code: def test_gammaincc_ddk_performance(benchmark):
      rng = np.random.default_rng(1)
      k = vector("k")
      x = vector("x")
  
      out = gammaincc(k, x)
      grad_fn = function(
          [k, x], grad(out.sum(), wrt=[k]), mode="FAST_RUN"
      )
      vals = [
          # Values that hit the second branch of the gradient
          np.full((1000,), 3.2),
          np.full((1000,), 0.01),
      ]
  
      verify_grad(gammaincc, vals, rng=rng)
      benchmark(grad_fn, *vals)
  
imports: import warnings
  import numpy
  import pytest
  from pytensor.gradient import verify_grad
  from pytensor.scalar import ScalarLoop
  from pytensor.tensor.elemwise import Elemwise
  from functools import partial
  import scipy.special
  import scipy.stats
  from pytensor import function, grad
  from pytensor import tensor
  from pytensor.compile.mode import get_default_mode
  from pytensor.configdefaults import config
  from pytensor.tensor import gammaincc, inplace, vector
  from tests import unittest_tools
  from tests.tensor.utils import _good_broadcast_unary_chi2sf, _good_broadcast_unary_normal, _good_broadcast_unary_normal_float, _good_broadcast_unary_normal_float_no_complex, _good_broadcast_unary_normal_float_no_complex_small_neg_range, _good_broadcast_unary_normal_no_complex, _grad_broadcast_unary_0_2_no_complex, _grad_broadcast_unary_abs1_no_complex, _grad_broadcast_unary_normal, _grad_broadcast_unary_normal_small_neg_range, check_floatX, copymod, integers_ranged, makeBroadcastTester, random_ranged, upcast_int8_nfunc
label_desc: Use image node_id 4 for calling a global function with example usage: test_gammaincc_ddk_performance(benchmark) without return types