def run_test(module):
    # cols have stack depths
    # rows have len(sys.modules)

    def print_line(h, *vals):
        if not h:
            print("%5s" % h, *["%6i" % v for v in vals])
        else:
            print("%5s" % h, *["%6.1f" % v for v in vals])

    def add_modules(n):
        import random
        import sys
        for _ in range(n):
            sys.modules[f"foo_{random.randint(0,2**64)}"] = module

    def measure(depth):
        import inspect
        import timeit

        def nest(level):
            if level > 0:
                return nest(level-1)
            else:
                dur = timeit.timeit(lambda: inspect.stack(), number=1)
                return dur * 1000

        return nest(depth)

    import sys
    print_line("", *[2**e for e in range(7)])
    for i in range(1, 5):
        add_modules(n=10**i)
        times = [measure(depth=2**e) for e in range(7)]
        print_line(len(sys.modules), *times)

python 3.11.0a7+ optimized build ====

# sys has no __file__ and doesn't enter getmodule cache
>>> import sys
>>> run_test(sys)
           1      2      4      8     16     32     64
   87    2.1    0.8    1.0    1.3    2.0    3.3    6.1
  187    2.0    2.5    2.7    3.6    5.5    9.5   16.8
 1187   13.6   15.7   19.1   26.3   39.6   67.4  123.3
11187  134.1  150.3  183.4  252.0  383.5  750.3 1189.8
>>> exit()

>>> import random
>>> run_test(random)
           1      2      4      8     16     32     64
   87    2.1    0.7    0.9    1.2    1.7    2.9    5.6
  187    2.3    1.1    1.5    1.8    2.5    4.3    7.8
 1187   17.0    4.3    5.6    7.1   11.1   18.6   33.9
11187  164.6   37.4   45.7   61.6   94.7  161.0  297.7
>>> exit()