bfloat and factorials



The recent discussion on the thread Re: [Maxima] plot numerical question
made me realize that I may be missing something about bigfloats.

Here I compare expr(bfloat(s)) with bfloat( expr(s) ) when
the expression involves factorials.

In the first case the results are equivalent.
In the second case the results differ but with a pattern.

case 1 agreement:

(%i12) e2f(s):=
       block([], local(ff),
      define(ff(x),factorial(x/4)),
      [bfloat(ff(s)), ff( bfloat(s))] )$

(%i13) for i thru 11 do print(i,e2f(i))$

1 [9.06402b-1,9.06402b-1] 
2 [8.86226b-1,8.86226b-1] 
3 [9.19062b-1,9.19062b-1] 
4 [1.0b0,9.99999b-1] 
5 [1.133b0,1.133b0] 
6 [1.32934b0,1.32934b0] 
7 [1.60835b0,1.60835b0] 
8 [2.0b0,1.99999b0] 
9 [2.54925b0,2.54925b0] 
10 [3.32335b0,3.32335b0] 
11 [4.42298b0,4.42298b0] 


case 2: disagreement with a pattern

(%i14) e3f(s):=
   block([ ],local(r4),
    define( r4(x), x!/(((x/4)!)^4 * 4^x)),
    [bfloat(r4(s)), r4(bfloat(s))] )$

(%i15) for i thru 11 do print(i,e3f(i))$

1 [8.22424b-17,3.70386b-1] 
2 [2.02642b-1,2.02642b-1] 
3 [2.91763b-17,1.31398b-1] 
4 [9.375b-2,9.375b-2] 
5 [1.57905b-17,7.11142b-2] 
6 [5.62895b-2,5.62895b-2] 
7 [1.02074b-17,4.59703b-2] 
8 [3.84521b-2,3.84521b-2] 
9 [7.27794b-18,3.27769b-2] 
10 [2.83699b-2,2.83699b-2] 
11 [5.5217b-18,2.48675b-2] 

What am I missing??

Ted Woollett