The artificial singularity, the point when the machine becomes capable of besting us and start improving itself hasn't happened yet. Or it might very well be already underway. Contrary to the popular view ot doesn't have to mean the machine suddenly becomes much smarter than us. It doesn't really have to match us in all accounts, just need to be able to improve itself in a meaningful way. The difference can be miniscule.
To compare the next singularity we can have a look at our own singularity, the point when we took of and left the animal world behind. We learned to improve ourselves over generations, passing our knowledge forward for our offsprings to build on top of it.
We aren't actually that far ahead of other animals, or at least we weren't back then. Unfortunately we still haven't gotten too far from those days. We are limited by our biology. Despite all the advancement in knowledge we haven't been able to improve ourselves in any meaningful way to truly pull us apart from our kins.