By the Schwartz–Zippel lemma, "Is this arithmetic formula identically zero?" is in coRP $\subseteq$ BPP $\subset$ P/poly, with the second inclusion by Adleman's theorem. By basically following the proof, but using the improved error bound that comes from the original algorithm only having one-sided error, one gets an algorithm that computes suitable advice. (equivalently, a suitable circuit)

Is there any known P/poly algorithm for this problem with advice that can be computed faster?

(I already know about www.cs.sfu.ca/~kabanets/Research/poly.html)