code: def test_modified_partial_sum_product_6(
      impl,
      sum_op,
      prod_op,
      vars1,
      vars2,
      x_dim,
      y_dim,
      sequences,
      time,
      tones,
  ):
      f1 = random_tensor(OrderedDict({}))
  
      f2 = random_tensor(
          OrderedDict(
              {"sequences": Bint[sequences], "x_0": Bint[x_dim]}
          )
      )
  
      f3 = random_tensor(
          OrderedDict(
              {
                  "sequences": Bint[sequences],
                  "time": Bint[time],
                  "x_prev": Bint[x_dim],
                  "x_curr": Bint[x_dim],
              }
          )
      )
  
      f4 = random_tensor(
          OrderedDict(
              {
                  "sequences": Bint[sequences],
                  "tones": Bint[tones],
                  "x_0": Bint[x_dim],
                  "y_0": Bint[y_dim],
              }
          )
      )
  
      f5 = random_tensor(
          OrderedDict(
              {
                  "sequences": Bint[sequences],
                  "time": Bint[time],
                  "tones": Bint[tones],
                  "x_curr": Bint[x_dim],
                  "y_curr": Bint[y_dim],
              }
          )
      )
  
      factors = [f1, f2, f3, f4, f5]
      plate_to_step = {
          "sequences": {},
          "time": frozenset({("x_0", "x_prev", "x_curr")}),
          "tones": {},
      }
  
      factors1 = impl(sum_op, prod_op, factors, vars1, plate_to_step)
      factors2 = impl(sum_op, prod_op, factors1, vars2, plate_to_step)
      actual = reduce(prod_op, factors2)
  
      with lazy:
          (
              unrolled_factors,
              unrolled_vars,
              remaining_plates,
          ) = partial_unroll(factors, vars1 | vars2, plate_to_step)
          expected = reduce(prod_op, unrolled_factors).reduce(
              sum_op, unrolled_vars
          )
      expected = apply_optimizer(expected)
  
      assert_close(actual, expected, atol=5e-4, rtol=5e-4)
  
imports: import os
  import re
  from collections import OrderedDict
  from functools import partial, reduce
  import pytest
  import funsor.ops
  from funsor.domains import Bint, Real, Reals
  from funsor.interpretations import compress_gaussians, eager, eager_or_die, lazy, moment_matching, reflect
  from funsor.interpreter import reinterpret
  from funsor.optimizer import apply_optimizer
  from funsor.sum_product import MarkovProduct, _partition, dynamic_partial_sum_product, mixed_sequential_sum_product, modified_partial_sum_product, naive_sarkka_bilmes_product, naive_sequential_sum_product, partial_sum_product, partial_unroll, sarkka_bilmes_product, sequential_sum_product, sum_product
  from funsor.tensor import Tensor, get_default_prototype
  from funsor.terms import Cat, Variable
  from funsor.testing import assert_close, random_gaussian, random_tensor
  from funsor.util import get_backend
label_desc: Use image node_id 18 for calling a global function with example usage: test_modified_partial_sum_product_6(impl, sum_op, prod_op, vars1, vars2, x_dim, y_dim, sequences, time, tones) without return types