They still could be caching them. The first time they encounter a factorial, they calculate it, throw it in a DB, and it's a quick DB access from then on.
It looks great, but its error handling could be improved. When I forgot to copy a bracket, it emptied the text box and gave me a generic error message. It would be helpful if it could at least give a line number for the error, and refill the text box. Also, putting "jsonifier" or something in front of the title would be great. When I have 15-20 tabs open, I only see 5-6 characters of the title, and "auto-f" doesn't allow for me to easily switch to something.
Other than that, it looks like a useful service, and well done.
I know about GTalk, and have used it in the past, but nobody uses it, possibly because nobody knows about it. The extent of most people's interactions with GMail are the Inbox and the Send Message workflow. Few people bother setting up contacts in GMail (it's all in their phones), and even fewer will actually click on a contact to be able to see the "Invite To Chat" button.
I'm a teenager in a public high school, and I have not seen a single person use Google+. This is not because Google+ is age limited, or because Google+ is inferior, but because nobody uses Google+. Already, most people I know (including non "techies"), use Facebook primarily for chat. The rest of the Facebook features are just "extra", and used occasionally. Unless Google can pull something revolutionary out of their hat (or Facebook has a major blunder) in regards to chat, they aren't going to be able to pull the teenage community over.
Note that this is from my personal experiences, and has a high probability of being completely wrong when you look at a broader population.