (t <= -6.5e-190)
		tmp = t_2;
	elseif (t <= -2e-303)
		tmp = t_1 + (i * (-4.0 * x));
	elseif (t <= 4.3e-58)
		tmp = t_2;
	else
		tmp = t * (y * ((-4.0 * (a / y)) + (18.0 * (x * z))));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[LessEqual[t, -2.25e+95], N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.8e-24], N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -6.5e-190], t$95$2, If[LessEqual[t, -2e-303], N[(t$95$1 + N[(i * N[(-4.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.3e-58], t$95$2, N[(t * N[(y * N[(N[(-4.0 * N[(a / y), $MachinePrecision]), $MachinePrecision] + N[(18.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -2.25000000000000008e95

   1. Initial program 82.5%

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

   3. Simplified 87.0%

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

   5. Taylor expanded in t around inf 82.8%

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

   6. Taylor expanded in t around inf 78.5%

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

   if -2.25000000000000008e95 < t < -1.8e-24

   1. Initial program 95.6%

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

   3. Simplified 95.7%

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

   5. Taylor expanded in x around inf 71.4%

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

   if -1.8e-24 < t < -6.4999999999999997e-190 or -1.99999999999999986e-303 < t < 4.2999999999999999e-58

   1. Initial program 91.6%

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

   3. Simplified 91.6%

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

   5. Taylor expanded in b around inf 68.6%

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

   if -6.4999999999999997e-190 < t < -1.99999999999999986e-303

   1. Initial program 69.9%

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

   3. Simplified 70.0%

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

   5. Taylor expanded in i around inf 72.2%

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

      1. associate-*r* 72.2%

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

      2. *-commutative 72.2%

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

      3. associate-*r* 72.2%

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

      4. *-commutative 72.2%

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

   7. Simplified 72.2%

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

   if 4.2999999999999999e-58 < t

   1. Initial program 93.6%

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

   3. Simplified 96.9%

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

   5. Taylor expanded in t around inf 71.0%

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

   6. Taylor expanded in y around inf 58.9%

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

   7. Taylor expanded in t around inf 59.8%

      \[\leadsto \color{blue}{t \cdot \left(y \cdot \left(-4 \cdot \frac{a}{y} + 18 \cdot \left(x \cdot z\right)\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.25 \cdot 10^{+95}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + -4 \cdot a\right)\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{-24}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{-190}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-303}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + i \cdot \left(-4 \cdot x\right)\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{-58}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot \left(-4 \cdot \frac{a}{y} + 18 \cdot \left(x \cdot z\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 59.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := b \cdot c + t\_1\\ t_3 := t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + -4 \cdot a\right)\\ \mathbf{if}\;t \leq -2.8 \cdot 10^{+95}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{-24}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;t \leq -1.25 \cdot 10^{-190}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-305}:\\ \;\;\;\;t\_1 + i \cdot \left(-4 \cdot x\right)\\ \mathbf{elif}\;t \leq 3.45 \cdot 10^{-59}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0)))
        (t_2 (+ (* b c) t_1))
        (t_3 (* t (+ (* 18.0 (* x (* y z))) (* -4.0 a)))))
   (if (<= t -2.8e+95)
     t_3
     (if (<= t -2.1e-24)
       (* x (- (* 18.0 (* t (* y z))) (* 4.0 i)))
       (if (<= t -1.25e-190)
         t_2
         (if (<= t -3.5e-305)
           (+ t_1 (* i (* -4.0 x)))
           (if (<= t 3.45e-59) t_2 t_3)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = (b * c) + t_1;
	double t_3 = t * ((18.0 * (x * (y * z))) + (-4.0 * a));
	double tmp;
	if (t <= -2.8e+95) {
		tmp = t_3;
	} else if (t <= -2.1e-24) {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	} else if (t <= -1.25e-190) {
		tmp = t_2;
	} else if (t <= -3.5e-305) {
		tmp = t_1 + (i * (-4.0 * x));
	} else if (t <= 3.45e-59) {
		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.
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 = (b * c) + t_1
    t_3 = t * ((18.0d0 * (x * (y * z))) + ((-4.0d0) * a))
    if (t <= (-2.8d+95)) then
        tmp = t_3
    else if (t <= (-2.1d-24)) then
        tmp = x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i))
    else if (t <= (-1.25d-190)) then
        tmp = t_2
    else if (t <= (-3.5d-305)) then
        tmp = t_1 + (i * ((-4.0d0) * x))
    else if (t <= 3.45d-59) 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;
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 = (b * c) + t_1;
	double t_3 = t * ((18.0 * (x * (y * z))) + (-4.0 * a));
	double tmp;
	if (t <= -2.8e+95) {
		tmp = t_3;
	} else if (t <= -2.1e-24) {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	} else if (t <= -1.25e-190) {
		tmp = t_2;
	} else if (t <= -3.5e-305) {
		tmp = t_1 + (i * (-4.0 * x));
	} else if (t <= 3.45e-59) {
		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])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	t_2 = (b * c) + t_1
	t_3 = t * ((18.0 * (x * (y * z))) + (-4.0 * a))
	tmp = 0
	if t <= -2.8e+95:
		tmp = t_3
	elif t <= -2.1e-24:
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i))
	elif t <= -1.25e-190:
		tmp = t_2
	elif t <= -3.5e-305:
		tmp = t_1 + (i * (-4.0 * x))
	elif t <= 3.45e-59:
		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])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * -27.0))
	t_2 = Float64(Float64(b * c) + t_1)
	t_3 = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) + Float64(-4.0 * a)))
	tmp = 0.0
	if (t <= -2.8e+95)
		tmp = t_3;
	elseif (t <= -2.1e-24)
		tmp = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)));
	elseif (t <= -1.25e-190)
		tmp = t_2;
	elseif (t <= -3.5e-305)
		tmp = Float64(t_1 + Float64(i * Float64(-4.0 * x)));
	elseif (t <= 3.45e-59)
		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])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * -27.0);
	t_2 = (b * c) + t_1;
	t_3 = t * ((18.0 * (x * (y * z))) + (-4.0 * a));
	tmp = 0.0;
	if (t <= -2.8e+95)
		tmp = t_3;
	elseif (t <= -2.1e-24)
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	elseif (t <= -1.25e-190)
		tmp = t_2;
	elseif (t <= -3.5e-305)
		tmp = t_1 + (i * (-4.0 * x));
	elseif (t <= 3.45e-59)
		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.
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[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.8e+95], t$95$3, If[LessEqual[t, -2.1e-24], N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.25e-190], t$95$2, If[LessEqual[t, -3.5e-305], N[(t$95$1 + N[(i * N[(-4.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.45e-59], t$95$2, t$95$3]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.7999999999999998e95 or 3.44999999999999991e-59 < t

   1. Initial program 89.0%

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

   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 t around inf 76.0%

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

   6. Taylor expanded in t around inf 68.6%

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

   if -2.7999999999999998e95 < t < -2.0999999999999999e-24

   1. Initial program 95.6%

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

   3. Simplified 95.7%

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

   5. Taylor expanded in x around inf 71.4%

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

   if -2.0999999999999999e-24 < t < -1.25000000000000009e-190 or -3.4999999999999998e-305 < t < 3.44999999999999991e-59

   1. Initial program 91.6%

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

   3. Simplified 91.6%

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

   5. Taylor expanded in b around inf 68.6%

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

   if -1.25000000000000009e-190 < t < -3.4999999999999998e-305

   1. Initial program 69.9%

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

   3. Simplified 70.0%

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

   5. Taylor expanded in i around inf 72.2%

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

      1. associate-*r* 72.2%

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

      2. *-commutative 72.2%

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

      3. associate-*r* 72.2%

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

      4. *-commutative 72.2%

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

   7. Simplified 72.2%

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

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+95}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + -4 \cdot a\right)\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{-24}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;t \leq -1.25 \cdot 10^{-190}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-305}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + i \cdot \left(-4 \cdot x\right)\\ \mathbf{elif}\;t \leq 3.45 \cdot 10^{-59}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + -4 \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 86.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq 2 \cdot 10^{+294}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(y \cdot z\right) \cdot \left(18 \cdot x\right) - a \cdot 4\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(b + -4 \cdot \frac{a \cdot t}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= (* b c) 2e+294)
   (-
    (+ (* b c) (* t (- (* (* y z) (* 18.0 x)) (* a 4.0))))
    (+ (* x (* 4.0 i)) (* j (* 27.0 k))))
   (* c (+ b (* -4.0 (/ (* a t) c))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b * c) <= 2e+294) {
		tmp = ((b * c) + (t * (((y * z) * (18.0 * x)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	} else {
		tmp = c * (b + (-4.0 * ((a * t) / c)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((b * c) <= 2d+294) then
        tmp = ((b * c) + (t * (((y * z) * (18.0d0 * x)) - (a * 4.0d0)))) - ((x * (4.0d0 * i)) + (j * (27.0d0 * k)))
    else
        tmp = c * (b + ((-4.0d0) * ((a * t) / c)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b * c) <= 2e+294) {
		tmp = ((b * c) + (t * (((y * z) * (18.0 * x)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	} else {
		tmp = c * (b + (-4.0 * ((a * t) / c)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (b * c) <= 2e+294:
		tmp = ((b * c) + (t * (((y * z) * (18.0 * x)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)))
	else:
		tmp = c * (b + (-4.0 * ((a * t) / c)))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (Float64(b * c) <= 2e+294)
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(Float64(y * z) * Float64(18.0 * x)) - Float64(a * 4.0)))) - Float64(Float64(x * Float64(4.0 * i)) + Float64(j * Float64(27.0 * k))));
	else
		tmp = Float64(c * Float64(b + Float64(-4.0 * Float64(Float64(a * t) / c))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((b * c) <= 2e+294)
		tmp = ((b * c) + (t * (((y * z) * (18.0 * x)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	else
		tmp = c * (b + (-4.0 * ((a * t) / c)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[N[(b * c), $MachinePrecision], 2e+294], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(N[(y * z), $MachinePrecision] * N[(18.0 * x), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision] + N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(b + N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < 2.00000000000000013e294

   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 90.5%

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

   if 2.00000000000000013e294 < (*.f64 b c)

   1. Initial program 66.7%

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

   3. Simplified 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 0 66.7%

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

   6. Taylor expanded in j around 0 77.8%

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

   7. Taylor expanded in c around inf 88.9%

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

      1. *-commutative 88.9%

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

   9. Simplified 88.9%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq 2 \cdot 10^{+294}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(y \cdot z\right) \cdot \left(18 \cdot x\right) - a \cdot 4\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(b + -4 \cdot \frac{a \cdot t}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 60.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := b \cdot c + t\_1\\ t_3 := t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + -4 \cdot a\right)\\ \mathbf{if}\;t \leq -7 \cdot 10^{-28}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq -2.15 \cdot 10^{-190}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.6 \cdot 10^{-304}:\\ \;\;\;\;t\_1 + i \cdot \left(-4 \cdot x\right)\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{-54}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0)))
        (t_2 (+ (* b c) t_1))
        (t_3 (* t (+ (* 18.0 (* x (* y z))) (* -4.0 a)))))
   (if (<= t -7e-28)
     t_3
     (if (<= t -2.15e-190)
       t_2
       (if (<= t -1.6e-304)
         (+ t_1 (* i (* -4.0 x)))
         (if (<= t 7.2e-54) t_2 t_3))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = (b * c) + t_1;
	double t_3 = t * ((18.0 * (x * (y * z))) + (-4.0 * a));
	double tmp;
	if (t <= -7e-28) {
		tmp = t_3;
	} else if (t <= -2.15e-190) {
		tmp = t_2;
	} else if (t <= -1.6e-304) {
		tmp = t_1 + (i * (-4.0 * x));
	} else if (t <= 7.2e-54) {
		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.
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 = (b * c) + t_1
    t_3 = t * ((18.0d0 * (x * (y * z))) + ((-4.0d0) * a))
    if (t <= (-7d-28)) then
        tmp = t_3
    else if (t <= (-2.15d-190)) then
        tmp = t_2
    else if (t <= (-1.6d-304)) then
        tmp = t_1 + (i * ((-4.0d0) * x))
    else if (t <= 7.2d-54) 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;
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 = (b * c) + t_1;
	double t_3 = t * ((18.0 * (x * (y * z))) + (-4.0 * a));
	double tmp;
	if (t <= -7e-28) {
		tmp = t_3;
	} else if (t <= -2.15e-190) {
		tmp = t_2;
	} else if (t <= -1.6e-304) {
		tmp = t_1 + (i * (-4.0 * x));
	} else if (t <= 7.2e-54) {
		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])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	t_2 = (b * c) + t_1
	t_3 = t * ((18.0 * (x * (y * z))) + (-4.0 * a))
	tmp = 0
	if t <= -7e-28:
		tmp = t_3
	elif t <= -2.15e-190:
		tmp = t_2
	elif t <= -1.6e-304:
		tmp = t_1 + (i * (-4.0 * x))
	elif t <= 7.2e-54:
		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])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * -27.0))
	t_2 = Float64(Float64(b * c) + t_1)
	t_3 = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) + Float64(-4.0 * a)))
	tmp = 0.0
	if (t <= -7e-28)
		tmp = t_3;
	elseif (t <= -2.15e-190)
		tmp = t_2;
	elseif (t <= -1.6e-304)
		tmp = Float64(t_1 + Float64(i * Float64(-4.0 * x)));
	elseif (t <= 7.2e-54)
		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])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * -27.0);
	t_2 = (b * c) + t_1;
	t_3 = t * ((18.0 * (x * (y * z))) + (-4.0 * a));
	tmp = 0.0;
	if (t <= -7e-28)
		tmp = t_3;
	elseif (t <= -2.15e-190)
		tmp = t_2;
	elseif (t <= -1.6e-304)
		tmp = t_1 + (i * (-4.0 * x));
	elseif (t <= 7.2e-54)
		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.
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[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7e-28], t$95$3, If[LessEqual[t, -2.15e-190], t$95$2, If[LessEqual[t, -1.6e-304], N[(t$95$1 + N[(i * N[(-4.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.2e-54], t$95$2, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.9999999999999999e-28 or 7.19999999999999953e-54 < t

   1. Initial program 90.3%

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

   3. Simplified 93.3%

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

   5. Taylor expanded in t around inf 74.2%

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

   6. Taylor expanded in t around inf 64.3%

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

   if -6.9999999999999999e-28 < t < -2.15e-190 or -1.59999999999999999e-304 < t < 7.19999999999999953e-54

   1. Initial program 91.5%

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

   3. Simplified 91.5%

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

   5. Taylor expanded in b around inf 69.2%

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

   if -2.15e-190 < t < -1.59999999999999999e-304

   1. Initial program 69.9%

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

   3. Simplified 70.0%

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

   5. Taylor expanded in i around inf 72.2%

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

      1. associate-*r* 72.2%

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

      2. *-commutative 72.2%

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

      3. associate-*r* 72.2%

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

      4. *-commutative 72.2%

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

   7. Simplified 72.2%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{-28}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + -4 \cdot a\right)\\ \mathbf{elif}\;t \leq -2.15 \cdot 10^{-190}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t \leq -1.6 \cdot 10^{-304}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + i \cdot \left(-4 \cdot x\right)\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{-54}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + -4 \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 81.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{-33} \lor \neg \left(t \leq 7.8 \cdot 10^{-103}\right):\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b \cdot c - \left(a \cdot t\right) \cdot 4\right) - i \cdot \left(x \cdot 4\right)\right) - k \cdot \left(27 \cdot j\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= t -1.35e-33) (not (<= t 7.8e-103)))
   (- (+ (* b c) (* t (- (* 18.0 (* x (* y z))) (* a 4.0)))) (* 4.0 (* x i)))
   (- (- (- (* b c) (* (* a t) 4.0)) (* i (* x 4.0))) (* k (* 27.0 j)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((t <= -1.35e-33) || !(t <= 7.8e-103)) {
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - (4.0 * (x * i));
	} else {
		tmp = (((b * c) - ((a * t) * 4.0)) - (i * (x * 4.0))) - (k * (27.0 * j));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((t <= (-1.35d-33)) .or. (.not. (t <= 7.8d-103))) then
        tmp = ((b * c) + (t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0)))) - (4.0d0 * (x * i))
    else
        tmp = (((b * c) - ((a * t) * 4.0d0)) - (i * (x * 4.0d0))) - (k * (27.0d0 * j))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((t <= -1.35e-33) || !(t <= 7.8e-103)) {
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - (4.0 * (x * i));
	} else {
		tmp = (((b * c) - ((a * t) * 4.0)) - (i * (x * 4.0))) - (k * (27.0 * j));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (t <= -1.35e-33) or not (t <= 7.8e-103):
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - (4.0 * (x * i))
	else:
		tmp = (((b * c) - ((a * t) * 4.0)) - (i * (x * 4.0))) - (k * (27.0 * j))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((t <= -1.35e-33) || !(t <= 7.8e-103))
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)))) - Float64(4.0 * Float64(x * i)));
	else
		tmp = Float64(Float64(Float64(Float64(b * c) - Float64(Float64(a * t) * 4.0)) - Float64(i * Float64(x * 4.0))) - Float64(k * Float64(27.0 * j)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((t <= -1.35e-33) || ~((t <= 7.8e-103)))
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - (4.0 * (x * i));
	else
		tmp = (((b * c) - ((a * t) * 4.0)) - (i * (x * 4.0))) - (k * (27.0 * j));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[t, -1.35e-33], N[Not[LessEqual[t, 7.8e-103]], $MachinePrecision]], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(b * c), $MachinePrecision] - N[(N[(a * t), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision] - N[(i * N[(x * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(27.0 * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.35e-33 or 7.8000000000000004e-103 < t

   1. Initial program 90.8%

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

   3. Simplified 92.3%

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

   5. Taylor expanded in j around 0 85.4%

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

   if -1.35e-33 < t < 7.8000000000000004e-103

   1. Initial program 85.3%

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

   3. Taylor expanded in x around 0 88.7%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{-33} \lor \neg \left(t \leq 7.8 \cdot 10^{-103}\right):\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b \cdot c - \left(a \cdot t\right) \cdot 4\right) - i \cdot \left(x \cdot 4\right)\right) - k \cdot \left(27 \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 82.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{if}\;t \leq -3.75 \cdot 10^{-65}:\\ \;\;\;\;t\_1 - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-99}:\\ \;\;\;\;\left(\left(b \cdot c - \left(a \cdot t\right) \cdot 4\right) - i \cdot \left(x \cdot 4\right)\right) - k \cdot \left(27 \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 - 4 \cdot \left(x \cdot i\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (+ (* b c) (* t (- (* 18.0 (* x (* y z))) (* a 4.0))))))
   (if (<= t -3.75e-65)
     (- t_1 (* 27.0 (* j k)))
     (if (<= t 4.5e-99)
       (- (- (- (* b c) (* (* a t) 4.0)) (* i (* x 4.0))) (* k (* 27.0 j)))
       (- t_1 (* 4.0 (* x i)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)));
	double tmp;
	if (t <= -3.75e-65) {
		tmp = t_1 - (27.0 * (j * k));
	} else if (t <= 4.5e-99) {
		tmp = (((b * c) - ((a * t) * 4.0)) - (i * (x * 4.0))) - (k * (27.0 * j));
	} else {
		tmp = t_1 - (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.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b * c) + (t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0)))
    if (t <= (-3.75d-65)) then
        tmp = t_1 - (27.0d0 * (j * k))
    else if (t <= 4.5d-99) then
        tmp = (((b * c) - ((a * t) * 4.0d0)) - (i * (x * 4.0d0))) - (k * (27.0d0 * j))
    else
        tmp = t_1 - (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;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)));
	double tmp;
	if (t <= -3.75e-65) {
		tmp = t_1 - (27.0 * (j * k));
	} else if (t <= 4.5e-99) {
		tmp = (((b * c) - ((a * t) * 4.0)) - (i * (x * 4.0))) - (k * (27.0 * j));
	} else {
		tmp = t_1 - (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])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))
	tmp = 0
	if t <= -3.75e-65:
		tmp = t_1 - (27.0 * (j * k))
	elif t <= 4.5e-99:
		tmp = (((b * c) - ((a * t) * 4.0)) - (i * (x * 4.0))) - (k * (27.0 * j))
	else:
		tmp = t_1 - (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])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) + Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0))))
	tmp = 0.0
	if (t <= -3.75e-65)
		tmp = Float64(t_1 - Float64(27.0 * Float64(j * k)));
	elseif (t <= 4.5e-99)
		tmp = Float64(Float64(Float64(Float64(b * c) - Float64(Float64(a * t) * 4.0)) - Float64(i * Float64(x * 4.0))) - Float64(k * Float64(27.0 * j)));
	else
		tmp = Float64(t_1 - 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])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)));
	tmp = 0.0;
	if (t <= -3.75e-65)
		tmp = t_1 - (27.0 * (j * k));
	elseif (t <= 4.5e-99)
		tmp = (((b * c) - ((a * t) * 4.0)) - (i * (x * 4.0))) - (k * (27.0 * j));
	else
		tmp = t_1 - (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.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.75e-65], N[(t$95$1 - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.5e-99], N[(N[(N[(N[(b * c), $MachinePrecision] - N[(N[(a * t), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision] - N[(i * N[(x * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(27.0 * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.7500000000000001e-65

   1. Initial program 87.4%

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

      1. distribute-rgt-out-- 88.6%

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

      2. associate-*r* 89.8%

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

      3. *-commutative 89.8%

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

      4. associate-*r* 88.6%

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

      5. *-commutative 88.6%

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

      6. associate-*l* 88.6%

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

   4. Applied egg-rr 88.6%

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

   5. Taylor expanded in i around 0 83.8%

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

   if -3.7500000000000001e-65 < t < 4.5000000000000003e-99

   1. Initial program 85.2%

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

   3. Taylor expanded in x around 0 88.8%

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

   if 4.5000000000000003e-99 < t

   1. Initial program 94.2%

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

   3. Simplified 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 j around 0 87.6%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.75 \cdot 10^{-65}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-99}:\\ \;\;\;\;\left(\left(b \cdot c - \left(a \cdot t\right) \cdot 4\right) - i \cdot \left(x \cdot 4\right)\right) - k \cdot \left(27 \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 53.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;b \cdot c \leq -2.5 \cdot 10^{-15}:\\ \;\;\;\;b \cdot c + t\_1\\ \mathbf{elif}\;b \cdot c \leq -2 \cdot 10^{-267}:\\ \;\;\;\;t\_1 + t \cdot \left(-4 \cdot a\right)\\ \mathbf{elif}\;b \cdot c \leq 5 \cdot 10^{+45}:\\ \;\;\;\;-4 \cdot \left(a \cdot t + x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(b + -4 \cdot \frac{a \cdot t}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0))))
   (if (<= (* b c) -2.5e-15)
     (+ (* b c) t_1)
     (if (<= (* b c) -2e-267)
       (+ t_1 (* t (* -4.0 a)))
       (if (<= (* b c) 5e+45)
         (* -4.0 (+ (* a t) (* x i)))
         (* c (+ b (* -4.0 (/ (* a t) c)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double tmp;
	if ((b * c) <= -2.5e-15) {
		tmp = (b * c) + t_1;
	} else if ((b * c) <= -2e-267) {
		tmp = t_1 + (t * (-4.0 * a));
	} else if ((b * c) <= 5e+45) {
		tmp = -4.0 * ((a * t) + (x * i));
	} else {
		tmp = c * (b + (-4.0 * ((a * t) / c)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * (k * (-27.0d0))
    if ((b * c) <= (-2.5d-15)) then
        tmp = (b * c) + t_1
    else if ((b * c) <= (-2d-267)) then
        tmp = t_1 + (t * ((-4.0d0) * a))
    else if ((b * c) <= 5d+45) then
        tmp = (-4.0d0) * ((a * t) + (x * i))
    else
        tmp = c * (b + ((-4.0d0) * ((a * t) / c)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double tmp;
	if ((b * c) <= -2.5e-15) {
		tmp = (b * c) + t_1;
	} else if ((b * c) <= -2e-267) {
		tmp = t_1 + (t * (-4.0 * a));
	} else if ((b * c) <= 5e+45) {
		tmp = -4.0 * ((a * t) + (x * i));
	} else {
		tmp = c * (b + (-4.0 * ((a * t) / c)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	tmp = 0
	if (b * c) <= -2.5e-15:
		tmp = (b * c) + t_1
	elif (b * c) <= -2e-267:
		tmp = t_1 + (t * (-4.0 * a))
	elif (b * c) <= 5e+45:
		tmp = -4.0 * ((a * t) + (x * i))
	else:
		tmp = c * (b + (-4.0 * ((a * t) / c)))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * -27.0))
	tmp = 0.0
	if (Float64(b * c) <= -2.5e-15)
		tmp = Float64(Float64(b * c) + t_1);
	elseif (Float64(b * c) <= -2e-267)
		tmp = Float64(t_1 + Float64(t * Float64(-4.0 * a)));
	elseif (Float64(b * c) <= 5e+45)
		tmp = Float64(-4.0 * Float64(Float64(a * t) + Float64(x * i)));
	else
		tmp = Float64(c * Float64(b + Float64(-4.0 * Float64(Float64(a * t) / c))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * -27.0);
	tmp = 0.0;
	if ((b * c) <= -2.5e-15)
		tmp = (b * c) + t_1;
	elseif ((b * c) <= -2e-267)
		tmp = t_1 + (t * (-4.0 * a));
	elseif ((b * c) <= 5e+45)
		tmp = -4.0 * ((a * t) + (x * i));
	else
		tmp = c * (b + (-4.0 * ((a * t) / c)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -2.5e-15], N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -2e-267], N[(t$95$1 + N[(t * N[(-4.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 5e+45], N[(-4.0 * N[(N[(a * t), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(b + N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 b c) < -2.5e-15

   1. Initial program 87.3%

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

   3. Simplified 87.4%

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

   5. Taylor expanded in b around inf 61.3%

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

   if -2.5e-15 < (*.f64 b c) < -2e-267

   1. Initial program 86.5%

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

   3. Simplified 88.8%

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

   5. Taylor expanded in a around inf 57.2%

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

      1. associate-*r* 57.2%

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

      2. *-commutative 57.2%

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

      3. metadata-eval 57.2%

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

      4. distribute-rgt-neg-in 57.2%

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

      5. *-commutative 57.2%

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

      6. distribute-rgt-neg-in 57.2%

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

      7. metadata-eval 57.2%

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

      8. *-commutative 57.2%

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

   7. Simplified 57.2%

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

   if -2e-267 < (*.f64 b c) < 5e45

   1. Initial program 92.1%

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

      1. distribute-rgt-out-- 93.3%

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

      2. associate-*r* 93.3%

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

      3. *-commutative 93.3%

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

      4. associate-*r* 93.3%

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

      5. *-commutative 93.3%

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

      6. associate-*l* 93.2%

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

   4. Applied egg-rr 93.2%

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

   5. Taylor expanded in t around inf 93.3%

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

   6. Taylor expanded in a around inf 72.1%

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

      1. *-commutative 72.1%

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

   8. Simplified 72.1%

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

   9. Taylor expanded in j around 0 53.3%

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

       1. cancel-sign-sub-inv 53.3%

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

       2. metadata-eval 53.3%

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

       3. +-commutative 53.3%

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

       4. *-commutative 53.3%

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

       5. distribute-lft-out 53.3%

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

       6. *-commutative 53.3%

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

   11. Simplified 53.3%

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

   if 5e45 < (*.f64 b c)

   1. Initial program 85.6%

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

   3. Simplified 87.4%

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

   5. Taylor expanded in x around 0 75.5%

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

   6. Taylor expanded in j around 0 67.5%

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

   7. Taylor expanded in c around inf 71.1%

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

      1. *-commutative 71.1%

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

   9. Simplified 71.1%

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

4. Final simplification 60.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2.5 \cdot 10^{-15}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq -2 \cdot 10^{-267}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(-4 \cdot a\right)\\ \mathbf{elif}\;b \cdot c \leq 5 \cdot 10^{+45}:\\ \;\;\;\;-4 \cdot \left(a \cdot t + x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(b + -4 \cdot \frac{a \cdot t}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 80.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\\ \mathbf{if}\;t \leq -8 \cdot 10^{+23}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(t\_1 + -4 \cdot a\right)\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{+86}:\\ \;\;\;\;\left(\left(b \cdot c - \left(a \cdot t\right) \cdot 4\right) - i \cdot \left(x \cdot 4\right)\right) - k \cdot \left(27 \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + t \cdot \left(t\_1 - a \cdot 4\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* 18.0 (* x (* y z)))))
   (if (<= t -8e+23)
     (+ (* j (* k -27.0)) (* t (+ t_1 (* -4.0 a))))
     (if (<= t 1.85e+86)
       (- (- (- (* b c) (* (* a t) 4.0)) (* i (* x 4.0))) (* k (* 27.0 j)))
       (+ (* b c) (* t (- t_1 (* a 4.0))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 18.0 * (x * (y * z));
	double tmp;
	if (t <= -8e+23) {
		tmp = (j * (k * -27.0)) + (t * (t_1 + (-4.0 * a)));
	} else if (t <= 1.85e+86) {
		tmp = (((b * c) - ((a * t) * 4.0)) - (i * (x * 4.0))) - (k * (27.0 * j));
	} else {
		tmp = (b * c) + (t * (t_1 - (a * 4.0)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 18.0d0 * (x * (y * z))
    if (t <= (-8d+23)) then
        tmp = (j * (k * (-27.0d0))) + (t * (t_1 + ((-4.0d0) * a)))
    else if (t <= 1.85d+86) then
        tmp = (((b * c) - ((a * t) * 4.0d0)) - (i * (x * 4.0d0))) - (k * (27.0d0 * j))
    else
        tmp = (b * c) + (t * (t_1 - (a * 4.0d0)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 18.0 * (x * (y * z));
	double tmp;
	if (t <= -8e+23) {
		tmp = (j * (k * -27.0)) + (t * (t_1 + (-4.0 * a)));
	} else if (t <= 1.85e+86) {
		tmp = (((b * c) - ((a * t) * 4.0)) - (i * (x * 4.0))) - (k * (27.0 * j));
	} else {
		tmp = (b * c) + (t * (t_1 - (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])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = 18.0 * (x * (y * z))
	tmp = 0
	if t <= -8e+23:
		tmp = (j * (k * -27.0)) + (t * (t_1 + (-4.0 * a)))
	elif t <= 1.85e+86:
		tmp = (((b * c) - ((a * t) * 4.0)) - (i * (x * 4.0))) - (k * (27.0 * j))
	else:
		tmp = (b * c) + (t * (t_1 - (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])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(18.0 * Float64(x * Float64(y * z)))
	tmp = 0.0
	if (t <= -8e+23)
		tmp = Float64(Float64(j * Float64(k * -27.0)) + Float64(t * Float64(t_1 + Float64(-4.0 * a))));
	elseif (t <= 1.85e+86)
		tmp = Float64(Float64(Float64(Float64(b * c) - Float64(Float64(a * t) * 4.0)) - Float64(i * Float64(x * 4.0))) - Float64(k * Float64(27.0 * j)));
	else
		tmp = Float64(Float64(b * c) + Float64(t * Float64(t_1 - 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])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = 18.0 * (x * (y * z));
	tmp = 0.0;
	if (t <= -8e+23)
		tmp = (j * (k * -27.0)) + (t * (t_1 + (-4.0 * a)));
	elseif (t <= 1.85e+86)
		tmp = (((b * c) - ((a * t) * 4.0)) - (i * (x * 4.0))) - (k * (27.0 * j));
	else
		tmp = (b * c) + (t * (t_1 - (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.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8e+23], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(t * N[(t$95$1 + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.85e+86], N[(N[(N[(N[(b * c), $MachinePrecision] - N[(N[(a * t), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision] - N[(i * N[(x * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(27.0 * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] + N[(t * N[(t$95$1 - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.9999999999999993e23

   1. Initial program 84.9%

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

   3. Simplified 89.9%

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

   5. Taylor expanded in t around inf 82.5%

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

   if -7.9999999999999993e23 < t < 1.84999999999999996e86

   1. Initial program 89.2%

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

   3. Taylor expanded in x around 0 85.2%

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

   if 1.84999999999999996e86 < t

   1. Initial program 90.4%

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

      1. distribute-rgt-out-- 95.2%

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

      2. associate-*r* 95.2%

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

      3. *-commutative 95.2%

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

      4. associate-*r* 95.2%

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

      5. *-commutative 95.2%

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

      6. associate-*l* 95.1%

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

   4. Applied egg-rr 95.1%

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

   5. Taylor expanded in i around 0 88.0%

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

   6. Taylor expanded in j around 0 87.2%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{+23}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + -4 \cdot a\right)\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{+86}:\\ \;\;\;\;\left(\left(b \cdot c - \left(a \cdot t\right) \cdot 4\right) - i \cdot \left(x \cdot 4\right)\right) - k \cdot \left(27 \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 76.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{-37} \lor \neg \left(t \leq 1.15 \cdot 10^{-41}\right):\\ \;\;\;\;b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - \left(27 \cdot \left(j \cdot k\right) + 4 \cdot \left(x \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= t -2.1e-37) (not (<= t 1.15e-41)))
   (+ (* b c) (* t (- (* 18.0 (* x (* y z))) (* a 4.0))))
   (- (* b c) (+ (* 27.0 (* j k)) (* 4.0 (* x i))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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 <= -2.1e-37) || !(t <= 1.15e-41)) {
		tmp = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)));
	} else {
		tmp = (b * c) - ((27.0 * (j * k)) + (4.0 * (x * i)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 <= (-2.1d-37)) .or. (.not. (t <= 1.15d-41))) then
        tmp = (b * c) + (t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0)))
    else
        tmp = (b * c) - ((27.0d0 * (j * k)) + (4.0d0 * (x * i)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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 <= -2.1e-37) || !(t <= 1.15e-41)) {
		tmp = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)));
	} else {
		tmp = (b * c) - ((27.0 * (j * k)) + (4.0 * (x * i)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (t <= -2.1e-37) or not (t <= 1.15e-41):
		tmp = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))
	else:
		tmp = (b * c) - ((27.0 * (j * k)) + (4.0 * (x * i)))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((t <= -2.1e-37) || !(t <= 1.15e-41))
		tmp = Float64(Float64(b * c) + Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0))));
	else
		tmp = Float64(Float64(b * c) - Float64(Float64(27.0 * Float64(j * k)) + Float64(4.0 * Float64(x * i))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((t <= -2.1e-37) || ~((t <= 1.15e-41)))
		tmp = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)));
	else
		tmp = (b * c) - ((27.0 * (j * k)) + (4.0 * (x * i)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[t, -2.1e-37], N[Not[LessEqual[t, 1.15e-41]], $MachinePrecision]], N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] - N[(N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision] + N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.1000000000000001e-37 or 1.15000000000000005e-41 < t

   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. Step-by-step derivation

      1. distribute-rgt-out-- 91.6%

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

      2. associate-*r* 91.6%

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

      3. *-commutative 91.6%

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

      4. associate-*r* 91.6%

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

      5. *-commutative 91.6%

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

      6. associate-*l* 91.6%

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

   4. Applied egg-rr 91.6%

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

   5. Taylor expanded in i around 0 84.4%

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

   6. Taylor expanded in j around 0 75.4%

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

   if -2.1000000000000001e-37 < t < 1.15000000000000005e-41

   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 85.8%

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

   5. Taylor expanded in t around 0 82.9%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{-37} \lor \neg \left(t \leq 1.15 \cdot 10^{-41}\right):\\ \;\;\;\;b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - \left(27 \cdot \left(j \cdot k\right) + 4 \cdot \left(x \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 75.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\\ \mathbf{if}\;t \leq -1.5 \cdot 10^{-17}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(t\_1 + -4 \cdot a\right)\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-42}:\\ \;\;\;\;b \cdot c - \left(27 \cdot \left(j \cdot k\right) + 4 \cdot \left(x \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + t \cdot \left(t\_1 - a \cdot 4\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* 18.0 (* x (* y z)))))
   (if (<= t -1.5e-17)
     (+ (* j (* k -27.0)) (* t (+ t_1 (* -4.0 a))))
     (if (<= t 5.2e-42)
       (- (* b c) (+ (* 27.0 (* j k)) (* 4.0 (* x i))))
       (+ (* b c) (* t (- t_1 (* a 4.0))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 18.0 * (x * (y * z));
	double tmp;
	if (t <= -1.5e-17) {
		tmp = (j * (k * -27.0)) + (t * (t_1 + (-4.0 * a)));
	} else if (t <= 5.2e-42) {
		tmp = (b * c) - ((27.0 * (j * k)) + (4.0 * (x * i)));
	} else {
		tmp = (b * c) + (t * (t_1 - (a * 4.0)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 18.0d0 * (x * (y * z))
    if (t <= (-1.5d-17)) then
        tmp = (j * (k * (-27.0d0))) + (t * (t_1 + ((-4.0d0) * a)))
    else if (t <= 5.2d-42) then
        tmp = (b * c) - ((27.0d0 * (j * k)) + (4.0d0 * (x * i)))
    else
        tmp = (b * c) + (t * (t_1 - (a * 4.0d0)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 18.0 * (x * (y * z));
	double tmp;
	if (t <= -1.5e-17) {
		tmp = (j * (k * -27.0)) + (t * (t_1 + (-4.0 * a)));
	} else if (t <= 5.2e-42) {
		tmp = (b * c) - ((27.0 * (j * k)) + (4.0 * (x * i)));
	} else {
		tmp = (b * c) + (t * (t_1 - (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])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = 18.0 * (x * (y * z))
	tmp = 0
	if t <= -1.5e-17:
		tmp = (j * (k * -27.0)) + (t * (t_1 + (-4.0 * a)))
	elif t <= 5.2e-42:
		tmp = (b * c) - ((27.0 * (j * k)) + (4.0 * (x * i)))
	else:
		tmp = (b * c) + (t * (t_1 - (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])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(18.0 * Float64(x * Float64(y * z)))
	tmp = 0.0
	if (t <= -1.5e-17)
		tmp = Float64(Float64(j * Float64(k * -27.0)) + Float64(t * Float64(t_1 + Float64(-4.0 * a))));
	elseif (t <= 5.2e-42)
		tmp = Float64(Float64(b * c) - Float64(Float64(27.0 * Float64(j * k)) + Float64(4.0 * Float64(x * i))));
	else
		tmp = Float64(Float64(b * c) + Float64(t * Float64(t_1 - 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])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = 18.0 * (x * (y * z));
	tmp = 0.0;
	if (t <= -1.5e-17)
		tmp = (j * (k * -27.0)) + (t * (t_1 + (-4.0 * a)));
	elseif (t <= 5.2e-42)
		tmp = (b * c) - ((27.0 * (j * k)) + (4.0 * (x * i)));
	else
		tmp = (b * c) + (t * (t_1 - (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.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.5e-17], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(t * N[(t$95$1 + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.2e-42], N[(N[(b * c), $MachinePrecision] - N[(N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision] + N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] + N[(t * N[(t$95$1 - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.50000000000000003e-17

   1. Initial program 86.9%

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

   3. Simplified 89.9%

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

   5. Taylor expanded in t around inf 78.8%

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

   if -1.50000000000000003e-17 < t < 5.2e-42

   1. Initial program 87.1%

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

   3. Simplified 86.4%

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

   5. Taylor expanded in t around 0 81.7%

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

   if 5.2e-42 < t

   1. Initial program 93.0%

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

      1. distribute-rgt-out-- 96.4%

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

      2. associate-*r* 94.8%

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

      3. *-commutative 94.8%

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

      4. associate-*r* 96.4%

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

      5. *-commutative 96.4%

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

      6. associate-*l* 96.4%

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

   4. Applied egg-rr 96.4%

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

   5. Taylor expanded in i around 0 86.5%

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

   6. Taylor expanded in j around 0 78.2%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{-17}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + -4 \cdot a\right)\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-42}:\\ \;\;\;\;b \cdot c - \left(27 \cdot \left(j \cdot k\right) + 4 \cdot \left(x \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 70.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{+103}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + -4 \cdot a\right)\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-41}:\\ \;\;\;\;\left(b \cdot c - i \cdot \left(x \cdot 4\right)\right) - k \cdot \left(27 \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot \left(-4 \cdot \frac{a}{y} + 18 \cdot \left(x \cdot z\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= t -1.8e+103)
   (* t (+ (* 18.0 (* x (* y z))) (* -4.0 a)))
   (if (<= t 2.8e-41)
     (- (- (* b c) (* i (* x 4.0))) (* k (* 27.0 j)))
     (* t (* y (+ (* -4.0 (/ a y)) (* 18.0 (* x z))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (t <= -1.8e+103) {
		tmp = t * ((18.0 * (x * (y * z))) + (-4.0 * a));
	} else if (t <= 2.8e-41) {
		tmp = ((b * c) - (i * (x * 4.0))) - (k * (27.0 * j));
	} else {
		tmp = t * (y * ((-4.0 * (a / y)) + (18.0 * (x * z))));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (t <= (-1.8d+103)) then
        tmp = t * ((18.0d0 * (x * (y * z))) + ((-4.0d0) * a))
    else if (t <= 2.8d-41) then
        tmp = ((b * c) - (i * (x * 4.0d0))) - (k * (27.0d0 * j))
    else
        tmp = t * (y * (((-4.0d0) * (a / y)) + (18.0d0 * (x * z))))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (t <= -1.8e+103) {
		tmp = t * ((18.0 * (x * (y * z))) + (-4.0 * a));
	} else if (t <= 2.8e-41) {
		tmp = ((b * c) - (i * (x * 4.0))) - (k * (27.0 * j));
	} else {
		tmp = t * (y * ((-4.0 * (a / y)) + (18.0 * (x * z))));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if t <= -1.8e+103:
		tmp = t * ((18.0 * (x * (y * z))) + (-4.0 * a))
	elif t <= 2.8e-41:
		tmp = ((b * c) - (i * (x * 4.0))) - (k * (27.0 * j))
	else:
		tmp = t * (y * ((-4.0 * (a / y)) + (18.0 * (x * z))))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (t <= -1.8e+103)
		tmp = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) + Float64(-4.0 * a)));
	elseif (t <= 2.8e-41)
		tmp = Float64(Float64(Float64(b * c) - Float64(i * Float64(x * 4.0))) - Float64(k * Float64(27.0 * j)));
	else
		tmp = Float64(t * Float64(y * Float64(Float64(-4.0 * Float64(a / y)) + Float64(18.0 * Float64(x * z)))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (t <= -1.8e+103)
		tmp = t * ((18.0 * (x * (y * z))) + (-4.0 * a));
	elseif (t <= 2.8e-41)
		tmp = ((b * c) - (i * (x * 4.0))) - (k * (27.0 * j));
	else
		tmp = t * (y * ((-4.0 * (a / y)) + (18.0 * (x * z))));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[t, -1.8e+103], N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.8e-41], N[(N[(N[(b * c), $MachinePrecision] - N[(i * N[(x * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(27.0 * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(y * N[(N[(-4.0 * N[(a / y), $MachinePrecision]), $MachinePrecision] + N[(18.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.80000000000000008e103

   1. Initial program 81.3%

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

   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 t around inf 86.2%

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

   6. Taylor expanded in t around inf 81.6%

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

   if -1.80000000000000008e103 < t < 2.8000000000000002e-41

   1. Initial program 88.7%

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

      1. distribute-rgt-out-- 88.7%

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

      2. associate-*r* 88.0%

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

      3. *-commutative 88.0%

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

      4. associate-*r* 88.7%

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

      5. *-commutative 88.7%

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

      6. associate-*l* 88.7%

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

   4. Applied egg-rr 88.7%

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

   5. Taylor expanded in t around 0 78.2%

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

   if 2.8000000000000002e-41 < t

   1. Initial program 93.0%

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

   3. Simplified 96.6%

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

   5. Taylor expanded in t around inf 73.0%

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

   6. Taylor expanded in y around inf 59.7%

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

   7. Taylor expanded in t around inf 62.3%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{+103}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + -4 \cdot a\right)\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-41}:\\ \;\;\;\;\left(b \cdot c - i \cdot \left(x \cdot 4\right)\right) - k \cdot \left(27 \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot \left(-4 \cdot \frac{a}{y} + 18 \cdot \left(x \cdot z\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 70.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{+102}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + -4 \cdot a\right)\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-41}:\\ \;\;\;\;b \cdot c - \left(27 \cdot \left(j \cdot k\right) + 4 \cdot \left(x \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot \left(-4 \cdot \frac{a}{y} + 18 \cdot \left(x \cdot z\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= t -9.5e+102)
   (* t (+ (* 18.0 (* x (* y z))) (* -4.0 a)))
   (if (<= t 1.4e-41)
     (- (* b c) (+ (* 27.0 (* j k)) (* 4.0 (* x i))))
     (* t (* y (+ (* -4.0 (/ a y)) (* 18.0 (* x z))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (t <= -9.5e+102) {
		tmp = t * ((18.0 * (x * (y * z))) + (-4.0 * a));
	} else if (t <= 1.4e-41) {
		tmp = (b * c) - ((27.0 * (j * k)) + (4.0 * (x * i)));
	} else {
		tmp = t * (y * ((-4.0 * (a / y)) + (18.0 * (x * z))));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (t <= (-9.5d+102)) then
        tmp = t * ((18.0d0 * (x * (y * z))) + ((-4.0d0) * a))
    else if (t <= 1.4d-41) then
        tmp = (b * c) - ((27.0d0 * (j * k)) + (4.0d0 * (x * i)))
    else
        tmp = t * (y * (((-4.0d0) * (a / y)) + (18.0d0 * (x * z))))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (t <= -9.5e+102) {
		tmp = t * ((18.0 * (x * (y * z))) + (-4.0 * a));
	} else if (t <= 1.4e-41) {
		tmp = (b * c) - ((27.0 * (j * k)) + (4.0 * (x * i)));
	} else {
		tmp = t * (y * ((-4.0 * (a / y)) + (18.0 * (x * z))));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if t <= -9.5e+102:
		tmp = t * ((18.0 * (x * (y * z))) + (-4.0 * a))
	elif t <= 1.4e-41:
		tmp = (b * c) - ((27.0 * (j * k)) + (4.0 * (x * i)))
	else:
		tmp = t * (y * ((-4.0 * (a / y)) + (18.0 * (x * z))))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (t <= -9.5e+102)
		tmp = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) + Float64(-4.0 * a)));
	elseif (t <= 1.4e-41)
		tmp = Float64(Float64(b * c) - Float64(Float64(27.0 * Float64(j * k)) + Float64(4.0 * Float64(x * i))));
	else
		tmp = Float64(t * Float64(y * Float64(Float64(-4.0 * Float64(a / y)) + Float64(18.0 * Float64(x * z)))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (t <= -9.5e+102)
		tmp = t * ((18.0 * (x * (y * z))) + (-4.0 * a));
	elseif (t <= 1.4e-41)
		tmp = (b * c) - ((27.0 * (j * k)) + (4.0 * (x * i)));
	else
		tmp = t * (y * ((-4.0 * (a / y)) + (18.0 * (x * z))));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[t, -9.5e+102], N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.4e-41], N[(N[(b * c), $MachinePrecision] - N[(N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision] + N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(y * N[(N[(-4.0 * N[(a / y), $MachinePrecision]), $MachinePrecision] + N[(18.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.4999999999999992e102

   1. Initial program 81.3%

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

   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 t around inf 86.2%

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

   6. Taylor expanded in t around inf 81.6%

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

   if -9.4999999999999992e102 < t < 1.4000000000000001e-41

   1. Initial program 88.7%

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

   3. Simplified 88.0%

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

   5. Taylor expanded in t around 0 78.2%

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

   if 1.4000000000000001e-41 < t

   1. Initial program 93.0%

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

   3. Simplified 96.6%

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

   5. Taylor expanded in t around inf 73.0%

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

   6. Taylor expanded in y around inf 59.7%

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

   7. Taylor expanded in t around inf 62.3%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{+102}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + -4 \cdot a\right)\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-41}:\\ \;\;\;\;b \cdot c - \left(27 \cdot \left(j \cdot k\right) + 4 \cdot \left(x \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot \left(-4 \cdot \frac{a}{y} + 18 \cdot \left(x \cdot z\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 54.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -4 \cdot 10^{+133}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(a \cdot t\right)\\ \mathbf{elif}\;b \cdot c \leq 2 \cdot 10^{+26}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + i \cdot \left(-4 \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(b + -4 \cdot \frac{a \cdot t}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= (* b c) -4e+133)
   (+ (* b c) (* -4.0 (* a t)))
   (if (<= (* b c) 2e+26)
     (+ (* j (* k -27.0)) (* i (* -4.0 x)))
     (* c (+ b (* -4.0 (/ (* a t) c)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b * c) <= -4e+133) {
		tmp = (b * c) + (-4.0 * (a * t));
	} else if ((b * c) <= 2e+26) {
		tmp = (j * (k * -27.0)) + (i * (-4.0 * x));
	} else {
		tmp = c * (b + (-4.0 * ((a * t) / c)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((b * c) <= (-4d+133)) then
        tmp = (b * c) + ((-4.0d0) * (a * t))
    else if ((b * c) <= 2d+26) then
        tmp = (j * (k * (-27.0d0))) + (i * ((-4.0d0) * x))
    else
        tmp = c * (b + ((-4.0d0) * ((a * t) / c)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b * c) <= -4e+133) {
		tmp = (b * c) + (-4.0 * (a * t));
	} else if ((b * c) <= 2e+26) {
		tmp = (j * (k * -27.0)) + (i * (-4.0 * x));
	} else {
		tmp = c * (b + (-4.0 * ((a * t) / c)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (b * c) <= -4e+133:
		tmp = (b * c) + (-4.0 * (a * t))
	elif (b * c) <= 2e+26:
		tmp = (j * (k * -27.0)) + (i * (-4.0 * x))
	else:
		tmp = c * (b + (-4.0 * ((a * t) / c)))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (Float64(b * c) <= -4e+133)
		tmp = Float64(Float64(b * c) + Float64(-4.0 * Float64(a * t)));
	elseif (Float64(b * c) <= 2e+26)
		tmp = Float64(Float64(j * Float64(k * -27.0)) + Float64(i * Float64(-4.0 * x)));
	else
		tmp = Float64(c * Float64(b + Float64(-4.0 * Float64(Float64(a * t) / c))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((b * c) <= -4e+133)
		tmp = (b * c) + (-4.0 * (a * t));
	elseif ((b * c) <= 2e+26)
		tmp = (j * (k * -27.0)) + (i * (-4.0 * x));
	else
		tmp = c * (b + (-4.0 * ((a * t) / c)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[N[(b * c), $MachinePrecision], -4e+133], N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 2e+26], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(i * N[(-4.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(b + N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -4.0000000000000001e133

   1. Initial program 85.2%

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

   3. Simplified 85.2%

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

   5. Taylor expanded in x around 0 82.7%

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

   6. Taylor expanded in j around 0 78.2%

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

   if -4.0000000000000001e133 < (*.f64 b c) < 2.0000000000000001e26

   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 90.6%

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

   5. Taylor expanded in i around inf 52.7%

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

      1. associate-*r* 52.7%

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

      2. *-commutative 52.7%

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

      3. associate-*r* 52.7%

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

      4. *-commutative 52.7%

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

   7. Simplified 52.7%

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

   if 2.0000000000000001e26 < (*.f64 b c)

   1. Initial program 86.8%

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

   3. Simplified 88.4%

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

   5. Taylor expanded in x around 0 72.8%

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

   6. Taylor expanded in j around 0 65.5%

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

   7. Taylor expanded in c around inf 70.4%

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

      1. *-commutative 70.4%

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

   9. Simplified 70.4%

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

4. Final simplification 60.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -4 \cdot 10^{+133}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(a \cdot t\right)\\ \mathbf{elif}\;b \cdot c \leq 2 \cdot 10^{+26}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + i \cdot \left(-4 \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(b + -4 \cdot \frac{a \cdot t}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 51.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -5 \cdot 10^{-83}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 5 \cdot 10^{+45}:\\ \;\;\;\;-4 \cdot \left(a \cdot t + x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(b + -4 \cdot \frac{a \cdot t}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= (* b c) -5e-83)
   (+ (* b c) (* j (* k -27.0)))
   (if (<= (* b c) 5e+45)
     (* -4.0 (+ (* a t) (* x i)))
     (* c (+ b (* -4.0 (/ (* a t) c)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b * c) <= -5e-83) {
		tmp = (b * c) + (j * (k * -27.0));
	} else if ((b * c) <= 5e+45) {
		tmp = -4.0 * ((a * t) + (x * i));
	} else {
		tmp = c * (b + (-4.0 * ((a * t) / c)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((b * c) <= (-5d-83)) then
        tmp = (b * c) + (j * (k * (-27.0d0)))
    else if ((b * c) <= 5d+45) then
        tmp = (-4.0d0) * ((a * t) + (x * i))
    else
        tmp = c * (b + ((-4.0d0) * ((a * t) / c)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b * c) <= -5e-83) {
		tmp = (b * c) + (j * (k * -27.0));
	} else if ((b * c) <= 5e+45) {
		tmp = -4.0 * ((a * t) + (x * i));
	} else {
		tmp = c * (b + (-4.0 * ((a * t) / c)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (b * c) <= -5e-83:
		tmp = (b * c) + (j * (k * -27.0))
	elif (b * c) <= 5e+45:
		tmp = -4.0 * ((a * t) + (x * i))
	else:
		tmp = c * (b + (-4.0 * ((a * t) / c)))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (Float64(b * c) <= -5e-83)
		tmp = Float64(Float64(b * c) + Float64(j * Float64(k * -27.0)));
	elseif (Float64(b * c) <= 5e+45)
		tmp = Float64(-4.0 * Float64(Float64(a * t) + Float64(x * i)));
	else
		tmp = Float64(c * Float64(b + Float64(-4.0 * Float64(Float64(a * t) / c))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((b * c) <= -5e-83)
		tmp = (b * c) + (j * (k * -27.0));
	elseif ((b * c) <= 5e+45)
		tmp = -4.0 * ((a * t) + (x * i));
	else
		tmp = c * (b + (-4.0 * ((a * t) / c)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[N[(b * c), $MachinePrecision], -5e-83], N[(N[(b * c), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 5e+45], N[(-4.0 * N[(N[(a * t), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(b + N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -5e-83

   1. Initial program 85.2%

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

   3. Simplified 86.4%

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

   5. Taylor expanded in b around inf 55.4%

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

   if -5e-83 < (*.f64 b c) < 5e45

   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. Step-by-step derivation

      1. distribute-rgt-out-- 93.6%

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

      2. associate-*r* 93.7%

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

      3. *-commutative 93.7%

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

      4. associate-*r* 93.6%

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

      5. *-commutative 93.6%

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

      6. associate-*l* 93.6%

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

   4. Applied egg-rr 93.6%

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

   5. Taylor expanded in t around inf 93.6%

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

   6. Taylor expanded in a around inf 72.2%

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

      1. *-commutative 72.2%

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

   8. Simplified 72.2%

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

   9. Taylor expanded in j around 0 50.4%

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

       1. cancel-sign-sub-inv 50.4%

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

       2. metadata-eval 50.4%

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

       3. +-commutative 50.4%

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

       4. *-commutative 50.4%

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

       5. distribute-lft-out 50.4%

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

       6. *-commutative 50.4%

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

   11. Simplified 50.4%

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

   if 5e45 < (*.f64 b c)

   1. Initial program 85.6%

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

   3. Simplified 87.4%

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

   5. Taylor expanded in x around 0 75.5%

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

   6. Taylor expanded in j around 0 67.5%

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

   7. Taylor expanded in c around inf 71.1%

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

      1. *-commutative 71.1%

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

   9. Simplified 71.1%

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

4. Final simplification 56.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -5 \cdot 10^{-83}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 5 \cdot 10^{+45}:\\ \;\;\;\;-4 \cdot \left(a \cdot t + x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(b + -4 \cdot \frac{a \cdot t}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 52.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -9 \cdot 10^{+130} \lor \neg \left(b \cdot c \leq 1.55 \cdot 10^{+49}\right):\\ \;\;\;\;b \cdot c + -4 \cdot \left(a \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(a \cdot t + x \cdot i\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= (* b c) -9e+130) (not (<= (* b c) 1.55e+49)))
   (+ (* b c) (* -4.0 (* a t)))
   (* -4.0 (+ (* a t) (* x i)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (((b * c) <= -9e+130) || !((b * c) <= 1.55e+49)) {
		tmp = (b * c) + (-4.0 * (a * t));
	} else {
		tmp = -4.0 * ((a * t) + (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.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (((b * c) <= (-9d+130)) .or. (.not. ((b * c) <= 1.55d+49))) then
        tmp = (b * c) + ((-4.0d0) * (a * t))
    else
        tmp = (-4.0d0) * ((a * t) + (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;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (((b * c) <= -9e+130) || !((b * c) <= 1.55e+49)) {
		tmp = (b * c) + (-4.0 * (a * t));
	} else {
		tmp = -4.0 * ((a * t) + (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])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if ((b * c) <= -9e+130) or not ((b * c) <= 1.55e+49):
		tmp = (b * c) + (-4.0 * (a * t))
	else:
		tmp = -4.0 * ((a * t) + (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])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((Float64(b * c) <= -9e+130) || !(Float64(b * c) <= 1.55e+49))
		tmp = Float64(Float64(b * c) + Float64(-4.0 * Float64(a * t)));
	else
		tmp = Float64(-4.0 * Float64(Float64(a * t) + 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])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (((b * c) <= -9e+130) || ~(((b * c) <= 1.55e+49)))
		tmp = (b * c) + (-4.0 * (a * t));
	else
		tmp = -4.0 * ((a * t) + (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.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[N[(b * c), $MachinePrecision], -9e+130], N[Not[LessEqual[N[(b * c), $MachinePrecision], 1.55e+49]], $MachinePrecision]], N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(N[(a * t), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -9.00000000000000078e130 or 1.54999999999999996e49 < (*.f64 b c)

   1. Initial program 85.4%

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

   3. Simplified 86.5%

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

   5. Taylor expanded in x around 0 78.5%

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

   6. Taylor expanded in j around 0 71.9%

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

   if -9.00000000000000078e130 < (*.f64 b c) < 1.54999999999999996e49

   1. Initial program 90.2%

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

      1. distribute-rgt-out-- 92.1%

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

      2. associate-*r* 90.3%

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

      3. *-commutative 90.3%

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

      4. associate-*r* 92.1%

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

      5. *-commutative 92.1%

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

      6. associate-*l* 92.1%

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

   4. Applied egg-rr 92.1%

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

   5. Taylor expanded in t around inf 87.8%

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

   6. Taylor expanded in a around inf 68.4%

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

      1. *-commutative 68.4%

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

   8. Simplified 68.4%

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

   9. Taylor expanded in j around 0 45.6%

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

       1. cancel-sign-sub-inv 45.6%

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

       2. metadata-eval 45.6%

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

       3. +-commutative 45.6%

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

       4. *-commutative 45.6%

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

       5. distribute-lft-out 45.6%

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

       6. *-commutative 45.6%

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

   11. Simplified 45.6%

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

4. Final simplification 55.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -9 \cdot 10^{+130} \lor \neg \left(b \cdot c \leq 1.55 \cdot 10^{+49}\right):\\ \;\;\;\;b \cdot c + -4 \cdot \left(a \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(a \cdot t + x \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 50.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.9 \cdot 10^{+217} \lor \neg \left(b \cdot c \leq 1.35 \cdot 10^{+194}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(a \cdot t + x \cdot i\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= (* b c) -1.9e+217) (not (<= (* b c) 1.35e+194)))
   (* b c)
   (* -4.0 (+ (* a t) (* x i)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (((b * c) <= -1.9e+217) || !((b * c) <= 1.35e+194)) {
		tmp = b * c;
	} else {
		tmp = -4.0 * ((a * t) + (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.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (((b * c) <= (-1.9d+217)) .or. (.not. ((b * c) <= 1.35d+194))) then
        tmp = b * c
    else
        tmp = (-4.0d0) * ((a * t) + (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;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (((b * c) <= -1.9e+217) || !((b * c) <= 1.35e+194)) {
		tmp = b * c;
	} else {
		tmp = -4.0 * ((a * t) + (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])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if ((b * c) <= -1.9e+217) or not ((b * c) <= 1.35e+194):
		tmp = b * c
	else:
		tmp = -4.0 * ((a * t) + (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])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((Float64(b * c) <= -1.9e+217) || !(Float64(b * c) <= 1.35e+194))
		tmp = Float64(b * c);
	else
		tmp = Float64(-4.0 * Float64(Float64(a * t) + 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])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (((b * c) <= -1.9e+217) || ~(((b * c) <= 1.35e+194)))
		tmp = b * c;
	else
		tmp = -4.0 * ((a * t) + (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.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[N[(b * c), $MachinePrecision], -1.9e+217], N[Not[LessEqual[N[(b * c), $MachinePrecision], 1.35e+194]], $MachinePrecision]], N[(b * c), $MachinePrecision], N[(-4.0 * N[(N[(a * t), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -1.90000000000000001e217 or 1.3500000000000001e194 < (*.f64 b c)

   1. Initial program 82.9%

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

   3. Simplified 86.3%

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

   5. Taylor expanded in b around inf 77.0%

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

   6. Taylor expanded in b around inf 74.5%

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

   if -1.90000000000000001e217 < (*.f64 b c) < 1.3500000000000001e194

   1. Initial program 90.1%

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

      1. distribute-rgt-out-- 91.6%

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

      2. associate-*r* 90.6%

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

      3. *-commutative 90.6%

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

      4. associate-*r* 91.6%

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

      5. *-commutative 91.6%

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

      6. associate-*l* 91.6%

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

   4. Applied egg-rr 91.6%

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

   5. Taylor expanded in t around inf 85.3%

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

   6. Taylor expanded in a around inf 66.0%

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

      1. *-commutative 66.0%

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

   8. Simplified 66.0%

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

   9. Taylor expanded in j around 0 45.8%

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

       1. cancel-sign-sub-inv 45.8%

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

       2. metadata-eval 45.8%

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

       3. +-commutative 45.8%

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

       4. *-commutative 45.8%

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

       5. distribute-lft-out 45.8%

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

       6. *-commutative 45.8%

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

   11. Simplified 45.8%

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

4. Final simplification 52.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.9 \cdot 10^{+217} \lor \neg \left(b \cdot c \leq 1.35 \cdot 10^{+194}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(a \cdot t + x \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 51.7% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -3.55 \cdot 10^{+33} \lor \neg \left(a \leq 10^{+100}\right):\\ \;\;\;\;-4 \cdot \left(a \cdot t + x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= a -3.55e+33) (not (<= a 1e+100)))
   (* -4.0 (+ (* a t) (* x i)))
   (+ (* b c) (* j (* k -27.0)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((a <= -3.55e+33) || !(a <= 1e+100)) {
		tmp = -4.0 * ((a * t) + (x * i));
	} else {
		tmp = (b * c) + (j * (k * -27.0));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((a <= (-3.55d+33)) .or. (.not. (a <= 1d+100))) then
        tmp = (-4.0d0) * ((a * t) + (x * i))
    else
        tmp = (b * c) + (j * (k * (-27.0d0)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((a <= -3.55e+33) || !(a <= 1e+100)) {
		tmp = -4.0 * ((a * t) + (x * i));
	} else {
		tmp = (b * c) + (j * (k * -27.0));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (a <= -3.55e+33) or not (a <= 1e+100):
		tmp = -4.0 * ((a * t) + (x * i))
	else:
		tmp = (b * c) + (j * (k * -27.0))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((a <= -3.55e+33) || !(a <= 1e+100))
		tmp = Float64(-4.0 * Float64(Float64(a * t) + Float64(x * i)));
	else
		tmp = Float64(Float64(b * c) + Float64(j * Float64(k * -27.0)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((a <= -3.55e+33) || ~((a <= 1e+100)))
		tmp = -4.0 * ((a * t) + (x * i));
	else
		tmp = (b * c) + (j * (k * -27.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[a, -3.55e+33], N[Not[LessEqual[a, 1e+100]], $MachinePrecision]], N[(-4.0 * N[(N[(a * t), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -3.54999999999999989e33 or 1.00000000000000002e100 < a

   1. Initial program 83.9%

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

      1. distribute-rgt-out-- 86.8%

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

      2. associate-*r* 87.7%

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

      3. *-commutative 87.7%

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

      4. associate-*r* 86.8%

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

      5. *-commutative 86.8%

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

      6. associate-*l* 86.8%

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

   4. Applied egg-rr 86.8%

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

   5. Taylor expanded in t around inf 82.2%

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

   6. Taylor expanded in a around inf 73.1%

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

      1. *-commutative 73.1%

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

   8. Simplified 73.1%

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

   9. Taylor expanded in j around 0 59.7%

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

       1. cancel-sign-sub-inv 59.7%

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

       2. metadata-eval 59.7%

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

       3. +-commutative 59.7%

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

       4. *-commutative 59.7%

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

       5. distribute-lft-out 59.7%

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

       6. *-commutative 59.7%

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

   11. Simplified 59.7%

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

   if -3.54999999999999989e33 < a < 1.00000000000000002e100

   1. Initial program 91.5%

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

   3. Simplified 89.6%

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

   5. Taylor expanded in b around inf 54.2%

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

4. Final simplification 56.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.55 \cdot 10^{+33} \lor \neg \left(a \leq 10^{+100}\right):\\ \;\;\;\;-4 \cdot \left(a \cdot t + x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 34.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2 \cdot 10^{+163} \lor \neg \left(b \cdot c \leq 7.8 \cdot 10^{+51}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= (* b c) -2e+163) (not (<= (* b c) 7.8e+51)))
   (* 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);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (((b * c) <= -2e+163) || !((b * c) <= 7.8e+51)) {
		tmp = 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.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (((b * c) <= (-2d+163)) .or. (.not. ((b * c) <= 7.8d+51))) then
        tmp = 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;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (((b * c) <= -2e+163) || !((b * c) <= 7.8e+51)) {
		tmp = 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])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if ((b * c) <= -2e+163) or not ((b * c) <= 7.8e+51):
		tmp = 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])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((Float64(b * c) <= -2e+163) || !(Float64(b * c) <= 7.8e+51))
		tmp = 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])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (((b * c) <= -2e+163) || ~(((b * c) <= 7.8e+51)))
		tmp = 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.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[N[(b * c), $MachinePrecision], -2e+163], N[Not[LessEqual[N[(b * c), $MachinePrecision], 7.8e+51]], $MachinePrecision]], N[(b * c), $MachinePrecision], N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -1.9999999999999999e163 or 7.79999999999999968e51 < (*.f64 b c)

   1. Initial program 85.7%

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

   3. Simplified 89.0%

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

   5. Taylor expanded in b around inf 67.1%

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

   6. Taylor expanded in b around inf 58.9%

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

   if -1.9999999999999999e163 < (*.f64 b c) < 7.79999999999999968e51

   1. Initial program 89.9%

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

      1. distribute-rgt-out-- 91.7%

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

      2. associate-*r* 90.0%

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

      3. *-commutative 90.0%

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

      4. associate-*r* 91.7%

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

      5. *-commutative 91.7%

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

      6. associate-*l* 91.7%

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

   4. Applied egg-rr 91.7%

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

   5. Taylor expanded in i around inf 30.5%

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

      1. *-commutative 30.5%

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

   7. Simplified 30.5%

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

4. Final simplification 40.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2 \cdot 10^{+163} \lor \neg \left(b \cdot c \leq 7.8 \cdot 10^{+51}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 37.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2.9 \cdot 10^{-15} \lor \neg \left(b \cdot c \leq 9 \cdot 10^{+25}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= (* b c) -2.9e-15) (not (<= (* b c) 9e+25)))
   (* b c)
   (* (* j k) -27.0)))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (((b * c) <= -2.9e-15) || !((b * c) <= 9e+25)) {
		tmp = b * c;
	} else {
		tmp = (j * k) * -27.0;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (((b * c) <= (-2.9d-15)) .or. (.not. ((b * c) <= 9d+25))) then
        tmp = b * c
    else
        tmp = (j * k) * (-27.0d0)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (((b * c) <= -2.9e-15) || !((b * c) <= 9e+25)) {
		tmp = b * c;
	} else {
		tmp = (j * k) * -27.0;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if ((b * c) <= -2.9e-15) or not ((b * c) <= 9e+25):
		tmp = b * c
	else:
		tmp = (j * k) * -27.0
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((Float64(b * c) <= -2.9e-15) || !(Float64(b * c) <= 9e+25))
		tmp = Float64(b * c);
	else
		tmp = Float64(Float64(j * k) * -27.0);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (((b * c) <= -2.9e-15) || ~(((b * c) <= 9e+25)))
		tmp = b * c;
	else
		tmp = (j * k) * -27.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[N[(b * c), $MachinePrecision], -2.9e-15], N[Not[LessEqual[N[(b * c), $MachinePrecision], 9e+25]], $MachinePrecision]], N[(b * c), $MachinePrecision], N[(N[(j * k), $MachinePrecision] * -27.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -2.90000000000000019e-15 or 9.0000000000000006e25 < (*.f64 b c)

   1. Initial program 87.2%

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

   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 58.1%

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

   6. Taylor expanded in b around inf 47.5%

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

   if -2.90000000000000019e-15 < (*.f64 b c) < 9.0000000000000006e25

   1. Initial program 89.7%

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

   3. Simplified 91.4%

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

   5. Taylor expanded in j around inf 28.2%

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

4. Final simplification 38.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2.9 \cdot 10^{-15} \lor \neg \left(b \cdot c \leq 9 \cdot 10^{+25}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 23.9% accurate, 10.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 88.4%

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

3. Simplified 90.0%

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

5. Taylor expanded in b around inf 44.9%

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

6. Taylor expanded in b around inf 26.9%

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

Developer Target 1: 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 2024172 
(FPCore (x y z t a b c i j k)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, E"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< t -8105407698770699/5000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (- (* (* 18 t) (* (* x y) z)) (* (+ (* a t) (* i x)) 4)) (- (* (* k j) 27) (* c b))) (if (< t 8284013971902611/50000000000000) (+ (- (* (* 18 y) (* x (* z t))) (* (+ (* a t) (* i x)) 4)) (- (* c b) (* 27 (* k j)))) (- (- (* (* 18 t) (* (* x y) z)) (* (+ (* a t) (* i x)) 4)) (- (* (* k j) 27) (* c b))))))

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