code: def test_computed_table_with_cpu_math_autogradcpu_fallthrough(self):
      global_m = C._dispatch_library("IMPL", "_", "AutogradCPU")
      result = self.commute(
          "foo",
          [
              # m.def("foo", [](const Tensor & x) { return x })
              lambda m: m.def_name_t_t("foo"),
              # m.impl("foo", torch::kCPU, [](const Tensor & x) { return x })
              lambda m: m.impl_t_t("foo", "CPU"),
          ],
      )
      state, table = result.state, result.table
      self.assertExpectedInline(
          state,
          """\
  name: test::foo
  schema: test::foo(Tensor _0) -> Tensor _0
  debug: registered at /dev/null:0
  alias analysis kind: CONSERVATIVE
  CPU: impl_t_t :: (Tensor _0) -> Tensor _0 [ boxed unboxed ]
  CompositeImplicitAutograd[alias]: default_def_name_t_t :: (Tensor _0) -> Tensor _0 [ boxed unboxed ]
  """,
      )
  
      # computed dispatch table is too big, so we only check on a few entries we're interested in.
      extracted_table = extract_dispatch_table_with_keys(
          table, dispatch_keys_to_check
      )
  
      self.assertExpectedInline(
          extracted_table,
          """\
  Undefined: default_def_name_t_t [math kernel]
  CPU: impl_t_t [kernel]
  CUDA: default_def_name_t_t [math kernel]
  XLA: default_def_name_t_t [math kernel]
  AutogradOther: default_def_name_t_t [math kernel]
  AutogradCPU: registered in pytorch framework [backend fallback]
  AutogradCUDA: default_def_name_t_t [math kernel]
  AutogradXLA: default_def_name_t_t [math kernel]
  """,
      )
  
imports: import torch._C
  from torch.testing._internal.common_utils import TestCase, run_tests
  from torch._python_dispatcher import PythonDispatcher
  from collections import namedtuple
  import itertools
  import os
  import re
  import torch.utils.cpp_extension
label_desc: Use image node_id 10 for calling the TestDispatch obj's underlying member method code with example usage: obj.test_computed_table_with_cpu_math_autogradcpu_fallthrough() without return types