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

Percentage Accurate: 85.7% → 92.2%

Time: 20.6s

Alternatives: 22

Speedup: 0.8×

• 49.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 92.2% accurate, 0.5× speedup

Math

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

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
         (-
          (-
           (+ (- (* (* (* (* 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 (* 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 = (((((((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 = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	}
	return tmp;
}

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (((((((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 = 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 = (((((((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 = 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(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(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 = (((((((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 = 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[(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[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 97.3%

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

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

   1. Initial program 0.0%

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

   3. Simplified 24.2%

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

   5. Taylor expanded in x around inf 76.0%

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

4. Final simplification 94.6%

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

Alternative 2: 89.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+117} \lor \neg \left(t \leq 0.0105\right):\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b \cdot c + \left(y \cdot \left(\left(x \cdot 18\right) \cdot \left(z \cdot t\right)\right) - t \cdot \left(a \cdot 4\right)\right)\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \end{array} \]

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 (<= t -5e+117) (not (<= t 0.0105)))
   (- (+ (* b c) (* t (- (* 18.0 (* x (* y z))) (* a 4.0)))) (* 27.0 (* j k)))
   (-
    (-
     (+ (* b c) (- (* y (* (* x 18.0) (* z t))) (* t (* 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) {
	double tmp;
	if ((t <= -5e+117) || !(t <= 0.0105)) {
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - (27.0 * (j * k));
	} else {
		tmp = (((b * c) + ((y * ((x * 18.0) * (z * t))) - (t * (a * 4.0)))) - ((x * 4.0) * i)) - ((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 ((t <= (-5d+117)) .or. (.not. (t <= 0.0105d0))) then
        tmp = ((b * c) + (t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0)))) - (27.0d0 * (j * k))
    else
        tmp = (((b * c) + ((y * ((x * 18.0d0) * (z * t))) - (t * (a * 4.0d0)))) - ((x * 4.0d0) * i)) - ((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 ((t <= -5e+117) || !(t <= 0.0105)) {
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - (27.0 * (j * k));
	} else {
		tmp = (((b * c) + ((y * ((x * 18.0) * (z * t))) - (t * (a * 4.0)))) - ((x * 4.0) * i)) - ((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 (t <= -5e+117) or not (t <= 0.0105):
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - (27.0 * (j * k))
	else:
		tmp = (((b * c) + ((y * ((x * 18.0) * (z * t))) - (t * (a * 4.0)))) - ((x * 4.0) * i)) - ((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 ((t <= -5e+117) || !(t <= 0.0105))
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)))) - Float64(27.0 * Float64(j * k)));
	else
		tmp = Float64(Float64(Float64(Float64(b * c) + Float64(Float64(y * Float64(Float64(x * 18.0) * Float64(z * t))) - Float64(t * Float64(a * 4.0)))) - Float64(Float64(x * 4.0) * i)) - 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 ((t <= -5e+117) || ~((t <= 0.0105)))
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - (27.0 * (j * k));
	else
		tmp = (((b * c) + ((y * ((x * 18.0) * (z * t))) - (t * (a * 4.0)))) - ((x * 4.0) * i)) - ((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[t, -5e+117], N[Not[LessEqual[t, 0.0105]], $MachinePrecision]], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(b * c), $MachinePrecision] + N[(N[(y * N[(N[(x * 18.0), $MachinePrecision] * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.99999999999999983e117 or 0.0105000000000000007 < t

   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 84.3%

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

   5. Taylor expanded in i around 0 87.5%

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

   if -4.99999999999999983e117 < t < 0.0105000000000000007

   1. Initial program 90.0%

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

      1. pow1 90.0%

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

      2. associate-*l* 91.8%

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

      3. *-commutative 91.8%

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

   4. Applied egg-rr 91.8%

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

      1. unpow1 91.8%

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

      2. associate-*l* 94.9%

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

      3. *-commutative 94.9%

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

   6. Simplified 94.9%

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

4. Final simplification 92.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+117} \lor \neg \left(t \leq 0.0105\right):\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b \cdot c + \left(y \cdot \left(\left(x \cdot 18\right) \cdot \left(z \cdot t\right)\right) - t \cdot \left(a \cdot 4\right)\right)\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 87.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{+190} \lor \neg \left(x \leq 3.05 \cdot 10^{+243}\right):\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \end{array} \end{array} \]

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 -1.45e+190) (not (<= x 3.05e+243)))
   (* x (- (* 18.0 (* t (* y z))) (* 4.0 i)))
   (-
    (+ (* 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) {
	double tmp;
	if ((x <= -1.45e+190) || !(x <= 3.05e+243)) {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	} else {
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (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 <= (-1.45d+190)) .or. (.not. (x <= 3.05d+243))) then
        tmp = x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i))
    else
        tmp = ((b * c) + (t * (((x * 18.0d0) * (y * z)) - (a * 4.0d0)))) - ((x * (4.0d0 * i)) + (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 <= -1.45e+190) || !(x <= 3.05e+243)) {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	} else {
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (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 <= -1.45e+190) or not (x <= 3.05e+243):
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i))
	else:
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (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 <= -1.45e+190) || !(x <= 3.05e+243))
		tmp = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)));
	else
		tmp = 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
	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 <= -1.45e+190) || ~((x <= 3.05e+243)))
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	else
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (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, -1.45e+190], N[Not[LessEqual[x, 3.05e+243]], $MachinePrecision]], N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 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. Split input into 2 regimes

2. if x < -1.44999999999999995e190 or 3.05000000000000011e243 < x

   1. Initial program 55.7%

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

   3. Simplified 60.4%

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

   5. Taylor expanded in x around inf 86.8%

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

   if -1.44999999999999995e190 < x < 3.05000000000000011e243

   1. Initial program 90.6%

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

   3. Simplified 91.3%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{+190} \lor \neg \left(x \leq 3.05 \cdot 10^{+243}\right):\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{+102} \lor \neg \left(t \leq 6.2 \cdot 10^{-5}\right):\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \end{array} \]

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 (<= t -5.2e+102) (not (<= t 6.2e-5)))
   (- (+ (* b c) (* t (- (* 18.0 (* x (* y z))) (* a 4.0)))) (* 27.0 (* j k)))
   (- (- (* b c) (* 4.0 (+ (* x i) (* 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 ((t <= -5.2e+102) || !(t <= 6.2e-5)) {
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - (27.0 * (j * k));
	} else {
		tmp = ((b * c) - (4.0 * ((x * i) + (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 ((t <= (-5.2d+102)) .or. (.not. (t <= 6.2d-5))) then
        tmp = ((b * c) + (t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0)))) - (27.0d0 * (j * k))
    else
        tmp = ((b * c) - (4.0d0 * ((x * i) + (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 ((t <= -5.2e+102) || !(t <= 6.2e-5)) {
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - (27.0 * (j * k));
	} else {
		tmp = ((b * c) - (4.0 * ((x * i) + (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 (t <= -5.2e+102) or not (t <= 6.2e-5):
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - (27.0 * (j * k))
	else:
		tmp = ((b * c) - (4.0 * ((x * i) + (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 ((t <= -5.2e+102) || !(t <= 6.2e-5))
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)))) - Float64(27.0 * Float64(j * k)));
	else
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(Float64(x * i) + 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 ((t <= -5.2e+102) || ~((t <= 6.2e-5)))
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - (27.0 * (j * k));
	else
		tmp = ((b * c) - (4.0 * ((x * i) + (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[t, -5.2e+102], N[Not[LessEqual[t, 6.2e-5]], $MachinePrecision]], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(N[(x * i), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.20000000000000013e102 or 6.20000000000000027e-5 < t

   1. Initial program 76.7%

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

   3. Simplified 83.9%

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

   5. Taylor expanded in i around 0 86.9%

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

   if -5.20000000000000013e102 < t < 6.20000000000000027e-5

   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 y around 0 88.8%

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

      1. distribute-lft-out 88.8%

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

      2. *-commutative 88.8%

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

   5. Simplified 88.8%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{+102} \lor \neg \left(t \leq 6.2 \cdot 10^{-5}\right):\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 68.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+150}:\\ \;\;\;\;b \cdot c - t\_1\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+153}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(x \cdot -4\right) - t\_1\\ \end{array} \end{array} \]

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 -2e+150)
     (- (* b c) t_1)
     (if (<= t_1 4e+153)
       (- (* b c) (* 4.0 (+ (* x i) (* t a))))
       (- (* i (* x -4.0)) t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (t_1 <= -2e+150) {
		tmp = (b * c) - t_1;
	} else if (t_1 <= 4e+153) {
		tmp = (b * c) - (4.0 * ((x * i) + (t * a)));
	} else {
		tmp = (i * (x * -4.0)) - t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (j * 27.0d0) * k
    if (t_1 <= (-2d+150)) then
        tmp = (b * c) - t_1
    else if (t_1 <= 4d+153) then
        tmp = (b * c) - (4.0d0 * ((x * i) + (t * a)))
    else
        tmp = (i * (x * (-4.0d0))) - t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (t_1 <= -2e+150) {
		tmp = (b * c) - t_1;
	} else if (t_1 <= 4e+153) {
		tmp = (b * c) - (4.0 * ((x * i) + (t * a)));
	} else {
		tmp = (i * (x * -4.0)) - t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	tmp = 0
	if t_1 <= -2e+150:
		tmp = (b * c) - t_1
	elif t_1 <= 4e+153:
		tmp = (b * c) - (4.0 * ((x * i) + (t * a)))
	else:
		tmp = (i * (x * -4.0)) - t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_1 <= -2e+150)
		tmp = Float64(Float64(b * c) - t_1);
	elseif (t_1 <= 4e+153)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(Float64(x * i) + Float64(t * a))));
	else
		tmp = Float64(Float64(i * Float64(x * -4.0)) - t_1);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * 27.0) * k;
	tmp = 0.0;
	if (t_1 <= -2e+150)
		tmp = (b * c) - t_1;
	elseif (t_1 <= 4e+153)
		tmp = (b * c) - (4.0 * ((x * i) + (t * a)));
	else
		tmp = (i * (x * -4.0)) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+150], N[(N[(b * c), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[t$95$1, 4e+153], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(N[(x * i), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(i * N[(x * -4.0), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -1.99999999999999996e150

   1. Initial program 86.4%

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

      1. pow1 86.4%

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

      2. associate-*l* 83.6%

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

      3. *-commutative 83.6%

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

   4. Applied egg-rr 83.6%

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

      1. unpow1 83.6%

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

      2. associate-*l* 86.3%

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

      3. *-commutative 86.3%

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

   6. Simplified 86.3%

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

   7. Taylor expanded in b around inf 86.3%

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

   if -1.99999999999999996e150 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 4e153

   1. Initial program 88.9%

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

      1. pow1 88.9%

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

      2. associate-*l* 87.2%

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

      3. *-commutative 87.2%

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

   4. Applied egg-rr 87.2%

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

      1. unpow1 87.2%

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

      2. associate-*l* 88.9%

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

      3. *-commutative 88.9%

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

   6. Simplified 88.9%

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

   7. Taylor expanded in y around 0 80.8%

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

      1. distribute-lft-out 80.8%

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

      2. *-commutative 80.8%

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

      3. *-commutative 80.8%

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

   9. Simplified 80.8%

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

   10. Taylor expanded in j around 0 74.3%

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

   if 4e153 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 64.8%

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

      1. pow1 64.8%

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

      2. associate-*l* 67.3%

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

      3. *-commutative 67.3%

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

   4. Applied egg-rr 67.3%

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

      1. unpow1 67.3%

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

      2. associate-*l* 67.3%

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

      3. *-commutative 67.3%

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

   6. Simplified 67.3%

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

   7. Taylor expanded in i around inf 75.6%

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

      1. metadata-eval 75.6%

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

      2. distribute-lft-neg-in 75.6%

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

      3. associate-*r* 75.6%

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

      4. *-commutative 75.6%

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

      5. associate-*r* 75.6%

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

      6. distribute-lft-neg-out 75.6%

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

      7. distribute-rgt-neg-in 75.6%

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

      8. metadata-eval 75.6%

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

      9. *-commutative 75.6%

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

      10. *-commutative 75.6%

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

      11. *-commutative 75.6%

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

   9. Simplified 75.6%

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

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \leq -2 \cdot 10^{+150}:\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 4 \cdot 10^{+153}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(x \cdot -4\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 80.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t \leq -1.25 \cdot 10^{+95} \lor \neg \left(t \leq 2.1 \cdot 10^{+172}\right):\\ \;\;\;\;t \cdot \left(z \cdot \left(x \cdot \left(y \cdot \left(--18\right)\right)\right) - a \cdot 4\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\right) - t\_1\\ \end{array} \end{array} \]

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 (or (<= t -1.25e+95) (not (<= t 2.1e+172)))
     (- (* t (- (* z (* x (* y (- -18.0)))) (* a 4.0))) t_1)
     (- (- (* b c) (* 4.0 (+ (* x i) (* 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 <= -1.25e+95) || !(t <= 2.1e+172)) {
		tmp = (t * ((z * (x * (y * -(-18.0)))) - (a * 4.0))) - t_1;
	} else {
		tmp = ((b * c) - (4.0 * ((x * i) + (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 <= (-1.25d+95)) .or. (.not. (t <= 2.1d+172))) then
        tmp = (t * ((z * (x * (y * -(-18.0d0)))) - (a * 4.0d0))) - t_1
    else
        tmp = ((b * c) - (4.0d0 * ((x * i) + (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 <= -1.25e+95) || !(t <= 2.1e+172)) {
		tmp = (t * ((z * (x * (y * -(-18.0)))) - (a * 4.0))) - t_1;
	} else {
		tmp = ((b * c) - (4.0 * ((x * i) + (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 <= -1.25e+95) or not (t <= 2.1e+172):
		tmp = (t * ((z * (x * (y * -(-18.0)))) - (a * 4.0))) - t_1
	else:
		tmp = ((b * c) - (4.0 * ((x * i) + (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 <= -1.25e+95) || !(t <= 2.1e+172))
		tmp = Float64(Float64(t * Float64(Float64(z * Float64(x * Float64(y * Float64(-(-18.0))))) - Float64(a * 4.0))) - t_1);
	else
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(Float64(x * i) + 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 <= -1.25e+95) || ~((t <= 2.1e+172)))
		tmp = (t * ((z * (x * (y * -(-18.0)))) - (a * 4.0))) - t_1;
	else
		tmp = ((b * c) - (4.0 * ((x * i) + (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[Or[LessEqual[t, -1.25e+95], N[Not[LessEqual[t, 2.1e+172]], $MachinePrecision]], N[(N[(t * N[(N[(z * N[(x * N[(y * (--18.0)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(N[(x * i), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.25000000000000006e95 or 2.1000000000000001e172 < t

   1. Initial program 70.4%

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

   3. Taylor expanded in t around -inf 83.2%

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

      1. associate-*r* 83.2%

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

      2. neg-mul-1 83.2%

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

      3. cancel-sign-sub-inv 83.2%

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

      4. metadata-eval 83.2%

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

      5. *-commutative 83.2%

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

      6. associate-*r* 83.2%

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

   5. Simplified 83.2%

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

   6. Taylor expanded in x around 0 83.2%

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

      1. associate-*r* 83.2%

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

      2. *-commutative 83.2%

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

      3. *-commutative 83.2%

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

      4. *-commutative 83.2%

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

      5. associate-*l* 84.5%

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

      6. *-commutative 84.5%

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

      7. associate-*l* 85.8%

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

   8. Simplified 85.8%

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

   if -1.25000000000000006e95 < t < 2.1000000000000001e172

   1. Initial program 90.3%

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

   3. Taylor expanded in y around 0 87.8%

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

      1. distribute-lft-out 87.8%

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

      2. *-commutative 87.8%

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

   5. Simplified 87.8%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{+95} \lor \neg \left(t \leq 2.1 \cdot 10^{+172}\right):\\ \;\;\;\;t \cdot \left(z \cdot \left(x \cdot \left(y \cdot \left(--18\right)\right)\right) - a \cdot 4\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 81.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t \leq -4.4 \cdot 10^{+94}:\\ \;\;\;\;t \cdot \left(z \cdot \left(x \cdot \left(y \cdot \left(--18\right)\right)\right) - a \cdot 4\right) - t\_1\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+90}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot \left(-4\right) - \left(y \cdot z\right) \cdot \left(x \cdot -18\right)\right) - t\_1\\ \end{array} \end{array} \]

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 -4.4e+94)
     (- (* t (- (* z (* x (* y (- -18.0)))) (* a 4.0))) t_1)
     (if (<= t 8.5e+90)
       (- (- (* b c) (* 4.0 (+ (* x i) (* t a)))) t_1)
       (- (* t (- (* a (- 4.0)) (* (* y z) (* x -18.0)))) 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 <= -4.4e+94) {
		tmp = (t * ((z * (x * (y * -(-18.0)))) - (a * 4.0))) - t_1;
	} else if (t <= 8.5e+90) {
		tmp = ((b * c) - (4.0 * ((x * i) + (t * a)))) - t_1;
	} else {
		tmp = (t * ((a * -4.0) - ((y * z) * (x * -18.0)))) - t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 <= (-4.4d+94)) then
        tmp = (t * ((z * (x * (y * -(-18.0d0)))) - (a * 4.0d0))) - t_1
    else if (t <= 8.5d+90) then
        tmp = ((b * c) - (4.0d0 * ((x * i) + (t * a)))) - t_1
    else
        tmp = (t * ((a * -4.0d0) - ((y * z) * (x * (-18.0d0))))) - t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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 <= -4.4e+94) {
		tmp = (t * ((z * (x * (y * -(-18.0)))) - (a * 4.0))) - t_1;
	} else if (t <= 8.5e+90) {
		tmp = ((b * c) - (4.0 * ((x * i) + (t * a)))) - t_1;
	} else {
		tmp = (t * ((a * -4.0) - ((y * z) * (x * -18.0)))) - t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	tmp = 0
	if t <= -4.4e+94:
		tmp = (t * ((z * (x * (y * -(-18.0)))) - (a * 4.0))) - t_1
	elif t <= 8.5e+90:
		tmp = ((b * c) - (4.0 * ((x * i) + (t * a)))) - t_1
	else:
		tmp = (t * ((a * -4.0) - ((y * z) * (x * -18.0)))) - t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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 <= -4.4e+94)
		tmp = Float64(Float64(t * Float64(Float64(z * Float64(x * Float64(y * Float64(-(-18.0))))) - Float64(a * 4.0))) - t_1);
	elseif (t <= 8.5e+90)
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(Float64(x * i) + Float64(t * a)))) - t_1);
	else
		tmp = Float64(Float64(t * Float64(Float64(a * Float64(-4.0)) - Float64(Float64(y * z) * Float64(x * -18.0)))) - t_1);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
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 <= -4.4e+94)
		tmp = (t * ((z * (x * (y * -(-18.0)))) - (a * 4.0))) - t_1;
	elseif (t <= 8.5e+90)
		tmp = ((b * c) - (4.0 * ((x * i) + (t * a)))) - t_1;
	else
		tmp = (t * ((a * -4.0) - ((y * z) * (x * -18.0)))) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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, -4.4e+94], N[(N[(t * N[(N[(z * N[(x * N[(y * (--18.0)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[t, 8.5e+90], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(N[(x * i), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(t * N[(N[(a * (-4.0)), $MachinePrecision] - N[(N[(y * z), $MachinePrecision] * N[(x * -18.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.40000000000000024e94

   1. Initial program 71.7%

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

   3. Taylor expanded in t around -inf 78.5%

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

      1. associate-*r* 78.5%

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

      2. neg-mul-1 78.5%

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

      3. cancel-sign-sub-inv 78.5%

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

      4. metadata-eval 78.5%

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

      5. *-commutative 78.5%

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

      6. associate-*r* 78.5%

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

   5. Simplified 78.5%

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

   6. Taylor expanded in x around 0 78.5%

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

      1. associate-*r* 78.5%

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

      2. *-commutative 78.5%

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

      3. *-commutative 78.5%

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

      4. *-commutative 78.5%

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

      5. associate-*l* 80.5%

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

      6. *-commutative 80.5%

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

      7. associate-*l* 82.5%

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

   8. Simplified 82.5%

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

   if -4.40000000000000024e94 < t < 8.5000000000000002e90

   1. Initial program 90.7%

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

   3. Taylor expanded in y around 0 88.6%

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

      1. distribute-lft-out 88.6%

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

      2. *-commutative 88.6%

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

   5. Simplified 88.6%

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

   if 8.5000000000000002e90 < t

   1. Initial program 73.6%

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

   3. Taylor expanded in t around -inf 87.0%

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

      1. associate-*r* 87.0%

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

      2. neg-mul-1 87.0%

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

      3. cancel-sign-sub-inv 87.0%

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

      4. metadata-eval 87.0%

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

      5. *-commutative 87.0%

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

      6. associate-*r* 87.0%

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

   5. Simplified 87.0%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.4 \cdot 10^{+94}:\\ \;\;\;\;t \cdot \left(z \cdot \left(x \cdot \left(y \cdot \left(--18\right)\right)\right) - a \cdot 4\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+90}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot \left(-4\right) - \left(y \cdot z\right) \cdot \left(x \cdot -18\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 59.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{if}\;x \leq -4.5 \cdot 10^{+25}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{-174}:\\ \;\;\;\;a \cdot \left(t \cdot -4\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+48}:\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (* x (- (* 18.0 (* t (* y z))) (* 4.0 i)))))
   (if (<= x -4.5e+25)
     t_1
     (if (<= x -1.8e-174)
       (+ (* a (* t -4.0)) (* j (* k -27.0)))
       (if (<= x 2.8e+48) (- (* b c) (* (* j 27.0) k)) 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 = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	double tmp;
	if (x <= -4.5e+25) {
		tmp = t_1;
	} else if (x <= -1.8e-174) {
		tmp = (a * (t * -4.0)) + (j * (k * -27.0));
	} else if (x <= 2.8e+48) {
		tmp = (b * c) - ((j * 27.0) * k);
	} 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 = x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i))
    if (x <= (-4.5d+25)) then
        tmp = t_1
    else if (x <= (-1.8d-174)) then
        tmp = (a * (t * (-4.0d0))) + (j * (k * (-27.0d0)))
    else if (x <= 2.8d+48) then
        tmp = (b * c) - ((j * 27.0d0) * k)
    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 = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	double tmp;
	if (x <= -4.5e+25) {
		tmp = t_1;
	} else if (x <= -1.8e-174) {
		tmp = (a * (t * -4.0)) + (j * (k * -27.0));
	} else if (x <= 2.8e+48) {
		tmp = (b * c) - ((j * 27.0) * k);
	} 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 = x * ((18.0 * (t * (y * z))) - (4.0 * i))
	tmp = 0
	if x <= -4.5e+25:
		tmp = t_1
	elif x <= -1.8e-174:
		tmp = (a * (t * -4.0)) + (j * (k * -27.0))
	elif x <= 2.8e+48:
		tmp = (b * c) - ((j * 27.0) * k)
	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(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)))
	tmp = 0.0
	if (x <= -4.5e+25)
		tmp = t_1;
	elseif (x <= -1.8e-174)
		tmp = Float64(Float64(a * Float64(t * -4.0)) + Float64(j * Float64(k * -27.0)));
	elseif (x <= 2.8e+48)
		tmp = Float64(Float64(b * c) - Float64(Float64(j * 27.0) * k));
	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 = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	tmp = 0.0;
	if (x <= -4.5e+25)
		tmp = t_1;
	elseif (x <= -1.8e-174)
		tmp = (a * (t * -4.0)) + (j * (k * -27.0));
	elseif (x <= 2.8e+48)
		tmp = (b * c) - ((j * 27.0) * k);
	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[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.5e+25], t$95$1, If[LessEqual[x, -1.8e-174], N[(N[(a * N[(t * -4.0), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.8e+48], N[(N[(b * c), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.5000000000000003e25 or 2.80000000000000012e48 < x

   1. Initial program 72.9%

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

   3. Simplified 79.4%

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

   5. Taylor expanded in x around inf 74.1%

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

   if -4.5000000000000003e25 < x < -1.79999999999999999e-174

   1. Initial program 81.5%

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

   3. Simplified 93.2%

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

   5. Taylor expanded in a around inf 66.1%

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

      1. metadata-eval 66.1%

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

      2. distribute-lft-neg-in 66.1%

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

      3. *-commutative 66.1%

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

      4. associate-*l* 66.1%

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

      5. distribute-lft-neg-in 66.1%

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

      6. distribute-lft-neg-in 66.1%

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

      7. metadata-eval 66.1%

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

   7. Simplified 66.1%

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

   if -1.79999999999999999e-174 < x < 2.80000000000000012e48

   1. Initial program 98.1%

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

      1. pow1 98.1%

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

      2. associate-*l* 94.3%

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

      3. *-commutative 94.3%

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

   4. Applied egg-rr 94.3%

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

      1. unpow1 94.3%

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

      2. associate-*l* 94.3%

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

      3. *-commutative 94.3%

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

   6. Simplified 94.3%

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

   7. Taylor expanded in b around inf 63.9%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{+25}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{-174}:\\ \;\;\;\;a \cdot \left(t \cdot -4\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+48}:\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 59.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{if}\;t \leq -1.4 \cdot 10^{+45}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-238}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-17}:\\ \;\;\;\;i \cdot \left(x \cdot -4\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (* t (- (* 18.0 (* x (* y z))) (* a 4.0)))))
   (if (<= t -1.4e+45)
     t_1
     (if (<= t 1.2e-238)
       (+ (* b c) (* j (* k -27.0)))
       (if (<= t 1.4e-17) (- (* i (* x -4.0)) (* (* j 27.0) k)) 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 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	double tmp;
	if (t <= -1.4e+45) {
		tmp = t_1;
	} else if (t <= 1.2e-238) {
		tmp = (b * c) + (j * (k * -27.0));
	} else if (t <= 1.4e-17) {
		tmp = (i * (x * -4.0)) - ((j * 27.0) * k);
	} 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 = t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0))
    if (t <= (-1.4d+45)) then
        tmp = t_1
    else if (t <= 1.2d-238) then
        tmp = (b * c) + (j * (k * (-27.0d0)))
    else if (t <= 1.4d-17) then
        tmp = (i * (x * (-4.0d0))) - ((j * 27.0d0) * k)
    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 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	double tmp;
	if (t <= -1.4e+45) {
		tmp = t_1;
	} else if (t <= 1.2e-238) {
		tmp = (b * c) + (j * (k * -27.0));
	} else if (t <= 1.4e-17) {
		tmp = (i * (x * -4.0)) - ((j * 27.0) * k);
	} 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 = t * ((18.0 * (x * (y * z))) - (a * 4.0))
	tmp = 0
	if t <= -1.4e+45:
		tmp = t_1
	elif t <= 1.2e-238:
		tmp = (b * c) + (j * (k * -27.0))
	elif t <= 1.4e-17:
		tmp = (i * (x * -4.0)) - ((j * 27.0) * k)
	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(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)))
	tmp = 0.0
	if (t <= -1.4e+45)
		tmp = t_1;
	elseif (t <= 1.2e-238)
		tmp = Float64(Float64(b * c) + Float64(j * Float64(k * -27.0)));
	elseif (t <= 1.4e-17)
		tmp = Float64(Float64(i * Float64(x * -4.0)) - Float64(Float64(j * 27.0) * k));
	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 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	tmp = 0.0;
	if (t <= -1.4e+45)
		tmp = t_1;
	elseif (t <= 1.2e-238)
		tmp = (b * c) + (j * (k * -27.0));
	elseif (t <= 1.4e-17)
		tmp = (i * (x * -4.0)) - ((j * 27.0) * k);
	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[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.4e+45], t$95$1, If[LessEqual[t, 1.2e-238], N[(N[(b * c), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.4e-17], N[(N[(i * N[(x * -4.0), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.4e45 or 1.3999999999999999e-17 < t

   1. Initial program 78.1%

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

   3. Simplified 84.0%

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

   5. Taylor expanded in t around inf 66.3%

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

   if -1.4e45 < t < 1.1999999999999999e-238

   1. Initial program 91.7%

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

   3. Simplified 90.7%

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

   5. Taylor expanded in b around inf 66.8%

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

   if 1.1999999999999999e-238 < t < 1.3999999999999999e-17

   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. Step-by-step derivation

      1. pow1 88.6%

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

      2. associate-*l* 92.2%

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

      3. *-commutative 92.2%

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

   4. Applied egg-rr 92.2%

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

      1. unpow1 92.2%

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

      2. associate-*l* 96.0%

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

      3. *-commutative 96.0%

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

   6. Simplified 96.0%

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

   7. Taylor expanded in i around inf 71.6%

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

      1. metadata-eval 71.6%

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

      2. distribute-lft-neg-in 71.6%

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

      3. associate-*r* 71.6%

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

      4. *-commutative 71.6%

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

      5. associate-*r* 71.6%

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

      6. distribute-lft-neg-out 71.6%

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

      7. distribute-rgt-neg-in 71.6%

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

      8. metadata-eval 71.6%

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

      9. *-commutative 71.6%

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

      10. *-commutative 71.6%

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

      11. *-commutative 71.6%

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

   9. Simplified 71.6%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{+45}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-238}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-17}:\\ \;\;\;\;i \cdot \left(x \cdot -4\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 36.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -4.5 \cdot 10^{+147}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq 6.6 \cdot 10^{-165}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 5.8 \cdot 10^{+114}:\\ \;\;\;\;\left(x \cdot i\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

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
 (if (<= (* b c) -4.5e+147)
   (* b c)
   (if (<= (* b c) 6.6e-165)
     (* j (* k -27.0))
     (if (<= (* b c) 5.8e+114) (* (* x i) -4.0) (* 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 tmp;
	if ((b * c) <= -4.5e+147) {
		tmp = b * c;
	} else if ((b * c) <= 6.6e-165) {
		tmp = j * (k * -27.0);
	} else if ((b * c) <= 5.8e+114) {
		tmp = (x * i) * -4.0;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((b * c) <= (-4.5d+147)) then
        tmp = b * c
    else if ((b * c) <= 6.6d-165) then
        tmp = j * (k * (-27.0d0))
    else if ((b * c) <= 5.8d+114) then
        tmp = (x * i) * (-4.0d0)
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b * c) <= -4.5e+147) {
		tmp = b * c;
	} else if ((b * c) <= 6.6e-165) {
		tmp = j * (k * -27.0);
	} else if ((b * c) <= 5.8e+114) {
		tmp = (x * i) * -4.0;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (b * c) <= -4.5e+147:
		tmp = b * c
	elif (b * c) <= 6.6e-165:
		tmp = j * (k * -27.0)
	elif (b * c) <= 5.8e+114:
		tmp = (x * i) * -4.0
	else:
		tmp = b * c
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (Float64(b * c) <= -4.5e+147)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= 6.6e-165)
		tmp = Float64(j * Float64(k * -27.0));
	elseif (Float64(b * c) <= 5.8e+114)
		tmp = Float64(Float64(x * i) * -4.0);
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((b * c) <= -4.5e+147)
		tmp = b * c;
	elseif ((b * c) <= 6.6e-165)
		tmp = j * (k * -27.0);
	elseif ((b * c) <= 5.8e+114)
		tmp = (x * i) * -4.0;
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[N[(b * c), $MachinePrecision], -4.5e+147], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 6.6e-165], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 5.8e+114], N[(N[(x * i), $MachinePrecision] * -4.0), $MachinePrecision], N[(b * c), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -4.50000000000000008e147 or 5.8000000000000001e114 < (*.f64 b c)

   1. Initial program 83.4%

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

      1. pow1 83.4%

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

      2. associate-*l* 82.2%

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

      3. *-commutative 82.2%

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

   4. Applied egg-rr 82.2%

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

      1. unpow1 82.2%

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

      2. associate-*l* 82.3%

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

      3. *-commutative 82.3%

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

   6. Simplified 82.3%

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

   7. Taylor expanded in y around 0 79.8%

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

      1. distribute-lft-out 79.8%

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

      2. *-commutative 79.8%

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

      3. *-commutative 79.8%

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

   9. Simplified 79.8%

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

   10. Taylor expanded in b around inf 53.7%

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

   if -4.50000000000000008e147 < (*.f64 b c) < 6.5999999999999996e-165

   1. Initial program 84.3%

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

   3. Simplified 86.9%

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

   5. Taylor expanded in j around inf 39.4%

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

      1. *-commutative 39.4%

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

      2. associate-*r* 39.5%

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

      3. *-commutative 39.5%

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

   7. Simplified 39.5%

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

   if 6.5999999999999996e-165 < (*.f64 b c) < 5.8000000000000001e114

   1. Initial program 88.1%

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

      1. pow1 88.1%

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

      2. associate-*l* 89.9%

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

      3. *-commutative 89.9%

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

   4. Applied egg-rr 89.9%

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

      1. unpow1 89.9%

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

      2. associate-*l* 93.9%

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

      3. *-commutative 93.9%

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

   6. Simplified 93.9%

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

   7. Taylor expanded in y around 0 75.8%

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

      1. distribute-lft-out 75.8%

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

      2. *-commutative 75.8%

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

      3. *-commutative 75.8%

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

   9. Simplified 75.8%

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

   10. Taylor expanded in x around inf 33.9%

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

4. Final simplification 43.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -4.5 \cdot 10^{+147}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq 6.6 \cdot 10^{-165}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 5.8 \cdot 10^{+114}:\\ \;\;\;\;\left(x \cdot i\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 36.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.8 \cdot 10^{+147}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq 7 \cdot 10^{-166}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \mathbf{elif}\;b \cdot c \leq 1.04 \cdot 10^{+114}:\\ \;\;\;\;\left(x \cdot i\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

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
 (if (<= (* b c) -1.8e+147)
   (* b c)
   (if (<= (* b c) 7e-166)
     (* (* j k) -27.0)
     (if (<= (* b c) 1.04e+114) (* (* x i) -4.0) (* 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 tmp;
	if ((b * c) <= -1.8e+147) {
		tmp = b * c;
	} else if ((b * c) <= 7e-166) {
		tmp = (j * k) * -27.0;
	} else if ((b * c) <= 1.04e+114) {
		tmp = (x * i) * -4.0;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((b * c) <= (-1.8d+147)) then
        tmp = b * c
    else if ((b * c) <= 7d-166) then
        tmp = (j * k) * (-27.0d0)
    else if ((b * c) <= 1.04d+114) then
        tmp = (x * i) * (-4.0d0)
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b * c) <= -1.8e+147) {
		tmp = b * c;
	} else if ((b * c) <= 7e-166) {
		tmp = (j * k) * -27.0;
	} else if ((b * c) <= 1.04e+114) {
		tmp = (x * i) * -4.0;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (b * c) <= -1.8e+147:
		tmp = b * c
	elif (b * c) <= 7e-166:
		tmp = (j * k) * -27.0
	elif (b * c) <= 1.04e+114:
		tmp = (x * i) * -4.0
	else:
		tmp = b * c
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (Float64(b * c) <= -1.8e+147)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= 7e-166)
		tmp = Float64(Float64(j * k) * -27.0);
	elseif (Float64(b * c) <= 1.04e+114)
		tmp = Float64(Float64(x * i) * -4.0);
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((b * c) <= -1.8e+147)
		tmp = b * c;
	elseif ((b * c) <= 7e-166)
		tmp = (j * k) * -27.0;
	elseif ((b * c) <= 1.04e+114)
		tmp = (x * i) * -4.0;
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[N[(b * c), $MachinePrecision], -1.8e+147], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 7e-166], N[(N[(j * k), $MachinePrecision] * -27.0), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1.04e+114], N[(N[(x * i), $MachinePrecision] * -4.0), $MachinePrecision], N[(b * c), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -1.8000000000000001e147 or 1.04e114 < (*.f64 b c)

   1. Initial program 83.4%

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

      1. pow1 83.4%

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

      2. associate-*l* 82.2%

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

      3. *-commutative 82.2%

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

   4. Applied egg-rr 82.2%

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

      1. unpow1 82.2%

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

      2. associate-*l* 82.3%

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

      3. *-commutative 82.3%

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

   6. Simplified 82.3%

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

   7. Taylor expanded in y around 0 79.8%

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

      1. distribute-lft-out 79.8%

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

      2. *-commutative 79.8%

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

      3. *-commutative 79.8%

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

   9. Simplified 79.8%

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

   10. Taylor expanded in b around inf 53.7%

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

   if -1.8000000000000001e147 < (*.f64 b c) < 6.9999999999999998e-166

   1. Initial program 84.3%

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

   3. Simplified 86.9%

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

   5. Taylor expanded in j around inf 39.4%

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

   if 6.9999999999999998e-166 < (*.f64 b c) < 1.04e114

   1. Initial program 88.1%

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

      1. pow1 88.1%

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

      2. associate-*l* 89.9%

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

      3. *-commutative 89.9%

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

   4. Applied egg-rr 89.9%

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

      1. unpow1 89.9%

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

      2. associate-*l* 93.9%

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

      3. *-commutative 93.9%

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

   6. Simplified 93.9%

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

   7. Taylor expanded in y around 0 75.8%

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

      1. distribute-lft-out 75.8%

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

      2. *-commutative 75.8%

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

      3. *-commutative 75.8%

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

   9. Simplified 75.8%

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

   10. Taylor expanded in x around inf 33.9%

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

4. Final simplification 43.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.8 \cdot 10^{+147}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq 7 \cdot 10^{-166}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \mathbf{elif}\;b \cdot c \leq 1.04 \cdot 10^{+114}:\\ \;\;\;\;\left(x \cdot i\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 32.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;k \leq -3.65 \cdot 10^{-34}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \mathbf{elif}\;k \leq 1.55 \cdot 10^{-273}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 1.02 \cdot 10^{-218}:\\ \;\;\;\;\left(18 \cdot t\right) \cdot \left(z \cdot \left(x \cdot y\right)\right)\\ \mathbf{elif}\;k \leq 1.1 \cdot 10^{-30}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= k -3.65e-34)
   (* (* j k) -27.0)
   (if (<= k 1.55e-273)
     (* b c)
     (if (<= k 1.02e-218)
       (* (* 18.0 t) (* z (* x y)))
       (if (<= k 1.1e-30) (* t (* a -4.0)) (* k (* j -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 (k <= -3.65e-34) {
		tmp = (j * k) * -27.0;
	} else if (k <= 1.55e-273) {
		tmp = b * c;
	} else if (k <= 1.02e-218) {
		tmp = (18.0 * t) * (z * (x * y));
	} else if (k <= 1.1e-30) {
		tmp = t * (a * -4.0);
	} else {
		tmp = k * (j * -27.0);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 (k <= (-3.65d-34)) then
        tmp = (j * k) * (-27.0d0)
    else if (k <= 1.55d-273) then
        tmp = b * c
    else if (k <= 1.02d-218) then
        tmp = (18.0d0 * t) * (z * (x * y))
    else if (k <= 1.1d-30) then
        tmp = t * (a * (-4.0d0))
    else
        tmp = k * (j * (-27.0d0))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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 (k <= -3.65e-34) {
		tmp = (j * k) * -27.0;
	} else if (k <= 1.55e-273) {
		tmp = b * c;
	} else if (k <= 1.02e-218) {
		tmp = (18.0 * t) * (z * (x * y));
	} else if (k <= 1.1e-30) {
		tmp = t * (a * -4.0);
	} else {
		tmp = k * (j * -27.0);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if k <= -3.65e-34:
		tmp = (j * k) * -27.0
	elif k <= 1.55e-273:
		tmp = b * c
	elif k <= 1.02e-218:
		tmp = (18.0 * t) * (z * (x * y))
	elif k <= 1.1e-30:
		tmp = t * (a * -4.0)
	else:
		tmp = k * (j * -27.0)
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (k <= -3.65e-34)
		tmp = Float64(Float64(j * k) * -27.0);
	elseif (k <= 1.55e-273)
		tmp = Float64(b * c);
	elseif (k <= 1.02e-218)
		tmp = Float64(Float64(18.0 * t) * Float64(z * Float64(x * y)));
	elseif (k <= 1.1e-30)
		tmp = Float64(t * Float64(a * -4.0));
	else
		tmp = Float64(k * Float64(j * -27.0));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (k <= -3.65e-34)
		tmp = (j * k) * -27.0;
	elseif (k <= 1.55e-273)
		tmp = b * c;
	elseif (k <= 1.02e-218)
		tmp = (18.0 * t) * (z * (x * y));
	elseif (k <= 1.1e-30)
		tmp = t * (a * -4.0);
	else
		tmp = k * (j * -27.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[k, -3.65e-34], N[(N[(j * k), $MachinePrecision] * -27.0), $MachinePrecision], If[LessEqual[k, 1.55e-273], N[(b * c), $MachinePrecision], If[LessEqual[k, 1.02e-218], N[(N[(18.0 * t), $MachinePrecision] * N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 1.1e-30], N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if k < -3.64999999999999998e-34

   1. Initial program 82.5%

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

   3. Simplified 88.4%

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

   5. Taylor expanded in j around inf 37.6%

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

   if -3.64999999999999998e-34 < k < 1.54999999999999994e-273

   1. Initial program 89.0%

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

      1. pow1 89.0%

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

      2. associate-*l* 87.4%

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

      3. *-commutative 87.4%

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

   4. Applied egg-rr 87.4%

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

      1. unpow1 87.4%

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

      2. associate-*l* 92.3%

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

      3. *-commutative 92.3%

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

   6. Simplified 92.3%

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

   7. Taylor expanded in y around 0 81.9%

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

      1. distribute-lft-out 81.9%

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

      2. *-commutative 81.9%

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

      3. *-commutative 81.9%

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

   9. Simplified 81.9%

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

   10. Taylor expanded in b around inf 30.7%

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

   if 1.54999999999999994e-273 < k < 1.02e-218

   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 99.8%

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

   5. Taylor expanded in t around inf 61.1%

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

   6. Taylor expanded in x around inf 51.1%

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

      1. *-commutative 51.1%

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

      2. associate-*r* 51.1%

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

      3. associate-*l* 51.1%

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

      4. *-commutative 51.1%

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

   8. Simplified 51.1%

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

   9. Taylor expanded in t around 0 51.1%

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

       1. associate-*r* 51.1%

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

       2. associate-*r* 61.0%

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

   11. Simplified 61.0%

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

   if 1.02e-218 < k < 1.09999999999999992e-30

   1. Initial program 89.7%

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

   3. Simplified 89.7%

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

   5. Taylor expanded in t around inf 65.4%

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

   6. Taylor expanded in x around 0 51.6%

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

      1. *-commutative 51.6%

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

   8. Simplified 51.6%

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

   if 1.09999999999999992e-30 < k

   1. Initial program 82.3%

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

      1. pow1 82.3%

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

      2. associate-*l* 82.4%

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

      3. *-commutative 82.4%

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

   4. Applied egg-rr 82.4%

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

      1. unpow1 82.4%

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

      2. associate-*l* 81.2%

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

      3. *-commutative 81.2%

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

   6. Simplified 81.2%

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

   7. Taylor expanded in y around 0 83.5%

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

      1. distribute-lft-out 83.5%

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

      2. *-commutative 83.5%

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

      3. *-commutative 83.5%

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

   9. Simplified 83.5%

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

   10. Taylor expanded in i around inf 78.2%

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

   11. Taylor expanded in j around inf 46.0%

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

       1. associate-*r* 46.1%

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

       2. *-commutative 46.1%

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

       3. *-commutative 46.1%

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

   13. Simplified 46.1%

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

4. Final simplification 41.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -3.65 \cdot 10^{-34}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \mathbf{elif}\;k \leq 1.55 \cdot 10^{-273}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 1.02 \cdot 10^{-218}:\\ \;\;\;\;\left(18 \cdot t\right) \cdot \left(z \cdot \left(x \cdot y\right)\right)\\ \mathbf{elif}\;k \leq 1.1 \cdot 10^{-30}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 72.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{+46} \lor \neg \left(x \leq 1.9 \cdot 10^{+51}\right):\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \end{array} \]

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 -2e+46) (not (<= x 1.9e+51)))
   (* 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 <= -2e+46) || !(x <= 1.9e+51)) {
		tmp = 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 <= (-2d+46)) .or. (.not. (x <= 1.9d+51))) then
        tmp = 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 <= -2e+46) || !(x <= 1.9e+51)) {
		tmp = 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 <= -2e+46) or not (x <= 1.9e+51):
		tmp = 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 <= -2e+46) || !(x <= 1.9e+51))
		tmp = 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 <= -2e+46) || ~((x <= 1.9e+51)))
		tmp = 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, -2e+46], N[Not[LessEqual[x, 1.9e+51]], $MachinePrecision]], N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $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 < -2e46 or 1.8999999999999999e51 < x

   1. Initial program 71.8%

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

   3. Simplified 78.6%

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

   5. Taylor expanded in x around inf 75.0%

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

   if -2e46 < x < 1.8999999999999999e51

   1. Initial program 93.5%

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

   3. Taylor expanded in x around 0 83.2%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{+46} \lor \neg \left(x \leq 1.9 \cdot 10^{+51}\right):\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 54.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -240 \lor \neg \left(b \cdot c \leq 1.25 \cdot 10^{+122}\right):\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(x \cdot -4\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \end{array} \]

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 (<= (* b c) -240.0) (not (<= (* b c) 1.25e+122)))
   (+ (* b c) (* j (* k -27.0)))
   (- (* i (* x -4.0)) (* (* 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 (((b * c) <= -240.0) || !((b * c) <= 1.25e+122)) {
		tmp = (b * c) + (j * (k * -27.0));
	} else {
		tmp = (i * (x * -4.0)) - ((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 (((b * c) <= (-240.0d0)) .or. (.not. ((b * c) <= 1.25d+122))) then
        tmp = (b * c) + (j * (k * (-27.0d0)))
    else
        tmp = (i * (x * (-4.0d0))) - ((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 (((b * c) <= -240.0) || !((b * c) <= 1.25e+122)) {
		tmp = (b * c) + (j * (k * -27.0));
	} else {
		tmp = (i * (x * -4.0)) - ((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 ((b * c) <= -240.0) or not ((b * c) <= 1.25e+122):
		tmp = (b * c) + (j * (k * -27.0))
	else:
		tmp = (i * (x * -4.0)) - ((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 ((Float64(b * c) <= -240.0) || !(Float64(b * c) <= 1.25e+122))
		tmp = Float64(Float64(b * c) + Float64(j * Float64(k * -27.0)));
	else
		tmp = Float64(Float64(i * Float64(x * -4.0)) - 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 (((b * c) <= -240.0) || ~(((b * c) <= 1.25e+122)))
		tmp = (b * c) + (j * (k * -27.0));
	else
		tmp = (i * (x * -4.0)) - ((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[N[(b * c), $MachinePrecision], -240.0], N[Not[LessEqual[N[(b * c), $MachinePrecision], 1.25e+122]], $MachinePrecision]], N[(N[(b * c), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(i * N[(x * -4.0), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -240 or 1.24999999999999997e122 < (*.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 84.7%

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

   5. Taylor expanded in b around inf 66.6%

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

   if -240 < (*.f64 b c) < 1.24999999999999997e122

   1. Initial program 86.2%

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

      1. pow1 86.2%

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

      2. associate-*l* 84.8%

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

      3. *-commutative 84.8%

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

   4. Applied egg-rr 84.8%

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

      1. unpow1 84.8%

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

      2. associate-*l* 87.5%

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

      3. *-commutative 87.5%

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

   6. Simplified 87.5%

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

   7. Taylor expanded in i around inf 59.8%

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

      1. metadata-eval 59.8%

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

      2. distribute-lft-neg-in 59.8%

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

      3. associate-*r* 59.8%

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

      4. *-commutative 59.8%

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

      5. associate-*r* 59.8%

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

      6. distribute-lft-neg-out 59.8%

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

      7. distribute-rgt-neg-in 59.8%

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

      8. metadata-eval 59.8%

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

      9. *-commutative 59.8%

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

      10. *-commutative 59.8%

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

      11. *-commutative 59.8%

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

   9. Simplified 59.8%

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

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -240 \lor \neg \left(b \cdot c \leq 1.25 \cdot 10^{+122}\right):\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(x \cdot -4\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 54.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;b \cdot c \leq -1.8 \lor \neg \left(b \cdot c \leq 4.8 \cdot 10^{+121}\right):\\ \;\;\;\;b \cdot c + t\_1\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(x \cdot -4\right) + t\_1\\ \end{array} \end{array} \]

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 (* k -27.0))))
   (if (or (<= (* b c) -1.8) (not (<= (* b c) 4.8e+121)))
     (+ (* b c) t_1)
     (+ (* i (* x -4.0)) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double tmp;
	if (((b * c) <= -1.8) || !((b * c) <= 4.8e+121)) {
		tmp = (b * c) + t_1;
	} else {
		tmp = (i * (x * -4.0)) + t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * (k * (-27.0d0))
    if (((b * c) <= (-1.8d0)) .or. (.not. ((b * c) <= 4.8d+121))) then
        tmp = (b * c) + t_1
    else
        tmp = (i * (x * (-4.0d0))) + t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double tmp;
	if (((b * c) <= -1.8) || !((b * c) <= 4.8e+121)) {
		tmp = (b * c) + t_1;
	} else {
		tmp = (i * (x * -4.0)) + t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	tmp = 0
	if ((b * c) <= -1.8) or not ((b * c) <= 4.8e+121):
		tmp = (b * c) + t_1
	else:
		tmp = (i * (x * -4.0)) + t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * -27.0))
	tmp = 0.0
	if ((Float64(b * c) <= -1.8) || !(Float64(b * c) <= 4.8e+121))
		tmp = Float64(Float64(b * c) + t_1);
	else
		tmp = Float64(Float64(i * Float64(x * -4.0)) + t_1);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * -27.0);
	tmp = 0.0;
	if (((b * c) <= -1.8) || ~(((b * c) <= 4.8e+121)))
		tmp = (b * c) + t_1;
	else
		tmp = (i * (x * -4.0)) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[N[(b * c), $MachinePrecision], -1.8], N[Not[LessEqual[N[(b * c), $MachinePrecision], 4.8e+121]], $MachinePrecision]], N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision], N[(N[(i * N[(x * -4.0), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -1.80000000000000004 or 4.8e121 < (*.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 84.7%

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

   5. Taylor expanded in b around inf 66.6%

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

   if -1.80000000000000004 < (*.f64 b c) < 4.8e121

   1. Initial program 86.2%

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

   3. Simplified 89.8%

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

   5. Taylor expanded in i around inf 59.9%

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

      1. associate-*r* 59.9%

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

      2. *-commutative 59.9%

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

      3. associate-*r* 59.9%

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

      4. *-commutative 59.9%

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

      5. *-commutative 59.9%

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

   7. Simplified 59.9%

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

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.8 \lor \neg \left(b \cdot c \leq 4.8 \cdot 10^{+121}\right):\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(x \cdot -4\right) + j \cdot \left(k \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 54.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -200:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 10^{+118}:\\ \;\;\;\;i \cdot \left(x \cdot -4\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(c - \left(j \cdot 27\right) \cdot \frac{k}{b}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= (* b c) -200.0)
   (+ (* b c) (* j (* k -27.0)))
   (if (<= (* b c) 1e+118)
     (- (* i (* x -4.0)) (* (* j 27.0) k))
     (* b (- c (* (* j 27.0) (/ k b)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b * c) <= -200.0) {
		tmp = (b * c) + (j * (k * -27.0));
	} else if ((b * c) <= 1e+118) {
		tmp = (i * (x * -4.0)) - ((j * 27.0) * k);
	} else {
		tmp = b * (c - ((j * 27.0) * (k / b)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((b * c) <= (-200.0d0)) then
        tmp = (b * c) + (j * (k * (-27.0d0)))
    else if ((b * c) <= 1d+118) then
        tmp = (i * (x * (-4.0d0))) - ((j * 27.0d0) * k)
    else
        tmp = b * (c - ((j * 27.0d0) * (k / b)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b * c) <= -200.0) {
		tmp = (b * c) + (j * (k * -27.0));
	} else if ((b * c) <= 1e+118) {
		tmp = (i * (x * -4.0)) - ((j * 27.0) * k);
	} else {
		tmp = b * (c - ((j * 27.0) * (k / b)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (b * c) <= -200.0:
		tmp = (b * c) + (j * (k * -27.0))
	elif (b * c) <= 1e+118:
		tmp = (i * (x * -4.0)) - ((j * 27.0) * k)
	else:
		tmp = b * (c - ((j * 27.0) * (k / b)))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (Float64(b * c) <= -200.0)
		tmp = Float64(Float64(b * c) + Float64(j * Float64(k * -27.0)));
	elseif (Float64(b * c) <= 1e+118)
		tmp = Float64(Float64(i * Float64(x * -4.0)) - Float64(Float64(j * 27.0) * k));
	else
		tmp = Float64(b * Float64(c - Float64(Float64(j * 27.0) * Float64(k / b))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((b * c) <= -200.0)
		tmp = (b * c) + (j * (k * -27.0));
	elseif ((b * c) <= 1e+118)
		tmp = (i * (x * -4.0)) - ((j * 27.0) * k);
	else
		tmp = b * (c - ((j * 27.0) * (k / b)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[N[(b * c), $MachinePrecision], -200.0], N[(N[(b * c), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1e+118], N[(N[(i * N[(x * -4.0), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], N[(b * N[(c - N[(N[(j * 27.0), $MachinePrecision] * N[(k / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -200

   1. Initial program 86.0%

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

   3. Simplified 87.6%

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

   5. Taylor expanded in b around inf 66.0%

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

   if -200 < (*.f64 b c) < 9.99999999999999967e117

   1. Initial program 86.2%

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

      1. pow1 86.2%

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

      2. associate-*l* 84.8%

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

      3. *-commutative 84.8%

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

   4. Applied egg-rr 84.8%

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

      1. unpow1 84.8%

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

      2. associate-*l* 87.5%

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

      3. *-commutative 87.5%

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

   6. Simplified 87.5%

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

   7. Taylor expanded in i around inf 59.8%

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

      1. metadata-eval 59.8%

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

      2. distribute-lft-neg-in 59.8%

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

      3. associate-*r* 59.8%

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

      4. *-commutative 59.8%

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

      5. associate-*r* 59.8%

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

      6. distribute-lft-neg-out 59.8%

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

      7. distribute-rgt-neg-in 59.8%

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

      8. metadata-eval 59.8%

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

      9. *-commutative 59.8%

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

      10. *-commutative 59.8%

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

      11. *-commutative 59.8%

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

   9. Simplified 59.8%

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

   if 9.99999999999999967e117 < (*.f64 b c)

   1. Initial program 76.9%

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

   3. Taylor expanded in t around 0 75.0%

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

   4. Taylor expanded in b around -inf 75.1%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(-1 \cdot c + \left(4 \cdot \frac{i \cdot x}{b} + 27 \cdot \frac{j \cdot k}{b}\right)\right)\right)} \]

   5. Taylor expanded in i around 0 70.0%

      \[\leadsto -1 \cdot \color{blue}{\left(b \cdot \left(-1 \cdot c + 27 \cdot \frac{j \cdot k}{b}\right)\right)} \]
   6. Step-by-step derivation

      1. neg-mul-1 70.0%

         \[\leadsto -1 \cdot \left(b \cdot \left(\color{blue}{\left(-c\right)} + 27 \cdot \frac{j \cdot k}{b}\right)\right) \]

      2. +-commutative 70.0%

         \[\leadsto -1 \cdot \left(b \cdot \color{blue}{\left(27 \cdot \frac{j \cdot k}{b} + \left(-c\right)\right)}\right) \]

      3. associate-*r/ 70.0%

         \[\leadsto -1 \cdot \left(b \cdot \left(27 \cdot \color{blue}{\left(j \cdot \frac{k}{b}\right)} + \left(-c\right)\right)\right) \]

      4. unsub-neg 70.0%

         \[\leadsto -1 \cdot \left(b \cdot \color{blue}{\left(27 \cdot \left(j \cdot \frac{k}{b}\right) - c\right)}\right) \]

      5. associate-*r* 70.0%

         \[\leadsto -1 \cdot \left(b \cdot \left(\color{blue}{\left(27 \cdot j\right) \cdot \frac{k}{b}} - c\right)\right) \]

   7. Simplified 70.0%

      \[\leadsto -1 \cdot \color{blue}{\left(b \cdot \left(\left(27 \cdot j\right) \cdot \frac{k}{b} - c\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -200:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 10^{+118}:\\ \;\;\;\;i \cdot \left(x \cdot -4\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(c - \left(j \cdot 27\right) \cdot \frac{k}{b}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 78.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{+106}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \end{array} \]

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 (<= x -3e+106)
   (* x (- (* 18.0 (* t (* y z))) (* 4.0 i)))
   (- (- (* b c) (* 4.0 (+ (* x i) (* 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 <= -3e+106) {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	} else {
		tmp = ((b * c) - (4.0 * ((x * i) + (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 <= (-3d+106)) then
        tmp = x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i))
    else
        tmp = ((b * c) - (4.0d0 * ((x * i) + (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 <= -3e+106) {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	} else {
		tmp = ((b * c) - (4.0 * ((x * i) + (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 <= -3e+106:
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i))
	else:
		tmp = ((b * c) - (4.0 * ((x * i) + (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 <= -3e+106)
		tmp = 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(Float64(x * i) + 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 <= -3e+106)
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	else
		tmp = ((b * c) - (4.0 * ((x * i) + (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[LessEqual[x, -3e+106], N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(N[(x * i), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.0000000000000001e106

   1. Initial program 65.8%

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

   3. Simplified 72.6%

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

   5. Taylor expanded in x around inf 80.5%

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

   if -3.0000000000000001e106 < x

   1. Initial program 88.7%

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

   3. Taylor expanded in y around 0 84.3%

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

      1. distribute-lft-out 84.3%

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

      2. *-commutative 84.3%

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

   5. Simplified 84.3%

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

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{+106}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 32.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;k \leq -3.15 \cdot 10^{-32}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \mathbf{elif}\;k \leq 1.75 \cdot 10^{-292}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 10^{-30}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= k -3.15e-32)
   (* (* j k) -27.0)
   (if (<= k 1.75e-292)
     (* b c)
     (if (<= k 1e-30) (* t (* a -4.0)) (* k (* j -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 (k <= -3.15e-32) {
		tmp = (j * k) * -27.0;
	} else if (k <= 1.75e-292) {
		tmp = b * c;
	} else if (k <= 1e-30) {
		tmp = t * (a * -4.0);
	} else {
		tmp = k * (j * -27.0);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 (k <= (-3.15d-32)) then
        tmp = (j * k) * (-27.0d0)
    else if (k <= 1.75d-292) then
        tmp = b * c
    else if (k <= 1d-30) then
        tmp = t * (a * (-4.0d0))
    else
        tmp = k * (j * (-27.0d0))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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 (k <= -3.15e-32) {
		tmp = (j * k) * -27.0;
	} else if (k <= 1.75e-292) {
		tmp = b * c;
	} else if (k <= 1e-30) {
		tmp = t * (a * -4.0);
	} else {
		tmp = k * (j * -27.0);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if k <= -3.15e-32:
		tmp = (j * k) * -27.0
	elif k <= 1.75e-292:
		tmp = b * c
	elif k <= 1e-30:
		tmp = t * (a * -4.0)
	else:
		tmp = k * (j * -27.0)
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (k <= -3.15e-32)
		tmp = Float64(Float64(j * k) * -27.0);
	elseif (k <= 1.75e-292)
		tmp = Float64(b * c);
	elseif (k <= 1e-30)
		tmp = Float64(t * Float64(a * -4.0));
	else
		tmp = Float64(k * Float64(j * -27.0));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (k <= -3.15e-32)
		tmp = (j * k) * -27.0;
	elseif (k <= 1.75e-292)
		tmp = b * c;
	elseif (k <= 1e-30)
		tmp = t * (a * -4.0);
	else
		tmp = k * (j * -27.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[k, -3.15e-32], N[(N[(j * k), $MachinePrecision] * -27.0), $MachinePrecision], If[LessEqual[k, 1.75e-292], N[(b * c), $MachinePrecision], If[LessEqual[k, 1e-30], N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if k < -3.1499999999999999e-32

   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 88.2%

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

   5. Taylor expanded in j around inf 38.1%

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

   if -3.1499999999999999e-32 < k < 1.75e-292

   1. Initial program 88.9%

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

      1. pow1 88.9%

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

      2. associate-*l* 87.2%

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

      3. *-commutative 87.2%

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

   4. Applied egg-rr 87.2%

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

      1. unpow1 87.2%

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

      2. associate-*l* 92.1%

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

      3. *-commutative 92.1%

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

   6. Simplified 92.1%

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

   7. Taylor expanded in y around 0 81.6%

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

      1. distribute-lft-out 81.6%

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

      2. *-commutative 81.6%

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

      3. *-commutative 81.6%

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

   9. Simplified 81.6%

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

   10. Taylor expanded in b around inf 31.1%

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

   if 1.75e-292 < k < 1e-30

   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 92.8%

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

   5. Taylor expanded in t around inf 66.1%

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

   6. Taylor expanded in x around 0 46.4%

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

      1. *-commutative 46.4%

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

   8. Simplified 46.4%

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

   if 1e-30 < k

   1. Initial program 82.3%

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

      1. pow1 82.3%

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

      2. associate-*l* 82.4%

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

      3. *-commutative 82.4%

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

   4. Applied egg-rr 82.4%

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

      1. unpow1 82.4%

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

      2. associate-*l* 81.2%

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

      3. *-commutative 81.2%

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

   6. Simplified 81.2%

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

   7. Taylor expanded in y around 0 83.5%

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

      1. distribute-lft-out 83.5%

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

      2. *-commutative 83.5%

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

      3. *-commutative 83.5%

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

   9. Simplified 83.5%

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

   10. Taylor expanded in i around inf 78.2%

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

   11. Taylor expanded in j around inf 46.0%

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

       1. associate-*r* 46.1%

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

       2. *-commutative 46.1%

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

       3. *-commutative 46.1%

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

   13. Simplified 46.1%

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

4. Final simplification 40.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -3.15 \cdot 10^{-32}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \mathbf{elif}\;k \leq 1.75 \cdot 10^{-292}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 10^{-30}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 37.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -4.8 \cdot 10^{+147} \lor \neg \left(b \cdot c \leq 2.55 \cdot 10^{+120}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= (* b c) -4.8e+147) (not (<= (* b c) 2.55e+120)))
   (* b c)
   (* (* j k) -27.0)))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (((b * c) <= -4.8e+147) || !((b * c) <= 2.55e+120)) {
		tmp = b * c;
	} else {
		tmp = (j * k) * -27.0;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (((b * c) <= (-4.8d+147)) .or. (.not. ((b * c) <= 2.55d+120))) then
        tmp = b * c
    else
        tmp = (j * k) * (-27.0d0)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (((b * c) <= -4.8e+147) || !((b * c) <= 2.55e+120)) {
		tmp = b * c;
	} else {
		tmp = (j * k) * -27.0;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if ((b * c) <= -4.8e+147) or not ((b * c) <= 2.55e+120):
		tmp = b * c
	else:
		tmp = (j * k) * -27.0
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((Float64(b * c) <= -4.8e+147) || !(Float64(b * c) <= 2.55e+120))
		tmp = Float64(b * c);
	else
		tmp = Float64(Float64(j * k) * -27.0);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (((b * c) <= -4.8e+147) || ~(((b * c) <= 2.55e+120)))
		tmp = b * c;
	else
		tmp = (j * k) * -27.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[N[(b * c), $MachinePrecision], -4.8e+147], N[Not[LessEqual[N[(b * c), $MachinePrecision], 2.55e+120]], $MachinePrecision]], N[(b * c), $MachinePrecision], N[(N[(j * k), $MachinePrecision] * -27.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -4.80000000000000004e147 or 2.55000000000000014e120 < (*.f64 b c)

   1. Initial program 83.0%

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

      1. pow1 83.0%

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

      2. associate-*l* 81.7%

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

      3. *-commutative 81.7%

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

   4. Applied egg-rr 81.7%

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

      1. unpow1 81.7%

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

      2. associate-*l* 81.9%

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

      3. *-commutative 81.9%

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

   6. Simplified 81.9%

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

   7. Taylor expanded in y around 0 79.3%

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

      1. distribute-lft-out 79.3%

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

      2. *-commutative 79.3%

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

      3. *-commutative 79.3%

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

   9. Simplified 79.3%

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

   10. Taylor expanded in b around inf 55.0%

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

   if -4.80000000000000004e147 < (*.f64 b c) < 2.55000000000000014e120

   1. Initial program 85.6%

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

   3. Simplified 89.1%

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

   5. Taylor expanded in j around inf 34.6%

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

4. Final simplification 41.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -4.8 \cdot 10^{+147} \lor \neg \left(b \cdot c \leq 2.55 \cdot 10^{+120}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 47.6% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{+171}:\\ \;\;\;\;t \cdot \left(y \cdot \left(18 \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;x \leq 1.46 \cdot 10^{+53}:\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot i\right) \cdot -4\\ \end{array} \end{array} \]

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
 (if (<= x -1.05e+171)
   (* t (* y (* 18.0 (* x z))))
   (if (<= x 1.46e+53) (- (* b c) (* (* j 27.0) k)) (* (* x i) -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 tmp;
	if (x <= -1.05e+171) {
		tmp = t * (y * (18.0 * (x * z)));
	} else if (x <= 1.46e+53) {
		tmp = (b * c) - ((j * 27.0) * k);
	} else {
		tmp = (x * i) * -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) :: tmp
    if (x <= (-1.05d+171)) then
        tmp = t * (y * (18.0d0 * (x * z)))
    else if (x <= 1.46d+53) then
        tmp = (b * c) - ((j * 27.0d0) * k)
    else
        tmp = (x * i) * (-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 tmp;
	if (x <= -1.05e+171) {
		tmp = t * (y * (18.0 * (x * z)));
	} else if (x <= 1.46e+53) {
		tmp = (b * c) - ((j * 27.0) * k);
	} else {
		tmp = (x * i) * -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):
	tmp = 0
	if x <= -1.05e+171:
		tmp = t * (y * (18.0 * (x * z)))
	elif x <= 1.46e+53:
		tmp = (b * c) - ((j * 27.0) * k)
	else:
		tmp = (x * i) * -4.0
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (x <= -1.05e+171)
		tmp = Float64(t * Float64(y * Float64(18.0 * Float64(x * z))));
	elseif (x <= 1.46e+53)
		tmp = Float64(Float64(b * c) - Float64(Float64(j * 27.0) * k));
	else
		tmp = Float64(Float64(x * i) * -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)
	tmp = 0.0;
	if (x <= -1.05e+171)
		tmp = t * (y * (18.0 * (x * z)));
	elseif (x <= 1.46e+53)
		tmp = (b * c) - ((j * 27.0) * k);
	else
		tmp = (x * i) * -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_] := If[LessEqual[x, -1.05e+171], N[(t * N[(y * N[(18.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.46e+53], N[(N[(b * c), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], N[(N[(x * i), $MachinePrecision] * -4.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.0500000000000001e171

   1. Initial program 66.5%

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

   3. Simplified 69.6%

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

   5. Taylor expanded in t around inf 55.2%

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

   6. Taylor expanded in y around inf 58.1%

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

   7. Taylor expanded in a around 0 58.2%

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

   if -1.0500000000000001e171 < x < 1.45999999999999999e53

   1. Initial program 91.4%

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

      1. pow1 91.4%

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

      2. associate-*l* 89.1%

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

      3. *-commutative 89.1%

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

   4. Applied egg-rr 89.1%

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

      1. unpow1 89.1%

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

      2. associate-*l* 89.1%

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

      3. *-commutative 89.1%

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

   6. Simplified 89.1%

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

   7. Taylor expanded in b around inf 58.6%

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

   if 1.45999999999999999e53 < x

   1. Initial program 73.0%

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

      1. pow1 73.0%

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

      2. associate-*l* 73.0%

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

      3. *-commutative 73.0%

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

   4. Applied egg-rr 73.0%

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

      1. unpow1 73.0%

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

      2. associate-*l* 81.1%

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

      3. *-commutative 81.1%

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

   6. Simplified 81.1%

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

   7. Taylor expanded in y around 0 69.1%

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

      1. distribute-lft-out 69.1%

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

      2. *-commutative 69.1%

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

      3. *-commutative 69.1%

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

   9. Simplified 69.1%

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

   10. Taylor expanded in x around inf 45.8%

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

4. Final simplification 56.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{+171}:\\ \;\;\;\;t \cdot \left(y \cdot \left(18 \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;x \leq 1.46 \cdot 10^{+53}:\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot i\right) \cdot -4\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 47.7% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{+171}:\\ \;\;\;\;t \cdot \left(y \cdot \left(18 \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;x \leq 1.46 \cdot 10^{+53}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot i\right) \cdot -4\\ \end{array} \end{array} \]

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
 (if (<= x -1.25e+171)
   (* t (* y (* 18.0 (* x z))))
   (if (<= x 1.46e+53) (+ (* b c) (* j (* k -27.0))) (* (* x i) -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 tmp;
	if (x <= -1.25e+171) {
		tmp = t * (y * (18.0 * (x * z)));
	} else if (x <= 1.46e+53) {
		tmp = (b * c) + (j * (k * -27.0));
	} else {
		tmp = (x * i) * -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) :: tmp
    if (x <= (-1.25d+171)) then
        tmp = t * (y * (18.0d0 * (x * z)))
    else if (x <= 1.46d+53) then
        tmp = (b * c) + (j * (k * (-27.0d0)))
    else
        tmp = (x * i) * (-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 tmp;
	if (x <= -1.25e+171) {
		tmp = t * (y * (18.0 * (x * z)));
	} else if (x <= 1.46e+53) {
		tmp = (b * c) + (j * (k * -27.0));
	} else {
		tmp = (x * i) * -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):
	tmp = 0
	if x <= -1.25e+171:
		tmp = t * (y * (18.0 * (x * z)))
	elif x <= 1.46e+53:
		tmp = (b * c) + (j * (k * -27.0))
	else:
		tmp = (x * i) * -4.0
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (x <= -1.25e+171)
		tmp = Float64(t * Float64(y * Float64(18.0 * Float64(x * z))));
	elseif (x <= 1.46e+53)
		tmp = Float64(Float64(b * c) + Float64(j * Float64(k * -27.0)));
	else
		tmp = Float64(Float64(x * i) * -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)
	tmp = 0.0;
	if (x <= -1.25e+171)
		tmp = t * (y * (18.0 * (x * z)));
	elseif (x <= 1.46e+53)
		tmp = (b * c) + (j * (k * -27.0));
	else
		tmp = (x * i) * -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_] := If[LessEqual[x, -1.25e+171], N[(t * N[(y * N[(18.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.46e+53], N[(N[(b * c), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * i), $MachinePrecision] * -4.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.2500000000000001e171

   1. Initial program 66.5%

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

   3. Simplified 69.6%

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

   5. Taylor expanded in t around inf 55.2%

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

   6. Taylor expanded in y around inf 58.1%

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

   7. Taylor expanded in a around 0 58.2%

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

   if -1.2500000000000001e171 < x < 1.45999999999999999e53

   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 91.1%

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

   5. Taylor expanded in b around inf 58.7%

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

   if 1.45999999999999999e53 < x

   1. Initial program 73.0%

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

      1. pow1 73.0%

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

      2. associate-*l* 73.0%

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

      3. *-commutative 73.0%

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

   4. Applied egg-rr 73.0%

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

      1. unpow1 73.0%

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

      2. associate-*l* 81.1%

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

      3. *-commutative 81.1%

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

   6. Simplified 81.1%

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

   7. Taylor expanded in y around 0 69.1%

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

      1. distribute-lft-out 69.1%

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

      2. *-commutative 69.1%

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

      3. *-commutative 69.1%

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

   9. Simplified 69.1%

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

   10. Taylor expanded in x around inf 45.8%

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

4. Final simplification 56.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{+171}:\\ \;\;\;\;t \cdot \left(y \cdot \left(18 \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;x \leq 1.46 \cdot 10^{+53}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot i\right) \cdot -4\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 23.1% 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 84.8%

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

   1. pow1 84.8%

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

   2. associate-*l* 83.5%

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

   3. *-commutative 83.5%

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

4. Applied egg-rr 83.5%

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

   1. unpow1 83.5%

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

   2. associate-*l* 85.1%

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

   3. *-commutative 85.1%

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

6. Simplified 85.1%

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

7. Taylor expanded in y around 0 80.3%

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

   1. distribute-lft-out 80.3%

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

   2. *-commutative 80.3%

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

   3. *-commutative 80.3%

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

9. Simplified 80.3%

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

10. Taylor expanded in b around inf 23.1%

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

Developer Target 1: 89.4% 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 2024123 
(FPCore (x y z t a b c i j k)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, E"
  :precision binary64

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

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