This sounds like unums, a proposed alternative to IEEE floats, where roughly speaking the significand can have variable size thus only boasting as much precision as the accuracy warrants.
Does it solve the equality issue? An epsilon tracker would allow you to say it's equal within the margin of error for the computation.
If so that makes them much more interesting to me. Floating point bugs manifest themselves at non linear parts such as equality and comparison operators.
I haven't really seen the issue of equality dealt with explicitly, but it appears that you can extract the bounds of the interval implied by a given unum. Essentially, it seems like an alternative to interval arithmetic with potentially tighter bounds and faster computation.
If so that makes them much more interesting to me. Floating point bugs manifest themselves at non linear parts such as equality and comparison operators.