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

Percentage Accurate: 85.4% → 92.0%

Time: 19.9s

Alternatives: 21

Speedup: 0.8×

• 50.1% 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: 85.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 92.0% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 96.1%

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

   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 20.0%

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

   5. Taylor expanded in x around inf 63.6%

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

4. Final simplification 92.3%

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

Alternative 2: 87.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.42 \cdot 10^{+240} \lor \neg \left(x \leq 9.8 \cdot 10^{+175}\right):\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b \cdot c + t \cdot \left(x \cdot \left(z \cdot \left(18 \cdot y\right)\right) - a \cdot 4\right)\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= x -1.42e+240) (not (<= x 9.8e+175)))
   (* x (- (* 18.0 (* t (* y z))) (* 4.0 i)))
   (-
    (- (+ (* b c) (* t (- (* x (* z (* 18.0 y))) (* a 4.0)))) (* (* x 4.0) i))
    (* (* j 27.0) k))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((x <= -1.42e+240) || !(x <= 9.8e+175)) {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	} else {
		tmp = (((b * c) + (t * ((x * (z * (18.0 * y))) - (a * 4.0)))) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((x <= (-1.42d+240)) .or. (.not. (x <= 9.8d+175))) then
        tmp = x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i))
    else
        tmp = (((b * c) + (t * ((x * (z * (18.0d0 * y))) - (a * 4.0d0)))) - ((x * 4.0d0) * i)) - ((j * 27.0d0) * k)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((x <= -1.42e+240) || !(x <= 9.8e+175)) {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	} else {
		tmp = (((b * c) + (t * ((x * (z * (18.0 * y))) - (a * 4.0)))) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (x <= -1.42e+240) or not (x <= 9.8e+175):
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i))
	else:
		tmp = (((b * c) + (t * ((x * (z * (18.0 * y))) - (a * 4.0)))) - ((x * 4.0) * i)) - ((j * 27.0) * k)
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((x <= -1.42e+240) || !(x <= 9.8e+175))
		tmp = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)));
	else
		tmp = Float64(Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(x * Float64(z * Float64(18.0 * y))) - Float64(a * 4.0)))) - Float64(Float64(x * 4.0) * i)) - Float64(Float64(j * 27.0) * k));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((x <= -1.42e+240) || ~((x <= 9.8e+175)))
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	else
		tmp = (((b * c) + (t * ((x * (z * (18.0 * y))) - (a * 4.0)))) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[x, -1.42e+240], N[Not[LessEqual[x, 9.8e+175]], $MachinePrecision]], N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(x * N[(z * N[(18.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.41999999999999999e240 or 9.80000000000000002e175 < x

   1. Initial program 59.4%

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

   3. Simplified 61.9%

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

   5. Taylor expanded in x around inf 94.9%

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

   if -1.41999999999999999e240 < x < 9.80000000000000002e175

   1. Initial program 89.5%

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

      1. distribute-rgt-out-- 91.3%

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

      2. associate-*r* 89.6%

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

      3. *-commutative 89.6%

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

      4. associate-*l* 89.6%

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

      5. associate-*r* 89.6%

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

   4. Applied egg-rr 89.6%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.42 \cdot 10^{+240} \lor \neg \left(x \leq 9.8 \cdot 10^{+175}\right):\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b \cdot c + t \cdot \left(x \cdot \left(z \cdot \left(18 \cdot y\right)\right) - a \cdot 4\right)\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 87.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{+235} \lor \neg \left(x \leq 1.7 \cdot 10^{+175}\right):\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= x -2.2e+235) (not (<= x 1.7e+175)))
   (* x (- (* 18.0 (* t (* y z))) (* 4.0 i)))
   (-
    (+ (* b c) (* t (- (* (* x 18.0) (* y z)) (* a 4.0))))
    (+ (* x (* 4.0 i)) (* j (* 27.0 k))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((x <= -2.2e+235) || !(x <= 1.7e+175)) {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	} else {
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((x <= (-2.2d+235)) .or. (.not. (x <= 1.7d+175))) then
        tmp = x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i))
    else
        tmp = ((b * c) + (t * (((x * 18.0d0) * (y * z)) - (a * 4.0d0)))) - ((x * (4.0d0 * i)) + (j * (27.0d0 * k)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((x <= -2.2e+235) || !(x <= 1.7e+175)) {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	} else {
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (x <= -2.2e+235) or not (x <= 1.7e+175):
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i))
	else:
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((x <= -2.2e+235) || !(x <= 1.7e+175))
		tmp = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)));
	else
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(Float64(x * 18.0) * Float64(y * z)) - Float64(a * 4.0)))) - Float64(Float64(x * Float64(4.0 * i)) + Float64(j * Float64(27.0 * k))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((x <= -2.2e+235) || ~((x <= 1.7e+175)))
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	else
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[x, -2.2e+235], N[Not[LessEqual[x, 1.7e+175]], $MachinePrecision]], N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(N[(x * 18.0), $MachinePrecision] * N[(y * z), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision] + N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.2e235 or 1.70000000000000014e175 < x

   1. Initial program 59.4%

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

   3. Simplified 61.9%

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

   5. Taylor expanded in x around inf 94.9%

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

   if -2.2e235 < x < 1.70000000000000014e175

   1. Initial program 89.5%

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

   3. Simplified 89.6%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{+235} \lor \neg \left(x \leq 1.7 \cdot 10^{+175}\right):\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 80.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -18000000000 \lor \neg \left(a \leq 2.25 \cdot 10^{+151}\right):\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + y \cdot \left(18 \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= a -18000000000.0) (not (<= a 2.25e+151)))
   (- (- (* b c) (* 4.0 (+ (* x i) (* t a)))) (* (* j 27.0) k))
   (-
    (+ (* b c) (* y (* 18.0 (* t (* x z)))))
    (+ (* x (* 4.0 i)) (* j (* 27.0 k))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((a <= -18000000000.0) || !(a <= 2.25e+151)) {
		tmp = ((b * c) - (4.0 * ((x * i) + (t * a)))) - ((j * 27.0) * k);
	} else {
		tmp = ((b * c) + (y * (18.0 * (t * (x * z))))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((a <= (-18000000000.0d0)) .or. (.not. (a <= 2.25d+151))) then
        tmp = ((b * c) - (4.0d0 * ((x * i) + (t * a)))) - ((j * 27.0d0) * k)
    else
        tmp = ((b * c) + (y * (18.0d0 * (t * (x * z))))) - ((x * (4.0d0 * i)) + (j * (27.0d0 * k)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((a <= -18000000000.0) || !(a <= 2.25e+151)) {
		tmp = ((b * c) - (4.0 * ((x * i) + (t * a)))) - ((j * 27.0) * k);
	} else {
		tmp = ((b * c) + (y * (18.0 * (t * (x * z))))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (a <= -18000000000.0) or not (a <= 2.25e+151):
		tmp = ((b * c) - (4.0 * ((x * i) + (t * a)))) - ((j * 27.0) * k)
	else:
		tmp = ((b * c) + (y * (18.0 * (t * (x * z))))) - ((x * (4.0 * i)) + (j * (27.0 * k)))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((a <= -18000000000.0) || !(a <= 2.25e+151))
		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(Float64(Float64(b * c) + Float64(y * Float64(18.0 * Float64(t * Float64(x * z))))) - Float64(Float64(x * Float64(4.0 * i)) + Float64(j * Float64(27.0 * k))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((a <= -18000000000.0) || ~((a <= 2.25e+151)))
		tmp = ((b * c) - (4.0 * ((x * i) + (t * a)))) - ((j * 27.0) * k);
	else
		tmp = ((b * c) + (y * (18.0 * (t * (x * z))))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[a, -18000000000.0], N[Not[LessEqual[a, 2.25e+151]], $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], N[(N[(N[(b * c), $MachinePrecision] + N[(y * N[(18.0 * N[(t * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision] + N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.8e10 or 2.2499999999999999e151 < a

   1. Initial program 82.2%

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

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

   if -1.8e10 < a < 2.2499999999999999e151

   1. Initial program 86.3%

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

   3. Simplified 85.2%

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

   5. Taylor expanded in y around inf 83.7%

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

   6. Taylor expanded in a around 0 84.4%

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

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -18000000000 \lor \neg \left(a \leq 2.25 \cdot 10^{+151}\right):\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + y \cdot \left(18 \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 77.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;z \leq -1.4 \cdot 10^{-14} \lor \neg \left(z \leq 9.2 \cdot 10^{+99}\right):\\ \;\;\;\;t \cdot \left(18 \cdot \left(z \cdot \left(x \cdot y\right)\right) + a \cdot -4\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\right) - t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)))
   (if (or (<= z -1.4e-14) (not (<= z 9.2e+99)))
     (- (* t (+ (* 18.0 (* z (* x y))) (* a -4.0))) t_1)
     (- (- (* b c) (* 4.0 (+ (* x i) (* t a)))) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if ((z <= -1.4e-14) || !(z <= 9.2e+99)) {
		tmp = (t * ((18.0 * (z * (x * y))) + (a * -4.0))) - t_1;
	} else {
		tmp = ((b * c) - (4.0 * ((x * i) + (t * a)))) - t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (j * 27.0d0) * k
    if ((z <= (-1.4d-14)) .or. (.not. (z <= 9.2d+99))) then
        tmp = (t * ((18.0d0 * (z * (x * y))) + (a * (-4.0d0)))) - t_1
    else
        tmp = ((b * c) - (4.0d0 * ((x * i) + (t * a)))) - t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if ((z <= -1.4e-14) || !(z <= 9.2e+99)) {
		tmp = (t * ((18.0 * (z * (x * y))) + (a * -4.0))) - t_1;
	} else {
		tmp = ((b * c) - (4.0 * ((x * i) + (t * a)))) - t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	tmp = 0
	if (z <= -1.4e-14) or not (z <= 9.2e+99):
		tmp = (t * ((18.0 * (z * (x * y))) + (a * -4.0))) - t_1
	else:
		tmp = ((b * c) - (4.0 * ((x * i) + (t * a)))) - t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if ((z <= -1.4e-14) || !(z <= 9.2e+99))
		tmp = Float64(Float64(t * Float64(Float64(18.0 * Float64(z * Float64(x * y))) + Float64(a * -4.0))) - t_1);
	else
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(Float64(x * i) + Float64(t * a)))) - t_1);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * 27.0) * k;
	tmp = 0.0;
	if ((z <= -1.4e-14) || ~((z <= 9.2e+99)))
		tmp = (t * ((18.0 * (z * (x * y))) + (a * -4.0))) - t_1;
	else
		tmp = ((b * c) - (4.0 * ((x * i) + (t * a)))) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[Or[LessEqual[z, -1.4e-14], N[Not[LessEqual[z, 9.2e+99]], $MachinePrecision]], N[(N[(t * N[(N[(18.0 * N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(N[(x * i), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.4e-14 or 9.20000000000000077e99 < z

   1. Initial program 82.4%

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

      1. distribute-rgt-out-- 84.1%

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

      2. associate-*r* 78.5%

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

      3. *-commutative 78.5%

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

      4. associate-*l* 78.5%

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

      5. associate-*r* 78.5%

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

   4. Applied egg-rr 78.5%

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

   5. Taylor expanded in t around inf 67.5%

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

      1. cancel-sign-sub-inv 67.5%

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

      2. associate-*r* 71.5%

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

      3. metadata-eval 71.5%

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

   7. Simplified 71.5%

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

   if -1.4e-14 < z < 9.20000000000000077e99

   1. Initial program 87.0%

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

   3. Taylor expanded in y around 0 83.8%

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

      1. distribute-lft-out 83.8%

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

      2. *-commutative 83.8%

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

   5. Simplified 83.8%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{-14} \lor \neg \left(z \leq 9.2 \cdot 10^{+99}\right):\\ \;\;\;\;t \cdot \left(18 \cdot \left(z \cdot \left(x \cdot y\right)\right) + a \cdot -4\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 76.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t \leq -5.2 \cdot 10^{+32} \lor \neg \left(t \leq 7 \cdot 10^{+114}\right):\\ \;\;\;\;t \cdot \left(18 \cdot \left(z \cdot \left(x \cdot y\right)\right) + a \cdot -4\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)))
   (if (or (<= t -5.2e+32) (not (<= t 7e+114)))
     (- (* t (+ (* 18.0 (* z (* x y))) (* a -4.0))) t_1)
     (- (- (* b c) (* 4.0 (* x i))) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if ((t <= -5.2e+32) || !(t <= 7e+114)) {
		tmp = (t * ((18.0 * (z * (x * y))) + (a * -4.0))) - t_1;
	} else {
		tmp = ((b * c) - (4.0 * (x * i))) - t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (j * 27.0d0) * k
    if ((t <= (-5.2d+32)) .or. (.not. (t <= 7d+114))) then
        tmp = (t * ((18.0d0 * (z * (x * y))) + (a * (-4.0d0)))) - t_1
    else
        tmp = ((b * c) - (4.0d0 * (x * i))) - t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if ((t <= -5.2e+32) || !(t <= 7e+114)) {
		tmp = (t * ((18.0 * (z * (x * y))) + (a * -4.0))) - t_1;
	} else {
		tmp = ((b * c) - (4.0 * (x * i))) - t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	tmp = 0
	if (t <= -5.2e+32) or not (t <= 7e+114):
		tmp = (t * ((18.0 * (z * (x * y))) + (a * -4.0))) - t_1
	else:
		tmp = ((b * c) - (4.0 * (x * i))) - t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if ((t <= -5.2e+32) || !(t <= 7e+114))
		tmp = Float64(Float64(t * Float64(Float64(18.0 * Float64(z * Float64(x * y))) + Float64(a * -4.0))) - t_1);
	else
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(x * i))) - t_1);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * 27.0) * k;
	tmp = 0.0;
	if ((t <= -5.2e+32) || ~((t <= 7e+114)))
		tmp = (t * ((18.0 * (z * (x * y))) + (a * -4.0))) - t_1;
	else
		tmp = ((b * c) - (4.0 * (x * i))) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[Or[LessEqual[t, -5.2e+32], N[Not[LessEqual[t, 7e+114]], $MachinePrecision]], N[(N[(t * N[(N[(18.0 * N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -5.2000000000000004e32 or 7.0000000000000001e114 < t

   1. Initial program 78.9%

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

      1. distribute-rgt-out-- 84.4%

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

      2. associate-*r* 85.6%

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

      3. *-commutative 85.6%

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

      4. associate-*l* 85.6%

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

      5. associate-*r* 85.6%

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

   4. Applied egg-rr 85.6%

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

   5. Taylor expanded in t around inf 79.3%

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

      1. cancel-sign-sub-inv 79.3%

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

      2. associate-*r* 79.2%

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

      3. metadata-eval 79.2%

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

   7. Simplified 79.2%

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

   if -5.2000000000000004e32 < t < 7.0000000000000001e114

   1. Initial program 88.1%

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

   3. Taylor expanded in t around 0 73.2%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{+32} \lor \neg \left(t \leq 7 \cdot 10^{+114}\right):\\ \;\;\;\;t \cdot \left(18 \cdot \left(z \cdot \left(x \cdot y\right)\right) + a \cdot -4\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 59.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{if}\;x \leq -3.5 \cdot 10^{+46}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -5.4 \cdot 10^{-26}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+17}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (- (* 18.0 (* t (* y z))) (* 4.0 i)))))
   (if (<= x -3.5e+46)
     t_1
     (if (<= x -5.4e-26)
       (* t (- (* 18.0 (* x (* y z))) (* a 4.0)))
       (if (<= x 2.3e+17) (+ (* b c) (* j (* k -27.0))) 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 * ((18.0 * (t * (y * z))) - (4.0 * i));
	double tmp;
	if (x <= -3.5e+46) {
		tmp = t_1;
	} else if (x <= -5.4e-26) {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	} else if (x <= 2.3e+17) {
		tmp = (b * c) + (j * (k * -27.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i))
    if (x <= (-3.5d+46)) then
        tmp = t_1
    else if (x <= (-5.4d-26)) then
        tmp = t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0))
    else if (x <= 2.3d+17) then
        tmp = (b * c) + (j * (k * (-27.0d0)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	double tmp;
	if (x <= -3.5e+46) {
		tmp = t_1;
	} else if (x <= -5.4e-26) {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	} else if (x <= 2.3e+17) {
		tmp = (b * c) + (j * (k * -27.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = x * ((18.0 * (t * (y * z))) - (4.0 * i))
	tmp = 0
	if x <= -3.5e+46:
		tmp = t_1
	elif x <= -5.4e-26:
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0))
	elif x <= 2.3e+17:
		tmp = (b * c) + (j * (k * -27.0))
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)))
	tmp = 0.0
	if (x <= -3.5e+46)
		tmp = t_1;
	elseif (x <= -5.4e-26)
		tmp = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)));
	elseif (x <= 2.3e+17)
		tmp = Float64(Float64(b * c) + Float64(j * Float64(k * -27.0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	tmp = 0.0;
	if (x <= -3.5e+46)
		tmp = t_1;
	elseif (x <= -5.4e-26)
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	elseif (x <= 2.3e+17)
		tmp = (b * c) + (j * (k * -27.0));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.5e+46], t$95$1, If[LessEqual[x, -5.4e-26], N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.3e+17], N[(N[(b * c), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.49999999999999985e46 or 2.3e17 < x

   1. Initial program 72.9%

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

   3. Simplified 78.1%

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

   5. Taylor expanded in x around inf 75.5%

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

   if -3.49999999999999985e46 < x < -5.39999999999999963e-26

   1. Initial program 84.4%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around inf 77.5%

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

   if -5.39999999999999963e-26 < x < 2.3e17

   1. Initial program 95.3%

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

   3. Simplified 90.3%

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

   5. Taylor expanded in b around inf 56.8%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{+46}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;x \leq -5.4 \cdot 10^{-26}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+17}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 47.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{if}\;z \leq -5.9 \cdot 10^{-5}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{-68}:\\ \;\;\;\;b \cdot \left(c + -4 \cdot \left(i \cdot \frac{x}{b}\right)\right)\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{+99}:\\ \;\;\;\;\left(x \cdot i\right) \cdot -4 - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (* t (- (* 18.0 (* x (* y z))) (* a 4.0)))))
   (if (<= z -5.9e-5)
     t_1
     (if (<= z 5.3e-68)
       (* b (+ c (* -4.0 (* i (/ x b)))))
       (if (<= z 7.4e+99) (- (* (* x i) -4.0) (* 27.0 (* j k))) t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	double tmp;
	if (z <= -5.9e-5) {
		tmp = t_1;
	} else if (z <= 5.3e-68) {
		tmp = b * (c + (-4.0 * (i * (x / b))));
	} else if (z <= 7.4e+99) {
		tmp = ((x * i) * -4.0) - (27.0 * (j * k));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0))
    if (z <= (-5.9d-5)) then
        tmp = t_1
    else if (z <= 5.3d-68) then
        tmp = b * (c + ((-4.0d0) * (i * (x / b))))
    else if (z <= 7.4d+99) then
        tmp = ((x * i) * (-4.0d0)) - (27.0d0 * (j * k))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	double tmp;
	if (z <= -5.9e-5) {
		tmp = t_1;
	} else if (z <= 5.3e-68) {
		tmp = b * (c + (-4.0 * (i * (x / b))));
	} else if (z <= 7.4e+99) {
		tmp = ((x * i) * -4.0) - (27.0 * (j * k));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = t * ((18.0 * (x * (y * z))) - (a * 4.0))
	tmp = 0
	if z <= -5.9e-5:
		tmp = t_1
	elif z <= 5.3e-68:
		tmp = b * (c + (-4.0 * (i * (x / b))))
	elif z <= 7.4e+99:
		tmp = ((x * i) * -4.0) - (27.0 * (j * k))
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)))
	tmp = 0.0
	if (z <= -5.9e-5)
		tmp = t_1;
	elseif (z <= 5.3e-68)
		tmp = Float64(b * Float64(c + Float64(-4.0 * Float64(i * Float64(x / b)))));
	elseif (z <= 7.4e+99)
		tmp = Float64(Float64(Float64(x * i) * -4.0) - Float64(27.0 * Float64(j * k)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	tmp = 0.0;
	if (z <= -5.9e-5)
		tmp = t_1;
	elseif (z <= 5.3e-68)
		tmp = b * (c + (-4.0 * (i * (x / b))));
	elseif (z <= 7.4e+99)
		tmp = ((x * i) * -4.0) - (27.0 * (j * k));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.9e-5], t$95$1, If[LessEqual[z, 5.3e-68], N[(b * N[(c + N[(-4.0 * N[(i * N[(x / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.4e+99], N[(N[(N[(x * i), $MachinePrecision] * -4.0), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.8999999999999998e-5 or 7.4000000000000002e99 < z

   1. Initial program 81.9%

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

   3. Simplified 77.9%

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

   5. Taylor expanded in t around inf 54.3%

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

   if -5.8999999999999998e-5 < z < 5.3e-68

   1. Initial program 87.4%

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

   3. Taylor expanded in t around 0 74.2%

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

   4. Taylor expanded in b around inf 67.8%

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

      1. associate-*r/ 67.8%

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

      2. mul-1-neg 67.8%

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

      3. associate-*r* 67.8%

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

      4. *-commutative 67.8%

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

      5. *-commutative 67.8%

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

      6. associate-*r* 67.8%

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

      7. distribute-neg-in 67.8%

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

      8. associate-*r* 67.8%

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

      9. distribute-lft-neg-out 67.8%

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

      10. *-commutative 67.8%

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

      11. distribute-rgt-neg-in 67.8%

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

      12. metadata-eval 67.8%

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

      13. associate-*r* 67.8%

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

      14. *-commutative 67.8%

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

      15. distribute-lft-neg-in 67.8%

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

      16. metadata-eval 67.8%

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

      17. *-commutative 67.8%

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

   6. Simplified 67.8%

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

   7. Taylor expanded in i around inf 59.1%

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

      1. associate-/l* 58.1%

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

   9. Simplified 58.1%

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

   if 5.3e-68 < z < 7.4000000000000002e99

   1. Initial program 87.0%

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

   3. Taylor expanded in t around 0 55.4%

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

   4. Taylor expanded in b around inf 45.5%

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

      1. associate-/l* 50.3%

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

   6. Simplified 50.3%

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

   7. Taylor expanded in b around 0 40.7%

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

4. Final simplification 53.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.9 \cdot 10^{-5}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{-68}:\\ \;\;\;\;b \cdot \left(c + -4 \cdot \left(i \cdot \frac{x}{b}\right)\right)\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{+99}:\\ \;\;\;\;\left(x \cdot i\right) \cdot -4 - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 48.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := b \cdot \left(c + -4 \cdot \left(i \cdot \frac{x}{b}\right)\right)\\ \mathbf{if}\;b \leq -4.1 \cdot 10^{+167}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -2.85 \cdot 10^{+19}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + a \cdot \left(t \cdot -4\right)\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{-78}:\\ \;\;\;\;\left(x \cdot i\right) \cdot -4 - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (* i (/ x b)))))))
   (if (<= b -4.1e+167)
     t_1
     (if (<= b -2.85e+19)
       (+ (* j (* k -27.0)) (* a (* t -4.0)))
       (if (<= b 3.5e-78) (- (* (* x i) -4.0) (* 27.0 (* j k))) t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = b * (c + (-4.0 * (i * (x / b))));
	double tmp;
	if (b <= -4.1e+167) {
		tmp = t_1;
	} else if (b <= -2.85e+19) {
		tmp = (j * (k * -27.0)) + (a * (t * -4.0));
	} else if (b <= 3.5e-78) {
		tmp = ((x * i) * -4.0) - (27.0 * (j * k));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (c + ((-4.0d0) * (i * (x / b))))
    if (b <= (-4.1d+167)) then
        tmp = t_1
    else if (b <= (-2.85d+19)) then
        tmp = (j * (k * (-27.0d0))) + (a * (t * (-4.0d0)))
    else if (b <= 3.5d-78) then
        tmp = ((x * i) * (-4.0d0)) - (27.0d0 * (j * k))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = b * (c + (-4.0 * (i * (x / b))));
	double tmp;
	if (b <= -4.1e+167) {
		tmp = t_1;
	} else if (b <= -2.85e+19) {
		tmp = (j * (k * -27.0)) + (a * (t * -4.0));
	} else if (b <= 3.5e-78) {
		tmp = ((x * i) * -4.0) - (27.0 * (j * k));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = b * (c + (-4.0 * (i * (x / b))))
	tmp = 0
	if b <= -4.1e+167:
		tmp = t_1
	elif b <= -2.85e+19:
		tmp = (j * (k * -27.0)) + (a * (t * -4.0))
	elif b <= 3.5e-78:
		tmp = ((x * i) * -4.0) - (27.0 * (j * k))
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(b * Float64(c + Float64(-4.0 * Float64(i * Float64(x / b)))))
	tmp = 0.0
	if (b <= -4.1e+167)
		tmp = t_1;
	elseif (b <= -2.85e+19)
		tmp = Float64(Float64(j * Float64(k * -27.0)) + Float64(a * Float64(t * -4.0)));
	elseif (b <= 3.5e-78)
		tmp = Float64(Float64(Float64(x * i) * -4.0) - Float64(27.0 * Float64(j * k)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = b * (c + (-4.0 * (i * (x / b))));
	tmp = 0.0;
	if (b <= -4.1e+167)
		tmp = t_1;
	elseif (b <= -2.85e+19)
		tmp = (j * (k * -27.0)) + (a * (t * -4.0));
	elseif (b <= 3.5e-78)
		tmp = ((x * i) * -4.0) - (27.0 * (j * k));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(b * N[(c + N[(-4.0 * N[(i * N[(x / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4.1e+167], t$95$1, If[LessEqual[b, -2.85e+19], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(a * N[(t * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.5e-78], N[(N[(N[(x * i), $MachinePrecision] * -4.0), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -4.1e167 or 3.4999999999999999e-78 < b

   1. Initial program 79.9%

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

   3. Taylor expanded in t around 0 60.3%

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

   4. Taylor expanded in b around inf 63.0%

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

      1. associate-*r/ 63.0%

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

      2. mul-1-neg 63.0%

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

      3. associate-*r* 63.0%

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

      4. *-commutative 63.0%

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

      5. *-commutative 63.0%

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

      6. associate-*r* 63.0%

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

      7. distribute-neg-in 63.0%

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

      8. associate-*r* 63.0%

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

      9. distribute-lft-neg-out 63.0%

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

      10. *-commutative 63.0%

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

      11. distribute-rgt-neg-in 63.0%

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

      12. metadata-eval 63.0%

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

      13. associate-*r* 63.0%

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

      14. *-commutative 63.0%

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

      15. distribute-lft-neg-in 63.0%

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

      16. metadata-eval 63.0%

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

      17. *-commutative 63.0%

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

   6. Simplified 63.0%

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

   7. Taylor expanded in i around inf 52.6%

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

      1. associate-/l* 52.6%

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

   9. Simplified 52.6%

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

   if -4.1e167 < b < -2.85e19

   1. Initial program 87.2%

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

   3. Simplified 93.7%

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

   5. Taylor expanded in a around inf 46.0%

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

      1. metadata-eval 46.0%

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

      2. distribute-lft-neg-in 46.0%

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

      3. *-commutative 46.0%

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

      4. associate-*l* 46.0%

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

      5. distribute-lft-neg-in 46.0%

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

      6. distribute-lft-neg-in 46.0%

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

      7. metadata-eval 46.0%

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

   7. Simplified 46.0%

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

   if -2.85e19 < b < 3.4999999999999999e-78

   1. Initial program 88.5%

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

   3. Taylor expanded in t around 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 b around inf 50.6%

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

      1. associate-/l* 49.6%

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

   6. Simplified 49.6%

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

   7. Taylor expanded in b around 0 49.9%

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

4. Final simplification 50.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.1 \cdot 10^{+167}:\\ \;\;\;\;b \cdot \left(c + -4 \cdot \left(i \cdot \frac{x}{b}\right)\right)\\ \mathbf{elif}\;b \leq -2.85 \cdot 10^{+19}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + a \cdot \left(t \cdot -4\right)\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{-78}:\\ \;\;\;\;\left(x \cdot i\right) \cdot -4 - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(c + -4 \cdot \left(i \cdot \frac{x}{b}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 48.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := b \cdot \left(c + -4 \cdot \left(i \cdot \frac{x}{b}\right)\right)\\ \mathbf{if}\;b \leq -4.1 \cdot 10^{+167}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -560000000000:\\ \;\;\;\;t\_1 + a \cdot \left(t \cdot -4\right)\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{-76}:\\ \;\;\;\;t\_1 + i \cdot \left(x \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0))) (t_2 (* b (+ c (* -4.0 (* i (/ x b)))))))
   (if (<= b -4.1e+167)
     t_2
     (if (<= b -560000000000.0)
       (+ t_1 (* a (* t -4.0)))
       (if (<= b 1.4e-76) (+ t_1 (* i (* x -4.0))) t_2)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = b * (c + (-4.0 * (i * (x / b))));
	double tmp;
	if (b <= -4.1e+167) {
		tmp = t_2;
	} else if (b <= -560000000000.0) {
		tmp = t_1 + (a * (t * -4.0));
	} else if (b <= 1.4e-76) {
		tmp = t_1 + (i * (x * -4.0));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * (k * (-27.0d0))
    t_2 = b * (c + ((-4.0d0) * (i * (x / b))))
    if (b <= (-4.1d+167)) then
        tmp = t_2
    else if (b <= (-560000000000.0d0)) then
        tmp = t_1 + (a * (t * (-4.0d0)))
    else if (b <= 1.4d-76) then
        tmp = t_1 + (i * (x * (-4.0d0)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = b * (c + (-4.0 * (i * (x / b))));
	double tmp;
	if (b <= -4.1e+167) {
		tmp = t_2;
	} else if (b <= -560000000000.0) {
		tmp = t_1 + (a * (t * -4.0));
	} else if (b <= 1.4e-76) {
		tmp = t_1 + (i * (x * -4.0));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	t_2 = b * (c + (-4.0 * (i * (x / b))))
	tmp = 0
	if b <= -4.1e+167:
		tmp = t_2
	elif b <= -560000000000.0:
		tmp = t_1 + (a * (t * -4.0))
	elif b <= 1.4e-76:
		tmp = t_1 + (i * (x * -4.0))
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * -27.0))
	t_2 = Float64(b * Float64(c + Float64(-4.0 * Float64(i * Float64(x / b)))))
	tmp = 0.0
	if (b <= -4.1e+167)
		tmp = t_2;
	elseif (b <= -560000000000.0)
		tmp = Float64(t_1 + Float64(a * Float64(t * -4.0)));
	elseif (b <= 1.4e-76)
		tmp = Float64(t_1 + Float64(i * Float64(x * -4.0)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * -27.0);
	t_2 = b * (c + (-4.0 * (i * (x / b))));
	tmp = 0.0;
	if (b <= -4.1e+167)
		tmp = t_2;
	elseif (b <= -560000000000.0)
		tmp = t_1 + (a * (t * -4.0));
	elseif (b <= 1.4e-76)
		tmp = t_1 + (i * (x * -4.0));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(c + N[(-4.0 * N[(i * N[(x / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4.1e+167], t$95$2, If[LessEqual[b, -560000000000.0], N[(t$95$1 + N[(a * N[(t * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.4e-76], N[(t$95$1 + N[(i * N[(x * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -4.1e167 or 1.40000000000000005e-76 < b

   1. Initial program 79.9%

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

   3. Taylor expanded in t around 0 60.3%

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

   4. Taylor expanded in b around inf 63.0%

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

      1. associate-*r/ 63.0%

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

      2. mul-1-neg 63.0%

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

      3. associate-*r* 63.0%

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

      4. *-commutative 63.0%

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

      5. *-commutative 63.0%

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

      6. associate-*r* 63.0%

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

      7. distribute-neg-in 63.0%

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

      8. associate-*r* 63.0%

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

      9. distribute-lft-neg-out 63.0%

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

      10. *-commutative 63.0%

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

      11. distribute-rgt-neg-in 63.0%

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

      12. metadata-eval 63.0%

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

      13. associate-*r* 63.0%

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

      14. *-commutative 63.0%

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

      15. distribute-lft-neg-in 63.0%

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

      16. metadata-eval 63.0%

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

      17. *-commutative 63.0%

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

   6. Simplified 63.0%

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

   7. Taylor expanded in i around inf 52.6%

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

      1. associate-/l* 52.6%

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

   9. Simplified 52.6%

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

   if -4.1e167 < b < -5.6e11

   1. Initial program 87.2%

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

   3. Simplified 93.7%

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

   5. Taylor expanded in a around inf 46.0%

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

      1. metadata-eval 46.0%

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

      2. distribute-lft-neg-in 46.0%

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

      3. *-commutative 46.0%

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

      4. associate-*l* 46.0%

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

      5. distribute-lft-neg-in 46.0%

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

      6. distribute-lft-neg-in 46.0%

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

      7. metadata-eval 46.0%

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

   7. Simplified 46.0%

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

   if -5.6e11 < b < 1.40000000000000005e-76

   1. Initial program 88.5%

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

   3. Simplified 90.3%

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

   5. Taylor expanded in i around inf 49.9%

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

      1. associate-*r* 49.9%

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

      2. *-commutative 49.9%

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

      3. associate-*r* 49.9%

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

      4. *-commutative 49.9%

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

      5. *-commutative 49.9%

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

   7. Simplified 49.9%

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

4. Final simplification 50.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.1 \cdot 10^{+167}:\\ \;\;\;\;b \cdot \left(c + -4 \cdot \left(i \cdot \frac{x}{b}\right)\right)\\ \mathbf{elif}\;b \leq -560000000000:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + a \cdot \left(t \cdot -4\right)\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{-76}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + i \cdot \left(x \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(c + -4 \cdot \left(i \cdot \frac{x}{b}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 72.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{+34} \lor \neg \left(t \leq 1.25 \cdot 10^{+114}\right):\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \end{array} \]

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 -6.5e+34) (not (<= t 1.25e+114)))
   (* t (- (* 18.0 (* x (* y z))) (* a 4.0)))
   (- (- (* b c) (* 4.0 (* x i))) (* (* j 27.0) k))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((t <= -6.5e+34) || !(t <= 1.25e+114)) {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	} else {
		tmp = ((b * c) - (4.0 * (x * i))) - ((j * 27.0) * k);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((t <= (-6.5d+34)) .or. (.not. (t <= 1.25d+114))) then
        tmp = t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0))
    else
        tmp = ((b * c) - (4.0d0 * (x * i))) - ((j * 27.0d0) * k)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((t <= -6.5e+34) || !(t <= 1.25e+114)) {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	} else {
		tmp = ((b * c) - (4.0 * (x * i))) - ((j * 27.0) * k);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (t <= -6.5e+34) or not (t <= 1.25e+114):
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0))
	else:
		tmp = ((b * c) - (4.0 * (x * i))) - ((j * 27.0) * k)
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((t <= -6.5e+34) || !(t <= 1.25e+114))
		tmp = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)));
	else
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(x * i))) - Float64(Float64(j * 27.0) * k));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((t <= -6.5e+34) || ~((t <= 1.25e+114)))
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	else
		tmp = ((b * c) - (4.0 * (x * i))) - ((j * 27.0) * k);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[t, -6.5e+34], N[Not[LessEqual[t, 1.25e+114]], $MachinePrecision]], N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6.50000000000000017e34 or 1.25e114 < t

   1. Initial program 78.9%

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

   3. Simplified 84.6%

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

   5. Taylor expanded in t around inf 73.0%

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

   if -6.50000000000000017e34 < t < 1.25e114

   1. Initial program 88.1%

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

   3. Taylor expanded in t around 0 73.2%

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

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{+34} \lor \neg \left(t \leq 1.25 \cdot 10^{+114}\right):\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 59.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{-79} \lor \neg \left(z \leq 1.2 \cdot 10^{+113}\right):\\ \;\;\;\;\left(z \cdot \left(x \cdot y\right)\right) \cdot \left(18 \cdot t\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\\ \end{array} \end{array} \]

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 (<= z -2.6e-79) (not (<= z 1.2e+113)))
   (- (* (* z (* x y)) (* 18.0 t)) (* (* j 27.0) k))
   (- (* b c) (* 4.0 (+ (* x i) (* 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 tmp;
	if ((z <= -2.6e-79) || !(z <= 1.2e+113)) {
		tmp = ((z * (x * y)) * (18.0 * t)) - ((j * 27.0) * k);
	} else {
		tmp = (b * c) - (4.0 * ((x * i) + (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) :: tmp
    if ((z <= (-2.6d-79)) .or. (.not. (z <= 1.2d+113))) then
        tmp = ((z * (x * y)) * (18.0d0 * t)) - ((j * 27.0d0) * k)
    else
        tmp = (b * c) - (4.0d0 * ((x * i) + (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 tmp;
	if ((z <= -2.6e-79) || !(z <= 1.2e+113)) {
		tmp = ((z * (x * y)) * (18.0 * t)) - ((j * 27.0) * k);
	} else {
		tmp = (b * c) - (4.0 * ((x * i) + (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):
	tmp = 0
	if (z <= -2.6e-79) or not (z <= 1.2e+113):
		tmp = ((z * (x * y)) * (18.0 * t)) - ((j * 27.0) * k)
	else:
		tmp = (b * c) - (4.0 * ((x * i) + (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)
	tmp = 0.0
	if ((z <= -2.6e-79) || !(z <= 1.2e+113))
		tmp = Float64(Float64(Float64(z * Float64(x * y)) * Float64(18.0 * t)) - Float64(Float64(j * 27.0) * k));
	else
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(Float64(x * i) + 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)
	tmp = 0.0;
	if ((z <= -2.6e-79) || ~((z <= 1.2e+113)))
		tmp = ((z * (x * y)) * (18.0 * t)) - ((j * 27.0) * k);
	else
		tmp = (b * c) - (4.0 * ((x * i) + (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_] := If[Or[LessEqual[z, -2.6e-79], N[Not[LessEqual[z, 1.2e+113]], $MachinePrecision]], N[(N[(N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision] * N[(18.0 * t), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(N[(x * i), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.59999999999999994e-79 or 1.19999999999999992e113 < z

   1. Initial program 84.1%

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

      1. distribute-rgt-out-- 85.6%

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

      2. associate-*r* 80.6%

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

      3. *-commutative 80.6%

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

      4. associate-*l* 80.5%

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

      5. associate-*r* 80.5%

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

   4. Applied egg-rr 80.5%

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

   5. Taylor expanded in y around inf 53.4%

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

      1. associate-*r* 53.5%

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

      2. associate-*r* 57.1%

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

   7. Simplified 57.1%

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

   if -2.59999999999999994e-79 < z < 1.19999999999999992e113

   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 y around 0 82.2%

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

      1. distribute-lft-out 82.2%

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

      2. *-commutative 82.2%

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

   5. Simplified 82.2%

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

   6. Taylor expanded in j around 0 71.0%

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

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{-79} \lor \neg \left(z \leq 1.2 \cdot 10^{+113}\right):\\ \;\;\;\;\left(z \cdot \left(x \cdot y\right)\right) \cdot \left(18 \cdot t\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 53.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -5 \cdot 10^{+30} \lor \neg \left(b \cdot c \leq 2 \cdot 10^{+181}\right):\\ \;\;\;\;b \cdot \left(c + -4 \cdot \left(i \cdot \frac{x}{b}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + i \cdot \left(x \cdot -4\right)\\ \end{array} \end{array} \]

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 (or (<= (* b c) -5e+30) (not (<= (* b c) 2e+181)))
   (* b (+ c (* -4.0 (* i (/ x b)))))
   (+ (* j (* k -27.0)) (* i (* x -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 (((b * c) <= -5e+30) || !((b * c) <= 2e+181)) {
		tmp = b * (c + (-4.0 * (i * (x / b))));
	} else {
		tmp = (j * (k * -27.0)) + (i * (x * -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 (((b * c) <= (-5d+30)) .or. (.not. ((b * c) <= 2d+181))) then
        tmp = b * (c + ((-4.0d0) * (i * (x / b))))
    else
        tmp = (j * (k * (-27.0d0))) + (i * (x * (-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 (((b * c) <= -5e+30) || !((b * c) <= 2e+181)) {
		tmp = b * (c + (-4.0 * (i * (x / b))));
	} else {
		tmp = (j * (k * -27.0)) + (i * (x * -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 ((b * c) <= -5e+30) or not ((b * c) <= 2e+181):
		tmp = b * (c + (-4.0 * (i * (x / b))))
	else:
		tmp = (j * (k * -27.0)) + (i * (x * -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 ((Float64(b * c) <= -5e+30) || !(Float64(b * c) <= 2e+181))
		tmp = Float64(b * Float64(c + Float64(-4.0 * Float64(i * Float64(x / b)))));
	else
		tmp = Float64(Float64(j * Float64(k * -27.0)) + Float64(i * Float64(x * -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 (((b * c) <= -5e+30) || ~(((b * c) <= 2e+181)))
		tmp = b * (c + (-4.0 * (i * (x / b))));
	else
		tmp = (j * (k * -27.0)) + (i * (x * -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[Or[LessEqual[N[(b * c), $MachinePrecision], -5e+30], N[Not[LessEqual[N[(b * c), $MachinePrecision], 2e+181]], $MachinePrecision]], N[(b * N[(c + N[(-4.0 * N[(i * N[(x / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(i * N[(x * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -4.9999999999999998e30 or 1.9999999999999998e181 < (*.f64 b c)

   1. Initial program 82.8%

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

   3. Taylor expanded in t around 0 74.2%

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

   4. Taylor expanded in b around inf 75.5%

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

      1. associate-*r/ 75.5%

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

      2. mul-1-neg 75.5%

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

      3. associate-*r* 75.5%

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

      4. *-commutative 75.5%

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

      5. *-commutative 75.5%

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

      6. associate-*r* 75.6%

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

      7. distribute-neg-in 75.6%

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

      8. associate-*r* 75.6%

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

      9. distribute-lft-neg-out 75.6%

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

      10. *-commutative 75.6%

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

      11. distribute-rgt-neg-in 75.6%

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

      12. metadata-eval 75.6%

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

      13. associate-*r* 75.5%

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

      14. *-commutative 75.5%

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

      15. distribute-lft-neg-in 75.5%

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

      16. metadata-eval 75.5%

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

      17. *-commutative 75.5%

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

   6. Simplified 75.5%

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

   7. Taylor expanded in i around inf 73.4%

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

      1. associate-/l* 72.4%

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

   9. Simplified 72.4%

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

   if -4.9999999999999998e30 < (*.f64 b c) < 1.9999999999999998e181

   1. Initial program 86.0%

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

   3. Simplified 87.3%

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

   5. Taylor expanded in i around inf 47.7%

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

      1. associate-*r* 47.7%

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

      2. *-commutative 47.7%

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

      3. associate-*r* 47.7%

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

      4. *-commutative 47.7%

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

      5. *-commutative 47.7%

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

   7. Simplified 47.7%

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

4. Final simplification 56.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -5 \cdot 10^{+30} \lor \neg \left(b \cdot c \leq 2 \cdot 10^{+181}\right):\\ \;\;\;\;b \cdot \left(c + -4 \cdot \left(i \cdot \frac{x}{b}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + i \cdot \left(x \cdot -4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 46.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(x \cdot i\right) \cdot -4\\ \mathbf{if}\;x \leq -2.3 \cdot 10^{+45}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+18}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{+174}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 i) -4.0)))
   (if (<= x -2.3e+45)
     t_1
     (if (<= x 7.5e+18)
       (+ (* b c) (* j (* k -27.0)))
       (if (<= x 2.2e+174) (* t (* 18.0 (* x (* y z)))) 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) * -4.0;
	double tmp;
	if (x <= -2.3e+45) {
		tmp = t_1;
	} else if (x <= 7.5e+18) {
		tmp = (b * c) + (j * (k * -27.0));
	} else if (x <= 2.2e+174) {
		tmp = t * (18.0 * (x * (y * z)));
	} 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 * i) * (-4.0d0)
    if (x <= (-2.3d+45)) then
        tmp = t_1
    else if (x <= 7.5d+18) then
        tmp = (b * c) + (j * (k * (-27.0d0)))
    else if (x <= 2.2d+174) then
        tmp = t * (18.0d0 * (x * (y * z)))
    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 * i) * -4.0;
	double tmp;
	if (x <= -2.3e+45) {
		tmp = t_1;
	} else if (x <= 7.5e+18) {
		tmp = (b * c) + (j * (k * -27.0));
	} else if (x <= 2.2e+174) {
		tmp = t * (18.0 * (x * (y * z)));
	} 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 * i) * -4.0
	tmp = 0
	if x <= -2.3e+45:
		tmp = t_1
	elif x <= 7.5e+18:
		tmp = (b * c) + (j * (k * -27.0))
	elif x <= 2.2e+174:
		tmp = t * (18.0 * (x * (y * z)))
	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(x * i) * -4.0)
	tmp = 0.0
	if (x <= -2.3e+45)
		tmp = t_1;
	elseif (x <= 7.5e+18)
		tmp = Float64(Float64(b * c) + Float64(j * Float64(k * -27.0)));
	elseif (x <= 2.2e+174)
		tmp = Float64(t * Float64(18.0 * Float64(x * Float64(y * z))));
	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 * i) * -4.0;
	tmp = 0.0;
	if (x <= -2.3e+45)
		tmp = t_1;
	elseif (x <= 7.5e+18)
		tmp = (b * c) + (j * (k * -27.0));
	elseif (x <= 2.2e+174)
		tmp = t * (18.0 * (x * (y * z)));
	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[(x * i), $MachinePrecision] * -4.0), $MachinePrecision]}, If[LessEqual[x, -2.3e+45], t$95$1, If[LessEqual[x, 7.5e+18], N[(N[(b * c), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.2e+174], N[(t * N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.30000000000000012e45 or 2.2000000000000002e174 < x

   1. Initial program 73.4%

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

   3. Taylor expanded in y around 0 62.9%

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

      1. distribute-lft-out 62.9%

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

      2. *-commutative 62.9%

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

   5. Simplified 62.9%

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

   6. Taylor expanded in i around inf 54.9%

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

      1. *-commutative 54.9%

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

   8. Simplified 54.9%

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

   if -2.30000000000000012e45 < x < 7.5e18

   1. Initial program 94.3%

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

   3. Simplified 91.1%

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

   5. Taylor expanded in b around inf 54.0%

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

   if 7.5e18 < x < 2.2000000000000002e174

   1. Initial program 71.8%

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

   3. Simplified 83.0%

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

   5. Taylor expanded in t around inf 61.0%

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

   6. Taylor expanded in x around inf 44.5%

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

4. Final simplification 53.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{+45}:\\ \;\;\;\;\left(x \cdot i\right) \cdot -4\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+18}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{+174}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot i\right) \cdot -4\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 30.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{if}\;z \leq -1.35 \cdot 10^{-79}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-284}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{+99}:\\ \;\;\;\;\left(x \cdot i\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* t (* 18.0 (* x (* y z))))))
   (if (<= z -1.35e-79)
     t_1
     (if (<= z -1.75e-284) (* b c) (if (<= z 7.4e+99) (* (* x i) -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 = t * (18.0 * (x * (y * z)));
	double tmp;
	if (z <= -1.35e-79) {
		tmp = t_1;
	} else if (z <= -1.75e-284) {
		tmp = b * c;
	} else if (z <= 7.4e+99) {
		tmp = (x * i) * -4.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (18.0d0 * (x * (y * z)))
    if (z <= (-1.35d-79)) then
        tmp = t_1
    else if (z <= (-1.75d-284)) then
        tmp = b * c
    else if (z <= 7.4d+99) then
        tmp = (x * i) * (-4.0d0)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * (18.0 * (x * (y * z)));
	double tmp;
	if (z <= -1.35e-79) {
		tmp = t_1;
	} else if (z <= -1.75e-284) {
		tmp = b * c;
	} else if (z <= 7.4e+99) {
		tmp = (x * i) * -4.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = t * (18.0 * (x * (y * z)))
	tmp = 0
	if z <= -1.35e-79:
		tmp = t_1
	elif z <= -1.75e-284:
		tmp = b * c
	elif z <= 7.4e+99:
		tmp = (x * i) * -4.0
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(t * Float64(18.0 * Float64(x * Float64(y * z))))
	tmp = 0.0
	if (z <= -1.35e-79)
		tmp = t_1;
	elseif (z <= -1.75e-284)
		tmp = Float64(b * c);
	elseif (z <= 7.4e+99)
		tmp = Float64(Float64(x * i) * -4.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = t * (18.0 * (x * (y * z)));
	tmp = 0.0;
	if (z <= -1.35e-79)
		tmp = t_1;
	elseif (z <= -1.75e-284)
		tmp = b * c;
	elseif (z <= 7.4e+99)
		tmp = (x * i) * -4.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(t * N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.35e-79], t$95$1, If[LessEqual[z, -1.75e-284], N[(b * c), $MachinePrecision], If[LessEqual[z, 7.4e+99], N[(N[(x * i), $MachinePrecision] * -4.0), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.3500000000000001e-79 or 7.4000000000000002e99 < z

   1. Initial program 83.9%

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

   3. Simplified 80.5%

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

   5. Taylor expanded in t around inf 50.1%

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

   6. Taylor expanded in x around inf 38.8%

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

   if -1.3500000000000001e-79 < z < -1.74999999999999988e-284

   1. Initial program 89.5%

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

   3. Taylor expanded in y around 0 95.0%

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

      1. distribute-lft-out 95.0%

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

      2. *-commutative 95.0%

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

   5. Simplified 95.0%

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

   6. Taylor expanded in b around inf 35.8%

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

   if -1.74999999999999988e-284 < z < 7.4000000000000002e99

   1. Initial program 84.3%

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

   3. Taylor expanded in y around 0 77.6%

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

      1. distribute-lft-out 77.6%

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

      2. *-commutative 77.6%

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

   5. Simplified 77.6%

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

   6. Taylor expanded in i around inf 37.2%

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

      1. *-commutative 37.2%

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

   8. Simplified 37.2%

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

4. Final simplification 37.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{-79}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-284}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{+99}:\\ \;\;\;\;\left(x \cdot i\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 63.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{+41} \lor \neg \left(x \leq 1.16 \cdot 10^{+55}\right):\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\\ \end{array} \end{array} \]

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
 (if (or (<= x -1.8e+41) (not (<= x 1.16e+55)))
   (* x (- (* 18.0 (* t (* y z))) (* 4.0 i)))
   (- (* b c) (* 4.0 (+ (* x i) (* 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 tmp;
	if ((x <= -1.8e+41) || !(x <= 1.16e+55)) {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	} else {
		tmp = (b * c) - (4.0 * ((x * i) + (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) :: tmp
    if ((x <= (-1.8d+41)) .or. (.not. (x <= 1.16d+55))) then
        tmp = x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i))
    else
        tmp = (b * c) - (4.0d0 * ((x * i) + (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 tmp;
	if ((x <= -1.8e+41) || !(x <= 1.16e+55)) {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	} else {
		tmp = (b * c) - (4.0 * ((x * i) + (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):
	tmp = 0
	if (x <= -1.8e+41) or not (x <= 1.16e+55):
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i))
	else:
		tmp = (b * c) - (4.0 * ((x * i) + (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)
	tmp = 0.0
	if ((x <= -1.8e+41) || !(x <= 1.16e+55))
		tmp = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)));
	else
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(Float64(x * i) + 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)
	tmp = 0.0;
	if ((x <= -1.8e+41) || ~((x <= 1.16e+55)))
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	else
		tmp = (b * c) - (4.0 * ((x * i) + (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_] := If[Or[LessEqual[x, -1.8e+41], N[Not[LessEqual[x, 1.16e+55]], $MachinePrecision]], N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(N[(x * i), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.80000000000000013e41 or 1.1599999999999999e55 < x

   1. Initial program 72.0%

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

   3. Simplified 77.6%

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

   5. Taylor expanded in x around inf 78.3%

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

   if -1.80000000000000013e41 < x < 1.1599999999999999e55

   1. Initial program 93.9%

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

   3. Taylor expanded in y around 0 84.2%

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

      1. distribute-lft-out 84.2%

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

      2. *-commutative 84.2%

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

   5. Simplified 84.2%

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

   6. Taylor expanded in j around 0 62.2%

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

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{+41} \lor \neg \left(x \leq 1.16 \cdot 10^{+55}\right):\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 58.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{-79}:\\ \;\;\;\;18 \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot t\right)\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+116}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \end{array} \end{array} \]

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 (<= z -2.3e-79)
   (+ (* 18.0 (* (* y z) (* x t))) (* j (* k -27.0)))
   (if (<= z 1.1e+116)
     (- (* b c) (* 4.0 (+ (* x i) (* t a))))
     (* 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 (z <= -2.3e-79) {
		tmp = (18.0 * ((y * z) * (x * t))) + (j * (k * -27.0));
	} else if (z <= 1.1e+116) {
		tmp = (b * c) - (4.0 * ((x * i) + (t * a)));
	} 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 (z <= (-2.3d-79)) then
        tmp = (18.0d0 * ((y * z) * (x * t))) + (j * (k * (-27.0d0)))
    else if (z <= 1.1d+116) then
        tmp = (b * c) - (4.0d0 * ((x * i) + (t * a)))
    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 (z <= -2.3e-79) {
		tmp = (18.0 * ((y * z) * (x * t))) + (j * (k * -27.0));
	} else if (z <= 1.1e+116) {
		tmp = (b * c) - (4.0 * ((x * i) + (t * a)));
	} 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 z <= -2.3e-79:
		tmp = (18.0 * ((y * z) * (x * t))) + (j * (k * -27.0))
	elif z <= 1.1e+116:
		tmp = (b * c) - (4.0 * ((x * i) + (t * a)))
	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 (z <= -2.3e-79)
		tmp = Float64(Float64(18.0 * Float64(Float64(y * z) * Float64(x * t))) + Float64(j * Float64(k * -27.0)));
	elseif (z <= 1.1e+116)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(Float64(x * i) + Float64(t * a))));
	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 (z <= -2.3e-79)
		tmp = (18.0 * ((y * z) * (x * t))) + (j * (k * -27.0));
	elseif (z <= 1.1e+116)
		tmp = (b * c) - (4.0 * ((x * i) + (t * a)));
	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[z, -2.3e-79], N[(N[(18.0 * N[(N[(y * z), $MachinePrecision] * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.1e+116], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(N[(x * i), $MachinePrecision] + N[(t * a), $MachinePrecision]), $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 z < -2.30000000000000012e-79

   1. Initial program 82.7%

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

   3. Simplified 83.9%

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

   5. Taylor expanded in y around inf 59.8%

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

      1. associate-*r* 60.1%

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

   7. Simplified 60.1%

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

   if -2.30000000000000012e-79 < z < 1.1e116

   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 y around 0 82.2%

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

      1. distribute-lft-out 82.2%

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

      2. *-commutative 82.2%

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

   5. Simplified 82.2%

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

   6. Taylor expanded in j around 0 71.0%

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

   if 1.1e116 < z

   1. Initial program 86.8%

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

   3. Simplified 76.0%

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

   5. Taylor expanded in t around inf 47.2%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{-79}:\\ \;\;\;\;18 \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot t\right)\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+116}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i + t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 42.1% accurate, 1.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{-15} \lor \neg \left(z \leq 6.2 \cdot 10^{+104}\right):\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(c + -4 \cdot \left(i \cdot \frac{x}{b}\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= z -4.5e-15) (not (<= z 6.2e+104)))
   (* t (* 18.0 (* x (* y z))))
   (* b (+ c (* -4.0 (* i (/ x b)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((z <= -4.5e-15) || !(z <= 6.2e+104)) {
		tmp = t * (18.0 * (x * (y * z)));
	} else {
		tmp = b * (c + (-4.0 * (i * (x / b))));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((z <= (-4.5d-15)) .or. (.not. (z <= 6.2d+104))) then
        tmp = t * (18.0d0 * (x * (y * z)))
    else
        tmp = b * (c + ((-4.0d0) * (i * (x / b))))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((z <= -4.5e-15) || !(z <= 6.2e+104)) {
		tmp = t * (18.0 * (x * (y * z)));
	} else {
		tmp = b * (c + (-4.0 * (i * (x / b))));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (z <= -4.5e-15) or not (z <= 6.2e+104):
		tmp = t * (18.0 * (x * (y * z)))
	else:
		tmp = b * (c + (-4.0 * (i * (x / b))))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((z <= -4.5e-15) || !(z <= 6.2e+104))
		tmp = Float64(t * Float64(18.0 * Float64(x * Float64(y * z))));
	else
		tmp = Float64(b * Float64(c + Float64(-4.0 * Float64(i * Float64(x / b)))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((z <= -4.5e-15) || ~((z <= 6.2e+104)))
		tmp = t * (18.0 * (x * (y * z)));
	else
		tmp = b * (c + (-4.0 * (i * (x / b))));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[z, -4.5e-15], N[Not[LessEqual[z, 6.2e+104]], $MachinePrecision]], N[(t * N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(c + N[(-4.0 * N[(i * N[(x / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.4999999999999998e-15 or 6.20000000000000033e104 < z

   1. Initial program 82.2%

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

   3. Simplified 78.3%

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

   5. Taylor expanded in t around inf 53.4%

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

   6. Taylor expanded in x around inf 42.7%

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

   if -4.4999999999999998e-15 < z < 6.20000000000000033e104

   1. Initial program 87.1%

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

   3. Taylor expanded in t around 0 68.6%

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

   4. Taylor expanded in b around inf 63.8%

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

      1. associate-*r/ 63.8%

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

      2. mul-1-neg 63.8%

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

      3. associate-*r* 63.8%

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

      4. *-commutative 63.8%

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

      5. *-commutative 63.8%

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

      6. associate-*r* 63.8%

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

      7. distribute-neg-in 63.8%

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

      8. associate-*r* 63.8%

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

      9. distribute-lft-neg-out 63.8%

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

      10. *-commutative 63.8%

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

      11. distribute-rgt-neg-in 63.8%

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

      12. metadata-eval 63.8%

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

      13. associate-*r* 63.8%

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

      14. *-commutative 63.8%

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

      15. distribute-lft-neg-in 63.8%

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

      16. metadata-eval 63.8%

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

      17. *-commutative 63.8%

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

   6. Simplified 63.8%

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

   7. Taylor expanded in i around inf 52.6%

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

      1. associate-/l* 53.2%

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

   9. Simplified 53.2%

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

4. Final simplification 48.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{-15} \lor \neg \left(z \leq 6.2 \cdot 10^{+104}\right):\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(c + -4 \cdot \left(i \cdot \frac{x}{b}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 34.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2.3 \cdot 10^{+195} \lor \neg \left(b \cdot c \leq 1.8 \cdot 10^{+181}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot i\right) \cdot -4\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= (* b c) -2.3e+195) (not (<= (* b c) 1.8e+181)))
   (* b c)
   (* (* 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 (((b * c) <= -2.3e+195) || !((b * c) <= 1.8e+181)) {
		tmp = b * c;
	} 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 (((b * c) <= (-2.3d+195)) .or. (.not. ((b * c) <= 1.8d+181))) then
        tmp = b * c
    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 (((b * c) <= -2.3e+195) || !((b * c) <= 1.8e+181)) {
		tmp = b * c;
	} 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 ((b * c) <= -2.3e+195) or not ((b * c) <= 1.8e+181):
		tmp = b * c
	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 ((Float64(b * c) <= -2.3e+195) || !(Float64(b * c) <= 1.8e+181))
		tmp = Float64(b * c);
	else
		tmp = Float64(Float64(x * i) * -4.0);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (((b * c) <= -2.3e+195) || ~(((b * c) <= 1.8e+181)))
		tmp = b * c;
	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[Or[LessEqual[N[(b * c), $MachinePrecision], -2.3e+195], N[Not[LessEqual[N[(b * c), $MachinePrecision], 1.8e+181]], $MachinePrecision]], N[(b * c), $MachinePrecision], N[(N[(x * i), $MachinePrecision] * -4.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -2.3000000000000001e195 or 1.79999999999999992e181 < (*.f64 b c)

   1. Initial program 79.8%

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

   3. Taylor expanded in y around 0 81.7%

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

      1. distribute-lft-out 81.7%

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

      2. *-commutative 81.7%

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

   5. Simplified 81.7%

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

   6. Taylor expanded in b around inf 76.6%

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

   if -2.3000000000000001e195 < (*.f64 b c) < 1.79999999999999992e181

   1. Initial program 86.2%

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

   3. Taylor expanded in y around 0 72.0%

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

      1. distribute-lft-out 72.0%

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

      2. *-commutative 72.0%

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

   5. Simplified 72.0%

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

   6. Taylor expanded in i around inf 28.1%

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

      1. *-commutative 28.1%

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

   8. Simplified 28.1%

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

4. Final simplification 38.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2.3 \cdot 10^{+195} \lor \neg \left(b \cdot c \leq 1.8 \cdot 10^{+181}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot i\right) \cdot -4\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 36.7% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.12 \cdot 10^{+154} \lor \neg \left(b \cdot c \leq 1.2 \cdot 10^{+181}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \end{array} \]

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) -1.12e+154) (not (<= (* b c) 1.2e+181)))
   (* 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) <= -1.12e+154) || !((b * c) <= 1.2e+181)) {
		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) <= (-1.12d+154)) .or. (.not. ((b * c) <= 1.2d+181))) 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) <= -1.12e+154) || !((b * c) <= 1.2e+181)) {
		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) <= -1.12e+154) or not ((b * c) <= 1.2e+181):
		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) <= -1.12e+154) || !(Float64(b * c) <= 1.2e+181))
		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) <= -1.12e+154) || ~(((b * c) <= 1.2e+181)))
		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], -1.12e+154], N[Not[LessEqual[N[(b * c), $MachinePrecision], 1.2e+181]], $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) < -1.11999999999999994e154 or 1.20000000000000001e181 < (*.f64 b c)

   1. Initial program 79.8%

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

   3. Taylor expanded in 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%

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

   6. Taylor expanded in b around inf 71.9%

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

   if -1.11999999999999994e154 < (*.f64 b c) < 1.20000000000000001e181

   1. Initial program 86.4%

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

   3. Simplified 88.0%

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

   5. Taylor expanded in j around inf 23.1%

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

4. Final simplification 34.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.12 \cdot 10^{+154} \lor \neg \left(b \cdot c \leq 1.2 \cdot 10^{+181}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 23.1% accurate, 10.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 84.9%

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

3. Taylor expanded in y around 0 74.0%

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

   1. distribute-lft-out 74.0%

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

   2. *-commutative 74.0%

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

5. Simplified 74.0%

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

6. Taylor expanded in b around inf 22.9%

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

Developer Target 1: 89.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a \cdot t + i \cdot x\right) \cdot 4\\ t_2 := \left(\left(18 \cdot t\right) \cdot \left(\left(x \cdot y\right) \cdot z\right) - t\_1\right) - \left(\left(k \cdot j\right) \cdot 27 - c \cdot b\right)\\ \mathbf{if}\;t < -1.6210815397541398 \cdot 10^{-69}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t < 165.68027943805222:\\ \;\;\;\;\left(\left(18 \cdot y\right) \cdot \left(x \cdot \left(z \cdot t\right)\right) - t\_1\right) + \left(c \cdot b - 27 \cdot \left(k \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (+ (* a t) (* i x)) 4.0))
        (t_2
         (-
          (- (* (* 18.0 t) (* (* x y) z)) t_1)
          (- (* (* k j) 27.0) (* c b)))))
   (if (< t -1.6210815397541398e-69)
     t_2
     (if (< t 165.68027943805222)
       (+ (- (* (* 18.0 y) (* x (* z t))) t_1) (- (* c b) (* 27.0 (* k j))))
       t_2))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((a * t) + (i * x)) * 4.0;
	double t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b));
	double tmp;
	if (t < -1.6210815397541398e-69) {
		tmp = t_2;
	} else if (t < 165.68027943805222) {
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((a * t) + (i * x)) * 4.0d0
    t_2 = (((18.0d0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0d0) - (c * b))
    if (t < (-1.6210815397541398d-69)) then
        tmp = t_2
    else if (t < 165.68027943805222d0) then
        tmp = (((18.0d0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0d0 * (k * j)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((a * t) + (i * x)) * 4.0;
	double t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b));
	double tmp;
	if (t < -1.6210815397541398e-69) {
		tmp = t_2;
	} else if (t < 165.68027943805222) {
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = ((a * t) + (i * x)) * 4.0
	t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b))
	tmp = 0
	if t < -1.6210815397541398e-69:
		tmp = t_2
	elif t < 165.68027943805222:
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(Float64(a * t) + Float64(i * x)) * 4.0)
	t_2 = Float64(Float64(Float64(Float64(18.0 * t) * Float64(Float64(x * y) * z)) - t_1) - Float64(Float64(Float64(k * j) * 27.0) - Float64(c * b)))
	tmp = 0.0
	if (t < -1.6210815397541398e-69)
		tmp = t_2;
	elseif (t < 165.68027943805222)
		tmp = Float64(Float64(Float64(Float64(18.0 * y) * Float64(x * Float64(z * t))) - t_1) + Float64(Float64(c * b) - Float64(27.0 * Float64(k * j))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = ((a * t) + (i * x)) * 4.0;
	t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b));
	tmp = 0.0;
	if (t < -1.6210815397541398e-69)
		tmp = t_2;
	elseif (t < 165.68027943805222)
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(N[(a * t), $MachinePrecision] + N[(i * x), $MachinePrecision]), $MachinePrecision] * 4.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(18.0 * t), $MachinePrecision] * N[(N[(x * y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] - N[(N[(N[(k * j), $MachinePrecision] * 27.0), $MachinePrecision] - N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -1.6210815397541398e-69], t$95$2, If[Less[t, 165.68027943805222], N[(N[(N[(N[(18.0 * y), $MachinePrecision] * N[(x * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] + N[(N[(c * b), $MachinePrecision] - N[(27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2024182 
(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)))