Taylor expansion at undeterminacies

[bfpc]

Consider

@variables x
f = (-1 + sqrt(1 + 4*(x^2)) + 2*x) / (2*x)

The Taylor series for $f$ is $1 + x - x^3 + 2 x^5 + O(x^6)$ (obtained using Wolfram Alpha). Symbolics.jl v7.0.2 complains:

julia> taylor(f, x, 0, 0:5)
ERROR: InexactError: Int64(NaN)
Stacktrace:
  [1] Int64
    @ .\float.jl:994 [inlined]
  [2] rationalize(::Type{Int64}, x::Float64, tol::Float64)
    @ Base .\rational.jl:212
  [3] rationalize
    @ .\rational.jl:266 [inlined]
  [4] rationalize(x::Float64)
    @ Base .\rational.jl:267
  [5] taylor_coeff(f::Num, x::Num, n::Int64; rationalize::Bool, kwargs::@Kwargs{})
    @ Symbolics HOME\.julia\packages\Symbolics\pxCra\src\taylor.jl:102
  [6] taylor_coeff
    @ HOME\.julia\packages\Symbolics\pxCra\src\taylor.jl:66 [inlined]
  [7] (::Symbolics.var"#210#211"{Bool, @Kwargs{}, Num, Num})(n::Int64)
    @ Symbolics .\none:0
  [8] MappingRF
    @ .\reduce.jl:100 [inlined]
  [9] _foldl_impl(op::Base.MappingRF{…}, init::Base._InitialValue, itr::UnitRange{…})
    @ Base .\reduce.jl:58
 [10] foldl_impl
    @ .\reduce.jl:48 [inlined]
 [11] mapfoldl_impl
    @ .\reduce.jl:44 [inlined]
 [12] mapfoldl
    @ .\reduce.jl:175 [inlined]
 [13] mapreduce
    @ .\reduce.jl:307 [inlined]
 [14] sum
    @ .\reduce.jl:532 [inlined]
 [15] sum
    @ .\reduce.jl:561 [inlined]
 [16] #taylor#209
    @ C:\Users\bernardo.paulo\.julia\packages\Symbolics\pxCra\src\taylor.jl:141 [inlined]
 [17] taylor(f::Num, x::Num, x0::Int64, n::UnitRange{Int64}; rationalize::Bool, kwargs::@Kwargs{})
    @ Symbolics HOME\.julia\packages\Symbolics\pxCra\src\taylor.jl:150
 [18] taylor(f::Num, x::Num, x0::Int64, n::UnitRange{Int64})
    @ Symbolics HOME\.julia\packages\Symbolics\pxCra\src\taylor.jl:143
 [19] top-level scope
    @ REPL[31]:1

Is this expected? If so, how to get a series expansion for $f$?