code: def check(
      self, f, t, delta, check_val=True, graph_input=False, P=None
  ):
      """
      check if the CSE modified graph of ``f``
      1) has delta less nodes, and
      2) do not reduce the number of nodes further on a second pass, and
      3) modified returned is true only if the number of nodes decreases.
  
      Args:
          f: function to be checked
          t: tensor to be passed to f
          delta: an integer >= -1.
                 If delta = -1, it only checks if the new graph has less or equal number of nodes
          check_val: if True, check if the output of f is correct
          graph_input: True is f is type GraphModule
          P: the pass to use. If None, use P_default
      """
      if graph_input:
          fx_g = f
      else:
          fx_g = make_fx(f)(t)
  
      if P is None:
          P = P_default
  
      res = P(fx_g)
      new_g = res.graph_module
      new_graph = new_g.graph
      modified = res.modified
  
      # the number of nodes decrease/ or stay the same
      old_num_nodes = len(fx_g.graph.nodes)
      new_num_nodes = len(new_graph.nodes)
  
      assert (
          new_num_nodes < old_num_nodes
      ) == modified, (
          "modified should be True if the number of nodes decrease"
      )
  
      if delta == -1:
          self.assertTrue(
              old_num_nodes >= new_num_nodes,
              (
                  f"number of nodes increased {old_num_nodes}, {new_num_nodes}"
              ),
          )
      else:
          self.assertTrue(
              old_num_nodes == new_num_nodes + delta,
              (
                  f"number of nodes not the same {old_num_nodes - delta}, {new_num_nodes}\n {fx_g.graph} \n {new_graph}"
              ),
          )
  
      # a second pass should not reduce more nodes
      res = P(new_g)
      pass_2_graph = res.graph_module.graph
      pass_2_num_nodes = len(pass_2_graph.nodes)
      self.assertTrue(
          pass_2_num_nodes == new_num_nodes,
          (
              f"second pass graph has less node {pass_2_num_nodes}, {new_num_nodes}\n {new_graph} \n {pass_2_graph}"
          ),
      )
  
      # check correctness
      if check_val:
          true_result = fx_g(t)
          our_result = new_g(t)
          if true_result is None:  # both return None
              self.assertTrue(
                  our_result is None,
                  f"true result is None, CSE result is {our_result}",
              )
          else:  # results returned are the same
              self.assertTrue(
                  torch.all(true_result == our_result),
                  (
                      f"results are different {true_result}, {our_result}"
                  ),
              )
  
imports: import torch
  from torch.testing._internal.common_utils import TestCase, run_tests
  from torch.fx.experimental.proxy_tensor import make_fx
  from torch.fx.passes.dialect.common.cse_pass import CSEPass, get_CSE_banned_ops
  from torch.fx import symbolic_trace
  import random
label_desc: Use image node_id 1 for calling a global function with example usage: check(f, t, delta, check_val, graph_input, P) without return types