I would just use one of the known approximations for the normal CDF 170. In a project of mine, I needed a better log erfc, which is essentially the same (see here 41). Here’s 37 a separate list of erc/erfc approximations. Just pick one that has characteristics you like and which is amenable to a stable log transformation. For me, I used the approximation from Karagiannidis & Lioumpas (2007) (from the erfc approximation link) but splitting/canceling with the log as much as possible. This has small relative error if x is a bit larger than 0; the larger relative error near 0 didn’t matter for me. This 52 is another good thread to take a look at.