Well, obviously it depends on what you're actually doing, but generically speaking, productivity per hour going down with more hours worked is pretty much universal. The exact form of the slowdown, when it occurs, and how severe it is will vary, of course.
Fixing the bugs introduced because people were working tired isn't true productivity - I mean, it's productive use of the worker, but it's like the broken window fallacy - fewer bugs would be better yet, because fixing a bug can easily cost more time than producing the original code took.
To consider a few different examples:
1. Coding/Office work: Bugs and/or mistakes start creeping in, requiring rework. I've also heard that as you increase office hours, you also start seeing less and non-productive office activities taking place more often. Meetings have their place, but do you need an hour long one with everybody every day? I've heard that these sorts of meetings tend to be the first to go when you reduce working hours.
2. Taxi driver: The obvious one here would be that a tired driver is dramatically more likely to get into an accident. It doesn't take many wrecked taxi cars to make working those taxi drivers economically negative. That's before you include the deaths, injuries, and such. It's part of why there are so many rules about commercial drivers.
3. Factory worker: This is similar to the coder. One mistake and you ruin a part, meaning you have to replace the part and start over, including any machine work done before the mistake was made. Maybe you can fix it, like welding material back in, or grinding to remove material you shouldn't have added. But that takes time as well.
To use some family careers:
Woodworker - finger meets circular saw
Lumberer - misjudges a cut, drops tree on self
Accountant - makes some weird math errors and judgement calls
Hell, consider the epitome of a "manual labor" job - ditchdigger. It should be obvious that a ditch digger at maximum effort can move much more dirt than one that is hardly trying - but they can only sustain maximum effort for a few minutes, while "hardly trying" is doing so so they can last the entire shift. Productivity, as measured in amount of dirt moved per hour, increases as you have them work fewer hours. When one is concerned more about total dirt moved per day? Then longer hours makes more sense, but there's going to be a limit there where you don't get any more dirt moved per hour worked. It'll probably even start declining.
So yeah, it doesn't really matter - brain meat and physical meat gets tired from work. They need that time off to work right. Mental work can be spread out more easily, perhaps.