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

Percentage Accurate: 85.5% → 91.4%

Time: 39.5s

Alternatives: 30

Speedup: 1.1×

• 51.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 91.4% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 95.7%

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

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

   1. Initial program 0.0%

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

   3. Simplified 38.7%

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

      1. associate-*r* 38.7%

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

      2. distribute-rgt-out-- 3.2%

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

      3. associate-*l* 3.2%

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

      4. *-commutative 3.2%

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

      5. *-commutative 3.2%

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

   6. Applied egg-rr 3.2%

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

   7. Taylor expanded in t around -inf 67.9%

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

      1. associate-*r* 67.9%

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

      2. neg-mul-1 67.9%

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

      3. cancel-sign-sub-inv 67.9%

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

      4. *-commutative 67.9%

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

      5. associate-*r* 71.0%

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

      6. metadata-eval 71.0%

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

   9. Simplified 71.0%

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

4. Final simplification 92.7%

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

Alternative 2: 35.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := k \cdot \left(j \cdot -27\right)\\ t_2 := \left(t \cdot a\right) \cdot -4\\ t_3 := \left(x \cdot i\right) \cdot -4\\ \mathbf{if}\;b \cdot c \leq -7.5 \cdot 10^{+39}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -3.6 \cdot 10^{-115}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \cdot c \leq -1.05 \cdot 10^{-279}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot c \leq 2.15 \cdot 10^{-300}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \cdot c \leq 7.4 \cdot 10^{-242}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot c \leq 1.46 \cdot 10^{-168}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \cdot c \leq 2.9 \cdot 10^{+67}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* k (* j -27.0))) (t_2 (* (* t a) -4.0)) (t_3 (* (* x i) -4.0)))
   (if (<= (* b c) -7.5e+39)
     (* b c)
     (if (<= (* b c) -3.6e-115)
       t_2
       (if (<= (* b c) -1.05e-279)
         t_1
         (if (<= (* b c) 2.15e-300)
           t_3
           (if (<= (* b c) 7.4e-242)
             t_1
             (if (<= (* b c) 1.46e-168)
               t_3
               (if (<= (* b c) 2.9e+67) t_2 (* b c))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = k * (j * -27.0);
	double t_2 = (t * a) * -4.0;
	double t_3 = (x * i) * -4.0;
	double tmp;
	if ((b * c) <= -7.5e+39) {
		tmp = b * c;
	} else if ((b * c) <= -3.6e-115) {
		tmp = t_2;
	} else if ((b * c) <= -1.05e-279) {
		tmp = t_1;
	} else if ((b * c) <= 2.15e-300) {
		tmp = t_3;
	} else if ((b * c) <= 7.4e-242) {
		tmp = t_1;
	} else if ((b * c) <= 1.46e-168) {
		tmp = t_3;
	} else if ((b * c) <= 2.9e+67) {
		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.
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 = (t * a) * (-4.0d0)
    t_3 = (x * i) * (-4.0d0)
    if ((b * c) <= (-7.5d+39)) then
        tmp = b * c
    else if ((b * c) <= (-3.6d-115)) then
        tmp = t_2
    else if ((b * c) <= (-1.05d-279)) then
        tmp = t_1
    else if ((b * c) <= 2.15d-300) then
        tmp = t_3
    else if ((b * c) <= 7.4d-242) then
        tmp = t_1
    else if ((b * c) <= 1.46d-168) then
        tmp = t_3
    else if ((b * c) <= 2.9d+67) 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;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = k * (j * -27.0);
	double t_2 = (t * a) * -4.0;
	double t_3 = (x * i) * -4.0;
	double tmp;
	if ((b * c) <= -7.5e+39) {
		tmp = b * c;
	} else if ((b * c) <= -3.6e-115) {
		tmp = t_2;
	} else if ((b * c) <= -1.05e-279) {
		tmp = t_1;
	} else if ((b * c) <= 2.15e-300) {
		tmp = t_3;
	} else if ((b * c) <= 7.4e-242) {
		tmp = t_1;
	} else if ((b * c) <= 1.46e-168) {
		tmp = t_3;
	} else if ((b * c) <= 2.9e+67) {
		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])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = k * (j * -27.0)
	t_2 = (t * a) * -4.0
	t_3 = (x * i) * -4.0
	tmp = 0
	if (b * c) <= -7.5e+39:
		tmp = b * c
	elif (b * c) <= -3.6e-115:
		tmp = t_2
	elif (b * c) <= -1.05e-279:
		tmp = t_1
	elif (b * c) <= 2.15e-300:
		tmp = t_3
	elif (b * c) <= 7.4e-242:
		tmp = t_1
	elif (b * c) <= 1.46e-168:
		tmp = t_3
	elif (b * c) <= 2.9e+67:
		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])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(k * Float64(j * -27.0))
	t_2 = Float64(Float64(t * a) * -4.0)
	t_3 = Float64(Float64(x * i) * -4.0)
	tmp = 0.0
	if (Float64(b * c) <= -7.5e+39)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -3.6e-115)
		tmp = t_2;
	elseif (Float64(b * c) <= -1.05e-279)
		tmp = t_1;
	elseif (Float64(b * c) <= 2.15e-300)
		tmp = t_3;
	elseif (Float64(b * c) <= 7.4e-242)
		tmp = t_1;
	elseif (Float64(b * c) <= 1.46e-168)
		tmp = t_3;
	elseif (Float64(b * c) <= 2.9e+67)
		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])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = k * (j * -27.0);
	t_2 = (t * a) * -4.0;
	t_3 = (x * i) * -4.0;
	tmp = 0.0;
	if ((b * c) <= -7.5e+39)
		tmp = b * c;
	elseif ((b * c) <= -3.6e-115)
		tmp = t_2;
	elseif ((b * c) <= -1.05e-279)
		tmp = t_1;
	elseif ((b * c) <= 2.15e-300)
		tmp = t_3;
	elseif ((b * c) <= 7.4e-242)
		tmp = t_1;
	elseif ((b * c) <= 1.46e-168)
		tmp = t_3;
	elseif ((b * c) <= 2.9e+67)
		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.
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[(t * a), $MachinePrecision] * -4.0), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * i), $MachinePrecision] * -4.0), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -7.5e+39], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -3.6e-115], t$95$2, If[LessEqual[N[(b * c), $MachinePrecision], -1.05e-279], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 2.15e-300], t$95$3, If[LessEqual[N[(b * c), $MachinePrecision], 7.4e-242], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 1.46e-168], t$95$3, If[LessEqual[N[(b * c), $MachinePrecision], 2.9e+67], t$95$2, N[(b * c), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 b c) < -7.5000000000000005e39 or 2.90000000000000023e67 < (*.f64 b c)

   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 87.4%

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

      1. associate-*r* 88.3%

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

      2. distribute-rgt-out-- 84.6%

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

      3. associate-*l* 82.8%

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

      4. *-commutative 82.8%

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

      5. *-commutative 82.8%

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

   6. Applied egg-rr 82.8%

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

   7. Taylor expanded in b around inf 50.1%

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

   if -7.5000000000000005e39 < (*.f64 b c) < -3.60000000000000009e-115 or 1.46e-168 < (*.f64 b c) < 2.90000000000000023e67

   1. Initial program 87.4%

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

   3. Simplified 88.8%

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

      1. associate-*r* 93.9%

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

      2. distribute-rgt-out-- 87.4%

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

      3. associate-*l* 88.9%

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

      4. *-commutative 88.9%

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

      5. *-commutative 88.9%

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

   6. Applied egg-rr 88.9%

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

   7. Taylor expanded in a around inf 41.1%

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

   if -3.60000000000000009e-115 < (*.f64 b c) < -1.05000000000000003e-279 or 2.15e-300 < (*.f64 b c) < 7.39999999999999994e-242

   1. Initial program 87.3%

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

   3. Simplified 96.6%

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

   5. Taylor expanded in j around inf 45.4%

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

      1. *-commutative 45.4%

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

      2. associate-*r* 45.5%

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

      3. *-commutative 45.5%

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

      4. associate-*l* 45.5%

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

   7. Simplified 45.5%

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

   if -1.05000000000000003e-279 < (*.f64 b c) < 2.15e-300 or 7.39999999999999994e-242 < (*.f64 b c) < 1.46e-168

   1. Initial program 79.2%

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

   3. Simplified 84.8%

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

      1. associate-*r* 77.4%

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

      2. distribute-rgt-out-- 77.4%

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

      3. associate-*l* 75.3%

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

      4. *-commutative 75.3%

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

      5. *-commutative 75.3%

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

   6. Applied egg-rr 75.3%

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

   7. Taylor expanded in i around inf 41.2%

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

      1. *-commutative 41.2%

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

      2. *-commutative 41.2%

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

   9. Simplified 41.2%

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

4. Final simplification 45.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -7.5 \cdot 10^{+39}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -3.6 \cdot 10^{-115}:\\ \;\;\;\;\left(t \cdot a\right) \cdot -4\\ \mathbf{elif}\;b \cdot c \leq -1.05 \cdot 10^{-279}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 2.15 \cdot 10^{-300}:\\ \;\;\;\;\left(x \cdot i\right) \cdot -4\\ \mathbf{elif}\;b \cdot c \leq 7.4 \cdot 10^{-242}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 1.46 \cdot 10^{-168}:\\ \;\;\;\;\left(x \cdot i\right) \cdot -4\\ \mathbf{elif}\;b \cdot c \leq 2.9 \cdot 10^{+67}:\\ \;\;\;\;\left(t \cdot a\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 34.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(t \cdot a\right) \cdot -4\\ t_2 := 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{if}\;b \cdot c \leq -9 \cdot 10^{+274}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -3.5 \cdot 10^{+113}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \cdot c \leq -8.5 \cdot 10^{+39}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -3.1 \cdot 10^{-175}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot c \leq -1.55 \cdot 10^{-279}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \cdot c \leq 9.6 \cdot 10^{-169}:\\ \;\;\;\;\left(x \cdot i\right) \cdot -4\\ \mathbf{elif}\;b \cdot c \leq 1.85 \cdot 10^{+67}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* t a) -4.0)) (t_2 (* 18.0 (* t (* x (* y z))))))
   (if (<= (* b c) -9e+274)
     (* b c)
     (if (<= (* b c) -3.5e+113)
       t_2
       (if (<= (* b c) -8.5e+39)
         (* b c)
         (if (<= (* b c) -3.1e-175)
           t_1
           (if (<= (* b c) -1.55e-279)
             t_2
             (if (<= (* b c) 9.6e-169)
               (* (* x i) -4.0)
               (if (<= (* b c) 1.85e+67) t_1 (* b c))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (t * a) * -4.0;
	double t_2 = 18.0 * (t * (x * (y * z)));
	double tmp;
	if ((b * c) <= -9e+274) {
		tmp = b * c;
	} else if ((b * c) <= -3.5e+113) {
		tmp = t_2;
	} else if ((b * c) <= -8.5e+39) {
		tmp = b * c;
	} else if ((b * c) <= -3.1e-175) {
		tmp = t_1;
	} else if ((b * c) <= -1.55e-279) {
		tmp = t_2;
	} else if ((b * c) <= 9.6e-169) {
		tmp = (x * i) * -4.0;
	} else if ((b * c) <= 1.85e+67) {
		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.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (t * a) * (-4.0d0)
    t_2 = 18.0d0 * (t * (x * (y * z)))
    if ((b * c) <= (-9d+274)) then
        tmp = b * c
    else if ((b * c) <= (-3.5d+113)) then
        tmp = t_2
    else if ((b * c) <= (-8.5d+39)) then
        tmp = b * c
    else if ((b * c) <= (-3.1d-175)) then
        tmp = t_1
    else if ((b * c) <= (-1.55d-279)) then
        tmp = t_2
    else if ((b * c) <= 9.6d-169) then
        tmp = (x * i) * (-4.0d0)
    else if ((b * c) <= 1.85d+67) 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;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (t * a) * -4.0;
	double t_2 = 18.0 * (t * (x * (y * z)));
	double tmp;
	if ((b * c) <= -9e+274) {
		tmp = b * c;
	} else if ((b * c) <= -3.5e+113) {
		tmp = t_2;
	} else if ((b * c) <= -8.5e+39) {
		tmp = b * c;
	} else if ((b * c) <= -3.1e-175) {
		tmp = t_1;
	} else if ((b * c) <= -1.55e-279) {
		tmp = t_2;
	} else if ((b * c) <= 9.6e-169) {
		tmp = (x * i) * -4.0;
	} else if ((b * c) <= 1.85e+67) {
		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])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (t * a) * -4.0
	t_2 = 18.0 * (t * (x * (y * z)))
	tmp = 0
	if (b * c) <= -9e+274:
		tmp = b * c
	elif (b * c) <= -3.5e+113:
		tmp = t_2
	elif (b * c) <= -8.5e+39:
		tmp = b * c
	elif (b * c) <= -3.1e-175:
		tmp = t_1
	elif (b * c) <= -1.55e-279:
		tmp = t_2
	elif (b * c) <= 9.6e-169:
		tmp = (x * i) * -4.0
	elif (b * c) <= 1.85e+67:
		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])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(t * a) * -4.0)
	t_2 = Float64(18.0 * Float64(t * Float64(x * Float64(y * z))))
	tmp = 0.0
	if (Float64(b * c) <= -9e+274)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -3.5e+113)
		tmp = t_2;
	elseif (Float64(b * c) <= -8.5e+39)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -3.1e-175)
		tmp = t_1;
	elseif (Float64(b * c) <= -1.55e-279)
		tmp = t_2;
	elseif (Float64(b * c) <= 9.6e-169)
		tmp = Float64(Float64(x * i) * -4.0);
	elseif (Float64(b * c) <= 1.85e+67)
		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])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (t * a) * -4.0;
	t_2 = 18.0 * (t * (x * (y * z)));
	tmp = 0.0;
	if ((b * c) <= -9e+274)
		tmp = b * c;
	elseif ((b * c) <= -3.5e+113)
		tmp = t_2;
	elseif ((b * c) <= -8.5e+39)
		tmp = b * c;
	elseif ((b * c) <= -3.1e-175)
		tmp = t_1;
	elseif ((b * c) <= -1.55e-279)
		tmp = t_2;
	elseif ((b * c) <= 9.6e-169)
		tmp = (x * i) * -4.0;
	elseif ((b * c) <= 1.85e+67)
		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.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(t * a), $MachinePrecision] * -4.0), $MachinePrecision]}, Block[{t$95$2 = N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -9e+274], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -3.5e+113], t$95$2, If[LessEqual[N[(b * c), $MachinePrecision], -8.5e+39], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -3.1e-175], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], -1.55e-279], t$95$2, If[LessEqual[N[(b * c), $MachinePrecision], 9.6e-169], N[(N[(x * i), $MachinePrecision] * -4.0), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1.85e+67], t$95$1, N[(b * c), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 b c) < -8.9999999999999995e274 or -3.5000000000000001e113 < (*.f64 b c) < -8.49999999999999971e39 or 1.8499999999999999e67 < (*.f64 b c)

   1. Initial program 80.1%

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

   3. Simplified 83.7%

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

      1. associate-*r* 84.9%

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

      2. distribute-rgt-out-- 81.3%

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

      3. associate-*l* 78.9%

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

      4. *-commutative 78.9%

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

      5. *-commutative 78.9%

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

   6. Applied egg-rr 78.9%

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

   7. Taylor expanded in b around inf 58.1%

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

   if -8.9999999999999995e274 < (*.f64 b c) < -3.5000000000000001e113 or -3.09999999999999999e-175 < (*.f64 b c) < -1.55e-279

   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 97.4%

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

   5. Taylor expanded in x around inf 59.4%

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

   6. Taylor expanded in t around inf 52.3%

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

   if -8.49999999999999971e39 < (*.f64 b c) < -3.09999999999999999e-175 or 9.60000000000000043e-169 < (*.f64 b c) < 1.8499999999999999e67

   1. Initial program 87.6%

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

   3. Simplified 90.2%

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

      1. associate-*r* 94.6%

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

      2. distribute-rgt-out-- 87.6%

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

      3. associate-*l* 88.9%

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

      4. *-commutative 88.9%

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

      5. *-commutative 88.9%

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

   6. Applied egg-rr 88.9%

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

   7. Taylor expanded in a around inf 39.9%

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

   if -1.55e-279 < (*.f64 b c) < 9.60000000000000043e-169

   1. Initial program 79.9%

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

   3. Simplified 86.6%

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

      1. associate-*r* 80.1%

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

      2. distribute-rgt-out-- 78.4%

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

      3. associate-*l* 76.5%

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

      4. *-commutative 76.5%

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

      5. *-commutative 76.5%

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

   6. Applied egg-rr 76.5%

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

   7. Taylor expanded in i around inf 36.6%

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

      1. *-commutative 36.6%

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

      2. *-commutative 36.6%

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

   9. Simplified 36.6%

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

4. Final simplification 47.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -9 \cdot 10^{+274}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -3.5 \cdot 10^{+113}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq -8.5 \cdot 10^{+39}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -3.1 \cdot 10^{-175}:\\ \;\;\;\;\left(t \cdot a\right) \cdot -4\\ \mathbf{elif}\;b \cdot c \leq -1.55 \cdot 10^{-279}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 9.6 \cdot 10^{-169}:\\ \;\;\;\;\left(x \cdot i\right) \cdot -4\\ \mathbf{elif}\;b \cdot c \leq 1.85 \cdot 10^{+67}:\\ \;\;\;\;\left(t \cdot a\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 35.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(t \cdot a\right) \cdot -4\\ \mathbf{if}\;b \cdot c \leq -1.7 \cdot 10^{+186}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -3.3 \cdot 10^{+113}:\\ \;\;\;\;x \cdot \left(z \cdot \left(18 \cdot \left(y \cdot t\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq -1.6 \cdot 10^{+40}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -2.45 \cdot 10^{-175}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot c \leq -8.5 \cdot 10^{-279}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 2 \cdot 10^{-171}:\\ \;\;\;\;\left(x \cdot i\right) \cdot -4\\ \mathbf{elif}\;b \cdot c \leq 3.5 \cdot 10^{+67}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* t a) -4.0)))
   (if (<= (* b c) -1.7e+186)
     (* b c)
     (if (<= (* b c) -3.3e+113)
       (* x (* z (* 18.0 (* y t))))
       (if (<= (* b c) -1.6e+40)
         (* b c)
         (if (<= (* b c) -2.45e-175)
           t_1
           (if (<= (* b c) -8.5e-279)
             (* 18.0 (* t (* x (* y z))))
             (if (<= (* b c) 2e-171)
               (* (* x i) -4.0)
               (if (<= (* b c) 3.5e+67) t_1 (* b c))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (t * a) * -4.0;
	double tmp;
	if ((b * c) <= -1.7e+186) {
		tmp = b * c;
	} else if ((b * c) <= -3.3e+113) {
		tmp = x * (z * (18.0 * (y * t)));
	} else if ((b * c) <= -1.6e+40) {
		tmp = b * c;
	} else if ((b * c) <= -2.45e-175) {
		tmp = t_1;
	} else if ((b * c) <= -8.5e-279) {
		tmp = 18.0 * (t * (x * (y * z)));
	} else if ((b * c) <= 2e-171) {
		tmp = (x * i) * -4.0;
	} else if ((b * c) <= 3.5e+67) {
		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.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t * a) * (-4.0d0)
    if ((b * c) <= (-1.7d+186)) then
        tmp = b * c
    else if ((b * c) <= (-3.3d+113)) then
        tmp = x * (z * (18.0d0 * (y * t)))
    else if ((b * c) <= (-1.6d+40)) then
        tmp = b * c
    else if ((b * c) <= (-2.45d-175)) then
        tmp = t_1
    else if ((b * c) <= (-8.5d-279)) then
        tmp = 18.0d0 * (t * (x * (y * z)))
    else if ((b * c) <= 2d-171) then
        tmp = (x * i) * (-4.0d0)
    else if ((b * c) <= 3.5d+67) 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;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (t * a) * -4.0;
	double tmp;
	if ((b * c) <= -1.7e+186) {
		tmp = b * c;
	} else if ((b * c) <= -3.3e+113) {
		tmp = x * (z * (18.0 * (y * t)));
	} else if ((b * c) <= -1.6e+40) {
		tmp = b * c;
	} else if ((b * c) <= -2.45e-175) {
		tmp = t_1;
	} else if ((b * c) <= -8.5e-279) {
		tmp = 18.0 * (t * (x * (y * z)));
	} else if ((b * c) <= 2e-171) {
		tmp = (x * i) * -4.0;
	} else if ((b * c) <= 3.5e+67) {
		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])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (t * a) * -4.0
	tmp = 0
	if (b * c) <= -1.7e+186:
		tmp = b * c
	elif (b * c) <= -3.3e+113:
		tmp = x * (z * (18.0 * (y * t)))
	elif (b * c) <= -1.6e+40:
		tmp = b * c
	elif (b * c) <= -2.45e-175:
		tmp = t_1
	elif (b * c) <= -8.5e-279:
		tmp = 18.0 * (t * (x * (y * z)))
	elif (b * c) <= 2e-171:
		tmp = (x * i) * -4.0
	elif (b * c) <= 3.5e+67:
		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])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(t * a) * -4.0)
	tmp = 0.0
	if (Float64(b * c) <= -1.7e+186)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -3.3e+113)
		tmp = Float64(x * Float64(z * Float64(18.0 * Float64(y * t))));
	elseif (Float64(b * c) <= -1.6e+40)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -2.45e-175)
		tmp = t_1;
	elseif (Float64(b * c) <= -8.5e-279)
		tmp = Float64(18.0 * Float64(t * Float64(x * Float64(y * z))));
	elseif (Float64(b * c) <= 2e-171)
		tmp = Float64(Float64(x * i) * -4.0);
	elseif (Float64(b * c) <= 3.5e+67)
		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])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (t * a) * -4.0;
	tmp = 0.0;
	if ((b * c) <= -1.7e+186)
		tmp = b * c;
	elseif ((b * c) <= -3.3e+113)
		tmp = x * (z * (18.0 * (y * t)));
	elseif ((b * c) <= -1.6e+40)
		tmp = b * c;
	elseif ((b * c) <= -2.45e-175)
		tmp = t_1;
	elseif ((b * c) <= -8.5e-279)
		tmp = 18.0 * (t * (x * (y * z)));
	elseif ((b * c) <= 2e-171)
		tmp = (x * i) * -4.0;
	elseif ((b * c) <= 3.5e+67)
		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.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(t * a), $MachinePrecision] * -4.0), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -1.7e+186], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -3.3e+113], N[(x * N[(z * N[(18.0 * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -1.6e+40], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -2.45e-175], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], -8.5e-279], N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 2e-171], N[(N[(x * i), $MachinePrecision] * -4.0), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 3.5e+67], t$95$1, N[(b * c), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 b c) < -1.70000000000000003e186 or -3.3000000000000003e113 < (*.f64 b c) < -1.5999999999999999e40 or 3.5e67 < (*.f64 b c)

   1. Initial program 82.8%

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

   3. Simplified 85.8%

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

      1. associate-*r* 86.8%

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

      2. distribute-rgt-out-- 83.8%

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

      3. associate-*l* 81.7%

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

      4. *-commutative 81.7%

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

      5. *-commutative 81.7%

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

   6. Applied egg-rr 81.7%

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

   7. Taylor expanded in b around inf 54.0%

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

   if -1.70000000000000003e186 < (*.f64 b c) < -3.3000000000000003e113

   1. Initial program 91.5%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 66.2%

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

   6. Taylor expanded in t around inf 58.4%

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

      1. associate-*r* 58.4%

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

      2. associate-*r* 58.4%

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

      3. *-commutative 58.4%

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

   8. Simplified 58.4%

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

   if -1.5999999999999999e40 < (*.f64 b c) < -2.44999999999999999e-175 or 2e-171 < (*.f64 b c) < 3.5e67

   1. Initial program 87.6%

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

   3. Simplified 90.2%

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

      1. associate-*r* 94.6%

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

      2. distribute-rgt-out-- 87.6%

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

      3. associate-*l* 88.9%

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

      4. *-commutative 88.9%

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

      5. *-commutative 88.9%

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

   6. Applied egg-rr 88.9%

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

   7. Taylor expanded in a around inf 39.9%

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

   if -2.44999999999999999e-175 < (*.f64 b c) < -8.5000000000000002e-279

   1. Initial program 87.3%

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

   3. Simplified 93.5%

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

   5. Taylor expanded in x around inf 69.7%

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

   6. Taylor expanded in t around inf 69.8%

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

   if -8.5000000000000002e-279 < (*.f64 b c) < 2e-171

   1. Initial program 79.9%

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

   3. Simplified 86.6%

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

      1. associate-*r* 80.1%

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

      2. distribute-rgt-out-- 78.4%

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

      3. associate-*l* 76.5%

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

      4. *-commutative 76.5%

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

      5. *-commutative 76.5%

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

   6. Applied egg-rr 76.5%

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

   7. Taylor expanded in i around inf 36.6%

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

      1. *-commutative 36.6%

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

      2. *-commutative 36.6%

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

   9. Simplified 36.6%

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

4. Final simplification 47.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.7 \cdot 10^{+186}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -3.3 \cdot 10^{+113}:\\ \;\;\;\;x \cdot \left(z \cdot \left(18 \cdot \left(y \cdot t\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq -1.6 \cdot 10^{+40}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -2.45 \cdot 10^{-175}:\\ \;\;\;\;\left(t \cdot a\right) \cdot -4\\ \mathbf{elif}\;b \cdot c \leq -8.5 \cdot 10^{-279}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 2 \cdot 10^{-171}:\\ \;\;\;\;\left(x \cdot i\right) \cdot -4\\ \mathbf{elif}\;b \cdot c \leq 3.5 \cdot 10^{+67}:\\ \;\;\;\;\left(t \cdot a\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 53.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ t_2 := j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;b \cdot c \leq -1.95 \cdot 10^{-51}:\\ \;\;\;\;b \cdot c + t_1\\ \mathbf{elif}\;b \cdot c \leq -2.8 \cdot 10^{-175}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;b \cdot c \leq -6 \cdot 10^{-280}:\\ \;\;\;\;t_1 + t_2\\ \mathbf{elif}\;b \cdot c \leq 6.4 \cdot 10^{-307}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 1.65 \cdot 10^{-171}:\\ \;\;\;\;t_2 + \left(x \cdot i\right) \cdot -4\\ \mathbf{elif}\;b \cdot c \leq 8.8 \cdot 10^{+63}:\\ \;\;\;\;t_2 + \left(t \cdot a\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* 18.0 (* t (* x (* y z))))) (t_2 (* j (* k -27.0))))
   (if (<= (* b c) -1.95e-51)
     (+ (* b c) t_1)
     (if (<= (* b c) -2.8e-175)
       (- (* t (* a -4.0)) (* (* j 27.0) k))
       (if (<= (* b c) -6e-280)
         (+ t_1 t_2)
         (if (<= (* b c) 6.4e-307)
           (* x (- (* 18.0 (* t (* y z))) (* 4.0 i)))
           (if (<= (* b c) 1.65e-171)
             (+ t_2 (* (* x i) -4.0))
             (if (<= (* b c) 8.8e+63)
               (+ t_2 (* (* t a) -4.0))
               (- (* 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);
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 * (x * (y * z)));
	double t_2 = j * (k * -27.0);
	double tmp;
	if ((b * c) <= -1.95e-51) {
		tmp = (b * c) + t_1;
	} else if ((b * c) <= -2.8e-175) {
		tmp = (t * (a * -4.0)) - ((j * 27.0) * k);
	} else if ((b * c) <= -6e-280) {
		tmp = t_1 + t_2;
	} else if ((b * c) <= 6.4e-307) {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	} else if ((b * c) <= 1.65e-171) {
		tmp = t_2 + ((x * i) * -4.0);
	} else if ((b * c) <= 8.8e+63) {
		tmp = t_2 + ((t * a) * -4.0);
	} else {
		tmp = (b * c) - (27.0 * (j * k));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 18.0d0 * (t * (x * (y * z)))
    t_2 = j * (k * (-27.0d0))
    if ((b * c) <= (-1.95d-51)) then
        tmp = (b * c) + t_1
    else if ((b * c) <= (-2.8d-175)) then
        tmp = (t * (a * (-4.0d0))) - ((j * 27.0d0) * k)
    else if ((b * c) <= (-6d-280)) then
        tmp = t_1 + t_2
    else if ((b * c) <= 6.4d-307) then
        tmp = x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i))
    else if ((b * c) <= 1.65d-171) then
        tmp = t_2 + ((x * i) * (-4.0d0))
    else if ((b * c) <= 8.8d+63) then
        tmp = t_2 + ((t * a) * (-4.0d0))
    else
        tmp = (b * c) - (27.0d0 * (j * k))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 18.0 * (t * (x * (y * z)));
	double t_2 = j * (k * -27.0);
	double tmp;
	if ((b * c) <= -1.95e-51) {
		tmp = (b * c) + t_1;
	} else if ((b * c) <= -2.8e-175) {
		tmp = (t * (a * -4.0)) - ((j * 27.0) * k);
	} else if ((b * c) <= -6e-280) {
		tmp = t_1 + t_2;
	} else if ((b * c) <= 6.4e-307) {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	} else if ((b * c) <= 1.65e-171) {
		tmp = t_2 + ((x * i) * -4.0);
	} else if ((b * c) <= 8.8e+63) {
		tmp = t_2 + ((t * a) * -4.0);
	} else {
		tmp = (b * c) - (27.0 * (j * k));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = 18.0 * (t * (x * (y * z)))
	t_2 = j * (k * -27.0)
	tmp = 0
	if (b * c) <= -1.95e-51:
		tmp = (b * c) + t_1
	elif (b * c) <= -2.8e-175:
		tmp = (t * (a * -4.0)) - ((j * 27.0) * k)
	elif (b * c) <= -6e-280:
		tmp = t_1 + t_2
	elif (b * c) <= 6.4e-307:
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i))
	elif (b * c) <= 1.65e-171:
		tmp = t_2 + ((x * i) * -4.0)
	elif (b * c) <= 8.8e+63:
		tmp = t_2 + ((t * a) * -4.0)
	else:
		tmp = (b * c) - (27.0 * (j * k))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(18.0 * Float64(t * Float64(x * Float64(y * z))))
	t_2 = Float64(j * Float64(k * -27.0))
	tmp = 0.0
	if (Float64(b * c) <= -1.95e-51)
		tmp = Float64(Float64(b * c) + t_1);
	elseif (Float64(b * c) <= -2.8e-175)
		tmp = Float64(Float64(t * Float64(a * -4.0)) - Float64(Float64(j * 27.0) * k));
	elseif (Float64(b * c) <= -6e-280)
		tmp = Float64(t_1 + t_2);
	elseif (Float64(b * c) <= 6.4e-307)
		tmp = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)));
	elseif (Float64(b * c) <= 1.65e-171)
		tmp = Float64(t_2 + Float64(Float64(x * i) * -4.0));
	elseif (Float64(b * c) <= 8.8e+63)
		tmp = Float64(t_2 + Float64(Float64(t * a) * -4.0));
	else
		tmp = Float64(Float64(b * c) - Float64(27.0 * Float64(j * k)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = 18.0 * (t * (x * (y * z)));
	t_2 = j * (k * -27.0);
	tmp = 0.0;
	if ((b * c) <= -1.95e-51)
		tmp = (b * c) + t_1;
	elseif ((b * c) <= -2.8e-175)
		tmp = (t * (a * -4.0)) - ((j * 27.0) * k);
	elseif ((b * c) <= -6e-280)
		tmp = t_1 + t_2;
	elseif ((b * c) <= 6.4e-307)
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	elseif ((b * c) <= 1.65e-171)
		tmp = t_2 + ((x * i) * -4.0);
	elseif ((b * c) <= 8.8e+63)
		tmp = t_2 + ((t * a) * -4.0);
	else
		tmp = (b * c) - (27.0 * (j * k));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -1.95e-51], N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -2.8e-175], N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -6e-280], N[(t$95$1 + t$95$2), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 6.4e-307], N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1.65e-171], N[(t$95$2 + N[(N[(x * i), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 8.8e+63], N[(t$95$2 + N[(N[(t * a), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if (*.f64 b c) < -1.9499999999999999e-51

   1. Initial program 84.2%

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

   3. Simplified 84.2%

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

   5. Taylor expanded in j around 0 78.8%

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

   6. Taylor expanded in i around 0 76.2%

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

   7. Taylor expanded in a around 0 65.5%

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

   if -1.9499999999999999e-51 < (*.f64 b c) < -2.8e-175

   1. Initial program 89.8%

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

   3. Taylor expanded in x around 0 89.4%

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

   4. Taylor expanded in a around inf 74.3%

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

      1. *-commutative 74.3%

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

      2. *-commutative 74.3%

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

      3. associate-*l* 74.3%

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

      4. *-commutative 74.3%

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

   6. Simplified 74.3%

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

   if -2.8e-175 < (*.f64 b c) < -5.99999999999999974e-280

   1. Initial program 87.3%

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

   3. Simplified 93.4%

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

   5. Taylor expanded in y around inf 89.3%

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

   if -5.99999999999999974e-280 < (*.f64 b c) < 6.40000000000000021e-307

   1. Initial program 83.1%

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

   3. Simplified 85.8%

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

   5. Taylor expanded in x around inf 54.1%

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

   if 6.40000000000000021e-307 < (*.f64 b c) < 1.6500000000000001e-171

   1. Initial program 74.3%

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

   3. Simplified 87.2%

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

   5. Taylor expanded in i around inf 74.8%

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

   if 1.6500000000000001e-171 < (*.f64 b c) < 8.7999999999999995e63

   1. Initial program 87.5%

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

   3. Simplified 90.8%

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

   5. Taylor expanded in a around inf 72.4%

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

      1. *-commutative 72.4%

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

   7. Simplified 72.4%

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

   if 8.7999999999999995e63 < (*.f64 b c)

   1. Initial program 82.9%

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

   3. Taylor expanded in x around 0 81.3%

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

   4. Taylor expanded in b around inf 68.0%

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

   5. Taylor expanded in j around 0 68.0%

      \[\leadsto b \cdot c - \color{blue}{27 \cdot \left(j \cdot k\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.95 \cdot 10^{-51}:\\ \;\;\;\;b \cdot c + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq -2.8 \cdot 10^{-175}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;b \cdot c \leq -6 \cdot 10^{-280}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 6.4 \cdot 10^{-307}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 1.65 \cdot 10^{-171}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + \left(x \cdot i\right) \cdot -4\\ \mathbf{elif}\;b \cdot c \leq 8.8 \cdot 10^{+63}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + \left(t \cdot a\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 72.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := 4 \cdot \left(x \cdot i\right)\\ t_2 := \left(j \cdot 27\right) \cdot k\\ t_3 := t \cdot \left(-18 \cdot \left(z \cdot \left(y \cdot \left(-x\right)\right)\right) - a \cdot 4\right) - t_2\\ t_4 := b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{if}\;x \leq -2.8 \cdot 10^{+117}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq -8.6 \cdot 10^{+29}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -580:\\ \;\;\;\;b \cdot c - \left(t_1 + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{-52}:\\ \;\;\;\;x \cdot \left(\left(y \cdot t\right) \cdot \left(18 \cdot z\right)\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq -3.55 \cdot 10^{-71}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -1.45 \cdot 10^{-191}:\\ \;\;\;\;\left(b \cdot c + \left(t \cdot a\right) \cdot -4\right) - t_1\\ \mathbf{elif}\;x \leq 6.9 \cdot 10^{-56}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - t_2\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* 4.0 (* x i)))
        (t_2 (* (* j 27.0) k))
        (t_3 (- (* t (- (* -18.0 (* z (* y (- x)))) (* a 4.0))) t_2))
        (t_4 (+ (* b c) (* x (- (* 18.0 (* t (* y z))) (* 4.0 i))))))
   (if (<= x -2.8e+117)
     t_4
     (if (<= x -8.6e+29)
       t_3
       (if (<= x -580.0)
         (- (* b c) (+ t_1 (* 27.0 (* j k))))
         (if (<= x -4.8e-52)
           (+ (* x (* (* y t) (* 18.0 z))) (* j (* k -27.0)))
           (if (<= x -3.55e-71)
             t_3
             (if (<= x -1.45e-191)
               (- (+ (* b c) (* (* t a) -4.0)) t_1)
               (if (<= x 6.9e-56)
                 (- (- (* b c) (* 4.0 (* t a))) t_2)
                 t_4)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 4.0 * (x * i);
	double t_2 = (j * 27.0) * k;
	double t_3 = (t * ((-18.0 * (z * (y * -x))) - (a * 4.0))) - t_2;
	double t_4 = (b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)));
	double tmp;
	if (x <= -2.8e+117) {
		tmp = t_4;
	} else if (x <= -8.6e+29) {
		tmp = t_3;
	} else if (x <= -580.0) {
		tmp = (b * c) - (t_1 + (27.0 * (j * k)));
	} else if (x <= -4.8e-52) {
		tmp = (x * ((y * t) * (18.0 * z))) + (j * (k * -27.0));
	} else if (x <= -3.55e-71) {
		tmp = t_3;
	} else if (x <= -1.45e-191) {
		tmp = ((b * c) + ((t * a) * -4.0)) - t_1;
	} else if (x <= 6.9e-56) {
		tmp = ((b * c) - (4.0 * (t * a))) - t_2;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = 4.0d0 * (x * i)
    t_2 = (j * 27.0d0) * k
    t_3 = (t * (((-18.0d0) * (z * (y * -x))) - (a * 4.0d0))) - t_2
    t_4 = (b * c) + (x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i)))
    if (x <= (-2.8d+117)) then
        tmp = t_4
    else if (x <= (-8.6d+29)) then
        tmp = t_3
    else if (x <= (-580.0d0)) then
        tmp = (b * c) - (t_1 + (27.0d0 * (j * k)))
    else if (x <= (-4.8d-52)) then
        tmp = (x * ((y * t) * (18.0d0 * z))) + (j * (k * (-27.0d0)))
    else if (x <= (-3.55d-71)) then
        tmp = t_3
    else if (x <= (-1.45d-191)) then
        tmp = ((b * c) + ((t * a) * (-4.0d0))) - t_1
    else if (x <= 6.9d-56) then
        tmp = ((b * c) - (4.0d0 * (t * a))) - t_2
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 4.0 * (x * i);
	double t_2 = (j * 27.0) * k;
	double t_3 = (t * ((-18.0 * (z * (y * -x))) - (a * 4.0))) - t_2;
	double t_4 = (b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)));
	double tmp;
	if (x <= -2.8e+117) {
		tmp = t_4;
	} else if (x <= -8.6e+29) {
		tmp = t_3;
	} else if (x <= -580.0) {
		tmp = (b * c) - (t_1 + (27.0 * (j * k)));
	} else if (x <= -4.8e-52) {
		tmp = (x * ((y * t) * (18.0 * z))) + (j * (k * -27.0));
	} else if (x <= -3.55e-71) {
		tmp = t_3;
	} else if (x <= -1.45e-191) {
		tmp = ((b * c) + ((t * a) * -4.0)) - t_1;
	} else if (x <= 6.9e-56) {
		tmp = ((b * c) - (4.0 * (t * a))) - t_2;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = 4.0 * (x * i)
	t_2 = (j * 27.0) * k
	t_3 = (t * ((-18.0 * (z * (y * -x))) - (a * 4.0))) - t_2
	t_4 = (b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)))
	tmp = 0
	if x <= -2.8e+117:
		tmp = t_4
	elif x <= -8.6e+29:
		tmp = t_3
	elif x <= -580.0:
		tmp = (b * c) - (t_1 + (27.0 * (j * k)))
	elif x <= -4.8e-52:
		tmp = (x * ((y * t) * (18.0 * z))) + (j * (k * -27.0))
	elif x <= -3.55e-71:
		tmp = t_3
	elif x <= -1.45e-191:
		tmp = ((b * c) + ((t * a) * -4.0)) - t_1
	elif x <= 6.9e-56:
		tmp = ((b * c) - (4.0 * (t * a))) - t_2
	else:
		tmp = t_4
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(4.0 * Float64(x * i))
	t_2 = Float64(Float64(j * 27.0) * k)
	t_3 = Float64(Float64(t * Float64(Float64(-18.0 * Float64(z * Float64(y * Float64(-x)))) - Float64(a * 4.0))) - t_2)
	t_4 = Float64(Float64(b * c) + Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i))))
	tmp = 0.0
	if (x <= -2.8e+117)
		tmp = t_4;
	elseif (x <= -8.6e+29)
		tmp = t_3;
	elseif (x <= -580.0)
		tmp = Float64(Float64(b * c) - Float64(t_1 + Float64(27.0 * Float64(j * k))));
	elseif (x <= -4.8e-52)
		tmp = Float64(Float64(x * Float64(Float64(y * t) * Float64(18.0 * z))) + Float64(j * Float64(k * -27.0)));
	elseif (x <= -3.55e-71)
		tmp = t_3;
	elseif (x <= -1.45e-191)
		tmp = Float64(Float64(Float64(b * c) + Float64(Float64(t * a) * -4.0)) - t_1);
	elseif (x <= 6.9e-56)
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(t * a))) - t_2);
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = 4.0 * (x * i);
	t_2 = (j * 27.0) * k;
	t_3 = (t * ((-18.0 * (z * (y * -x))) - (a * 4.0))) - t_2;
	t_4 = (b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)));
	tmp = 0.0;
	if (x <= -2.8e+117)
		tmp = t_4;
	elseif (x <= -8.6e+29)
		tmp = t_3;
	elseif (x <= -580.0)
		tmp = (b * c) - (t_1 + (27.0 * (j * k)));
	elseif (x <= -4.8e-52)
		tmp = (x * ((y * t) * (18.0 * z))) + (j * (k * -27.0));
	elseif (x <= -3.55e-71)
		tmp = t_3;
	elseif (x <= -1.45e-191)
		tmp = ((b * c) + ((t * a) * -4.0)) - t_1;
	elseif (x <= 6.9e-56)
		tmp = ((b * c) - (4.0 * (t * a))) - t_2;
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t * N[(N[(-18.0 * N[(z * N[(y * (-x)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision]}, Block[{t$95$4 = 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]}, If[LessEqual[x, -2.8e+117], t$95$4, If[LessEqual[x, -8.6e+29], t$95$3, If[LessEqual[x, -580.0], N[(N[(b * c), $MachinePrecision] - N[(t$95$1 + N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -4.8e-52], N[(N[(x * N[(N[(y * t), $MachinePrecision] * N[(18.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3.55e-71], t$95$3, If[LessEqual[x, -1.45e-191], N[(N[(N[(b * c), $MachinePrecision] + N[(N[(t * a), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[x, 6.9e-56], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], t$95$4]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -2.79999999999999997e117 or 6.8999999999999996e-56 < x

   1. Initial program 77.5%

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

   3. Taylor expanded in x around 0 88.7%

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

   4. Taylor expanded in a around 0 86.7%

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

   5. Taylor expanded in j around 0 78.8%

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

   if -2.79999999999999997e117 < x < -8.6000000000000006e29 or -4.8000000000000003e-52 < x < -3.55000000000000004e-71

   1. Initial program 75.1%

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

   3. Taylor expanded in x around 0 75.6%

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

   4. Taylor expanded in t around -inf 89.9%

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

      1. associate-*r* 89.9%

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

      2. neg-mul-1 89.9%

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

      3. cancel-sign-sub-inv 89.9%

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

      4. metadata-eval 89.9%

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

      5. associate-*r* 85.2%

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

      6. *-commutative 85.2%

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

   6. Simplified 85.2%

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

   if -8.6000000000000006e29 < x < -580

   1. Initial program 100.0%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in t around 0 99.7%

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

   if -580 < x < -4.8000000000000003e-52

   1. Initial program 82.2%

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

   3. Simplified 91.5%

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

   5. Taylor expanded in y around inf 74.0%

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

      1. *-commutative 74.0%

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

      2. associate-*r* 74.0%

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

      3. associate-*l* 74.0%

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

      4. *-commutative 74.0%

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

      5. *-commutative 74.0%

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

      6. associate-*r* 82.3%

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

      7. associate-*l* 82.2%

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

   7. Simplified 82.2%

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

   if -3.55000000000000004e-71 < x < -1.45e-191

   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 80.3%

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

   5. Taylor expanded in j around 0 84.2%

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

   6. Taylor expanded in y around 0 88.1%

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

   if -1.45e-191 < x < 6.8999999999999996e-56

   1. Initial program 93.3%

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

   3. Taylor expanded in x around 0 88.0%

      \[\leadsto \color{blue}{\left(b \cdot c - 4 \cdot \left(a \cdot t\right)\right)} - \left(j \cdot 27\right) \cdot k \]
3. Recombined 6 regimes into one program.

4. Final simplification 84.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{+117}:\\ \;\;\;\;b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;x \leq -8.6 \cdot 10^{+29}:\\ \;\;\;\;t \cdot \left(-18 \cdot \left(z \cdot \left(y \cdot \left(-x\right)\right)\right) - a \cdot 4\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;x \leq -580:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{-52}:\\ \;\;\;\;x \cdot \left(\left(y \cdot t\right) \cdot \left(18 \cdot z\right)\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq -3.55 \cdot 10^{-71}:\\ \;\;\;\;t \cdot \left(-18 \cdot \left(z \cdot \left(y \cdot \left(-x\right)\right)\right) - a \cdot 4\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;x \leq -1.45 \cdot 10^{-191}:\\ \;\;\;\;\left(b \cdot c + \left(t \cdot a\right) \cdot -4\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;x \leq 6.9 \cdot 10^{-56}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 59.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ t_2 := b \cdot c + \left(t \cdot a\right) \cdot -4\\ t_3 := t \cdot \left(a \cdot -4\right) - t_1\\ t_4 := x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) + i \cdot -4\right)\\ \mathbf{if}\;x \leq -6.8 \cdot 10^{+61}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq -0.22:\\ \;\;\;\;b \cdot c - t_1\\ \mathbf{elif}\;x \leq -5.2 \cdot 10^{-17}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq -2.7 \cdot 10^{-71}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{-279}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-127}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-26}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k))
        (t_2 (+ (* b c) (* (* t a) -4.0)))
        (t_3 (- (* t (* a -4.0)) t_1))
        (t_4 (* x (+ (* 18.0 (* z (* y t))) (* i -4.0)))))
   (if (<= x -6.8e+61)
     t_4
     (if (<= x -0.22)
       (- (* b c) t_1)
       (if (<= x -5.2e-17)
         t_4
         (if (<= x -2.7e-71)
           t_3
           (if (<= x 6.8e-279)
             t_2
             (if (<= x 1.3e-127) t_3 (if (<= x 1.15e-26) t_2 t_4)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double t_2 = (b * c) + ((t * a) * -4.0);
	double t_3 = (t * (a * -4.0)) - t_1;
	double t_4 = x * ((18.0 * (z * (y * t))) + (i * -4.0));
	double tmp;
	if (x <= -6.8e+61) {
		tmp = t_4;
	} else if (x <= -0.22) {
		tmp = (b * c) - t_1;
	} else if (x <= -5.2e-17) {
		tmp = t_4;
	} else if (x <= -2.7e-71) {
		tmp = t_3;
	} else if (x <= 6.8e-279) {
		tmp = t_2;
	} else if (x <= 1.3e-127) {
		tmp = t_3;
	} else if (x <= 1.15e-26) {
		tmp = t_2;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = (j * 27.0d0) * k
    t_2 = (b * c) + ((t * a) * (-4.0d0))
    t_3 = (t * (a * (-4.0d0))) - t_1
    t_4 = x * ((18.0d0 * (z * (y * t))) + (i * (-4.0d0)))
    if (x <= (-6.8d+61)) then
        tmp = t_4
    else if (x <= (-0.22d0)) then
        tmp = (b * c) - t_1
    else if (x <= (-5.2d-17)) then
        tmp = t_4
    else if (x <= (-2.7d-71)) then
        tmp = t_3
    else if (x <= 6.8d-279) then
        tmp = t_2
    else if (x <= 1.3d-127) then
        tmp = t_3
    else if (x <= 1.15d-26) then
        tmp = t_2
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double t_2 = (b * c) + ((t * a) * -4.0);
	double t_3 = (t * (a * -4.0)) - t_1;
	double t_4 = x * ((18.0 * (z * (y * t))) + (i * -4.0));
	double tmp;
	if (x <= -6.8e+61) {
		tmp = t_4;
	} else if (x <= -0.22) {
		tmp = (b * c) - t_1;
	} else if (x <= -5.2e-17) {
		tmp = t_4;
	} else if (x <= -2.7e-71) {
		tmp = t_3;
	} else if (x <= 6.8e-279) {
		tmp = t_2;
	} else if (x <= 1.3e-127) {
		tmp = t_3;
	} else if (x <= 1.15e-26) {
		tmp = t_2;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	t_2 = (b * c) + ((t * a) * -4.0)
	t_3 = (t * (a * -4.0)) - t_1
	t_4 = x * ((18.0 * (z * (y * t))) + (i * -4.0))
	tmp = 0
	if x <= -6.8e+61:
		tmp = t_4
	elif x <= -0.22:
		tmp = (b * c) - t_1
	elif x <= -5.2e-17:
		tmp = t_4
	elif x <= -2.7e-71:
		tmp = t_3
	elif x <= 6.8e-279:
		tmp = t_2
	elif x <= 1.3e-127:
		tmp = t_3
	elif x <= 1.15e-26:
		tmp = t_2
	else:
		tmp = t_4
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	t_2 = Float64(Float64(b * c) + Float64(Float64(t * a) * -4.0))
	t_3 = Float64(Float64(t * Float64(a * -4.0)) - t_1)
	t_4 = Float64(x * Float64(Float64(18.0 * Float64(z * Float64(y * t))) + Float64(i * -4.0)))
	tmp = 0.0
	if (x <= -6.8e+61)
		tmp = t_4;
	elseif (x <= -0.22)
		tmp = Float64(Float64(b * c) - t_1);
	elseif (x <= -5.2e-17)
		tmp = t_4;
	elseif (x <= -2.7e-71)
		tmp = t_3;
	elseif (x <= 6.8e-279)
		tmp = t_2;
	elseif (x <= 1.3e-127)
		tmp = t_3;
	elseif (x <= 1.15e-26)
		tmp = t_2;
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * 27.0) * k;
	t_2 = (b * c) + ((t * a) * -4.0);
	t_3 = (t * (a * -4.0)) - t_1;
	t_4 = x * ((18.0 * (z * (y * t))) + (i * -4.0));
	tmp = 0.0;
	if (x <= -6.8e+61)
		tmp = t_4;
	elseif (x <= -0.22)
		tmp = (b * c) - t_1;
	elseif (x <= -5.2e-17)
		tmp = t_4;
	elseif (x <= -2.7e-71)
		tmp = t_3;
	elseif (x <= 6.8e-279)
		tmp = t_2;
	elseif (x <= 1.3e-127)
		tmp = t_3;
	elseif (x <= 1.15e-26)
		tmp = t_2;
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] + N[(N[(t * a), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]}, Block[{t$95$4 = N[(x * N[(N[(18.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6.8e+61], t$95$4, If[LessEqual[x, -0.22], N[(N[(b * c), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[x, -5.2e-17], t$95$4, If[LessEqual[x, -2.7e-71], t$95$3, If[LessEqual[x, 6.8e-279], t$95$2, If[LessEqual[x, 1.3e-127], t$95$3, If[LessEqual[x, 1.15e-26], t$95$2, t$95$4]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -6.80000000000000051e61 or -0.220000000000000001 < x < -5.20000000000000006e-17 or 1.15000000000000004e-26 < x

   1. Initial program 76.0%

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

   3. Simplified 87.6%

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

   5. Taylor expanded in x around inf 71.4%

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

      1. cancel-sign-sub-inv 71.4%

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

      2. associate-*r* 72.9%

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

      3. metadata-eval 72.9%

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

   7. Applied egg-rr 72.9%

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

   if -6.80000000000000051e61 < x < -0.220000000000000001

   1. Initial program 80.0%

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

   3. Taylor expanded in x around 0 80.0%

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

   4. Taylor expanded in b around inf 80.3%

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

   if -5.20000000000000006e-17 < x < -2.7000000000000001e-71 or 6.8000000000000003e-279 < x < 1.29999999999999995e-127

   1. Initial program 93.1%

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

   3. Taylor expanded in x around 0 80.0%

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

   4. Taylor expanded in a around inf 69.2%

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

      1. *-commutative 69.2%

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

      2. *-commutative 69.2%

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

      3. associate-*l* 69.2%

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

      4. *-commutative 69.2%

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

   6. Simplified 69.2%

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

   if -2.7000000000000001e-71 < x < 6.8000000000000003e-279 or 1.29999999999999995e-127 < x < 1.15000000000000004e-26

   1. Initial program 91.5%

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

   3. Simplified 89.2%

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

   5. Taylor expanded in j around 0 78.8%

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

   6. Taylor expanded in x around 0 73.7%

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

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{+61}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) + i \cdot -4\right)\\ \mathbf{elif}\;x \leq -0.22:\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;x \leq -5.2 \cdot 10^{-17}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) + i \cdot -4\right)\\ \mathbf{elif}\;x \leq -2.7 \cdot 10^{-71}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{-279}:\\ \;\;\;\;b \cdot c + \left(t \cdot a\right) \cdot -4\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-127}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-26}:\\ \;\;\;\;b \cdot c + \left(t \cdot a\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) + i \cdot -4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 59.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ t_2 := b \cdot c + \left(t \cdot a\right) \cdot -4\\ t_3 := t \cdot \left(a \cdot -4\right) - t_1\\ t_4 := x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) + i \cdot -4\right)\\ \mathbf{if}\;x \leq -1.3 \cdot 10^{+59}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq -0.024:\\ \;\;\;\;b \cdot c - t_1\\ \mathbf{elif}\;x \leq -3.4 \cdot 10^{-9}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq -2.9 \cdot 10^{-71}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-278}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{-126}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 3.65 \cdot 10^{-23}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k))
        (t_2 (+ (* b c) (* (* t a) -4.0)))
        (t_3 (- (* t (* a -4.0)) t_1))
        (t_4 (* x (+ (* 18.0 (* z (* y t))) (* i -4.0)))))
   (if (<= x -1.3e+59)
     t_4
     (if (<= x -0.024)
       (- (* b c) t_1)
       (if (<= x -3.4e-9)
         t_4
         (if (<= x -2.9e-71)
           t_3
           (if (<= x 1.1e-278)
             t_2
             (if (<= x 9.2e-126)
               t_3
               (if (<= x 3.65e-23)
                 t_2
                 (* x (- (* 18.0 (* t (* y z))) (* 4.0 i))))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double t_2 = (b * c) + ((t * a) * -4.0);
	double t_3 = (t * (a * -4.0)) - t_1;
	double t_4 = x * ((18.0 * (z * (y * t))) + (i * -4.0));
	double tmp;
	if (x <= -1.3e+59) {
		tmp = t_4;
	} else if (x <= -0.024) {
		tmp = (b * c) - t_1;
	} else if (x <= -3.4e-9) {
		tmp = t_4;
	} else if (x <= -2.9e-71) {
		tmp = t_3;
	} else if (x <= 1.1e-278) {
		tmp = t_2;
	} else if (x <= 9.2e-126) {
		tmp = t_3;
	} else if (x <= 3.65e-23) {
		tmp = t_2;
	} else {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 = (j * 27.0d0) * k
    t_2 = (b * c) + ((t * a) * (-4.0d0))
    t_3 = (t * (a * (-4.0d0))) - t_1
    t_4 = x * ((18.0d0 * (z * (y * t))) + (i * (-4.0d0)))
    if (x <= (-1.3d+59)) then
        tmp = t_4
    else if (x <= (-0.024d0)) then
        tmp = (b * c) - t_1
    else if (x <= (-3.4d-9)) then
        tmp = t_4
    else if (x <= (-2.9d-71)) then
        tmp = t_3
    else if (x <= 1.1d-278) then
        tmp = t_2
    else if (x <= 9.2d-126) then
        tmp = t_3
    else if (x <= 3.65d-23) then
        tmp = t_2
    else
        tmp = x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double t_2 = (b * c) + ((t * a) * -4.0);
	double t_3 = (t * (a * -4.0)) - t_1;
	double t_4 = x * ((18.0 * (z * (y * t))) + (i * -4.0));
	double tmp;
	if (x <= -1.3e+59) {
		tmp = t_4;
	} else if (x <= -0.024) {
		tmp = (b * c) - t_1;
	} else if (x <= -3.4e-9) {
		tmp = t_4;
	} else if (x <= -2.9e-71) {
		tmp = t_3;
	} else if (x <= 1.1e-278) {
		tmp = t_2;
	} else if (x <= 9.2e-126) {
		tmp = t_3;
	} else if (x <= 3.65e-23) {
		tmp = t_2;
	} else {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	t_2 = (b * c) + ((t * a) * -4.0)
	t_3 = (t * (a * -4.0)) - t_1
	t_4 = x * ((18.0 * (z * (y * t))) + (i * -4.0))
	tmp = 0
	if x <= -1.3e+59:
		tmp = t_4
	elif x <= -0.024:
		tmp = (b * c) - t_1
	elif x <= -3.4e-9:
		tmp = t_4
	elif x <= -2.9e-71:
		tmp = t_3
	elif x <= 1.1e-278:
		tmp = t_2
	elif x <= 9.2e-126:
		tmp = t_3
	elif x <= 3.65e-23:
		tmp = t_2
	else:
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	t_2 = Float64(Float64(b * c) + Float64(Float64(t * a) * -4.0))
	t_3 = Float64(Float64(t * Float64(a * -4.0)) - t_1)
	t_4 = Float64(x * Float64(Float64(18.0 * Float64(z * Float64(y * t))) + Float64(i * -4.0)))
	tmp = 0.0
	if (x <= -1.3e+59)
		tmp = t_4;
	elseif (x <= -0.024)
		tmp = Float64(Float64(b * c) - t_1);
	elseif (x <= -3.4e-9)
		tmp = t_4;
	elseif (x <= -2.9e-71)
		tmp = t_3;
	elseif (x <= 1.1e-278)
		tmp = t_2;
	elseif (x <= 9.2e-126)
		tmp = t_3;
	elseif (x <= 3.65e-23)
		tmp = t_2;
	else
		tmp = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * 27.0) * k;
	t_2 = (b * c) + ((t * a) * -4.0);
	t_3 = (t * (a * -4.0)) - t_1;
	t_4 = x * ((18.0 * (z * (y * t))) + (i * -4.0));
	tmp = 0.0;
	if (x <= -1.3e+59)
		tmp = t_4;
	elseif (x <= -0.024)
		tmp = (b * c) - t_1;
	elseif (x <= -3.4e-9)
		tmp = t_4;
	elseif (x <= -2.9e-71)
		tmp = t_3;
	elseif (x <= 1.1e-278)
		tmp = t_2;
	elseif (x <= 9.2e-126)
		tmp = t_3;
	elseif (x <= 3.65e-23)
		tmp = t_2;
	else
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] + N[(N[(t * a), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]}, Block[{t$95$4 = N[(x * N[(N[(18.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.3e+59], t$95$4, If[LessEqual[x, -0.024], N[(N[(b * c), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[x, -3.4e-9], t$95$4, If[LessEqual[x, -2.9e-71], t$95$3, If[LessEqual[x, 1.1e-278], t$95$2, If[LessEqual[x, 9.2e-126], t$95$3, If[LessEqual[x, 3.65e-23], t$95$2, N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -1.3e59 or -0.024 < x < -3.3999999999999998e-9

   1. Initial program 71.1%

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

   3. Simplified 85.4%

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

   5. Taylor expanded in x around inf 73.3%

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

      1. cancel-sign-sub-inv 73.3%

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

      2. associate-*r* 76.4%

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

      3. metadata-eval 76.4%

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

   7. Applied egg-rr 76.4%

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

   if -1.3e59 < x < -0.024

   1. Initial program 80.0%

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

   3. Taylor expanded in x around 0 80.0%

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

   4. Taylor expanded in b around inf 80.3%

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

   if -3.3999999999999998e-9 < x < -2.8999999999999999e-71 or 1.1e-278 < x < 9.20000000000000043e-126

   1. Initial program 93.1%

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

   3. Taylor expanded in x around 0 80.0%

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

   4. Taylor expanded in a around inf 69.2%

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

      1. *-commutative 69.2%

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

      2. *-commutative 69.2%

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

      3. associate-*l* 69.2%

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

      4. *-commutative 69.2%

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

   6. Simplified 69.2%

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

   if -2.8999999999999999e-71 < x < 1.1e-278 or 9.20000000000000043e-126 < x < 3.65000000000000002e-23

   1. Initial program 91.5%

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

   3. Simplified 89.2%

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

   5. Taylor expanded in j around 0 78.8%

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

   6. Taylor expanded in x around 0 73.7%

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

   if 3.65000000000000002e-23 < x

   1. Initial program 81.2%

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

   3. Simplified 89.8%

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

   5. Taylor expanded in x around inf 69.3%

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

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{+59}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) + i \cdot -4\right)\\ \mathbf{elif}\;x \leq -0.024:\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;x \leq -3.4 \cdot 10^{-9}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) + i \cdot -4\right)\\ \mathbf{elif}\;x \leq -2.9 \cdot 10^{-71}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-278}:\\ \;\;\;\;b \cdot c + \left(t \cdot a\right) \cdot -4\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{-126}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;x \leq 3.65 \cdot 10^{-23}:\\ \;\;\;\;b \cdot c + \left(t \cdot a\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 72.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ t_2 := 4 \cdot \left(x \cdot i\right)\\ t_3 := x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) + i \cdot -4\right)\\ \mathbf{if}\;x \leq -3.7 \cdot 10^{+78}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -6.5:\\ \;\;\;\;b \cdot c - \left(t_2 + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{elif}\;x \leq -1.42 \cdot 10^{-8}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-63}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 960:\\ \;\;\;\;\left(b \cdot c + \left(t \cdot a\right) \cdot -4\right) - t_2\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{+17}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (- (- (* b c) (* 4.0 (* t a))) (* (* j 27.0) k)))
        (t_2 (* 4.0 (* x i)))
        (t_3 (* x (+ (* 18.0 (* z (* y t))) (* i -4.0)))))
   (if (<= x -3.7e+78)
     t_3
     (if (<= x -6.5)
       (- (* b c) (+ t_2 (* 27.0 (* j k))))
       (if (<= x -1.42e-8)
         t_3
         (if (<= x 7.5e-63)
           t_1
           (if (<= x 960.0)
             (- (+ (* b c) (* (* t a) -4.0)) t_2)
             (if (<= x 3.1e+17)
               t_1
               (* x (- (* 18.0 (* t (* y z))) (* 4.0 i)))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k);
	double t_2 = 4.0 * (x * i);
	double t_3 = x * ((18.0 * (z * (y * t))) + (i * -4.0));
	double tmp;
	if (x <= -3.7e+78) {
		tmp = t_3;
	} else if (x <= -6.5) {
		tmp = (b * c) - (t_2 + (27.0 * (j * k)));
	} else if (x <= -1.42e-8) {
		tmp = t_3;
	} else if (x <= 7.5e-63) {
		tmp = t_1;
	} else if (x <= 960.0) {
		tmp = ((b * c) + ((t * a) * -4.0)) - t_2;
	} else if (x <= 3.1e+17) {
		tmp = t_1;
	} else {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 = ((b * c) - (4.0d0 * (t * a))) - ((j * 27.0d0) * k)
    t_2 = 4.0d0 * (x * i)
    t_3 = x * ((18.0d0 * (z * (y * t))) + (i * (-4.0d0)))
    if (x <= (-3.7d+78)) then
        tmp = t_3
    else if (x <= (-6.5d0)) then
        tmp = (b * c) - (t_2 + (27.0d0 * (j * k)))
    else if (x <= (-1.42d-8)) then
        tmp = t_3
    else if (x <= 7.5d-63) then
        tmp = t_1
    else if (x <= 960.0d0) then
        tmp = ((b * c) + ((t * a) * (-4.0d0))) - t_2
    else if (x <= 3.1d+17) then
        tmp = t_1
    else
        tmp = x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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))) - ((j * 27.0) * k);
	double t_2 = 4.0 * (x * i);
	double t_3 = x * ((18.0 * (z * (y * t))) + (i * -4.0));
	double tmp;
	if (x <= -3.7e+78) {
		tmp = t_3;
	} else if (x <= -6.5) {
		tmp = (b * c) - (t_2 + (27.0 * (j * k)));
	} else if (x <= -1.42e-8) {
		tmp = t_3;
	} else if (x <= 7.5e-63) {
		tmp = t_1;
	} else if (x <= 960.0) {
		tmp = ((b * c) + ((t * a) * -4.0)) - t_2;
	} else if (x <= 3.1e+17) {
		tmp = t_1;
	} else {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k)
	t_2 = 4.0 * (x * i)
	t_3 = x * ((18.0 * (z * (y * t))) + (i * -4.0))
	tmp = 0
	if x <= -3.7e+78:
		tmp = t_3
	elif x <= -6.5:
		tmp = (b * c) - (t_2 + (27.0 * (j * k)))
	elif x <= -1.42e-8:
		tmp = t_3
	elif x <= 7.5e-63:
		tmp = t_1
	elif x <= 960.0:
		tmp = ((b * c) + ((t * a) * -4.0)) - t_2
	elif x <= 3.1e+17:
		tmp = t_1
	else:
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(t * a))) - Float64(Float64(j * 27.0) * k))
	t_2 = Float64(4.0 * Float64(x * i))
	t_3 = Float64(x * Float64(Float64(18.0 * Float64(z * Float64(y * t))) + Float64(i * -4.0)))
	tmp = 0.0
	if (x <= -3.7e+78)
		tmp = t_3;
	elseif (x <= -6.5)
		tmp = Float64(Float64(b * c) - Float64(t_2 + Float64(27.0 * Float64(j * k))));
	elseif (x <= -1.42e-8)
		tmp = t_3;
	elseif (x <= 7.5e-63)
		tmp = t_1;
	elseif (x <= 960.0)
		tmp = Float64(Float64(Float64(b * c) + Float64(Float64(t * a) * -4.0)) - t_2);
	elseif (x <= 3.1e+17)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k);
	t_2 = 4.0 * (x * i);
	t_3 = x * ((18.0 * (z * (y * t))) + (i * -4.0));
	tmp = 0.0;
	if (x <= -3.7e+78)
		tmp = t_3;
	elseif (x <= -6.5)
		tmp = (b * c) - (t_2 + (27.0 * (j * k)));
	elseif (x <= -1.42e-8)
		tmp = t_3;
	elseif (x <= 7.5e-63)
		tmp = t_1;
	elseif (x <= 960.0)
		tmp = ((b * c) + ((t * a) * -4.0)) - t_2;
	elseif (x <= 3.1e+17)
		tmp = t_1;
	else
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(N[(18.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.7e+78], t$95$3, If[LessEqual[x, -6.5], N[(N[(b * c), $MachinePrecision] - N[(t$95$2 + N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.42e-8], t$95$3, If[LessEqual[x, 7.5e-63], t$95$1, If[LessEqual[x, 960.0], N[(N[(N[(b * c), $MachinePrecision] + N[(N[(t * a), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], If[LessEqual[x, 3.1e+17], t$95$1, N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -3.69999999999999985e78 or -6.5 < x < -1.41999999999999998e-8

   1. Initial program 71.1%

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

   3. Simplified 85.4%

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

   5. Taylor expanded in x around inf 73.3%

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

      1. cancel-sign-sub-inv 73.3%

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

      2. associate-*r* 76.4%

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

      3. metadata-eval 76.4%

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

   7. Applied egg-rr 76.4%

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

   if -3.69999999999999985e78 < x < -6.5

   1. Initial program 80.0%

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

   3. Simplified 89.8%

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

   5. Taylor expanded in t around 0 90.1%

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

   if -1.41999999999999998e-8 < x < 7.5000000000000003e-63 or 960 < x < 3.1e17

   1. Initial program 92.1%

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

   3. Taylor expanded in x around 0 84.5%

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

   if 7.5000000000000003e-63 < x < 960

   1. Initial program 88.7%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in j around 0 100.0%

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

   6. Taylor expanded in y around 0 78.3%

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

   if 3.1e17 < x

   1. Initial program 79.8%

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

   3. Simplified 87.9%

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

   5. Taylor expanded in x around inf 72.3%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.7 \cdot 10^{+78}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) + i \cdot -4\right)\\ \mathbf{elif}\;x \leq -6.5:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{elif}\;x \leq -1.42 \cdot 10^{-8}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) + i \cdot -4\right)\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-63}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;x \leq 960:\\ \;\;\;\;\left(b \cdot c + \left(t \cdot a\right) \cdot -4\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{+17}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 82.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := 4 \cdot \left(t \cdot a\right)\\ t_2 := x \cdot \left(y \cdot z\right)\\ t_3 := \left(j \cdot 27\right) \cdot k\\ t_4 := 4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;t_3 \leq -4 \cdot 10^{+52}:\\ \;\;\;\;\left(b \cdot c - \left(t_1 + t_4\right)\right) - t_3\\ \mathbf{elif}\;t_3 \leq 5 \cdot 10^{+58}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot t_2 - a \cdot 4\right)\right) - t_4\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b \cdot c + 18 \cdot \left(t \cdot t_2\right)\right) - t_1\right) - t_3\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* 4.0 (* t a)))
        (t_2 (* x (* y z)))
        (t_3 (* (* j 27.0) k))
        (t_4 (* 4.0 (* x i))))
   (if (<= t_3 -4e+52)
     (- (- (* b c) (+ t_1 t_4)) t_3)
     (if (<= t_3 5e+58)
       (- (+ (* b c) (* t (- (* 18.0 t_2) (* a 4.0)))) t_4)
       (- (- (+ (* b c) (* 18.0 (* t t_2))) t_1) t_3)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 4.0 * (t * a);
	double t_2 = x * (y * z);
	double t_3 = (j * 27.0) * k;
	double t_4 = 4.0 * (x * i);
	double tmp;
	if (t_3 <= -4e+52) {
		tmp = ((b * c) - (t_1 + t_4)) - t_3;
	} else if (t_3 <= 5e+58) {
		tmp = ((b * c) + (t * ((18.0 * t_2) - (a * 4.0)))) - t_4;
	} else {
		tmp = (((b * c) + (18.0 * (t * t_2))) - t_1) - t_3;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = 4.0d0 * (t * a)
    t_2 = x * (y * z)
    t_3 = (j * 27.0d0) * k
    t_4 = 4.0d0 * (x * i)
    if (t_3 <= (-4d+52)) then
        tmp = ((b * c) - (t_1 + t_4)) - t_3
    else if (t_3 <= 5d+58) then
        tmp = ((b * c) + (t * ((18.0d0 * t_2) - (a * 4.0d0)))) - t_4
    else
        tmp = (((b * c) + (18.0d0 * (t * t_2))) - t_1) - t_3
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 4.0 * (t * a);
	double t_2 = x * (y * z);
	double t_3 = (j * 27.0) * k;
	double t_4 = 4.0 * (x * i);
	double tmp;
	if (t_3 <= -4e+52) {
		tmp = ((b * c) - (t_1 + t_4)) - t_3;
	} else if (t_3 <= 5e+58) {
		tmp = ((b * c) + (t * ((18.0 * t_2) - (a * 4.0)))) - t_4;
	} else {
		tmp = (((b * c) + (18.0 * (t * t_2))) - t_1) - t_3;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = 4.0 * (t * a)
	t_2 = x * (y * z)
	t_3 = (j * 27.0) * k
	t_4 = 4.0 * (x * i)
	tmp = 0
	if t_3 <= -4e+52:
		tmp = ((b * c) - (t_1 + t_4)) - t_3
	elif t_3 <= 5e+58:
		tmp = ((b * c) + (t * ((18.0 * t_2) - (a * 4.0)))) - t_4
	else:
		tmp = (((b * c) + (18.0 * (t * t_2))) - t_1) - t_3
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(4.0 * Float64(t * a))
	t_2 = Float64(x * Float64(y * z))
	t_3 = Float64(Float64(j * 27.0) * k)
	t_4 = Float64(4.0 * Float64(x * i))
	tmp = 0.0
	if (t_3 <= -4e+52)
		tmp = Float64(Float64(Float64(b * c) - Float64(t_1 + t_4)) - t_3);
	elseif (t_3 <= 5e+58)
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(18.0 * t_2) - Float64(a * 4.0)))) - t_4);
	else
		tmp = Float64(Float64(Float64(Float64(b * c) + Float64(18.0 * Float64(t * t_2))) - t_1) - t_3);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = 4.0 * (t * a);
	t_2 = x * (y * z);
	t_3 = (j * 27.0) * k;
	t_4 = 4.0 * (x * i);
	tmp = 0.0;
	if (t_3 <= -4e+52)
		tmp = ((b * c) - (t_1 + t_4)) - t_3;
	elseif (t_3 <= 5e+58)
		tmp = ((b * c) + (t * ((18.0 * t_2) - (a * 4.0)))) - t_4;
	else
		tmp = (((b * c) + (18.0 * (t * t_2))) - t_1) - t_3;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, Block[{t$95$4 = N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, -4e+52], N[(N[(N[(b * c), $MachinePrecision] - N[(t$95$1 + t$95$4), $MachinePrecision]), $MachinePrecision] - t$95$3), $MachinePrecision], If[LessEqual[t$95$3, 5e+58], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(18.0 * t$95$2), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$4), $MachinePrecision], N[(N[(N[(N[(b * c), $MachinePrecision] + N[(18.0 * N[(t * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] - t$95$3), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j 27) k) < -4e52

   1. Initial program 80.5%

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

   3. Taylor expanded in y around 0 81.9%

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

   if -4e52 < (*.f64 (*.f64 j 27) k) < 4.99999999999999986e58

   1. Initial program 84.1%

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

   3. Simplified 88.7%

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

   5. Taylor expanded in j around 0 89.3%

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

   if 4.99999999999999986e58 < (*.f64 (*.f64 j 27) k)

   1. Initial program 89.3%

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

   3. Taylor expanded in i around 0 89.3%

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

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \leq -4 \cdot 10^{+52}:\\ \;\;\;\;\left(b \cdot c - \left(4 \cdot \left(t \cdot a\right) + 4 \cdot \left(x \cdot i\right)\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 5 \cdot 10^{+58}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b \cdot c + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 69.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := 4 \cdot \left(x \cdot i\right)\\ t_2 := b \cdot c - \left(t_1 + 27 \cdot \left(j \cdot k\right)\right)\\ t_3 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t_3 \leq -1 \cdot 10^{+80}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_3 \leq 10^{+33}:\\ \;\;\;\;\left(b \cdot c + \left(t \cdot a\right) \cdot -4\right) - t_1\\ \mathbf{elif}\;t_3 \leq 2 \cdot 10^{+153}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* 4.0 (* x i)))
        (t_2 (- (* b c) (+ t_1 (* 27.0 (* j k)))))
        (t_3 (* (* j 27.0) k)))
   (if (<= t_3 -1e+80)
     t_2
     (if (<= t_3 1e+33)
       (- (+ (* b c) (* (* t a) -4.0)) t_1)
       (if (<= t_3 2e+153)
         (+ (* 18.0 (* t (* x (* y z)))) (* j (* k -27.0)))
         t_2)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 4.0 * (x * i);
	double t_2 = (b * c) - (t_1 + (27.0 * (j * k)));
	double t_3 = (j * 27.0) * k;
	double tmp;
	if (t_3 <= -1e+80) {
		tmp = t_2;
	} else if (t_3 <= 1e+33) {
		tmp = ((b * c) + ((t * a) * -4.0)) - t_1;
	} else if (t_3 <= 2e+153) {
		tmp = (18.0 * (t * (x * (y * z)))) + (j * (k * -27.0));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = 4.0d0 * (x * i)
    t_2 = (b * c) - (t_1 + (27.0d0 * (j * k)))
    t_3 = (j * 27.0d0) * k
    if (t_3 <= (-1d+80)) then
        tmp = t_2
    else if (t_3 <= 1d+33) then
        tmp = ((b * c) + ((t * a) * (-4.0d0))) - t_1
    else if (t_3 <= 2d+153) then
        tmp = (18.0d0 * (t * (x * (y * z)))) + (j * (k * (-27.0d0)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 4.0 * (x * i);
	double t_2 = (b * c) - (t_1 + (27.0 * (j * k)));
	double t_3 = (j * 27.0) * k;
	double tmp;
	if (t_3 <= -1e+80) {
		tmp = t_2;
	} else if (t_3 <= 1e+33) {
		tmp = ((b * c) + ((t * a) * -4.0)) - t_1;
	} else if (t_3 <= 2e+153) {
		tmp = (18.0 * (t * (x * (y * z)))) + (j * (k * -27.0));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = 4.0 * (x * i)
	t_2 = (b * c) - (t_1 + (27.0 * (j * k)))
	t_3 = (j * 27.0) * k
	tmp = 0
	if t_3 <= -1e+80:
		tmp = t_2
	elif t_3 <= 1e+33:
		tmp = ((b * c) + ((t * a) * -4.0)) - t_1
	elif t_3 <= 2e+153:
		tmp = (18.0 * (t * (x * (y * z)))) + (j * (k * -27.0))
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(4.0 * Float64(x * i))
	t_2 = Float64(Float64(b * c) - Float64(t_1 + Float64(27.0 * Float64(j * k))))
	t_3 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_3 <= -1e+80)
		tmp = t_2;
	elseif (t_3 <= 1e+33)
		tmp = Float64(Float64(Float64(b * c) + Float64(Float64(t * a) * -4.0)) - t_1);
	elseif (t_3 <= 2e+153)
		tmp = Float64(Float64(18.0 * Float64(t * Float64(x * Float64(y * z)))) + Float64(j * Float64(k * -27.0)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = 4.0 * (x * i);
	t_2 = (b * c) - (t_1 + (27.0 * (j * k)));
	t_3 = (j * 27.0) * k;
	tmp = 0.0;
	if (t_3 <= -1e+80)
		tmp = t_2;
	elseif (t_3 <= 1e+33)
		tmp = ((b * c) + ((t * a) * -4.0)) - t_1;
	elseif (t_3 <= 2e+153)
		tmp = (18.0 * (t * (x * (y * z)))) + (j * (k * -27.0));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] - N[(t$95$1 + N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$3, -1e+80], t$95$2, If[LessEqual[t$95$3, 1e+33], N[(N[(N[(b * c), $MachinePrecision] + N[(N[(t * a), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[t$95$3, 2e+153], N[(N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j 27) k) < -1e80 or 2e153 < (*.f64 (*.f64 j 27) k)

   1. Initial program 82.1%

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

   3. Simplified 85.6%

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

   5. Taylor expanded in t around 0 78.4%

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

   if -1e80 < (*.f64 (*.f64 j 27) k) < 9.9999999999999995e32

   1. Initial program 84.7%

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

   3. Simplified 89.3%

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

   5. Taylor expanded in j around 0 88.7%

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

   6. Taylor expanded in y around 0 71.5%

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

   if 9.9999999999999995e32 < (*.f64 (*.f64 j 27) k) < 2e153

   1. Initial program 87.7%

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

   3. Simplified 91.8%

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

   5. Taylor expanded in y around inf 64.3%

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

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \leq -1 \cdot 10^{+80}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 10^{+33}:\\ \;\;\;\;\left(b \cdot c + \left(t \cdot a\right) \cdot -4\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 2 \cdot 10^{+153}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 81.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := 4 \cdot \left(t \cdot a\right)\\ t_2 := \left(j \cdot 27\right) \cdot k\\ t_3 := 4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;t_2 \leq -4 \cdot 10^{+52}:\\ \;\;\;\;\left(b \cdot c - \left(t_1 + t_3\right)\right) - t_2\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+160}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\right) - t_3\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - t_1\right) - t_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* 4.0 (* t a))) (t_2 (* (* j 27.0) k)) (t_3 (* 4.0 (* x i))))
   (if (<= t_2 -4e+52)
     (- (- (* b c) (+ t_1 t_3)) t_2)
     (if (<= t_2 5e+160)
       (- (+ (* b c) (* t (- (* 18.0 (* x (* y z))) (* a 4.0)))) t_3)
       (- (- (* b c) t_1) t_2)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 4.0 * (t * a);
	double t_2 = (j * 27.0) * k;
	double t_3 = 4.0 * (x * i);
	double tmp;
	if (t_2 <= -4e+52) {
		tmp = ((b * c) - (t_1 + t_3)) - t_2;
	} else if (t_2 <= 5e+160) {
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - t_3;
	} else {
		tmp = ((b * c) - t_1) - t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 * (t * a)
    t_2 = (j * 27.0d0) * k
    t_3 = 4.0d0 * (x * i)
    if (t_2 <= (-4d+52)) then
        tmp = ((b * c) - (t_1 + t_3)) - t_2
    else if (t_2 <= 5d+160) then
        tmp = ((b * c) + (t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0)))) - t_3
    else
        tmp = ((b * c) - t_1) - t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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 = (j * 27.0) * k;
	double t_3 = 4.0 * (x * i);
	double tmp;
	if (t_2 <= -4e+52) {
		tmp = ((b * c) - (t_1 + t_3)) - t_2;
	} else if (t_2 <= 5e+160) {
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - t_3;
	} else {
		tmp = ((b * c) - t_1) - t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = 4.0 * (t * a)
	t_2 = (j * 27.0) * k
	t_3 = 4.0 * (x * i)
	tmp = 0
	if t_2 <= -4e+52:
		tmp = ((b * c) - (t_1 + t_3)) - t_2
	elif t_2 <= 5e+160:
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - t_3
	else:
		tmp = ((b * c) - t_1) - t_2
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(4.0 * Float64(t * a))
	t_2 = Float64(Float64(j * 27.0) * k)
	t_3 = Float64(4.0 * Float64(x * i))
	tmp = 0.0
	if (t_2 <= -4e+52)
		tmp = Float64(Float64(Float64(b * c) - Float64(t_1 + t_3)) - t_2);
	elseif (t_2 <= 5e+160)
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)))) - t_3);
	else
		tmp = Float64(Float64(Float64(b * c) - t_1) - t_2);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = 4.0 * (t * a);
	t_2 = (j * 27.0) * k;
	t_3 = 4.0 * (x * i);
	tmp = 0.0;
	if (t_2 <= -4e+52)
		tmp = ((b * c) - (t_1 + t_3)) - t_2;
	elseif (t_2 <= 5e+160)
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - t_3;
	else
		tmp = ((b * c) - t_1) - t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, Block[{t$95$3 = N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -4e+52], N[(N[(N[(b * c), $MachinePrecision] - N[(t$95$1 + t$95$3), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], If[LessEqual[t$95$2, 5e+160], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$3), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] - t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j 27) k) < -4e52

   1. Initial program 80.5%

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

   3. Taylor expanded in y around 0 81.9%

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

   if -4e52 < (*.f64 (*.f64 j 27) k) < 5.0000000000000002e160

   1. Initial program 85.0%

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

   3. Simplified 89.2%

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

   5. Taylor expanded in j around 0 86.8%

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

   if 5.0000000000000002e160 < (*.f64 (*.f64 j 27) k)

   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. Taylor expanded in x around 0 87.3%

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

4. Final simplification 85.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \leq -4 \cdot 10^{+52}:\\ \;\;\;\;\left(b \cdot c - \left(4 \cdot \left(t \cdot a\right) + 4 \cdot \left(x \cdot i\right)\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 5 \cdot 10^{+160}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 53.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t_2 \leq -5 \cdot 10^{+176}:\\ \;\;\;\;t_1 + \left(x \cdot i\right) \cdot -4\\ \mathbf{elif}\;t_2 \leq 10^{-322}:\\ \;\;\;\;b \cdot c + \left(t \cdot a\right) \cdot -4\\ \mathbf{elif}\;t_2 \leq 10^{+131}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + t_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0))) (t_2 (* (* j 27.0) k)))
   (if (<= t_2 -5e+176)
     (+ t_1 (* (* x i) -4.0))
     (if (<= t_2 1e-322)
       (+ (* b c) (* (* t a) -4.0))
       (if (<= t_2 1e+131)
         (* t (- (* 18.0 (* x (* y z))) (* a 4.0)))
         (+ (* b c) t_1))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = (j * 27.0) * k;
	double tmp;
	if (t_2 <= -5e+176) {
		tmp = t_1 + ((x * i) * -4.0);
	} else if (t_2 <= 1e-322) {
		tmp = (b * c) + ((t * a) * -4.0);
	} else if (t_2 <= 1e+131) {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	} else {
		tmp = (b * c) + t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * (k * (-27.0d0))
    t_2 = (j * 27.0d0) * k
    if (t_2 <= (-5d+176)) then
        tmp = t_1 + ((x * i) * (-4.0d0))
    else if (t_2 <= 1d-322) then
        tmp = (b * c) + ((t * a) * (-4.0d0))
    else if (t_2 <= 1d+131) then
        tmp = t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0))
    else
        tmp = (b * c) + t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = (j * 27.0) * k;
	double tmp;
	if (t_2 <= -5e+176) {
		tmp = t_1 + ((x * i) * -4.0);
	} else if (t_2 <= 1e-322) {
		tmp = (b * c) + ((t * a) * -4.0);
	} else if (t_2 <= 1e+131) {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	} else {
		tmp = (b * c) + t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	t_2 = (j * 27.0) * k
	tmp = 0
	if t_2 <= -5e+176:
		tmp = t_1 + ((x * i) * -4.0)
	elif t_2 <= 1e-322:
		tmp = (b * c) + ((t * a) * -4.0)
	elif t_2 <= 1e+131:
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0))
	else:
		tmp = (b * c) + t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * -27.0))
	t_2 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_2 <= -5e+176)
		tmp = Float64(t_1 + Float64(Float64(x * i) * -4.0));
	elseif (t_2 <= 1e-322)
		tmp = Float64(Float64(b * c) + Float64(Float64(t * a) * -4.0));
	elseif (t_2 <= 1e+131)
		tmp = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)));
	else
		tmp = Float64(Float64(b * c) + t_1);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * -27.0);
	t_2 = (j * 27.0) * k;
	tmp = 0.0;
	if (t_2 <= -5e+176)
		tmp = t_1 + ((x * i) * -4.0);
	elseif (t_2 <= 1e-322)
		tmp = (b * c) + ((t * a) * -4.0);
	elseif (t_2 <= 1e+131)
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	else
		tmp = (b * c) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+176], N[(t$95$1 + N[(N[(x * i), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e-322], N[(N[(b * c), $MachinePrecision] + N[(N[(t * a), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+131], N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 j 27) k) < -5e176

   1. Initial program 76.8%

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

   3. Simplified 79.5%

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

   5. Taylor expanded in i around inf 77.2%

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

   if -5e176 < (*.f64 (*.f64 j 27) k) < 9.88131e-323

   1. Initial program 84.1%

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

   3. Simplified 88.8%

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

   5. Taylor expanded in j around 0 84.6%

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

   6. Taylor expanded in x around 0 55.4%

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

   if 9.88131e-323 < (*.f64 (*.f64 j 27) k) < 9.9999999999999991e130

   1. Initial program 86.8%

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

   3. Simplified 93.4%

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

   5. Taylor expanded in t around inf 60.3%

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

   if 9.9999999999999991e130 < (*.f64 (*.f64 j 27) k)

   1. Initial program 88.0%

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

   3. Simplified 88.0%

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

   5. Taylor expanded in b around inf 79.6%

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

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \leq -5 \cdot 10^{+176}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + \left(x \cdot i\right) \cdot -4\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 10^{-322}:\\ \;\;\;\;b \cdot c + \left(t \cdot a\right) \cdot -4\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 10^{+131}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 49.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c + \left(t \cdot a\right) \cdot -4\\ t_2 := b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;j \leq -2.6 \cdot 10^{+172}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -1.7 \cdot 10^{+146}:\\ \;\;\;\;x \cdot \left(z \cdot \left(18 \cdot \left(y \cdot t\right)\right)\right)\\ \mathbf{elif}\;j \leq -9.2 \cdot 10^{+94}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -1.36 \cdot 10^{-219}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -5.8 \cdot 10^{-266}:\\ \;\;\;\;\left(t \cdot \left(18 \cdot y\right)\right) \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq 3.4 \cdot 10^{-90}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (+ (* b c) (* (* t a) -4.0))) (t_2 (+ (* b c) (* j (* k -27.0)))))
   (if (<= j -2.6e+172)
     t_2
     (if (<= j -1.7e+146)
       (* x (* z (* 18.0 (* y t))))
       (if (<= j -9.2e+94)
         t_2
         (if (<= j -1.36e-219)
           t_1
           (if (<= j -5.8e-266)
             (* (* t (* 18.0 y)) (* x z))
             (if (<= j 3.4e-90) t_1 t_2))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) + ((t * a) * -4.0);
	double t_2 = (b * c) + (j * (k * -27.0));
	double tmp;
	if (j <= -2.6e+172) {
		tmp = t_2;
	} else if (j <= -1.7e+146) {
		tmp = x * (z * (18.0 * (y * t)));
	} else if (j <= -9.2e+94) {
		tmp = t_2;
	} else if (j <= -1.36e-219) {
		tmp = t_1;
	} else if (j <= -5.8e-266) {
		tmp = (t * (18.0 * y)) * (x * z);
	} else if (j <= 3.4e-90) {
		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.
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) + ((t * a) * (-4.0d0))
    t_2 = (b * c) + (j * (k * (-27.0d0)))
    if (j <= (-2.6d+172)) then
        tmp = t_2
    else if (j <= (-1.7d+146)) then
        tmp = x * (z * (18.0d0 * (y * t)))
    else if (j <= (-9.2d+94)) then
        tmp = t_2
    else if (j <= (-1.36d-219)) then
        tmp = t_1
    else if (j <= (-5.8d-266)) then
        tmp = (t * (18.0d0 * y)) * (x * z)
    else if (j <= 3.4d-90) 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;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) + ((t * a) * -4.0);
	double t_2 = (b * c) + (j * (k * -27.0));
	double tmp;
	if (j <= -2.6e+172) {
		tmp = t_2;
	} else if (j <= -1.7e+146) {
		tmp = x * (z * (18.0 * (y * t)));
	} else if (j <= -9.2e+94) {
		tmp = t_2;
	} else if (j <= -1.36e-219) {
		tmp = t_1;
	} else if (j <= -5.8e-266) {
		tmp = (t * (18.0 * y)) * (x * z);
	} else if (j <= 3.4e-90) {
		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])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) + ((t * a) * -4.0)
	t_2 = (b * c) + (j * (k * -27.0))
	tmp = 0
	if j <= -2.6e+172:
		tmp = t_2
	elif j <= -1.7e+146:
		tmp = x * (z * (18.0 * (y * t)))
	elif j <= -9.2e+94:
		tmp = t_2
	elif j <= -1.36e-219:
		tmp = t_1
	elif j <= -5.8e-266:
		tmp = (t * (18.0 * y)) * (x * z)
	elif j <= 3.4e-90:
		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])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) + Float64(Float64(t * a) * -4.0))
	t_2 = Float64(Float64(b * c) + Float64(j * Float64(k * -27.0)))
	tmp = 0.0
	if (j <= -2.6e+172)
		tmp = t_2;
	elseif (j <= -1.7e+146)
		tmp = Float64(x * Float64(z * Float64(18.0 * Float64(y * t))));
	elseif (j <= -9.2e+94)
		tmp = t_2;
	elseif (j <= -1.36e-219)
		tmp = t_1;
	elseif (j <= -5.8e-266)
		tmp = Float64(Float64(t * Float64(18.0 * y)) * Float64(x * z));
	elseif (j <= 3.4e-90)
		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])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) + ((t * a) * -4.0);
	t_2 = (b * c) + (j * (k * -27.0));
	tmp = 0.0;
	if (j <= -2.6e+172)
		tmp = t_2;
	elseif (j <= -1.7e+146)
		tmp = x * (z * (18.0 * (y * t)));
	elseif (j <= -9.2e+94)
		tmp = t_2;
	elseif (j <= -1.36e-219)
		tmp = t_1;
	elseif (j <= -5.8e-266)
		tmp = (t * (18.0 * y)) * (x * z);
	elseif (j <= 3.4e-90)
		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.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] + N[(N[(t * a), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -2.6e+172], t$95$2, If[LessEqual[j, -1.7e+146], N[(x * N[(z * N[(18.0 * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -9.2e+94], t$95$2, If[LessEqual[j, -1.36e-219], t$95$1, If[LessEqual[j, -5.8e-266], N[(N[(t * N[(18.0 * y), $MachinePrecision]), $MachinePrecision] * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.4e-90], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -2.6e172 or -1.69999999999999995e146 < j < -9.1999999999999999e94 or 3.39999999999999994e-90 < j

   1. Initial program 83.0%

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

   3. Simplified 88.8%

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

   5. Taylor expanded in b around inf 53.8%

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

   if -2.6e172 < j < -1.69999999999999995e146

   1. Initial program 75.0%

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

   3. Simplified 75.0%

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

   5. Taylor expanded in x around inf 75.7%

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

   6. Taylor expanded in t around inf 75.7%

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

      1. associate-*r* 75.7%

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

      2. associate-*r* 75.7%

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

      3. *-commutative 75.7%

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

   8. Simplified 75.7%

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

   if -9.1999999999999999e94 < j < -1.35999999999999997e-219 or -5.79999999999999991e-266 < j < 3.39999999999999994e-90

   1. Initial program 86.6%

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

   3. Simplified 89.8%

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

   5. Taylor expanded in j around 0 82.7%

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

   6. Taylor expanded in x around 0 51.6%

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

   if -1.35999999999999997e-219 < j < -5.79999999999999991e-266

   1. Initial program 68.0%

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

   3. Taylor expanded in x around 0 68.0%

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

   4. Taylor expanded in a around 0 57.1%

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

   5. Taylor expanded in t around inf 35.6%

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

      1. associate-*r* 35.6%

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

      2. *-commutative 35.6%

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

      3. associate-*l* 46.3%

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

      4. associate-*l* 56.7%

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

      5. associate-*r* 56.5%

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

      6. *-commutative 56.5%

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

      7. associate-*l* 56.5%

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

   7. Simplified 56.5%

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

4. Final simplification 53.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.6 \cdot 10^{+172}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;j \leq -1.7 \cdot 10^{+146}:\\ \;\;\;\;x \cdot \left(z \cdot \left(18 \cdot \left(y \cdot t\right)\right)\right)\\ \mathbf{elif}\;j \leq -9.2 \cdot 10^{+94}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;j \leq -1.36 \cdot 10^{-219}:\\ \;\;\;\;b \cdot c + \left(t \cdot a\right) \cdot -4\\ \mathbf{elif}\;j \leq -5.8 \cdot 10^{-266}:\\ \;\;\;\;\left(t \cdot \left(18 \cdot y\right)\right) \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq 3.4 \cdot 10^{-90}:\\ \;\;\;\;b \cdot c + \left(t \cdot a\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 50.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;j \leq -2 \cdot 10^{+172}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -3.05 \cdot 10^{+144}:\\ \;\;\;\;x \cdot \left(z \cdot \left(18 \cdot \left(y \cdot t\right)\right)\right)\\ \mathbf{elif}\;j \leq -8.8 \cdot 10^{+95}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -1.35 \cdot 10^{-224}:\\ \;\;\;\;b \cdot c + \left(t \cdot a\right) \cdot -4\\ \mathbf{elif}\;j \leq -3.7 \cdot 10^{-242}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;j \leq 1.7 \cdot 10^{-88}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (+ (* b c) (* j (* k -27.0)))))
   (if (<= j -2e+172)
     t_1
     (if (<= j -3.05e+144)
       (* x (* z (* 18.0 (* y t))))
       (if (<= j -8.8e+95)
         t_1
         (if (<= j -1.35e-224)
           (+ (* b c) (* (* t a) -4.0))
           (if (<= j -3.7e-242)
             (* 18.0 (* t (* x (* y z))))
             (if (<= j 1.7e-88) (- (* b c) (* 4.0 (* x i))) t_1))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) + (j * (k * -27.0));
	double tmp;
	if (j <= -2e+172) {
		tmp = t_1;
	} else if (j <= -3.05e+144) {
		tmp = x * (z * (18.0 * (y * t)));
	} else if (j <= -8.8e+95) {
		tmp = t_1;
	} else if (j <= -1.35e-224) {
		tmp = (b * c) + ((t * a) * -4.0);
	} else if (j <= -3.7e-242) {
		tmp = 18.0 * (t * (x * (y * z)));
	} else if (j <= 1.7e-88) {
		tmp = (b * c) - (4.0 * (x * i));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b * c) + (j * (k * (-27.0d0)))
    if (j <= (-2d+172)) then
        tmp = t_1
    else if (j <= (-3.05d+144)) then
        tmp = x * (z * (18.0d0 * (y * t)))
    else if (j <= (-8.8d+95)) then
        tmp = t_1
    else if (j <= (-1.35d-224)) then
        tmp = (b * c) + ((t * a) * (-4.0d0))
    else if (j <= (-3.7d-242)) then
        tmp = 18.0d0 * (t * (x * (y * z)))
    else if (j <= 1.7d-88) then
        tmp = (b * c) - (4.0d0 * (x * i))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) + (j * (k * -27.0));
	double tmp;
	if (j <= -2e+172) {
		tmp = t_1;
	} else if (j <= -3.05e+144) {
		tmp = x * (z * (18.0 * (y * t)));
	} else if (j <= -8.8e+95) {
		tmp = t_1;
	} else if (j <= -1.35e-224) {
		tmp = (b * c) + ((t * a) * -4.0);
	} else if (j <= -3.7e-242) {
		tmp = 18.0 * (t * (x * (y * z)));
	} else if (j <= 1.7e-88) {
		tmp = (b * c) - (4.0 * (x * i));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) + (j * (k * -27.0))
	tmp = 0
	if j <= -2e+172:
		tmp = t_1
	elif j <= -3.05e+144:
		tmp = x * (z * (18.0 * (y * t)))
	elif j <= -8.8e+95:
		tmp = t_1
	elif j <= -1.35e-224:
		tmp = (b * c) + ((t * a) * -4.0)
	elif j <= -3.7e-242:
		tmp = 18.0 * (t * (x * (y * z)))
	elif j <= 1.7e-88:
		tmp = (b * c) - (4.0 * (x * i))
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) + Float64(j * Float64(k * -27.0)))
	tmp = 0.0
	if (j <= -2e+172)
		tmp = t_1;
	elseif (j <= -3.05e+144)
		tmp = Float64(x * Float64(z * Float64(18.0 * Float64(y * t))));
	elseif (j <= -8.8e+95)
		tmp = t_1;
	elseif (j <= -1.35e-224)
		tmp = Float64(Float64(b * c) + Float64(Float64(t * a) * -4.0));
	elseif (j <= -3.7e-242)
		tmp = Float64(18.0 * Float64(t * Float64(x * Float64(y * z))));
	elseif (j <= 1.7e-88)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) + (j * (k * -27.0));
	tmp = 0.0;
	if (j <= -2e+172)
		tmp = t_1;
	elseif (j <= -3.05e+144)
		tmp = x * (z * (18.0 * (y * t)));
	elseif (j <= -8.8e+95)
		tmp = t_1;
	elseif (j <= -1.35e-224)
		tmp = (b * c) + ((t * a) * -4.0);
	elseif (j <= -3.7e-242)
		tmp = 18.0 * (t * (x * (y * z)));
	elseif (j <= 1.7e-88)
		tmp = (b * c) - (4.0 * (x * i));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -2e+172], t$95$1, If[LessEqual[j, -3.05e+144], N[(x * N[(z * N[(18.0 * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -8.8e+95], t$95$1, If[LessEqual[j, -1.35e-224], N[(N[(b * c), $MachinePrecision] + N[(N[(t * a), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -3.7e-242], N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.7e-88], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -2.0000000000000002e172 or -3.04999999999999986e144 < j < -8.7999999999999996e95 or 1.69999999999999987e-88 < j

   1. Initial program 83.0%

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

   3. Simplified 88.8%

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

   5. Taylor expanded in b around inf 53.8%

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

   if -2.0000000000000002e172 < j < -3.04999999999999986e144

   1. Initial program 75.0%

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

   3. Simplified 75.0%

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

   5. Taylor expanded in x around inf 75.7%

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

   6. Taylor expanded in t around inf 75.7%

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

      1. associate-*r* 75.7%

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

      2. associate-*r* 75.7%

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

      3. *-commutative 75.7%

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

   8. Simplified 75.7%

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

   if -8.7999999999999996e95 < j < -1.34999999999999999e-224

   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 88.9%

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

   5. Taylor expanded in j around 0 77.7%

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

   6. Taylor expanded in x around 0 48.2%

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

   if -1.34999999999999999e-224 < j < -3.69999999999999997e-242

   1. Initial program 35.3%

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

   3. Simplified 68.6%

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

   5. Taylor expanded in x around inf 35.6%

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

   6. Taylor expanded in t around inf 35.6%

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

   if -3.69999999999999997e-242 < j < 1.69999999999999987e-88

   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 90.3%

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

   5. Taylor expanded in j around 0 88.7%

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

   6. Taylor expanded in t around 0 52.1%

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

4. Final simplification 51.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2 \cdot 10^{+172}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;j \leq -3.05 \cdot 10^{+144}:\\ \;\;\;\;x \cdot \left(z \cdot \left(18 \cdot \left(y \cdot t\right)\right)\right)\\ \mathbf{elif}\;j \leq -8.8 \cdot 10^{+95}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;j \leq -1.35 \cdot 10^{-224}:\\ \;\;\;\;b \cdot c + \left(t \cdot a\right) \cdot -4\\ \mathbf{elif}\;j \leq -3.7 \cdot 10^{-242}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;j \leq 1.7 \cdot 10^{-88}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 54.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ t_2 := j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;b \cdot c \leq -1.05 \cdot 10^{+40}:\\ \;\;\;\;b \cdot c + 18 \cdot \left(t \cdot t_1\right)\\ \mathbf{elif}\;b \cdot c \leq 1.5 \cdot 10^{-274}:\\ \;\;\;\;t \cdot \left(18 \cdot t_1 - a \cdot 4\right)\\ \mathbf{elif}\;b \cdot c \leq 1.35 \cdot 10^{-171}:\\ \;\;\;\;t_2 + \left(x \cdot i\right) \cdot -4\\ \mathbf{elif}\;b \cdot c \leq 6.4 \cdot 10^{+66}:\\ \;\;\;\;t_2 + \left(t \cdot a\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* x (* y z))) (t_2 (* j (* k -27.0))))
   (if (<= (* b c) -1.05e+40)
     (+ (* b c) (* 18.0 (* t t_1)))
     (if (<= (* b c) 1.5e-274)
       (* t (- (* 18.0 t_1) (* a 4.0)))
       (if (<= (* b c) 1.35e-171)
         (+ t_2 (* (* x i) -4.0))
         (if (<= (* b c) 6.4e+66)
           (+ t_2 (* (* t a) -4.0))
           (- (* 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);
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 * (y * z);
	double t_2 = j * (k * -27.0);
	double tmp;
	if ((b * c) <= -1.05e+40) {
		tmp = (b * c) + (18.0 * (t * t_1));
	} else if ((b * c) <= 1.5e-274) {
		tmp = t * ((18.0 * t_1) - (a * 4.0));
	} else if ((b * c) <= 1.35e-171) {
		tmp = t_2 + ((x * i) * -4.0);
	} else if ((b * c) <= 6.4e+66) {
		tmp = t_2 + ((t * a) * -4.0);
	} else {
		tmp = (b * c) - (27.0 * (j * k));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (y * z)
    t_2 = j * (k * (-27.0d0))
    if ((b * c) <= (-1.05d+40)) then
        tmp = (b * c) + (18.0d0 * (t * t_1))
    else if ((b * c) <= 1.5d-274) then
        tmp = t * ((18.0d0 * t_1) - (a * 4.0d0))
    else if ((b * c) <= 1.35d-171) then
        tmp = t_2 + ((x * i) * (-4.0d0))
    else if ((b * c) <= 6.4d+66) then
        tmp = t_2 + ((t * a) * (-4.0d0))
    else
        tmp = (b * c) - (27.0d0 * (j * k))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = x * (y * z);
	double t_2 = j * (k * -27.0);
	double tmp;
	if ((b * c) <= -1.05e+40) {
		tmp = (b * c) + (18.0 * (t * t_1));
	} else if ((b * c) <= 1.5e-274) {
		tmp = t * ((18.0 * t_1) - (a * 4.0));
	} else if ((b * c) <= 1.35e-171) {
		tmp = t_2 + ((x * i) * -4.0);
	} else if ((b * c) <= 6.4e+66) {
		tmp = t_2 + ((t * a) * -4.0);
	} else {
		tmp = (b * c) - (27.0 * (j * k));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = x * (y * z)
	t_2 = j * (k * -27.0)
	tmp = 0
	if (b * c) <= -1.05e+40:
		tmp = (b * c) + (18.0 * (t * t_1))
	elif (b * c) <= 1.5e-274:
		tmp = t * ((18.0 * t_1) - (a * 4.0))
	elif (b * c) <= 1.35e-171:
		tmp = t_2 + ((x * i) * -4.0)
	elif (b * c) <= 6.4e+66:
		tmp = t_2 + ((t * a) * -4.0)
	else:
		tmp = (b * c) - (27.0 * (j * k))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(x * Float64(y * z))
	t_2 = Float64(j * Float64(k * -27.0))
	tmp = 0.0
	if (Float64(b * c) <= -1.05e+40)
		tmp = Float64(Float64(b * c) + Float64(18.0 * Float64(t * t_1)));
	elseif (Float64(b * c) <= 1.5e-274)
		tmp = Float64(t * Float64(Float64(18.0 * t_1) - Float64(a * 4.0)));
	elseif (Float64(b * c) <= 1.35e-171)
		tmp = Float64(t_2 + Float64(Float64(x * i) * -4.0));
	elseif (Float64(b * c) <= 6.4e+66)
		tmp = Float64(t_2 + Float64(Float64(t * a) * -4.0));
	else
		tmp = Float64(Float64(b * c) - Float64(27.0 * Float64(j * k)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = x * (y * z);
	t_2 = j * (k * -27.0);
	tmp = 0.0;
	if ((b * c) <= -1.05e+40)
		tmp = (b * c) + (18.0 * (t * t_1));
	elseif ((b * c) <= 1.5e-274)
		tmp = t * ((18.0 * t_1) - (a * 4.0));
	elseif ((b * c) <= 1.35e-171)
		tmp = t_2 + ((x * i) * -4.0);
	elseif ((b * c) <= 6.4e+66)
		tmp = t_2 + ((t * a) * -4.0);
	else
		tmp = (b * c) - (27.0 * (j * k));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -1.05e+40], N[(N[(b * c), $MachinePrecision] + N[(18.0 * N[(t * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1.5e-274], N[(t * N[(N[(18.0 * t$95$1), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1.35e-171], N[(t$95$2 + N[(N[(x * i), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 6.4e+66], N[(t$95$2 + N[(N[(t * a), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 b c) < -1.05000000000000005e40

   1. Initial program 84.4%

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

   3. Simplified 86.2%

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

   5. Taylor expanded in j around 0 81.3%

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

   6. Taylor expanded in i around 0 79.8%

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

   7. Taylor expanded in a around 0 70.2%

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

   if -1.05000000000000005e40 < (*.f64 b c) < 1.49999999999999989e-274

   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 89.4%

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

   5. Taylor expanded in t around inf 59.0%

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

   if 1.49999999999999989e-274 < (*.f64 b c) < 1.35000000000000007e-171

   1. Initial program 74.1%

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

   3. Simplified 84.5%

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

   5. Taylor expanded in i around inf 79.8%

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

   if 1.35000000000000007e-171 < (*.f64 b c) < 6.3999999999999999e66

   1. Initial program 87.5%

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

   3. Simplified 90.8%

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

   5. Taylor expanded in a around inf 72.4%

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

      1. *-commutative 72.4%

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

   7. Simplified 72.4%

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

   if 6.3999999999999999e66 < (*.f64 b c)

   1. Initial program 82.9%

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

   3. Taylor expanded in x around 0 81.3%

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

   4. Taylor expanded in b around inf 68.0%

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

   5. Taylor expanded in j around 0 68.0%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.05 \cdot 10^{+40}:\\ \;\;\;\;b \cdot c + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 1.5 \cdot 10^{-274}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;b \cdot c \leq 1.35 \cdot 10^{-171}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + \left(x \cdot i\right) \cdot -4\\ \mathbf{elif}\;b \cdot c \leq 6.4 \cdot 10^{+66}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + \left(t \cdot a\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 53.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{+80}:\\ \;\;\;\;b \cdot c - t_1\\ \mathbf{elif}\;t_1 \leq 10^{-5}:\\ \;\;\;\;b \cdot c + \left(t \cdot a\right) \cdot -4\\ \mathbf{elif}\;t_1 \leq 10^{+78}:\\ \;\;\;\;\left(t \cdot \left(18 \cdot y\right)\right) \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)))
   (if (<= t_1 -1e+80)
     (- (* b c) t_1)
     (if (<= t_1 1e-5)
       (+ (* b c) (* (* t a) -4.0))
       (if (<= t_1 1e+78)
         (* (* t (* 18.0 y)) (* x z))
         (+ (* b c) (* j (* k -27.0))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (t_1 <= -1e+80) {
		tmp = (b * c) - t_1;
	} else if (t_1 <= 1e-5) {
		tmp = (b * c) + ((t * a) * -4.0);
	} else if (t_1 <= 1e+78) {
		tmp = (t * (18.0 * y)) * (x * z);
	} else {
		tmp = (b * c) + (j * (k * -27.0));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (j * 27.0d0) * k
    if (t_1 <= (-1d+80)) then
        tmp = (b * c) - t_1
    else if (t_1 <= 1d-5) then
        tmp = (b * c) + ((t * a) * (-4.0d0))
    else if (t_1 <= 1d+78) then
        tmp = (t * (18.0d0 * y)) * (x * z)
    else
        tmp = (b * c) + (j * (k * (-27.0d0)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (t_1 <= -1e+80) {
		tmp = (b * c) - t_1;
	} else if (t_1 <= 1e-5) {
		tmp = (b * c) + ((t * a) * -4.0);
	} else if (t_1 <= 1e+78) {
		tmp = (t * (18.0 * y)) * (x * z);
	} else {
		tmp = (b * c) + (j * (k * -27.0));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	tmp = 0
	if t_1 <= -1e+80:
		tmp = (b * c) - t_1
	elif t_1 <= 1e-5:
		tmp = (b * c) + ((t * a) * -4.0)
	elif t_1 <= 1e+78:
		tmp = (t * (18.0 * y)) * (x * z)
	else:
		tmp = (b * c) + (j * (k * -27.0))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_1 <= -1e+80)
		tmp = Float64(Float64(b * c) - t_1);
	elseif (t_1 <= 1e-5)
		tmp = Float64(Float64(b * c) + Float64(Float64(t * a) * -4.0));
	elseif (t_1 <= 1e+78)
		tmp = Float64(Float64(t * Float64(18.0 * y)) * Float64(x * z));
	else
		tmp = Float64(Float64(b * c) + Float64(j * Float64(k * -27.0)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * 27.0) * k;
	tmp = 0.0;
	if (t_1 <= -1e+80)
		tmp = (b * c) - t_1;
	elseif (t_1 <= 1e-5)
		tmp = (b * c) + ((t * a) * -4.0);
	elseif (t_1 <= 1e+78)
		tmp = (t * (18.0 * y)) * (x * z);
	else
		tmp = (b * c) + (j * (k * -27.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+80], N[(N[(b * c), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[t$95$1, 1e-5], N[(N[(b * c), $MachinePrecision] + N[(N[(t * a), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+78], N[(N[(t * N[(18.0 * y), $MachinePrecision]), $MachinePrecision] * N[(x * z), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 j 27) k) < -1e80

   1. Initial program 78.9%

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

   3. Taylor expanded in x around 0 76.8%

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

   4. Taylor expanded in b around inf 65.9%

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

   if -1e80 < (*.f64 (*.f64 j 27) k) < 1.00000000000000008e-5

   1. Initial program 84.1%

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

   3. Simplified 88.9%

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

   5. Taylor expanded in j around 0 88.2%

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

   6. Taylor expanded in x around 0 55.8%

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

   if 1.00000000000000008e-5 < (*.f64 (*.f64 j 27) k) < 1.00000000000000001e78

   1. Initial program 85.2%

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

   3. Taylor expanded in x around 0 90.9%

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

   4. Taylor expanded in a around 0 82.2%

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

   5. Taylor expanded in t around inf 51.9%

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

      1. associate-*r* 51.8%

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

      2. *-commutative 51.8%

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

      3. associate-*l* 51.6%

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

      4. associate-*l* 56.2%

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

      5. associate-*r* 56.4%

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

      6. *-commutative 56.4%

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

      7. associate-*l* 56.3%

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

   7. Simplified 56.3%

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

   if 1.00000000000000001e78 < (*.f64 (*.f64 j 27) k)

   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 90.3%

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

   5. Taylor expanded in b around inf 73.6%

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

4. Final simplification 60.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \leq -1 \cdot 10^{+80}:\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 10^{-5}:\\ \;\;\;\;b \cdot c + \left(t \cdot a\right) \cdot -4\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 10^{+78}:\\ \;\;\;\;\left(t \cdot \left(18 \cdot y\right)\right) \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 53.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t_2 \leq -5 \cdot 10^{+176}:\\ \;\;\;\;t_1 + \left(x \cdot i\right) \cdot -4\\ \mathbf{elif}\;t_2 \leq 10^{-5}:\\ \;\;\;\;b \cdot c + \left(t \cdot a\right) \cdot -4\\ \mathbf{elif}\;t_2 \leq 10^{+78}:\\ \;\;\;\;\left(t \cdot \left(18 \cdot y\right)\right) \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + t_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0))) (t_2 (* (* j 27.0) k)))
   (if (<= t_2 -5e+176)
     (+ t_1 (* (* x i) -4.0))
     (if (<= t_2 1e-5)
       (+ (* b c) (* (* t a) -4.0))
       (if (<= t_2 1e+78) (* (* t (* 18.0 y)) (* x z)) (+ (* b c) t_1))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = (j * 27.0) * k;
	double tmp;
	if (t_2 <= -5e+176) {
		tmp = t_1 + ((x * i) * -4.0);
	} else if (t_2 <= 1e-5) {
		tmp = (b * c) + ((t * a) * -4.0);
	} else if (t_2 <= 1e+78) {
		tmp = (t * (18.0 * y)) * (x * z);
	} else {
		tmp = (b * c) + t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * (k * (-27.0d0))
    t_2 = (j * 27.0d0) * k
    if (t_2 <= (-5d+176)) then
        tmp = t_1 + ((x * i) * (-4.0d0))
    else if (t_2 <= 1d-5) then
        tmp = (b * c) + ((t * a) * (-4.0d0))
    else if (t_2 <= 1d+78) then
        tmp = (t * (18.0d0 * y)) * (x * z)
    else
        tmp = (b * c) + t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = (j * 27.0) * k;
	double tmp;
	if (t_2 <= -5e+176) {
		tmp = t_1 + ((x * i) * -4.0);
	} else if (t_2 <= 1e-5) {
		tmp = (b * c) + ((t * a) * -4.0);
	} else if (t_2 <= 1e+78) {
		tmp = (t * (18.0 * y)) * (x * z);
	} else {
		tmp = (b * c) + t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	t_2 = (j * 27.0) * k
	tmp = 0
	if t_2 <= -5e+176:
		tmp = t_1 + ((x * i) * -4.0)
	elif t_2 <= 1e-5:
		tmp = (b * c) + ((t * a) * -4.0)
	elif t_2 <= 1e+78:
		tmp = (t * (18.0 * y)) * (x * z)
	else:
		tmp = (b * c) + t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * -27.0))
	t_2 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_2 <= -5e+176)
		tmp = Float64(t_1 + Float64(Float64(x * i) * -4.0));
	elseif (t_2 <= 1e-5)
		tmp = Float64(Float64(b * c) + Float64(Float64(t * a) * -4.0));
	elseif (t_2 <= 1e+78)
		tmp = Float64(Float64(t * Float64(18.0 * y)) * Float64(x * z));
	else
		tmp = Float64(Float64(b * c) + t_1);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * -27.0);
	t_2 = (j * 27.0) * k;
	tmp = 0.0;
	if (t_2 <= -5e+176)
		tmp = t_1 + ((x * i) * -4.0);
	elseif (t_2 <= 1e-5)
		tmp = (b * c) + ((t * a) * -4.0);
	elseif (t_2 <= 1e+78)
		tmp = (t * (18.0 * y)) * (x * z);
	else
		tmp = (b * c) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+176], N[(t$95$1 + N[(N[(x * i), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e-5], N[(N[(b * c), $MachinePrecision] + N[(N[(t * a), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+78], N[(N[(t * N[(18.0 * y), $MachinePrecision]), $MachinePrecision] * N[(x * z), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 j 27) k) < -5e176

   1. Initial program 76.8%

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

   3. Simplified 79.5%

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

   5. Taylor expanded in i around inf 77.2%

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

   if -5e176 < (*.f64 (*.f64 j 27) k) < 1.00000000000000008e-5

   1. Initial program 84.2%

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

   3. Simplified 89.8%

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

   5. Taylor expanded in j around 0 87.1%

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

   6. Taylor expanded in x around 0 55.5%

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

   if 1.00000000000000008e-5 < (*.f64 (*.f64 j 27) k) < 1.00000000000000001e78

   1. Initial program 85.2%

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

   3. Taylor expanded in x around 0 90.9%

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

   4. Taylor expanded in a around 0 82.2%

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

   5. Taylor expanded in t around inf 51.9%

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

      1. associate-*r* 51.8%

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

      2. *-commutative 51.8%

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

      3. associate-*l* 51.6%

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

      4. associate-*l* 56.2%

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

      5. associate-*r* 56.4%

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

      6. *-commutative 56.4%

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

      7. associate-*l* 56.3%

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

   7. Simplified 56.3%

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

   if 1.00000000000000001e78 < (*.f64 (*.f64 j 27) k)

   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 90.3%

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

   5. Taylor expanded in b around inf 73.6%

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

4. Final simplification 61.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \leq -5 \cdot 10^{+176}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + \left(x \cdot i\right) \cdot -4\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 10^{-5}:\\ \;\;\;\;b \cdot c + \left(t \cdot a\right) \cdot -4\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 10^{+78}:\\ \;\;\;\;\left(t \cdot \left(18 \cdot y\right)\right) \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 57.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ t_2 := b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{if}\;z \leq -2.25 \cdot 10^{-57}:\\ \;\;\;\;t_1 + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;z \leq -3.65 \cdot 10^{-155}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-300}:\\ \;\;\;\;b \cdot c + \left(t \cdot a\right) \cdot -4\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+85}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + t_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* 18.0 (* t (* x (* y z)))))
        (t_2 (- (* b c) (+ (* 4.0 (* x i)) (* 27.0 (* j k))))))
   (if (<= z -2.25e-57)
     (+ t_1 (* j (* k -27.0)))
     (if (<= z -3.65e-155)
       t_2
       (if (<= z -8.5e-300)
         (+ (* b c) (* (* t a) -4.0))
         (if (<= z 3.5e+85) t_2 (+ (* b c) t_1)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 18.0 * (t * (x * (y * z)));
	double t_2 = (b * c) - ((4.0 * (x * i)) + (27.0 * (j * k)));
	double tmp;
	if (z <= -2.25e-57) {
		tmp = t_1 + (j * (k * -27.0));
	} else if (z <= -3.65e-155) {
		tmp = t_2;
	} else if (z <= -8.5e-300) {
		tmp = (b * c) + ((t * a) * -4.0);
	} else if (z <= 3.5e+85) {
		tmp = t_2;
	} else {
		tmp = (b * c) + t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 18.0d0 * (t * (x * (y * z)))
    t_2 = (b * c) - ((4.0d0 * (x * i)) + (27.0d0 * (j * k)))
    if (z <= (-2.25d-57)) then
        tmp = t_1 + (j * (k * (-27.0d0)))
    else if (z <= (-3.65d-155)) then
        tmp = t_2
    else if (z <= (-8.5d-300)) then
        tmp = (b * c) + ((t * a) * (-4.0d0))
    else if (z <= 3.5d+85) then
        tmp = t_2
    else
        tmp = (b * c) + t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 18.0 * (t * (x * (y * z)));
	double t_2 = (b * c) - ((4.0 * (x * i)) + (27.0 * (j * k)));
	double tmp;
	if (z <= -2.25e-57) {
		tmp = t_1 + (j * (k * -27.0));
	} else if (z <= -3.65e-155) {
		tmp = t_2;
	} else if (z <= -8.5e-300) {
		tmp = (b * c) + ((t * a) * -4.0);
	} else if (z <= 3.5e+85) {
		tmp = t_2;
	} else {
		tmp = (b * c) + t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = 18.0 * (t * (x * (y * z)))
	t_2 = (b * c) - ((4.0 * (x * i)) + (27.0 * (j * k)))
	tmp = 0
	if z <= -2.25e-57:
		tmp = t_1 + (j * (k * -27.0))
	elif z <= -3.65e-155:
		tmp = t_2
	elif z <= -8.5e-300:
		tmp = (b * c) + ((t * a) * -4.0)
	elif z <= 3.5e+85:
		tmp = t_2
	else:
		tmp = (b * c) + t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(18.0 * Float64(t * Float64(x * Float64(y * z))))
	t_2 = Float64(Float64(b * c) - Float64(Float64(4.0 * Float64(x * i)) + Float64(27.0 * Float64(j * k))))
	tmp = 0.0
	if (z <= -2.25e-57)
		tmp = Float64(t_1 + Float64(j * Float64(k * -27.0)));
	elseif (z <= -3.65e-155)
		tmp = t_2;
	elseif (z <= -8.5e-300)
		tmp = Float64(Float64(b * c) + Float64(Float64(t * a) * -4.0));
	elseif (z <= 3.5e+85)
		tmp = t_2;
	else
		tmp = Float64(Float64(b * c) + t_1);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = 18.0 * (t * (x * (y * z)));
	t_2 = (b * c) - ((4.0 * (x * i)) + (27.0 * (j * k)));
	tmp = 0.0;
	if (z <= -2.25e-57)
		tmp = t_1 + (j * (k * -27.0));
	elseif (z <= -3.65e-155)
		tmp = t_2;
	elseif (z <= -8.5e-300)
		tmp = (b * c) + ((t * a) * -4.0);
	elseif (z <= 3.5e+85)
		tmp = t_2;
	else
		tmp = (b * c) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] - N[(N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision] + N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.25e-57], N[(t$95$1 + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.65e-155], t$95$2, If[LessEqual[z, -8.5e-300], N[(N[(b * c), $MachinePrecision] + N[(N[(t * a), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.5e+85], t$95$2, N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.24999999999999986e-57

   1. Initial program 81.1%

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

   3. Simplified 79.7%

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

   5. Taylor expanded in y around inf 49.2%

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

   if -2.24999999999999986e-57 < z < -3.65000000000000017e-155 or -8.4999999999999995e-300 < z < 3.50000000000000005e85

   1. Initial program 84.8%

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

   3. Simplified 93.6%

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

   5. Taylor expanded in t around 0 65.9%

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

   if -3.65000000000000017e-155 < z < -8.4999999999999995e-300

   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 93.5%

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

   5. Taylor expanded in j around 0 89.3%

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

   6. Taylor expanded in x around 0 69.8%

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

   if 3.50000000000000005e85 < z

   1. Initial program 79.3%

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

   3. Simplified 87.6%

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

   5. Taylor expanded in j around 0 79.7%

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

   6. Taylor expanded in i around 0 81.9%

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

   7. Taylor expanded in a around 0 72.0%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{-57}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;z \leq -3.65 \cdot 10^{-155}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-300}:\\ \;\;\;\;b \cdot c + \left(t \cdot a\right) \cdot -4\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+85}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 70.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{+56}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{elif}\;t_1 \leq 10^{+93}:\\ \;\;\;\;b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - t_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)))
   (if (<= t_1 -5e+56)
     (- (* b c) (+ (* 4.0 (* x i)) (* 27.0 (* j k))))
     (if (<= t_1 1e+93)
       (+ (* b c) (* t (- (* 18.0 (* x (* y z))) (* a 4.0))))
       (- (- (* b c) (* 4.0 (* t a))) t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (t_1 <= -5e+56) {
		tmp = (b * c) - ((4.0 * (x * i)) + (27.0 * (j * k)));
	} else if (t_1 <= 1e+93) {
		tmp = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)));
	} else {
		tmp = ((b * c) - (4.0 * (t * a))) - t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 <= (-5d+56)) then
        tmp = (b * c) - ((4.0d0 * (x * i)) + (27.0d0 * (j * k)))
    else if (t_1 <= 1d+93) then
        tmp = (b * c) + (t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0)))
    else
        tmp = ((b * c) - (4.0d0 * (t * a))) - t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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 <= -5e+56) {
		tmp = (b * c) - ((4.0 * (x * i)) + (27.0 * (j * k)));
	} else if (t_1 <= 1e+93) {
		tmp = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)));
	} else {
		tmp = ((b * c) - (4.0 * (t * a))) - t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	tmp = 0
	if t_1 <= -5e+56:
		tmp = (b * c) - ((4.0 * (x * i)) + (27.0 * (j * k)))
	elif t_1 <= 1e+93:
		tmp = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))
	else:
		tmp = ((b * c) - (4.0 * (t * a))) - t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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 <= -5e+56)
		tmp = Float64(Float64(b * c) - Float64(Float64(4.0 * Float64(x * i)) + Float64(27.0 * Float64(j * k))));
	elseif (t_1 <= 1e+93)
		tmp = Float64(Float64(b * c) + Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0))));
	else
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(t * a))) - t_1);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
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 <= -5e+56)
		tmp = (b * c) - ((4.0 * (x * i)) + (27.0 * (j * k)));
	elseif (t_1 <= 1e+93)
		tmp = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)));
	else
		tmp = ((b * c) - (4.0 * (t * a))) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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, -5e+56], N[(N[(b * c), $MachinePrecision] - N[(N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision] + N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+93], N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j 27) k) < -5.00000000000000024e56

   1. Initial program 79.8%

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

   3. Simplified 86.4%

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

   5. Taylor expanded in t around 0 74.0%

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

   if -5.00000000000000024e56 < (*.f64 (*.f64 j 27) k) < 1.00000000000000004e93

   1. Initial program 84.4%

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

   3. Simplified 88.8%

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

   5. Taylor expanded in j around 0 86.9%

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

   6. Taylor expanded in i around 0 75.6%

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

   if 1.00000000000000004e93 < (*.f64 (*.f64 j 27) k)

   1. Initial program 89.6%

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

   3. Taylor expanded in x around 0 82.1%

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

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \leq -5 \cdot 10^{+56}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 10^{+93}:\\ \;\;\;\;b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 44.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{+149}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;x \leq -2.75 \cdot 10^{+117}:\\ \;\;\;\;\left(x \cdot i\right) \cdot -4\\ \mathbf{elif}\;x \leq -4.6 \cdot 10^{-25}:\\ \;\;\;\;x \cdot \left(z \cdot \left(18 \cdot \left(y \cdot t\right)\right)\right)\\ \mathbf{elif}\;x \leq -5.5 \cdot 10^{-71}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{+16}:\\ \;\;\;\;b \cdot c + \left(t \cdot a\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot \left(18 \cdot y\right)\right) \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= x -4.2e+149)
   (* 18.0 (* t (* x (* y z))))
   (if (<= x -2.75e+117)
     (* (* x i) -4.0)
     (if (<= x -4.6e-25)
       (* x (* z (* 18.0 (* y t))))
       (if (<= x -5.5e-71)
         (* (* j k) -27.0)
         (if (<= x 1.35e+16)
           (+ (* b c) (* (* t a) -4.0))
           (* (* t (* 18.0 y)) (* x z))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (x <= -4.2e+149) {
		tmp = 18.0 * (t * (x * (y * z)));
	} else if (x <= -2.75e+117) {
		tmp = (x * i) * -4.0;
	} else if (x <= -4.6e-25) {
		tmp = x * (z * (18.0 * (y * t)));
	} else if (x <= -5.5e-71) {
		tmp = (j * k) * -27.0;
	} else if (x <= 1.35e+16) {
		tmp = (b * c) + ((t * a) * -4.0);
	} else {
		tmp = (t * (18.0 * y)) * (x * z);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (x <= (-4.2d+149)) then
        tmp = 18.0d0 * (t * (x * (y * z)))
    else if (x <= (-2.75d+117)) then
        tmp = (x * i) * (-4.0d0)
    else if (x <= (-4.6d-25)) then
        tmp = x * (z * (18.0d0 * (y * t)))
    else if (x <= (-5.5d-71)) then
        tmp = (j * k) * (-27.0d0)
    else if (x <= 1.35d+16) then
        tmp = (b * c) + ((t * a) * (-4.0d0))
    else
        tmp = (t * (18.0d0 * y)) * (x * z)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (x <= -4.2e+149) {
		tmp = 18.0 * (t * (x * (y * z)));
	} else if (x <= -2.75e+117) {
		tmp = (x * i) * -4.0;
	} else if (x <= -4.6e-25) {
		tmp = x * (z * (18.0 * (y * t)));
	} else if (x <= -5.5e-71) {
		tmp = (j * k) * -27.0;
	} else if (x <= 1.35e+16) {
		tmp = (b * c) + ((t * a) * -4.0);
	} else {
		tmp = (t * (18.0 * y)) * (x * z);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if x <= -4.2e+149:
		tmp = 18.0 * (t * (x * (y * z)))
	elif x <= -2.75e+117:
		tmp = (x * i) * -4.0
	elif x <= -4.6e-25:
		tmp = x * (z * (18.0 * (y * t)))
	elif x <= -5.5e-71:
		tmp = (j * k) * -27.0
	elif x <= 1.35e+16:
		tmp = (b * c) + ((t * a) * -4.0)
	else:
		tmp = (t * (18.0 * y)) * (x * z)
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (x <= -4.2e+149)
		tmp = Float64(18.0 * Float64(t * Float64(x * Float64(y * z))));
	elseif (x <= -2.75e+117)
		tmp = Float64(Float64(x * i) * -4.0);
	elseif (x <= -4.6e-25)
		tmp = Float64(x * Float64(z * Float64(18.0 * Float64(y * t))));
	elseif (x <= -5.5e-71)
		tmp = Float64(Float64(j * k) * -27.0);
	elseif (x <= 1.35e+16)
		tmp = Float64(Float64(b * c) + Float64(Float64(t * a) * -4.0));
	else
		tmp = Float64(Float64(t * Float64(18.0 * y)) * Float64(x * z));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (x <= -4.2e+149)
		tmp = 18.0 * (t * (x * (y * z)));
	elseif (x <= -2.75e+117)
		tmp = (x * i) * -4.0;
	elseif (x <= -4.6e-25)
		tmp = x * (z * (18.0 * (y * t)));
	elseif (x <= -5.5e-71)
		tmp = (j * k) * -27.0;
	elseif (x <= 1.35e+16)
		tmp = (b * c) + ((t * a) * -4.0);
	else
		tmp = (t * (18.0 * y)) * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[x, -4.2e+149], N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.75e+117], N[(N[(x * i), $MachinePrecision] * -4.0), $MachinePrecision], If[LessEqual[x, -4.6e-25], N[(x * N[(z * N[(18.0 * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -5.5e-71], N[(N[(j * k), $MachinePrecision] * -27.0), $MachinePrecision], If[LessEqual[x, 1.35e+16], N[(N[(b * c), $MachinePrecision] + N[(N[(t * a), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision], N[(N[(t * N[(18.0 * y), $MachinePrecision]), $MachinePrecision] * N[(x * z), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -4.2000000000000003e149

   1. Initial program 73.4%

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

   3. Simplified 82.0%

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

   5. Taylor expanded in x around inf 78.5%

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

   6. Taylor expanded in t around inf 60.6%

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

   if -4.2000000000000003e149 < x < -2.74999999999999982e117

   1. Initial program 64.0%

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

   3. Simplified 81.8%

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

      1. associate-*r* 64.0%

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

      2. distribute-rgt-out-- 64.0%

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

      3. associate-*l* 63.6%

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

      4. *-commutative 63.6%

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

      5. *-commutative 63.6%

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

   6. Applied egg-rr 63.6%

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

   7. Taylor expanded in i around inf 69.0%

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

      1. *-commutative 69.0%

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

      2. *-commutative 69.0%

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

   9. Simplified 69.0%

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

   if -2.74999999999999982e117 < x < -4.5999999999999998e-25

   1. Initial program 74.4%

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

   3. Simplified 92.7%

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

   5. Taylor expanded in x around inf 49.6%

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

   6. Taylor expanded in t around inf 42.2%

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

      1. associate-*r* 45.6%

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

      2. associate-*r* 45.6%

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

      3. *-commutative 45.6%

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

   8. Simplified 45.6%

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

   if -4.5999999999999998e-25 < x < -5.4999999999999997e-71

   1. Initial program 99.6%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in j around inf 63.3%

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

   if -5.4999999999999997e-71 < x < 1.35e16

   1. Initial program 91.4%

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

   3. Simplified 89.1%

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

   5. Taylor expanded in j around 0 72.6%

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

   6. Taylor expanded in x around 0 62.3%

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

   if 1.35e16 < x

   1. Initial program 79.8%

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

   3. Taylor expanded in x around 0 91.7%

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

   4. Taylor expanded in a around 0 88.0%

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

   5. Taylor expanded in t around inf 52.5%

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

      1. associate-*r* 52.5%

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

      2. *-commutative 52.5%

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

      3. associate-*l* 54.4%

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

      4. associate-*l* 54.4%

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

      5. associate-*r* 54.4%

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

      6. *-commutative 54.4%

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

      7. associate-*l* 54.4%

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

   7. Simplified 54.4%

      \[\leadsto \color{blue}{\left(t \cdot \left(y \cdot 18\right)\right) \cdot \left(z \cdot x\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 59.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{+149}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;x \leq -2.75 \cdot 10^{+117}:\\ \;\;\;\;\left(x \cdot i\right) \cdot -4\\ \mathbf{elif}\;x \leq -4.6 \cdot 10^{-25}:\\ \;\;\;\;x \cdot \left(z \cdot \left(18 \cdot \left(y \cdot t\right)\right)\right)\\ \mathbf{elif}\;x \leq -5.5 \cdot 10^{-71}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{+16}:\\ \;\;\;\;b \cdot c + \left(t \cdot a\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot \left(18 \cdot y\right)\right) \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 84.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;x \leq -6 \cdot 10^{-34} \lor \neg \left(x \leq 650000000000\right):\\ \;\;\;\;\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - t_1\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - \left(4 \cdot \left(t \cdot a\right) + 4 \cdot \left(x \cdot i\right)\right)\right) - t_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)))
   (if (or (<= x -6e-34) (not (<= x 650000000000.0)))
     (- (+ (* b c) (* x (- (* 18.0 (* t (* y z))) (* 4.0 i)))) t_1)
     (- (- (* b c) (+ (* 4.0 (* t a)) (* 4.0 (* x i)))) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if ((x <= -6e-34) || !(x <= 650000000000.0)) {
		tmp = ((b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)))) - t_1;
	} else {
		tmp = ((b * c) - ((4.0 * (t * a)) + (4.0 * (x * i)))) - t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 ((x <= (-6d-34)) .or. (.not. (x <= 650000000000.0d0))) then
        tmp = ((b * c) + (x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i)))) - t_1
    else
        tmp = ((b * c) - ((4.0d0 * (t * a)) + (4.0d0 * (x * i)))) - t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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 ((x <= -6e-34) || !(x <= 650000000000.0)) {
		tmp = ((b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)))) - t_1;
	} else {
		tmp = ((b * c) - ((4.0 * (t * a)) + (4.0 * (x * i)))) - t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	tmp = 0
	if (x <= -6e-34) or not (x <= 650000000000.0):
		tmp = ((b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)))) - t_1
	else:
		tmp = ((b * c) - ((4.0 * (t * a)) + (4.0 * (x * i)))) - t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if ((x <= -6e-34) || !(x <= 650000000000.0))
		tmp = Float64(Float64(Float64(b * c) + Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)))) - t_1);
	else
		tmp = Float64(Float64(Float64(b * c) - Float64(Float64(4.0 * Float64(t * a)) + Float64(4.0 * Float64(x * i)))) - t_1);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * 27.0) * k;
	tmp = 0.0;
	if ((x <= -6e-34) || ~((x <= 650000000000.0)))
		tmp = ((b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)))) - t_1;
	else
		tmp = ((b * c) - ((4.0 * (t * a)) + (4.0 * (x * i)))) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[Or[LessEqual[x, -6e-34], N[Not[LessEqual[x, 650000000000.0]], $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] - t$95$1), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] - N[(N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -6e-34 or 6.5e11 < x

   1. Initial program 75.6%

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

   3. Taylor expanded in x around 0 86.8%

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

   4. Taylor expanded in a around 0 85.5%

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

   if -6e-34 < x < 6.5e11

   1. Initial program 91.8%

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

   3. Taylor expanded in y around 0 88.3%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{-34} \lor \neg \left(x \leq 650000000000\right):\\ \;\;\;\;\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - \left(4 \cdot \left(t \cdot a\right) + 4 \cdot \left(x \cdot i\right)\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 75.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;z \leq -9.2 \cdot 10^{-57}:\\ \;\;\;\;t \cdot \left(-18 \cdot \left(z \cdot \left(y \cdot \left(-x\right)\right)\right) - a \cdot 4\right) - t_1\\ \mathbf{elif}\;z \leq 10^{+71}:\\ \;\;\;\;\left(b \cdot c - \left(4 \cdot \left(t \cdot a\right) + 4 \cdot \left(x \cdot i\right)\right)\right) - t_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)))
   (if (<= z -9.2e-57)
     (- (* t (- (* -18.0 (* z (* y (- x)))) (* a 4.0))) t_1)
     (if (<= z 1e+71)
       (- (- (* b c) (+ (* 4.0 (* t a)) (* 4.0 (* x i)))) t_1)
       (+ (* b c) (* t (- (* 18.0 (* x (* y z))) (* a 4.0))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (z <= -9.2e-57) {
		tmp = (t * ((-18.0 * (z * (y * -x))) - (a * 4.0))) - t_1;
	} else if (z <= 1e+71) {
		tmp = ((b * c) - ((4.0 * (t * a)) + (4.0 * (x * i)))) - t_1;
	} else {
		tmp = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (j * 27.0d0) * k
    if (z <= (-9.2d-57)) then
        tmp = (t * (((-18.0d0) * (z * (y * -x))) - (a * 4.0d0))) - t_1
    else if (z <= 1d+71) then
        tmp = ((b * c) - ((4.0d0 * (t * a)) + (4.0d0 * (x * i)))) - t_1
    else
        tmp = (b * c) + (t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (z <= -9.2e-57) {
		tmp = (t * ((-18.0 * (z * (y * -x))) - (a * 4.0))) - t_1;
	} else if (z <= 1e+71) {
		tmp = ((b * c) - ((4.0 * (t * a)) + (4.0 * (x * i)))) - t_1;
	} else {
		tmp = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	tmp = 0
	if z <= -9.2e-57:
		tmp = (t * ((-18.0 * (z * (y * -x))) - (a * 4.0))) - t_1
	elif z <= 1e+71:
		tmp = ((b * c) - ((4.0 * (t * a)) + (4.0 * (x * i)))) - t_1
	else:
		tmp = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (z <= -9.2e-57)
		tmp = Float64(Float64(t * Float64(Float64(-18.0 * Float64(z * Float64(y * Float64(-x)))) - Float64(a * 4.0))) - t_1);
	elseif (z <= 1e+71)
		tmp = Float64(Float64(Float64(b * c) - Float64(Float64(4.0 * Float64(t * a)) + Float64(4.0 * Float64(x * i)))) - t_1);
	else
		tmp = Float64(Float64(b * c) + Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * 27.0) * k;
	tmp = 0.0;
	if (z <= -9.2e-57)
		tmp = (t * ((-18.0 * (z * (y * -x))) - (a * 4.0))) - t_1;
	elseif (z <= 1e+71)
		tmp = ((b * c) - ((4.0 * (t * a)) + (4.0 * (x * i)))) - t_1;
	else
		tmp = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[z, -9.2e-57], N[(N[(t * N[(N[(-18.0 * N[(z * N[(y * (-x)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[z, 1e+71], N[(N[(N[(b * c), $MachinePrecision] - N[(N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.2000000000000001e-57

   1. Initial program 81.1%

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

   3. Taylor expanded in x around 0 73.9%

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

   4. Taylor expanded in t around -inf 60.5%

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

      1. associate-*r* 60.5%

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

      2. neg-mul-1 60.5%

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

      3. cancel-sign-sub-inv 60.5%

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

      4. metadata-eval 60.5%

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

      5. associate-*r* 62.2%

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

      6. *-commutative 62.2%

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

   6. Simplified 62.2%

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

   if -9.2000000000000001e-57 < z < 1e71

   1. Initial program 88.6%

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

   3. Taylor expanded in y around 0 83.6%

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

   if 1e71 < z

   1. Initial program 76.1%

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

   3. Simplified 88.1%

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

   5. Taylor expanded in j around 0 80.5%

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

   6. Taylor expanded in i around 0 82.6%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{-57}:\\ \;\;\;\;t \cdot \left(-18 \cdot \left(z \cdot \left(y \cdot \left(-x\right)\right)\right) - a \cdot 4\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;z \leq 10^{+71}:\\ \;\;\;\;\left(b \cdot c - \left(4 \cdot \left(t \cdot a\right) + 4 \cdot \left(x \cdot i\right)\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 86.8% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 84.1%

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

3. Simplified 88.3%

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

5. Final simplification 88.3%

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

Alternative 25: 76.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{-21} \lor \neg \left(x \leq 5 \cdot 10^{-56}\right):\\ \;\;\;\;b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= x -7.5e-21) (not (<= x 5e-56)))
   (+ (* b c) (* x (- (* 18.0 (* t (* y z))) (* 4.0 i))))
   (- (- (* b c) (* 4.0 (* t a))) (* (* j 27.0) k))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((x <= -7.5e-21) || !(x <= 5e-56)) {
		tmp = (b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)));
	} else {
		tmp = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((x <= (-7.5d-21)) .or. (.not. (x <= 5d-56))) then
        tmp = (b * c) + (x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i)))
    else
        tmp = ((b * c) - (4.0d0 * (t * a))) - ((j * 27.0d0) * k)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((x <= -7.5e-21) || !(x <= 5e-56)) {
		tmp = (b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)));
	} else {
		tmp = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (x <= -7.5e-21) or not (x <= 5e-56):
		tmp = (b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)))
	else:
		tmp = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k)
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((x <= -7.5e-21) || !(x <= 5e-56))
		tmp = Float64(Float64(b * c) + Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i))));
	else
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(t * a))) - Float64(Float64(j * 27.0) * k));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((x <= -7.5e-21) || ~((x <= 5e-56)))
		tmp = (b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)));
	else
		tmp = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[x, -7.5e-21], N[Not[LessEqual[x, 5e-56]], $MachinePrecision]], 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[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7.50000000000000072e-21 or 4.99999999999999997e-56 < x

   1. Initial program 77.0%

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

   3. Taylor expanded in x around 0 86.6%

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

   4. Taylor expanded in a around 0 85.1%

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

   5. Taylor expanded in j around 0 75.2%

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

   if -7.50000000000000072e-21 < x < 4.99999999999999997e-56

   1. Initial program 91.8%

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

   3. Taylor expanded in x around 0 84.0%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{-21} \lor \neg \left(x \leq 5 \cdot 10^{-56}\right):\\ \;\;\;\;b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 31.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot k\right) \cdot -27\\ \mathbf{if}\;b \leq -6.5 \cdot 10^{+86}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \leq -4.6 \cdot 10^{-127}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -8 \cdot 10^{-306}:\\ \;\;\;\;\left(t \cdot a\right) \cdot -4\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{-47}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j k) -27.0)))
   (if (<= b -6.5e+86)
     (* b c)
     (if (<= b -4.6e-127)
       t_1
       (if (<= b -8e-306)
         (* (* t a) -4.0)
         (if (<= b 1.25e-47) t_1 (* b c)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * k) * -27.0;
	double tmp;
	if (b <= -6.5e+86) {
		tmp = b * c;
	} else if (b <= -4.6e-127) {
		tmp = t_1;
	} else if (b <= -8e-306) {
		tmp = (t * a) * -4.0;
	} else if (b <= 1.25e-47) {
		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.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (j * k) * (-27.0d0)
    if (b <= (-6.5d+86)) then
        tmp = b * c
    else if (b <= (-4.6d-127)) then
        tmp = t_1
    else if (b <= (-8d-306)) then
        tmp = (t * a) * (-4.0d0)
    else if (b <= 1.25d-47) 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;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * k) * -27.0;
	double tmp;
	if (b <= -6.5e+86) {
		tmp = b * c;
	} else if (b <= -4.6e-127) {
		tmp = t_1;
	} else if (b <= -8e-306) {
		tmp = (t * a) * -4.0;
	} else if (b <= 1.25e-47) {
		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])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * k) * -27.0
	tmp = 0
	if b <= -6.5e+86:
		tmp = b * c
	elif b <= -4.6e-127:
		tmp = t_1
	elif b <= -8e-306:
		tmp = (t * a) * -4.0
	elif b <= 1.25e-47:
		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])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * k) * -27.0)
	tmp = 0.0
	if (b <= -6.5e+86)
		tmp = Float64(b * c);
	elseif (b <= -4.6e-127)
		tmp = t_1;
	elseif (b <= -8e-306)
		tmp = Float64(Float64(t * a) * -4.0);
	elseif (b <= 1.25e-47)
		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])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * k) * -27.0;
	tmp = 0.0;
	if (b <= -6.5e+86)
		tmp = b * c;
	elseif (b <= -4.6e-127)
		tmp = t_1;
	elseif (b <= -8e-306)
		tmp = (t * a) * -4.0;
	elseif (b <= 1.25e-47)
		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.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * k), $MachinePrecision] * -27.0), $MachinePrecision]}, If[LessEqual[b, -6.5e+86], N[(b * c), $MachinePrecision], If[LessEqual[b, -4.6e-127], t$95$1, If[LessEqual[b, -8e-306], N[(N[(t * a), $MachinePrecision] * -4.0), $MachinePrecision], If[LessEqual[b, 1.25e-47], t$95$1, N[(b * c), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -6.49999999999999996e86 or 1.25000000000000003e-47 < b

   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 87.8%

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

      1. associate-*r* 87.8%

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

      2. distribute-rgt-out-- 84.0%

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

      3. associate-*l* 82.4%

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

      4. *-commutative 82.4%

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

      5. *-commutative 82.4%

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

   6. Applied egg-rr 82.4%

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

   7. Taylor expanded in b around inf 35.7%

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

   if -6.49999999999999996e86 < b < -4.60000000000000038e-127 or -8.00000000000000022e-306 < b < 1.25000000000000003e-47

   1. Initial program 84.1%

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

   3. Simplified 89.9%

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

   5. Taylor expanded in j around inf 31.7%

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

   if -4.60000000000000038e-127 < b < -8.00000000000000022e-306

   1. Initial program 84.9%

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

   3. Simplified 88.7%

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

      1. associate-*r* 85.1%

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

      2. distribute-rgt-out-- 81.2%

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

      3. associate-*l* 84.8%

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

      4. *-commutative 84.8%

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

      5. *-commutative 84.8%

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

   6. Applied egg-rr 84.8%

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

   7. Taylor expanded in a around inf 26.3%

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

4. Final simplification 33.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.5 \cdot 10^{+86}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \leq -4.6 \cdot 10^{-127}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \mathbf{elif}\;b \leq -8 \cdot 10^{-306}:\\ \;\;\;\;\left(t \cdot a\right) \cdot -4\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{-47}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 32.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;b \leq -3.2 \cdot 10^{+86}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \leq -1.3 \cdot 10^{-126}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.45 \cdot 10^{-307}:\\ \;\;\;\;\left(t \cdot a\right) \cdot -4\\ \mathbf{elif}\;b \leq 1.3 \cdot 10^{-47}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0))))
   (if (<= b -3.2e+86)
     (* b c)
     (if (<= b -1.3e-126)
       t_1
       (if (<= b 1.45e-307)
         (* (* t a) -4.0)
         (if (<= b 1.3e-47) t_1 (* b c)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double tmp;
	if (b <= -3.2e+86) {
		tmp = b * c;
	} else if (b <= -1.3e-126) {
		tmp = t_1;
	} else if (b <= 1.45e-307) {
		tmp = (t * a) * -4.0;
	} else if (b <= 1.3e-47) {
		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.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * (k * (-27.0d0))
    if (b <= (-3.2d+86)) then
        tmp = b * c
    else if (b <= (-1.3d-126)) then
        tmp = t_1
    else if (b <= 1.45d-307) then
        tmp = (t * a) * (-4.0d0)
    else if (b <= 1.3d-47) 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;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double tmp;
	if (b <= -3.2e+86) {
		tmp = b * c;
	} else if (b <= -1.3e-126) {
		tmp = t_1;
	} else if (b <= 1.45e-307) {
		tmp = (t * a) * -4.0;
	} else if (b <= 1.3e-47) {
		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])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	tmp = 0
	if b <= -3.2e+86:
		tmp = b * c
	elif b <= -1.3e-126:
		tmp = t_1
	elif b <= 1.45e-307:
		tmp = (t * a) * -4.0
	elif b <= 1.3e-47:
		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])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * -27.0))
	tmp = 0.0
	if (b <= -3.2e+86)
		tmp = Float64(b * c);
	elseif (b <= -1.3e-126)
		tmp = t_1;
	elseif (b <= 1.45e-307)
		tmp = Float64(Float64(t * a) * -4.0);
	elseif (b <= 1.3e-47)
		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])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * -27.0);
	tmp = 0.0;
	if (b <= -3.2e+86)
		tmp = b * c;
	elseif (b <= -1.3e-126)
		tmp = t_1;
	elseif (b <= 1.45e-307)
		tmp = (t * a) * -4.0;
	elseif (b <= 1.3e-47)
		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.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.2e+86], N[(b * c), $MachinePrecision], If[LessEqual[b, -1.3e-126], t$95$1, If[LessEqual[b, 1.45e-307], N[(N[(t * a), $MachinePrecision] * -4.0), $MachinePrecision], If[LessEqual[b, 1.3e-47], t$95$1, N[(b * c), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.2e86 or 1.3e-47 < b

   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 87.8%

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

      1. associate-*r* 87.8%

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

      2. distribute-rgt-out-- 84.0%

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

      3. associate-*l* 82.4%

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

      4. *-commutative 82.4%

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

      5. *-commutative 82.4%

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

   6. Applied egg-rr 82.4%

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

   7. Taylor expanded in b around inf 35.7%

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

   if -3.2e86 < b < -1.3e-126 or 1.45e-307 < b < 1.3e-47

   1. Initial program 83.9%

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

   3. Taylor expanded in x around 0 83.9%

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

   4. Taylor expanded in j around inf 31.9%

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

      1. *-commutative 31.9%

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

      2. associate-*r* 32.0%

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

   6. Simplified 32.0%

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

   if -1.3e-126 < b < 1.45e-307

   1. Initial program 85.4%

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

   3. Simplified 89.1%

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

      1. associate-*r* 85.6%

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

      2. distribute-rgt-out-- 81.9%

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

      3. associate-*l* 85.4%

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

      4. *-commutative 85.4%

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

      5. *-commutative 85.4%

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

   6. Applied egg-rr 85.4%

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

   7. Taylor expanded in a around inf 29.0%

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

4. Final simplification 33.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.2 \cdot 10^{+86}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \leq -1.3 \cdot 10^{-126}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;b \leq 1.45 \cdot 10^{-307}:\\ \;\;\;\;\left(t \cdot a\right) \cdot -4\\ \mathbf{elif}\;b \leq 1.3 \cdot 10^{-47}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 28: 31.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := k \cdot \left(j \cdot -27\right)\\ \mathbf{if}\;b \leq -8.5 \cdot 10^{+86}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \leq -2.8 \cdot 10^{-125}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -2.1 \cdot 10^{-306}:\\ \;\;\;\;\left(t \cdot a\right) \cdot -4\\ \mathbf{elif}\;b \leq 1.12 \cdot 10^{-47}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* k (* j -27.0))))
   (if (<= b -8.5e+86)
     (* b c)
     (if (<= b -2.8e-125)
       t_1
       (if (<= b -2.1e-306)
         (* (* t a) -4.0)
         (if (<= b 1.12e-47) t_1 (* b c)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = k * (j * -27.0);
	double tmp;
	if (b <= -8.5e+86) {
		tmp = b * c;
	} else if (b <= -2.8e-125) {
		tmp = t_1;
	} else if (b <= -2.1e-306) {
		tmp = (t * a) * -4.0;
	} else if (b <= 1.12e-47) {
		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.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = k * (j * (-27.0d0))
    if (b <= (-8.5d+86)) then
        tmp = b * c
    else if (b <= (-2.8d-125)) then
        tmp = t_1
    else if (b <= (-2.1d-306)) then
        tmp = (t * a) * (-4.0d0)
    else if (b <= 1.12d-47) 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;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = k * (j * -27.0);
	double tmp;
	if (b <= -8.5e+86) {
		tmp = b * c;
	} else if (b <= -2.8e-125) {
		tmp = t_1;
	} else if (b <= -2.1e-306) {
		tmp = (t * a) * -4.0;
	} else if (b <= 1.12e-47) {
		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])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = k * (j * -27.0)
	tmp = 0
	if b <= -8.5e+86:
		tmp = b * c
	elif b <= -2.8e-125:
		tmp = t_1
	elif b <= -2.1e-306:
		tmp = (t * a) * -4.0
	elif b <= 1.12e-47:
		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])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(k * Float64(j * -27.0))
	tmp = 0.0
	if (b <= -8.5e+86)
		tmp = Float64(b * c);
	elseif (b <= -2.8e-125)
		tmp = t_1;
	elseif (b <= -2.1e-306)
		tmp = Float64(Float64(t * a) * -4.0);
	elseif (b <= 1.12e-47)
		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])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = k * (j * -27.0);
	tmp = 0.0;
	if (b <= -8.5e+86)
		tmp = b * c;
	elseif (b <= -2.8e-125)
		tmp = t_1;
	elseif (b <= -2.1e-306)
		tmp = (t * a) * -4.0;
	elseif (b <= 1.12e-47)
		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.
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[b, -8.5e+86], N[(b * c), $MachinePrecision], If[LessEqual[b, -2.8e-125], t$95$1, If[LessEqual[b, -2.1e-306], N[(N[(t * a), $MachinePrecision] * -4.0), $MachinePrecision], If[LessEqual[b, 1.12e-47], t$95$1, N[(b * c), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -8.5000000000000005e86 or 1.12000000000000002e-47 < b

   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 87.8%

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

      1. associate-*r* 87.8%

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

      2. distribute-rgt-out-- 84.0%

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

      3. associate-*l* 82.4%

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

      4. *-commutative 82.4%

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

      5. *-commutative 82.4%

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

   6. Applied egg-rr 82.4%

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

   7. Taylor expanded in b around inf 35.7%

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

   if -8.5000000000000005e86 < b < -2.8e-125 or -2.1000000000000001e-306 < b < 1.12000000000000002e-47

   1. Initial program 84.1%

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

   3. Simplified 89.9%

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

   5. Taylor expanded in j around inf 31.7%

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

      1. *-commutative 31.7%

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

      2. associate-*r* 31.7%

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

      3. *-commutative 31.7%

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

      4. associate-*l* 31.7%

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

   7. Simplified 31.7%

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

   if -2.8e-125 < b < -2.1000000000000001e-306

   1. Initial program 84.9%

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

   3. Simplified 88.7%

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

      1. associate-*r* 85.1%

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

      2. distribute-rgt-out-- 81.2%

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

      3. associate-*l* 84.8%

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

      4. *-commutative 84.8%

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

      5. *-commutative 84.8%

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

   6. Applied egg-rr 84.8%

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

   7. Taylor expanded in a around inf 26.3%

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

4. Final simplification 33.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8.5 \cdot 10^{+86}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \leq -2.8 \cdot 10^{-125}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;b \leq -2.1 \cdot 10^{-306}:\\ \;\;\;\;\left(t \cdot a\right) \cdot -4\\ \mathbf{elif}\;b \leq 1.12 \cdot 10^{-47}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 29: 32.8% accurate, 2.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -1.35 \cdot 10^{+86} \lor \neg \left(b \leq 7.2 \cdot 10^{-48}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= b -1.35e+86) (not (<= b 7.2e-48))) (* b c) (* (* j k) -27.0)))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b <= -1.35e+86) || !(b <= 7.2e-48)) {
		tmp = b * c;
	} else {
		tmp = (j * k) * -27.0;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((b <= (-1.35d+86)) .or. (.not. (b <= 7.2d-48))) then
        tmp = b * c
    else
        tmp = (j * k) * (-27.0d0)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b <= -1.35e+86) || !(b <= 7.2e-48)) {
		tmp = b * c;
	} else {
		tmp = (j * k) * -27.0;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (b <= -1.35e+86) or not (b <= 7.2e-48):
		tmp = b * c
	else:
		tmp = (j * k) * -27.0
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((b <= -1.35e+86) || !(b <= 7.2e-48))
		tmp = Float64(b * c);
	else
		tmp = Float64(Float64(j * k) * -27.0);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((b <= -1.35e+86) || ~((b <= 7.2e-48)))
		tmp = b * c;
	else
		tmp = (j * k) * -27.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[b, -1.35e+86], N[Not[LessEqual[b, 7.2e-48]], $MachinePrecision]], N[(b * c), $MachinePrecision], N[(N[(j * k), $MachinePrecision] * -27.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.35000000000000009e86 or 7.2000000000000003e-48 < b

   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 87.8%

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

      1. associate-*r* 87.8%

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

      2. distribute-rgt-out-- 84.0%

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

      3. associate-*l* 82.4%

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

      4. *-commutative 82.4%

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

      5. *-commutative 82.4%

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

   6. Applied egg-rr 82.4%

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

   7. Taylor expanded in b around inf 35.7%

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

   if -1.35000000000000009e86 < b < 7.2000000000000003e-48

   1. Initial program 84.2%

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

   3. Simplified 89.7%

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

   5. Taylor expanded in j around inf 28.8%

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

4. Final simplification 32.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.35 \cdot 10^{+86} \lor \neg \left(b \leq 7.2 \cdot 10^{-48}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \end{array} \]
5. Add Preprocessing

Alternative 30: 23.5% accurate, 10.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 84.1%

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

3. Simplified 88.3%

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

   1. associate-*r* 88.5%

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

   2. distribute-rgt-out-- 84.2%

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

   3. associate-*l* 83.3%

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

   4. *-commutative 83.3%

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

   5. *-commutative 83.3%

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

6. Applied egg-rr 83.3%

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

7. Taylor expanded in b around inf 23.6%

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

8. Final simplification 23.6%

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

Developer target: 89.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a \cdot t + i \cdot x\right) \cdot 4\\ t_2 := \left(\left(18 \cdot t\right) \cdot \left(\left(x \cdot y\right) \cdot z\right) - t_1\right) - \left(\left(k \cdot j\right) \cdot 27 - c \cdot b\right)\\ \mathbf{if}\;t < -1.6210815397541398 \cdot 10^{-69}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t < 165.68027943805222:\\ \;\;\;\;\left(\left(18 \cdot y\right) \cdot \left(x \cdot \left(z \cdot t\right)\right) - t_1\right) + \left(c \cdot b - 27 \cdot \left(k \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (+ (* a t) (* i x)) 4.0))
        (t_2
         (-
          (- (* (* 18.0 t) (* (* x y) z)) t_1)
          (- (* (* k j) 27.0) (* c b)))))
   (if (< t -1.6210815397541398e-69)
     t_2
     (if (< t 165.68027943805222)
       (+ (- (* (* 18.0 y) (* x (* z t))) t_1) (- (* c b) (* 27.0 (* k j))))
       t_2))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((a * t) + (i * x)) * 4.0;
	double t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b));
	double tmp;
	if (t < -1.6210815397541398e-69) {
		tmp = t_2;
	} else if (t < 165.68027943805222) {
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((a * t) + (i * x)) * 4.0d0
    t_2 = (((18.0d0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0d0) - (c * b))
    if (t < (-1.6210815397541398d-69)) then
        tmp = t_2
    else if (t < 165.68027943805222d0) then
        tmp = (((18.0d0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0d0 * (k * j)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((a * t) + (i * x)) * 4.0;
	double t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b));
	double tmp;
	if (t < -1.6210815397541398e-69) {
		tmp = t_2;
	} else if (t < 165.68027943805222) {
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = ((a * t) + (i * x)) * 4.0
	t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b))
	tmp = 0
	if t < -1.6210815397541398e-69:
		tmp = t_2
	elif t < 165.68027943805222:
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(Float64(a * t) + Float64(i * x)) * 4.0)
	t_2 = Float64(Float64(Float64(Float64(18.0 * t) * Float64(Float64(x * y) * z)) - t_1) - Float64(Float64(Float64(k * j) * 27.0) - Float64(c * b)))
	tmp = 0.0
	if (t < -1.6210815397541398e-69)
		tmp = t_2;
	elseif (t < 165.68027943805222)
		tmp = Float64(Float64(Float64(Float64(18.0 * y) * Float64(x * Float64(z * t))) - t_1) + Float64(Float64(c * b) - Float64(27.0 * Float64(k * j))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = ((a * t) + (i * x)) * 4.0;
	t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b));
	tmp = 0.0;
	if (t < -1.6210815397541398e-69)
		tmp = t_2;
	elseif (t < 165.68027943805222)
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(N[(a * t), $MachinePrecision] + N[(i * x), $MachinePrecision]), $MachinePrecision] * 4.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(18.0 * t), $MachinePrecision] * N[(N[(x * y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] - N[(N[(N[(k * j), $MachinePrecision] * 27.0), $MachinePrecision] - N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -1.6210815397541398e-69], t$95$2, If[Less[t, 165.68027943805222], N[(N[(N[(N[(18.0 * y), $MachinePrecision] * N[(x * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] + N[(N[(c * b), $MachinePrecision] - N[(27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2024019 
(FPCore (x y z t a b c i j k)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, E"
  :precision binary64

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

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