Probably just luck? setprecision(20) doesn’t work for my d=6 example above, but in any case my example shows that there is some randomness in whether the problem occurs.
Clearly, there’s a bug here. It’s usually a distraction, in my experience, to try to perform too much mathematical analysis of a bug. Better to just fix the bug.
I submitted an issue with a simple test case, in which the incorrect results are obtained for ComplexF64 as well (BigFloat is just a distraction here): sometimes returns bogus duplicate roots · Issue #25 · giordano/PolynomialRoots.jl · GitHub