I suppose this could be called a feature since the routine will fail if you
comment out the error since it needs a sign change to find the root. But
perhaps the refine_root could check return the evaluated root in that range
if it can be found explicitly.

Perhaps it would be better to evaluate RootOf instances:

>>> RootOf(x**5+x**3+1,0)
RootOf(x**5 + x**3 + 1, 0)
>>> _.n()
-0.837619774826962
>>> RootOf(eq,0).n()  # your equation
0.381966011250105

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