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As Szabolcs suggests, cranking up WorkingPrecision (or for that matter, just forcing Plot[] to use arbitrary precision) helps a lot. In this answer, I've taken the liberty to slightly simplify your barycentric interpolant as well: f[x_] := Sin[x] Ni3[n_Integer, x_] := (x - n) Binomial[x, n] Sum[(-1)^(n - k) Binomial[n, k] f[k]/(x - k), {k, 0, n}, ...