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Aren't roots continuous functions of the coefficients?

Why would that matter? I was thinking “If you’d use 4-bit ‘IEEE’ floats, it wouldn’t be very surprising to see an anomaly like this. Would it be for 5-bit ones? 6-bit? What’s a large enough number of bits?”

I also said “For this problem, I don’t see how that would give different results as picking any number in [-1, +1]” because I think 64 is (more than) large enough, but still, I think you’d need an argument if you want to draw a mathematically sound conclusion “this is worth looking into” from such a simulation.

True, the function could in principle have a structure such that sampling it at m/2*n gives a misleading impression of its behavior outside that set. I can't think of an actual function which behaves like that, though (IANAM).

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