This has nothing to do with intervals as such.
@biginterval 1 contains an interval of 0 width, and then:
julia> exponent(0.0)
ERROR: DomainError with 0.0:
Cannot be subnormal converted to 0.
Stacktrace:
[1] (::Base.Math.var"#throw2#4")(::Float64) at ./math.jl:784
[2] exponent(::Float64) at ./math.jl:789
[3] top-level scope at REPL[7]:100:
It does not make sense to ask for the floating-point exponent of 0.0.