Google/Waymo's California DMV disengagement report for 2016 reports 0.20 disengagements per 1000 miles, or one disengagement per 5000 miles.[1] Google's cars drove 635,868 miles autonomously in 2016, so there's enough driving behind this for that number to be meaningful. This is 4x better than 2015, incidentally. CA DMV accident and disengagement reports are worth reading, since they're one of the few objective data sources available on automatic driving. So far, nobody has been willing to turn a self-driving car over to Top Gear or Road and Track.
Google/Waymo is thus three orders of magnitude better than Uber, and about two orders of magnitude better than anybody else who tests in California.
[1] https://www.dmv.ca.gov/portal/wcm/connect/946b3502-c959-4e3b...