First, the video:
This unclassified USAF video of BFM training gone (almost) wrong was originally posted by AviationWeek who provided more information:
After only 22 sec., the F-16 was nose-down almost 50 deg. below the horizon and going supersonic. The shocked instructor called “2 recover!” as the student passed 12,320 ft. at 587 kt. Two seconds later, with the nose down in a 55-deg. dive, altitude at 10,800 ft. and speed passing 613 kt., the worried instructor again calls “2 recover!” In a little less than another 2 sec., as the now frantic instructor makes a third call for the student pilot to pull up, the Auto-GCAS executes a recovery maneuver at 8,760 ft. and 652 kt.
The student pilot at this point comes around and pulls back on the stick, momentarily increasing Gs beyond the Auto-GCAS standard recovery level of 5 to 9.1. Minimum altitude by now is around 4,370 ft., with as little as 2,940 ft. indicated on the radar altimeter. From loss-of-control to recovery takes just under 30 sec.
Even starting at over 17,000 feet, it's amazing how quickly things can go downhill (no pun intended), but kudos to the developers of Auto-GCAS; Lockheed-Martin, NASA, and the Air Force Research Laboratory. It looks like there's one more pilot who owes you guys a beer!