Required precision of a pricing library

How accurate does a derivative pricing function need to be?

Accurate enough that pricing error is small relative to the bid-offer spread and to model uncertainty, while staying fast and smooth. Errors far below the spread add nothing commercially, but the function must be stable and smooth in its inputs so that Greeks computed by bumping are not dominated by noise, and consistent so that hedges and risk reports agree. The right trade-off depends on whether it is used for quoting, risk or calibration.