xnum :
((6-4*sqrt(2))*log(3-2*sqrt(2))+(3-2*sqrt(2))*log(17-12*sqrt(2))+32-24*sqrt(2));
xden :(48*sqrt(2)-72)*(log(sqrt(2)+1)+sqrt(2))/3;
x : xnum/xden;
fpprec:40;
bfloat(radcan(x^16)); produces 1. Actually, the number
1.000000000000000009792437985633294125296b0.
bfloat(radcan(x^32)); produces 0.0b0.
So, we have this situation:
there is a number p such p^16 is 1, but p^32 is zero.
To see more about this, look at sci.math.symbolic, or
http://12000.org/my_notes/simplification_in_CAS/index.htm