2_16

In interval arithmetic, equivalent algebraic expressions
may lead to different answers because interval arithmetic
does not strictly follow the rules of arithmetic in
algebra. Any algebraic identity that has more than one
occurence of an uncertain variable in it's RHS would "fail"
in interval arithmetic.

If one were to devise an interval-arithmetic package, one
would have to implement identity to introduce a way for the
user to get reciprocals. Just because two intervals are equal
does not mean their division would lead to one, but the SAME
interval divided by itself should lead to one.

Perhaps it is possible to devise such an arithmetic package,
but that seems very hard (as the problem hint states), and
I am not even going to attempt doing such a thing.

As a start to that interval package, one would have to devise
a way to reduce algebraic expressions to their simplest form
with the least number of occurences of uncertain variables.