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

Percentage Accurate: 85.2% → 91.5%

Time: 33.4s

Alternatives: 22

Speedup: 0.8×

• 50.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 91.5% accurate, 0.2× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 95.6%

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

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

   1. Initial program 0.0%

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

   3. Simplified 22.6%

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

   5. Taylor expanded in x around inf 61.4%

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

      1. fma-def 61.4%

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

      2. associate-*r* 58.2%

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

   7. Simplified 58.2%

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

4. Final simplification 91.1%

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

Alternative 2: 87.8% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
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 = (j * (k * -27.0)) + (-4.0 * (t * a));
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 95.6%

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

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

   1. Initial program 0.0%

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

   3. Simplified 22.6%

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

   5. Taylor expanded in a around inf 52.5%

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

      1. *-commutative 52.5%

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

   7. Simplified 52.5%

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

4. Final simplification 90.4%

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

Alternative 3: 78.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ t_2 := 4 \cdot \left(x \cdot i\right)\\ t_3 := \left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\right) - t_2\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{+266}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;t_1 \leq -5 \cdot 10^{+190}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_1 \leq -1 \cdot 10^{-25}:\\ \;\;\;\;\left(b \cdot c - t_2\right) - t_1\\ \mathbf{elif}\;t_1 \leq 10^{+116}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - t_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k))
        (t_2 (* 4.0 (* x i)))
        (t_3 (- (+ (* b c) (* t (- (* 18.0 (* x (* y z))) (* a 4.0)))) t_2)))
   (if (<= t_1 -2e+266)
     (+ (* j (* k -27.0)) (* -4.0 (* t a)))
     (if (<= t_1 -5e+190)
       t_3
       (if (<= t_1 -1e-25)
         (- (- (* b c) t_2) t_1)
         (if (<= t_1 1e+116) t_3 (- (- (* b c) (* 4.0 (* t a))) t_1)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double t_2 = 4.0 * (x * i);
	double t_3 = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - t_2;
	double tmp;
	if (t_1 <= -2e+266) {
		tmp = (j * (k * -27.0)) + (-4.0 * (t * a));
	} else if (t_1 <= -5e+190) {
		tmp = t_3;
	} else if (t_1 <= -1e-25) {
		tmp = ((b * c) - t_2) - t_1;
	} else if (t_1 <= 1e+116) {
		tmp = t_3;
	} else {
		tmp = ((b * c) - (4.0 * (t * a))) - t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (j * 27.0d0) * k
    t_2 = 4.0d0 * (x * i)
    t_3 = ((b * c) + (t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0)))) - t_2
    if (t_1 <= (-2d+266)) then
        tmp = (j * (k * (-27.0d0))) + ((-4.0d0) * (t * a))
    else if (t_1 <= (-5d+190)) then
        tmp = t_3
    else if (t_1 <= (-1d-25)) then
        tmp = ((b * c) - t_2) - t_1
    else if (t_1 <= 1d+116) then
        tmp = t_3
    else
        tmp = ((b * c) - (4.0d0 * (t * a))) - t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double t_2 = 4.0 * (x * i);
	double t_3 = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - t_2;
	double tmp;
	if (t_1 <= -2e+266) {
		tmp = (j * (k * -27.0)) + (-4.0 * (t * a));
	} else if (t_1 <= -5e+190) {
		tmp = t_3;
	} else if (t_1 <= -1e-25) {
		tmp = ((b * c) - t_2) - t_1;
	} else if (t_1 <= 1e+116) {
		tmp = t_3;
	} else {
		tmp = ((b * c) - (4.0 * (t * a))) - t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	t_2 = 4.0 * (x * i)
	t_3 = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - t_2
	tmp = 0
	if t_1 <= -2e+266:
		tmp = (j * (k * -27.0)) + (-4.0 * (t * a))
	elif t_1 <= -5e+190:
		tmp = t_3
	elif t_1 <= -1e-25:
		tmp = ((b * c) - t_2) - t_1
	elif t_1 <= 1e+116:
		tmp = t_3
	else:
		tmp = ((b * c) - (4.0 * (t * a))) - t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	t_2 = Float64(4.0 * Float64(x * i))
	t_3 = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)))) - t_2)
	tmp = 0.0
	if (t_1 <= -2e+266)
		tmp = Float64(Float64(j * Float64(k * -27.0)) + Float64(-4.0 * Float64(t * a)));
	elseif (t_1 <= -5e+190)
		tmp = t_3;
	elseif (t_1 <= -1e-25)
		tmp = Float64(Float64(Float64(b * c) - t_2) - t_1);
	elseif (t_1 <= 1e+116)
		tmp = t_3;
	else
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(t * a))) - t_1);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * 27.0) * k;
	t_2 = 4.0 * (x * i);
	t_3 = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - t_2;
	tmp = 0.0;
	if (t_1 <= -2e+266)
		tmp = (j * (k * -27.0)) + (-4.0 * (t * a));
	elseif (t_1 <= -5e+190)
		tmp = t_3;
	elseif (t_1 <= -1e-25)
		tmp = ((b * c) - t_2) - t_1;
	elseif (t_1 <= 1e+116)
		tmp = t_3;
	else
		tmp = ((b * c) - (4.0 * (t * a))) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, Block[{t$95$2 = N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+266], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -5e+190], t$95$3, If[LessEqual[t$95$1, -1e-25], N[(N[(N[(b * c), $MachinePrecision] - t$95$2), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[t$95$1, 1e+116], t$95$3, N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 j 27) k) < -2.0000000000000001e266

   1. Initial program 55.5%

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

   3. Simplified 59.2%

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

   5. Taylor expanded in a around inf 82.2%

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

      1. *-commutative 82.2%

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

   7. Simplified 82.2%

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

   if -2.0000000000000001e266 < (*.f64 (*.f64 j 27) k) < -5.00000000000000036e190 or -1.00000000000000004e-25 < (*.f64 (*.f64 j 27) k) < 1.00000000000000002e116

   1. Initial program 89.9%

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

   3. Simplified 90.7%

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

   5. Taylor expanded in j around 0 87.1%

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

   if -5.00000000000000036e190 < (*.f64 (*.f64 j 27) k) < -1.00000000000000004e-25

   1. Initial program 81.2%

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

   3. Taylor expanded in t around 0 76.2%

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

   if 1.00000000000000002e116 < (*.f64 (*.f64 j 27) k)

   1. Initial program 82.5%

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

   3. Taylor expanded in x around 0 76.8%

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

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \leq -2 \cdot 10^{+266}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq -5 \cdot 10^{+190}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq -1 \cdot 10^{-25}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 10^{+116}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 48.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c - 4 \cdot \left(t \cdot a\right)\\ t_2 := j \cdot \left(k \cdot -27\right)\\ t_3 := t_2 + x \cdot \left(i \cdot -4\right)\\ \mathbf{if}\;j \leq -2.7 \cdot 10^{+203}:\\ \;\;\;\;t_2 + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;j \leq -1 \cdot 10^{+102}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq -4.4 \cdot 10^{+35}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -1.35 \cdot 10^{-17}:\\ \;\;\;\;18 \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot t\right)\right)\\ \mathbf{elif}\;j \leq 2 \cdot 10^{-198}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 1.56 \cdot 10^{-114}:\\ \;\;\;\;z \cdot \left(t \cdot \left(x \cdot \left(18 \cdot y\right)\right)\right)\\ \mathbf{elif}\;j \leq 4.4 \cdot 10^{-28}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right) + k \cdot \left(j \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (- (* b c) (* 4.0 (* t a))))
        (t_2 (* j (* k -27.0)))
        (t_3 (+ t_2 (* x (* i -4.0)))))
   (if (<= j -2.7e+203)
     (+ t_2 (* -4.0 (* t a)))
     (if (<= j -1e+102)
       t_3
       (if (<= j -4.4e+35)
         t_1
         (if (<= j -1.35e-17)
           (* 18.0 (* (* y z) (* x t)))
           (if (<= j 2e-198)
             t_1
             (if (<= j 1.56e-114)
               (* z (* t (* x (* 18.0 y))))
               (if (<= j 4.4e-28)
                 (+ (* t (* a -4.0)) (* k (* j -27.0)))
                 t_3)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) - (4.0 * (t * a));
	double t_2 = j * (k * -27.0);
	double t_3 = t_2 + (x * (i * -4.0));
	double tmp;
	if (j <= -2.7e+203) {
		tmp = t_2 + (-4.0 * (t * a));
	} else if (j <= -1e+102) {
		tmp = t_3;
	} else if (j <= -4.4e+35) {
		tmp = t_1;
	} else if (j <= -1.35e-17) {
		tmp = 18.0 * ((y * z) * (x * t));
	} else if (j <= 2e-198) {
		tmp = t_1;
	} else if (j <= 1.56e-114) {
		tmp = z * (t * (x * (18.0 * y)));
	} else if (j <= 4.4e-28) {
		tmp = (t * (a * -4.0)) + (k * (j * -27.0));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (b * c) - (4.0d0 * (t * a))
    t_2 = j * (k * (-27.0d0))
    t_3 = t_2 + (x * (i * (-4.0d0)))
    if (j <= (-2.7d+203)) then
        tmp = t_2 + ((-4.0d0) * (t * a))
    else if (j <= (-1d+102)) then
        tmp = t_3
    else if (j <= (-4.4d+35)) then
        tmp = t_1
    else if (j <= (-1.35d-17)) then
        tmp = 18.0d0 * ((y * z) * (x * t))
    else if (j <= 2d-198) then
        tmp = t_1
    else if (j <= 1.56d-114) then
        tmp = z * (t * (x * (18.0d0 * y)))
    else if (j <= 4.4d-28) then
        tmp = (t * (a * (-4.0d0))) + (k * (j * (-27.0d0)))
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) - (4.0 * (t * a));
	double t_2 = j * (k * -27.0);
	double t_3 = t_2 + (x * (i * -4.0));
	double tmp;
	if (j <= -2.7e+203) {
		tmp = t_2 + (-4.0 * (t * a));
	} else if (j <= -1e+102) {
		tmp = t_3;
	} else if (j <= -4.4e+35) {
		tmp = t_1;
	} else if (j <= -1.35e-17) {
		tmp = 18.0 * ((y * z) * (x * t));
	} else if (j <= 2e-198) {
		tmp = t_1;
	} else if (j <= 1.56e-114) {
		tmp = z * (t * (x * (18.0 * y)));
	} else if (j <= 4.4e-28) {
		tmp = (t * (a * -4.0)) + (k * (j * -27.0));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) - (4.0 * (t * a))
	t_2 = j * (k * -27.0)
	t_3 = t_2 + (x * (i * -4.0))
	tmp = 0
	if j <= -2.7e+203:
		tmp = t_2 + (-4.0 * (t * a))
	elif j <= -1e+102:
		tmp = t_3
	elif j <= -4.4e+35:
		tmp = t_1
	elif j <= -1.35e-17:
		tmp = 18.0 * ((y * z) * (x * t))
	elif j <= 2e-198:
		tmp = t_1
	elif j <= 1.56e-114:
		tmp = z * (t * (x * (18.0 * y)))
	elif j <= 4.4e-28:
		tmp = (t * (a * -4.0)) + (k * (j * -27.0))
	else:
		tmp = t_3
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) - Float64(4.0 * Float64(t * a)))
	t_2 = Float64(j * Float64(k * -27.0))
	t_3 = Float64(t_2 + Float64(x * Float64(i * -4.0)))
	tmp = 0.0
	if (j <= -2.7e+203)
		tmp = Float64(t_2 + Float64(-4.0 * Float64(t * a)));
	elseif (j <= -1e+102)
		tmp = t_3;
	elseif (j <= -4.4e+35)
		tmp = t_1;
	elseif (j <= -1.35e-17)
		tmp = Float64(18.0 * Float64(Float64(y * z) * Float64(x * t)));
	elseif (j <= 2e-198)
		tmp = t_1;
	elseif (j <= 1.56e-114)
		tmp = Float64(z * Float64(t * Float64(x * Float64(18.0 * y))));
	elseif (j <= 4.4e-28)
		tmp = Float64(Float64(t * Float64(a * -4.0)) + Float64(k * Float64(j * -27.0)));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) - (4.0 * (t * a));
	t_2 = j * (k * -27.0);
	t_3 = t_2 + (x * (i * -4.0));
	tmp = 0.0;
	if (j <= -2.7e+203)
		tmp = t_2 + (-4.0 * (t * a));
	elseif (j <= -1e+102)
		tmp = t_3;
	elseif (j <= -4.4e+35)
		tmp = t_1;
	elseif (j <= -1.35e-17)
		tmp = 18.0 * ((y * z) * (x * t));
	elseif (j <= 2e-198)
		tmp = t_1;
	elseif (j <= 1.56e-114)
		tmp = z * (t * (x * (18.0 * y)));
	elseif (j <= 4.4e-28)
		tmp = (t * (a * -4.0)) + (k * (j * -27.0));
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 + N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -2.7e+203], N[(t$95$2 + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1e+102], t$95$3, If[LessEqual[j, -4.4e+35], t$95$1, If[LessEqual[j, -1.35e-17], N[(18.0 * N[(N[(y * z), $MachinePrecision] * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2e-198], t$95$1, If[LessEqual[j, 1.56e-114], N[(z * N[(t * N[(x * N[(18.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 4.4e-28], N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if j < -2.7e203

   1. Initial program 74.0%

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

   3. Simplified 77.6%

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

   5. Taylor expanded in a around inf 78.4%

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

      1. *-commutative 78.4%

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

   7. Simplified 78.4%

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

   if -2.7e203 < j < -9.99999999999999977e101 or 4.39999999999999992e-28 < j

   1. Initial program 79.4%

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

   3. Simplified 79.6%

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

   5. Taylor expanded in i around inf 55.0%

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

      1. associate-*r* 55.0%

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

      2. *-commutative 55.0%

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

   7. Simplified 55.0%

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

   if -9.99999999999999977e101 < j < -4.3999999999999997e35 or -1.3500000000000001e-17 < j < 1.9999999999999998e-198

   1. Initial program 87.9%

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

   3. Simplified 90.1%

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

      1. associate-*r* 87.9%

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

      2. distribute-rgt-out-- 87.9%

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

      3. associate-+l- 87.9%

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

      4. associate-*l* 88.8%

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

      5. *-commutative 88.8%

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

      6. *-commutative 88.8%

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

      7. fma-neg 88.8%

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

   6. Applied egg-rr 88.8%

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

   7. Taylor expanded in x around inf 81.8%

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

      1. associate-*r* 81.8%

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

      2. *-commutative 81.8%

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

   9. Simplified 81.8%

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

   10. Taylor expanded in x around 0 56.0%

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

   if -4.3999999999999997e35 < j < -1.3500000000000001e-17

   1. Initial program 83.3%

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

   3. Simplified 83.1%

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

      1. associate-*r* 83.1%

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

      2. distribute-rgt-out-- 83.1%

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

      3. associate-*l* 83.1%

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

      4. *-commutative 83.1%

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

      5. *-commutative 83.1%

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

   6. Applied egg-rr 83.1%

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

   7. Taylor expanded in y around inf 67.8%

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

      1. associate-*r* 67.8%

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

   9. Simplified 67.8%

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

   if 1.9999999999999998e-198 < j < 1.5599999999999999e-114

   1. Initial program 90.8%

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

   3. Simplified 86.4%

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

      1. associate-*r* 90.8%

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

      2. distribute-rgt-out-- 90.8%

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

      3. associate-*l* 86.2%

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

      4. *-commutative 86.2%

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

      5. *-commutative 86.2%

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

   6. Applied egg-rr 86.2%

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

   7. Taylor expanded in y around inf 20.0%

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

      1. *-commutative 20.0%

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

      2. associate-*r* 20.0%

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

      3. associate-*r* 20.0%

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

      4. *-commutative 20.0%

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

      5. associate-*r* 20.2%

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

      6. *-commutative 20.2%

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

      7. *-commutative 20.2%

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

      8. associate-*l* 20.1%

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

      9. *-commutative 20.1%

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

      10. associate-*l* 20.2%

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

   9. Simplified 20.2%

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

   if 1.5599999999999999e-114 < j < 4.39999999999999992e-28

   1. Initial program 93.7%

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

   3. Taylor expanded in x around 0 45.9%

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

   4. Taylor expanded in b around 0 43.8%

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

      1. mul-1-neg 43.8%

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

      2. associate-*r* 43.8%

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

      3. *-commutative 43.8%

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

      4. *-commutative 43.8%

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

      5. associate-*r* 43.8%

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

      6. *-commutative 43.8%

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

      7. associate-*r* 43.8%

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

      8. distribute-neg-in 43.8%

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

      9. distribute-rgt-neg-in 43.8%

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

      10. distribute-rgt-neg-in 43.8%

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

      11. metadata-eval 43.8%

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

      12. associate-*r* 43.8%

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

      13. distribute-lft-neg-out 43.8%

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

      14. *-commutative 43.8%

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

      15. distribute-rgt-neg-in 43.8%

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

      16. metadata-eval 43.8%

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

   6. Simplified 43.8%

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

4. Final simplification 54.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.7 \cdot 10^{+203}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;j \leq -1 \cdot 10^{+102}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;j \leq -4.4 \cdot 10^{+35}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;j \leq -1.35 \cdot 10^{-17}:\\ \;\;\;\;18 \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot t\right)\right)\\ \mathbf{elif}\;j \leq 2 \cdot 10^{-198}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;j \leq 1.56 \cdot 10^{-114}:\\ \;\;\;\;z \cdot \left(t \cdot \left(x \cdot \left(18 \cdot y\right)\right)\right)\\ \mathbf{elif}\;j \leq 4.4 \cdot 10^{-28}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right) + k \cdot \left(j \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + x \cdot \left(i \cdot -4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 32.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ t_2 := -27 \cdot \left(j \cdot k\right)\\ \mathbf{if}\;j \leq -2.8 \cdot 10^{+150}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -3.2 \cdot 10^{+103}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;j \leq -1.3 \cdot 10^{+78}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;j \leq -3.3 \cdot 10^{+41}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -1.45 \cdot 10^{-19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 2.45 \cdot 10^{-206}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;j \leq 3.3 \cdot 10^{-114}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* 18.0 (* t (* x (* y z))))) (t_2 (* -27.0 (* j k))))
   (if (<= j -2.8e+150)
     t_2
     (if (<= j -3.2e+103)
       (* x (* i -4.0))
       (if (<= j -1.3e+78)
         (* -4.0 (* t a))
         (if (<= j -3.3e+41)
           t_2
           (if (<= j -1.45e-19)
             t_1
             (if (<= j 2.45e-206)
               (* b c)
               (if (<= j 3.3e-114) t_1 (* k (* j -27.0)))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 18.0 * (t * (x * (y * z)));
	double t_2 = -27.0 * (j * k);
	double tmp;
	if (j <= -2.8e+150) {
		tmp = t_2;
	} else if (j <= -3.2e+103) {
		tmp = x * (i * -4.0);
	} else if (j <= -1.3e+78) {
		tmp = -4.0 * (t * a);
	} else if (j <= -3.3e+41) {
		tmp = t_2;
	} else if (j <= -1.45e-19) {
		tmp = t_1;
	} else if (j <= 2.45e-206) {
		tmp = b * c;
	} else if (j <= 3.3e-114) {
		tmp = t_1;
	} else {
		tmp = k * (j * -27.0);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 18.0d0 * (t * (x * (y * z)))
    t_2 = (-27.0d0) * (j * k)
    if (j <= (-2.8d+150)) then
        tmp = t_2
    else if (j <= (-3.2d+103)) then
        tmp = x * (i * (-4.0d0))
    else if (j <= (-1.3d+78)) then
        tmp = (-4.0d0) * (t * a)
    else if (j <= (-3.3d+41)) then
        tmp = t_2
    else if (j <= (-1.45d-19)) then
        tmp = t_1
    else if (j <= 2.45d-206) then
        tmp = b * c
    else if (j <= 3.3d-114) then
        tmp = t_1
    else
        tmp = k * (j * (-27.0d0))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 18.0 * (t * (x * (y * z)));
	double t_2 = -27.0 * (j * k);
	double tmp;
	if (j <= -2.8e+150) {
		tmp = t_2;
	} else if (j <= -3.2e+103) {
		tmp = x * (i * -4.0);
	} else if (j <= -1.3e+78) {
		tmp = -4.0 * (t * a);
	} else if (j <= -3.3e+41) {
		tmp = t_2;
	} else if (j <= -1.45e-19) {
		tmp = t_1;
	} else if (j <= 2.45e-206) {
		tmp = b * c;
	} else if (j <= 3.3e-114) {
		tmp = t_1;
	} else {
		tmp = k * (j * -27.0);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = 18.0 * (t * (x * (y * z)))
	t_2 = -27.0 * (j * k)
	tmp = 0
	if j <= -2.8e+150:
		tmp = t_2
	elif j <= -3.2e+103:
		tmp = x * (i * -4.0)
	elif j <= -1.3e+78:
		tmp = -4.0 * (t * a)
	elif j <= -3.3e+41:
		tmp = t_2
	elif j <= -1.45e-19:
		tmp = t_1
	elif j <= 2.45e-206:
		tmp = b * c
	elif j <= 3.3e-114:
		tmp = t_1
	else:
		tmp = k * (j * -27.0)
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(18.0 * Float64(t * Float64(x * Float64(y * z))))
	t_2 = Float64(-27.0 * Float64(j * k))
	tmp = 0.0
	if (j <= -2.8e+150)
		tmp = t_2;
	elseif (j <= -3.2e+103)
		tmp = Float64(x * Float64(i * -4.0));
	elseif (j <= -1.3e+78)
		tmp = Float64(-4.0 * Float64(t * a));
	elseif (j <= -3.3e+41)
		tmp = t_2;
	elseif (j <= -1.45e-19)
		tmp = t_1;
	elseif (j <= 2.45e-206)
		tmp = Float64(b * c);
	elseif (j <= 3.3e-114)
		tmp = t_1;
	else
		tmp = Float64(k * Float64(j * -27.0));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = 18.0 * (t * (x * (y * z)));
	t_2 = -27.0 * (j * k);
	tmp = 0.0;
	if (j <= -2.8e+150)
		tmp = t_2;
	elseif (j <= -3.2e+103)
		tmp = x * (i * -4.0);
	elseif (j <= -1.3e+78)
		tmp = -4.0 * (t * a);
	elseif (j <= -3.3e+41)
		tmp = t_2;
	elseif (j <= -1.45e-19)
		tmp = t_1;
	elseif (j <= 2.45e-206)
		tmp = b * c;
	elseif (j <= 3.3e-114)
		tmp = t_1;
	else
		tmp = k * (j * -27.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -2.8e+150], t$95$2, If[LessEqual[j, -3.2e+103], N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.3e+78], N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -3.3e+41], t$95$2, If[LessEqual[j, -1.45e-19], t$95$1, If[LessEqual[j, 2.45e-206], N[(b * c), $MachinePrecision], If[LessEqual[j, 3.3e-114], t$95$1, N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if j < -2.80000000000000009e150 or -1.3e78 < j < -3.3e41

   1. Initial program 80.0%

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

   3. Simplified 82.4%

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

   5. Taylor expanded in j around inf 55.2%

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

   if -2.80000000000000009e150 < j < -3.19999999999999993e103

   1. Initial program 90.9%

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

   3. Simplified 90.8%

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

      1. associate-*r* 90.9%

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

      2. distribute-rgt-out-- 90.9%

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

      3. associate-+l- 90.9%

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

      4. associate-*l* 73.2%

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

      5. *-commutative 73.2%

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

      6. *-commutative 73.2%

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

      7. fma-neg 73.2%

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

   6. Applied egg-rr 73.2%

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

   7. Taylor expanded in i around inf 19.7%

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

      1. *-commutative 19.7%

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

      2. *-commutative 19.7%

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

      3. associate-*r* 19.7%

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

   9. Simplified 19.7%

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

   if -3.19999999999999993e103 < j < -1.3e78

   1. Initial program 75.0%

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

   3. Simplified 100.0%

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

      1. associate-*r* 75.0%

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

      2. distribute-rgt-out-- 75.0%

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

      3. associate-+l- 75.0%

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

      4. associate-*l* 75.0%

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

      5. *-commutative 75.0%

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

      6. *-commutative 75.0%

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

      7. fma-neg 75.0%

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

   6. Applied egg-rr 75.0%

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

   7. Taylor expanded in a around inf 51.4%

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

      1. *-commutative 51.4%

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

      2. *-commutative 51.4%

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

   9. Simplified 51.4%

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

   if -3.3e41 < j < -1.45e-19 or 2.45e-206 < j < 3.30000000000000035e-114

   1. Initial program 91.3%

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

   3. Simplified 88.6%

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

      1. associate-*r* 91.3%

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

      2. distribute-rgt-out-- 91.3%

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

      3. associate-*l* 88.4%

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

      4. *-commutative 88.4%

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

      5. *-commutative 88.4%

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

   6. Applied egg-rr 88.4%

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

   7. Taylor expanded in y around inf 30.3%

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

   if -1.45e-19 < j < 2.45e-206

   1. Initial program 86.1%

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

   3. Simplified 87.5%

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

      1. associate-*r* 86.1%

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

      2. distribute-rgt-out-- 86.1%

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

      3. associate-+l- 86.1%

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

      4. associate-*l* 88.4%

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

      5. *-commutative 88.4%

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

      6. *-commutative 88.4%

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

      7. fma-neg 88.5%

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

   6. Applied egg-rr 88.5%

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

   7. Taylor expanded in b around inf 36.0%

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

   if 3.30000000000000035e-114 < j

   1. Initial program 80.8%

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

   3. Simplified 82.1%

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

      1. associate-*r* 80.8%

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

      2. distribute-rgt-out-- 80.8%

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

      3. associate-+l- 80.8%

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

      4. associate-*l* 80.9%

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

      5. *-commutative 80.9%

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

      6. *-commutative 80.9%

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

      7. fma-neg 80.9%

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

   6. Applied egg-rr 80.9%

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

   7. Taylor expanded in j around inf 35.9%

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

      1. associate-*r* 35.8%

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

      2. *-commutative 35.8%

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

      3. *-commutative 35.8%

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

   9. Simplified 35.8%

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

4. Final simplification 37.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.8 \cdot 10^{+150}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;j \leq -3.2 \cdot 10^{+103}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;j \leq -1.3 \cdot 10^{+78}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;j \leq -3.3 \cdot 10^{+41}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;j \leq -1.45 \cdot 10^{-19}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;j \leq 2.45 \cdot 10^{-206}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;j \leq 3.3 \cdot 10^{-114}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 87.6% accurate, 0.8× speedup

Math

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

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= (* (* j 27.0) k) (- INFINITY))
   (* -27.0 (* j k))
   (-
    (+ (* 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);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (((j * 27.0) * k) <= -((double) INFINITY)) {
		tmp = -27.0 * (j * k);
	} else {
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	}
	return tmp;
}

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (((j * 27.0) * k) <= -Double.POSITIVE_INFINITY) {
		tmp = -27.0 * (j * k);
	} 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])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if ((j * 27.0) * k) <= -math.inf:
		tmp = -27.0 * (j * k)
	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])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (Float64(Float64(j * 27.0) * k) <= Float64(-Inf))
		tmp = Float64(-27.0 * Float64(j * k));
	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])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (((j * 27.0) * k) <= -Inf)
		tmp = -27.0 * (j * k);
	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.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision], (-Infinity)], N[(-27.0 * N[(j * k), $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 (*.f64 (*.f64 j 27) k) < -inf.0

   1. Initial program 42.9%

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

   3. Simplified 47.6%

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

   5. Taylor expanded in j around inf 85.7%

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

   if -inf.0 < (*.f64 (*.f64 j 27) k)

   1. Initial program 87.7%

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

   3. Simplified 88.7%

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

4. Final simplification 88.5%

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

Alternative 7: 62.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ t_2 := x \cdot \left(z \cdot \left(y \cdot \left(18 \cdot t\right)\right) - 4 \cdot i\right)\\ \mathbf{if}\;y \leq -8.6 \cdot 10^{+250}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{+176}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{+117}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-29}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (- (- (* b c) (* 4.0 (* t a))) (* (* j 27.0) k)))
        (t_2 (* x (- (* z (* y (* 18.0 t))) (* 4.0 i)))))
   (if (<= y -8.6e+250)
     t_2
     (if (<= y -2.9e+176)
       t_1
       (if (<= y -7.2e+117)
         (* x (- (* 18.0 (* t (* y z))) (* 4.0 i)))
         (if (<= y 8.2e-29) t_1 t_2))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k);
	double t_2 = x * ((z * (y * (18.0 * t))) - (4.0 * i));
	double tmp;
	if (y <= -8.6e+250) {
		tmp = t_2;
	} else if (y <= -2.9e+176) {
		tmp = t_1;
	} else if (y <= -7.2e+117) {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	} else if (y <= 8.2e-29) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((b * c) - (4.0d0 * (t * a))) - ((j * 27.0d0) * k)
    t_2 = x * ((z * (y * (18.0d0 * t))) - (4.0d0 * i))
    if (y <= (-8.6d+250)) then
        tmp = t_2
    else if (y <= (-2.9d+176)) then
        tmp = t_1
    else if (y <= (-7.2d+117)) then
        tmp = x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i))
    else if (y <= 8.2d-29) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k);
	double t_2 = x * ((z * (y * (18.0 * t))) - (4.0 * i));
	double tmp;
	if (y <= -8.6e+250) {
		tmp = t_2;
	} else if (y <= -2.9e+176) {
		tmp = t_1;
	} else if (y <= -7.2e+117) {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	} else if (y <= 8.2e-29) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k)
	t_2 = x * ((z * (y * (18.0 * t))) - (4.0 * i))
	tmp = 0
	if y <= -8.6e+250:
		tmp = t_2
	elif y <= -2.9e+176:
		tmp = t_1
	elif y <= -7.2e+117:
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i))
	elif y <= 8.2e-29:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(t * a))) - Float64(Float64(j * 27.0) * k))
	t_2 = Float64(x * Float64(Float64(z * Float64(y * Float64(18.0 * t))) - Float64(4.0 * i)))
	tmp = 0.0
	if (y <= -8.6e+250)
		tmp = t_2;
	elseif (y <= -2.9e+176)
		tmp = t_1;
	elseif (y <= -7.2e+117)
		tmp = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)));
	elseif (y <= 8.2e-29)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k);
	t_2 = x * ((z * (y * (18.0 * t))) - (4.0 * i));
	tmp = 0.0;
	if (y <= -8.6e+250)
		tmp = t_2;
	elseif (y <= -2.9e+176)
		tmp = t_1;
	elseif (y <= -7.2e+117)
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	elseif (y <= 8.2e-29)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(z * N[(y * N[(18.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8.6e+250], t$95$2, If[LessEqual[y, -2.9e+176], t$95$1, If[LessEqual[y, -7.2e+117], N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.2e-29], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.6e250 or 8.1999999999999996e-29 < y

   1. Initial program 76.9%

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

   3. Simplified 77.1%

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

   5. Taylor expanded in x around inf 58.2%

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

      1. expm1-log1p-u 35.0%

         \[\leadsto x \cdot \left(\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\right)} - 4 \cdot i\right) \]

      2. expm1-udef 35.0%

         \[\leadsto x \cdot \left(\color{blue}{\left(e^{\mathsf{log1p}\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} - 1\right)} - 4 \cdot i\right) \]

      3. associate-*r* 35.0%

         \[\leadsto x \cdot \left(\left(e^{\mathsf{log1p}\left(\color{blue}{\left(18 \cdot t\right) \cdot \left(y \cdot z\right)}\right)} - 1\right) - 4 \cdot i\right) \]

   7. Applied egg-rr 35.0%

      \[\leadsto x \cdot \left(\color{blue}{\left(e^{\mathsf{log1p}\left(\left(18 \cdot t\right) \cdot \left(y \cdot z\right)\right)} - 1\right)} - 4 \cdot i\right) \]
   8. Step-by-step derivation

      1. expm1-def 35.0%

         \[\leadsto x \cdot \left(\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\left(18 \cdot t\right) \cdot \left(y \cdot z\right)\right)\right)} - 4 \cdot i\right) \]

      2. expm1-log1p 58.2%

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

      3. associate-*r* 59.6%

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

      4. *-commutative 59.6%

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

   9. Simplified 59.6%

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

   if -8.6e250 < y < -2.9000000000000001e176 or -7.20000000000000025e117 < y < 8.1999999999999996e-29

   1. Initial program 88.0%

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

   3. Taylor expanded in x around 0 72.8%

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

   if -2.9000000000000001e176 < y < -7.20000000000000025e117

   1. Initial program 75.2%

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

   3. Simplified 69.5%

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

   5. Taylor expanded in x around inf 58.0%

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

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.6 \cdot 10^{+250}:\\ \;\;\;\;x \cdot \left(z \cdot \left(y \cdot \left(18 \cdot t\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{+176}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{+117}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-29}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot \left(y \cdot \left(18 \cdot t\right)\right) - 4 \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 59.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+90} \lor \neg \left(t \leq 2.4 \cdot 10^{+19}\right) \land \left(t \leq 5.6 \cdot 10^{+87} \lor \neg \left(t \leq 2.26 \cdot 10^{+111}\right)\right):\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= t -5e+90)
         (and (not (<= t 2.4e+19)) (or (<= t 5.6e+87) (not (<= t 2.26e+111)))))
   (* t (- (* 18.0 (* x (* y z))) (* a 4.0)))
   (+ (* b c) (* j (* k -27.0)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((t <= -5e+90) || (!(t <= 2.4e+19) && ((t <= 5.6e+87) || !(t <= 2.26e+111)))) {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	} else {
		tmp = (b * c) + (j * (k * -27.0));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((t <= (-5d+90)) .or. (.not. (t <= 2.4d+19)) .and. (t <= 5.6d+87) .or. (.not. (t <= 2.26d+111))) then
        tmp = t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0))
    else
        tmp = (b * c) + (j * (k * (-27.0d0)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((t <= -5e+90) || (!(t <= 2.4e+19) && ((t <= 5.6e+87) || !(t <= 2.26e+111)))) {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	} else {
		tmp = (b * c) + (j * (k * -27.0));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (t <= -5e+90) or (not (t <= 2.4e+19) and ((t <= 5.6e+87) or not (t <= 2.26e+111))):
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0))
	else:
		tmp = (b * c) + (j * (k * -27.0))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((t <= -5e+90) || (!(t <= 2.4e+19) && ((t <= 5.6e+87) || !(t <= 2.26e+111))))
		tmp = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)));
	else
		tmp = Float64(Float64(b * c) + Float64(j * Float64(k * -27.0)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((t <= -5e+90) || (~((t <= 2.4e+19)) && ((t <= 5.6e+87) || ~((t <= 2.26e+111)))))
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	else
		tmp = (b * c) + (j * (k * -27.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[t, -5e+90], And[N[Not[LessEqual[t, 2.4e+19]], $MachinePrecision], Or[LessEqual[t, 5.6e+87], N[Not[LessEqual[t, 2.26e+111]], $MachinePrecision]]]], N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.0000000000000004e90 or 2.4e19 < t < 5.6000000000000003e87 or 2.26000000000000011e111 < t

   1. Initial program 90.9%

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

   3. Simplified 92.0%

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

   5. Taylor expanded in t around inf 73.0%

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

   if -5.0000000000000004e90 < t < 2.4e19 or 5.6000000000000003e87 < t < 2.26000000000000011e111

   1. Initial program 79.6%

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

   3. Simplified 82.3%

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

   5. Taylor expanded in b around inf 59.0%

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

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+90} \lor \neg \left(t \leq 2.4 \cdot 10^{+19}\right) \land \left(t \leq 5.6 \cdot 10^{+87} \lor \neg \left(t \leq 2.26 \cdot 10^{+111}\right)\right):\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 57.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{if}\;t \leq -1.02 \cdot 10^{+91}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-157}:\\ \;\;\;\;b \cdot c + t_1\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{+44}:\\ \;\;\;\;t_1 + 18 \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot t\right)\right)\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+110}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 (* t (- (* 18.0 (* x (* y z))) (* a 4.0)))))
   (if (<= t -1.02e+91)
     t_2
     (if (<= t 1.05e-157)
       (+ (* b c) t_1)
       (if (<= t 6.8e+44)
         (+ t_1 (* 18.0 (* (* y z) (* x t))))
         (if (<= t 2.8e+110) (- (* b c) (* 4.0 (* t a))) t_2))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	double tmp;
	if (t <= -1.02e+91) {
		tmp = t_2;
	} else if (t <= 1.05e-157) {
		tmp = (b * c) + t_1;
	} else if (t <= 6.8e+44) {
		tmp = t_1 + (18.0 * ((y * z) * (x * t)));
	} else if (t <= 2.8e+110) {
		tmp = (b * c) - (4.0 * (t * a));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * (k * (-27.0d0))
    t_2 = t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0))
    if (t <= (-1.02d+91)) then
        tmp = t_2
    else if (t <= 1.05d-157) then
        tmp = (b * c) + t_1
    else if (t <= 6.8d+44) then
        tmp = t_1 + (18.0d0 * ((y * z) * (x * t)))
    else if (t <= 2.8d+110) then
        tmp = (b * c) - (4.0d0 * (t * a))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	double tmp;
	if (t <= -1.02e+91) {
		tmp = t_2;
	} else if (t <= 1.05e-157) {
		tmp = (b * c) + t_1;
	} else if (t <= 6.8e+44) {
		tmp = t_1 + (18.0 * ((y * z) * (x * t)));
	} else if (t <= 2.8e+110) {
		tmp = (b * c) - (4.0 * (t * a));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	t_2 = t * ((18.0 * (x * (y * z))) - (a * 4.0))
	tmp = 0
	if t <= -1.02e+91:
		tmp = t_2
	elif t <= 1.05e-157:
		tmp = (b * c) + t_1
	elif t <= 6.8e+44:
		tmp = t_1 + (18.0 * ((y * z) * (x * t)))
	elif t <= 2.8e+110:
		tmp = (b * c) - (4.0 * (t * a))
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * -27.0))
	t_2 = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)))
	tmp = 0.0
	if (t <= -1.02e+91)
		tmp = t_2;
	elseif (t <= 1.05e-157)
		tmp = Float64(Float64(b * c) + t_1);
	elseif (t <= 6.8e+44)
		tmp = Float64(t_1 + Float64(18.0 * Float64(Float64(y * z) * Float64(x * t))));
	elseif (t <= 2.8e+110)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(t * a)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * -27.0);
	t_2 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	tmp = 0.0;
	if (t <= -1.02e+91)
		tmp = t_2;
	elseif (t <= 1.05e-157)
		tmp = (b * c) + t_1;
	elseif (t <= 6.8e+44)
		tmp = t_1 + (18.0 * ((y * z) * (x * t)));
	elseif (t <= 2.8e+110)
		tmp = (b * c) - (4.0 * (t * a));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.02e+91], t$95$2, If[LessEqual[t, 1.05e-157], N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[t, 6.8e+44], N[(t$95$1 + N[(18.0 * N[(N[(y * z), $MachinePrecision] * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.8e+110], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.01999999999999992e91 or 2.79999999999999987e110 < t

   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 90.8%

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

   5. Taylor expanded in t around inf 74.4%

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

   if -1.01999999999999992e91 < t < 1.05e-157

   1. Initial program 76.9%

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

   3. Simplified 80.4%

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

   5. Taylor expanded in b around inf 60.8%

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

   if 1.05e-157 < t < 6.8e44

   1. Initial program 89.8%

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

   3. Simplified 89.8%

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

   5. Taylor expanded in y around inf 47.7%

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

      1. associate-*r* 55.0%

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

   7. Simplified 55.0%

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

   if 6.8e44 < t < 2.79999999999999987e110

   1. Initial program 93.1%

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

   3. Simplified 93.1%

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

      1. associate-*r* 93.1%

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

      2. distribute-rgt-out-- 93.1%

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

      3. associate-+l- 93.1%

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

      4. associate-*l* 79.8%

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

      5. *-commutative 79.8%

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

      6. *-commutative 79.8%

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

      7. fma-neg 79.9%

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

   6. Applied egg-rr 79.9%

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

   7. Taylor expanded in x around inf 79.9%

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

      1. associate-*r* 79.9%

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

      2. *-commutative 79.9%

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

   9. Simplified 79.9%

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

   10. Taylor expanded in x around 0 74.0%

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

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.02 \cdot 10^{+91}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-157}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{+44}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + 18 \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot t\right)\right)\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+110}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 49.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\\ \mathbf{if}\;j \leq -1.95 \cdot 10^{+149}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -1.32 \cdot 10^{+104}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;j \leq 2 \cdot 10^{-198}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;j \leq 9.5 \cdot 10^{-115}:\\ \;\;\;\;z \cdot \left(t \cdot \left(x \cdot \left(18 \cdot y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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)) (* -4.0 (* t a)))))
   (if (<= j -1.95e+149)
     t_1
     (if (<= j -1.32e+104)
       (- (* b c) (* 4.0 (* x i)))
       (if (<= j 2e-198)
         (- (* b c) (* 4.0 (* t a)))
         (if (<= j 9.5e-115) (* z (* t (* x (* 18.0 y)))) t_1))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * (k * -27.0)) + (-4.0 * (t * a));
	double tmp;
	if (j <= -1.95e+149) {
		tmp = t_1;
	} else if (j <= -1.32e+104) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if (j <= 2e-198) {
		tmp = (b * c) - (4.0 * (t * a));
	} else if (j <= 9.5e-115) {
		tmp = z * (t * (x * (18.0 * y)));
	} 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.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (j * (k * (-27.0d0))) + ((-4.0d0) * (t * a))
    if (j <= (-1.95d+149)) then
        tmp = t_1
    else if (j <= (-1.32d+104)) then
        tmp = (b * c) - (4.0d0 * (x * i))
    else if (j <= 2d-198) then
        tmp = (b * c) - (4.0d0 * (t * a))
    else if (j <= 9.5d-115) then
        tmp = z * (t * (x * (18.0d0 * y)))
    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;
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)) + (-4.0 * (t * a));
	double tmp;
	if (j <= -1.95e+149) {
		tmp = t_1;
	} else if (j <= -1.32e+104) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if (j <= 2e-198) {
		tmp = (b * c) - (4.0 * (t * a));
	} else if (j <= 9.5e-115) {
		tmp = z * (t * (x * (18.0 * y)));
	} 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])
[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)) + (-4.0 * (t * a))
	tmp = 0
	if j <= -1.95e+149:
		tmp = t_1
	elif j <= -1.32e+104:
		tmp = (b * c) - (4.0 * (x * i))
	elif j <= 2e-198:
		tmp = (b * c) - (4.0 * (t * a))
	elif j <= 9.5e-115:
		tmp = z * (t * (x * (18.0 * y)))
	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])
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 * Float64(k * -27.0)) + Float64(-4.0 * Float64(t * a)))
	tmp = 0.0
	if (j <= -1.95e+149)
		tmp = t_1;
	elseif (j <= -1.32e+104)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)));
	elseif (j <= 2e-198)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(t * a)));
	elseif (j <= 9.5e-115)
		tmp = Float64(z * Float64(t * Float64(x * Float64(18.0 * y))));
	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])){:}
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)) + (-4.0 * (t * a));
	tmp = 0.0;
	if (j <= -1.95e+149)
		tmp = t_1;
	elseif (j <= -1.32e+104)
		tmp = (b * c) - (4.0 * (x * i));
	elseif (j <= 2e-198)
		tmp = (b * c) - (4.0 * (t * a));
	elseif (j <= 9.5e-115)
		tmp = z * (t * (x * (18.0 * y)));
	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.
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 * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.95e+149], t$95$1, If[LessEqual[j, -1.32e+104], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2e-198], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 9.5e-115], N[(z * N[(t * N[(x * N[(18.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -1.95e149 or 9.4999999999999996e-115 < j

   1. Initial program 79.4%

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

   3. Simplified 81.1%

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

   5. Taylor expanded in a around inf 54.9%

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

      1. *-commutative 54.9%

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

   7. Simplified 54.9%

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

   if -1.95e149 < j < -1.32000000000000003e104

   1. Initial program 90.0%

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

   3. Taylor expanded in t around 0 71.0%

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

   4. Taylor expanded in j around 0 31.0%

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

   if -1.32000000000000003e104 < j < 1.9999999999999998e-198

   1. Initial program 87.7%

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

   3. Simplified 89.7%

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

      1. associate-*r* 87.6%

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

      2. distribute-rgt-out-- 87.6%

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

      3. associate-+l- 87.6%

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

      4. associate-*l* 88.4%

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

      5. *-commutative 88.4%

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

      6. *-commutative 88.4%

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

      7. fma-neg 88.4%

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

   6. Applied egg-rr 88.4%

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

   7. Taylor expanded in x around inf 80.9%

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

      1. associate-*r* 80.9%

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

      2. *-commutative 80.9%

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

   9. Simplified 80.9%

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

   10. Taylor expanded in x around 0 52.9%

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

   if 1.9999999999999998e-198 < j < 9.4999999999999996e-115

   1. Initial program 90.3%

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

   3. Simplified 85.8%

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

      1. associate-*r* 90.3%

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

      2. distribute-rgt-out-- 90.3%

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

      3. associate-*l* 85.6%

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

      4. *-commutative 85.6%

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

      5. *-commutative 85.6%

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

   6. Applied egg-rr 85.6%

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

   7. Taylor expanded in y around inf 20.8%

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

      1. *-commutative 20.8%

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

      2. associate-*r* 20.9%

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

      3. associate-*r* 20.9%

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

      4. *-commutative 20.9%

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

      5. associate-*r* 21.0%

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

      6. *-commutative 21.0%

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

      7. *-commutative 21.0%

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

      8. associate-*l* 21.0%

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

      9. *-commutative 21.0%

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

      10. associate-*l* 21.0%

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

   9. Simplified 21.0%

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

4. Final simplification 50.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.95 \cdot 10^{+149}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;j \leq -1.32 \cdot 10^{+104}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;j \leq 2 \cdot 10^{-198}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;j \leq 9.5 \cdot 10^{-115}:\\ \;\;\;\;z \cdot \left(t \cdot \left(x \cdot \left(18 \cdot y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 49.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;j \leq -1.75 \cdot 10^{+149}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;j \leq -9.5 \cdot 10^{+101}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;j \leq 2.9 \cdot 10^{-198}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;j \leq 7.7 \cdot 10^{-115}:\\ \;\;\;\;z \cdot \left(t \cdot \left(x \cdot \left(18 \cdot y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right) + k \cdot \left(j \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= j -1.75e+149)
   (+ (* j (* k -27.0)) (* -4.0 (* t a)))
   (if (<= j -9.5e+101)
     (- (* b c) (* 4.0 (* x i)))
     (if (<= j 2.9e-198)
       (- (* b c) (* 4.0 (* t a)))
       (if (<= j 7.7e-115)
         (* z (* t (* x (* 18.0 y))))
         (+ (* t (* a -4.0)) (* k (* j -27.0))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (j <= -1.75e+149) {
		tmp = (j * (k * -27.0)) + (-4.0 * (t * a));
	} else if (j <= -9.5e+101) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if (j <= 2.9e-198) {
		tmp = (b * c) - (4.0 * (t * a));
	} else if (j <= 7.7e-115) {
		tmp = z * (t * (x * (18.0 * y)));
	} else {
		tmp = (t * (a * -4.0)) + (k * (j * -27.0));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (j <= (-1.75d+149)) then
        tmp = (j * (k * (-27.0d0))) + ((-4.0d0) * (t * a))
    else if (j <= (-9.5d+101)) then
        tmp = (b * c) - (4.0d0 * (x * i))
    else if (j <= 2.9d-198) then
        tmp = (b * c) - (4.0d0 * (t * a))
    else if (j <= 7.7d-115) then
        tmp = z * (t * (x * (18.0d0 * y)))
    else
        tmp = (t * (a * (-4.0d0))) + (k * (j * (-27.0d0)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (j <= -1.75e+149) {
		tmp = (j * (k * -27.0)) + (-4.0 * (t * a));
	} else if (j <= -9.5e+101) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if (j <= 2.9e-198) {
		tmp = (b * c) - (4.0 * (t * a));
	} else if (j <= 7.7e-115) {
		tmp = z * (t * (x * (18.0 * y)));
	} else {
		tmp = (t * (a * -4.0)) + (k * (j * -27.0));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if j <= -1.75e+149:
		tmp = (j * (k * -27.0)) + (-4.0 * (t * a))
	elif j <= -9.5e+101:
		tmp = (b * c) - (4.0 * (x * i))
	elif j <= 2.9e-198:
		tmp = (b * c) - (4.0 * (t * a))
	elif j <= 7.7e-115:
		tmp = z * (t * (x * (18.0 * y)))
	else:
		tmp = (t * (a * -4.0)) + (k * (j * -27.0))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (j <= -1.75e+149)
		tmp = Float64(Float64(j * Float64(k * -27.0)) + Float64(-4.0 * Float64(t * a)));
	elseif (j <= -9.5e+101)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)));
	elseif (j <= 2.9e-198)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(t * a)));
	elseif (j <= 7.7e-115)
		tmp = Float64(z * Float64(t * Float64(x * Float64(18.0 * y))));
	else
		tmp = Float64(Float64(t * Float64(a * -4.0)) + Float64(k * Float64(j * -27.0)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (j <= -1.75e+149)
		tmp = (j * (k * -27.0)) + (-4.0 * (t * a));
	elseif (j <= -9.5e+101)
		tmp = (b * c) - (4.0 * (x * i));
	elseif (j <= 2.9e-198)
		tmp = (b * c) - (4.0 * (t * a));
	elseif (j <= 7.7e-115)
		tmp = z * (t * (x * (18.0 * y)));
	else
		tmp = (t * (a * -4.0)) + (k * (j * -27.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[j, -1.75e+149], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -9.5e+101], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.9e-198], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 7.7e-115], N[(z * N[(t * N[(x * N[(18.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -1.75000000000000006e149

   1. Initial program 75.0%

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

   3. Simplified 78.0%

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

   5. Taylor expanded in a around inf 66.7%

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

      1. *-commutative 66.7%

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

   7. Simplified 66.7%

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

   if -1.75000000000000006e149 < j < -9.49999999999999947e101

   1. Initial program 90.0%

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

   3. Taylor expanded in t around 0 71.0%

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

   4. Taylor expanded in j around 0 31.0%

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

   if -9.49999999999999947e101 < j < 2.90000000000000001e-198

   1. Initial program 87.7%

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

   3. Simplified 89.7%

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

      1. associate-*r* 87.6%

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

      2. distribute-rgt-out-- 87.6%

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

      3. associate-+l- 87.6%

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

      4. associate-*l* 88.4%

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

      5. *-commutative 88.4%

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

      6. *-commutative 88.4%

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

      7. fma-neg 88.4%

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

   6. Applied egg-rr 88.4%

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

   7. Taylor expanded in x around inf 80.9%

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

      1. associate-*r* 80.9%

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

      2. *-commutative 80.9%

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

   9. Simplified 80.9%

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

   10. Taylor expanded in x around 0 52.9%

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

   if 2.90000000000000001e-198 < j < 7.7000000000000002e-115

   1. Initial program 90.3%

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

   3. Simplified 85.8%

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

      1. associate-*r* 90.3%

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

      2. distribute-rgt-out-- 90.3%

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

      3. associate-*l* 85.6%

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

      4. *-commutative 85.6%

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

      5. *-commutative 85.6%

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

   6. Applied egg-rr 85.6%

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

   7. Taylor expanded in y around inf 20.8%

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

      1. *-commutative 20.8%

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

      2. associate-*r* 20.9%

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

      3. associate-*r* 20.9%

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

      4. *-commutative 20.9%

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

      5. associate-*r* 21.0%

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

      6. *-commutative 21.0%

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

      7. *-commutative 21.0%

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

      8. associate-*l* 21.0%

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

      9. *-commutative 21.0%

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

      10. associate-*l* 21.0%

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

   9. Simplified 21.0%

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

   if 7.7000000000000002e-115 < j

   1. Initial program 81.0%

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

   3. Taylor expanded in x around 0 60.5%

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

   4. Taylor expanded in b around 0 50.6%

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

      1. mul-1-neg 50.6%

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

      2. associate-*r* 50.6%

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

      3. *-commutative 50.6%

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

      4. *-commutative 50.6%

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

      5. associate-*r* 50.5%

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

      6. *-commutative 50.5%

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

      7. associate-*r* 50.6%

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

      8. distribute-neg-in 50.6%

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

      9. distribute-rgt-neg-in 50.6%

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

      10. distribute-rgt-neg-in 50.6%

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

      11. metadata-eval 50.6%

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

      12. associate-*r* 50.5%

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

      13. distribute-lft-neg-out 50.5%

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

      14. *-commutative 50.5%

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

      15. distribute-rgt-neg-in 50.5%

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

      16. metadata-eval 50.5%

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

   6. Simplified 50.5%

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

4. Final simplification 50.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.75 \cdot 10^{+149}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;j \leq -9.5 \cdot 10^{+101}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;j \leq 2.9 \cdot 10^{-198}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;j \leq 7.7 \cdot 10^{-115}:\\ \;\;\;\;z \cdot \left(t \cdot \left(x \cdot \left(18 \cdot y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right) + k \cdot \left(j \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 71.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ t_2 := t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{if}\;t \leq -1.85 \cdot 10^{+233}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -7.2 \cdot 10^{-63}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - t_1\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{+111}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k))
        (t_2 (* t (- (* 18.0 (* x (* y z))) (* a 4.0)))))
   (if (<= t -1.85e+233)
     t_2
     (if (<= t -7.2e-63)
       (- (- (* b c) (* 4.0 (* t a))) t_1)
       (if (<= t 2.1e+111) (- (- (* b c) (* 4.0 (* x i))) t_1) t_2)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double t_2 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	double tmp;
	if (t <= -1.85e+233) {
		tmp = t_2;
	} else if (t <= -7.2e-63) {
		tmp = ((b * c) - (4.0 * (t * a))) - t_1;
	} else if (t <= 2.1e+111) {
		tmp = ((b * c) - (4.0 * (x * i))) - t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (j * 27.0d0) * k
    t_2 = t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0))
    if (t <= (-1.85d+233)) then
        tmp = t_2
    else if (t <= (-7.2d-63)) then
        tmp = ((b * c) - (4.0d0 * (t * a))) - t_1
    else if (t <= 2.1d+111) then
        tmp = ((b * c) - (4.0d0 * (x * i))) - t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double t_2 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	double tmp;
	if (t <= -1.85e+233) {
		tmp = t_2;
	} else if (t <= -7.2e-63) {
		tmp = ((b * c) - (4.0 * (t * a))) - t_1;
	} else if (t <= 2.1e+111) {
		tmp = ((b * c) - (4.0 * (x * i))) - t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	t_2 = t * ((18.0 * (x * (y * z))) - (a * 4.0))
	tmp = 0
	if t <= -1.85e+233:
		tmp = t_2
	elif t <= -7.2e-63:
		tmp = ((b * c) - (4.0 * (t * a))) - t_1
	elif t <= 2.1e+111:
		tmp = ((b * c) - (4.0 * (x * i))) - t_1
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	t_2 = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)))
	tmp = 0.0
	if (t <= -1.85e+233)
		tmp = t_2;
	elseif (t <= -7.2e-63)
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(t * a))) - t_1);
	elseif (t <= 2.1e+111)
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(x * i))) - t_1);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * 27.0) * k;
	t_2 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	tmp = 0.0;
	if (t <= -1.85e+233)
		tmp = t_2;
	elseif (t <= -7.2e-63)
		tmp = ((b * c) - (4.0 * (t * a))) - t_1;
	elseif (t <= 2.1e+111)
		tmp = ((b * c) - (4.0 * (x * i))) - t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.85e+233], t$95$2, If[LessEqual[t, -7.2e-63], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[t, 2.1e+111], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.8499999999999999e233 or 2.09999999999999995e111 < t

   1. Initial program 87.7%

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

   3. Simplified 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

   5. Taylor expanded in t around inf 81.6%

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

   if -1.8499999999999999e233 < t < -7.20000000000000016e-63

   1. Initial program 91.4%

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

   3. Taylor expanded in x around 0 71.4%

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

   if -7.20000000000000016e-63 < t < 2.09999999999999995e111

   1. Initial program 79.5%

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

   3. Taylor expanded in t around 0 72.1%

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

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.85 \cdot 10^{+233}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq -7.2 \cdot 10^{-63}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{+111}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 33.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := 18 \cdot \left(t \cdot \left(y \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{if}\;j \leq -2.9 \cdot 10^{+150}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;j \leq -1.9 \cdot 10^{-19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 4.8 \cdot 10^{-209}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;j \leq 3.3 \cdot 10^{-114}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* 18.0 (* t (* y (* x z))))))
   (if (<= j -2.9e+150)
     (* -27.0 (* j k))
     (if (<= j -1.9e-19)
       t_1
       (if (<= j 4.8e-209)
         (* b c)
         (if (<= j 3.3e-114) t_1 (* k (* j -27.0))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 18.0 * (t * (y * (x * z)));
	double tmp;
	if (j <= -2.9e+150) {
		tmp = -27.0 * (j * k);
	} else if (j <= -1.9e-19) {
		tmp = t_1;
	} else if (j <= 4.8e-209) {
		tmp = b * c;
	} else if (j <= 3.3e-114) {
		tmp = t_1;
	} else {
		tmp = k * (j * -27.0);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 18.0d0 * (t * (y * (x * z)))
    if (j <= (-2.9d+150)) then
        tmp = (-27.0d0) * (j * k)
    else if (j <= (-1.9d-19)) then
        tmp = t_1
    else if (j <= 4.8d-209) then
        tmp = b * c
    else if (j <= 3.3d-114) then
        tmp = t_1
    else
        tmp = k * (j * (-27.0d0))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 18.0 * (t * (y * (x * z)));
	double tmp;
	if (j <= -2.9e+150) {
		tmp = -27.0 * (j * k);
	} else if (j <= -1.9e-19) {
		tmp = t_1;
	} else if (j <= 4.8e-209) {
		tmp = b * c;
	} else if (j <= 3.3e-114) {
		tmp = t_1;
	} else {
		tmp = k * (j * -27.0);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = 18.0 * (t * (y * (x * z)))
	tmp = 0
	if j <= -2.9e+150:
		tmp = -27.0 * (j * k)
	elif j <= -1.9e-19:
		tmp = t_1
	elif j <= 4.8e-209:
		tmp = b * c
	elif j <= 3.3e-114:
		tmp = t_1
	else:
		tmp = k * (j * -27.0)
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(18.0 * Float64(t * Float64(y * Float64(x * z))))
	tmp = 0.0
	if (j <= -2.9e+150)
		tmp = Float64(-27.0 * Float64(j * k));
	elseif (j <= -1.9e-19)
		tmp = t_1;
	elseif (j <= 4.8e-209)
		tmp = Float64(b * c);
	elseif (j <= 3.3e-114)
		tmp = t_1;
	else
		tmp = Float64(k * Float64(j * -27.0));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = 18.0 * (t * (y * (x * z)));
	tmp = 0.0;
	if (j <= -2.9e+150)
		tmp = -27.0 * (j * k);
	elseif (j <= -1.9e-19)
		tmp = t_1;
	elseif (j <= 4.8e-209)
		tmp = b * c;
	elseif (j <= 3.3e-114)
		tmp = t_1;
	else
		tmp = k * (j * -27.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(18.0 * N[(t * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -2.9e+150], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.9e-19], t$95$1, If[LessEqual[j, 4.8e-209], N[(b * c), $MachinePrecision], If[LessEqual[j, 3.3e-114], t$95$1, N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -2.90000000000000011e150

   1. Initial program 74.1%

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

   3. Simplified 77.3%

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

   5. Taylor expanded in j around inf 58.9%

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

   if -2.90000000000000011e150 < j < -1.9e-19 or 4.8000000000000002e-209 < j < 3.30000000000000035e-114

   1. Initial program 91.5%

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

   3. Simplified 91.5%

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

      1. associate-*r* 91.4%

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

      2. distribute-rgt-out-- 91.4%

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

      3. associate-*l* 84.8%

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

      4. *-commutative 84.8%

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

      5. *-commutative 84.8%

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

   6. Applied egg-rr 84.8%

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

   7. Taylor expanded in y around inf 27.4%

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

      1. expm1-log1p-u 18.0%

         \[\leadsto 18 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right)} \]

      2. expm1-udef 17.9%

         \[\leadsto 18 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} - 1\right)} \]

      3. associate-*r* 18.1%

         \[\leadsto 18 \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{\left(t \cdot x\right) \cdot \left(y \cdot z\right)}\right)} - 1\right) \]

   9. Applied egg-rr 18.1%

      \[\leadsto 18 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(\left(t \cdot x\right) \cdot \left(y \cdot z\right)\right)} - 1\right)} \]
   10. Step-by-step derivation

       1. expm1-def 18.2%

          \[\leadsto 18 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\left(t \cdot x\right) \cdot \left(y \cdot z\right)\right)\right)} \]

       2. expm1-log1p 29.0%

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

       3. associate-*r* 27.4%

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

       4. *-commutative 27.4%

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

       5. associate-*l* 29.1%

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

   11. Simplified 29.1%

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

   if -1.9e-19 < j < 4.8000000000000002e-209

   1. Initial program 86.1%

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

   3. Simplified 87.5%

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

      1. associate-*r* 86.1%

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

      2. distribute-rgt-out-- 86.1%

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

      3. associate-+l- 86.1%

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

      4. associate-*l* 88.4%

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

      5. *-commutative 88.4%

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

      6. *-commutative 88.4%

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

      7. fma-neg 88.5%

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

   6. Applied egg-rr 88.5%

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

   7. Taylor expanded in b around inf 36.0%

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

   if 3.30000000000000035e-114 < j

   1. Initial program 80.8%

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

   3. Simplified 82.1%

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

      1. associate-*r* 80.8%

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

      2. distribute-rgt-out-- 80.8%

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

      3. associate-+l- 80.8%

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

      4. associate-*l* 80.9%

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

      5. *-commutative 80.9%

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

      6. *-commutative 80.9%

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

      7. fma-neg 80.9%

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

   6. Applied egg-rr 80.9%

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

   7. Taylor expanded in j around inf 35.9%

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

      1. associate-*r* 35.8%

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

      2. *-commutative 35.8%

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

      3. *-commutative 35.8%

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

   9. Simplified 35.8%

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

4. Final simplification 37.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.9 \cdot 10^{+150}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;j \leq -1.9 \cdot 10^{-19}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(y \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;j \leq 4.8 \cdot 10^{-209}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;j \leq 3.3 \cdot 10^{-114}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(y \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 33.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;j \leq -3.25 \cdot 10^{+150}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;j \leq -1.08 \cdot 10^{-79}:\\ \;\;\;\;18 \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot t\right)\right)\\ \mathbf{elif}\;j \leq 4.4 \cdot 10^{-204}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;j \leq 3.3 \cdot 10^{-114}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(y \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= j -3.25e+150)
   (* -27.0 (* j k))
   (if (<= j -1.08e-79)
     (* 18.0 (* (* y z) (* x t)))
     (if (<= j 4.4e-204)
       (* b c)
       (if (<= j 3.3e-114) (* 18.0 (* t (* y (* x z)))) (* k (* j -27.0)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (j <= -3.25e+150) {
		tmp = -27.0 * (j * k);
	} else if (j <= -1.08e-79) {
		tmp = 18.0 * ((y * z) * (x * t));
	} else if (j <= 4.4e-204) {
		tmp = b * c;
	} else if (j <= 3.3e-114) {
		tmp = 18.0 * (t * (y * (x * z)));
	} else {
		tmp = k * (j * -27.0);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (j <= (-3.25d+150)) then
        tmp = (-27.0d0) * (j * k)
    else if (j <= (-1.08d-79)) then
        tmp = 18.0d0 * ((y * z) * (x * t))
    else if (j <= 4.4d-204) then
        tmp = b * c
    else if (j <= 3.3d-114) then
        tmp = 18.0d0 * (t * (y * (x * z)))
    else
        tmp = k * (j * (-27.0d0))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (j <= -3.25e+150) {
		tmp = -27.0 * (j * k);
	} else if (j <= -1.08e-79) {
		tmp = 18.0 * ((y * z) * (x * t));
	} else if (j <= 4.4e-204) {
		tmp = b * c;
	} else if (j <= 3.3e-114) {
		tmp = 18.0 * (t * (y * (x * z)));
	} else {
		tmp = k * (j * -27.0);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if j <= -3.25e+150:
		tmp = -27.0 * (j * k)
	elif j <= -1.08e-79:
		tmp = 18.0 * ((y * z) * (x * t))
	elif j <= 4.4e-204:
		tmp = b * c
	elif j <= 3.3e-114:
		tmp = 18.0 * (t * (y * (x * z)))
	else:
		tmp = k * (j * -27.0)
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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 (j <= -3.25e+150)
		tmp = Float64(-27.0 * Float64(j * k));
	elseif (j <= -1.08e-79)
		tmp = Float64(18.0 * Float64(Float64(y * z) * Float64(x * t)));
	elseif (j <= 4.4e-204)
		tmp = Float64(b * c);
	elseif (j <= 3.3e-114)
		tmp = Float64(18.0 * Float64(t * Float64(y * Float64(x * z))));
	else
		tmp = Float64(k * Float64(j * -27.0));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (j <= -3.25e+150)
		tmp = -27.0 * (j * k);
	elseif (j <= -1.08e-79)
		tmp = 18.0 * ((y * z) * (x * t));
	elseif (j <= 4.4e-204)
		tmp = b * c;
	elseif (j <= 3.3e-114)
		tmp = 18.0 * (t * (y * (x * z)));
	else
		tmp = k * (j * -27.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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[j, -3.25e+150], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.08e-79], N[(18.0 * N[(N[(y * z), $MachinePrecision] * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 4.4e-204], N[(b * c), $MachinePrecision], If[LessEqual[j, 3.3e-114], N[(18.0 * N[(t * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -3.25000000000000016e150

   1. Initial program 74.1%

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

   3. Simplified 77.3%

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

   5. Taylor expanded in j around inf 58.9%

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

   if -3.25000000000000016e150 < j < -1.0800000000000001e-79

   1. Initial program 90.9%

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

   3. Simplified 95.4%

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

      1. associate-*r* 90.9%

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

      2. distribute-rgt-out-- 90.9%

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

      3. associate-*l* 84.2%

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

      4. *-commutative 84.2%

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

      5. *-commutative 84.2%

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

   6. Applied egg-rr 84.2%

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

   7. Taylor expanded in y around inf 31.3%

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

      1. associate-*r* 33.5%

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

   9. Simplified 33.5%

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

   if -1.0800000000000001e-79 < j < 4.3999999999999997e-204

   1. Initial program 85.9%

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

   3. Simplified 86.1%

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

      1. associate-*r* 85.9%

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

      2. distribute-rgt-out-- 85.9%

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

      3. associate-+l- 85.9%

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

      4. associate-*l* 88.5%

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

      5. *-commutative 88.5%

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

      6. *-commutative 88.5%

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

      7. fma-neg 88.6%

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

   6. Applied egg-rr 88.6%

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

   7. Taylor expanded in b around inf 37.2%

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

   if 4.3999999999999997e-204 < j < 3.30000000000000035e-114

   1. Initial program 91.2%

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

   3. Simplified 87.0%

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

      1. associate-*r* 91.2%

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

      2. distribute-rgt-out-- 91.2%

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

      3. associate-*l* 86.8%

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

      4. *-commutative 86.8%

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

      5. *-commutative 86.8%

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

   6. Applied egg-rr 86.8%

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

   7. Taylor expanded in y around inf 19.4%

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

      1. expm1-log1p-u 14.3%

         \[\leadsto 18 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right)} \]

      2. expm1-udef 14.1%

         \[\leadsto 18 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} - 1\right)} \]

      3. associate-*r* 14.1%

         \[\leadsto 18 \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{\left(t \cdot x\right) \cdot \left(y \cdot z\right)}\right)} - 1\right) \]

   9. Applied egg-rr 14.1%

      \[\leadsto 18 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(\left(t \cdot x\right) \cdot \left(y \cdot z\right)\right)} - 1\right)} \]
   10. Step-by-step derivation

       1. expm1-def 14.4%

          \[\leadsto 18 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\left(t \cdot x\right) \cdot \left(y \cdot z\right)\right)\right)} \]

       2. expm1-log1p 19.4%

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

       3. associate-*r* 19.4%

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

       4. *-commutative 19.4%

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

       5. associate-*l* 23.6%

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

   11. Simplified 23.6%

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

   if 3.30000000000000035e-114 < j

   1. Initial program 80.8%

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

   3. Simplified 82.1%

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

      1. associate-*r* 80.8%

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

      2. distribute-rgt-out-- 80.8%

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

      3. associate-+l- 80.8%

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

      4. associate-*l* 80.9%

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

      5. *-commutative 80.9%

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

      6. *-commutative 80.9%

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

      7. fma-neg 80.9%

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

   6. Applied egg-rr 80.9%

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

   7. Taylor expanded in j around inf 35.9%

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

      1. associate-*r* 35.8%

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

      2. *-commutative 35.8%

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

      3. *-commutative 35.8%

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

   9. Simplified 35.8%

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

4. Final simplification 37.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -3.25 \cdot 10^{+150}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;j \leq -1.08 \cdot 10^{-79}:\\ \;\;\;\;18 \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot t\right)\right)\\ \mathbf{elif}\;j \leq 4.4 \cdot 10^{-204}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;j \leq 3.3 \cdot 10^{-114}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(y \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 33.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;j \leq -2.8 \cdot 10^{+150}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;j \leq -2.7 \cdot 10^{-80}:\\ \;\;\;\;18 \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot t\right)\right)\\ \mathbf{elif}\;j \leq 1.75 \cdot 10^{-198}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;j \leq 3.3 \cdot 10^{-114}:\\ \;\;\;\;z \cdot \left(t \cdot \left(x \cdot \left(18 \cdot y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= j -2.8e+150)
   (* -27.0 (* j k))
   (if (<= j -2.7e-80)
     (* 18.0 (* (* y z) (* x t)))
     (if (<= j 1.75e-198)
       (* b c)
       (if (<= j 3.3e-114) (* z (* t (* x (* 18.0 y)))) (* k (* j -27.0)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (j <= -2.8e+150) {
		tmp = -27.0 * (j * k);
	} else if (j <= -2.7e-80) {
		tmp = 18.0 * ((y * z) * (x * t));
	} else if (j <= 1.75e-198) {
		tmp = b * c;
	} else if (j <= 3.3e-114) {
		tmp = z * (t * (x * (18.0 * y)));
	} else {
		tmp = k * (j * -27.0);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (j <= (-2.8d+150)) then
        tmp = (-27.0d0) * (j * k)
    else if (j <= (-2.7d-80)) then
        tmp = 18.0d0 * ((y * z) * (x * t))
    else if (j <= 1.75d-198) then
        tmp = b * c
    else if (j <= 3.3d-114) then
        tmp = z * (t * (x * (18.0d0 * y)))
    else
        tmp = k * (j * (-27.0d0))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (j <= -2.8e+150) {
		tmp = -27.0 * (j * k);
	} else if (j <= -2.7e-80) {
		tmp = 18.0 * ((y * z) * (x * t));
	} else if (j <= 1.75e-198) {
		tmp = b * c;
	} else if (j <= 3.3e-114) {
		tmp = z * (t * (x * (18.0 * y)));
	} else {
		tmp = k * (j * -27.0);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if j <= -2.8e+150:
		tmp = -27.0 * (j * k)
	elif j <= -2.7e-80:
		tmp = 18.0 * ((y * z) * (x * t))
	elif j <= 1.75e-198:
		tmp = b * c
	elif j <= 3.3e-114:
		tmp = z * (t * (x * (18.0 * y)))
	else:
		tmp = k * (j * -27.0)
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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 (j <= -2.8e+150)
		tmp = Float64(-27.0 * Float64(j * k));
	elseif (j <= -2.7e-80)
		tmp = Float64(18.0 * Float64(Float64(y * z) * Float64(x * t)));
	elseif (j <= 1.75e-198)
		tmp = Float64(b * c);
	elseif (j <= 3.3e-114)
		tmp = Float64(z * Float64(t * Float64(x * Float64(18.0 * y))));
	else
		tmp = Float64(k * Float64(j * -27.0));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (j <= -2.8e+150)
		tmp = -27.0 * (j * k);
	elseif (j <= -2.7e-80)
		tmp = 18.0 * ((y * z) * (x * t));
	elseif (j <= 1.75e-198)
		tmp = b * c;
	elseif (j <= 3.3e-114)
		tmp = z * (t * (x * (18.0 * y)));
	else
		tmp = k * (j * -27.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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[j, -2.8e+150], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -2.7e-80], N[(18.0 * N[(N[(y * z), $MachinePrecision] * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.75e-198], N[(b * c), $MachinePrecision], If[LessEqual[j, 3.3e-114], N[(z * N[(t * N[(x * N[(18.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -2.80000000000000009e150

   1. Initial program 74.1%

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

   3. Simplified 77.3%

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

   5. Taylor expanded in j around inf 58.9%

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

   if -2.80000000000000009e150 < j < -2.7000000000000002e-80

   1. Initial program 90.9%

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

   3. Simplified 95.4%

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

      1. associate-*r* 90.9%

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

      2. distribute-rgt-out-- 90.9%

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

      3. associate-*l* 84.2%

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

      4. *-commutative 84.2%

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

      5. *-commutative 84.2%

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

   6. Applied egg-rr 84.2%

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

   7. Taylor expanded in y around inf 31.3%

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

      1. associate-*r* 33.5%

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

   9. Simplified 33.5%

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

   if -2.7000000000000002e-80 < j < 1.75000000000000013e-198

   1. Initial program 86.1%

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

   3. Simplified 86.3%

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

      1. associate-*r* 86.1%

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

      2. distribute-rgt-out-- 86.1%

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

      3. associate-+l- 86.1%

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

      4. associate-*l* 88.7%

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

      5. *-commutative 88.7%

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

      6. *-commutative 88.7%

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

      7. fma-neg 88.7%

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

   6. Applied egg-rr 88.7%

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

   7. Taylor expanded in b around inf 36.7%

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

   if 1.75000000000000013e-198 < j < 3.30000000000000035e-114

   1. Initial program 90.8%

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

   3. Simplified 86.4%

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

      1. associate-*r* 90.8%

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

      2. distribute-rgt-out-- 90.8%

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

      3. associate-*l* 86.2%

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

      4. *-commutative 86.2%

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

      5. *-commutative 86.2%

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

   6. Applied egg-rr 86.2%

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

   7. Taylor expanded in y around inf 20.0%

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

      1. *-commutative 20.0%

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

      2. associate-*r* 20.0%

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

      3. associate-*r* 20.0%

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

      4. *-commutative 20.0%

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

      5. associate-*r* 20.2%

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

      6. *-commutative 20.2%

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

      7. *-commutative 20.2%

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

      8. associate-*l* 20.1%

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

      9. *-commutative 20.1%

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

      10. associate-*l* 20.2%

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

   9. Simplified 20.2%

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

   if 3.30000000000000035e-114 < j

   1. Initial program 80.8%

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

   3. Simplified 82.1%

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

      1. associate-*r* 80.8%

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

      2. distribute-rgt-out-- 80.8%

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

      3. associate-+l- 80.8%

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

      4. associate-*l* 80.9%

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

      5. *-commutative 80.9%

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

      6. *-commutative 80.9%

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

      7. fma-neg 80.9%

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

   6. Applied egg-rr 80.9%

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

   7. Taylor expanded in j around inf 35.9%

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

      1. associate-*r* 35.8%

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

      2. *-commutative 35.8%

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

      3. *-commutative 35.8%

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

   9. Simplified 35.8%

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

4. Final simplification 37.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.8 \cdot 10^{+150}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;j \leq -2.7 \cdot 10^{-80}:\\ \;\;\;\;18 \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot t\right)\right)\\ \mathbf{elif}\;j \leq 1.75 \cdot 10^{-198}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;j \leq 3.3 \cdot 10^{-114}:\\ \;\;\;\;z \cdot \left(t \cdot \left(x \cdot \left(18 \cdot y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 49.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;j \leq -7.5 \cdot 10^{+135}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 6.5 \cdot 10^{-204}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;j \leq 3.2 \cdot 10^{-128}:\\ \;\;\;\;z \cdot \left(t \cdot \left(x \cdot \left(18 \cdot y\right)\right)\right)\\ \mathbf{elif}\;j \leq 1.7 \cdot 10^{-93}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (+ (* b c) (* j (* k -27.0)))))
   (if (<= j -7.5e+135)
     t_1
     (if (<= j 6.5e-204)
       (- (* b c) (* 4.0 (* t a)))
       (if (<= j 3.2e-128)
         (* z (* t (* x (* 18.0 y))))
         (if (<= j 1.7e-93) (- (* 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);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) + (j * (k * -27.0));
	double tmp;
	if (j <= -7.5e+135) {
		tmp = t_1;
	} else if (j <= 6.5e-204) {
		tmp = (b * c) - (4.0 * (t * a));
	} else if (j <= 3.2e-128) {
		tmp = z * (t * (x * (18.0 * y)));
	} else if (j <= 1.7e-93) {
		tmp = (b * c) - (4.0 * (x * i));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b * c) + (j * (k * (-27.0d0)))
    if (j <= (-7.5d+135)) then
        tmp = t_1
    else if (j <= 6.5d-204) then
        tmp = (b * c) - (4.0d0 * (t * a))
    else if (j <= 3.2d-128) then
        tmp = z * (t * (x * (18.0d0 * y)))
    else if (j <= 1.7d-93) then
        tmp = (b * c) - (4.0d0 * (x * i))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) + (j * (k * -27.0));
	double tmp;
	if (j <= -7.5e+135) {
		tmp = t_1;
	} else if (j <= 6.5e-204) {
		tmp = (b * c) - (4.0 * (t * a));
	} else if (j <= 3.2e-128) {
		tmp = z * (t * (x * (18.0 * y)));
	} else if (j <= 1.7e-93) {
		tmp = (b * c) - (4.0 * (x * i));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) + (j * (k * -27.0))
	tmp = 0
	if j <= -7.5e+135:
		tmp = t_1
	elif j <= 6.5e-204:
		tmp = (b * c) - (4.0 * (t * a))
	elif j <= 3.2e-128:
		tmp = z * (t * (x * (18.0 * y)))
	elif j <= 1.7e-93:
		tmp = (b * c) - (4.0 * (x * i))
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) + Float64(j * Float64(k * -27.0)))
	tmp = 0.0
	if (j <= -7.5e+135)
		tmp = t_1;
	elseif (j <= 6.5e-204)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(t * a)));
	elseif (j <= 3.2e-128)
		tmp = Float64(z * Float64(t * Float64(x * Float64(18.0 * y))));
	elseif (j <= 1.7e-93)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) + (j * (k * -27.0));
	tmp = 0.0;
	if (j <= -7.5e+135)
		tmp = t_1;
	elseif (j <= 6.5e-204)
		tmp = (b * c) - (4.0 * (t * a));
	elseif (j <= 3.2e-128)
		tmp = z * (t * (x * (18.0 * y)));
	elseif (j <= 1.7e-93)
		tmp = (b * c) - (4.0 * (x * i));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -7.5e+135], t$95$1, If[LessEqual[j, 6.5e-204], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.2e-128], N[(z * N[(t * N[(x * N[(18.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.7e-93], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -7.49999999999999947e135 or 1.70000000000000001e-93 < j

   1. Initial program 80.0%

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

   3. Simplified 81.7%

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

   5. Taylor expanded in b around inf 50.2%

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

   if -7.49999999999999947e135 < j < 6.49999999999999939e-204

   1. Initial program 87.1%

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

   3. Simplified 89.0%

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

      1. associate-*r* 87.1%

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

      2. distribute-rgt-out-- 87.1%

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

      3. associate-+l- 87.1%

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

      4. associate-*l* 86.9%

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

      5. *-commutative 86.9%

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

      6. *-commutative 86.9%

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

      7. fma-neg 86.9%

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

   6. Applied egg-rr 86.9%

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

   7. Taylor expanded in x around inf 77.7%

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

      1. associate-*r* 77.7%

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

      2. *-commutative 77.7%

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

   9. Simplified 77.7%

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

   10. Taylor expanded in x around 0 51.5%

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

   if 6.49999999999999939e-204 < j < 3.1999999999999998e-128

   1. Initial program 88.8%

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

   3. Simplified 83.4%

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

      1. associate-*r* 88.8%

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

      2. distribute-rgt-out-- 88.8%

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

      3. associate-*l* 83.2%

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

      4. *-commutative 83.2%

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

      5. *-commutative 83.2%

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

   6. Applied egg-rr 83.2%

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

   7. Taylor expanded in y around inf 13.3%

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

      1. *-commutative 13.3%

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

      2. associate-*r* 13.3%

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

      3. associate-*r* 13.3%

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

      4. *-commutative 13.3%

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

      5. associate-*r* 13.5%

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

      6. *-commutative 13.5%

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

      7. *-commutative 13.5%

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

      8. associate-*l* 13.5%

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

      9. *-commutative 13.5%

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

      10. associate-*l* 13.5%

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

   9. Simplified 13.5%

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

   if 3.1999999999999998e-128 < j < 1.70000000000000001e-93

   1. Initial program 99.7%

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

   3. Taylor expanded in t around 0 52.7%

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

   4. Taylor expanded in j around 0 51.9%

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

4. Final simplification 48.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -7.5 \cdot 10^{+135}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;j \leq 6.5 \cdot 10^{-204}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;j \leq 3.2 \cdot 10^{-128}:\\ \;\;\;\;z \cdot \left(t \cdot \left(x \cdot \left(18 \cdot y\right)\right)\right)\\ \mathbf{elif}\;j \leq 1.7 \cdot 10^{-93}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 32.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;j \leq -2.8 \cdot 10^{+150}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;j \leq -1.1 \cdot 10^{+102}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;j \leq -6.2 \cdot 10^{-43}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;j \leq 3.3 \cdot 10^{-114}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= j -2.8e+150)
   (* -27.0 (* j k))
   (if (<= j -1.1e+102)
     (* x (* i -4.0))
     (if (<= j -6.2e-43)
       (* -4.0 (* t a))
       (if (<= j 3.3e-114) (* b c) (* k (* j -27.0)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (j <= -2.8e+150) {
		tmp = -27.0 * (j * k);
	} else if (j <= -1.1e+102) {
		tmp = x * (i * -4.0);
	} else if (j <= -6.2e-43) {
		tmp = -4.0 * (t * a);
	} else if (j <= 3.3e-114) {
		tmp = b * c;
	} else {
		tmp = k * (j * -27.0);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (j <= (-2.8d+150)) then
        tmp = (-27.0d0) * (j * k)
    else if (j <= (-1.1d+102)) then
        tmp = x * (i * (-4.0d0))
    else if (j <= (-6.2d-43)) then
        tmp = (-4.0d0) * (t * a)
    else if (j <= 3.3d-114) then
        tmp = b * c
    else
        tmp = k * (j * (-27.0d0))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (j <= -2.8e+150) {
		tmp = -27.0 * (j * k);
	} else if (j <= -1.1e+102) {
		tmp = x * (i * -4.0);
	} else if (j <= -6.2e-43) {
		tmp = -4.0 * (t * a);
	} else if (j <= 3.3e-114) {
		tmp = b * c;
	} else {
		tmp = k * (j * -27.0);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if j <= -2.8e+150:
		tmp = -27.0 * (j * k)
	elif j <= -1.1e+102:
		tmp = x * (i * -4.0)
	elif j <= -6.2e-43:
		tmp = -4.0 * (t * a)
	elif j <= 3.3e-114:
		tmp = b * c
	else:
		tmp = k * (j * -27.0)
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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 (j <= -2.8e+150)
		tmp = Float64(-27.0 * Float64(j * k));
	elseif (j <= -1.1e+102)
		tmp = Float64(x * Float64(i * -4.0));
	elseif (j <= -6.2e-43)
		tmp = Float64(-4.0 * Float64(t * a));
	elseif (j <= 3.3e-114)
		tmp = Float64(b * c);
	else
		tmp = Float64(k * Float64(j * -27.0));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (j <= -2.8e+150)
		tmp = -27.0 * (j * k);
	elseif (j <= -1.1e+102)
		tmp = x * (i * -4.0);
	elseif (j <= -6.2e-43)
		tmp = -4.0 * (t * a);
	elseif (j <= 3.3e-114)
		tmp = b * c;
	else
		tmp = k * (j * -27.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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[j, -2.8e+150], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.1e+102], N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -6.2e-43], N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.3e-114], N[(b * c), $MachinePrecision], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -2.80000000000000009e150

   1. Initial program 74.1%

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

   3. Simplified 77.3%

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

   5. Taylor expanded in j around inf 58.9%

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

   if -2.80000000000000009e150 < j < -1.10000000000000004e102

   1. Initial program 90.9%

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

   3. Simplified 90.8%

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

      1. associate-*r* 90.9%

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

      2. distribute-rgt-out-- 90.9%

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

      3. associate-+l- 90.9%

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

      4. associate-*l* 73.2%

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

      5. *-commutative 73.2%

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

      6. *-commutative 73.2%

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

      7. fma-neg 73.2%

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

   6. Applied egg-rr 73.2%

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

   7. Taylor expanded in i around inf 19.7%

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

      1. *-commutative 19.7%

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

      2. *-commutative 19.7%

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

      3. associate-*r* 19.7%

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

   9. Simplified 19.7%

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

   if -1.10000000000000004e102 < j < -6.1999999999999999e-43

   1. Initial program 89.3%

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

   3. Simplified 96.4%

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

      1. associate-*r* 89.2%

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

      2. distribute-rgt-out-- 89.2%

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

      3. associate-+l- 89.2%

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

      4. associate-*l* 85.7%

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

      5. *-commutative 85.7%

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

      6. *-commutative 85.7%

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

      7. fma-neg 85.7%

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

   6. Applied egg-rr 85.7%

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

   7. Taylor expanded in a around inf 26.6%

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

      1. *-commutative 26.6%

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

      2. *-commutative 26.6%

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

   9. Simplified 26.6%

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

   if -6.1999999999999999e-43 < j < 3.30000000000000035e-114

   1. Initial program 87.9%

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

   3. Simplified 87.0%

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

      1. associate-*r* 87.9%

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

      2. distribute-rgt-out-- 87.9%

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

      3. associate-+l- 87.9%

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

      4. associate-*l* 88.7%

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

      5. *-commutative 88.7%

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

      6. *-commutative 88.7%

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

      7. fma-neg 88.7%

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

   6. Applied egg-rr 88.7%

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

   7. Taylor expanded in b around inf 35.9%

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

   if 3.30000000000000035e-114 < j

   1. Initial program 80.8%

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

   3. Simplified 82.1%

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

      1. associate-*r* 80.8%

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

      2. distribute-rgt-out-- 80.8%

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

      3. associate-+l- 80.8%

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

      4. associate-*l* 80.9%

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

      5. *-commutative 80.9%

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

      6. *-commutative 80.9%

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

      7. fma-neg 80.9%

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

   6. Applied egg-rr 80.9%

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

   7. Taylor expanded in j around inf 35.9%

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

      1. associate-*r* 35.8%

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

      2. *-commutative 35.8%

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

      3. *-commutative 35.8%

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

   9. Simplified 35.8%

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

4. Final simplification 36.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.8 \cdot 10^{+150}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;j \leq -1.1 \cdot 10^{+102}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;j \leq -6.2 \cdot 10^{-43}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;j \leq 3.3 \cdot 10^{-114}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 51.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.55 \cdot 10^{+92} \lor \neg \left(t \leq 1.1 \cdot 10^{-8}\right):\\ \;\;\;\;b \cdot c - 4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= t -1.55e+92) (not (<= t 1.1e-8)))
   (- (* b c) (* 4.0 (* t a)))
   (+ (* b c) (* j (* k -27.0)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((t <= -1.55e+92) || !(t <= 1.1e-8)) {
		tmp = (b * c) - (4.0 * (t * a));
	} else {
		tmp = (b * c) + (j * (k * -27.0));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((t <= (-1.55d+92)) .or. (.not. (t <= 1.1d-8))) then
        tmp = (b * c) - (4.0d0 * (t * a))
    else
        tmp = (b * c) + (j * (k * (-27.0d0)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((t <= -1.55e+92) || !(t <= 1.1e-8)) {
		tmp = (b * c) - (4.0 * (t * a));
	} else {
		tmp = (b * c) + (j * (k * -27.0));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (t <= -1.55e+92) or not (t <= 1.1e-8):
		tmp = (b * c) - (4.0 * (t * a))
	else:
		tmp = (b * c) + (j * (k * -27.0))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((t <= -1.55e+92) || !(t <= 1.1e-8))
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(t * a)));
	else
		tmp = Float64(Float64(b * c) + Float64(j * Float64(k * -27.0)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((t <= -1.55e+92) || ~((t <= 1.1e-8)))
		tmp = (b * c) - (4.0 * (t * a));
	else
		tmp = (b * c) + (j * (k * -27.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[t, -1.55e+92], N[Not[LessEqual[t, 1.1e-8]], $MachinePrecision]], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.5500000000000001e92 or 1.0999999999999999e-8 < t

   1. Initial program 91.2%

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

   3. Simplified 92.1%

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

      1. associate-*r* 91.2%

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

      2. distribute-rgt-out-- 91.2%

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

      3. associate-+l- 91.2%

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

      4. associate-*l* 82.6%

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

      5. *-commutative 82.6%

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

      6. *-commutative 82.6%

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

      7. fma-neg 82.6%

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

   6. Applied egg-rr 82.6%

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

   7. Taylor expanded in x around inf 77.7%

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

      1. associate-*r* 77.7%

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

      2. *-commutative 77.7%

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

   9. Simplified 77.7%

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

   10. Taylor expanded in x around 0 52.1%

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

   if -1.5500000000000001e92 < t < 1.0999999999999999e-8

   1. Initial program 78.3%

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

   3. Simplified 81.2%

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

   5. Taylor expanded in b around inf 57.0%

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

4. Final simplification 54.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.55 \cdot 10^{+92} \lor \neg \left(t \leq 1.1 \cdot 10^{-8}\right):\\ \;\;\;\;b \cdot c - 4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 47.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{+195}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{+111}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= t -1e+195)
   (* -4.0 (* t a))
   (if (<= t 5.8e+111)
     (+ (* b c) (* j (* k -27.0)))
     (* 18.0 (* t (* x (* y z)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (t <= -1e+195) {
		tmp = -4.0 * (t * a);
	} else if (t <= 5.8e+111) {
		tmp = (b * c) + (j * (k * -27.0));
	} else {
		tmp = 18.0 * (t * (x * (y * z)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (t <= (-1d+195)) then
        tmp = (-4.0d0) * (t * a)
    else if (t <= 5.8d+111) then
        tmp = (b * c) + (j * (k * (-27.0d0)))
    else
        tmp = 18.0d0 * (t * (x * (y * z)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (t <= -1e+195) {
		tmp = -4.0 * (t * a);
	} else if (t <= 5.8e+111) {
		tmp = (b * c) + (j * (k * -27.0));
	} else {
		tmp = 18.0 * (t * (x * (y * z)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if t <= -1e+195:
		tmp = -4.0 * (t * a)
	elif t <= 5.8e+111:
		tmp = (b * c) + (j * (k * -27.0))
	else:
		tmp = 18.0 * (t * (x * (y * z)))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (t <= -1e+195)
		tmp = Float64(-4.0 * Float64(t * a));
	elseif (t <= 5.8e+111)
		tmp = Float64(Float64(b * c) + Float64(j * Float64(k * -27.0)));
	else
		tmp = Float64(18.0 * Float64(t * Float64(x * Float64(y * z))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (t <= -1e+195)
		tmp = -4.0 * (t * a);
	elseif (t <= 5.8e+111)
		tmp = (b * c) + (j * (k * -27.0));
	else
		tmp = 18.0 * (t * (x * (y * z)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[t, -1e+195], N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.8e+111], N[(N[(b * c), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.99999999999999977e194

   1. Initial program 90.4%

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

   3. Simplified 90.4%

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

      1. associate-*r* 90.4%

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

      2. distribute-rgt-out-- 90.4%

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

      3. associate-+l- 90.4%

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

      4. associate-*l* 85.9%

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

      5. *-commutative 85.9%

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

      6. *-commutative 85.9%

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

      7. fma-neg 85.9%

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

   6. Applied egg-rr 85.9%

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

   7. Taylor expanded in a around inf 53.5%

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

      1. *-commutative 53.5%

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

      2. *-commutative 53.5%

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

   9. Simplified 53.5%

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

   if -9.99999999999999977e194 < t < 5.7999999999999999e111

   1. Initial program 82.8%

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

   3. Simplified 85.0%

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

   5. Taylor expanded in b around inf 54.3%

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

   if 5.7999999999999999e111 < t

   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 88.8%

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

      1. associate-*r* 86.3%

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

      2. distribute-rgt-out-- 86.3%

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

      3. associate-*l* 77.4%

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

      4. *-commutative 77.4%

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

      5. *-commutative 77.4%

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

   6. Applied egg-rr 77.4%

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

   7. Taylor expanded in y around inf 44.3%

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

4. Final simplification 52.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{+195}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{+111}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 32.9% accurate, 2.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;j \leq -4.4 \cdot 10^{+141} \lor \neg \left(j \leq 3.3 \cdot 10^{-114}\right):\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= j -4.4e+141) (not (<= j 3.3e-114))) (* -27.0 (* j k)) (* b c)))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((j <= -4.4e+141) || !(j <= 3.3e-114)) {
		tmp = -27.0 * (j * k);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((j <= (-4.4d+141)) .or. (.not. (j <= 3.3d-114))) then
        tmp = (-27.0d0) * (j * k)
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((j <= -4.4e+141) || !(j <= 3.3e-114)) {
		tmp = -27.0 * (j * k);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (j <= -4.4e+141) or not (j <= 3.3e-114):
		tmp = -27.0 * (j * k)
	else:
		tmp = b * c
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((j <= -4.4e+141) || !(j <= 3.3e-114))
		tmp = Float64(-27.0 * Float64(j * k));
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((j <= -4.4e+141) || ~((j <= 3.3e-114)))
		tmp = -27.0 * (j * k);
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[j, -4.4e+141], N[Not[LessEqual[j, 3.3e-114]], $MachinePrecision]], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if j < -4.4e141 or 3.30000000000000035e-114 < j

   1. Initial program 79.9%

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

   3. Simplified 81.6%

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

   5. Taylor expanded in j around inf 41.9%

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

   if -4.4e141 < j < 3.30000000000000035e-114

   1. Initial program 88.0%

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

   3. Simplified 88.8%

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

      1. associate-*r* 88.0%

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

      2. distribute-rgt-out-- 88.0%

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

      3. associate-+l- 88.0%

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

      4. associate-*l* 87.1%

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

      5. *-commutative 87.1%

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

      6. *-commutative 87.1%

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

      7. fma-neg 87.1%

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

   6. Applied egg-rr 87.1%

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

   7. Taylor expanded in b around inf 30.8%

      \[\leadsto \color{blue}{b \cdot c} \]
3. Recombined 2 regimes into one program.

4. Final simplification 36.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -4.4 \cdot 10^{+141} \lor \neg \left(j \leq 3.3 \cdot 10^{-114}\right):\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 32.9% accurate, 2.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;j \leq -2.3 \cdot 10^{+141}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;j \leq 2.8 \cdot 10^{-114}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= j -2.3e+141)
   (* -27.0 (* j k))
   (if (<= j 2.8e-114) (* b c) (* k (* j -27.0)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (j <= -2.3e+141) {
		tmp = -27.0 * (j * k);
	} else if (j <= 2.8e-114) {
		tmp = b * c;
	} else {
		tmp = k * (j * -27.0);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (j <= (-2.3d+141)) then
        tmp = (-27.0d0) * (j * k)
    else if (j <= 2.8d-114) then
        tmp = b * c
    else
        tmp = k * (j * (-27.0d0))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (j <= -2.3e+141) {
		tmp = -27.0 * (j * k);
	} else if (j <= 2.8e-114) {
		tmp = b * c;
	} else {
		tmp = k * (j * -27.0);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if j <= -2.3e+141:
		tmp = -27.0 * (j * k)
	elif j <= 2.8e-114:
		tmp = b * c
	else:
		tmp = k * (j * -27.0)
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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 (j <= -2.3e+141)
		tmp = Float64(-27.0 * Float64(j * k));
	elseif (j <= 2.8e-114)
		tmp = Float64(b * c);
	else
		tmp = Float64(k * Float64(j * -27.0));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (j <= -2.3e+141)
		tmp = -27.0 * (j * k);
	elseif (j <= 2.8e-114)
		tmp = b * c;
	else
		tmp = k * (j * -27.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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[j, -2.3e+141], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.8e-114], N[(b * c), $MachinePrecision], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if j < -2.3000000000000002e141

   1. Initial program 77.7%

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

   3. Simplified 80.4%

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

   5. Taylor expanded in j around inf 56.6%

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

   if -2.3000000000000002e141 < j < 2.8000000000000001e-114

   1. Initial program 88.0%

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

   3. Simplified 88.8%

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

      1. associate-*r* 88.0%

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

      2. distribute-rgt-out-- 88.0%

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

      3. associate-+l- 88.0%

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

      4. associate-*l* 87.1%

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

      5. *-commutative 87.1%

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

      6. *-commutative 87.1%

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

      7. fma-neg 87.1%

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

   6. Applied egg-rr 87.1%

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

   7. Taylor expanded in b around inf 30.8%

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

   if 2.8000000000000001e-114 < j

   1. Initial program 80.8%

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

   3. Simplified 82.1%

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

      1. associate-*r* 80.8%

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

      2. distribute-rgt-out-- 80.8%

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

      3. associate-+l- 80.8%

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

      4. associate-*l* 80.9%

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

      5. *-commutative 80.9%

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

      6. *-commutative 80.9%

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

      7. fma-neg 80.9%

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

   6. Applied egg-rr 80.9%

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

   7. Taylor expanded in j around inf 35.9%

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

      1. associate-*r* 35.8%

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

      2. *-commutative 35.8%

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

      3. *-commutative 35.8%

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

   9. Simplified 35.8%

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

4. Final simplification 36.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.3 \cdot 10^{+141}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;j \leq 2.8 \cdot 10^{-114}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 23.5% accurate, 10.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 84.1%

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

3. Simplified 84.9%

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

   1. associate-*r* 84.1%

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

   2. distribute-rgt-out-- 84.1%

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

   3. associate-+l- 84.1%

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

   4. associate-*l* 82.5%

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

   5. *-commutative 82.5%

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

   6. *-commutative 82.5%

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

   7. fma-neg 82.5%

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

6. Applied egg-rr 82.5%

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

7. Taylor expanded in b around inf 23.5%

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

8. Final simplification 23.5%

   \[\leadsto b \cdot c \]
9. Add Preprocessing

Developer target: 89.2% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024021 
(FPCore (x y z t a b c i j k)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, E"
  :precision binary64

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

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