code: def test_invoke_in_pt2_compiled_autograd_side_effect(self):
      def _side_effect_stateful_fn2(x, obj):
          obj.counter = obj.counter + 1
          return _multiply(x)
  
      def _side_effectful_invoke2(grad, fn):
          return trace_wrapped(grad, fn=fn)
  
      graph = None
  
      def compiler_fn(gm):
          def inner_compiler(gm_, example_inputs_):
              nonlocal graph
              self.assertEqual(graph, None)
              graph = gm_
              return inductor.compile(gm_, example_inputs_)
  
          return torch.compile(
              gm, backend=inner_compiler, fullgraph=True, dynamic=True
          )
  
      for backend in ["eager", "aot_eager", "inductor"]:
          torch._dynamo.reset()
          x = torch.tensor([0.5, 0.5], requires_grad=True)
          y = torch.tensor([0.5, 0.5], requires_grad=True)
  
          class MyObj:
              def __init__(self):
                  self.counter = 0
  
          obj = MyObj()
          inner_fn = functools.partial(
              _side_effect_stateful_fn2, obj=obj
          )
          hook_fn = functools.partial(
              _side_effectful_invoke2, fn=inner_fn
          )
          x.register_hook(hook_fn)
  
          def fn(x, y):
              return x + y
  
          fn = torch._dynamo.optimize(backend, nopython=True)(fn)
          out = fn(x, y)
          grad_out = torch.tensor([2.0, 2.0])
          with compiled_autograd.enable(compiler_fn):
              out.backward(grad_out)
          actual = normalize_gm(graph.print_readable(False))
          self.assertEqual(obj.counter, 1)
          self.assertEqual(x.grad, grad_out + grad_out)
          self.assertExpectedInline(
              actual,
              """\
  class GraphModule(torch.nn.Module):
      def forward(self, s0 : torch.SymInt, L_inputs_0_ : torch.Tensor, L_inputs_1_ : torch.Tensor, L_inputs_2_ : torch.Tensor):
          getitem = L_inputs_0_
          getitem_1 = L_inputs_1_
          getitem_2 = L_inputs_2_
  
          accumulate_grad__default = torch.ops.inductor.accumulate_grad_.default(getitem_1, getitem);  getitem_1 = None
  
          call_hook = getitem * getitem;  getitem = None
  
          accumulate_grad__default_1 = torch.ops.inductor.accumulate_grad_.default(getitem_2, call_hook);  getitem_2 = call_hook = None
          return ()
  """,
          )
  
          out = fn(x, y)
          out.backward(grad_out)
          self.assertEqual(obj.counter, 2)
  
          out = fn(x, y)
          out.backward(grad_out)
          self.assertEqual(obj.counter, 3)
          graph = None
  
imports: import functools
  import torch
  import torch._dynamo.test_case
  import torch._dynamo.testing
  import torch._dynamo.utils
  from torch import _inductor
  from torch._dynamo import compiled_autograd
  from torch._dynamo._trace_wrapped_higher_order_op import trace_wrapped
  from torch._dynamo.testing import normalize_gm
  from torch._dynamo.utils import counters
  from torch.fx.experimental.proxy_tensor import make_fx
label_desc: Use image node_id 6 for calling the BackwardHigherOrderOpTests obj's underlying member method code with example usage: obj.test_invoke_in_pt2_compiled_autograd_side_effect() and returns: _multiply, trace_wrapped, torch, inductor, unknown