Found another example that shows horrible performance when using itertools.product:

def gen():
  l = [itertools.permutations(range(10)) for _ in range(10)]
  g = itertools.product(*l)
  for i in g:
    yield i

A simple next() to this generator takes 16 seconds on my desktop.

I use this recursive product() instead and the performance is acceptable:

def product(*args):
    if len(args) == 1:
        for i in args[0]:
            yield [i]
    else:
        for i in args[0]:
            for j in product(*args[1:]):
                j.append(i)
                yield j