old_contents: import math
  import torch
  from gpytorch.lazy import ToeplitzLazyVariable
  from torch.autograd import Variable
  
  
  def test_exact_gp_mll():
      labels_var = Variable(torch.randn(4))
  
      # Test case
      c1_var = Variable(torch.Tensor([5, 1, 2, 0]), requires_grad=True)
      c2_var = Variable(torch.Tensor([12.5, 2.5, 5, 0]), requires_grad=True)
      toeplitz_lazy_var = ToeplitzLazyVariable(c1_var) * 2.5
      actual = ToeplitzLazyVariable(c2_var)
  
      # Test forward
      mll_res = toeplitz_lazy_var.exact_gp_marginal_log_likelihood(labels_var)
      mll_actual = actual.exact_gp_marginal_log_likelihood(labels_var)
      assert(math.fabs(mll_res.data.squeeze()[0] - mll_actual.data.squeeze()[0]) < 6e-1)
  
      # Test backwards
      mll_res.backward()
      mll_actual.backward()
      assert(math.fabs(c1_var.grad.data[0] - c2_var.grad.data[0]) < 1)
  
  
  def test_getitem():
      c1_var = Variable(torch.Tensor([5, 1, 2, 0]), requires_grad=True)
      c2_var = Variable(torch.Tensor([12.5, 2.5, 5, 0]), requires_grad=True)
      toeplitz_lazy_var = ToeplitzLazyVariable(c1_var) * 2.5
      actual = ToeplitzLazyVariable(c2_var)
  
      assert torch.norm(actual[2:, 2:].evaluate().data - toeplitz_lazy_var[2:, 2:].evaluate().data) < 1e-3
  
new_contents: import math
  import torch
  import gpytorch
  from gpytorch.lazy import ToeplitzLazyVariable
  from torch.autograd import Variable
  
  
  def test_exact_gp_mll():
      labels_var = Variable(torch.randn(4))
  
      # Test case
      c1_var = Variable(torch.Tensor([5, 1, 2, 0]), requires_grad=True)
      c2_var = Variable(torch.Tensor([12.5, 2.5, 5, 0]), requires_grad=True)
      toeplitz_lazy_var = ToeplitzLazyVariable(c1_var) * 2.5
      actual = ToeplitzLazyVariable(c2_var)
  
      # Test forward
      with gpytorch.settings.num_trace_samples(1000):
          mll_res = toeplitz_lazy_var.exact_gp_marginal_log_likelihood(labels_var)
          mll_actual = actual.exact_gp_marginal_log_likelihood(labels_var)
  
      # Test backwards
      mll_res.backward()
      mll_actual.backward()
  
      assert(math.fabs(mll_res.data.squeeze()[0] - mll_actual.data.squeeze()[0]) < 6e-1)
      assert(math.fabs(c1_var.grad.data[0] - c2_var.grad.data[0]) < 1)
  
  
  def test_getitem():
      c1_var = Variable(torch.Tensor([5, 1, 2, 0]), requires_grad=True)
      c2_var = Variable(torch.Tensor([12.5, 2.5, 5, 0]), requires_grad=True)
      toeplitz_lazy_var = ToeplitzLazyVariable(c1_var) * 2.5
      actual = ToeplitzLazyVariable(c2_var)
  
      assert torch.norm(actual[2:, 2:].evaluate().data - toeplitz_lazy_var[2:, 2:].evaluate().data) < 1e-3
  
subject: Improve stability of constant mul lazy variable test