Are there solutions that don't meet the formal definition but still perform just as good as if they did in practical situations? (As in the formal definition i

Are there solutions that don't meet the formal definition but still perform just as good as if they did in practical situations? (As in the formal definition is not what we actually need to get a consistent and reliable system for our real-world application. We need something a little less and then suddenly it's possible to get a similar solution that actually provides C A and P.)