code: def test_logaddexp():
      lae_xy = logaddexp(x, y)
      ref_xy = log(exp(x) + exp(y))
      for wrt, deriv_order in product([x, y, z], range(3)):
          assert (
              lae_xy.diff(wrt, deriv_order)
              - ref_xy.diff(wrt, deriv_order)
          ).rewrite(log).simplify() == 0
  
      one_third_e = 1 * exp(1) / 3
      two_thirds_e = 2 * exp(1) / 3
      logThirdE = log(one_third_e)
      logTwoThirdsE = log(two_thirds_e)
      lae_sum_to_e = logaddexp(logThirdE, logTwoThirdsE)
      assert lae_sum_to_e.rewrite(log) == 1
      assert lae_sum_to_e.simplify() == 1
      was = logaddexp(2, 3)
      assert srepr(was) == srepr(was.simplify())
  
file_path: sympy/sympy/codegen/tests/test_numpy_nodes.py
imports: from itertools import product
  from sympy.core.singleton import S
  from sympy.core.symbol import symbols
  from sympy.functions.elementary.exponential import exp, log
  from sympy.printing.repr import srepr
  from sympy.codegen.numpy_nodes import logaddexp, logaddexp2
label_desc: Use image node_id 1 for calling a global function with example usage: test_logaddexp() without return types