For some operations, interval arithmetic yields inaccurate results, either because the result of lifting some operations to intervals does not result in intervals (bitwise operations, for example) or for the sake of simplicity of implementation.
However, one important property holds for all operations. Suppose I, J are intervals and op is an operation. If x is an element of I and y is an element of J, then x op y is an element of I op J.
In other words, the resulting interval might be an overestimate, but it is never an underestimate.