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

Percentage Accurate: 85.2% → 91.1%

Time: 26.2s

Alternatives: 34

Speedup: 0.9×

• 50.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 91.1% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 97.4%

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

   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 16.7%

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

   5. Taylor expanded in t around inf 63.0%

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

      1. cancel-sign-sub-inv 63.0%

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

      2. associate-*r* 62.6%

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

      3. metadata-eval 62.6%

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

   7. Applied egg-rr 62.6%

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

4. Final simplification 94.2%

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

Alternative 2: 80.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+70} \lor \neg \left(t\_1 \leq 2 \cdot 10^{-13}\right):\\ \;\;\;\;\left(\left(z \cdot \left(x \cdot y\right)\right) \cdot \left(18 \cdot t\right) - 4 \cdot \left(x \cdot i + t \cdot a\right)\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - t \cdot \left(a \cdot 4 - 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)))
   (if (or (<= t_1 -1e+70) (not (<= t_1 2e-13)))
     (- (- (* (* z (* x y)) (* 18.0 t)) (* 4.0 (+ (* x i) (* t a)))) t_1)
     (-
      (- (* b c) (* t (- (* a 4.0) (* 18.0 (* x (* y z))))))
      (* 4.0 (* x i))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if ((t_1 <= -1e+70) || !(t_1 <= 2e-13)) {
		tmp = (((z * (x * y)) * (18.0 * t)) - (4.0 * ((x * i) + (t * a)))) - t_1;
	} else {
		tmp = ((b * c) - (t * ((a * 4.0) - (18.0 * (x * (y * z)))))) - (4.0 * (x * i));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (j * 27.0d0) * k
    if ((t_1 <= (-1d+70)) .or. (.not. (t_1 <= 2d-13))) then
        tmp = (((z * (x * y)) * (18.0d0 * t)) - (4.0d0 * ((x * i) + (t * a)))) - t_1
    else
        tmp = ((b * c) - (t * ((a * 4.0d0) - (18.0d0 * (x * (y * z)))))) - (4.0d0 * (x * i))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if ((t_1 <= -1e+70) || !(t_1 <= 2e-13)) {
		tmp = (((z * (x * y)) * (18.0 * t)) - (4.0 * ((x * i) + (t * a)))) - t_1;
	} else {
		tmp = ((b * c) - (t * ((a * 4.0) - (18.0 * (x * (y * z)))))) - (4.0 * (x * i));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	tmp = 0
	if (t_1 <= -1e+70) or not (t_1 <= 2e-13):
		tmp = (((z * (x * y)) * (18.0 * t)) - (4.0 * ((x * i) + (t * a)))) - t_1
	else:
		tmp = ((b * c) - (t * ((a * 4.0) - (18.0 * (x * (y * z)))))) - (4.0 * (x * i))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if ((t_1 <= -1e+70) || !(t_1 <= 2e-13))
		tmp = Float64(Float64(Float64(Float64(z * Float64(x * y)) * Float64(18.0 * t)) - Float64(4.0 * Float64(Float64(x * i) + Float64(t * a)))) - t_1);
	else
		tmp = Float64(Float64(Float64(b * c) - Float64(t * Float64(Float64(a * 4.0) - Float64(18.0 * Float64(x * Float64(y * z)))))) - Float64(4.0 * Float64(x * i)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * 27.0) * k;
	tmp = 0.0;
	if ((t_1 <= -1e+70) || ~((t_1 <= 2e-13)))
		tmp = (((z * (x * y)) * (18.0 * t)) - (4.0 * ((x * i) + (t * a)))) - t_1;
	else
		tmp = ((b * c) - (t * ((a * 4.0) - (18.0 * (x * (y * z)))))) - (4.0 * (x * i));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e+70], N[Not[LessEqual[t$95$1, 2e-13]], $MachinePrecision]], N[(N[(N[(N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision] * N[(18.0 * t), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(N[(x * i), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] - N[(t * N[(N[(a * 4.0), $MachinePrecision] - N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -1.00000000000000007e70 or 2.0000000000000001e-13 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 83.9%

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

   3. Taylor expanded in b around 0 80.9%

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

      1. associate-*r* 77.1%

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

      2. distribute-lft-out 77.1%

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

      3. *-commutative 77.1%

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

   5. Simplified 77.1%

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

   6. Taylor expanded in t around 0 80.9%

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

      1. associate-*r* 80.9%

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

      2. associate-*r* 81.9%

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

   8. Simplified 81.9%

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

   if -1.00000000000000007e70 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 2.0000000000000001e-13

   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 90.8%

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

   5. Taylor expanded in j around 0 89.6%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \leq -1 \cdot 10^{+70} \lor \neg \left(\left(j \cdot 27\right) \cdot k \leq 2 \cdot 10^{-13}\right):\\ \;\;\;\;\left(\left(z \cdot \left(x \cdot y\right)\right) \cdot \left(18 \cdot t\right) - 4 \cdot \left(x \cdot i + t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - t \cdot \left(a \cdot 4 - 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 80.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+70} \lor \neg \left(t\_1 \leq 2 \cdot 10^{-34}\right):\\ \;\;\;\;\left(18 \cdot \left(x \cdot \left(t \cdot \left(y \cdot z\right)\right)\right) - 4 \cdot \left(x \cdot i + t \cdot a\right)\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - t \cdot \left(a \cdot 4 - 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)))
   (if (or (<= t_1 -1e+70) (not (<= t_1 2e-34)))
     (- (- (* 18.0 (* x (* t (* y z)))) (* 4.0 (+ (* x i) (* t a)))) t_1)
     (-
      (- (* b c) (* t (- (* a 4.0) (* 18.0 (* x (* y z))))))
      (* 4.0 (* x i))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if ((t_1 <= -1e+70) || !(t_1 <= 2e-34)) {
		tmp = ((18.0 * (x * (t * (y * z)))) - (4.0 * ((x * i) + (t * a)))) - t_1;
	} else {
		tmp = ((b * c) - (t * ((a * 4.0) - (18.0 * (x * (y * z)))))) - (4.0 * (x * i));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (j * 27.0d0) * k
    if ((t_1 <= (-1d+70)) .or. (.not. (t_1 <= 2d-34))) then
        tmp = ((18.0d0 * (x * (t * (y * z)))) - (4.0d0 * ((x * i) + (t * a)))) - t_1
    else
        tmp = ((b * c) - (t * ((a * 4.0d0) - (18.0d0 * (x * (y * z)))))) - (4.0d0 * (x * i))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if ((t_1 <= -1e+70) || !(t_1 <= 2e-34)) {
		tmp = ((18.0 * (x * (t * (y * z)))) - (4.0 * ((x * i) + (t * a)))) - t_1;
	} else {
		tmp = ((b * c) - (t * ((a * 4.0) - (18.0 * (x * (y * z)))))) - (4.0 * (x * i));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	tmp = 0
	if (t_1 <= -1e+70) or not (t_1 <= 2e-34):
		tmp = ((18.0 * (x * (t * (y * z)))) - (4.0 * ((x * i) + (t * a)))) - t_1
	else:
		tmp = ((b * c) - (t * ((a * 4.0) - (18.0 * (x * (y * z)))))) - (4.0 * (x * i))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if ((t_1 <= -1e+70) || !(t_1 <= 2e-34))
		tmp = Float64(Float64(Float64(18.0 * Float64(x * Float64(t * Float64(y * z)))) - Float64(4.0 * Float64(Float64(x * i) + Float64(t * a)))) - t_1);
	else
		tmp = Float64(Float64(Float64(b * c) - Float64(t * Float64(Float64(a * 4.0) - Float64(18.0 * Float64(x * Float64(y * z)))))) - Float64(4.0 * Float64(x * i)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * 27.0) * k;
	tmp = 0.0;
	if ((t_1 <= -1e+70) || ~((t_1 <= 2e-34)))
		tmp = ((18.0 * (x * (t * (y * z)))) - (4.0 * ((x * i) + (t * a)))) - t_1;
	else
		tmp = ((b * c) - (t * ((a * 4.0) - (18.0 * (x * (y * z)))))) - (4.0 * (x * i));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e+70], N[Not[LessEqual[t$95$1, 2e-34]], $MachinePrecision]], N[(N[(N[(18.0 * N[(x * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(N[(x * i), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] - N[(t * N[(N[(a * 4.0), $MachinePrecision] - N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -1.00000000000000007e70 or 1.99999999999999986e-34 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 83.5%

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

   3. Taylor expanded in b around 0 79.8%

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

      1. associate-*r* 77.1%

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

      2. distribute-lft-out 77.1%

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

      3. *-commutative 77.1%

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

   5. Simplified 77.1%

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

   6. Taylor expanded in t around 0 79.8%

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

      1. associate-*r* 77.1%

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

      2. *-commutative 77.1%

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

      3. associate-*l* 79.9%

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

      4. *-commutative 79.9%

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

   8. Simplified 79.9%

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

   if -1.00000000000000007e70 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 1.99999999999999986e-34

   1. Initial program 91.8%

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

   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

   5. Taylor expanded in j around 0 90.0%

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

4. Final simplification 85.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \leq -1 \cdot 10^{+70} \lor \neg \left(\left(j \cdot 27\right) \cdot k \leq 2 \cdot 10^{-34}\right):\\ \;\;\;\;\left(18 \cdot \left(x \cdot \left(t \cdot \left(y \cdot z\right)\right)\right) - 4 \cdot \left(x \cdot i + t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - t \cdot \left(a \cdot 4 - 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 86.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{+97}:\\ \;\;\;\;t \cdot \left(-18 \cdot \left(z \cdot \left(x \cdot \left(-y\right)\right)\right) - 4 \cdot \left(a + i \cdot \frac{x}{t}\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+110}:\\ \;\;\;\;\left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot \left(z \cdot t\right) + \left(b \cdot c - t \cdot \left(a \cdot 4\right)\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - t \cdot \left(a \cdot 4 - 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= t -1e+97)
   (-
    (* t (- (* -18.0 (* z (* x (- y)))) (* 4.0 (+ a (* i (/ x t))))))
    (* (* j 27.0) k))
   (if (<= t 1.4e+110)
     (-
      (+ (* (* x (* 18.0 y)) (* z t)) (- (* b c) (* t (* a 4.0))))
      (+ (* x (* 4.0 i)) (* j (* 27.0 k))))
     (-
      (- (* b c) (* t (- (* a 4.0) (* 18.0 (* x (* y z))))))
      (* 4.0 (* x i))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (t <= -1e+97) {
		tmp = (t * ((-18.0 * (z * (x * -y))) - (4.0 * (a + (i * (x / t)))))) - ((j * 27.0) * k);
	} else if (t <= 1.4e+110) {
		tmp = (((x * (18.0 * y)) * (z * t)) + ((b * c) - (t * (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	} else {
		tmp = ((b * c) - (t * ((a * 4.0) - (18.0 * (x * (y * z)))))) - (4.0 * (x * i));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (t <= (-1d+97)) then
        tmp = (t * (((-18.0d0) * (z * (x * -y))) - (4.0d0 * (a + (i * (x / t)))))) - ((j * 27.0d0) * k)
    else if (t <= 1.4d+110) then
        tmp = (((x * (18.0d0 * y)) * (z * t)) + ((b * c) - (t * (a * 4.0d0)))) - ((x * (4.0d0 * i)) + (j * (27.0d0 * k)))
    else
        tmp = ((b * c) - (t * ((a * 4.0d0) - (18.0d0 * (x * (y * z)))))) - (4.0d0 * (x * i))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (t <= -1e+97) {
		tmp = (t * ((-18.0 * (z * (x * -y))) - (4.0 * (a + (i * (x / t)))))) - ((j * 27.0) * k);
	} else if (t <= 1.4e+110) {
		tmp = (((x * (18.0 * y)) * (z * t)) + ((b * c) - (t * (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	} else {
		tmp = ((b * c) - (t * ((a * 4.0) - (18.0 * (x * (y * z)))))) - (4.0 * (x * i));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if t <= -1e+97:
		tmp = (t * ((-18.0 * (z * (x * -y))) - (4.0 * (a + (i * (x / t)))))) - ((j * 27.0) * k)
	elif t <= 1.4e+110:
		tmp = (((x * (18.0 * y)) * (z * t)) + ((b * c) - (t * (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)))
	else:
		tmp = ((b * c) - (t * ((a * 4.0) - (18.0 * (x * (y * z)))))) - (4.0 * (x * i))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (t <= -1e+97)
		tmp = Float64(Float64(t * Float64(Float64(-18.0 * Float64(z * Float64(x * Float64(-y)))) - Float64(4.0 * Float64(a + Float64(i * Float64(x / t)))))) - Float64(Float64(j * 27.0) * k));
	elseif (t <= 1.4e+110)
		tmp = Float64(Float64(Float64(Float64(x * Float64(18.0 * y)) * Float64(z * t)) + Float64(Float64(b * c) - Float64(t * Float64(a * 4.0)))) - Float64(Float64(x * Float64(4.0 * i)) + Float64(j * Float64(27.0 * k))));
	else
		tmp = Float64(Float64(Float64(b * c) - Float64(t * Float64(Float64(a * 4.0) - Float64(18.0 * Float64(x * Float64(y * z)))))) - Float64(4.0 * Float64(x * i)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (t <= -1e+97)
		tmp = (t * ((-18.0 * (z * (x * -y))) - (4.0 * (a + (i * (x / t)))))) - ((j * 27.0) * k);
	elseif (t <= 1.4e+110)
		tmp = (((x * (18.0 * y)) * (z * t)) + ((b * c) - (t * (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	else
		tmp = ((b * c) - (t * ((a * 4.0) - (18.0 * (x * (y * z)))))) - (4.0 * (x * i));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[t, -1e+97], N[(N[(t * N[(N[(-18.0 * N[(z * N[(x * (-y)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(a + N[(i * N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.4e+110], N[(N[(N[(N[(x * N[(18.0 * y), $MachinePrecision]), $MachinePrecision] * N[(z * t), $MachinePrecision]), $MachinePrecision] + N[(N[(b * c), $MachinePrecision] - N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision] + N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] - N[(t * N[(N[(a * 4.0), $MachinePrecision] - N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.0000000000000001e97

   1. Initial program 85.0%

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

   3. Taylor expanded in b around 0 90.0%

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

      1. associate-*r* 87.6%

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

      2. distribute-lft-out 87.6%

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

      3. *-commutative 87.6%

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

   5. Simplified 87.6%

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

   6. Taylor expanded in t around -inf 95.0%

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

      1. mul-1-neg 95.0%

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

      2. *-commutative 95.0%

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

      3. distribute-rgt-neg-in 95.0%

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

      4. associate--l+ 95.0%

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

      5. *-commutative 95.0%

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

      6. associate-*r* 94.9%

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

      7. cancel-sign-sub-inv 94.9%

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

      8. metadata-eval 94.9%

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

      9. +-commutative 94.9%

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

      10. distribute-lft-out 94.9%

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

      11. associate-/l* 92.4%

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

   8. Simplified 92.4%

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

   if -1.0000000000000001e97 < t < 1.39999999999999993e110

   1. Initial program 90.7%

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

   3. Simplified 87.6%

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

      1. associate-*r* 91.2%

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

      2. distribute-rgt-out-- 90.7%

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

      3. associate-+l- 90.7%

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

      4. associate-*l* 91.6%

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

      5. fma-neg 92.2%

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

      6. associate-*l* 92.2%

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

      7. *-commutative 92.2%

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

   6. Applied egg-rr 92.2%

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

      1. fma-undefine 91.6%

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

      2. unsub-neg 91.6%

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

      3. *-commutative 91.6%

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

   8. Simplified 91.6%

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

   if 1.39999999999999993e110 < t

   1. Initial program 79.0%

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

   3. Simplified 81.7%

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

   5. Taylor expanded in j around 0 90.9%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{+97}:\\ \;\;\;\;t \cdot \left(-18 \cdot \left(z \cdot \left(x \cdot \left(-y\right)\right)\right) - 4 \cdot \left(a + i \cdot \frac{x}{t}\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+110}:\\ \;\;\;\;\left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot \left(z \cdot t\right) + \left(b \cdot c - t \cdot \left(a \cdot 4\right)\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - t \cdot \left(a \cdot 4 - 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := x \cdot i + t \cdot a\\ t_2 := \left(j \cdot 27\right) \cdot k\\ t_3 := t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{if}\;t \leq -3.1 \cdot 10^{+187}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{+112}:\\ \;\;\;\;-4 \cdot t\_1 - t\_2\\ \mathbf{elif}\;t \leq -5.8 \cdot 10^{-129}:\\ \;\;\;\;\left(b \cdot c + \left(x \cdot \left(18 \cdot y\right)\right) \cdot \left(z \cdot t\right)\right) - x \cdot \left(4 \cdot i\right)\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+123}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot t\_1\right) - t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (+ (* x i) (* t a)))
        (t_2 (* (* j 27.0) k))
        (t_3 (* t (- (* 18.0 (* x (* y z))) (* a 4.0)))))
   (if (<= t -3.1e+187)
     t_3
     (if (<= t -1.15e+112)
       (- (* -4.0 t_1) t_2)
       (if (<= t -5.8e-129)
         (- (+ (* b c) (* (* x (* 18.0 y)) (* z t))) (* x (* 4.0 i)))
         (if (<= t 6e+123) (- (- (* b c) (* 4.0 t_1)) t_2) t_3))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (x * i) + (t * a);
	double t_2 = (j * 27.0) * k;
	double t_3 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	double tmp;
	if (t <= -3.1e+187) {
		tmp = t_3;
	} else if (t <= -1.15e+112) {
		tmp = (-4.0 * t_1) - t_2;
	} else if (t <= -5.8e-129) {
		tmp = ((b * c) + ((x * (18.0 * y)) * (z * t))) - (x * (4.0 * i));
	} else if (t <= 6e+123) {
		tmp = ((b * c) - (4.0 * t_1)) - t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (x * i) + (t * a)
    t_2 = (j * 27.0d0) * k
    t_3 = t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0))
    if (t <= (-3.1d+187)) then
        tmp = t_3
    else if (t <= (-1.15d+112)) then
        tmp = ((-4.0d0) * t_1) - t_2
    else if (t <= (-5.8d-129)) then
        tmp = ((b * c) + ((x * (18.0d0 * y)) * (z * t))) - (x * (4.0d0 * i))
    else if (t <= 6d+123) then
        tmp = ((b * c) - (4.0d0 * t_1)) - t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (x * i) + (t * a);
	double t_2 = (j * 27.0) * k;
	double t_3 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	double tmp;
	if (t <= -3.1e+187) {
		tmp = t_3;
	} else if (t <= -1.15e+112) {
		tmp = (-4.0 * t_1) - t_2;
	} else if (t <= -5.8e-129) {
		tmp = ((b * c) + ((x * (18.0 * y)) * (z * t))) - (x * (4.0 * i));
	} else if (t <= 6e+123) {
		tmp = ((b * c) - (4.0 * t_1)) - t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (x * i) + (t * a)
	t_2 = (j * 27.0) * k
	t_3 = t * ((18.0 * (x * (y * z))) - (a * 4.0))
	tmp = 0
	if t <= -3.1e+187:
		tmp = t_3
	elif t <= -1.15e+112:
		tmp = (-4.0 * t_1) - t_2
	elif t <= -5.8e-129:
		tmp = ((b * c) + ((x * (18.0 * y)) * (z * t))) - (x * (4.0 * i))
	elif t <= 6e+123:
		tmp = ((b * c) - (4.0 * t_1)) - t_2
	else:
		tmp = t_3
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(x * i) + Float64(t * a))
	t_2 = Float64(Float64(j * 27.0) * k)
	t_3 = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)))
	tmp = 0.0
	if (t <= -3.1e+187)
		tmp = t_3;
	elseif (t <= -1.15e+112)
		tmp = Float64(Float64(-4.0 * t_1) - t_2);
	elseif (t <= -5.8e-129)
		tmp = Float64(Float64(Float64(b * c) + Float64(Float64(x * Float64(18.0 * y)) * Float64(z * t))) - Float64(x * Float64(4.0 * i)));
	elseif (t <= 6e+123)
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * t_1)) - t_2);
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (x * i) + (t * a);
	t_2 = (j * 27.0) * k;
	t_3 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	tmp = 0.0;
	if (t <= -3.1e+187)
		tmp = t_3;
	elseif (t <= -1.15e+112)
		tmp = (-4.0 * t_1) - t_2;
	elseif (t <= -5.8e-129)
		tmp = ((b * c) + ((x * (18.0 * y)) * (z * t))) - (x * (4.0 * i));
	elseif (t <= 6e+123)
		tmp = ((b * c) - (4.0 * t_1)) - t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(x * i), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.1e+187], t$95$3, If[LessEqual[t, -1.15e+112], N[(N[(-4.0 * t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision], If[LessEqual[t, -5.8e-129], N[(N[(N[(b * c), $MachinePrecision] + N[(N[(x * N[(18.0 * y), $MachinePrecision]), $MachinePrecision] * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6e+123], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * t$95$1), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], t$95$3]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3.10000000000000012e187 or 6.00000000000000016e123 < t

   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 85.1%

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

   5. Taylor expanded in t around inf 85.6%

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

   if -3.10000000000000012e187 < t < -1.15e112

   1. Initial program 88.2%

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

   3. Taylor expanded in b around 0 99.9%

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

      1. associate-*r* 100.0%

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

      2. distribute-lft-out 100.0%

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

      3. *-commutative 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around 0 77.5%

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

   if -1.15e112 < t < -5.80000000000000034e-129

   1. Initial program 92.4%

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

   3. Simplified 83.6%

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

      1. associate-*r* 92.4%

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

      2. distribute-rgt-out-- 92.4%

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

      3. associate-+l- 92.4%

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

      4. associate-*l* 92.4%

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

      5. fma-neg 92.4%

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

      6. associate-*l* 90.6%

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

      7. *-commutative 90.6%

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

   6. Applied egg-rr 90.6%

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

      1. fma-undefine 90.6%

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

      2. unsub-neg 90.6%

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

      3. *-commutative 90.6%

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

   8. Simplified 90.6%

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

   9. Taylor expanded in x around inf 86.8%

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

       1. associate-*r* 86.8%

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

       2. *-commutative 86.8%

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

   11. Simplified 86.8%

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

   12. Taylor expanded in t around 0 75.7%

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

       1. neg-mul-1 75.7%

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

       2. distribute-rgt-neg-in 75.7%

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

   14. Simplified 75.7%

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

   if -5.80000000000000034e-129 < t < 6.00000000000000016e123

   1. Initial program 90.1%

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

   3. Taylor expanded in y around 0 87.9%

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

      1. distribute-lft-out 87.9%

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

      2. *-commutative 87.9%

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

   5. Simplified 87.9%

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

4. Final simplification 84.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{+187}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{+112}:\\ \;\;\;\;-4 \cdot \left(x \cdot i + t \cdot a\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;t \leq -5.8 \cdot 10^{-129}:\\ \;\;\;\;\left(b \cdot c + \left(x \cdot \left(18 \cdot y\right)\right) \cdot \left(z \cdot t\right)\right) - x \cdot \left(4 \cdot i\right)\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+123}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 79.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t \leq -2 \cdot 10^{+93}:\\ \;\;\;\;t \cdot \left(-18 \cdot \left(z \cdot \left(x \cdot \left(-y\right)\right)\right) - 4 \cdot \left(a + i \cdot \frac{x}{t}\right)\right) - t\_1\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-211}:\\ \;\;\;\;\left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot \left(z \cdot t\right) + \left(b \cdot c - t \cdot \left(a \cdot 4\right)\right)\right) - x \cdot \left(4 \cdot i\right)\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+106}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - t \cdot \left(a \cdot 4 - 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)))
   (if (<= t -2e+93)
     (- (* t (- (* -18.0 (* z (* x (- y)))) (* 4.0 (+ a (* i (/ x t)))))) t_1)
     (if (<= t -1.15e-211)
       (-
        (+ (* (* x (* 18.0 y)) (* z t)) (- (* b c) (* t (* a 4.0))))
        (* x (* 4.0 i)))
       (if (<= t 3.4e+106)
         (- (- (* b c) (* 4.0 (+ (* x i) (* t a)))) t_1)
         (-
          (- (* b c) (* t (- (* a 4.0) (* 18.0 (* x (* y z))))))
          (* 4.0 (* x i))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (t <= -2e+93) {
		tmp = (t * ((-18.0 * (z * (x * -y))) - (4.0 * (a + (i * (x / t)))))) - t_1;
	} else if (t <= -1.15e-211) {
		tmp = (((x * (18.0 * y)) * (z * t)) + ((b * c) - (t * (a * 4.0)))) - (x * (4.0 * i));
	} else if (t <= 3.4e+106) {
		tmp = ((b * c) - (4.0 * ((x * i) + (t * a)))) - t_1;
	} else {
		tmp = ((b * c) - (t * ((a * 4.0) - (18.0 * (x * (y * z)))))) - (4.0 * (x * i));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (j * 27.0d0) * k
    if (t <= (-2d+93)) then
        tmp = (t * (((-18.0d0) * (z * (x * -y))) - (4.0d0 * (a + (i * (x / t)))))) - t_1
    else if (t <= (-1.15d-211)) then
        tmp = (((x * (18.0d0 * y)) * (z * t)) + ((b * c) - (t * (a * 4.0d0)))) - (x * (4.0d0 * i))
    else if (t <= 3.4d+106) then
        tmp = ((b * c) - (4.0d0 * ((x * i) + (t * a)))) - t_1
    else
        tmp = ((b * c) - (t * ((a * 4.0d0) - (18.0d0 * (x * (y * z)))))) - (4.0d0 * (x * i))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (t <= -2e+93) {
		tmp = (t * ((-18.0 * (z * (x * -y))) - (4.0 * (a + (i * (x / t)))))) - t_1;
	} else if (t <= -1.15e-211) {
		tmp = (((x * (18.0 * y)) * (z * t)) + ((b * c) - (t * (a * 4.0)))) - (x * (4.0 * i));
	} else if (t <= 3.4e+106) {
		tmp = ((b * c) - (4.0 * ((x * i) + (t * a)))) - t_1;
	} else {
		tmp = ((b * c) - (t * ((a * 4.0) - (18.0 * (x * (y * z)))))) - (4.0 * (x * i));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	tmp = 0
	if t <= -2e+93:
		tmp = (t * ((-18.0 * (z * (x * -y))) - (4.0 * (a + (i * (x / t)))))) - t_1
	elif t <= -1.15e-211:
		tmp = (((x * (18.0 * y)) * (z * t)) + ((b * c) - (t * (a * 4.0)))) - (x * (4.0 * i))
	elif t <= 3.4e+106:
		tmp = ((b * c) - (4.0 * ((x * i) + (t * a)))) - t_1
	else:
		tmp = ((b * c) - (t * ((a * 4.0) - (18.0 * (x * (y * z)))))) - (4.0 * (x * i))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t <= -2e+93)
		tmp = Float64(Float64(t * Float64(Float64(-18.0 * Float64(z * Float64(x * Float64(-y)))) - Float64(4.0 * Float64(a + Float64(i * Float64(x / t)))))) - t_1);
	elseif (t <= -1.15e-211)
		tmp = Float64(Float64(Float64(Float64(x * Float64(18.0 * y)) * Float64(z * t)) + Float64(Float64(b * c) - Float64(t * Float64(a * 4.0)))) - Float64(x * Float64(4.0 * i)));
	elseif (t <= 3.4e+106)
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(Float64(x * i) + Float64(t * a)))) - t_1);
	else
		tmp = Float64(Float64(Float64(b * c) - Float64(t * Float64(Float64(a * 4.0) - Float64(18.0 * Float64(x * Float64(y * z)))))) - Float64(4.0 * Float64(x * i)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * 27.0) * k;
	tmp = 0.0;
	if (t <= -2e+93)
		tmp = (t * ((-18.0 * (z * (x * -y))) - (4.0 * (a + (i * (x / t)))))) - t_1;
	elseif (t <= -1.15e-211)
		tmp = (((x * (18.0 * y)) * (z * t)) + ((b * c) - (t * (a * 4.0)))) - (x * (4.0 * i));
	elseif (t <= 3.4e+106)
		tmp = ((b * c) - (4.0 * ((x * i) + (t * a)))) - t_1;
	else
		tmp = ((b * c) - (t * ((a * 4.0) - (18.0 * (x * (y * z)))))) - (4.0 * (x * i));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t, -2e+93], N[(N[(t * N[(N[(-18.0 * N[(z * N[(x * (-y)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(a + N[(i * N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[t, -1.15e-211], N[(N[(N[(N[(x * N[(18.0 * y), $MachinePrecision]), $MachinePrecision] * N[(z * t), $MachinePrecision]), $MachinePrecision] + N[(N[(b * c), $MachinePrecision] - N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.4e+106], 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[(N[(b * c), $MachinePrecision] - N[(t * N[(N[(a * 4.0), $MachinePrecision] - N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.00000000000000009e93

   1. Initial program 85.7%

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

   3. Taylor expanded in b around 0 90.4%

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

      1. associate-*r* 88.2%

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

      2. distribute-lft-out 88.2%

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

      3. *-commutative 88.2%

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

   5. Simplified 88.2%

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

   6. Taylor expanded in t around -inf 95.2%

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

      1. mul-1-neg 95.2%

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

      2. *-commutative 95.2%

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

      3. distribute-rgt-neg-in 95.2%

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

      4. associate--l+ 95.2%

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

      5. *-commutative 95.2%

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

      6. associate-*r* 95.1%

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

      7. cancel-sign-sub-inv 95.1%

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

      8. metadata-eval 95.1%

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

      9. +-commutative 95.1%

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

      10. distribute-lft-out 95.1%

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

      11. associate-/l* 92.7%

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

   8. Simplified 92.7%

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

   if -2.00000000000000009e93 < t < -1.14999999999999994e-211

   1. Initial program 92.8%

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

   3. Simplified 84.7%

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

      1. associate-*r* 92.8%

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

      2. distribute-rgt-out-- 92.8%

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

      3. associate-+l- 92.8%

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

      4. associate-*l* 92.7%

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

      5. fma-neg 92.7%

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

      6. associate-*l* 92.7%

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

      7. *-commutative 92.7%

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

   6. Applied egg-rr 92.7%

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

      1. fma-undefine 92.7%

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

      2. unsub-neg 92.7%

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

      3. *-commutative 92.7%

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

   8. Simplified 92.7%

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

   9. Taylor expanded in x around inf 84.4%

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

       1. associate-*r* 84.4%

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

       2. *-commutative 84.4%

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

   11. Simplified 84.4%

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

   if -1.14999999999999994e-211 < t < 3.39999999999999994e106

   1. Initial program 89.2%

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

   3. Taylor expanded in y around 0 89.3%

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

      1. distribute-lft-out 89.3%

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

      2. *-commutative 89.3%

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

   5. Simplified 89.3%

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

   if 3.39999999999999994e106 < t

   1. Initial program 79.0%

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

   3. Simplified 81.7%

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

   5. Taylor expanded in j around 0 90.9%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{+93}:\\ \;\;\;\;t \cdot \left(-18 \cdot \left(z \cdot \left(x \cdot \left(-y\right)\right)\right) - 4 \cdot \left(a + i \cdot \frac{x}{t}\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-211}:\\ \;\;\;\;\left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot \left(z \cdot t\right) + \left(b \cdot c - t \cdot \left(a \cdot 4\right)\right)\right) - x \cdot \left(4 \cdot i\right)\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+106}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - t \cdot \left(a \cdot 4 - 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 77.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := 4 \cdot \left(x \cdot i + t \cdot a\right)\\ t_2 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t \leq -1.55 \cdot 10^{+94}:\\ \;\;\;\;\left(18 \cdot \left(x \cdot \left(t \cdot \left(y \cdot z\right)\right)\right) - t\_1\right) - t\_2\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-211}:\\ \;\;\;\;\left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot \left(z \cdot t\right) + \left(b \cdot c - t \cdot \left(a \cdot 4\right)\right)\right) - x \cdot \left(4 \cdot i\right)\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+106}:\\ \;\;\;\;\left(b \cdot c - t\_1\right) - t\_2\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - t \cdot \left(a \cdot 4 - 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* 4.0 (+ (* x i) (* t a)))) (t_2 (* (* j 27.0) k)))
   (if (<= t -1.55e+94)
     (- (- (* 18.0 (* x (* t (* y z)))) t_1) t_2)
     (if (<= t -1.15e-211)
       (-
        (+ (* (* x (* 18.0 y)) (* z t)) (- (* b c) (* t (* a 4.0))))
        (* x (* 4.0 i)))
       (if (<= t 3.5e+106)
         (- (- (* b c) t_1) t_2)
         (-
          (- (* b c) (* t (- (* a 4.0) (* 18.0 (* x (* y z))))))
          (* 4.0 (* x i))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 4.0 * ((x * i) + (t * a));
	double t_2 = (j * 27.0) * k;
	double tmp;
	if (t <= -1.55e+94) {
		tmp = ((18.0 * (x * (t * (y * z)))) - t_1) - t_2;
	} else if (t <= -1.15e-211) {
		tmp = (((x * (18.0 * y)) * (z * t)) + ((b * c) - (t * (a * 4.0)))) - (x * (4.0 * i));
	} else if (t <= 3.5e+106) {
		tmp = ((b * c) - t_1) - t_2;
	} else {
		tmp = ((b * c) - (t * ((a * 4.0) - (18.0 * (x * (y * z)))))) - (4.0 * (x * i));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 4.0d0 * ((x * i) + (t * a))
    t_2 = (j * 27.0d0) * k
    if (t <= (-1.55d+94)) then
        tmp = ((18.0d0 * (x * (t * (y * z)))) - t_1) - t_2
    else if (t <= (-1.15d-211)) then
        tmp = (((x * (18.0d0 * y)) * (z * t)) + ((b * c) - (t * (a * 4.0d0)))) - (x * (4.0d0 * i))
    else if (t <= 3.5d+106) then
        tmp = ((b * c) - t_1) - t_2
    else
        tmp = ((b * c) - (t * ((a * 4.0d0) - (18.0d0 * (x * (y * z)))))) - (4.0d0 * (x * i))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 4.0 * ((x * i) + (t * a));
	double t_2 = (j * 27.0) * k;
	double tmp;
	if (t <= -1.55e+94) {
		tmp = ((18.0 * (x * (t * (y * z)))) - t_1) - t_2;
	} else if (t <= -1.15e-211) {
		tmp = (((x * (18.0 * y)) * (z * t)) + ((b * c) - (t * (a * 4.0)))) - (x * (4.0 * i));
	} else if (t <= 3.5e+106) {
		tmp = ((b * c) - t_1) - t_2;
	} else {
		tmp = ((b * c) - (t * ((a * 4.0) - (18.0 * (x * (y * z)))))) - (4.0 * (x * i));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = 4.0 * ((x * i) + (t * a))
	t_2 = (j * 27.0) * k
	tmp = 0
	if t <= -1.55e+94:
		tmp = ((18.0 * (x * (t * (y * z)))) - t_1) - t_2
	elif t <= -1.15e-211:
		tmp = (((x * (18.0 * y)) * (z * t)) + ((b * c) - (t * (a * 4.0)))) - (x * (4.0 * i))
	elif t <= 3.5e+106:
		tmp = ((b * c) - t_1) - t_2
	else:
		tmp = ((b * c) - (t * ((a * 4.0) - (18.0 * (x * (y * z)))))) - (4.0 * (x * i))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(4.0 * Float64(Float64(x * i) + Float64(t * a)))
	t_2 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t <= -1.55e+94)
		tmp = Float64(Float64(Float64(18.0 * Float64(x * Float64(t * Float64(y * z)))) - t_1) - t_2);
	elseif (t <= -1.15e-211)
		tmp = Float64(Float64(Float64(Float64(x * Float64(18.0 * y)) * Float64(z * t)) + Float64(Float64(b * c) - Float64(t * Float64(a * 4.0)))) - Float64(x * Float64(4.0 * i)));
	elseif (t <= 3.5e+106)
		tmp = Float64(Float64(Float64(b * c) - t_1) - t_2);
	else
		tmp = Float64(Float64(Float64(b * c) - Float64(t * Float64(Float64(a * 4.0) - Float64(18.0 * Float64(x * Float64(y * z)))))) - Float64(4.0 * Float64(x * i)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = 4.0 * ((x * i) + (t * a));
	t_2 = (j * 27.0) * k;
	tmp = 0.0;
	if (t <= -1.55e+94)
		tmp = ((18.0 * (x * (t * (y * z)))) - t_1) - t_2;
	elseif (t <= -1.15e-211)
		tmp = (((x * (18.0 * y)) * (z * t)) + ((b * c) - (t * (a * 4.0)))) - (x * (4.0 * i));
	elseif (t <= 3.5e+106)
		tmp = ((b * c) - t_1) - t_2;
	else
		tmp = ((b * c) - (t * ((a * 4.0) - (18.0 * (x * (y * z)))))) - (4.0 * (x * i));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(4.0 * N[(N[(x * i), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t, -1.55e+94], N[(N[(N[(18.0 * N[(x * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision], If[LessEqual[t, -1.15e-211], N[(N[(N[(N[(x * N[(18.0 * y), $MachinePrecision]), $MachinePrecision] * N[(z * t), $MachinePrecision]), $MachinePrecision] + N[(N[(b * c), $MachinePrecision] - N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.5e+106], N[(N[(N[(b * c), $MachinePrecision] - t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] - N[(t * N[(N[(a * 4.0), $MachinePrecision] - N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.54999999999999996e94

   1. Initial program 85.7%

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

   3. Taylor expanded in b around 0 90.4%

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

      1. associate-*r* 88.2%

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

      2. distribute-lft-out 88.2%

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

      3. *-commutative 88.2%

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

   5. Simplified 88.2%

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

   6. Taylor expanded in t around 0 90.4%

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

      1. associate-*r* 88.2%

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

      2. *-commutative 88.2%

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

      3. associate-*l* 90.4%

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

      4. *-commutative 90.4%

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

   8. Simplified 90.4%

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

   if -1.54999999999999996e94 < t < -1.14999999999999994e-211

   1. Initial program 92.8%

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

   3. Simplified 84.7%

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

      1. associate-*r* 92.8%

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

      2. distribute-rgt-out-- 92.8%

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

      3. associate-+l- 92.8%

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

      4. associate-*l* 92.7%

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

      5. fma-neg 92.7%

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

      6. associate-*l* 92.7%

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

      7. *-commutative 92.7%

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

   6. Applied egg-rr 92.7%

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

      1. fma-undefine 92.7%

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

      2. unsub-neg 92.7%

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

      3. *-commutative 92.7%

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

   8. Simplified 92.7%

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

   9. Taylor expanded in x around inf 84.4%

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

       1. associate-*r* 84.4%

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

       2. *-commutative 84.4%

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

   11. Simplified 84.4%

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

   if -1.14999999999999994e-211 < t < 3.49999999999999981e106

   1. Initial program 89.2%

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

   3. Taylor expanded in y around 0 89.3%

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

      1. distribute-lft-out 89.3%

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

      2. *-commutative 89.3%

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

   5. Simplified 89.3%

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

   if 3.49999999999999981e106 < t

   1. Initial program 79.0%

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

   3. Simplified 81.7%

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

   5. Taylor expanded in j around 0 90.9%

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

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.55 \cdot 10^{+94}:\\ \;\;\;\;\left(18 \cdot \left(x \cdot \left(t \cdot \left(y \cdot z\right)\right)\right) - 4 \cdot \left(x \cdot i + t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-211}:\\ \;\;\;\;\left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot \left(z \cdot t\right) + \left(b \cdot c - t \cdot \left(a \cdot 4\right)\right)\right) - x \cdot \left(4 \cdot i\right)\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+106}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - t \cdot \left(a \cdot 4 - 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 85.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 3.4 \cdot 10^{+253}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot 18\right) - a \cdot 4\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-4 \cdot \frac{x \cdot i}{z} + 18 \cdot \left(t \cdot \left(x \cdot y\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= z 3.4e+253)
   (-
    (+ (* b c) (* t (- (* (* y z) (* x 18.0)) (* a 4.0))))
    (+ (* x (* 4.0 i)) (* j (* 27.0 k))))
   (* z (+ (* -4.0 (/ (* x i) z)) (* 18.0 (* t (* x y)))))))

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 (z <= 3.4e+253) {
		tmp = ((b * c) + (t * (((y * z) * (x * 18.0)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	} else {
		tmp = z * ((-4.0 * ((x * i) / z)) + (18.0 * (t * (x * y))));
	}
	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 (z <= 3.4d+253) then
        tmp = ((b * c) + (t * (((y * z) * (x * 18.0d0)) - (a * 4.0d0)))) - ((x * (4.0d0 * i)) + (j * (27.0d0 * k)))
    else
        tmp = z * (((-4.0d0) * ((x * i) / z)) + (18.0d0 * (t * (x * y))))
    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 (z <= 3.4e+253) {
		tmp = ((b * c) + (t * (((y * z) * (x * 18.0)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	} else {
		tmp = z * ((-4.0 * ((x * i) / z)) + (18.0 * (t * (x * y))));
	}
	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 z <= 3.4e+253:
		tmp = ((b * c) + (t * (((y * z) * (x * 18.0)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)))
	else:
		tmp = z * ((-4.0 * ((x * i) / z)) + (18.0 * (t * (x * y))))
	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 (z <= 3.4e+253)
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(Float64(y * z) * Float64(x * 18.0)) - Float64(a * 4.0)))) - Float64(Float64(x * Float64(4.0 * i)) + Float64(j * Float64(27.0 * k))));
	else
		tmp = Float64(z * Float64(Float64(-4.0 * Float64(Float64(x * i) / z)) + Float64(18.0 * Float64(t * Float64(x * y)))));
	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 (z <= 3.4e+253)
		tmp = ((b * c) + (t * (((y * z) * (x * 18.0)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	else
		tmp = z * ((-4.0 * ((x * i) / z)) + (18.0 * (t * (x * y))));
	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[z, 3.4e+253], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(N[(y * z), $MachinePrecision] * N[(x * 18.0), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision] + N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(-4.0 * N[(N[(x * i), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(18.0 * N[(t * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 3.40000000000000017e253

   1. Initial program 89.2%

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

   3. Simplified 88.4%

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

   if 3.40000000000000017e253 < z

   1. Initial program 72.1%

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

   3. Simplified 65.7%

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

   5. Taylor expanded in x around inf 59.0%

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

   6. Taylor expanded in z around inf 79.1%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 3.4 \cdot 10^{+253}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot 18\right) - a \cdot 4\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-4 \cdot \frac{x \cdot i}{z} + 18 \cdot \left(t \cdot \left(x \cdot y\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 85.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 5.2 \cdot 10^{+253}:\\ \;\;\;\;\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - t \cdot \left(a \cdot 4 - x \cdot \left(z \cdot \left(18 \cdot y\right)\right)\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-4 \cdot \frac{x \cdot i}{z} + 18 \cdot \left(t \cdot \left(x \cdot y\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= z 5.2e+253)
   (-
    (- (- (* b c) (* (* x 4.0) i)) (* t (- (* a 4.0) (* x (* z (* 18.0 y))))))
    (* (* j 27.0) k))
   (* z (+ (* -4.0 (/ (* x i) z)) (* 18.0 (* t (* x y)))))))

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 (z <= 5.2e+253) {
		tmp = (((b * c) - ((x * 4.0) * i)) - (t * ((a * 4.0) - (x * (z * (18.0 * y)))))) - ((j * 27.0) * k);
	} else {
		tmp = z * ((-4.0 * ((x * i) / z)) + (18.0 * (t * (x * y))));
	}
	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 (z <= 5.2d+253) then
        tmp = (((b * c) - ((x * 4.0d0) * i)) - (t * ((a * 4.0d0) - (x * (z * (18.0d0 * y)))))) - ((j * 27.0d0) * k)
    else
        tmp = z * (((-4.0d0) * ((x * i) / z)) + (18.0d0 * (t * (x * y))))
    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 (z <= 5.2e+253) {
		tmp = (((b * c) - ((x * 4.0) * i)) - (t * ((a * 4.0) - (x * (z * (18.0 * y)))))) - ((j * 27.0) * k);
	} else {
		tmp = z * ((-4.0 * ((x * i) / z)) + (18.0 * (t * (x * y))));
	}
	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 z <= 5.2e+253:
		tmp = (((b * c) - ((x * 4.0) * i)) - (t * ((a * 4.0) - (x * (z * (18.0 * y)))))) - ((j * 27.0) * k)
	else:
		tmp = z * ((-4.0 * ((x * i) / z)) + (18.0 * (t * (x * y))))
	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 (z <= 5.2e+253)
		tmp = Float64(Float64(Float64(Float64(b * c) - Float64(Float64(x * 4.0) * i)) - Float64(t * Float64(Float64(a * 4.0) - Float64(x * Float64(z * Float64(18.0 * y)))))) - Float64(Float64(j * 27.0) * k));
	else
		tmp = Float64(z * Float64(Float64(-4.0 * Float64(Float64(x * i) / z)) + Float64(18.0 * Float64(t * Float64(x * y)))));
	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 (z <= 5.2e+253)
		tmp = (((b * c) - ((x * 4.0) * i)) - (t * ((a * 4.0) - (x * (z * (18.0 * y)))))) - ((j * 27.0) * k);
	else
		tmp = z * ((-4.0 * ((x * i) / z)) + (18.0 * (t * (x * y))));
	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[z, 5.2e+253], N[(N[(N[(N[(b * c), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] - N[(t * N[(N[(a * 4.0), $MachinePrecision] - N[(x * N[(z * N[(18.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(-4.0 * N[(N[(x * i), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(18.0 * N[(t * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 5.2e253

   1. Initial program 89.2%

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

      1. associate--l+ 89.2%

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

      2. distribute-rgt-out-- 90.1%

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

      3. associate-*r* 88.4%

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

      4. associate-*l* 88.5%

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

      5. associate-*r* 88.1%

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

      6. *-commutative 88.1%

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

   4. Applied egg-rr 88.1%

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

   if 5.2e253 < z

   1. Initial program 72.1%

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

   3. Simplified 65.7%

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

   5. Taylor expanded in x around inf 59.0%

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

   6. Taylor expanded in z around inf 79.1%

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

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 5.2 \cdot 10^{+253}:\\ \;\;\;\;\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - t \cdot \left(a \cdot 4 - x \cdot \left(z \cdot \left(18 \cdot y\right)\right)\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-4 \cdot \frac{x \cdot i}{z} + 18 \cdot \left(t \cdot \left(x \cdot y\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 35.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -5 \cdot 10^{+179}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -5 \cdot 10^{-173}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 2 \cdot 10^{+79}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 10^{+168}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= (* b c) -5e+179)
   (* b c)
   (if (<= (* b c) -5e-173)
     (* j (* k -27.0))
     (if (<= (* b c) 2e+79)
       (* x (* i -4.0))
       (if (<= (* b c) 1e+168) (* -4.0 (* t a)) (* b c))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b * c) <= -5e+179) {
		tmp = b * c;
	} else if ((b * c) <= -5e-173) {
		tmp = j * (k * -27.0);
	} else if ((b * c) <= 2e+79) {
		tmp = x * (i * -4.0);
	} else if ((b * c) <= 1e+168) {
		tmp = -4.0 * (t * a);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((b * c) <= (-5d+179)) then
        tmp = b * c
    else if ((b * c) <= (-5d-173)) then
        tmp = j * (k * (-27.0d0))
    else if ((b * c) <= 2d+79) then
        tmp = x * (i * (-4.0d0))
    else if ((b * c) <= 1d+168) then
        tmp = (-4.0d0) * (t * a)
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b * c) <= -5e+179) {
		tmp = b * c;
	} else if ((b * c) <= -5e-173) {
		tmp = j * (k * -27.0);
	} else if ((b * c) <= 2e+79) {
		tmp = x * (i * -4.0);
	} else if ((b * c) <= 1e+168) {
		tmp = -4.0 * (t * a);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (b * c) <= -5e+179:
		tmp = b * c
	elif (b * c) <= -5e-173:
		tmp = j * (k * -27.0)
	elif (b * c) <= 2e+79:
		tmp = x * (i * -4.0)
	elif (b * c) <= 1e+168:
		tmp = -4.0 * (t * a)
	else:
		tmp = b * c
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (Float64(b * c) <= -5e+179)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -5e-173)
		tmp = Float64(j * Float64(k * -27.0));
	elseif (Float64(b * c) <= 2e+79)
		tmp = Float64(x * Float64(i * -4.0));
	elseif (Float64(b * c) <= 1e+168)
		tmp = Float64(-4.0 * Float64(t * a));
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((b * c) <= -5e+179)
		tmp = b * c;
	elseif ((b * c) <= -5e-173)
		tmp = j * (k * -27.0);
	elseif ((b * c) <= 2e+79)
		tmp = x * (i * -4.0);
	elseif ((b * c) <= 1e+168)
		tmp = -4.0 * (t * a);
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[N[(b * c), $MachinePrecision], -5e+179], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -5e-173], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 2e+79], N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1e+168], N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 b c) < -5e179 or 9.9999999999999993e167 < (*.f64 b c)

   1. Initial program 79.6%

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

      1. associate--l+ 79.6%

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

      2. distribute-rgt-out-- 81.5%

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

      3. associate-*r* 79.6%

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

      4. associate-*l* 79.6%

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

      5. associate-*r* 79.6%

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

      6. *-commutative 79.6%

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

   4. Applied egg-rr 79.6%

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

   5. Taylor expanded in b around inf 68.9%

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

   if -5e179 < (*.f64 b c) < -5.0000000000000002e-173

   1. Initial program 84.8%

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

   3. Simplified 86.6%

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

      1. associate-*r* 88.1%

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

      2. distribute-rgt-out-- 84.7%

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

      3. associate-+l- 84.7%

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

      4. associate-*l* 81.2%

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

      5. fma-neg 82.9%

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

      6. associate-*l* 82.9%

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

      7. *-commutative 82.9%

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

   6. Applied egg-rr 82.9%

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

      1. fma-undefine 81.2%

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

      2. unsub-neg 81.2%

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

      3. *-commutative 81.2%

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

   8. Simplified 81.2%

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

   9. Taylor expanded in j around inf 34.0%

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

       1. metadata-eval 34.0%

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

       2. distribute-lft-neg-in 34.0%

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

       3. associate-*r* 34.1%

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

       4. *-commutative 34.1%

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

       5. associate-*r* 34.0%

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

       6. distribute-rgt-neg-in 34.0%

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

       7. distribute-lft-neg-in 34.0%

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

       8. metadata-eval 34.0%

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

       9. *-commutative 34.0%

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

   11. Simplified 34.0%

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

   if -5.0000000000000002e-173 < (*.f64 b c) < 1.99999999999999993e79

   1. Initial program 92.7%

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

   3. Simplified 90.3%

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

      1. associate-*r* 92.7%

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

      2. distribute-rgt-out-- 92.7%

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

      3. associate-+l- 92.7%

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

      4. associate-*l* 90.1%

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

      5. fma-neg 90.1%

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

      6. associate-*l* 89.4%

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

      7. *-commutative 89.4%

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

   6. Applied egg-rr 89.4%

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

      1. fma-undefine 89.4%

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

      2. unsub-neg 89.4%

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

      3. *-commutative 89.4%

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

   8. Simplified 89.4%

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

   9. Taylor expanded in i around inf 32.1%

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

       1. associate-*r* 32.1%

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

       2. metadata-eval 32.1%

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

       3. distribute-lft-neg-in 32.1%

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

       4. distribute-lft-neg-in 32.1%

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

       5. *-commutative 32.1%

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

       6. distribute-rgt-neg-in 32.1%

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

       7. distribute-lft-neg-in 32.1%

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

       8. metadata-eval 32.1%

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

       9. *-commutative 32.1%

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

   11. Simplified 32.1%

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

   if 1.99999999999999993e79 < (*.f64 b c) < 9.9999999999999993e167

   1. Initial program 94.9%

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

   3. Simplified 90.2%

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

      1. associate-*r* 95.0%

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

      2. distribute-rgt-out-- 95.0%

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

      3. associate-+l- 95.0%

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

      4. associate-*l* 85.0%

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

      5. fma-neg 85.0%

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

      6. associate-*l* 84.9%

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

      7. *-commutative 84.9%

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

   6. Applied egg-rr 84.9%

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

      1. fma-undefine 84.9%

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

      2. unsub-neg 84.9%

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

      3. *-commutative 84.9%

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

   8. Simplified 84.9%

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

   9. Taylor expanded in a around inf 43.2%

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

       1. *-commutative 43.2%

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

       2. *-commutative 43.2%

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

   11. Simplified 43.2%

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

4. Final simplification 41.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -5 \cdot 10^{+179}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -5 \cdot 10^{-173}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 2 \cdot 10^{+79}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 10^{+168}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 80.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{-116} \lor \neg \left(t \leq 1.8 \cdot 10^{+115}\right):\\ \;\;\;\;\left(b \cdot c - t \cdot \left(a \cdot 4 - 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \end{array} \]

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 (or (<= t -4.5e-116) (not (<= t 1.8e+115)))
   (- (- (* b c) (* t (- (* a 4.0) (* 18.0 (* x (* y z)))))) (* 4.0 (* x 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 ((t <= -4.5e-116) || !(t <= 1.8e+115)) {
		tmp = ((b * c) - (t * ((a * 4.0) - (18.0 * (x * (y * z)))))) - (4.0 * (x * 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 ((t <= (-4.5d-116)) .or. (.not. (t <= 1.8d+115))) then
        tmp = ((b * c) - (t * ((a * 4.0d0) - (18.0d0 * (x * (y * z)))))) - (4.0d0 * (x * 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 ((t <= -4.5e-116) || !(t <= 1.8e+115)) {
		tmp = ((b * c) - (t * ((a * 4.0) - (18.0 * (x * (y * z)))))) - (4.0 * (x * 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 (t <= -4.5e-116) or not (t <= 1.8e+115):
		tmp = ((b * c) - (t * ((a * 4.0) - (18.0 * (x * (y * z)))))) - (4.0 * (x * 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 ((t <= -4.5e-116) || !(t <= 1.8e+115))
		tmp = Float64(Float64(Float64(b * c) - Float64(t * Float64(Float64(a * 4.0) - Float64(18.0 * Float64(x * Float64(y * z)))))) - Float64(4.0 * Float64(x * 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 ((t <= -4.5e-116) || ~((t <= 1.8e+115)))
		tmp = ((b * c) - (t * ((a * 4.0) - (18.0 * (x * (y * z)))))) - (4.0 * (x * 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[Or[LessEqual[t, -4.5e-116], N[Not[LessEqual[t, 1.8e+115]], $MachinePrecision]], N[(N[(N[(b * c), $MachinePrecision] - N[(t * N[(N[(a * 4.0), $MachinePrecision] - N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(x * 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 t < -4.50000000000000012e-116 or 1.8e115 < t

   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 85.4%

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

   5. Taylor expanded in j around 0 81.6%

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

   if -4.50000000000000012e-116 < t < 1.8e115

   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 87.4%

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

      1. distribute-lft-out 87.4%

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

      2. *-commutative 87.4%

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

   5. Simplified 87.4%

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

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{-116} \lor \neg \left(t \leq 1.8 \cdot 10^{+115}\right):\\ \;\;\;\;\left(b \cdot c - t \cdot \left(a \cdot 4 - 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 69.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := x \cdot i + t \cdot a\\ t_2 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+70} \lor \neg \left(t\_2 \leq 5 \cdot 10^{+80}\right):\\ \;\;\;\;-4 \cdot t\_1 - t\_2\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 4 \cdot t\_1\\ \end{array} \end{array} \]

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 i) (* t a))) (t_2 (* (* j 27.0) k)))
   (if (or (<= t_2 -1e+70) (not (<= t_2 5e+80)))
     (- (* -4.0 t_1) t_2)
     (- (* b c) (* 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 = (x * i) + (t * a);
	double t_2 = (j * 27.0) * k;
	double tmp;
	if ((t_2 <= -1e+70) || !(t_2 <= 5e+80)) {
		tmp = (-4.0 * t_1) - t_2;
	} else {
		tmp = (b * c) - (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) :: t_2
    real(8) :: tmp
    t_1 = (x * i) + (t * a)
    t_2 = (j * 27.0d0) * k
    if ((t_2 <= (-1d+70)) .or. (.not. (t_2 <= 5d+80))) then
        tmp = ((-4.0d0) * t_1) - t_2
    else
        tmp = (b * c) - (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 = (x * i) + (t * a);
	double t_2 = (j * 27.0) * k;
	double tmp;
	if ((t_2 <= -1e+70) || !(t_2 <= 5e+80)) {
		tmp = (-4.0 * t_1) - t_2;
	} else {
		tmp = (b * c) - (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 = (x * i) + (t * a)
	t_2 = (j * 27.0) * k
	tmp = 0
	if (t_2 <= -1e+70) or not (t_2 <= 5e+80):
		tmp = (-4.0 * t_1) - t_2
	else:
		tmp = (b * c) - (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(x * i) + Float64(t * a))
	t_2 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if ((t_2 <= -1e+70) || !(t_2 <= 5e+80))
		tmp = Float64(Float64(-4.0 * t_1) - t_2);
	else
		tmp = Float64(Float64(b * c) - Float64(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 = (x * i) + (t * a);
	t_2 = (j * 27.0) * k;
	tmp = 0.0;
	if ((t_2 <= -1e+70) || ~((t_2 <= 5e+80)))
		tmp = (-4.0 * t_1) - t_2;
	else
		tmp = (b * c) - (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[(x * i), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[Or[LessEqual[t$95$2, -1e+70], N[Not[LessEqual[t$95$2, 5e+80]], $MachinePrecision]], N[(N[(-4.0 * t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision], N[(N[(b * c), $MachinePrecision] - N[(4.0 * t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -1.00000000000000007e70 or 4.99999999999999961e80 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 83.5%

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

   3. Taylor expanded in b around 0 82.3%

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

      1. associate-*r* 78.2%

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

      2. distribute-lft-out 78.2%

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

      3. *-commutative 78.2%

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

   5. Simplified 78.2%

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

   6. Taylor expanded in y around 0 74.1%

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

   if -1.00000000000000007e70 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 4.99999999999999961e80

   1. Initial program 91.3%

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

   3. Simplified 89.5%

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

      1. associate-*r* 93.2%

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

      2. distribute-rgt-out-- 91.3%

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

      3. associate-+l- 91.3%

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

      4. associate-*l* 88.6%

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

      5. fma-neg 89.3%

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

      6. associate-*l* 88.7%

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

      7. *-commutative 88.7%

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

   6. Applied egg-rr 88.7%

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

      1. fma-undefine 88.0%

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

      2. unsub-neg 88.0%

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

      3. *-commutative 88.0%

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

   8. Simplified 88.0%

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

   9. Taylor expanded in x around inf 86.9%

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

       1. associate-*r* 86.9%

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

       2. *-commutative 86.9%

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

   11. Simplified 86.9%

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

   12. Taylor expanded in y around 0 70.3%

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

       1. distribute-lft-out 70.3%

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

       2. *-commutative 70.3%

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

   14. Simplified 70.3%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \leq -1 \cdot 10^{+70} \lor \neg \left(\left(j \cdot 27\right) \cdot k \leq 5 \cdot 10^{+80}\right):\\ \;\;\;\;-4 \cdot \left(x \cdot i + t \cdot a\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 52.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;b \cdot c \leq -4 \cdot 10^{+31}:\\ \;\;\;\;b \cdot c + t\_1\\ \mathbf{elif}\;b \cdot c \leq -5 \cdot 10^{-88}:\\ \;\;\;\;t \cdot \left(z \cdot \left(y \cdot \left(x \cdot 18\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 2 \cdot 10^{+79}:\\ \;\;\;\;t\_1 + i \cdot \left(x \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(t \cdot a\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0))))
   (if (<= (* b c) -4e+31)
     (+ (* b c) t_1)
     (if (<= (* b c) -5e-88)
       (* t (* z (* y (* x 18.0))))
       (if (<= (* b c) 2e+79)
         (+ t_1 (* i (* x -4.0)))
         (- (* b c) (* 4.0 (* t a))))))))

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) <= -4e+31) {
		tmp = (b * c) + t_1;
	} else if ((b * c) <= -5e-88) {
		tmp = t * (z * (y * (x * 18.0)));
	} else if ((b * c) <= 2e+79) {
		tmp = t_1 + (i * (x * -4.0));
	} else {
		tmp = (b * c) - (4.0 * (t * a));
	}
	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) <= (-4d+31)) then
        tmp = (b * c) + t_1
    else if ((b * c) <= (-5d-88)) then
        tmp = t * (z * (y * (x * 18.0d0)))
    else if ((b * c) <= 2d+79) then
        tmp = t_1 + (i * (x * (-4.0d0)))
    else
        tmp = (b * c) - (4.0d0 * (t * a))
    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) <= -4e+31) {
		tmp = (b * c) + t_1;
	} else if ((b * c) <= -5e-88) {
		tmp = t * (z * (y * (x * 18.0)));
	} else if ((b * c) <= 2e+79) {
		tmp = t_1 + (i * (x * -4.0));
	} else {
		tmp = (b * c) - (4.0 * (t * a));
	}
	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) <= -4e+31:
		tmp = (b * c) + t_1
	elif (b * c) <= -5e-88:
		tmp = t * (z * (y * (x * 18.0)))
	elif (b * c) <= 2e+79:
		tmp = t_1 + (i * (x * -4.0))
	else:
		tmp = (b * c) - (4.0 * (t * a))
	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) <= -4e+31)
		tmp = Float64(Float64(b * c) + t_1);
	elseif (Float64(b * c) <= -5e-88)
		tmp = Float64(t * Float64(z * Float64(y * Float64(x * 18.0))));
	elseif (Float64(b * c) <= 2e+79)
		tmp = Float64(t_1 + Float64(i * Float64(x * -4.0)));
	else
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(t * a)));
	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) <= -4e+31)
		tmp = (b * c) + t_1;
	elseif ((b * c) <= -5e-88)
		tmp = t * (z * (y * (x * 18.0)));
	elseif ((b * c) <= 2e+79)
		tmp = t_1 + (i * (x * -4.0));
	else
		tmp = (b * c) - (4.0 * (t * a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -4e+31], N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -5e-88], N[(t * N[(z * N[(y * N[(x * 18.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 2e+79], N[(t$95$1 + N[(i * N[(x * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 b c) < -3.9999999999999999e31

   1. Initial program 82.6%

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

   3. Simplified 84.3%

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

   5. Taylor expanded in b around inf 62.5%

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

   if -3.9999999999999999e31 < (*.f64 b c) < -5.00000000000000009e-88

   1. Initial program 77.7%

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

   3. Simplified 83.2%

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

   5. Taylor expanded in t around inf 72.6%

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

   6. Taylor expanded in x around inf 61.9%

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

      1. associate-*r* 61.9%

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

      2. associate-*r* 61.9%

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

      3. associate-*r* 61.9%

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

   8. Simplified 61.9%

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

   if -5.00000000000000009e-88 < (*.f64 b c) < 1.99999999999999993e79

   1. Initial program 92.0%

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

   3. Simplified 89.8%

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

   5. Taylor expanded in i around inf 51.9%

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

      1. metadata-eval 51.9%

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

      2. distribute-lft-neg-in 51.9%

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

      3. *-commutative 51.9%

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

      4. associate-*r* 51.9%

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

      5. distribute-rgt-neg-in 51.9%

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

      6. distribute-rgt-neg-in 51.9%

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

      7. metadata-eval 51.9%

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

      8. *-commutative 51.9%

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

   7. Simplified 51.9%

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

   if 1.99999999999999993e79 < (*.f64 b c)

   1. Initial program 89.7%

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

   3. Taylor expanded in x around 0 73.6%

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

   4. Taylor expanded in j around 0 68.9%

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

4. Final simplification 57.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -4 \cdot 10^{+31}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq -5 \cdot 10^{-88}:\\ \;\;\;\;t \cdot \left(z \cdot \left(y \cdot \left(x \cdot 18\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 2 \cdot 10^{+79}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + i \cdot \left(x \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 37.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -5 \cdot 10^{+179}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -5 \cdot 10^{+59}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq 4 \cdot 10^{+157}:\\ \;\;\;\;t \cdot \left(z \cdot \left(y \cdot \left(x \cdot 18\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= (* b c) -5e+179)
   (* b c)
   (if (<= (* b c) -5e+59)
     (* -27.0 (* j k))
     (if (<= (* b c) 4e+157) (* t (* z (* y (* x 18.0)))) (* 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) <= -5e+179) {
		tmp = b * c;
	} else if ((b * c) <= -5e+59) {
		tmp = -27.0 * (j * k);
	} else if ((b * c) <= 4e+157) {
		tmp = t * (z * (y * (x * 18.0)));
	} 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) <= (-5d+179)) then
        tmp = b * c
    else if ((b * c) <= (-5d+59)) then
        tmp = (-27.0d0) * (j * k)
    else if ((b * c) <= 4d+157) then
        tmp = t * (z * (y * (x * 18.0d0)))
    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) <= -5e+179) {
		tmp = b * c;
	} else if ((b * c) <= -5e+59) {
		tmp = -27.0 * (j * k);
	} else if ((b * c) <= 4e+157) {
		tmp = t * (z * (y * (x * 18.0)));
	} 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) <= -5e+179:
		tmp = b * c
	elif (b * c) <= -5e+59:
		tmp = -27.0 * (j * k)
	elif (b * c) <= 4e+157:
		tmp = t * (z * (y * (x * 18.0)))
	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) <= -5e+179)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -5e+59)
		tmp = Float64(-27.0 * Float64(j * k));
	elseif (Float64(b * c) <= 4e+157)
		tmp = Float64(t * Float64(z * Float64(y * Float64(x * 18.0))));
	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) <= -5e+179)
		tmp = b * c;
	elseif ((b * c) <= -5e+59)
		tmp = -27.0 * (j * k);
	elseif ((b * c) <= 4e+157)
		tmp = t * (z * (y * (x * 18.0)));
	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], -5e+179], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -5e+59], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 4e+157], N[(t * N[(z * N[(y * N[(x * 18.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -5e179 or 3.99999999999999993e157 < (*.f64 b c)

   1. Initial program 81.6%

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

      1. associate--l+ 81.6%

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

      2. distribute-rgt-out-- 83.3%

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

      3. associate-*r* 81.7%

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

      4. associate-*l* 81.7%

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

      5. associate-*r* 81.7%

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

      6. *-commutative 81.7%

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

   4. Applied egg-rr 81.7%

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

   5. Taylor expanded in b around inf 65.6%

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

   if -5e179 < (*.f64 b c) < -4.9999999999999997e59

   1. Initial program 86.6%

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

   3. Simplified 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 45.6%

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

   if -4.9999999999999997e59 < (*.f64 b c) < 3.99999999999999993e157

   1. Initial program 90.8%

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

   3. Simplified 89.1%

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

   5. Taylor expanded in t around inf 51.4%

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

   6. Taylor expanded in x around inf 33.4%

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

      1. associate-*r* 35.5%

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

      2. associate-*r* 35.5%

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

      3. associate-*r* 35.6%

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

   8. Simplified 35.6%

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

4. Final simplification 43.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -5 \cdot 10^{+179}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -5 \cdot 10^{+59}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq 4 \cdot 10^{+157}:\\ \;\;\;\;t \cdot \left(z \cdot \left(y \cdot \left(x \cdot 18\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 37.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -5 \cdot 10^{+179}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -5 \cdot 10^{+59}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq 4 \cdot 10^{+157}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= (* b c) -5e+179)
   (* b c)
   (if (<= (* b c) -5e+59)
     (* -27.0 (* j k))
     (if (<= (* b c) 4e+157) (* 18.0 (* t (* x (* y z)))) (* 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) <= -5e+179) {
		tmp = b * c;
	} else if ((b * c) <= -5e+59) {
		tmp = -27.0 * (j * k);
	} else if ((b * c) <= 4e+157) {
		tmp = 18.0 * (t * (x * (y * z)));
	} 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) <= (-5d+179)) then
        tmp = b * c
    else if ((b * c) <= (-5d+59)) then
        tmp = (-27.0d0) * (j * k)
    else if ((b * c) <= 4d+157) then
        tmp = 18.0d0 * (t * (x * (y * z)))
    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) <= -5e+179) {
		tmp = b * c;
	} else if ((b * c) <= -5e+59) {
		tmp = -27.0 * (j * k);
	} else if ((b * c) <= 4e+157) {
		tmp = 18.0 * (t * (x * (y * z)));
	} 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) <= -5e+179:
		tmp = b * c
	elif (b * c) <= -5e+59:
		tmp = -27.0 * (j * k)
	elif (b * c) <= 4e+157:
		tmp = 18.0 * (t * (x * (y * z)))
	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) <= -5e+179)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -5e+59)
		tmp = Float64(-27.0 * Float64(j * k));
	elseif (Float64(b * c) <= 4e+157)
		tmp = Float64(18.0 * Float64(t * Float64(x * Float64(y * z))));
	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) <= -5e+179)
		tmp = b * c;
	elseif ((b * c) <= -5e+59)
		tmp = -27.0 * (j * k);
	elseif ((b * c) <= 4e+157)
		tmp = 18.0 * (t * (x * (y * z)));
	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], -5e+179], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -5e+59], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 4e+157], N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -5e179 or 3.99999999999999993e157 < (*.f64 b c)

   1. Initial program 81.6%

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

      1. associate--l+ 81.6%

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

      2. distribute-rgt-out-- 83.3%

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

      3. associate-*r* 81.7%

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

      4. associate-*l* 81.7%

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

      5. associate-*r* 81.7%

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

      6. *-commutative 81.7%

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

   4. Applied egg-rr 81.7%

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

   5. Taylor expanded in b around inf 65.6%

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

   if -5e179 < (*.f64 b c) < -4.9999999999999997e59

   1. Initial program 86.6%

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

   3. Simplified 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 45.6%

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

   if -4.9999999999999997e59 < (*.f64 b c) < 3.99999999999999993e157

   1. Initial program 90.8%

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

   3. Simplified 89.1%

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

      1. associate-*r* 91.4%

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

      2. distribute-rgt-out-- 90.8%

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

      3. associate-+l- 90.8%

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

      4. associate-*l* 87.3%

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

      5. fma-neg 87.3%

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

      6. associate-*l* 86.7%

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

      7. *-commutative 86.7%

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

   6. Applied egg-rr 86.7%

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

      1. fma-undefine 86.7%

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

      2. unsub-neg 86.7%

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

      3. *-commutative 86.7%

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

   8. Simplified 86.7%

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

   9. Taylor expanded in x around inf 71.3%

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

       1. associate-*r* 71.3%

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

       2. *-commutative 71.3%

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

   11. Simplified 71.3%

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

   12. Taylor expanded in y around inf 33.4%

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

Alternative 16: 48.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;x \leq -1.02 \cdot 10^{+164}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;x \leq -7.2 \cdot 10^{-32}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{-235}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{+96}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (- (* b c) (* 4.0 (* x i)))))
   (if (<= x -1.02e+164)
     (* 18.0 (* t (* x (* y z))))
     (if (<= x -7.2e-32)
       t_1
       (if (<= x 1.45e-235)
         (+ (* -4.0 (* t a)) (* j (* k -27.0)))
         (if (<= x 4.8e+96) (- (* b c) (* 4.0 (* t a))) t_1))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) - (4.0 * (x * i));
	double tmp;
	if (x <= -1.02e+164) {
		tmp = 18.0 * (t * (x * (y * z)));
	} else if (x <= -7.2e-32) {
		tmp = t_1;
	} else if (x <= 1.45e-235) {
		tmp = (-4.0 * (t * a)) + (j * (k * -27.0));
	} else if (x <= 4.8e+96) {
		tmp = (b * c) - (4.0 * (t * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b * c) - (4.0d0 * (x * i))
    if (x <= (-1.02d+164)) then
        tmp = 18.0d0 * (t * (x * (y * z)))
    else if (x <= (-7.2d-32)) then
        tmp = t_1
    else if (x <= 1.45d-235) then
        tmp = ((-4.0d0) * (t * a)) + (j * (k * (-27.0d0)))
    else if (x <= 4.8d+96) then
        tmp = (b * c) - (4.0d0 * (t * a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) - (4.0 * (x * i));
	double tmp;
	if (x <= -1.02e+164) {
		tmp = 18.0 * (t * (x * (y * z)));
	} else if (x <= -7.2e-32) {
		tmp = t_1;
	} else if (x <= 1.45e-235) {
		tmp = (-4.0 * (t * a)) + (j * (k * -27.0));
	} else if (x <= 4.8e+96) {
		tmp = (b * c) - (4.0 * (t * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) - (4.0 * (x * i))
	tmp = 0
	if x <= -1.02e+164:
		tmp = 18.0 * (t * (x * (y * z)))
	elif x <= -7.2e-32:
		tmp = t_1
	elif x <= 1.45e-235:
		tmp = (-4.0 * (t * a)) + (j * (k * -27.0))
	elif x <= 4.8e+96:
		tmp = (b * c) - (4.0 * (t * a))
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)))
	tmp = 0.0
	if (x <= -1.02e+164)
		tmp = Float64(18.0 * Float64(t * Float64(x * Float64(y * z))));
	elseif (x <= -7.2e-32)
		tmp = t_1;
	elseif (x <= 1.45e-235)
		tmp = Float64(Float64(-4.0 * Float64(t * a)) + Float64(j * Float64(k * -27.0)));
	elseif (x <= 4.8e+96)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(t * a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) - (4.0 * (x * i));
	tmp = 0.0;
	if (x <= -1.02e+164)
		tmp = 18.0 * (t * (x * (y * z)));
	elseif (x <= -7.2e-32)
		tmp = t_1;
	elseif (x <= 1.45e-235)
		tmp = (-4.0 * (t * a)) + (j * (k * -27.0));
	elseif (x <= 4.8e+96)
		tmp = (b * c) - (4.0 * (t * a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.02e+164], N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -7.2e-32], t$95$1, If[LessEqual[x, 1.45e-235], N[(N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.8e+96], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.02e164

   1. Initial program 73.7%

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

   3. Simplified 84.1%

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

      1. associate-*r* 79.0%

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

      2. distribute-rgt-out-- 73.7%

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

      3. associate-+l- 73.7%

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

      4. associate-*l* 73.6%

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

      5. fma-neg 73.6%

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

      6. associate-*l* 73.7%

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

      7. *-commutative 73.7%

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

   6. Applied egg-rr 73.7%

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

      1. fma-undefine 73.7%

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

      2. unsub-neg 73.7%

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

      3. *-commutative 73.7%

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

   8. Simplified 73.7%

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

   9. Taylor expanded in x around inf 74.1%

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

       1. associate-*r* 74.1%

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

       2. *-commutative 74.1%

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

   11. Simplified 74.1%

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

   12. Taylor expanded in y around inf 73.9%

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

   if -1.02e164 < x < -7.19999999999999986e-32 or 4.79999999999999986e96 < x

   1. Initial program 81.0%

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

   3. Taylor expanded in t around 0 61.6%

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

   4. Taylor expanded in j around 0 52.9%

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

   if -7.19999999999999986e-32 < x < 1.45000000000000004e-235

   1. Initial program 94.2%

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

   3. Simplified 87.1%

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

   5. Taylor expanded in a around inf 63.0%

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

      1. *-commutative 63.0%

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

   7. Simplified 63.0%

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

   if 1.45000000000000004e-235 < x < 4.79999999999999986e96

   1. Initial program 97.1%

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

   3. Taylor expanded in x around 0 67.7%

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

   4. Taylor expanded in j around 0 56.3%

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

4. Final simplification 58.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.02 \cdot 10^{+164}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;x \leq -7.2 \cdot 10^{-32}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{-235}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{+96}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 77.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;x \leq -2.8 \cdot 10^{+17}:\\ \;\;\;\;\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) - 4 \cdot \left(x \cdot i\right)\right) - t\_1\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{+152}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) - 4 \cdot i\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)))
   (if (<= x -2.8e+17)
     (- (- (* 18.0 (* t (* x (* y z)))) (* 4.0 (* x i))) t_1)
     (if (<= x 1.5e+152)
       (- (- (* b c) (* 4.0 (+ (* x i) (* t a)))) t_1)
       (* x (- (* 18.0 (* z (* y t))) (* 4.0 i)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (x <= -2.8e+17) {
		tmp = ((18.0 * (t * (x * (y * z)))) - (4.0 * (x * i))) - t_1;
	} else if (x <= 1.5e+152) {
		tmp = ((b * c) - (4.0 * ((x * i) + (t * a)))) - t_1;
	} else {
		tmp = x * ((18.0 * (z * (y * t))) - (4.0 * i));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (j * 27.0d0) * k
    if (x <= (-2.8d+17)) then
        tmp = ((18.0d0 * (t * (x * (y * z)))) - (4.0d0 * (x * i))) - t_1
    else if (x <= 1.5d+152) then
        tmp = ((b * c) - (4.0d0 * ((x * i) + (t * a)))) - t_1
    else
        tmp = x * ((18.0d0 * (z * (y * t))) - (4.0d0 * i))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (x <= -2.8e+17) {
		tmp = ((18.0 * (t * (x * (y * z)))) - (4.0 * (x * i))) - t_1;
	} else if (x <= 1.5e+152) {
		tmp = ((b * c) - (4.0 * ((x * i) + (t * a)))) - t_1;
	} else {
		tmp = x * ((18.0 * (z * (y * t))) - (4.0 * i));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	tmp = 0
	if x <= -2.8e+17:
		tmp = ((18.0 * (t * (x * (y * z)))) - (4.0 * (x * i))) - t_1
	elif x <= 1.5e+152:
		tmp = ((b * c) - (4.0 * ((x * i) + (t * a)))) - t_1
	else:
		tmp = x * ((18.0 * (z * (y * t))) - (4.0 * i))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (x <= -2.8e+17)
		tmp = Float64(Float64(Float64(18.0 * Float64(t * Float64(x * Float64(y * z)))) - Float64(4.0 * Float64(x * i))) - t_1);
	elseif (x <= 1.5e+152)
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(Float64(x * i) + Float64(t * a)))) - t_1);
	else
		tmp = Float64(x * Float64(Float64(18.0 * Float64(z * Float64(y * t))) - Float64(4.0 * i)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * 27.0) * k;
	tmp = 0.0;
	if (x <= -2.8e+17)
		tmp = ((18.0 * (t * (x * (y * z)))) - (4.0 * (x * i))) - t_1;
	elseif (x <= 1.5e+152)
		tmp = ((b * c) - (4.0 * ((x * i) + (t * a)))) - t_1;
	else
		tmp = x * ((18.0 * (z * (y * t))) - (4.0 * i));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[x, -2.8e+17], N[(N[(N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[x, 1.5e+152], 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[(x * N[(N[(18.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.8e17

   1. Initial program 85.9%

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

   3. Taylor expanded in b around 0 89.4%

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

      1. associate-*r* 83.5%

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

      2. distribute-lft-out 83.5%

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

      3. *-commutative 83.5%

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

   5. Simplified 83.5%

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

   6. Taylor expanded in a around 0 87.6%

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

   if -2.8e17 < x < 1.49999999999999995e152

   1. Initial program 93.1%

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

   3. Taylor expanded in y around 0 81.6%

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

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

   5. Simplified 81.6%

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

   if 1.49999999999999995e152 < x

   1. Initial program 74.0%

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

   3. Simplified 76.1%

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

   5. Taylor expanded in x around inf 78.6%

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

      1. pow1 78.6%

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

   7. Applied egg-rr 78.6%

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

      1. unpow1 78.6%

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

      2. associate-*r* 80.8%

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

   9. Simplified 80.8%

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

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{+17}:\\ \;\;\;\;\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) - 4 \cdot \left(x \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{+152}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) - 4 \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 75.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -6.6 \cdot 10^{+19}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + -4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{+152}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) - 4 \cdot i\right)\\ \end{array} \end{array} \]

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
 (if (<= x -6.6e+19)
   (+ (* 18.0 (* t (* x (* y z)))) (* -4.0 (* x i)))
   (if (<= x 1.05e+152)
     (- (- (* b c) (* 4.0 (+ (* x i) (* t a)))) (* (* j 27.0) k))
     (* x (- (* 18.0 (* z (* y t))) (* 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 tmp;
	if (x <= -6.6e+19) {
		tmp = (18.0 * (t * (x * (y * z)))) + (-4.0 * (x * i));
	} else if (x <= 1.05e+152) {
		tmp = ((b * c) - (4.0 * ((x * i) + (t * a)))) - ((j * 27.0) * k);
	} else {
		tmp = x * ((18.0 * (z * (y * t))) - (4.0 * i));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (x <= (-6.6d+19)) then
        tmp = (18.0d0 * (t * (x * (y * z)))) + ((-4.0d0) * (x * i))
    else if (x <= 1.05d+152) then
        tmp = ((b * c) - (4.0d0 * ((x * i) + (t * a)))) - ((j * 27.0d0) * k)
    else
        tmp = x * ((18.0d0 * (z * (y * t))) - (4.0d0 * i))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (x <= -6.6e+19) {
		tmp = (18.0 * (t * (x * (y * z)))) + (-4.0 * (x * i));
	} else if (x <= 1.05e+152) {
		tmp = ((b * c) - (4.0 * ((x * i) + (t * a)))) - ((j * 27.0) * k);
	} else {
		tmp = x * ((18.0 * (z * (y * t))) - (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):
	tmp = 0
	if x <= -6.6e+19:
		tmp = (18.0 * (t * (x * (y * z)))) + (-4.0 * (x * i))
	elif x <= 1.05e+152:
		tmp = ((b * c) - (4.0 * ((x * i) + (t * a)))) - ((j * 27.0) * k)
	else:
		tmp = x * ((18.0 * (z * (y * t))) - (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)
	tmp = 0.0
	if (x <= -6.6e+19)
		tmp = Float64(Float64(18.0 * Float64(t * Float64(x * Float64(y * z)))) + Float64(-4.0 * Float64(x * i)));
	elseif (x <= 1.05e+152)
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(Float64(x * i) + Float64(t * a)))) - Float64(Float64(j * 27.0) * k));
	else
		tmp = Float64(x * Float64(Float64(18.0 * Float64(z * Float64(y * t))) - 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)
	tmp = 0.0;
	if (x <= -6.6e+19)
		tmp = (18.0 * (t * (x * (y * z)))) + (-4.0 * (x * i));
	elseif (x <= 1.05e+152)
		tmp = ((b * c) - (4.0 * ((x * i) + (t * a)))) - ((j * 27.0) * k);
	else
		tmp = x * ((18.0 * (z * (y * t))) - (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_] := If[LessEqual[x, -6.6e+19], N[(N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.05e+152], 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], N[(x * N[(N[(18.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.6e19

   1. Initial program 85.9%

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

   3. Simplified 91.9%

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

   5. Taylor expanded in x around inf 74.0%

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

   6. Taylor expanded in t around 0 75.9%

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

   if -6.6e19 < x < 1.0500000000000001e152

   1. Initial program 93.1%

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

   3. Taylor expanded in y around 0 81.6%

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

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

   5. Simplified 81.6%

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

   if 1.0500000000000001e152 < x

   1. Initial program 74.0%

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

   3. Simplified 76.1%

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

   5. Taylor expanded in x around inf 78.6%

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

      1. pow1 78.6%

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

   7. Applied egg-rr 78.6%

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

      1. unpow1 78.6%

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

      2. associate-*r* 80.8%

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

   9. Simplified 80.8%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.6 \cdot 10^{+19}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + -4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{+152}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) - 4 \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 67.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -5.6 \cdot 10^{+14}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + -4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{-174}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;x \leq 2.85 \cdot 10^{+107}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) - 4 \cdot i\right)\\ \end{array} \end{array} \]

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
 (if (<= x -5.6e+14)
   (+ (* 18.0 (* t (* x (* y z)))) (* -4.0 (* x i)))
   (if (<= x 2.9e-174)
     (- (- (* b c) (* 4.0 (* t a))) (* (* j 27.0) k))
     (if (<= x 2.85e+107)
       (- (* b c) (* 4.0 (+ (* x i) (* t a))))
       (* x (- (* 18.0 (* z (* y t))) (* 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 tmp;
	if (x <= -5.6e+14) {
		tmp = (18.0 * (t * (x * (y * z)))) + (-4.0 * (x * i));
	} else if (x <= 2.9e-174) {
		tmp = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k);
	} else if (x <= 2.85e+107) {
		tmp = (b * c) - (4.0 * ((x * i) + (t * a)));
	} else {
		tmp = x * ((18.0 * (z * (y * t))) - (4.0 * i));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (x <= (-5.6d+14)) then
        tmp = (18.0d0 * (t * (x * (y * z)))) + ((-4.0d0) * (x * i))
    else if (x <= 2.9d-174) then
        tmp = ((b * c) - (4.0d0 * (t * a))) - ((j * 27.0d0) * k)
    else if (x <= 2.85d+107) then
        tmp = (b * c) - (4.0d0 * ((x * i) + (t * a)))
    else
        tmp = x * ((18.0d0 * (z * (y * t))) - (4.0d0 * i))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (x <= -5.6e+14) {
		tmp = (18.0 * (t * (x * (y * z)))) + (-4.0 * (x * i));
	} else if (x <= 2.9e-174) {
		tmp = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k);
	} else if (x <= 2.85e+107) {
		tmp = (b * c) - (4.0 * ((x * i) + (t * a)));
	} else {
		tmp = x * ((18.0 * (z * (y * t))) - (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):
	tmp = 0
	if x <= -5.6e+14:
		tmp = (18.0 * (t * (x * (y * z)))) + (-4.0 * (x * i))
	elif x <= 2.9e-174:
		tmp = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k)
	elif x <= 2.85e+107:
		tmp = (b * c) - (4.0 * ((x * i) + (t * a)))
	else:
		tmp = x * ((18.0 * (z * (y * t))) - (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)
	tmp = 0.0
	if (x <= -5.6e+14)
		tmp = Float64(Float64(18.0 * Float64(t * Float64(x * Float64(y * z)))) + Float64(-4.0 * Float64(x * i)));
	elseif (x <= 2.9e-174)
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(t * a))) - Float64(Float64(j * 27.0) * k));
	elseif (x <= 2.85e+107)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(Float64(x * i) + Float64(t * a))));
	else
		tmp = Float64(x * Float64(Float64(18.0 * Float64(z * Float64(y * t))) - 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)
	tmp = 0.0;
	if (x <= -5.6e+14)
		tmp = (18.0 * (t * (x * (y * z)))) + (-4.0 * (x * i));
	elseif (x <= 2.9e-174)
		tmp = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k);
	elseif (x <= 2.85e+107)
		tmp = (b * c) - (4.0 * ((x * i) + (t * a)));
	else
		tmp = x * ((18.0 * (z * (y * t))) - (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_] := If[LessEqual[x, -5.6e+14], N[(N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.9e-174], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.85e+107], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(N[(x * i), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(18.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -5.6e14

   1. Initial program 85.9%

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

   3. Simplified 91.9%

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

   5. Taylor expanded in x around inf 74.0%

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

   6. Taylor expanded in t around 0 75.9%

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

   if -5.6e14 < x < 2.9000000000000001e-174

   1. Initial program 92.6%

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

   3. Taylor expanded in x around 0 78.8%

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

   if 2.9000000000000001e-174 < x < 2.84999999999999986e107

   1. Initial program 96.4%

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

   3. Simplified 94.6%

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

      1. associate-*r* 96.4%

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

      2. distribute-rgt-out-- 96.4%

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

      3. associate-+l- 96.4%

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

      4. associate-*l* 98.0%

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

      5. fma-neg 98.0%

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

      6. associate-*l* 98.0%

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

      7. *-commutative 98.0%

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

   6. Applied egg-rr 98.0%

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

      1. fma-undefine 98.0%

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

      2. unsub-neg 98.0%

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

      3. *-commutative 98.0%

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

   8. Simplified 98.0%

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

   9. Taylor expanded in x around inf 88.9%

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

       1. associate-*r* 88.9%

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

       2. *-commutative 88.9%

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

   11. Simplified 88.9%

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

   12. Taylor expanded in y around 0 72.6%

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

       1. distribute-lft-out 72.6%

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

       2. *-commutative 72.6%

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

   14. Simplified 72.6%

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

   if 2.84999999999999986e107 < x

   1. Initial program 75.5%

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

   3. Simplified 78.9%

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

   5. Taylor expanded in x around inf 74.4%

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

      1. pow1 74.4%

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

   7. Applied egg-rr 74.4%

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

      1. unpow1 74.4%

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

      2. associate-*r* 77.9%

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

   9. Simplified 77.9%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.6 \cdot 10^{+14}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + -4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{-174}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;x \leq 2.85 \cdot 10^{+107}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) - 4 \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 58.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{-8}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + -4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-234}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{+110}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) - 4 \cdot i\right)\\ \end{array} \end{array} \]

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
 (if (<= x -7e-8)
   (+ (* 18.0 (* t (* x (* y z)))) (* -4.0 (* x i)))
   (if (<= x 1.2e-234)
     (+ (* -4.0 (* t a)) (* j (* k -27.0)))
     (if (<= x 7.2e+110)
       (- (* b c) (* 4.0 (+ (* x i) (* t a))))
       (* x (- (* 18.0 (* z (* y t))) (* 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 tmp;
	if (x <= -7e-8) {
		tmp = (18.0 * (t * (x * (y * z)))) + (-4.0 * (x * i));
	} else if (x <= 1.2e-234) {
		tmp = (-4.0 * (t * a)) + (j * (k * -27.0));
	} else if (x <= 7.2e+110) {
		tmp = (b * c) - (4.0 * ((x * i) + (t * a)));
	} else {
		tmp = x * ((18.0 * (z * (y * t))) - (4.0 * i));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (x <= (-7d-8)) then
        tmp = (18.0d0 * (t * (x * (y * z)))) + ((-4.0d0) * (x * i))
    else if (x <= 1.2d-234) then
        tmp = ((-4.0d0) * (t * a)) + (j * (k * (-27.0d0)))
    else if (x <= 7.2d+110) then
        tmp = (b * c) - (4.0d0 * ((x * i) + (t * a)))
    else
        tmp = x * ((18.0d0 * (z * (y * t))) - (4.0d0 * i))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (x <= -7e-8) {
		tmp = (18.0 * (t * (x * (y * z)))) + (-4.0 * (x * i));
	} else if (x <= 1.2e-234) {
		tmp = (-4.0 * (t * a)) + (j * (k * -27.0));
	} else if (x <= 7.2e+110) {
		tmp = (b * c) - (4.0 * ((x * i) + (t * a)));
	} else {
		tmp = x * ((18.0 * (z * (y * t))) - (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):
	tmp = 0
	if x <= -7e-8:
		tmp = (18.0 * (t * (x * (y * z)))) + (-4.0 * (x * i))
	elif x <= 1.2e-234:
		tmp = (-4.0 * (t * a)) + (j * (k * -27.0))
	elif x <= 7.2e+110:
		tmp = (b * c) - (4.0 * ((x * i) + (t * a)))
	else:
		tmp = x * ((18.0 * (z * (y * t))) - (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)
	tmp = 0.0
	if (x <= -7e-8)
		tmp = Float64(Float64(18.0 * Float64(t * Float64(x * Float64(y * z)))) + Float64(-4.0 * Float64(x * i)));
	elseif (x <= 1.2e-234)
		tmp = Float64(Float64(-4.0 * Float64(t * a)) + Float64(j * Float64(k * -27.0)));
	elseif (x <= 7.2e+110)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(Float64(x * i) + Float64(t * a))));
	else
		tmp = Float64(x * Float64(Float64(18.0 * Float64(z * Float64(y * t))) - 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)
	tmp = 0.0;
	if (x <= -7e-8)
		tmp = (18.0 * (t * (x * (y * z)))) + (-4.0 * (x * i));
	elseif (x <= 1.2e-234)
		tmp = (-4.0 * (t * a)) + (j * (k * -27.0));
	elseif (x <= 7.2e+110)
		tmp = (b * c) - (4.0 * ((x * i) + (t * a)));
	else
		tmp = x * ((18.0 * (z * (y * t))) - (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_] := If[LessEqual[x, -7e-8], N[(N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.2e-234], N[(N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.2e+110], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(N[(x * i), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(18.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -7.00000000000000048e-8

   1. Initial program 86.5%

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

   3. Simplified 92.2%

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

   5. Taylor expanded in x around inf 73.1%

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

   6. Taylor expanded in t around 0 74.9%

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

   if -7.00000000000000048e-8 < x < 1.1999999999999999e-234

   1. Initial program 90.9%

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

   3. Simplified 85.8%

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

   5. Taylor expanded in a around inf 60.4%

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

      1. *-commutative 60.4%

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

   7. Simplified 60.4%

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

   if 1.1999999999999999e-234 < x < 7.1999999999999994e110

   1. Initial program 97.2%

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

   3. Simplified 91.7%

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

      1. associate-*r* 97.2%

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

      2. distribute-rgt-out-- 97.2%

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

      3. associate-+l- 97.2%

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

      4. associate-*l* 94.2%

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

      5. fma-neg 94.2%

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

      6. associate-*l* 92.8%

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

      7. *-commutative 92.8%

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

   6. Applied egg-rr 92.8%

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

      1. fma-undefine 92.8%

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

      2. unsub-neg 92.8%

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

      3. *-commutative 92.8%

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

   8. Simplified 92.8%

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

   9. Taylor expanded in x around inf 83.1%

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

       1. associate-*r* 83.1%

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

       2. *-commutative 83.1%

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

   11. Simplified 83.1%

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

   12. Taylor expanded in y around 0 69.6%

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

       1. distribute-lft-out 69.6%

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

       2. *-commutative 69.6%

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

   14. Simplified 69.6%

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

   if 7.1999999999999994e110 < x

   1. Initial program 75.5%

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

   3. Simplified 78.9%

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

   5. Taylor expanded in x around inf 74.4%

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

      1. pow1 74.4%

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

   7. Applied egg-rr 74.4%

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

      1. unpow1 74.4%

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

      2. associate-*r* 77.9%

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

   9. Simplified 77.9%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{-8}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + -4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-234}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{+110}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) - 4 \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 60.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -8.4 \cdot 10^{-8}:\\ \;\;\;\;x \cdot \left(\left(y \cdot z\right) \cdot \left(18 \cdot t\right) + i \cdot -4\right)\\ \mathbf{elif}\;x \leq 9.8 \cdot 10^{-235}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq 9.8 \cdot 10^{+107}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) - 4 \cdot i\right)\\ \end{array} \end{array} \]

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
 (if (<= x -8.4e-8)
   (* x (+ (* (* y z) (* 18.0 t)) (* i -4.0)))
   (if (<= x 9.8e-235)
     (+ (* -4.0 (* t a)) (* j (* k -27.0)))
     (if (<= x 9.8e+107)
       (- (* b c) (* 4.0 (+ (* x i) (* t a))))
       (* x (- (* 18.0 (* z (* y t))) (* 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 tmp;
	if (x <= -8.4e-8) {
		tmp = x * (((y * z) * (18.0 * t)) + (i * -4.0));
	} else if (x <= 9.8e-235) {
		tmp = (-4.0 * (t * a)) + (j * (k * -27.0));
	} else if (x <= 9.8e+107) {
		tmp = (b * c) - (4.0 * ((x * i) + (t * a)));
	} else {
		tmp = x * ((18.0 * (z * (y * t))) - (4.0 * i));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (x <= (-8.4d-8)) then
        tmp = x * (((y * z) * (18.0d0 * t)) + (i * (-4.0d0)))
    else if (x <= 9.8d-235) then
        tmp = ((-4.0d0) * (t * a)) + (j * (k * (-27.0d0)))
    else if (x <= 9.8d+107) then
        tmp = (b * c) - (4.0d0 * ((x * i) + (t * a)))
    else
        tmp = x * ((18.0d0 * (z * (y * t))) - (4.0d0 * i))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (x <= -8.4e-8) {
		tmp = x * (((y * z) * (18.0 * t)) + (i * -4.0));
	} else if (x <= 9.8e-235) {
		tmp = (-4.0 * (t * a)) + (j * (k * -27.0));
	} else if (x <= 9.8e+107) {
		tmp = (b * c) - (4.0 * ((x * i) + (t * a)));
	} else {
		tmp = x * ((18.0 * (z * (y * t))) - (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):
	tmp = 0
	if x <= -8.4e-8:
		tmp = x * (((y * z) * (18.0 * t)) + (i * -4.0))
	elif x <= 9.8e-235:
		tmp = (-4.0 * (t * a)) + (j * (k * -27.0))
	elif x <= 9.8e+107:
		tmp = (b * c) - (4.0 * ((x * i) + (t * a)))
	else:
		tmp = x * ((18.0 * (z * (y * t))) - (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)
	tmp = 0.0
	if (x <= -8.4e-8)
		tmp = Float64(x * Float64(Float64(Float64(y * z) * Float64(18.0 * t)) + Float64(i * -4.0)));
	elseif (x <= 9.8e-235)
		tmp = Float64(Float64(-4.0 * Float64(t * a)) + Float64(j * Float64(k * -27.0)));
	elseif (x <= 9.8e+107)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(Float64(x * i) + Float64(t * a))));
	else
		tmp = Float64(x * Float64(Float64(18.0 * Float64(z * Float64(y * t))) - 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)
	tmp = 0.0;
	if (x <= -8.4e-8)
		tmp = x * (((y * z) * (18.0 * t)) + (i * -4.0));
	elseif (x <= 9.8e-235)
		tmp = (-4.0 * (t * a)) + (j * (k * -27.0));
	elseif (x <= 9.8e+107)
		tmp = (b * c) - (4.0 * ((x * i) + (t * a)));
	else
		tmp = x * ((18.0 * (z * (y * t))) - (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_] := If[LessEqual[x, -8.4e-8], N[(x * N[(N[(N[(y * z), $MachinePrecision] * N[(18.0 * t), $MachinePrecision]), $MachinePrecision] + N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9.8e-235], N[(N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9.8e+107], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(N[(x * i), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(18.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -8.39999999999999978e-8

   1. Initial program 86.5%

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

      1. associate--l+ 86.5%

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

      2. distribute-rgt-out-- 88.4%

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

      3. associate-*r* 92.2%

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

      4. associate-*l* 92.2%

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

      5. associate-*r* 92.2%

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

      6. *-commutative 92.2%

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

   4. Applied egg-rr 92.2%

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

   5. Taylor expanded in x around inf 73.1%

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

      1. cancel-sign-sub-inv 73.1%

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

      2. associate-*r* 73.1%

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

      3. metadata-eval 73.1%

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

   7. Simplified 73.1%

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

   if -8.39999999999999978e-8 < x < 9.79999999999999931e-235

   1. Initial program 90.9%

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

   3. Simplified 85.8%

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

   5. Taylor expanded in a around inf 60.4%

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

      1. *-commutative 60.4%

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

   7. Simplified 60.4%

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

   if 9.79999999999999931e-235 < x < 9.8000000000000003e107

   1. Initial program 97.2%

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

   3. Simplified 91.7%

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

      1. associate-*r* 97.2%

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

      2. distribute-rgt-out-- 97.2%

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

      3. associate-+l- 97.2%

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

      4. associate-*l* 94.2%

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

      5. fma-neg 94.2%

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

      6. associate-*l* 92.8%

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

      7. *-commutative 92.8%

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

   6. Applied egg-rr 92.8%

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

      1. fma-undefine 92.8%

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

      2. unsub-neg 92.8%

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

      3. *-commutative 92.8%

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

   8. Simplified 92.8%

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

   9. Taylor expanded in x around inf 83.1%

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

       1. associate-*r* 83.1%

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

       2. *-commutative 83.1%

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

   11. Simplified 83.1%

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

   12. Taylor expanded in y around 0 69.6%

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

       1. distribute-lft-out 69.6%

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

       2. *-commutative 69.6%

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

   14. Simplified 69.6%

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

   if 9.8000000000000003e107 < x

   1. Initial program 75.5%

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

   3. Simplified 78.9%

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

   5. Taylor expanded in x around inf 74.4%

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

      1. pow1 74.4%

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

   7. Applied egg-rr 74.4%

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

      1. unpow1 74.4%

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

      2. associate-*r* 77.9%

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

   9. Simplified 77.9%

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

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.4 \cdot 10^{-8}:\\ \;\;\;\;x \cdot \left(\left(y \cdot z\right) \cdot \left(18 \cdot t\right) + i \cdot -4\right)\\ \mathbf{elif}\;x \leq 9.8 \cdot 10^{-235}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq 9.8 \cdot 10^{+107}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) - 4 \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 57.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{-8}:\\ \;\;\;\;x \cdot \left(\left(y \cdot z\right) \cdot \left(18 \cdot t\right) + i \cdot -4\right)\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-235}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-92}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) - 4 \cdot i\right)\\ \end{array} \end{array} \]

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
 (if (<= x -6.5e-8)
   (* x (+ (* (* y z) (* 18.0 t)) (* i -4.0)))
   (if (<= x 1.6e-235)
     (+ (* -4.0 (* t a)) (* j (* k -27.0)))
     (if (<= x 3.2e-92)
       (- (* b c) (* 4.0 (* t a)))
       (* x (- (* 18.0 (* z (* y t))) (* 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 tmp;
	if (x <= -6.5e-8) {
		tmp = x * (((y * z) * (18.0 * t)) + (i * -4.0));
	} else if (x <= 1.6e-235) {
		tmp = (-4.0 * (t * a)) + (j * (k * -27.0));
	} else if (x <= 3.2e-92) {
		tmp = (b * c) - (4.0 * (t * a));
	} else {
		tmp = x * ((18.0 * (z * (y * t))) - (4.0 * i));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (x <= (-6.5d-8)) then
        tmp = x * (((y * z) * (18.0d0 * t)) + (i * (-4.0d0)))
    else if (x <= 1.6d-235) then
        tmp = ((-4.0d0) * (t * a)) + (j * (k * (-27.0d0)))
    else if (x <= 3.2d-92) then
        tmp = (b * c) - (4.0d0 * (t * a))
    else
        tmp = x * ((18.0d0 * (z * (y * t))) - (4.0d0 * i))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (x <= -6.5e-8) {
		tmp = x * (((y * z) * (18.0 * t)) + (i * -4.0));
	} else if (x <= 1.6e-235) {
		tmp = (-4.0 * (t * a)) + (j * (k * -27.0));
	} else if (x <= 3.2e-92) {
		tmp = (b * c) - (4.0 * (t * a));
	} else {
		tmp = x * ((18.0 * (z * (y * t))) - (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):
	tmp = 0
	if x <= -6.5e-8:
		tmp = x * (((y * z) * (18.0 * t)) + (i * -4.0))
	elif x <= 1.6e-235:
		tmp = (-4.0 * (t * a)) + (j * (k * -27.0))
	elif x <= 3.2e-92:
		tmp = (b * c) - (4.0 * (t * a))
	else:
		tmp = x * ((18.0 * (z * (y * t))) - (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)
	tmp = 0.0
	if (x <= -6.5e-8)
		tmp = Float64(x * Float64(Float64(Float64(y * z) * Float64(18.0 * t)) + Float64(i * -4.0)));
	elseif (x <= 1.6e-235)
		tmp = Float64(Float64(-4.0 * Float64(t * a)) + Float64(j * Float64(k * -27.0)));
	elseif (x <= 3.2e-92)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(t * a)));
	else
		tmp = Float64(x * Float64(Float64(18.0 * Float64(z * Float64(y * t))) - 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)
	tmp = 0.0;
	if (x <= -6.5e-8)
		tmp = x * (((y * z) * (18.0 * t)) + (i * -4.0));
	elseif (x <= 1.6e-235)
		tmp = (-4.0 * (t * a)) + (j * (k * -27.0));
	elseif (x <= 3.2e-92)
		tmp = (b * c) - (4.0 * (t * a));
	else
		tmp = x * ((18.0 * (z * (y * t))) - (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_] := If[LessEqual[x, -6.5e-8], N[(x * N[(N[(N[(y * z), $MachinePrecision] * N[(18.0 * t), $MachinePrecision]), $MachinePrecision] + N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.6e-235], N[(N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.2e-92], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(18.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -6.49999999999999997e-8

   1. Initial program 86.5%

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

      1. associate--l+ 86.5%

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

      2. distribute-rgt-out-- 88.4%

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

      3. associate-*r* 92.2%

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

      4. associate-*l* 92.2%

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

      5. associate-*r* 92.2%

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

      6. *-commutative 92.2%

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

   4. Applied egg-rr 92.2%

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

   5. Taylor expanded in x around inf 73.1%

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

      1. cancel-sign-sub-inv 73.1%

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

      2. associate-*r* 73.1%

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

      3. metadata-eval 73.1%

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

   7. Simplified 73.1%

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

   if -6.49999999999999997e-8 < x < 1.6000000000000001e-235

   1. Initial program 90.9%

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

   3. Simplified 85.8%

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

   5. Taylor expanded in a around inf 60.4%

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

      1. *-commutative 60.4%

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

   7. Simplified 60.4%

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

   if 1.6000000000000001e-235 < x < 3.1999999999999997e-92

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 77.1%

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

   4. Taylor expanded in j around 0 68.3%

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

   if 3.1999999999999997e-92 < x

   1. Initial program 82.9%

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

   3. Simplified 85.0%

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

   5. Taylor expanded in x around inf 62.3%

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

      1. pow1 62.3%

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

   7. Applied egg-rr 62.3%

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

      1. unpow1 62.3%

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

      2. associate-*r* 64.5%

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

   9. Simplified 64.5%

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

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{-8}:\\ \;\;\;\;x \cdot \left(\left(y \cdot z\right) \cdot \left(18 \cdot t\right) + i \cdot -4\right)\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-235}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-92}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) - 4 \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 57.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{-7}:\\ \;\;\;\;x \cdot \left(\left(y \cdot z\right) \cdot \left(18 \cdot t\right) + i \cdot -4\right)\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{-235}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{+57}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \end{array} \end{array} \]

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
 (if (<= x -1.15e-7)
   (* x (+ (* (* y z) (* 18.0 t)) (* i -4.0)))
   (if (<= x 2.7e-235)
     (+ (* -4.0 (* t a)) (* j (* k -27.0)))
     (if (<= x 4.5e+57)
       (- (* b c) (* 4.0 (* t a)))
       (* 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 tmp;
	if (x <= -1.15e-7) {
		tmp = x * (((y * z) * (18.0 * t)) + (i * -4.0));
	} else if (x <= 2.7e-235) {
		tmp = (-4.0 * (t * a)) + (j * (k * -27.0));
	} else if (x <= 4.5e+57) {
		tmp = (b * c) - (4.0 * (t * a));
	} else {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (x <= (-1.15d-7)) then
        tmp = x * (((y * z) * (18.0d0 * t)) + (i * (-4.0d0)))
    else if (x <= 2.7d-235) then
        tmp = ((-4.0d0) * (t * a)) + (j * (k * (-27.0d0)))
    else if (x <= 4.5d+57) then
        tmp = (b * c) - (4.0d0 * (t * a))
    else
        tmp = x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (x <= -1.15e-7) {
		tmp = x * (((y * z) * (18.0 * t)) + (i * -4.0));
	} else if (x <= 2.7e-235) {
		tmp = (-4.0 * (t * a)) + (j * (k * -27.0));
	} else if (x <= 4.5e+57) {
		tmp = (b * c) - (4.0 * (t * a));
	} 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):
	tmp = 0
	if x <= -1.15e-7:
		tmp = x * (((y * z) * (18.0 * t)) + (i * -4.0))
	elif x <= 2.7e-235:
		tmp = (-4.0 * (t * a)) + (j * (k * -27.0))
	elif x <= 4.5e+57:
		tmp = (b * c) - (4.0 * (t * a))
	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)
	tmp = 0.0
	if (x <= -1.15e-7)
		tmp = Float64(x * Float64(Float64(Float64(y * z) * Float64(18.0 * t)) + Float64(i * -4.0)));
	elseif (x <= 2.7e-235)
		tmp = Float64(Float64(-4.0 * Float64(t * a)) + Float64(j * Float64(k * -27.0)));
	elseif (x <= 4.5e+57)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(t * a)));
	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)
	tmp = 0.0;
	if (x <= -1.15e-7)
		tmp = x * (((y * z) * (18.0 * t)) + (i * -4.0));
	elseif (x <= 2.7e-235)
		tmp = (-4.0 * (t * a)) + (j * (k * -27.0));
	elseif (x <= 4.5e+57)
		tmp = (b * c) - (4.0 * (t * a));
	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_] := If[LessEqual[x, -1.15e-7], N[(x * N[(N[(N[(y * z), $MachinePrecision] * N[(18.0 * t), $MachinePrecision]), $MachinePrecision] + N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.7e-235], N[(N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.5e+57], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.14999999999999997e-7

   1. Initial program 86.5%

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

      1. associate--l+ 86.5%

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

      2. distribute-rgt-out-- 88.4%

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

      3. associate-*r* 92.2%

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

      4. associate-*l* 92.2%

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

      5. associate-*r* 92.2%

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

      6. *-commutative 92.2%

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

   4. Applied egg-rr 92.2%

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

   5. Taylor expanded in x around inf 73.1%

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

      1. cancel-sign-sub-inv 73.1%

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

      2. associate-*r* 73.1%

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

      3. metadata-eval 73.1%

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

   7. Simplified 73.1%

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

   if -1.14999999999999997e-7 < x < 2.7000000000000002e-235

   1. Initial program 90.9%

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

   3. Simplified 85.8%

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

   5. Taylor expanded in a around inf 60.4%

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

      1. *-commutative 60.4%

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

   7. Simplified 60.4%

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

   if 2.7000000000000002e-235 < x < 4.49999999999999996e57

   1. Initial program 96.7%

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

   3. Taylor expanded in x around 0 67.2%

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

   4. Taylor expanded in j around 0 58.8%

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

   if 4.49999999999999996e57 < x

   1. Initial program 79.8%

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

   3. Simplified 82.6%

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

   5. Taylor expanded in x around inf 70.3%

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

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{-7}:\\ \;\;\;\;x \cdot \left(\left(y \cdot z\right) \cdot \left(18 \cdot t\right) + i \cdot -4\right)\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{-235}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{+57}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 57.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := x \cdot \left(\left(y \cdot z\right) \cdot \left(18 \cdot t\right) + i \cdot -4\right)\\ \mathbf{if}\;x \leq -8 \cdot 10^{-8}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-237}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{+56}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* x (+ (* (* y z) (* 18.0 t)) (* i -4.0)))))
   (if (<= x -8e-8)
     t_1
     (if (<= x 7e-237)
       (+ (* -4.0 (* t a)) (* j (* k -27.0)))
       (if (<= x 6.2e+56) (- (* b c) (* 4.0 (* t a))) t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = x * (((y * z) * (18.0 * t)) + (i * -4.0));
	double tmp;
	if (x <= -8e-8) {
		tmp = t_1;
	} else if (x <= 7e-237) {
		tmp = (-4.0 * (t * a)) + (j * (k * -27.0));
	} else if (x <= 6.2e+56) {
		tmp = (b * c) - (4.0 * (t * a));
	} 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 * (((y * z) * (18.0d0 * t)) + (i * (-4.0d0)))
    if (x <= (-8d-8)) then
        tmp = t_1
    else if (x <= 7d-237) then
        tmp = ((-4.0d0) * (t * a)) + (j * (k * (-27.0d0)))
    else if (x <= 6.2d+56) then
        tmp = (b * c) - (4.0d0 * (t * a))
    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 * (((y * z) * (18.0 * t)) + (i * -4.0));
	double tmp;
	if (x <= -8e-8) {
		tmp = t_1;
	} else if (x <= 7e-237) {
		tmp = (-4.0 * (t * a)) + (j * (k * -27.0));
	} else if (x <= 6.2e+56) {
		tmp = (b * c) - (4.0 * (t * a));
	} 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 * (((y * z) * (18.0 * t)) + (i * -4.0))
	tmp = 0
	if x <= -8e-8:
		tmp = t_1
	elif x <= 7e-237:
		tmp = (-4.0 * (t * a)) + (j * (k * -27.0))
	elif x <= 6.2e+56:
		tmp = (b * c) - (4.0 * (t * a))
	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(Float64(y * z) * Float64(18.0 * t)) + Float64(i * -4.0)))
	tmp = 0.0
	if (x <= -8e-8)
		tmp = t_1;
	elseif (x <= 7e-237)
		tmp = Float64(Float64(-4.0 * Float64(t * a)) + Float64(j * Float64(k * -27.0)));
	elseif (x <= 6.2e+56)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(t * a)));
	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 * (((y * z) * (18.0 * t)) + (i * -4.0));
	tmp = 0.0;
	if (x <= -8e-8)
		tmp = t_1;
	elseif (x <= 7e-237)
		tmp = (-4.0 * (t * a)) + (j * (k * -27.0));
	elseif (x <= 6.2e+56)
		tmp = (b * c) - (4.0 * (t * a));
	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[(N[(y * z), $MachinePrecision] * N[(18.0 * t), $MachinePrecision]), $MachinePrecision] + N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -8e-8], t$95$1, If[LessEqual[x, 7e-237], N[(N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.2e+56], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -8.0000000000000002e-8 or 6.20000000000000009e56 < x

   1. Initial program 82.7%

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

      1. associate--l+ 82.7%

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

      2. distribute-rgt-out-- 84.3%

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

      3. associate-*r* 86.7%

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

      4. associate-*l* 86.7%

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

      5. associate-*r* 86.7%

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

      6. *-commutative 86.7%

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

   4. Applied egg-rr 86.7%

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

   5. Taylor expanded in x around inf 71.5%

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

      1. cancel-sign-sub-inv 71.5%

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

      2. associate-*r* 71.5%

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

      3. metadata-eval 71.5%

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

   7. Simplified 71.5%

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

   if -8.0000000000000002e-8 < x < 6.99999999999999966e-237

   1. Initial program 90.9%

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

   3. Simplified 85.8%

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

   5. Taylor expanded in a around inf 60.4%

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

      1. *-commutative 60.4%

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

   7. Simplified 60.4%

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

   if 6.99999999999999966e-237 < x < 6.20000000000000009e56

   1. Initial program 96.7%

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

   3. Taylor expanded in x around 0 67.2%

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

   4. Taylor expanded in j around 0 58.8%

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

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{-8}:\\ \;\;\;\;x \cdot \left(\left(y \cdot z\right) \cdot \left(18 \cdot t\right) + i \cdot -4\right)\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-237}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{+56}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(y \cdot z\right) \cdot \left(18 \cdot t\right) + i \cdot -4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 36.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -9 \cdot 10^{+159}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -7.6 \cdot 10^{-175}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 2.3 \cdot 10^{+157}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= (* b c) -9e+159)
   (* b c)
   (if (<= (* b c) -7.6e-175)
     (* j (* k -27.0))
     (if (<= (* b c) 2.3e+157) (* 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) <= -9e+159) {
		tmp = b * c;
	} else if ((b * c) <= -7.6e-175) {
		tmp = j * (k * -27.0);
	} else if ((b * c) <= 2.3e+157) {
		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) <= (-9d+159)) then
        tmp = b * c
    else if ((b * c) <= (-7.6d-175)) then
        tmp = j * (k * (-27.0d0))
    else if ((b * c) <= 2.3d+157) 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) <= -9e+159) {
		tmp = b * c;
	} else if ((b * c) <= -7.6e-175) {
		tmp = j * (k * -27.0);
	} else if ((b * c) <= 2.3e+157) {
		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) <= -9e+159:
		tmp = b * c
	elif (b * c) <= -7.6e-175:
		tmp = j * (k * -27.0)
	elif (b * c) <= 2.3e+157:
		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) <= -9e+159)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -7.6e-175)
		tmp = Float64(j * Float64(k * -27.0));
	elseif (Float64(b * c) <= 2.3e+157)
		tmp = Float64(x * Float64(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) <= -9e+159)
		tmp = b * c;
	elseif ((b * c) <= -7.6e-175)
		tmp = j * (k * -27.0);
	elseif ((b * c) <= 2.3e+157)
		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], -9e+159], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -7.6e-175], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 2.3e+157], N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -9.00000000000000053e159 or 2.30000000000000004e157 < (*.f64 b c)

   1. Initial program 81.6%

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

      1. associate--l+ 81.6%

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

      2. distribute-rgt-out-- 83.3%

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

      3. associate-*r* 81.7%

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

      4. associate-*l* 81.7%

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

      5. associate-*r* 81.7%

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

      6. *-commutative 81.7%

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

   4. Applied egg-rr 81.7%

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

   5. Taylor expanded in b around inf 65.6%

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

   if -9.00000000000000053e159 < (*.f64 b c) < -7.6e-175

   1. Initial program 84.8%

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

   3. Simplified 86.6%

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

      1. associate-*r* 88.1%

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

      2. distribute-rgt-out-- 84.7%

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

      3. associate-+l- 84.7%

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

      4. associate-*l* 81.2%

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

      5. fma-neg 82.9%

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

      6. associate-*l* 82.9%

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

      7. *-commutative 82.9%

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

   6. Applied egg-rr 82.9%

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

      1. fma-undefine 81.2%

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

      2. unsub-neg 81.2%

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

      3. *-commutative 81.2%

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

   8. Simplified 81.2%

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

   9. Taylor expanded in j around inf 34.0%

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

       1. metadata-eval 34.0%

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

       2. distribute-lft-neg-in 34.0%

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

       3. associate-*r* 34.1%

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

       4. *-commutative 34.1%

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

       5. associate-*r* 34.0%

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

       6. distribute-rgt-neg-in 34.0%

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

       7. distribute-lft-neg-in 34.0%

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

       8. metadata-eval 34.0%

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

       9. *-commutative 34.0%

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

   11. Simplified 34.0%

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

   if -7.6e-175 < (*.f64 b c) < 2.30000000000000004e157

   1. Initial program 92.7%

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

   3. Simplified 89.8%

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

      1. associate-*r* 92.7%

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

      2. distribute-rgt-out-- 92.7%

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

      3. associate-+l- 92.7%

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

      4. associate-*l* 89.7%

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

      5. fma-neg 89.7%

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

      6. associate-*l* 89.0%

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

      7. *-commutative 89.0%

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

   6. Applied egg-rr 89.0%

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

      1. fma-undefine 89.0%

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

      2. unsub-neg 89.0%

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

      3. *-commutative 89.0%

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

   8. Simplified 89.0%

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

   9. Taylor expanded in i around inf 29.9%

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

       1. associate-*r* 29.9%

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

       2. metadata-eval 29.9%

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

       3. distribute-lft-neg-in 29.9%

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

       4. distribute-lft-neg-in 29.9%

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

       5. *-commutative 29.9%

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

       6. distribute-rgt-neg-in 29.9%

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

       7. distribute-lft-neg-in 29.9%

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

       8. metadata-eval 29.9%

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

       9. *-commutative 29.9%

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

   11. Simplified 29.9%

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

Alternative 26: 48.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.75 \cdot 10^{+32}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{-278}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{+98}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= x -1.75e+32)
   (* 18.0 (* t (* x (* y z))))
   (if (<= x 1.7e-278)
     (- (* b c) (* 27.0 (* j k)))
     (if (<= x 5.5e+98)
       (- (* b c) (* 4.0 (* t a)))
       (- (* b c) (* 4.0 (* x i)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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 <= -1.75e+32) {
		tmp = 18.0 * (t * (x * (y * z)));
	} else if (x <= 1.7e-278) {
		tmp = (b * c) - (27.0 * (j * k));
	} else if (x <= 5.5e+98) {
		tmp = (b * c) - (4.0 * (t * a));
	} else {
		tmp = (b * c) - (4.0 * (x * i));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 <= (-1.75d+32)) then
        tmp = 18.0d0 * (t * (x * (y * z)))
    else if (x <= 1.7d-278) then
        tmp = (b * c) - (27.0d0 * (j * k))
    else if (x <= 5.5d+98) then
        tmp = (b * c) - (4.0d0 * (t * a))
    else
        tmp = (b * c) - (4.0d0 * (x * i))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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 <= -1.75e+32) {
		tmp = 18.0 * (t * (x * (y * z)));
	} else if (x <= 1.7e-278) {
		tmp = (b * c) - (27.0 * (j * k));
	} else if (x <= 5.5e+98) {
		tmp = (b * c) - (4.0 * (t * a));
	} else {
		tmp = (b * c) - (4.0 * (x * i));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if x <= -1.75e+32:
		tmp = 18.0 * (t * (x * (y * z)))
	elif x <= 1.7e-278:
		tmp = (b * c) - (27.0 * (j * k))
	elif x <= 5.5e+98:
		tmp = (b * c) - (4.0 * (t * a))
	else:
		tmp = (b * c) - (4.0 * (x * i))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (x <= -1.75e+32)
		tmp = Float64(18.0 * Float64(t * Float64(x * Float64(y * z))));
	elseif (x <= 1.7e-278)
		tmp = Float64(Float64(b * c) - Float64(27.0 * Float64(j * k)));
	elseif (x <= 5.5e+98)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(t * a)));
	else
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (x <= -1.75e+32)
		tmp = 18.0 * (t * (x * (y * z)));
	elseif (x <= 1.7e-278)
		tmp = (b * c) - (27.0 * (j * k));
	elseif (x <= 5.5e+98)
		tmp = (b * c) - (4.0 * (t * a));
	else
		tmp = (b * c) - (4.0 * (x * i));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[x, -1.75e+32], N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.7e-278], N[(N[(b * c), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.5e+98], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.75e32

   1. Initial program 85.0%

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

   3. Simplified 91.4%

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

      1. associate-*r* 87.2%

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

      2. distribute-rgt-out-- 85.0%

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

      3. associate-+l- 85.0%

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

      4. associate-*l* 85.0%

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

      5. fma-neg 85.0%

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

      6. associate-*l* 85.0%

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

      7. *-commutative 85.0%

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

   6. Applied egg-rr 85.0%

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

      1. fma-undefine 85.0%

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

      2. unsub-neg 85.0%

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

      3. *-commutative 85.0%

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

   8. Simplified 85.0%

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

   9. Taylor expanded in x around inf 77.0%

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

       1. associate-*r* 77.0%

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

       2. *-commutative 77.0%

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

   11. Simplified 77.0%

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

   12. Taylor expanded in y around inf 52.0%

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

   if -1.75e32 < x < 1.7e-278

   1. Initial program 90.1%

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

   3. Taylor expanded in t around 0 63.0%

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

   4. Taylor expanded in i around 0 57.1%

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

   if 1.7e-278 < x < 5.49999999999999946e98

   1. Initial program 97.5%

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

   3. Taylor expanded in x around 0 71.0%

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

   4. Taylor expanded in j around 0 56.2%

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

   if 5.49999999999999946e98 < x

   1. Initial program 76.4%

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

   3. Taylor expanded in t around 0 58.7%

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

   4. Taylor expanded in j around 0 56.8%

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

4. Final simplification 55.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.75 \cdot 10^{+32}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{-278}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{+98}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 47.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -2.95 \cdot 10^{+32}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-278}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{+96}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= x -2.95e+32)
   (* 18.0 (* t (* x (* y z))))
   (if (<= x 3.5e-278)
     (+ (* b c) (* j (* k -27.0)))
     (if (<= x 8.5e+96)
       (- (* b c) (* 4.0 (* t a)))
       (- (* b c) (* 4.0 (* x i)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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 <= -2.95e+32) {
		tmp = 18.0 * (t * (x * (y * z)));
	} else if (x <= 3.5e-278) {
		tmp = (b * c) + (j * (k * -27.0));
	} else if (x <= 8.5e+96) {
		tmp = (b * c) - (4.0 * (t * a));
	} else {
		tmp = (b * c) - (4.0 * (x * i));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 <= (-2.95d+32)) then
        tmp = 18.0d0 * (t * (x * (y * z)))
    else if (x <= 3.5d-278) then
        tmp = (b * c) + (j * (k * (-27.0d0)))
    else if (x <= 8.5d+96) then
        tmp = (b * c) - (4.0d0 * (t * a))
    else
        tmp = (b * c) - (4.0d0 * (x * i))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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 <= -2.95e+32) {
		tmp = 18.0 * (t * (x * (y * z)));
	} else if (x <= 3.5e-278) {
		tmp = (b * c) + (j * (k * -27.0));
	} else if (x <= 8.5e+96) {
		tmp = (b * c) - (4.0 * (t * a));
	} else {
		tmp = (b * c) - (4.0 * (x * i));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if x <= -2.95e+32:
		tmp = 18.0 * (t * (x * (y * z)))
	elif x <= 3.5e-278:
		tmp = (b * c) + (j * (k * -27.0))
	elif x <= 8.5e+96:
		tmp = (b * c) - (4.0 * (t * a))
	else:
		tmp = (b * c) - (4.0 * (x * i))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (x <= -2.95e+32)
		tmp = Float64(18.0 * Float64(t * Float64(x * Float64(y * z))));
	elseif (x <= 3.5e-278)
		tmp = Float64(Float64(b * c) + Float64(j * Float64(k * -27.0)));
	elseif (x <= 8.5e+96)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(t * a)));
	else
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (x <= -2.95e+32)
		tmp = 18.0 * (t * (x * (y * z)));
	elseif (x <= 3.5e-278)
		tmp = (b * c) + (j * (k * -27.0));
	elseif (x <= 8.5e+96)
		tmp = (b * c) - (4.0 * (t * a));
	else
		tmp = (b * c) - (4.0 * (x * i));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[x, -2.95e+32], N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.5e-278], N[(N[(b * c), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8.5e+96], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.94999999999999983e32

   1. Initial program 85.0%

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

   3. Simplified 91.4%

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

      1. associate-*r* 87.2%

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

      2. distribute-rgt-out-- 85.0%

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

      3. associate-+l- 85.0%

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

      4. associate-*l* 85.0%

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

      5. fma-neg 85.0%

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

      6. associate-*l* 85.0%

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

      7. *-commutative 85.0%

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

   6. Applied egg-rr 85.0%

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

      1. fma-undefine 85.0%

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

      2. unsub-neg 85.0%

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

      3. *-commutative 85.0%

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

   8. Simplified 85.0%

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

   9. Taylor expanded in x around inf 77.0%

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

       1. associate-*r* 77.0%

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

       2. *-commutative 77.0%

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

   11. Simplified 77.0%

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

   12. Taylor expanded in y around inf 52.0%

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

   if -2.94999999999999983e32 < x < 3.4999999999999997e-278

   1. Initial program 90.1%

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

   3. Simplified 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 57.0%

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

   if 3.4999999999999997e-278 < x < 8.50000000000000025e96

   1. Initial program 97.5%

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

   3. Taylor expanded in x around 0 71.0%

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

   4. Taylor expanded in j around 0 56.2%

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

   if 8.50000000000000025e96 < x

   1. Initial program 76.4%

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

   3. Taylor expanded in t around 0 58.7%

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

   4. Taylor expanded in j around 0 56.8%

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

4. Final simplification 55.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.95 \cdot 10^{+32}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-278}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{+96}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 28: 46.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{+32}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-278}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{+114}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= x -2.9e+32)
   (* 18.0 (* t (* x (* y z))))
   (if (<= x 3e-278)
     (+ (* b c) (* j (* k -27.0)))
     (if (<= x 3.6e+114) (- (* b c) (* 4.0 (* t a))) (* 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 <= -2.9e+32) {
		tmp = 18.0 * (t * (x * (y * z)));
	} else if (x <= 3e-278) {
		tmp = (b * c) + (j * (k * -27.0));
	} else if (x <= 3.6e+114) {
		tmp = (b * c) - (4.0 * (t * a));
	} 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 <= (-2.9d+32)) then
        tmp = 18.0d0 * (t * (x * (y * z)))
    else if (x <= 3d-278) then
        tmp = (b * c) + (j * (k * (-27.0d0)))
    else if (x <= 3.6d+114) then
        tmp = (b * c) - (4.0d0 * (t * a))
    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 <= -2.9e+32) {
		tmp = 18.0 * (t * (x * (y * z)));
	} else if (x <= 3e-278) {
		tmp = (b * c) + (j * (k * -27.0));
	} else if (x <= 3.6e+114) {
		tmp = (b * c) - (4.0 * (t * a));
	} 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 <= -2.9e+32:
		tmp = 18.0 * (t * (x * (y * z)))
	elif x <= 3e-278:
		tmp = (b * c) + (j * (k * -27.0))
	elif x <= 3.6e+114:
		tmp = (b * c) - (4.0 * (t * a))
	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 <= -2.9e+32)
		tmp = Float64(18.0 * Float64(t * Float64(x * Float64(y * z))));
	elseif (x <= 3e-278)
		tmp = Float64(Float64(b * c) + Float64(j * Float64(k * -27.0)));
	elseif (x <= 3.6e+114)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(t * a)));
	else
		tmp = Float64(x * Float64(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 <= -2.9e+32)
		tmp = 18.0 * (t * (x * (y * z)));
	elseif (x <= 3e-278)
		tmp = (b * c) + (j * (k * -27.0));
	elseif (x <= 3.6e+114)
		tmp = (b * c) - (4.0 * (t * a));
	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, -2.9e+32], N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3e-278], N[(N[(b * c), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.6e+114], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.90000000000000003e32

   1. Initial program 85.0%

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

   3. Simplified 91.4%

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

      1. associate-*r* 87.2%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot z} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. distribute-rgt-out-- 85.0%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. associate-+l- 85.0%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(\left(a \cdot 4\right) \cdot t - b \cdot c\right)\right)} - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      4. associate-*l* 85.0%

         \[\leadsto \left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot \left(z \cdot t\right)} - \left(\left(a \cdot 4\right) \cdot t - b \cdot c\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      5. fma-neg 85.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\left(x \cdot 18\right) \cdot y, z \cdot t, -\left(\left(a \cdot 4\right) \cdot t - b \cdot c\right)\right)} - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      6. associate-*l* 85.0%

         \[\leadsto \mathsf{fma}\left(\color{blue}{x \cdot \left(18 \cdot y\right)}, z \cdot t, -\left(\left(a \cdot 4\right) \cdot t - b \cdot c\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      7. *-commutative 85.0%

         \[\leadsto \mathsf{fma}\left(x \cdot \left(18 \cdot y\right), z \cdot t, -\left(\color{blue}{t \cdot \left(a \cdot 4\right)} - b \cdot c\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   6. Applied egg-rr 85.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x \cdot \left(18 \cdot y\right), z \cdot t, -\left(t \cdot \left(a \cdot 4\right) - b \cdot c\right)\right)} - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
   7. Step-by-step derivation

      1. fma-undefine 85.0%

         \[\leadsto \color{blue}{\left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot \left(z \cdot t\right) + \left(-\left(t \cdot \left(a \cdot 4\right) - b \cdot c\right)\right)\right)} - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. unsub-neg 85.0%

         \[\leadsto \color{blue}{\left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot \left(z \cdot t\right) - \left(t \cdot \left(a \cdot 4\right) - b \cdot c\right)\right)} - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. *-commutative 85.0%

         \[\leadsto \left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot \color{blue}{\left(t \cdot z\right)} - \left(t \cdot \left(a \cdot 4\right) - b \cdot c\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   8. Simplified 85.0%

      \[\leadsto \color{blue}{\left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot \left(t \cdot z\right) - \left(t \cdot \left(a \cdot 4\right) - b \cdot c\right)\right)} - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   9. Taylor expanded in x around inf 77.0%

      \[\leadsto \left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot \left(t \cdot z\right) - \left(t \cdot \left(a \cdot 4\right) - b \cdot c\right)\right) - \color{blue}{4 \cdot \left(i \cdot x\right)} \]
   10. Step-by-step derivation

       1. associate-*r* 77.0%

          \[\leadsto \left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot \left(t \cdot z\right) - \left(t \cdot \left(a \cdot 4\right) - b \cdot c\right)\right) - \color{blue}{\left(4 \cdot i\right) \cdot x} \]

       2. *-commutative 77.0%

          \[\leadsto \left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot \left(t \cdot z\right) - \left(t \cdot \left(a \cdot 4\right) - b \cdot c\right)\right) - \color{blue}{x \cdot \left(4 \cdot i\right)} \]

   11. Simplified 77.0%

       \[\leadsto \left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot \left(t \cdot z\right) - \left(t \cdot \left(a \cdot 4\right) - b \cdot c\right)\right) - \color{blue}{x \cdot \left(4 \cdot i\right)} \]

   12. Taylor expanded in y around inf 52.0%

       \[\leadsto \color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]

   if -2.90000000000000003e32 < x < 3e-278

   1. Initial program 90.1%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 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 57.0%

      \[\leadsto \color{blue}{b \cdot c} + j \cdot \left(k \cdot -27\right) \]

   if 3e-278 < x < 3.6000000000000001e114

   1. Initial program 97.6%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 69.7%

      \[\leadsto \color{blue}{\left(b \cdot c - 4 \cdot \left(a \cdot t\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   4. Taylor expanded in j around 0 55.5%

      \[\leadsto \color{blue}{b \cdot c - 4 \cdot \left(a \cdot t\right)} \]

   if 3.6000000000000001e114 < x

   1. Initial program 75.1%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 78.5%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-*r* 76.9%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot z} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. distribute-rgt-out-- 75.1%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. associate-+l- 75.1%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(\left(a \cdot 4\right) \cdot t - b \cdot c\right)\right)} - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      4. associate-*l* 71.5%

         \[\leadsto \left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot \left(z \cdot t\right)} - \left(\left(a \cdot 4\right) \cdot t - b \cdot c\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      5. fma-neg 71.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\left(x \cdot 18\right) \cdot y, z \cdot t, -\left(\left(a \cdot 4\right) \cdot t - b \cdot c\right)\right)} - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      6. associate-*l* 71.6%

         \[\leadsto \mathsf{fma}\left(\color{blue}{x \cdot \left(18 \cdot y\right)}, z \cdot t, -\left(\left(a \cdot 4\right) \cdot t - b \cdot c\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      7. *-commutative 71.6%

         \[\leadsto \mathsf{fma}\left(x \cdot \left(18 \cdot y\right), z \cdot t, -\left(\color{blue}{t \cdot \left(a \cdot 4\right)} - b \cdot c\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   6. Applied egg-rr 71.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x \cdot \left(18 \cdot y\right), z \cdot t, -\left(t \cdot \left(a \cdot 4\right) - b \cdot c\right)\right)} - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
   7. Step-by-step derivation

      1. fma-undefine 71.6%

         \[\leadsto \color{blue}{\left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot \left(z \cdot t\right) + \left(-\left(t \cdot \left(a \cdot 4\right) - b \cdot c\right)\right)\right)} - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. unsub-neg 71.6%

         \[\leadsto \color{blue}{\left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot \left(z \cdot t\right) - \left(t \cdot \left(a \cdot 4\right) - b \cdot c\right)\right)} - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. *-commutative 71.6%

         \[\leadsto \left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot \color{blue}{\left(t \cdot z\right)} - \left(t \cdot \left(a \cdot 4\right) - b \cdot c\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   8. Simplified 71.6%

      \[\leadsto \color{blue}{\left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot \left(t \cdot z\right) - \left(t \cdot \left(a \cdot 4\right) - b \cdot c\right)\right)} - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   9. Taylor expanded in i around inf 46.2%

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right)} \]
   10. Step-by-step derivation

       1. associate-*r* 46.2%

          \[\leadsto \color{blue}{\left(-4 \cdot i\right) \cdot x} \]

       2. metadata-eval 46.2%

          \[\leadsto \left(\color{blue}{\left(-4\right)} \cdot i\right) \cdot x \]

       3. distribute-lft-neg-in 46.2%

          \[\leadsto \color{blue}{\left(-4 \cdot i\right)} \cdot x \]

       4. distribute-lft-neg-in 46.2%

          \[\leadsto \color{blue}{-\left(4 \cdot i\right) \cdot x} \]

       5. *-commutative 46.2%

          \[\leadsto -\color{blue}{x \cdot \left(4 \cdot i\right)} \]

       6. distribute-rgt-neg-in 46.2%

          \[\leadsto \color{blue}{x \cdot \left(-4 \cdot i\right)} \]

       7. distribute-lft-neg-in 46.2%

          \[\leadsto x \cdot \color{blue}{\left(\left(-4\right) \cdot i\right)} \]

       8. metadata-eval 46.2%

          \[\leadsto x \cdot \left(\color{blue}{-4} \cdot i\right) \]

       9. *-commutative 46.2%

          \[\leadsto x \cdot \color{blue}{\left(i \cdot -4\right)} \]

   11. Simplified 46.2%

       \[\leadsto \color{blue}{x \cdot \left(i \cdot -4\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 53.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{+32}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-278}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{+114}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 29: 57.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{-103} \lor \neg \left(t \leq 5.6 \cdot 10^{+49}\right):\\ \;\;\;\;t \cdot \left(18 \cdot \left(z \cdot \left(x \cdot y\right)\right) + a \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= t -1.65e-103) (not (<= t 5.6e+49)))
   (* t (+ (* 18.0 (* z (* x y))) (* a -4.0)))
   (- (* b c) (* 4.0 (* x i)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((t <= -1.65e-103) || !(t <= 5.6e+49)) {
		tmp = t * ((18.0 * (z * (x * y))) + (a * -4.0));
	} else {
		tmp = (b * c) - (4.0 * (x * i));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((t <= (-1.65d-103)) .or. (.not. (t <= 5.6d+49))) then
        tmp = t * ((18.0d0 * (z * (x * y))) + (a * (-4.0d0)))
    else
        tmp = (b * c) - (4.0d0 * (x * i))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((t <= -1.65e-103) || !(t <= 5.6e+49)) {
		tmp = t * ((18.0 * (z * (x * y))) + (a * -4.0));
	} else {
		tmp = (b * c) - (4.0 * (x * i));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (t <= -1.65e-103) or not (t <= 5.6e+49):
		tmp = t * ((18.0 * (z * (x * y))) + (a * -4.0))
	else:
		tmp = (b * c) - (4.0 * (x * i))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((t <= -1.65e-103) || !(t <= 5.6e+49))
		tmp = Float64(t * Float64(Float64(18.0 * Float64(z * Float64(x * y))) + Float64(a * -4.0)));
	else
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((t <= -1.65e-103) || ~((t <= 5.6e+49)))
		tmp = t * ((18.0 * (z * (x * y))) + (a * -4.0));
	else
		tmp = (b * c) - (4.0 * (x * i));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[t, -1.65e-103], N[Not[LessEqual[t, 5.6e+49]], $MachinePrecision]], N[(t * N[(N[(18.0 * N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.64999999999999995e-103 or 5.5999999999999996e49 < t

   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 85.6%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 63.5%

      \[\leadsto \color{blue}{t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)} \]
   6. Step-by-step derivation

      1. cancel-sign-sub-inv 63.5%

         \[\leadsto t \cdot \color{blue}{\left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + \left(-4\right) \cdot a\right)} \]

      2. associate-*r* 65.6%

         \[\leadsto t \cdot \left(18 \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot z\right)} + \left(-4\right) \cdot a\right) \]

      3. metadata-eval 65.6%

         \[\leadsto t \cdot \left(18 \cdot \left(\left(x \cdot y\right) \cdot z\right) + \color{blue}{-4} \cdot a\right) \]

   7. Applied egg-rr 65.6%

      \[\leadsto t \cdot \color{blue}{\left(18 \cdot \left(\left(x \cdot y\right) \cdot z\right) + -4 \cdot a\right)} \]

   if -1.64999999999999995e-103 < t < 5.5999999999999996e49

   1. Initial program 91.2%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 79.7%

      \[\leadsto \color{blue}{\left(b \cdot c - 4 \cdot \left(i \cdot x\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   4. Taylor expanded in j around 0 56.4%

      \[\leadsto \color{blue}{b \cdot c - 4 \cdot \left(i \cdot x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{-103} \lor \neg \left(t \leq 5.6 \cdot 10^{+49}\right):\\ \;\;\;\;t \cdot \left(18 \cdot \left(z \cdot \left(x \cdot y\right)\right) + a \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 30: 57.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{-103}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(z \cdot \left(x \cdot y\right)\right) + a \cdot -4\right)\\ \mathbf{elif}\;t \leq 3.05 \cdot 10^{+50}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= t -1.6e-103)
   (* t (+ (* 18.0 (* z (* x y))) (* a -4.0)))
   (if (<= t 3.05e+50)
     (- (* b c) (* 4.0 (* x i)))
     (* t (- (* 18.0 (* x (* y z))) (* a 4.0))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (t <= -1.6e-103) {
		tmp = t * ((18.0 * (z * (x * y))) + (a * -4.0));
	} else if (t <= 3.05e+50) {
		tmp = (b * c) - (4.0 * (x * i));
	} else {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (t <= (-1.6d-103)) then
        tmp = t * ((18.0d0 * (z * (x * y))) + (a * (-4.0d0)))
    else if (t <= 3.05d+50) then
        tmp = (b * c) - (4.0d0 * (x * i))
    else
        tmp = t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (t <= -1.6e-103) {
		tmp = t * ((18.0 * (z * (x * y))) + (a * -4.0));
	} else if (t <= 3.05e+50) {
		tmp = (b * c) - (4.0 * (x * i));
	} else {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if t <= -1.6e-103:
		tmp = t * ((18.0 * (z * (x * y))) + (a * -4.0))
	elif t <= 3.05e+50:
		tmp = (b * c) - (4.0 * (x * i))
	else:
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (t <= -1.6e-103)
		tmp = Float64(t * Float64(Float64(18.0 * Float64(z * Float64(x * y))) + Float64(a * -4.0)));
	elseif (t <= 3.05e+50)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)));
	else
		tmp = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (t <= -1.6e-103)
		tmp = t * ((18.0 * (z * (x * y))) + (a * -4.0));
	elseif (t <= 3.05e+50)
		tmp = (b * c) - (4.0 * (x * i));
	else
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[t, -1.6e-103], N[(t * N[(N[(18.0 * N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.05e+50], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.59999999999999988e-103

   1. Initial program 87.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 85.6%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 57.1%

      \[\leadsto \color{blue}{t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)} \]
   6. Step-by-step derivation

      1. cancel-sign-sub-inv 57.1%

         \[\leadsto t \cdot \color{blue}{\left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + \left(-4\right) \cdot a\right)} \]

      2. associate-*r* 61.6%

         \[\leadsto t \cdot \left(18 \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot z\right)} + \left(-4\right) \cdot a\right) \]

      3. metadata-eval 61.6%

         \[\leadsto t \cdot \left(18 \cdot \left(\left(x \cdot y\right) \cdot z\right) + \color{blue}{-4} \cdot a\right) \]

   7. Applied egg-rr 61.6%

      \[\leadsto t \cdot \color{blue}{\left(18 \cdot \left(\left(x \cdot y\right) \cdot z\right) + -4 \cdot a\right)} \]

   if -1.59999999999999988e-103 < t < 3.05000000000000013e50

   1. Initial program 91.2%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 79.7%

      \[\leadsto \color{blue}{\left(b \cdot c - 4 \cdot \left(i \cdot x\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   4. Taylor expanded in j around 0 56.4%

      \[\leadsto \color{blue}{b \cdot c - 4 \cdot \left(i \cdot x\right)} \]

   if 3.05000000000000013e50 < t

   1. Initial program 81.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 85.6%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 74.3%

      \[\leadsto \color{blue}{t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 61.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{-103}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(z \cdot \left(x \cdot y\right)\right) + a \cdot -4\right)\\ \mathbf{elif}\;t \leq 3.05 \cdot 10^{+50}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 31: 57.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{-103}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(z \cdot \left(x \cdot y\right)\right) + a \cdot -4\right)\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+50}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot -4 + \left(y \cdot z\right) \cdot \left(x \cdot 18\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= t -1.1e-103)
   (* t (+ (* 18.0 (* z (* x y))) (* a -4.0)))
   (if (<= t 4e+50)
     (- (* b c) (* 4.0 (* x i)))
     (* t (+ (* a -4.0) (* (* y z) (* x 18.0)))))))

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 (t <= -1.1e-103) {
		tmp = t * ((18.0 * (z * (x * y))) + (a * -4.0));
	} else if (t <= 4e+50) {
		tmp = (b * c) - (4.0 * (x * i));
	} else {
		tmp = t * ((a * -4.0) + ((y * z) * (x * 18.0)));
	}
	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 (t <= (-1.1d-103)) then
        tmp = t * ((18.0d0 * (z * (x * y))) + (a * (-4.0d0)))
    else if (t <= 4d+50) then
        tmp = (b * c) - (4.0d0 * (x * i))
    else
        tmp = t * ((a * (-4.0d0)) + ((y * z) * (x * 18.0d0)))
    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 (t <= -1.1e-103) {
		tmp = t * ((18.0 * (z * (x * y))) + (a * -4.0));
	} else if (t <= 4e+50) {
		tmp = (b * c) - (4.0 * (x * i));
	} else {
		tmp = t * ((a * -4.0) + ((y * z) * (x * 18.0)));
	}
	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 t <= -1.1e-103:
		tmp = t * ((18.0 * (z * (x * y))) + (a * -4.0))
	elif t <= 4e+50:
		tmp = (b * c) - (4.0 * (x * i))
	else:
		tmp = t * ((a * -4.0) + ((y * z) * (x * 18.0)))
	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 (t <= -1.1e-103)
		tmp = Float64(t * Float64(Float64(18.0 * Float64(z * Float64(x * y))) + Float64(a * -4.0)));
	elseif (t <= 4e+50)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)));
	else
		tmp = Float64(t * Float64(Float64(a * -4.0) + Float64(Float64(y * z) * Float64(x * 18.0))));
	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 (t <= -1.1e-103)
		tmp = t * ((18.0 * (z * (x * y))) + (a * -4.0));
	elseif (t <= 4e+50)
		tmp = (b * c) - (4.0 * (x * i));
	else
		tmp = t * ((a * -4.0) + ((y * z) * (x * 18.0)));
	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[t, -1.1e-103], N[(t * N[(N[(18.0 * N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4e+50], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(a * -4.0), $MachinePrecision] + N[(N[(y * z), $MachinePrecision] * N[(x * 18.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.1e-103

   1. Initial program 87.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 85.6%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 57.1%

      \[\leadsto \color{blue}{t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)} \]
   6. Step-by-step derivation

      1. cancel-sign-sub-inv 57.1%

         \[\leadsto t \cdot \color{blue}{\left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + \left(-4\right) \cdot a\right)} \]

      2. associate-*r* 61.6%

         \[\leadsto t \cdot \left(18 \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot z\right)} + \left(-4\right) \cdot a\right) \]

      3. metadata-eval 61.6%

         \[\leadsto t \cdot \left(18 \cdot \left(\left(x \cdot y\right) \cdot z\right) + \color{blue}{-4} \cdot a\right) \]

   7. Applied egg-rr 61.6%

      \[\leadsto t \cdot \color{blue}{\left(18 \cdot \left(\left(x \cdot y\right) \cdot z\right) + -4 \cdot a\right)} \]

   if -1.1e-103 < t < 4.0000000000000003e50

   1. Initial program 91.2%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 79.7%

      \[\leadsto \color{blue}{\left(b \cdot c - 4 \cdot \left(i \cdot x\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   4. Taylor expanded in j around 0 56.4%

      \[\leadsto \color{blue}{b \cdot c - 4 \cdot \left(i \cdot x\right)} \]

   if 4.0000000000000003e50 < t

   1. Initial program 81.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 85.6%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-*r* 83.8%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot z} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. distribute-rgt-out-- 81.7%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. associate-+l- 81.7%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(\left(a \cdot 4\right) \cdot t - b \cdot c\right)\right)} - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      4. associate-*l* 73.5%

         \[\leadsto \left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot \left(z \cdot t\right)} - \left(\left(a \cdot 4\right) \cdot t - b \cdot c\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      5. fma-neg 75.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\left(x \cdot 18\right) \cdot y, z \cdot t, -\left(\left(a \cdot 4\right) \cdot t - b \cdot c\right)\right)} - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      6. associate-*l* 75.6%

         \[\leadsto \mathsf{fma}\left(\color{blue}{x \cdot \left(18 \cdot y\right)}, z \cdot t, -\left(\left(a \cdot 4\right) \cdot t - b \cdot c\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      7. *-commutative 75.6%

         \[\leadsto \mathsf{fma}\left(x \cdot \left(18 \cdot y\right), z \cdot t, -\left(\color{blue}{t \cdot \left(a \cdot 4\right)} - b \cdot c\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   6. Applied egg-rr 75.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x \cdot \left(18 \cdot y\right), z \cdot t, -\left(t \cdot \left(a \cdot 4\right) - b \cdot c\right)\right)} - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
   7. Step-by-step derivation

      1. fma-undefine 73.5%

         \[\leadsto \color{blue}{\left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot \left(z \cdot t\right) + \left(-\left(t \cdot \left(a \cdot 4\right) - b \cdot c\right)\right)\right)} - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. unsub-neg 73.5%

         \[\leadsto \color{blue}{\left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot \left(z \cdot t\right) - \left(t \cdot \left(a \cdot 4\right) - b \cdot c\right)\right)} - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. *-commutative 73.5%

         \[\leadsto \left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot \color{blue}{\left(t \cdot z\right)} - \left(t \cdot \left(a \cdot 4\right) - b \cdot c\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   8. Simplified 73.5%

      \[\leadsto \color{blue}{\left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot \left(t \cdot z\right) - \left(t \cdot \left(a \cdot 4\right) - b \cdot c\right)\right)} - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   9. Taylor expanded in x around inf 72.1%

      \[\leadsto \left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot \left(t \cdot z\right) - \left(t \cdot \left(a \cdot 4\right) - b \cdot c\right)\right) - \color{blue}{4 \cdot \left(i \cdot x\right)} \]
   10. Step-by-step derivation

       1. associate-*r* 72.1%

          \[\leadsto \left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot \left(t \cdot z\right) - \left(t \cdot \left(a \cdot 4\right) - b \cdot c\right)\right) - \color{blue}{\left(4 \cdot i\right) \cdot x} \]

       2. *-commutative 72.1%

          \[\leadsto \left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot \left(t \cdot z\right) - \left(t \cdot \left(a \cdot 4\right) - b \cdot c\right)\right) - \color{blue}{x \cdot \left(4 \cdot i\right)} \]

   11. Simplified 72.1%

       \[\leadsto \left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot \left(t \cdot z\right) - \left(t \cdot \left(a \cdot 4\right) - b \cdot c\right)\right) - \color{blue}{x \cdot \left(4 \cdot i\right)} \]

   12. Taylor expanded in t around inf 74.3%

       \[\leadsto \color{blue}{t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)} \]
   13. Step-by-step derivation

       1. cancel-sign-sub-inv 74.3%

          \[\leadsto t \cdot \color{blue}{\left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + \left(-4\right) \cdot a\right)} \]

       2. associate-*r* 74.2%

          \[\leadsto t \cdot \left(\color{blue}{\left(18 \cdot x\right) \cdot \left(y \cdot z\right)} + \left(-4\right) \cdot a\right) \]

       3. metadata-eval 74.2%

          \[\leadsto t \cdot \left(\left(18 \cdot x\right) \cdot \left(y \cdot z\right) + \color{blue}{-4} \cdot a\right) \]

       4. *-commutative 74.2%

          \[\leadsto t \cdot \left(\left(18 \cdot x\right) \cdot \left(y \cdot z\right) + \color{blue}{a \cdot -4}\right) \]

   14. Simplified 74.2%

       \[\leadsto \color{blue}{t \cdot \left(\left(18 \cdot x\right) \cdot \left(y \cdot z\right) + a \cdot -4\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 61.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{-103}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(z \cdot \left(x \cdot y\right)\right) + a \cdot -4\right)\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+50}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot -4 + \left(y \cdot z\right) \cdot \left(x \cdot 18\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 32: 38.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.06 \cdot 10^{+160} \lor \neg \left(b \cdot c \leq 2.1 \cdot 10^{+160}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= (* b c) -1.06e+160) (not (<= (* b c) 2.1e+160)))
   (* b c)
   (* -27.0 (* j k))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (((b * c) <= -1.06e+160) || !((b * c) <= 2.1e+160)) {
		tmp = b * c;
	} else {
		tmp = -27.0 * (j * k);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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) <= (-1.06d+160)) .or. (.not. ((b * c) <= 2.1d+160))) then
        tmp = b * c
    else
        tmp = (-27.0d0) * (j * k)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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) <= -1.06e+160) || !((b * c) <= 2.1e+160)) {
		tmp = b * c;
	} else {
		tmp = -27.0 * (j * k);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if ((b * c) <= -1.06e+160) or not ((b * c) <= 2.1e+160):
		tmp = b * c
	else:
		tmp = -27.0 * (j * k)
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((Float64(b * c) <= -1.06e+160) || !(Float64(b * c) <= 2.1e+160))
		tmp = Float64(b * c);
	else
		tmp = Float64(-27.0 * Float64(j * k));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (((b * c) <= -1.06e+160) || ~(((b * c) <= 2.1e+160)))
		tmp = b * c;
	else
		tmp = -27.0 * (j * k);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[N[(b * c), $MachinePrecision], -1.06e+160], N[Not[LessEqual[N[(b * c), $MachinePrecision], 2.1e+160]], $MachinePrecision]], N[(b * c), $MachinePrecision], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -1.0599999999999999e160 or 2.09999999999999997e160 < (*.f64 b c)

   1. Initial program 81.6%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate--l+ 81.6%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)} - \left(j \cdot 27\right) \cdot k \]

      2. distribute-rgt-out-- 83.3%

         \[\leadsto \left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k \]

      3. associate-*r* 81.7%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)} - a \cdot 4\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k \]

      4. associate-*l* 81.7%

         \[\leadsto \left(t \cdot \left(\color{blue}{x \cdot \left(18 \cdot \left(y \cdot z\right)\right)} - a \cdot 4\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k \]

      5. associate-*r* 81.7%

         \[\leadsto \left(t \cdot \left(x \cdot \color{blue}{\left(\left(18 \cdot y\right) \cdot z\right)} - a \cdot 4\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k \]

      6. *-commutative 81.7%

         \[\leadsto \left(t \cdot \left(x \cdot \left(\left(18 \cdot y\right) \cdot z\right) - a \cdot 4\right) + \left(b \cdot c - \color{blue}{i \cdot \left(x \cdot 4\right)}\right)\right) - \left(j \cdot 27\right) \cdot k \]

   4. Applied egg-rr 81.7%

      \[\leadsto \color{blue}{\left(t \cdot \left(x \cdot \left(\left(18 \cdot y\right) \cdot z\right) - a \cdot 4\right) + \left(b \cdot c - i \cdot \left(x \cdot 4\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   5. Taylor expanded in b around inf 65.6%

      \[\leadsto \color{blue}{b \cdot c} \]

   if -1.0599999999999999e160 < (*.f64 b c) < 2.09999999999999997e160

   1. Initial program 90.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 88.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in j around inf 24.9%

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 34.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.06 \cdot 10^{+160} \lor \neg \left(b \cdot c \leq 2.1 \cdot 10^{+160}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 33: 47.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{+31}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{+139}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= x -2.2e+31)
   (* 18.0 (* t (* x (* y z))))
   (if (<= x 2.7e+139) (+ (* 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 <= -2.2e+31) {
		tmp = 18.0 * (t * (x * (y * z)));
	} else if (x <= 2.7e+139) {
		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 <= (-2.2d+31)) then
        tmp = 18.0d0 * (t * (x * (y * z)))
    else if (x <= 2.7d+139) 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 <= -2.2e+31) {
		tmp = 18.0 * (t * (x * (y * z)));
	} else if (x <= 2.7e+139) {
		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 <= -2.2e+31:
		tmp = 18.0 * (t * (x * (y * z)))
	elif x <= 2.7e+139:
		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 <= -2.2e+31)
		tmp = Float64(18.0 * Float64(t * Float64(x * Float64(y * z))));
	elseif (x <= 2.7e+139)
		tmp = Float64(Float64(b * c) + Float64(j * Float64(k * -27.0)));
	else
		tmp = Float64(x * Float64(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 <= -2.2e+31)
		tmp = 18.0 * (t * (x * (y * z)));
	elseif (x <= 2.7e+139)
		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, -2.2e+31], N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.7e+139], N[(N[(b * c), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.2000000000000001e31

   1. Initial program 85.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 91.4%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-*r* 87.2%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot z} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. distribute-rgt-out-- 85.0%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. associate-+l- 85.0%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(\left(a \cdot 4\right) \cdot t - b \cdot c\right)\right)} - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      4. associate-*l* 85.0%

         \[\leadsto \left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot \left(z \cdot t\right)} - \left(\left(a \cdot 4\right) \cdot t - b \cdot c\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      5. fma-neg 85.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\left(x \cdot 18\right) \cdot y, z \cdot t, -\left(\left(a \cdot 4\right) \cdot t - b \cdot c\right)\right)} - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      6. associate-*l* 85.0%

         \[\leadsto \mathsf{fma}\left(\color{blue}{x \cdot \left(18 \cdot y\right)}, z \cdot t, -\left(\left(a \cdot 4\right) \cdot t - b \cdot c\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      7. *-commutative 85.0%

         \[\leadsto \mathsf{fma}\left(x \cdot \left(18 \cdot y\right), z \cdot t, -\left(\color{blue}{t \cdot \left(a \cdot 4\right)} - b \cdot c\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   6. Applied egg-rr 85.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x \cdot \left(18 \cdot y\right), z \cdot t, -\left(t \cdot \left(a \cdot 4\right) - b \cdot c\right)\right)} - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
   7. Step-by-step derivation

      1. fma-undefine 85.0%

         \[\leadsto \color{blue}{\left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot \left(z \cdot t\right) + \left(-\left(t \cdot \left(a \cdot 4\right) - b \cdot c\right)\right)\right)} - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. unsub-neg 85.0%

         \[\leadsto \color{blue}{\left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot \left(z \cdot t\right) - \left(t \cdot \left(a \cdot 4\right) - b \cdot c\right)\right)} - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. *-commutative 85.0%

         \[\leadsto \left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot \color{blue}{\left(t \cdot z\right)} - \left(t \cdot \left(a \cdot 4\right) - b \cdot c\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   8. Simplified 85.0%

      \[\leadsto \color{blue}{\left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot \left(t \cdot z\right) - \left(t \cdot \left(a \cdot 4\right) - b \cdot c\right)\right)} - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   9. Taylor expanded in x around inf 77.0%

      \[\leadsto \left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot \left(t \cdot z\right) - \left(t \cdot \left(a \cdot 4\right) - b \cdot c\right)\right) - \color{blue}{4 \cdot \left(i \cdot x\right)} \]
   10. Step-by-step derivation

       1. associate-*r* 77.0%

          \[\leadsto \left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot \left(t \cdot z\right) - \left(t \cdot \left(a \cdot 4\right) - b \cdot c\right)\right) - \color{blue}{\left(4 \cdot i\right) \cdot x} \]

       2. *-commutative 77.0%

          \[\leadsto \left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot \left(t \cdot z\right) - \left(t \cdot \left(a \cdot 4\right) - b \cdot c\right)\right) - \color{blue}{x \cdot \left(4 \cdot i\right)} \]

   11. Simplified 77.0%

       \[\leadsto \left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot \left(t \cdot z\right) - \left(t \cdot \left(a \cdot 4\right) - b \cdot c\right)\right) - \color{blue}{x \cdot \left(4 \cdot i\right)} \]

   12. Taylor expanded in y around inf 52.0%

       \[\leadsto \color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]

   if -2.2000000000000001e31 < x < 2.6999999999999998e139

   1. Initial program 93.6%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 89.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 50.1%

      \[\leadsto \color{blue}{b \cdot c} + j \cdot \left(k \cdot -27\right) \]

   if 2.6999999999999998e139 < x

   1. Initial program 75.1%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 76.9%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-*r* 75.1%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot z} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. distribute-rgt-out-- 75.1%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. associate-+l- 75.1%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(\left(a \cdot 4\right) \cdot t - b \cdot c\right)\right)} - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      4. associate-*l* 71.3%

         \[\leadsto \left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot \left(z \cdot t\right)} - \left(\left(a \cdot 4\right) \cdot t - b \cdot c\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      5. fma-neg 71.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\left(x \cdot 18\right) \cdot y, z \cdot t, -\left(\left(a \cdot 4\right) \cdot t - b \cdot c\right)\right)} - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      6. associate-*l* 71.3%

         \[\leadsto \mathsf{fma}\left(\color{blue}{x \cdot \left(18 \cdot y\right)}, z \cdot t, -\left(\left(a \cdot 4\right) \cdot t - b \cdot c\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      7. *-commutative 71.3%

         \[\leadsto \mathsf{fma}\left(x \cdot \left(18 \cdot y\right), z \cdot t, -\left(\color{blue}{t \cdot \left(a \cdot 4\right)} - b \cdot c\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   6. Applied egg-rr 71.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x \cdot \left(18 \cdot y\right), z \cdot t, -\left(t \cdot \left(a \cdot 4\right) - b \cdot c\right)\right)} - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
   7. Step-by-step derivation

      1. fma-undefine 71.3%

         \[\leadsto \color{blue}{\left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot \left(z \cdot t\right) + \left(-\left(t \cdot \left(a \cdot 4\right) - b \cdot c\right)\right)\right)} - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. unsub-neg 71.3%

         \[\leadsto \color{blue}{\left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot \left(z \cdot t\right) - \left(t \cdot \left(a \cdot 4\right) - b \cdot c\right)\right)} - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. *-commutative 71.3%

         \[\leadsto \left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot \color{blue}{\left(t \cdot z\right)} - \left(t \cdot \left(a \cdot 4\right) - b \cdot c\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   8. Simplified 71.3%

      \[\leadsto \color{blue}{\left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot \left(t \cdot z\right) - \left(t \cdot \left(a \cdot 4\right) - b \cdot c\right)\right)} - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   9. Taylor expanded in i around inf 47.8%

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right)} \]
   10. Step-by-step derivation

       1. associate-*r* 47.8%

          \[\leadsto \color{blue}{\left(-4 \cdot i\right) \cdot x} \]

       2. metadata-eval 47.8%

          \[\leadsto \left(\color{blue}{\left(-4\right)} \cdot i\right) \cdot x \]

       3. distribute-lft-neg-in 47.8%

          \[\leadsto \color{blue}{\left(-4 \cdot i\right)} \cdot x \]

       4. distribute-lft-neg-in 47.8%

          \[\leadsto \color{blue}{-\left(4 \cdot i\right) \cdot x} \]

       5. *-commutative 47.8%

          \[\leadsto -\color{blue}{x \cdot \left(4 \cdot i\right)} \]

       6. distribute-rgt-neg-in 47.8%

          \[\leadsto \color{blue}{x \cdot \left(-4 \cdot i\right)} \]

       7. distribute-lft-neg-in 47.8%

          \[\leadsto x \cdot \color{blue}{\left(\left(-4\right) \cdot i\right)} \]

       8. metadata-eval 47.8%

          \[\leadsto x \cdot \left(\color{blue}{-4} \cdot i\right) \]

       9. *-commutative 47.8%

          \[\leadsto x \cdot \color{blue}{\left(i \cdot -4\right)} \]

   11. Simplified 47.8%

       \[\leadsto \color{blue}{x \cdot \left(i \cdot -4\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 34: 24.2% accurate, 10.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ b \cdot c \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k) :precision binary64 (* b c))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	return b * c;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    code = b * c
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	return b * c;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	return b * c

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	return Float64(b * c)
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp = code(x, y, z, t, a, b, c, i, j, k)
	tmp = b * c;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := N[(b * c), $MachinePrecision]

Derivation

1. Initial program 88.3%

   \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
2. Add Preprocessing
3. Step-by-step derivation

   1. associate--l+ 88.3%

      \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   2. distribute-rgt-out-- 89.5%

      \[\leadsto \left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k \]

   3. associate-*r* 87.2%

      \[\leadsto \left(t \cdot \left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)} - a \cdot 4\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k \]

   4. associate-*l* 87.2%

      \[\leadsto \left(t \cdot \left(\color{blue}{x \cdot \left(18 \cdot \left(y \cdot z\right)\right)} - a \cdot 4\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k \]

   5. associate-*r* 86.8%

      \[\leadsto \left(t \cdot \left(x \cdot \color{blue}{\left(\left(18 \cdot y\right) \cdot z\right)} - a \cdot 4\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k \]

   6. *-commutative 86.8%

      \[\leadsto \left(t \cdot \left(x \cdot \left(\left(18 \cdot y\right) \cdot z\right) - a \cdot 4\right) + \left(b \cdot c - \color{blue}{i \cdot \left(x \cdot 4\right)}\right)\right) - \left(j \cdot 27\right) \cdot k \]

4. Applied egg-rr 86.8%

   \[\leadsto \color{blue}{\left(t \cdot \left(x \cdot \left(\left(18 \cdot y\right) \cdot z\right) - a \cdot 4\right) + \left(b \cdot c - i \cdot \left(x \cdot 4\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]

5. Taylor expanded in b around inf 21.3%

   \[\leadsto \color{blue}{b \cdot c} \]
6. Add Preprocessing

Developer Target 1: 89.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a \cdot t + i \cdot x\right) \cdot 4\\ t_2 := \left(\left(18 \cdot t\right) \cdot \left(\left(x \cdot y\right) \cdot z\right) - t\_1\right) - \left(\left(k \cdot j\right) \cdot 27 - c \cdot b\right)\\ \mathbf{if}\;t < -1.6210815397541398 \cdot 10^{-69}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t < 165.68027943805222:\\ \;\;\;\;\left(\left(18 \cdot y\right) \cdot \left(x \cdot \left(z \cdot t\right)\right) - t\_1\right) + \left(c \cdot b - 27 \cdot \left(k \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (+ (* a t) (* i x)) 4.0))
        (t_2
         (-
          (- (* (* 18.0 t) (* (* x y) z)) t_1)
          (- (* (* k j) 27.0) (* c b)))))
   (if (< t -1.6210815397541398e-69)
     t_2
     (if (< t 165.68027943805222)
       (+ (- (* (* 18.0 y) (* x (* z t))) t_1) (- (* c b) (* 27.0 (* k j))))
       t_2))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((a * t) + (i * x)) * 4.0;
	double t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b));
	double tmp;
	if (t < -1.6210815397541398e-69) {
		tmp = t_2;
	} else if (t < 165.68027943805222) {
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((a * t) + (i * x)) * 4.0d0
    t_2 = (((18.0d0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0d0) - (c * b))
    if (t < (-1.6210815397541398d-69)) then
        tmp = t_2
    else if (t < 165.68027943805222d0) then
        tmp = (((18.0d0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0d0 * (k * j)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((a * t) + (i * x)) * 4.0;
	double t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b));
	double tmp;
	if (t < -1.6210815397541398e-69) {
		tmp = t_2;
	} else if (t < 165.68027943805222) {
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = ((a * t) + (i * x)) * 4.0
	t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b))
	tmp = 0
	if t < -1.6210815397541398e-69:
		tmp = t_2
	elif t < 165.68027943805222:
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(Float64(a * t) + Float64(i * x)) * 4.0)
	t_2 = Float64(Float64(Float64(Float64(18.0 * t) * Float64(Float64(x * y) * z)) - t_1) - Float64(Float64(Float64(k * j) * 27.0) - Float64(c * b)))
	tmp = 0.0
	if (t < -1.6210815397541398e-69)
		tmp = t_2;
	elseif (t < 165.68027943805222)
		tmp = Float64(Float64(Float64(Float64(18.0 * y) * Float64(x * Float64(z * t))) - t_1) + Float64(Float64(c * b) - Float64(27.0 * Float64(k * j))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = ((a * t) + (i * x)) * 4.0;
	t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b));
	tmp = 0.0;
	if (t < -1.6210815397541398e-69)
		tmp = t_2;
	elseif (t < 165.68027943805222)
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(N[(a * t), $MachinePrecision] + N[(i * x), $MachinePrecision]), $MachinePrecision] * 4.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(18.0 * t), $MachinePrecision] * N[(N[(x * y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] - N[(N[(N[(k * j), $MachinePrecision] * 27.0), $MachinePrecision] - N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -1.6210815397541398e-69], t$95$2, If[Less[t, 165.68027943805222], N[(N[(N[(N[(18.0 * y), $MachinePrecision] * N[(x * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] + N[(N[(c * b), $MachinePrecision] - N[(27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2024148 
(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)))