BS methodologies are also aware of the increased cost of late discovery, so they spend more time and money early on trying to catch the mistakes. The idea is that we can afford to spend x60 on every requirements assertion, so we can afford to write so much more. Personally, I think this backfires, because the actual time spent on requirements is much more than x60, and the cost of programming changes is also higher. As usual, XP goes farther in this direction than any other methodology. Programmer happens to have just written a unit test for that, unit test shows up the mistake.
Programmer fixes it, reruns test, checks in the software.
Call it 4-20 minutes. Compare that with Programmer misses a test case. Test department or whoever does final check on this beast has spent untold hours inventing weird and wonderful tests. Tester fills in bug log with test that fails and information available. If we are really lucky, they pass on the bug reports to the original programmer team.