missing_it->second--;
        VLOG(1) << "Op " << op_id << " missing " << missing_it->second
                << " output gradients";
        if (missing_it->second == 0) {
          op_stack.insert(op_stack.begin(), op_id);
        }
      }
    }
  }
  if (!state.op_tape.empty()) {
    return tensorflow::errors::Internal("Invalid tape state.");
  }
  if (result.size() != source_tensor_ids.size()) {