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

Percentage Accurate: 84.9% → 90.3%

Time: 18.6s

Alternatives: 20

Speedup: 0.9×

• 51.7% 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: 84.9% 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: 90.3% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (x * 4.0) * i;
	double t_2 = (j * 27.0) * k;
	double tmp;
	if (((((((((x * 18.0) * y) * z) * t) - (t * (a * 4.0))) + (b * c)) - t_1) - t_2) <= Double.POSITIVE_INFINITY) {
		tmp = (((b * c) + (t * ((z * (x * (18.0 * y))) - (a * 4.0)))) - t_1) - t_2;
	} else {
		tmp = (b * c) + (t * ((a * -4.0) + (18.0 * (x * (y * 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])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (x * 4.0) * i
	t_2 = (j * 27.0) * k
	tmp = 0
	if ((((((((x * 18.0) * y) * z) * t) - (t * (a * 4.0))) + (b * c)) - t_1) - t_2) <= math.inf:
		tmp = (((b * c) + (t * ((z * (x * (18.0 * y))) - (a * 4.0)))) - t_1) - t_2
	else:
		tmp = (b * c) + (t * ((a * -4.0) + (18.0 * (x * (y * z)))))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(x * 4.0) * i)
	t_2 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 18.0) * y) * z) * t) - Float64(t * Float64(a * 4.0))) + Float64(b * c)) - t_1) - t_2) <= Inf)
		tmp = Float64(Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(z * Float64(x * Float64(18.0 * y))) - Float64(a * 4.0)))) - t_1) - t_2);
	else
		tmp = Float64(Float64(b * c) + Float64(t * Float64(Float64(a * -4.0) + Float64(18.0 * Float64(x * Float64(y * 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])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (x * 4.0) * i;
	t_2 = (j * 27.0) * k;
	tmp = 0.0;
	if (((((((((x * 18.0) * y) * z) * t) - (t * (a * 4.0))) + (b * c)) - t_1) - t_2) <= Inf)
		tmp = (((b * c) + (t * ((z * (x * (18.0 * y))) - (a * 4.0)))) - t_1) - t_2;
	else
		tmp = (b * c) + (t * ((a * -4.0) + (18.0 * (x * (y * 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.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[N[(N[(N[(N[(N[(N[(N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision] - N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * c), $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[(18.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision], N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(a * -4.0), $MachinePrecision] + N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

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 94.2%

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

      1. distribute-rgt-out-- 94.2%

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

      2. *-commutative 94.2%

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

      3. associate-*l* 94.2%

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

   4. Applied egg-rr 94.2%

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

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

   1. Initial program 0.0%

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

   3. Simplified 45.5%

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

   5. Taylor expanded in i around 0 59.1%

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

   6. Taylor expanded in k around 0 54.8%

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

4. Final simplification 90.8%

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

Alternative 2: 35.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := -27 \cdot \left(j \cdot k\right)\\ t_2 := -4 \cdot \left(t \cdot a\right)\\ \mathbf{if}\;b \cdot c \leq -0.00128:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -5.5 \cdot 10^{-189}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq 3.6 \cdot 10^{-290}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \cdot c \leq 1.75 \cdot 10^{-143}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq 5.3 \cdot 10^{-44}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \cdot c \leq 6000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq 5.2 \cdot 10^{+127}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* -27.0 (* j k))) (t_2 (* -4.0 (* t a))))
   (if (<= (* b c) -0.00128)
     (* b c)
     (if (<= (* b c) -5.5e-189)
       t_1
       (if (<= (* b c) 3.6e-290)
         t_2
         (if (<= (* b c) 1.75e-143)
           t_1
           (if (<= (* b c) 5.3e-44)
             t_2
             (if (<= (* b c) 6000.0)
               t_1
               (if (<= (* b c) 5.2e+127) t_2 (* b c))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -27.0 * (j * k);
	double t_2 = -4.0 * (t * a);
	double tmp;
	if ((b * c) <= -0.00128) {
		tmp = b * c;
	} else if ((b * c) <= -5.5e-189) {
		tmp = t_1;
	} else if ((b * c) <= 3.6e-290) {
		tmp = t_2;
	} else if ((b * c) <= 1.75e-143) {
		tmp = t_1;
	} else if ((b * c) <= 5.3e-44) {
		tmp = t_2;
	} else if ((b * c) <= 6000.0) {
		tmp = t_1;
	} else if ((b * c) <= 5.2e+127) {
		tmp = t_2;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (-27.0d0) * (j * k)
    t_2 = (-4.0d0) * (t * a)
    if ((b * c) <= (-0.00128d0)) then
        tmp = b * c
    else if ((b * c) <= (-5.5d-189)) then
        tmp = t_1
    else if ((b * c) <= 3.6d-290) then
        tmp = t_2
    else if ((b * c) <= 1.75d-143) then
        tmp = t_1
    else if ((b * c) <= 5.3d-44) then
        tmp = t_2
    else if ((b * c) <= 6000.0d0) then
        tmp = t_1
    else if ((b * c) <= 5.2d+127) then
        tmp = t_2
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -27.0 * (j * k);
	double t_2 = -4.0 * (t * a);
	double tmp;
	if ((b * c) <= -0.00128) {
		tmp = b * c;
	} else if ((b * c) <= -5.5e-189) {
		tmp = t_1;
	} else if ((b * c) <= 3.6e-290) {
		tmp = t_2;
	} else if ((b * c) <= 1.75e-143) {
		tmp = t_1;
	} else if ((b * c) <= 5.3e-44) {
		tmp = t_2;
	} else if ((b * c) <= 6000.0) {
		tmp = t_1;
	} else if ((b * c) <= 5.2e+127) {
		tmp = t_2;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = -27.0 * (j * k)
	t_2 = -4.0 * (t * a)
	tmp = 0
	if (b * c) <= -0.00128:
		tmp = b * c
	elif (b * c) <= -5.5e-189:
		tmp = t_1
	elif (b * c) <= 3.6e-290:
		tmp = t_2
	elif (b * c) <= 1.75e-143:
		tmp = t_1
	elif (b * c) <= 5.3e-44:
		tmp = t_2
	elif (b * c) <= 6000.0:
		tmp = t_1
	elif (b * c) <= 5.2e+127:
		tmp = t_2
	else:
		tmp = b * c
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(-27.0 * Float64(j * k))
	t_2 = Float64(-4.0 * Float64(t * a))
	tmp = 0.0
	if (Float64(b * c) <= -0.00128)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -5.5e-189)
		tmp = t_1;
	elseif (Float64(b * c) <= 3.6e-290)
		tmp = t_2;
	elseif (Float64(b * c) <= 1.75e-143)
		tmp = t_1;
	elseif (Float64(b * c) <= 5.3e-44)
		tmp = t_2;
	elseif (Float64(b * c) <= 6000.0)
		tmp = t_1;
	elseif (Float64(b * c) <= 5.2e+127)
		tmp = t_2;
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = -27.0 * (j * k);
	t_2 = -4.0 * (t * a);
	tmp = 0.0;
	if ((b * c) <= -0.00128)
		tmp = b * c;
	elseif ((b * c) <= -5.5e-189)
		tmp = t_1;
	elseif ((b * c) <= 3.6e-290)
		tmp = t_2;
	elseif ((b * c) <= 1.75e-143)
		tmp = t_1;
	elseif ((b * c) <= 5.3e-44)
		tmp = t_2;
	elseif ((b * c) <= 6000.0)
		tmp = t_1;
	elseif ((b * c) <= 5.2e+127)
		tmp = t_2;
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -0.00128], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -5.5e-189], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 3.6e-290], t$95$2, If[LessEqual[N[(b * c), $MachinePrecision], 1.75e-143], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 5.3e-44], t$95$2, If[LessEqual[N[(b * c), $MachinePrecision], 6000.0], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 5.2e+127], t$95$2, N[(b * c), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -0.0012800000000000001 or 5.2000000000000004e127 < (*.f64 b c)

   1. Initial program 84.0%

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

   3. Simplified 87.0%

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

   5. Taylor expanded in b around inf 53.1%

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

   if -0.0012800000000000001 < (*.f64 b c) < -5.4999999999999999e-189 or 3.59999999999999979e-290 < (*.f64 b c) < 1.75000000000000003e-143 or 5.29999999999999971e-44 < (*.f64 b c) < 6e3

   1. Initial program 82.3%

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

   3. Simplified 86.8%

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

   5. Taylor expanded in k around inf 40.6%

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

   if -5.4999999999999999e-189 < (*.f64 b c) < 3.59999999999999979e-290 or 1.75000000000000003e-143 < (*.f64 b c) < 5.29999999999999971e-44 or 6e3 < (*.f64 b c) < 5.2000000000000004e127

   1. Initial program 91.2%

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

   3. Simplified 93.4%

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

   5. Taylor expanded in a around inf 43.0%

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

4. Final simplification 46.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -0.00128:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -5.5 \cdot 10^{-189}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq 3.6 \cdot 10^{-290}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;b \cdot c \leq 1.75 \cdot 10^{-143}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq 5.3 \cdot 10^{-44}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;b \cdot c \leq 6000:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq 5.2 \cdot 10^{+127}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 36.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := -4 \cdot \left(t \cdot a\right)\\ t_2 := -27 \cdot \left(j \cdot k\right)\\ \mathbf{if}\;b \cdot c \leq -6.5 \cdot 10^{+58}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -4.2 \cdot 10^{-66}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(z \cdot \left(x \cdot t\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq -3.5 \cdot 10^{-190}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \cdot c \leq 2.05 \cdot 10^{-290}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq 1.6 \cdot 10^{-143}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \cdot c \leq 4.5 \cdot 10^{+127}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* -4.0 (* t a))) (t_2 (* -27.0 (* j k))))
   (if (<= (* b c) -6.5e+58)
     (* b c)
     (if (<= (* b c) -4.2e-66)
       (* 18.0 (* y (* z (* x t))))
       (if (<= (* b c) -3.5e-190)
         t_2
         (if (<= (* b c) 2.05e-290)
           t_1
           (if (<= (* b c) 1.6e-143)
             t_2
             (if (<= (* b c) 4.5e+127) t_1 (* b c)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -4.0 * (t * a);
	double t_2 = -27.0 * (j * k);
	double tmp;
	if ((b * c) <= -6.5e+58) {
		tmp = b * c;
	} else if ((b * c) <= -4.2e-66) {
		tmp = 18.0 * (y * (z * (x * t)));
	} else if ((b * c) <= -3.5e-190) {
		tmp = t_2;
	} else if ((b * c) <= 2.05e-290) {
		tmp = t_1;
	} else if ((b * c) <= 1.6e-143) {
		tmp = t_2;
	} else if ((b * c) <= 4.5e+127) {
		tmp = t_1;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (-4.0d0) * (t * a)
    t_2 = (-27.0d0) * (j * k)
    if ((b * c) <= (-6.5d+58)) then
        tmp = b * c
    else if ((b * c) <= (-4.2d-66)) then
        tmp = 18.0d0 * (y * (z * (x * t)))
    else if ((b * c) <= (-3.5d-190)) then
        tmp = t_2
    else if ((b * c) <= 2.05d-290) then
        tmp = t_1
    else if ((b * c) <= 1.6d-143) then
        tmp = t_2
    else if ((b * c) <= 4.5d+127) then
        tmp = t_1
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -4.0 * (t * a);
	double t_2 = -27.0 * (j * k);
	double tmp;
	if ((b * c) <= -6.5e+58) {
		tmp = b * c;
	} else if ((b * c) <= -4.2e-66) {
		tmp = 18.0 * (y * (z * (x * t)));
	} else if ((b * c) <= -3.5e-190) {
		tmp = t_2;
	} else if ((b * c) <= 2.05e-290) {
		tmp = t_1;
	} else if ((b * c) <= 1.6e-143) {
		tmp = t_2;
	} else if ((b * c) <= 4.5e+127) {
		tmp = t_1;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = -4.0 * (t * a)
	t_2 = -27.0 * (j * k)
	tmp = 0
	if (b * c) <= -6.5e+58:
		tmp = b * c
	elif (b * c) <= -4.2e-66:
		tmp = 18.0 * (y * (z * (x * t)))
	elif (b * c) <= -3.5e-190:
		tmp = t_2
	elif (b * c) <= 2.05e-290:
		tmp = t_1
	elif (b * c) <= 1.6e-143:
		tmp = t_2
	elif (b * c) <= 4.5e+127:
		tmp = t_1
	else:
		tmp = b * c
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(-4.0 * Float64(t * a))
	t_2 = Float64(-27.0 * Float64(j * k))
	tmp = 0.0
	if (Float64(b * c) <= -6.5e+58)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -4.2e-66)
		tmp = Float64(18.0 * Float64(y * Float64(z * Float64(x * t))));
	elseif (Float64(b * c) <= -3.5e-190)
		tmp = t_2;
	elseif (Float64(b * c) <= 2.05e-290)
		tmp = t_1;
	elseif (Float64(b * c) <= 1.6e-143)
		tmp = t_2;
	elseif (Float64(b * c) <= 4.5e+127)
		tmp = t_1;
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = -4.0 * (t * a);
	t_2 = -27.0 * (j * k);
	tmp = 0.0;
	if ((b * c) <= -6.5e+58)
		tmp = b * c;
	elseif ((b * c) <= -4.2e-66)
		tmp = 18.0 * (y * (z * (x * t)));
	elseif ((b * c) <= -3.5e-190)
		tmp = t_2;
	elseif ((b * c) <= 2.05e-290)
		tmp = t_1;
	elseif ((b * c) <= 1.6e-143)
		tmp = t_2;
	elseif ((b * c) <= 4.5e+127)
		tmp = t_1;
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -6.5e+58], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -4.2e-66], N[(18.0 * N[(y * N[(z * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -3.5e-190], t$95$2, If[LessEqual[N[(b * c), $MachinePrecision], 2.05e-290], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 1.6e-143], t$95$2, If[LessEqual[N[(b * c), $MachinePrecision], 4.5e+127], t$95$1, N[(b * c), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 b c) < -6.49999999999999998e58 or 4.50000000000000034e127 < (*.f64 b c)

   1. Initial program 84.6%

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

   3. Simplified 84.7%

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

   5. Taylor expanded in b around inf 59.6%

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

   if -6.49999999999999998e58 < (*.f64 b c) < -4.2000000000000001e-66

   1. Initial program 74.0%

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

   3. Simplified 93.4%

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

   5. Taylor expanded in y around inf 45.5%

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

      1. *-commutative 45.5%

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

   7. Applied egg-rr 45.5%

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

      1. associate-*r* 45.5%

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

   9. Simplified 45.5%

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

   10. Taylor expanded in t around 0 45.5%

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

       1. associate-*r* 45.4%

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

       2. *-commutative 45.4%

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

       3. associate-*r* 45.5%

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

       4. associate-*r* 45.5%

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

       5. associate-*l* 48.6%

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

       6. *-commutative 48.6%

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

       7. associate-*r* 48.6%

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

       8. *-commutative 48.6%

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

       9. *-commutative 48.6%

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

   12. Simplified 48.6%

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

   if -4.2000000000000001e-66 < (*.f64 b c) < -3.4999999999999999e-190 or 2.0500000000000001e-290 < (*.f64 b c) < 1.5999999999999999e-143

   1. Initial program 92.5%

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

   3. Simplified 95.1%

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

   5. Taylor expanded in k around inf 40.9%

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

   if -3.4999999999999999e-190 < (*.f64 b c) < 2.0500000000000001e-290 or 1.5999999999999999e-143 < (*.f64 b c) < 4.50000000000000034e127

   1. Initial program 88.3%

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

   3. Simplified 89.4%

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

   5. Taylor expanded in a around inf 39.6%

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

4. Final simplification 47.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -6.5 \cdot 10^{+58}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -4.2 \cdot 10^{-66}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(z \cdot \left(x \cdot t\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq -3.5 \cdot 10^{-190}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq 2.05 \cdot 10^{-290}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;b \cdot c \leq 1.6 \cdot 10^{-143}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq 4.5 \cdot 10^{+127}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 69.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ t_2 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+300}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right) - j \cdot \left(27 \cdot k\right)\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{+53} \lor \neg \left(t\_1 \leq 5 \cdot 10^{+40}\right):\\ \;\;\;\;k \cdot \left(j \cdot -27\right) + \left(b \cdot c + 18 \cdot \left(t \cdot t\_2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + t \cdot \left(a \cdot -4 + 18 \cdot t\_2\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)) (t_2 (* x (* y z))))
   (if (<= t_1 -1e+300)
     (- (* -4.0 (* x i)) (* j (* 27.0 k)))
     (if (or (<= t_1 -5e+53) (not (<= t_1 5e+40)))
       (+ (* k (* j -27.0)) (+ (* b c) (* 18.0 (* t t_2))))
       (+ (* b c) (* t (+ (* a -4.0) (* 18.0 t_2))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double t_2 = x * (y * z);
	double tmp;
	if (t_1 <= -1e+300) {
		tmp = (-4.0 * (x * i)) - (j * (27.0 * k));
	} else if ((t_1 <= -5e+53) || !(t_1 <= 5e+40)) {
		tmp = (k * (j * -27.0)) + ((b * c) + (18.0 * (t * t_2)));
	} else {
		tmp = (b * c) + (t * ((a * -4.0) + (18.0 * t_2)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (j * 27.0d0) * k
    t_2 = x * (y * z)
    if (t_1 <= (-1d+300)) then
        tmp = ((-4.0d0) * (x * i)) - (j * (27.0d0 * k))
    else if ((t_1 <= (-5d+53)) .or. (.not. (t_1 <= 5d+40))) then
        tmp = (k * (j * (-27.0d0))) + ((b * c) + (18.0d0 * (t * t_2)))
    else
        tmp = (b * c) + (t * ((a * (-4.0d0)) + (18.0d0 * t_2)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double t_2 = x * (y * z);
	double tmp;
	if (t_1 <= -1e+300) {
		tmp = (-4.0 * (x * i)) - (j * (27.0 * k));
	} else if ((t_1 <= -5e+53) || !(t_1 <= 5e+40)) {
		tmp = (k * (j * -27.0)) + ((b * c) + (18.0 * (t * t_2)));
	} else {
		tmp = (b * c) + (t * ((a * -4.0) + (18.0 * t_2)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	t_2 = x * (y * z)
	tmp = 0
	if t_1 <= -1e+300:
		tmp = (-4.0 * (x * i)) - (j * (27.0 * k))
	elif (t_1 <= -5e+53) or not (t_1 <= 5e+40):
		tmp = (k * (j * -27.0)) + ((b * c) + (18.0 * (t * t_2)))
	else:
		tmp = (b * c) + (t * ((a * -4.0) + (18.0 * t_2)))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	t_2 = Float64(x * Float64(y * z))
	tmp = 0.0
	if (t_1 <= -1e+300)
		tmp = Float64(Float64(-4.0 * Float64(x * i)) - Float64(j * Float64(27.0 * k)));
	elseif ((t_1 <= -5e+53) || !(t_1 <= 5e+40))
		tmp = Float64(Float64(k * Float64(j * -27.0)) + Float64(Float64(b * c) + Float64(18.0 * Float64(t * t_2))));
	else
		tmp = Float64(Float64(b * c) + Float64(t * Float64(Float64(a * -4.0) + Float64(18.0 * t_2))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * 27.0) * k;
	t_2 = x * (y * z);
	tmp = 0.0;
	if (t_1 <= -1e+300)
		tmp = (-4.0 * (x * i)) - (j * (27.0 * k));
	elseif ((t_1 <= -5e+53) || ~((t_1 <= 5e+40)))
		tmp = (k * (j * -27.0)) + ((b * c) + (18.0 * (t * t_2)));
	else
		tmp = (b * c) + (t * ((a * -4.0) + (18.0 * t_2)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+300], N[(N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision] - N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t$95$1, -5e+53], N[Not[LessEqual[t$95$1, 5e+40]], $MachinePrecision]], N[(N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision] + N[(N[(b * c), $MachinePrecision] + N[(18.0 * N[(t * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(a * -4.0), $MachinePrecision] + N[(18.0 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -1.0000000000000001e300

   1. Initial program 50.3%

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

      1. distribute-rgt-out-- 55.8%

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

      2. *-commutative 55.8%

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

      3. associate-*l* 55.8%

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

   4. Applied egg-rr 55.8%

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

   5. Taylor expanded in i around inf 83.6%

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

   6. Taylor expanded in j around 0 88.9%

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

      1. *-commutative 88.9%

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

      2. associate-*l* 88.8%

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

      3. *-commutative 88.8%

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

      4. *-commutative 88.8%

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

   8. Simplified 88.8%

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

   if -1.0000000000000001e300 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -5.0000000000000004e53 or 5.00000000000000003e40 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 85.8%

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

   3. Simplified 91.6%

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

   5. Taylor expanded in i around 0 85.0%

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

   6. Taylor expanded in a around 0 78.1%

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

   if -5.0000000000000004e53 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 5.00000000000000003e40

   1. Initial program 90.4%

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

   3. Simplified 90.5%

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

   5. Taylor expanded in i around 0 75.6%

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

   6. Taylor expanded in k around 0 71.9%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \leq -1 \cdot 10^{+300}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right) - j \cdot \left(27 \cdot k\right)\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq -5 \cdot 10^{+53} \lor \neg \left(\left(j \cdot 27\right) \cdot k \leq 5 \cdot 10^{+40}\right):\\ \;\;\;\;k \cdot \left(j \cdot -27\right) + \left(b \cdot c + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + t \cdot \left(a \cdot -4 + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 32.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := -4 \cdot \left(x \cdot i\right)\\ t_2 := 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ t_3 := -4 \cdot \left(t \cdot a\right)\\ \mathbf{if}\;t \leq -5.6 \cdot 10^{+274}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{+89}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-180}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \leq -9.5 \cdot 10^{-249}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;t \leq 2.45 \cdot 10^{-201}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;t \leq 0.00026:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{+34}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 2.15 \cdot 10^{+111}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* -4.0 (* x i)))
        (t_2 (* 18.0 (* t (* x (* y z)))))
        (t_3 (* -4.0 (* t a))))
   (if (<= t -5.6e+274)
     t_3
     (if (<= t -3.8e+89)
       t_2
       (if (<= t -1.15e-180)
         (* -27.0 (* j k))
         (if (<= t -9.5e-249)
           (* b c)
           (if (<= t 2.45e-201)
             (* k (* j -27.0))
             (if (<= t 0.00026)
               t_1
               (if (<= t 1.45e+34) t_2 (if (<= t 2.15e+111) t_1 t_3))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -4.0 * (x * i);
	double t_2 = 18.0 * (t * (x * (y * z)));
	double t_3 = -4.0 * (t * a);
	double tmp;
	if (t <= -5.6e+274) {
		tmp = t_3;
	} else if (t <= -3.8e+89) {
		tmp = t_2;
	} else if (t <= -1.15e-180) {
		tmp = -27.0 * (j * k);
	} else if (t <= -9.5e-249) {
		tmp = b * c;
	} else if (t <= 2.45e-201) {
		tmp = k * (j * -27.0);
	} else if (t <= 0.00026) {
		tmp = t_1;
	} else if (t <= 1.45e+34) {
		tmp = t_2;
	} else if (t <= 2.15e+111) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (-4.0d0) * (x * i)
    t_2 = 18.0d0 * (t * (x * (y * z)))
    t_3 = (-4.0d0) * (t * a)
    if (t <= (-5.6d+274)) then
        tmp = t_3
    else if (t <= (-3.8d+89)) then
        tmp = t_2
    else if (t <= (-1.15d-180)) then
        tmp = (-27.0d0) * (j * k)
    else if (t <= (-9.5d-249)) then
        tmp = b * c
    else if (t <= 2.45d-201) then
        tmp = k * (j * (-27.0d0))
    else if (t <= 0.00026d0) then
        tmp = t_1
    else if (t <= 1.45d+34) then
        tmp = t_2
    else if (t <= 2.15d+111) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -4.0 * (x * i);
	double t_2 = 18.0 * (t * (x * (y * z)));
	double t_3 = -4.0 * (t * a);
	double tmp;
	if (t <= -5.6e+274) {
		tmp = t_3;
	} else if (t <= -3.8e+89) {
		tmp = t_2;
	} else if (t <= -1.15e-180) {
		tmp = -27.0 * (j * k);
	} else if (t <= -9.5e-249) {
		tmp = b * c;
	} else if (t <= 2.45e-201) {
		tmp = k * (j * -27.0);
	} else if (t <= 0.00026) {
		tmp = t_1;
	} else if (t <= 1.45e+34) {
		tmp = t_2;
	} else if (t <= 2.15e+111) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = -4.0 * (x * i)
	t_2 = 18.0 * (t * (x * (y * z)))
	t_3 = -4.0 * (t * a)
	tmp = 0
	if t <= -5.6e+274:
		tmp = t_3
	elif t <= -3.8e+89:
		tmp = t_2
	elif t <= -1.15e-180:
		tmp = -27.0 * (j * k)
	elif t <= -9.5e-249:
		tmp = b * c
	elif t <= 2.45e-201:
		tmp = k * (j * -27.0)
	elif t <= 0.00026:
		tmp = t_1
	elif t <= 1.45e+34:
		tmp = t_2
	elif t <= 2.15e+111:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(-4.0 * Float64(x * i))
	t_2 = Float64(18.0 * Float64(t * Float64(x * Float64(y * z))))
	t_3 = Float64(-4.0 * Float64(t * a))
	tmp = 0.0
	if (t <= -5.6e+274)
		tmp = t_3;
	elseif (t <= -3.8e+89)
		tmp = t_2;
	elseif (t <= -1.15e-180)
		tmp = Float64(-27.0 * Float64(j * k));
	elseif (t <= -9.5e-249)
		tmp = Float64(b * c);
	elseif (t <= 2.45e-201)
		tmp = Float64(k * Float64(j * -27.0));
	elseif (t <= 0.00026)
		tmp = t_1;
	elseif (t <= 1.45e+34)
		tmp = t_2;
	elseif (t <= 2.15e+111)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = -4.0 * (x * i);
	t_2 = 18.0 * (t * (x * (y * z)));
	t_3 = -4.0 * (t * a);
	tmp = 0.0;
	if (t <= -5.6e+274)
		tmp = t_3;
	elseif (t <= -3.8e+89)
		tmp = t_2;
	elseif (t <= -1.15e-180)
		tmp = -27.0 * (j * k);
	elseif (t <= -9.5e-249)
		tmp = b * c;
	elseif (t <= 2.45e-201)
		tmp = k * (j * -27.0);
	elseif (t <= 0.00026)
		tmp = t_1;
	elseif (t <= 1.45e+34)
		tmp = t_2;
	elseif (t <= 2.15e+111)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.6e+274], t$95$3, If[LessEqual[t, -3.8e+89], t$95$2, If[LessEqual[t, -1.15e-180], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -9.5e-249], N[(b * c), $MachinePrecision], If[LessEqual[t, 2.45e-201], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 0.00026], t$95$1, If[LessEqual[t, 1.45e+34], t$95$2, If[LessEqual[t, 2.15e+111], t$95$1, t$95$3]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -5.60000000000000017e274 or 2.14999999999999997e111 < t

   1. Initial program 93.4%

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

   3. Simplified 95.6%

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

   5. Taylor expanded in a around inf 54.8%

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

   if -5.60000000000000017e274 < t < -3.80000000000000023e89 or 2.59999999999999977e-4 < t < 1.4500000000000001e34

   1. Initial program 78.7%

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

   3. Simplified 93.3%

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

   5. Taylor expanded in y around inf 62.9%

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

   if -3.80000000000000023e89 < t < -1.14999999999999998e-180

   1. Initial program 88.3%

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

   3. Simplified 82.6%

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

   5. Taylor expanded in k around inf 35.4%

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

   if -1.14999999999999998e-180 < t < -9.4999999999999997e-249

   1. Initial program 95.8%

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

   3. Simplified 91.6%

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

   5. Taylor expanded in b around inf 60.0%

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

   if -9.4999999999999997e-249 < t < 2.4499999999999998e-201

   1. Initial program 80.1%

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

      1. distribute-rgt-out-- 80.1%

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

      2. *-commutative 80.1%

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

      3. associate-*l* 80.1%

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

   4. Applied egg-rr 80.1%

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

   5. Taylor expanded in j around inf 51.3%

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

      1. *-commutative 51.3%

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

      2. *-commutative 51.3%

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

      3. associate-*r* 51.3%

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

   7. Simplified 51.3%

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

   if 2.4499999999999998e-201 < t < 2.59999999999999977e-4 or 1.4500000000000001e34 < t < 2.14999999999999997e111

   1. Initial program 83.7%

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

   3. Simplified 87.6%

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

   5. Taylor expanded in i around inf 38.6%

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

4. Final simplification 49.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.6 \cdot 10^{+274}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{+89}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-180}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \leq -9.5 \cdot 10^{-249}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;t \leq 2.45 \cdot 10^{-201}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;t \leq 0.00026:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{+34}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq 2.15 \cdot 10^{+111}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 36.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := 18 \cdot \left(t \cdot \left(y \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{if}\;b \cdot c \leq -2.4 \cdot 10^{+58}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -3.5 \cdot 10^{-65}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq -1.12 \cdot 10^{-194}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq -3.7 \cdot 10^{-270}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq 1.95 \cdot 10^{+127}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* 18.0 (* t (* y (* x z))))))
   (if (<= (* b c) -2.4e+58)
     (* b c)
     (if (<= (* b c) -3.5e-65)
       t_1
       (if (<= (* b c) -1.12e-194)
         (* -27.0 (* j k))
         (if (<= (* b c) -3.7e-270)
           t_1
           (if (<= (* b c) 1.95e+127) (* -4.0 (* t a)) (* b c))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 18.0 * (t * (y * (x * z)));
	double tmp;
	if ((b * c) <= -2.4e+58) {
		tmp = b * c;
	} else if ((b * c) <= -3.5e-65) {
		tmp = t_1;
	} else if ((b * c) <= -1.12e-194) {
		tmp = -27.0 * (j * k);
	} else if ((b * c) <= -3.7e-270) {
		tmp = t_1;
	} else if ((b * c) <= 1.95e+127) {
		tmp = -4.0 * (t * a);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 18.0d0 * (t * (y * (x * z)))
    if ((b * c) <= (-2.4d+58)) then
        tmp = b * c
    else if ((b * c) <= (-3.5d-65)) then
        tmp = t_1
    else if ((b * c) <= (-1.12d-194)) then
        tmp = (-27.0d0) * (j * k)
    else if ((b * c) <= (-3.7d-270)) then
        tmp = t_1
    else if ((b * c) <= 1.95d+127) then
        tmp = (-4.0d0) * (t * a)
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 18.0 * (t * (y * (x * z)));
	double tmp;
	if ((b * c) <= -2.4e+58) {
		tmp = b * c;
	} else if ((b * c) <= -3.5e-65) {
		tmp = t_1;
	} else if ((b * c) <= -1.12e-194) {
		tmp = -27.0 * (j * k);
	} else if ((b * c) <= -3.7e-270) {
		tmp = t_1;
	} else if ((b * c) <= 1.95e+127) {
		tmp = -4.0 * (t * a);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = 18.0 * (t * (y * (x * z)))
	tmp = 0
	if (b * c) <= -2.4e+58:
		tmp = b * c
	elif (b * c) <= -3.5e-65:
		tmp = t_1
	elif (b * c) <= -1.12e-194:
		tmp = -27.0 * (j * k)
	elif (b * c) <= -3.7e-270:
		tmp = t_1
	elif (b * c) <= 1.95e+127:
		tmp = -4.0 * (t * a)
	else:
		tmp = b * c
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(18.0 * Float64(t * Float64(y * Float64(x * z))))
	tmp = 0.0
	if (Float64(b * c) <= -2.4e+58)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -3.5e-65)
		tmp = t_1;
	elseif (Float64(b * c) <= -1.12e-194)
		tmp = Float64(-27.0 * Float64(j * k));
	elseif (Float64(b * c) <= -3.7e-270)
		tmp = t_1;
	elseif (Float64(b * c) <= 1.95e+127)
		tmp = Float64(-4.0 * Float64(t * a));
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = 18.0 * (t * (y * (x * z)));
	tmp = 0.0;
	if ((b * c) <= -2.4e+58)
		tmp = b * c;
	elseif ((b * c) <= -3.5e-65)
		tmp = t_1;
	elseif ((b * c) <= -1.12e-194)
		tmp = -27.0 * (j * k);
	elseif ((b * c) <= -3.7e-270)
		tmp = t_1;
	elseif ((b * c) <= 1.95e+127)
		tmp = -4.0 * (t * a);
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(18.0 * N[(t * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -2.4e+58], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -3.5e-65], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], -1.12e-194], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -3.7e-270], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 1.95e+127], N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 b c) < -2.4e58 or 1.94999999999999991e127 < (*.f64 b c)

   1. Initial program 84.6%

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

   3. Simplified 84.7%

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

   5. Taylor expanded in b around inf 59.6%

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

   if -2.4e58 < (*.f64 b c) < -3.50000000000000005e-65 or -1.12000000000000001e-194 < (*.f64 b c) < -3.7000000000000001e-270

   1. Initial program 74.7%

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

   3. Simplified 84.8%

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

   5. Taylor expanded in y around inf 45.4%

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

      1. *-commutative 45.4%

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

   7. Applied egg-rr 45.4%

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

      1. associate-*r* 47.8%

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

   9. Simplified 47.8%

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

   if -3.50000000000000005e-65 < (*.f64 b c) < -1.12000000000000001e-194

   1. Initial program 96.6%

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

   3. Simplified 96.7%

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

   5. Taylor expanded in k around inf 38.7%

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

   if -3.7000000000000001e-270 < (*.f64 b c) < 1.94999999999999991e127

   1. Initial program 88.6%

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

   3. Simplified 92.4%

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

   5. Taylor expanded in a around inf 36.5%

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

4. Final simplification 46.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2.4 \cdot 10^{+58}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -3.5 \cdot 10^{-65}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(y \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq -1.12 \cdot 10^{-194}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq -3.7 \cdot 10^{-270}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(y \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 1.95 \cdot 10^{+127}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 59.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := -4 \cdot \left(t \cdot a\right)\\ t_2 := x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ t_3 := k \cdot \left(j \cdot -27\right)\\ t_4 := t\_3 + t\_1\\ \mathbf{if}\;x \leq -4.1 \cdot 10^{-38}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -2.7 \cdot 10^{-216}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-113}:\\ \;\;\;\;b \cdot c + t\_1\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{-9}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{+46}:\\ \;\;\;\;b \cdot c + t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* -4.0 (* t a)))
        (t_2 (* x (- (* 18.0 (* t (* y z))) (* 4.0 i))))
        (t_3 (* k (* j -27.0)))
        (t_4 (+ t_3 t_1)))
   (if (<= x -4.1e-38)
     t_2
     (if (<= x -2.7e-216)
       t_4
       (if (<= x 1.4e-113)
         (+ (* b c) t_1)
         (if (<= x 3.8e-9) t_4 (if (<= x 6.2e+46) (+ (* b c) t_3) t_2)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -4.0 * (t * a);
	double t_2 = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	double t_3 = k * (j * -27.0);
	double t_4 = t_3 + t_1;
	double tmp;
	if (x <= -4.1e-38) {
		tmp = t_2;
	} else if (x <= -2.7e-216) {
		tmp = t_4;
	} else if (x <= 1.4e-113) {
		tmp = (b * c) + t_1;
	} else if (x <= 3.8e-9) {
		tmp = t_4;
	} else if (x <= 6.2e+46) {
		tmp = (b * c) + t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = (-4.0d0) * (t * a)
    t_2 = x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i))
    t_3 = k * (j * (-27.0d0))
    t_4 = t_3 + t_1
    if (x <= (-4.1d-38)) then
        tmp = t_2
    else if (x <= (-2.7d-216)) then
        tmp = t_4
    else if (x <= 1.4d-113) then
        tmp = (b * c) + t_1
    else if (x <= 3.8d-9) then
        tmp = t_4
    else if (x <= 6.2d+46) then
        tmp = (b * c) + t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -4.0 * (t * a);
	double t_2 = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	double t_3 = k * (j * -27.0);
	double t_4 = t_3 + t_1;
	double tmp;
	if (x <= -4.1e-38) {
		tmp = t_2;
	} else if (x <= -2.7e-216) {
		tmp = t_4;
	} else if (x <= 1.4e-113) {
		tmp = (b * c) + t_1;
	} else if (x <= 3.8e-9) {
		tmp = t_4;
	} else if (x <= 6.2e+46) {
		tmp = (b * c) + t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = -4.0 * (t * a)
	t_2 = x * ((18.0 * (t * (y * z))) - (4.0 * i))
	t_3 = k * (j * -27.0)
	t_4 = t_3 + t_1
	tmp = 0
	if x <= -4.1e-38:
		tmp = t_2
	elif x <= -2.7e-216:
		tmp = t_4
	elif x <= 1.4e-113:
		tmp = (b * c) + t_1
	elif x <= 3.8e-9:
		tmp = t_4
	elif x <= 6.2e+46:
		tmp = (b * c) + t_3
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(-4.0 * Float64(t * a))
	t_2 = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)))
	t_3 = Float64(k * Float64(j * -27.0))
	t_4 = Float64(t_3 + t_1)
	tmp = 0.0
	if (x <= -4.1e-38)
		tmp = t_2;
	elseif (x <= -2.7e-216)
		tmp = t_4;
	elseif (x <= 1.4e-113)
		tmp = Float64(Float64(b * c) + t_1);
	elseif (x <= 3.8e-9)
		tmp = t_4;
	elseif (x <= 6.2e+46)
		tmp = Float64(Float64(b * c) + t_3);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = -4.0 * (t * a);
	t_2 = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	t_3 = k * (j * -27.0);
	t_4 = t_3 + t_1;
	tmp = 0.0;
	if (x <= -4.1e-38)
		tmp = t_2;
	elseif (x <= -2.7e-216)
		tmp = t_4;
	elseif (x <= 1.4e-113)
		tmp = (b * c) + t_1;
	elseif (x <= 3.8e-9)
		tmp = t_4;
	elseif (x <= 6.2e+46)
		tmp = (b * c) + t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$3 + t$95$1), $MachinePrecision]}, If[LessEqual[x, -4.1e-38], t$95$2, If[LessEqual[x, -2.7e-216], t$95$4, If[LessEqual[x, 1.4e-113], N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[x, 3.8e-9], t$95$4, If[LessEqual[x, 6.2e+46], N[(N[(b * c), $MachinePrecision] + t$95$3), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -4.0999999999999998e-38 or 6.1999999999999995e46 < x

   1. Initial program 77.6%

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

   3. Taylor expanded in x around inf 64.8%

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

   if -4.0999999999999998e-38 < x < -2.6999999999999999e-216 or 1.4e-113 < x < 3.80000000000000011e-9

   1. Initial program 95.1%

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

   3. Simplified 93.5%

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

   5. Taylor expanded in a around inf 70.1%

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

      1. *-commutative 70.1%

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

   7. Simplified 70.1%

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

   if -2.6999999999999999e-216 < x < 1.4e-113

   1. Initial program 93.7%

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

      1. distribute-rgt-out-- 95.3%

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

      2. *-commutative 95.3%

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

      3. associate-*l* 95.3%

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

   4. Applied egg-rr 95.3%

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

   5. Taylor expanded in x around 0 81.4%

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

   6. Taylor expanded in j around 0 70.8%

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

   if 3.80000000000000011e-9 < x < 6.1999999999999995e46

   1. Initial program 86.4%

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

   3. Simplified 93.5%

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

   5. Taylor expanded in b around inf 65.4%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.1 \cdot 10^{-38}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;x \leq -2.7 \cdot 10^{-216}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-113}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{-9}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{+46}:\\ \;\;\;\;b \cdot c + k \cdot \left(j \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 58.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := k \cdot \left(j \cdot -27\right)\\ t_2 := -4 \cdot \left(x \cdot i\right)\\ t_3 := t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{if}\;t \leq -1 \cdot 10^{+88}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq -2.65 \cdot 10^{-237}:\\ \;\;\;\;b \cdot c + t\_1\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-189}:\\ \;\;\;\;t\_1 + t\_2\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-157}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-52}:\\ \;\;\;\;t\_2 - j \cdot \left(27 \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* k (* j -27.0)))
        (t_2 (* -4.0 (* x i)))
        (t_3 (* t (- (* 18.0 (* x (* y z))) (* a 4.0)))))
   (if (<= t -1e+88)
     t_3
     (if (<= t -2.65e-237)
       (+ (* b c) t_1)
       (if (<= t 3.2e-189)
         (+ t_1 t_2)
         (if (<= t 3.6e-157)
           (+ (* b c) (* -4.0 (* t a)))
           (if (<= t 2.9e-52) (- t_2 (* j (* 27.0 k))) t_3)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = k * (j * -27.0);
	double t_2 = -4.0 * (x * i);
	double t_3 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	double tmp;
	if (t <= -1e+88) {
		tmp = t_3;
	} else if (t <= -2.65e-237) {
		tmp = (b * c) + t_1;
	} else if (t <= 3.2e-189) {
		tmp = t_1 + t_2;
	} else if (t <= 3.6e-157) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else if (t <= 2.9e-52) {
		tmp = t_2 - (j * (27.0 * k));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = k * (j * (-27.0d0))
    t_2 = (-4.0d0) * (x * i)
    t_3 = t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0))
    if (t <= (-1d+88)) then
        tmp = t_3
    else if (t <= (-2.65d-237)) then
        tmp = (b * c) + t_1
    else if (t <= 3.2d-189) then
        tmp = t_1 + t_2
    else if (t <= 3.6d-157) then
        tmp = (b * c) + ((-4.0d0) * (t * a))
    else if (t <= 2.9d-52) then
        tmp = t_2 - (j * (27.0d0 * k))
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = k * (j * -27.0);
	double t_2 = -4.0 * (x * i);
	double t_3 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	double tmp;
	if (t <= -1e+88) {
		tmp = t_3;
	} else if (t <= -2.65e-237) {
		tmp = (b * c) + t_1;
	} else if (t <= 3.2e-189) {
		tmp = t_1 + t_2;
	} else if (t <= 3.6e-157) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else if (t <= 2.9e-52) {
		tmp = t_2 - (j * (27.0 * k));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = k * (j * -27.0)
	t_2 = -4.0 * (x * i)
	t_3 = t * ((18.0 * (x * (y * z))) - (a * 4.0))
	tmp = 0
	if t <= -1e+88:
		tmp = t_3
	elif t <= -2.65e-237:
		tmp = (b * c) + t_1
	elif t <= 3.2e-189:
		tmp = t_1 + t_2
	elif t <= 3.6e-157:
		tmp = (b * c) + (-4.0 * (t * a))
	elif t <= 2.9e-52:
		tmp = t_2 - (j * (27.0 * k))
	else:
		tmp = t_3
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(k * Float64(j * -27.0))
	t_2 = Float64(-4.0 * Float64(x * i))
	t_3 = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)))
	tmp = 0.0
	if (t <= -1e+88)
		tmp = t_3;
	elseif (t <= -2.65e-237)
		tmp = Float64(Float64(b * c) + t_1);
	elseif (t <= 3.2e-189)
		tmp = Float64(t_1 + t_2);
	elseif (t <= 3.6e-157)
		tmp = Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a)));
	elseif (t <= 2.9e-52)
		tmp = Float64(t_2 - Float64(j * Float64(27.0 * k)));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = k * (j * -27.0);
	t_2 = -4.0 * (x * i);
	t_3 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	tmp = 0.0;
	if (t <= -1e+88)
		tmp = t_3;
	elseif (t <= -2.65e-237)
		tmp = (b * c) + t_1;
	elseif (t <= 3.2e-189)
		tmp = t_1 + t_2;
	elseif (t <= 3.6e-157)
		tmp = (b * c) + (-4.0 * (t * a));
	elseif (t <= 2.9e-52)
		tmp = t_2 - (j * (27.0 * k));
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1e+88], t$95$3, If[LessEqual[t, -2.65e-237], N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[t, 3.2e-189], N[(t$95$1 + t$95$2), $MachinePrecision], If[LessEqual[t, 3.6e-157], N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.9e-52], N[(t$95$2 - N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -9.99999999999999959e87 or 2.9000000000000002e-52 < t

   1. Initial program 85.5%

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

   3. Taylor expanded in t around inf 71.2%

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

   if -9.99999999999999959e87 < t < -2.64999999999999977e-237

   1. Initial program 90.2%

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

   3. Simplified 84.7%

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

   5. Taylor expanded in b around inf 61.8%

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

   if -2.64999999999999977e-237 < t < 3.2000000000000001e-189

   1. Initial program 80.5%

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

   3. Simplified 87.7%

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

   5. Taylor expanded in i around inf 72.8%

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

   if 3.2000000000000001e-189 < t < 3.6e-157

   1. Initial program 84.8%

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

      1. distribute-rgt-out-- 84.8%

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

      2. *-commutative 84.8%

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

      3. associate-*l* 84.8%

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

   4. Applied egg-rr 84.8%

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

   5. Taylor expanded in x around 0 83.9%

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

   6. Taylor expanded in j around 0 83.9%

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

   if 3.6e-157 < t < 2.9000000000000002e-52

   1. Initial program 86.9%

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

      1. distribute-rgt-out-- 86.9%

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

      2. *-commutative 86.9%

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

      3. associate-*l* 86.9%

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

   4. Applied egg-rr 86.9%

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

   5. Taylor expanded in i around inf 60.9%

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

   6. Taylor expanded in j around 0 65.1%

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

      1. *-commutative 65.1%

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

      2. associate-*l* 65.1%

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

      3. *-commutative 65.1%

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

      4. *-commutative 65.1%

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

   8. Simplified 65.1%

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

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{+88}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq -2.65 \cdot 10^{-237}:\\ \;\;\;\;b \cdot c + k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-189}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right) + -4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-157}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-52}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right) - j \cdot \left(27 \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 52.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+117}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right) - j \cdot \left(27 \cdot k\right)\\ \mathbf{elif}\;t\_1 \leq 10^{-34}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;t\_1 \leq 10^{+49}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(z \cdot \left(x \cdot t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + k \cdot \left(j \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)))
   (if (<= t_1 -2e+117)
     (- (* -4.0 (* x i)) (* j (* 27.0 k)))
     (if (<= t_1 1e-34)
       (+ (* b c) (* -4.0 (* t a)))
       (if (<= t_1 1e+49)
         (* 18.0 (* y (* z (* x t))))
         (+ (* b c) (* k (* j -27.0))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (t_1 <= -2e+117) {
		tmp = (-4.0 * (x * i)) - (j * (27.0 * k));
	} else if (t_1 <= 1e-34) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else if (t_1 <= 1e+49) {
		tmp = 18.0 * (y * (z * (x * t)));
	} else {
		tmp = (b * c) + (k * (j * -27.0));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (j * 27.0d0) * k
    if (t_1 <= (-2d+117)) then
        tmp = ((-4.0d0) * (x * i)) - (j * (27.0d0 * k))
    else if (t_1 <= 1d-34) then
        tmp = (b * c) + ((-4.0d0) * (t * a))
    else if (t_1 <= 1d+49) then
        tmp = 18.0d0 * (y * (z * (x * t)))
    else
        tmp = (b * c) + (k * (j * (-27.0d0)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (t_1 <= -2e+117) {
		tmp = (-4.0 * (x * i)) - (j * (27.0 * k));
	} else if (t_1 <= 1e-34) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else if (t_1 <= 1e+49) {
		tmp = 18.0 * (y * (z * (x * t)));
	} else {
		tmp = (b * c) + (k * (j * -27.0));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	tmp = 0
	if t_1 <= -2e+117:
		tmp = (-4.0 * (x * i)) - (j * (27.0 * k))
	elif t_1 <= 1e-34:
		tmp = (b * c) + (-4.0 * (t * a))
	elif t_1 <= 1e+49:
		tmp = 18.0 * (y * (z * (x * t)))
	else:
		tmp = (b * c) + (k * (j * -27.0))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_1 <= -2e+117)
		tmp = Float64(Float64(-4.0 * Float64(x * i)) - Float64(j * Float64(27.0 * k)));
	elseif (t_1 <= 1e-34)
		tmp = Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a)));
	elseif (t_1 <= 1e+49)
		tmp = Float64(18.0 * Float64(y * Float64(z * Float64(x * t))));
	else
		tmp = Float64(Float64(b * c) + Float64(k * Float64(j * -27.0)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * 27.0) * k;
	tmp = 0.0;
	if (t_1 <= -2e+117)
		tmp = (-4.0 * (x * i)) - (j * (27.0 * k));
	elseif (t_1 <= 1e-34)
		tmp = (b * c) + (-4.0 * (t * a));
	elseif (t_1 <= 1e+49)
		tmp = 18.0 * (y * (z * (x * t)));
	else
		tmp = (b * c) + (k * (j * -27.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+117], N[(N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision] - N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e-34], N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+49], N[(18.0 * N[(y * N[(z * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] + N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -2.0000000000000001e117

   1. Initial program 74.0%

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

      1. distribute-rgt-out-- 78.8%

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

      2. *-commutative 78.8%

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

      3. associate-*l* 78.8%

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

   4. Applied egg-rr 78.8%

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

   5. Taylor expanded in i around inf 69.9%

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

   6. Taylor expanded in j around 0 72.1%

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

      1. *-commutative 72.1%

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

      2. associate-*l* 72.2%

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

      3. *-commutative 72.2%

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

      4. *-commutative 72.2%

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

   8. Simplified 72.2%

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

   if -2.0000000000000001e117 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 9.99999999999999928e-35

   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. Step-by-step derivation

      1. distribute-rgt-out-- 89.9%

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

      2. *-commutative 89.9%

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

      3. associate-*l* 89.9%

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

   4. Applied egg-rr 89.9%

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

   5. Taylor expanded in x around 0 60.1%

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

   6. Taylor expanded in j around 0 56.0%

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

   if 9.99999999999999928e-35 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 9.99999999999999946e48

   1. Initial program 94.0%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 54.1%

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

      1. *-commutative 54.1%

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

   7. Applied egg-rr 54.1%

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

      1. associate-*r* 54.1%

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

   9. Simplified 54.1%

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

   10. Taylor expanded in t around 0 54.1%

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

       1. associate-*r* 54.1%

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

       2. *-commutative 54.1%

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

       3. associate-*r* 54.1%

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

       4. associate-*r* 54.1%

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

       5. associate-*l* 48.6%

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

       6. *-commutative 48.6%

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

       7. associate-*r* 48.6%

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

       8. *-commutative 48.6%

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

       9. *-commutative 48.6%

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

   12. Simplified 48.6%

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

   if 9.99999999999999946e48 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 83.6%

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

   3. Simplified 88.3%

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

   5. Taylor expanded in b around inf 68.5%

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

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \leq -2 \cdot 10^{+117}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right) - j \cdot \left(27 \cdot k\right)\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 10^{-34}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 10^{+49}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(z \cdot \left(x \cdot t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + k \cdot \left(j \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 52.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := k \cdot \left(j \cdot -27\right)\\ t_2 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+117}:\\ \;\;\;\;t\_1 + -4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t\_2 \leq 10^{-34}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;t\_2 \leq 10^{+49}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(z \cdot \left(x \cdot t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* k (* j -27.0))) (t_2 (* (* j 27.0) k)))
   (if (<= t_2 -2e+117)
     (+ t_1 (* -4.0 (* x i)))
     (if (<= t_2 1e-34)
       (+ (* b c) (* -4.0 (* t a)))
       (if (<= t_2 1e+49) (* 18.0 (* y (* z (* x t)))) (+ (* b c) t_1))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = k * (j * -27.0);
	double t_2 = (j * 27.0) * k;
	double tmp;
	if (t_2 <= -2e+117) {
		tmp = t_1 + (-4.0 * (x * i));
	} else if (t_2 <= 1e-34) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else if (t_2 <= 1e+49) {
		tmp = 18.0 * (y * (z * (x * t)));
	} else {
		tmp = (b * c) + t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = k * (j * (-27.0d0))
    t_2 = (j * 27.0d0) * k
    if (t_2 <= (-2d+117)) then
        tmp = t_1 + ((-4.0d0) * (x * i))
    else if (t_2 <= 1d-34) then
        tmp = (b * c) + ((-4.0d0) * (t * a))
    else if (t_2 <= 1d+49) then
        tmp = 18.0d0 * (y * (z * (x * t)))
    else
        tmp = (b * c) + t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = k * (j * -27.0);
	double t_2 = (j * 27.0) * k;
	double tmp;
	if (t_2 <= -2e+117) {
		tmp = t_1 + (-4.0 * (x * i));
	} else if (t_2 <= 1e-34) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else if (t_2 <= 1e+49) {
		tmp = 18.0 * (y * (z * (x * t)));
	} else {
		tmp = (b * c) + t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = k * (j * -27.0)
	t_2 = (j * 27.0) * k
	tmp = 0
	if t_2 <= -2e+117:
		tmp = t_1 + (-4.0 * (x * i))
	elif t_2 <= 1e-34:
		tmp = (b * c) + (-4.0 * (t * a))
	elif t_2 <= 1e+49:
		tmp = 18.0 * (y * (z * (x * t)))
	else:
		tmp = (b * c) + t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(k * Float64(j * -27.0))
	t_2 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_2 <= -2e+117)
		tmp = Float64(t_1 + Float64(-4.0 * Float64(x * i)));
	elseif (t_2 <= 1e-34)
		tmp = Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a)));
	elseif (t_2 <= 1e+49)
		tmp = Float64(18.0 * Float64(y * Float64(z * Float64(x * t))));
	else
		tmp = Float64(Float64(b * c) + t_1);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = k * (j * -27.0);
	t_2 = (j * 27.0) * k;
	tmp = 0.0;
	if (t_2 <= -2e+117)
		tmp = t_1 + (-4.0 * (x * i));
	elseif (t_2 <= 1e-34)
		tmp = (b * c) + (-4.0 * (t * a));
	elseif (t_2 <= 1e+49)
		tmp = 18.0 * (y * (z * (x * t)));
	else
		tmp = (b * c) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+117], N[(t$95$1 + N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e-34], N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+49], N[(18.0 * N[(y * N[(z * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -2.0000000000000001e117

   1. Initial program 74.0%

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

   3. Simplified 85.7%

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

   5. Taylor expanded in i around inf 69.9%

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

   if -2.0000000000000001e117 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 9.99999999999999928e-35

   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. Step-by-step derivation

      1. distribute-rgt-out-- 89.9%

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

      2. *-commutative 89.9%

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

      3. associate-*l* 89.9%

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

   4. Applied egg-rr 89.9%

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

   5. Taylor expanded in x around 0 60.1%

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

   6. Taylor expanded in j around 0 56.0%

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

   if 9.99999999999999928e-35 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 9.99999999999999946e48

   1. Initial program 94.0%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 54.1%

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

      1. *-commutative 54.1%

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

   7. Applied egg-rr 54.1%

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

      1. associate-*r* 54.1%

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

   9. Simplified 54.1%

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

   10. Taylor expanded in t around 0 54.1%

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

       1. associate-*r* 54.1%

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

       2. *-commutative 54.1%

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

       3. associate-*r* 54.1%

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

       4. associate-*r* 54.1%

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

       5. associate-*l* 48.6%

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

       6. *-commutative 48.6%

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

       7. associate-*r* 48.6%

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

       8. *-commutative 48.6%

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

       9. *-commutative 48.6%

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

   12. Simplified 48.6%

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

   if 9.99999999999999946e48 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 83.6%

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

   3. Simplified 88.3%

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

   5. Taylor expanded in b around inf 68.5%

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

4. Final simplification 59.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \leq -2 \cdot 10^{+117}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right) + -4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 10^{-34}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 10^{+49}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(z \cdot \left(x \cdot t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + k \cdot \left(j \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 51.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+117}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t\_1 \leq 10^{-34}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;t\_1 \leq 10^{+49}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(z \cdot \left(x \cdot t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + k \cdot \left(j \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)))
   (if (<= t_1 -2e+117)
     (* j (* k -27.0))
     (if (<= t_1 1e-34)
       (+ (* b c) (* -4.0 (* t a)))
       (if (<= t_1 1e+49)
         (* 18.0 (* y (* z (* x t))))
         (+ (* b c) (* k (* j -27.0))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (t_1 <= -2e+117) {
		tmp = j * (k * -27.0);
	} else if (t_1 <= 1e-34) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else if (t_1 <= 1e+49) {
		tmp = 18.0 * (y * (z * (x * t)));
	} else {
		tmp = (b * c) + (k * (j * -27.0));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (j * 27.0d0) * k
    if (t_1 <= (-2d+117)) then
        tmp = j * (k * (-27.0d0))
    else if (t_1 <= 1d-34) then
        tmp = (b * c) + ((-4.0d0) * (t * a))
    else if (t_1 <= 1d+49) then
        tmp = 18.0d0 * (y * (z * (x * t)))
    else
        tmp = (b * c) + (k * (j * (-27.0d0)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (t_1 <= -2e+117) {
		tmp = j * (k * -27.0);
	} else if (t_1 <= 1e-34) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else if (t_1 <= 1e+49) {
		tmp = 18.0 * (y * (z * (x * t)));
	} else {
		tmp = (b * c) + (k * (j * -27.0));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	tmp = 0
	if t_1 <= -2e+117:
		tmp = j * (k * -27.0)
	elif t_1 <= 1e-34:
		tmp = (b * c) + (-4.0 * (t * a))
	elif t_1 <= 1e+49:
		tmp = 18.0 * (y * (z * (x * t)))
	else:
		tmp = (b * c) + (k * (j * -27.0))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_1 <= -2e+117)
		tmp = Float64(j * Float64(k * -27.0));
	elseif (t_1 <= 1e-34)
		tmp = Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a)));
	elseif (t_1 <= 1e+49)
		tmp = Float64(18.0 * Float64(y * Float64(z * Float64(x * t))));
	else
		tmp = Float64(Float64(b * c) + Float64(k * Float64(j * -27.0)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * 27.0) * k;
	tmp = 0.0;
	if (t_1 <= -2e+117)
		tmp = j * (k * -27.0);
	elseif (t_1 <= 1e-34)
		tmp = (b * c) + (-4.0 * (t * a));
	elseif (t_1 <= 1e+49)
		tmp = 18.0 * (y * (z * (x * t)));
	else
		tmp = (b * c) + (k * (j * -27.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+117], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e-34], N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+49], N[(18.0 * N[(y * N[(z * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] + N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -2.0000000000000001e117

   1. Initial program 74.0%

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

      1. distribute-rgt-out-- 78.8%

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

      2. *-commutative 78.8%

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

      3. associate-*l* 78.8%

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

   4. Applied egg-rr 78.8%

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

   5. Taylor expanded in a around inf 63.8%

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

   6. Taylor expanded in a around 0 63.2%

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

      1. metadata-eval 63.2%

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

      2. distribute-lft-neg-in 63.2%

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

      3. associate-*r* 61.0%

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

      4. *-commutative 61.0%

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

      5. associate-*r* 63.3%

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

      6. distribute-rgt-neg-in 63.3%

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

      7. distribute-lft-neg-in 63.3%

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

      8. metadata-eval 63.3%

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

   8. Simplified 63.3%

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

   if -2.0000000000000001e117 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 9.99999999999999928e-35

   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. Step-by-step derivation

      1. distribute-rgt-out-- 89.9%

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

      2. *-commutative 89.9%

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

      3. associate-*l* 89.9%

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

   4. Applied egg-rr 89.9%

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

   5. Taylor expanded in x around 0 60.1%

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

   6. Taylor expanded in j around 0 56.0%

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

   if 9.99999999999999928e-35 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 9.99999999999999946e48

   1. Initial program 94.0%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 54.1%

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

      1. *-commutative 54.1%

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

   7. Applied egg-rr 54.1%

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

      1. associate-*r* 54.1%

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

   9. Simplified 54.1%

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

   10. Taylor expanded in t around 0 54.1%

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

       1. associate-*r* 54.1%

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

       2. *-commutative 54.1%

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

       3. associate-*r* 54.1%

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

       4. associate-*r* 54.1%

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

       5. associate-*l* 48.6%

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

       6. *-commutative 48.6%

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

       7. associate-*r* 48.6%

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

       8. *-commutative 48.6%

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

       9. *-commutative 48.6%

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

   12. Simplified 48.6%

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

   if 9.99999999999999946e48 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 83.6%

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

   3. Simplified 88.3%

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

   5. Taylor expanded in b around inf 68.5%

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

4. Final simplification 58.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \leq -2 \cdot 10^{+117}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 10^{-34}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 10^{+49}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(z \cdot \left(x \cdot t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + k \cdot \left(j \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 72.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{if}\;x \leq -1.6 \cdot 10^{+176}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -1.08 \cdot 10^{+142}:\\ \;\;\;\;b \cdot c + t \cdot \left(a \cdot -4 + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;x \leq -9.2 \cdot 10^{+75} \lor \neg \left(x \leq 1.05 \cdot 10^{+47}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(t \cdot a\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* x (- (* 18.0 (* t (* y z))) (* 4.0 i)))))
   (if (<= x -1.6e+176)
     t_1
     (if (<= x -1.08e+142)
       (+ (* b c) (* t (+ (* a -4.0) (* 18.0 (* x (* y z))))))
       (if (or (<= x -9.2e+75) (not (<= x 1.05e+47)))
         t_1
         (- (* b c) (+ (* 4.0 (* t a)) (* 27.0 (* j k)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	double tmp;
	if (x <= -1.6e+176) {
		tmp = t_1;
	} else if (x <= -1.08e+142) {
		tmp = (b * c) + (t * ((a * -4.0) + (18.0 * (x * (y * z)))));
	} else if ((x <= -9.2e+75) || !(x <= 1.05e+47)) {
		tmp = t_1;
	} else {
		tmp = (b * c) - ((4.0 * (t * a)) + (27.0 * (j * k)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i))
    if (x <= (-1.6d+176)) then
        tmp = t_1
    else if (x <= (-1.08d+142)) then
        tmp = (b * c) + (t * ((a * (-4.0d0)) + (18.0d0 * (x * (y * z)))))
    else if ((x <= (-9.2d+75)) .or. (.not. (x <= 1.05d+47))) then
        tmp = t_1
    else
        tmp = (b * c) - ((4.0d0 * (t * a)) + (27.0d0 * (j * k)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	double tmp;
	if (x <= -1.6e+176) {
		tmp = t_1;
	} else if (x <= -1.08e+142) {
		tmp = (b * c) + (t * ((a * -4.0) + (18.0 * (x * (y * z)))));
	} else if ((x <= -9.2e+75) || !(x <= 1.05e+47)) {
		tmp = t_1;
	} else {
		tmp = (b * c) - ((4.0 * (t * a)) + (27.0 * (j * k)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = x * ((18.0 * (t * (y * z))) - (4.0 * i))
	tmp = 0
	if x <= -1.6e+176:
		tmp = t_1
	elif x <= -1.08e+142:
		tmp = (b * c) + (t * ((a * -4.0) + (18.0 * (x * (y * z)))))
	elif (x <= -9.2e+75) or not (x <= 1.05e+47):
		tmp = t_1
	else:
		tmp = (b * c) - ((4.0 * (t * a)) + (27.0 * (j * k)))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)))
	tmp = 0.0
	if (x <= -1.6e+176)
		tmp = t_1;
	elseif (x <= -1.08e+142)
		tmp = Float64(Float64(b * c) + Float64(t * Float64(Float64(a * -4.0) + Float64(18.0 * Float64(x * Float64(y * z))))));
	elseif ((x <= -9.2e+75) || !(x <= 1.05e+47))
		tmp = t_1;
	else
		tmp = Float64(Float64(b * c) - Float64(Float64(4.0 * Float64(t * a)) + Float64(27.0 * Float64(j * k))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	tmp = 0.0;
	if (x <= -1.6e+176)
		tmp = t_1;
	elseif (x <= -1.08e+142)
		tmp = (b * c) + (t * ((a * -4.0) + (18.0 * (x * (y * z)))));
	elseif ((x <= -9.2e+75) || ~((x <= 1.05e+47)))
		tmp = t_1;
	else
		tmp = (b * c) - ((4.0 * (t * a)) + (27.0 * (j * k)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.6e+176], t$95$1, If[LessEqual[x, -1.08e+142], N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(a * -4.0), $MachinePrecision] + N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -9.2e+75], N[Not[LessEqual[x, 1.05e+47]], $MachinePrecision]], t$95$1, N[(N[(b * c), $MachinePrecision] - N[(N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.5999999999999999e176 or -1.08e142 < x < -9.1999999999999994e75 or 1.05e47 < x

   1. Initial program 76.4%

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

   3. Taylor expanded in x around inf 70.3%

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

   if -1.5999999999999999e176 < x < -1.08e142

   1. Initial program 60.4%

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

   3. Simplified 90.0%

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

   5. Taylor expanded in i around 0 90.0%

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

   6. Taylor expanded in k around 0 90.4%

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

   if -9.1999999999999994e75 < x < 1.05e47

   1. Initial program 93.6%

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

   3. Taylor expanded in x around 0 78.1%

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

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{+176}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;x \leq -1.08 \cdot 10^{+142}:\\ \;\;\;\;b \cdot c + t \cdot \left(a \cdot -4 + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;x \leq -9.2 \cdot 10^{+75} \lor \neg \left(x \leq 1.05 \cdot 10^{+47}\right):\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(t \cdot a\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 81.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{-37} \lor \neg \left(x \leq 9.5 \cdot 10^{-25}\right):\\ \;\;\;\;\left(\left(b \cdot c + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(a \cdot -4 + 18 \cdot \left(z \cdot \left(x \cdot y\right)\right)\right)\right) + k \cdot \left(j \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= x -5e-37) (not (<= x 9.5e-25)))
   (-
    (- (+ (* b c) (* 18.0 (* t (* x (* y z))))) (* (* x 4.0) i))
    (* (* j 27.0) k))
   (+
    (+ (* b c) (* t (+ (* a -4.0) (* 18.0 (* z (* x y))))))
    (* k (* j -27.0)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((x <= -5e-37) || !(x <= 9.5e-25)) {
		tmp = (((b * c) + (18.0 * (t * (x * (y * z))))) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	} else {
		tmp = ((b * c) + (t * ((a * -4.0) + (18.0 * (z * (x * y)))))) + (k * (j * -27.0));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((x <= (-5d-37)) .or. (.not. (x <= 9.5d-25))) then
        tmp = (((b * c) + (18.0d0 * (t * (x * (y * z))))) - ((x * 4.0d0) * i)) - ((j * 27.0d0) * k)
    else
        tmp = ((b * c) + (t * ((a * (-4.0d0)) + (18.0d0 * (z * (x * y)))))) + (k * (j * (-27.0d0)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((x <= -5e-37) || !(x <= 9.5e-25)) {
		tmp = (((b * c) + (18.0 * (t * (x * (y * z))))) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	} else {
		tmp = ((b * c) + (t * ((a * -4.0) + (18.0 * (z * (x * y)))))) + (k * (j * -27.0));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (x <= -5e-37) or not (x <= 9.5e-25):
		tmp = (((b * c) + (18.0 * (t * (x * (y * z))))) - ((x * 4.0) * i)) - ((j * 27.0) * k)
	else:
		tmp = ((b * c) + (t * ((a * -4.0) + (18.0 * (z * (x * y)))))) + (k * (j * -27.0))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((x <= -5e-37) || !(x <= 9.5e-25))
		tmp = Float64(Float64(Float64(Float64(b * c) + Float64(18.0 * Float64(t * Float64(x * Float64(y * z))))) - Float64(Float64(x * 4.0) * i)) - Float64(Float64(j * 27.0) * k));
	else
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(a * -4.0) + Float64(18.0 * Float64(z * Float64(x * y)))))) + Float64(k * Float64(j * -27.0)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((x <= -5e-37) || ~((x <= 9.5e-25)))
		tmp = (((b * c) + (18.0 * (t * (x * (y * z))))) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	else
		tmp = ((b * c) + (t * ((a * -4.0) + (18.0 * (z * (x * y)))))) + (k * (j * -27.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[x, -5e-37], N[Not[LessEqual[x, 9.5e-25]], $MachinePrecision]], N[(N[(N[(N[(b * c), $MachinePrecision] + N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(a * -4.0), $MachinePrecision] + N[(18.0 * N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.9999999999999997e-37 or 9.50000000000000065e-25 < x

   1. Initial program 78.6%

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

   3. Taylor expanded in x around inf 80.4%

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

   if -4.9999999999999997e-37 < x < 9.50000000000000065e-25

   1. Initial program 94.9%

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

   3. Simplified 90.0%

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

   5. Taylor expanded in i around 0 86.0%

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

      1. *-commutative 86.0%

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

      2. +-commutative 86.0%

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

      3. associate-*r* 92.6%

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

      4. *-commutative 92.6%

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

   7. Applied egg-rr 92.6%

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

4. Final simplification 86.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{-37} \lor \neg \left(x \leq 9.5 \cdot 10^{-25}\right):\\ \;\;\;\;\left(\left(b \cdot c + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(a \cdot -4 + 18 \cdot \left(z \cdot \left(x \cdot y\right)\right)\right)\right) + k \cdot \left(j \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 87.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{+62}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(a \cdot -4 + 18 \cdot \left(z \cdot \left(x \cdot y\right)\right)\right)\right) + k \cdot \left(j \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - \left(4 \cdot \left(t \cdot a\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= t -1.3e+62)
   (+
    (+ (* b c) (* t (+ (* a -4.0) (* 18.0 (* z (* x y))))))
    (* k (* j -27.0)))
   (-
    (+ (* b c) (* x (- (* 18.0 (* t (* y z))) (* 4.0 i))))
    (+ (* 4.0 (* t a)) (* 27.0 (* j k))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (t <= -1.3e+62) {
		tmp = ((b * c) + (t * ((a * -4.0) + (18.0 * (z * (x * y)))))) + (k * (j * -27.0));
	} else {
		tmp = ((b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)))) - ((4.0 * (t * a)) + (27.0 * (j * k)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (t <= (-1.3d+62)) then
        tmp = ((b * c) + (t * ((a * (-4.0d0)) + (18.0d0 * (z * (x * y)))))) + (k * (j * (-27.0d0)))
    else
        tmp = ((b * c) + (x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i)))) - ((4.0d0 * (t * a)) + (27.0d0 * (j * k)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (t <= -1.3e+62) {
		tmp = ((b * c) + (t * ((a * -4.0) + (18.0 * (z * (x * y)))))) + (k * (j * -27.0));
	} else {
		tmp = ((b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)))) - ((4.0 * (t * a)) + (27.0 * (j * k)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if t <= -1.3e+62:
		tmp = ((b * c) + (t * ((a * -4.0) + (18.0 * (z * (x * y)))))) + (k * (j * -27.0))
	else:
		tmp = ((b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)))) - ((4.0 * (t * a)) + (27.0 * (j * k)))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (t <= -1.3e+62)
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(a * -4.0) + Float64(18.0 * Float64(z * Float64(x * y)))))) + Float64(k * Float64(j * -27.0)));
	else
		tmp = Float64(Float64(Float64(b * c) + Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)))) - Float64(Float64(4.0 * Float64(t * a)) + Float64(27.0 * Float64(j * k))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (t <= -1.3e+62)
		tmp = ((b * c) + (t * ((a * -4.0) + (18.0 * (z * (x * y)))))) + (k * (j * -27.0));
	else
		tmp = ((b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)))) - ((4.0 * (t * a)) + (27.0 * (j * k)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[t, -1.3e+62], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(a * -4.0), $MachinePrecision] + N[(18.0 * N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] + N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.29999999999999992e62

   1. Initial program 83.5%

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

   3. Simplified 92.5%

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

   5. Taylor expanded in i around 0 95.5%

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

      1. *-commutative 95.5%

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

      2. +-commutative 95.5%

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

      3. associate-*r* 93.9%

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

      4. *-commutative 93.9%

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

   7. Applied egg-rr 93.9%

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

   if -1.29999999999999992e62 < t

   1. Initial program 86.8%

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

   3. Taylor expanded in x around 0 89.3%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{+62}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(a \cdot -4 + 18 \cdot \left(z \cdot \left(x \cdot y\right)\right)\right)\right) + k \cdot \left(j \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - \left(4 \cdot \left(t \cdot a\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 75.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \leq -1 \cdot 10^{+300}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right) - j \cdot \left(27 \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(a \cdot -4 + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) + k \cdot \left(j \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= (* (* j 27.0) k) -1e+300)
   (- (* -4.0 (* x i)) (* j (* 27.0 k)))
   (+
    (+ (* b c) (* t (+ (* a -4.0) (* 18.0 (* x (* y z))))))
    (* k (* j -27.0)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (((j * 27.0) * k) <= -1e+300) {
		tmp = (-4.0 * (x * i)) - (j * (27.0 * k));
	} else {
		tmp = ((b * c) + (t * ((a * -4.0) + (18.0 * (x * (y * z)))))) + (k * (j * -27.0));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (((j * 27.0d0) * k) <= (-1d+300)) then
        tmp = ((-4.0d0) * (x * i)) - (j * (27.0d0 * k))
    else
        tmp = ((b * c) + (t * ((a * (-4.0d0)) + (18.0d0 * (x * (y * z)))))) + (k * (j * (-27.0d0)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (((j * 27.0) * k) <= -1e+300) {
		tmp = (-4.0 * (x * i)) - (j * (27.0 * k));
	} else {
		tmp = ((b * c) + (t * ((a * -4.0) + (18.0 * (x * (y * z)))))) + (k * (j * -27.0));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if ((j * 27.0) * k) <= -1e+300:
		tmp = (-4.0 * (x * i)) - (j * (27.0 * k))
	else:
		tmp = ((b * c) + (t * ((a * -4.0) + (18.0 * (x * (y * z)))))) + (k * (j * -27.0))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (Float64(Float64(j * 27.0) * k) <= -1e+300)
		tmp = Float64(Float64(-4.0 * Float64(x * i)) - Float64(j * Float64(27.0 * k)));
	else
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(a * -4.0) + Float64(18.0 * Float64(x * Float64(y * z)))))) + Float64(k * Float64(j * -27.0)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (((j * 27.0) * k) <= -1e+300)
		tmp = (-4.0 * (x * i)) - (j * (27.0 * k));
	else
		tmp = ((b * c) + (t * ((a * -4.0) + (18.0 * (x * (y * z)))))) + (k * (j * -27.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision], -1e+300], N[(N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision] - N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(a * -4.0), $MachinePrecision] + N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -1.0000000000000001e300

   1. Initial program 50.3%

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

      1. distribute-rgt-out-- 55.8%

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

      2. *-commutative 55.8%

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

      3. associate-*l* 55.8%

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

   4. Applied egg-rr 55.8%

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

   5. Taylor expanded in i around inf 83.6%

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

   6. Taylor expanded in j around 0 88.9%

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

      1. *-commutative 88.9%

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

      2. associate-*l* 88.8%

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

      3. *-commutative 88.8%

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

      4. *-commutative 88.8%

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

   8. Simplified 88.8%

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

   if -1.0000000000000001e300 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 88.8%

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

   3. Simplified 90.9%

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

   5. Taylor expanded in i around 0 78.9%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \leq -1 \cdot 10^{+300}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right) - j \cdot \left(27 \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(a \cdot -4 + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) + k \cdot \left(j \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 45.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c + -4 \cdot \left(t \cdot a\right)\\ t_2 := -27 \cdot \left(j \cdot k\right)\\ \mathbf{if}\;j \leq -5.2 \cdot 10^{+124}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -2 \cdot 10^{+43}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -5 \cdot 10^{-27}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;j \leq 0.00035:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (+ (* b c) (* -4.0 (* t a)))) (t_2 (* -27.0 (* j k))))
   (if (<= j -5.2e+124)
     t_2
     (if (<= j -2e+43)
       t_1
       (if (<= j -5e-27)
         (* 18.0 (* t (* x (* y z))))
         (if (<= j 0.00035) t_1 t_2))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) + (-4.0 * (t * a));
	double t_2 = -27.0 * (j * k);
	double tmp;
	if (j <= -5.2e+124) {
		tmp = t_2;
	} else if (j <= -2e+43) {
		tmp = t_1;
	} else if (j <= -5e-27) {
		tmp = 18.0 * (t * (x * (y * z)));
	} else if (j <= 0.00035) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (b * c) + ((-4.0d0) * (t * a))
    t_2 = (-27.0d0) * (j * k)
    if (j <= (-5.2d+124)) then
        tmp = t_2
    else if (j <= (-2d+43)) then
        tmp = t_1
    else if (j <= (-5d-27)) then
        tmp = 18.0d0 * (t * (x * (y * z)))
    else if (j <= 0.00035d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) + (-4.0 * (t * a));
	double t_2 = -27.0 * (j * k);
	double tmp;
	if (j <= -5.2e+124) {
		tmp = t_2;
	} else if (j <= -2e+43) {
		tmp = t_1;
	} else if (j <= -5e-27) {
		tmp = 18.0 * (t * (x * (y * z)));
	} else if (j <= 0.00035) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) + (-4.0 * (t * a))
	t_2 = -27.0 * (j * k)
	tmp = 0
	if j <= -5.2e+124:
		tmp = t_2
	elif j <= -2e+43:
		tmp = t_1
	elif j <= -5e-27:
		tmp = 18.0 * (t * (x * (y * z)))
	elif j <= 0.00035:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a)))
	t_2 = Float64(-27.0 * Float64(j * k))
	tmp = 0.0
	if (j <= -5.2e+124)
		tmp = t_2;
	elseif (j <= -2e+43)
		tmp = t_1;
	elseif (j <= -5e-27)
		tmp = Float64(18.0 * Float64(t * Float64(x * Float64(y * z))));
	elseif (j <= 0.00035)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) + (-4.0 * (t * a));
	t_2 = -27.0 * (j * k);
	tmp = 0.0;
	if (j <= -5.2e+124)
		tmp = t_2;
	elseif (j <= -2e+43)
		tmp = t_1;
	elseif (j <= -5e-27)
		tmp = 18.0 * (t * (x * (y * z)));
	elseif (j <= 0.00035)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -5.2e+124], t$95$2, If[LessEqual[j, -2e+43], t$95$1, If[LessEqual[j, -5e-27], N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 0.00035], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if j < -5.2000000000000001e124 or 3.49999999999999996e-4 < j

   1. Initial program 83.2%

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

   3. Simplified 87.3%

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

   5. Taylor expanded in k around inf 43.8%

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

   if -5.2000000000000001e124 < j < -2.00000000000000003e43 or -5.0000000000000002e-27 < j < 3.49999999999999996e-4

   1. Initial program 88.0%

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

      1. distribute-rgt-out-- 90.7%

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

      2. *-commutative 90.7%

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

      3. associate-*l* 90.7%

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

   4. Applied egg-rr 90.7%

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

   5. Taylor expanded in x around 0 59.4%

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

   6. Taylor expanded in j around 0 51.5%

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

   if -2.00000000000000003e43 < j < -5.0000000000000002e-27

   1. Initial program 85.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 50.9%

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

4. Final simplification 48.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -5.2 \cdot 10^{+124}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;j \leq -2 \cdot 10^{+43}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;j \leq -5 \cdot 10^{-27}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;j \leq 0.00035:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 76.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := k \cdot \left(j \cdot -27\right)\\ \mathbf{if}\;i \leq -3.5 \cdot 10^{+199}:\\ \;\;\;\;t\_1 + -4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(a \cdot -4 + 18 \cdot \left(z \cdot \left(x \cdot y\right)\right)\right)\right) + t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* k (* j -27.0))))
   (if (<= i -3.5e+199)
     (+ t_1 (* -4.0 (* x i)))
     (+ (+ (* b c) (* t (+ (* a -4.0) (* 18.0 (* z (* x y)))))) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = k * (j * -27.0);
	double tmp;
	if (i <= -3.5e+199) {
		tmp = t_1 + (-4.0 * (x * i));
	} else {
		tmp = ((b * c) + (t * ((a * -4.0) + (18.0 * (z * (x * y)))))) + t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = k * (j * (-27.0d0))
    if (i <= (-3.5d+199)) then
        tmp = t_1 + ((-4.0d0) * (x * i))
    else
        tmp = ((b * c) + (t * ((a * (-4.0d0)) + (18.0d0 * (z * (x * y)))))) + t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = k * (j * -27.0);
	double tmp;
	if (i <= -3.5e+199) {
		tmp = t_1 + (-4.0 * (x * i));
	} else {
		tmp = ((b * c) + (t * ((a * -4.0) + (18.0 * (z * (x * y)))))) + t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = k * (j * -27.0)
	tmp = 0
	if i <= -3.5e+199:
		tmp = t_1 + (-4.0 * (x * i))
	else:
		tmp = ((b * c) + (t * ((a * -4.0) + (18.0 * (z * (x * y)))))) + t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(k * Float64(j * -27.0))
	tmp = 0.0
	if (i <= -3.5e+199)
		tmp = Float64(t_1 + Float64(-4.0 * Float64(x * i)));
	else
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(a * -4.0) + Float64(18.0 * Float64(z * Float64(x * y)))))) + t_1);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = k * (j * -27.0);
	tmp = 0.0;
	if (i <= -3.5e+199)
		tmp = t_1 + (-4.0 * (x * i));
	else
		tmp = ((b * c) + (t * ((a * -4.0) + (18.0 * (z * (x * y)))))) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -3.5e+199], N[(t$95$1 + N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(a * -4.0), $MachinePrecision] + N[(18.0 * N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if i < -3.49999999999999981e199

   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 95.8%

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

   5. Taylor expanded in i around inf 75.9%

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

   if -3.49999999999999981e199 < i

   1. Initial program 85.5%

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

   3. Simplified 88.5%

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

   5. Taylor expanded in i around 0 80.0%

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

      1. *-commutative 80.0%

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

      2. +-commutative 80.0%

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

      3. associate-*r* 80.5%

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

      4. *-commutative 80.5%

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

   7. Applied egg-rr 80.5%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -3.5 \cdot 10^{+199}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right) + -4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(a \cdot -4 + 18 \cdot \left(z \cdot \left(x \cdot y\right)\right)\right)\right) + k \cdot \left(j \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 72.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+74} \lor \neg \left(x \leq 1.5 \cdot 10^{+47}\right):\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(t \cdot a\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= x -9.5e+74) (not (<= x 1.5e+47)))
   (* x (- (* 18.0 (* t (* y z))) (* 4.0 i)))
   (- (* b c) (+ (* 4.0 (* t a)) (* 27.0 (* j k))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((x <= -9.5e+74) || !(x <= 1.5e+47)) {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	} else {
		tmp = (b * c) - ((4.0 * (t * a)) + (27.0 * (j * k)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((x <= (-9.5d+74)) .or. (.not. (x <= 1.5d+47))) then
        tmp = x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i))
    else
        tmp = (b * c) - ((4.0d0 * (t * a)) + (27.0d0 * (j * k)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((x <= -9.5e+74) || !(x <= 1.5e+47)) {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	} else {
		tmp = (b * c) - ((4.0 * (t * a)) + (27.0 * (j * k)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (x <= -9.5e+74) or not (x <= 1.5e+47):
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i))
	else:
		tmp = (b * c) - ((4.0 * (t * a)) + (27.0 * (j * k)))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((x <= -9.5e+74) || !(x <= 1.5e+47))
		tmp = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)));
	else
		tmp = Float64(Float64(b * c) - Float64(Float64(4.0 * Float64(t * a)) + Float64(27.0 * Float64(j * k))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((x <= -9.5e+74) || ~((x <= 1.5e+47)))
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	else
		tmp = (b * c) - ((4.0 * (t * a)) + (27.0 * (j * k)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[x, -9.5e+74], N[Not[LessEqual[x, 1.5e+47]], $MachinePrecision]], N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] - N[(N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -9.5000000000000006e74 or 1.5000000000000001e47 < x

   1. Initial program 74.8%

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

   3. Taylor expanded in x around inf 67.6%

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

   if -9.5000000000000006e74 < x < 1.5000000000000001e47

   1. Initial program 93.6%

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

   3. Taylor expanded in x around 0 78.1%

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

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+74} \lor \neg \left(x \leq 1.5 \cdot 10^{+47}\right):\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(t \cdot a\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 36.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -0.00088 \lor \neg \left(b \cdot c \leq 1.22 \cdot 10^{+107}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= (* b c) -0.00088) (not (<= (* b c) 1.22e+107)))
   (* b c)
   (* -27.0 (* j k))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (((b * c) <= -0.00088) || !((b * c) <= 1.22e+107)) {
		tmp = b * c;
	} else {
		tmp = -27.0 * (j * k);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (((b * c) <= (-0.00088d0)) .or. (.not. ((b * c) <= 1.22d+107))) then
        tmp = b * c
    else
        tmp = (-27.0d0) * (j * k)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (((b * c) <= -0.00088) || !((b * c) <= 1.22e+107)) {
		tmp = b * c;
	} else {
		tmp = -27.0 * (j * k);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if ((b * c) <= -0.00088) or not ((b * c) <= 1.22e+107):
		tmp = b * c
	else:
		tmp = -27.0 * (j * k)
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((Float64(b * c) <= -0.00088) || !(Float64(b * c) <= 1.22e+107))
		tmp = Float64(b * c);
	else
		tmp = Float64(-27.0 * Float64(j * k));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (((b * c) <= -0.00088) || ~(((b * c) <= 1.22e+107)))
		tmp = b * c;
	else
		tmp = -27.0 * (j * k);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[N[(b * c), $MachinePrecision], -0.00088], N[Not[LessEqual[N[(b * c), $MachinePrecision], 1.22e+107]], $MachinePrecision]], N[(b * c), $MachinePrecision], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -8.80000000000000031e-4 or 1.22e107 < (*.f64 b c)

   1. Initial program 84.5%

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

   3. Simplified 86.4%

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

   5. Taylor expanded in b around inf 51.6%

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

   if -8.80000000000000031e-4 < (*.f64 b c) < 1.22e107

   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 91.0%

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

   5. Taylor expanded in k around inf 28.8%

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

4. Final simplification 37.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -0.00088 \lor \neg \left(b \cdot c \leq 1.22 \cdot 10^{+107}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 23.9% accurate, 10.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 86.1%

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

3. Simplified 89.2%

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

5. Taylor expanded in b around inf 22.7%

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

Developer target: 89.2% 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 2024097 
(FPCore (x y z t a b c i j k)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, E"
  :precision binary64

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

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