Example 1:
> verbosity=1!;
> a = 1+ 2^(-55)+2^(-115);
> TD(a);
1.00000000000000002775557561562891353466491600711096
> prec=110!;
> TD(a);
Warning: double rounding occurred on invoking the triple-double rounding operator.
Try to increase the working precision.
1.000000000000000027755575615628913