code: def saved_variables(
      formula: str,
      nctypes: List[NamedCType],
      var_names: Tuple[str, ...],
  ) -> Tuple[str, Tuple[SavedAttribute, ...]]:
      def stride_expr(name: str) -> str:
          assert var_names == (name,), (
              'Replacement for ".strides()" is currently only supported for single derivatives of the same tensor '
              'that ".strides()" is being called on.'
          )
          return f'strides_or_error({name}, "{name}")'
  
      REPLACEMENTS: List[Tuple[str, Dict[str, Any]]] = [
          # replace self.sym_sizes() with self_sym_sizes
          (
              r"{}.sym_sizes\(\)",
              {
                  "suffix": "_sym_sizes",
                  "nctype": lambda name: NamedCType(
                      name, BaseCType(symIntArrayRefT)
                  ),
              },
          ),
          # replace self->sym_sizes() with self_sym_sizes_opt
          (
              r"{}->sym_sizes\(\)",
              {
                  "suffix": "_sym_sizes_opt",
                  "nctype": lambda name: NamedCType(
                      name, OptionalCType(BaseCType(symIntArrayRefT))
                  ),
                  "expr": lambda name: f"{name}.has_value() ? c10::optional<c10::SymIntArrayRef>({name}->sym_sizes()) : c10::nullopt",
              },
          ),
          # replace self.sym_blocksize() with self_sym_blocksize_opt
          (
              r"{}.sym_blocksize\(\)",
              {
                  "suffix": "_self_sym_blocksize_opt",
                  "nctype": lambda name: NamedCType(
                      name, OptionalCType(BaseCType(symIntArrayRefT))
                  ),
                  "expr": lambda name: f"at::sparse_csr::getSymIntBlockSize({name})",
              },
          ),
          # replace self.options() with self_options
          (
              r"{}.options\(\)",
              {
                  "suffix": "_options",
                  "nctype": lambda name: NamedCType(
                      name, BaseCType(tensorOptionsT)
                  ),
              },
          ),
          # replace zeros_like(self) with self_info
          (
              r"zeros_like\({}\)",
              {
                  "suffix": "_info",
                  "nctype": lambda name: NamedCType(
                      name, BaseCType(typeAndSizeT)
                  ),
                  "expr": lambda name: name,  # at save-time
                  "res": lambda name: name
                  + "_info.zeros()",  # at eval-time
              },
          ),
          # replace self.sym_size(2) with self_sym_size_2
          (
              r"{}.sym_size\((-?\w+)\)",
              {
                  "suffix": lambda m: f"_sym_argsize_{m.groups()[0].replace('-', 'minus_')}",
                  "nctype": lambda name: NamedCType(
                      name, BaseCType(SymIntT)
                  ),
              },
          ),
          # replace self.numel() with self_numel
          (
              r"{}.numel\(\)",
              {
                  "suffix": "_numel",
                  "nctype": lambda name: NamedCType(
                      name, BaseCType(longT)
                  ),
              },
          ),
          # replace self.sym_numel() with self_sym_numel
          (
              r"{}.sym_numel\(\)",
              {
                  "suffix": "_sym_numel",
                  "nctype": lambda name: NamedCType(
                      name, BaseCType(SymIntT)
                  ),
              },
          ),
          # replace to_args_sizes(self) with self_args_sizes
          (
              r"to_args_sizes\({}\)",
              {
                  "suffix": "_args_sizes",
                  "nctype": lambda name: NamedCType(
                      name, VectorCType(VectorCType(BaseCType(longT)))
                  ),
              },
          ),
          # replace to_args_sizes_symint(self) with self_args_sizes
          (
              r"to_args_sizes_symint\({}\)",
              {
                  "suffix": "_args_sizes_symint",
                  "nctype": lambda name: NamedCType(
                      name, VectorCType(VectorCType(BaseCType(SymIntT)))
                  ),
              },
          ),
          # replace to_args_scalartypes(self) with self_args_scalartypes
          (
              r"to_args_scalartypes\({}\)",
              {
                  "suffix": "_args_scalartypes",
                  "nctype": lambda name: NamedCType(
                      name, VectorCType(BaseCType(scalarTypeT))
                  ),
              },
          ),
          # replace TensorGeometry(self) with self_geometry
          (
              r"TensorGeometry\({}\)",
              {
                  "suffix": "_geometry",
                  "nctype": lambda name: NamedCType(
                      name, BaseCType(tensorGeometryT)
                  ),
              },
          ),
          (
              r"{}.scalar_type\(\)",
              {
                  "suffix": "_scalar_type",
                  "nctype": lambda name: NamedCType(
                      name, BaseCType(scalarTypeT)
                  ),
              },
          ),
          # replace self.dim() with self_dim
          (
              r"{}.dim\(\)",
              {
                  "suffix": "_dim",
                  "nctype": lambda name: NamedCType(
                      name, BaseCType(longT)
                  ),
              },
          ),
          # replace self.sym_strides() with self_sym_strides
          (
              r"{}.sym_strides\(\)",
              {
                  "suffix": "_sym_strides",
                  "nctype": lambda name: NamedCType(
                      name, BaseCType(symIntArrayRefT)
                  ),
                  "expr": stride_expr,
              },
          ),
          # replace self.layout() with self_layout
          (
              r"{}.layout\(\)",
              {
                  "suffix": "_layout",
                  "nctype": lambda name: NamedCType(
                      name, BaseCType(layoutT)
                  ),
              },
          ),
          # replace self.is_conj() with self_conjugate
          (
              r"{}.is_conj\(\)",
              {
                  "suffix": "_conjugate",
                  "nctype": lambda name: NamedCType(
                      name, BaseCType(boolT)
                  ),
              },
          ),
      ]
  
      # find which arguments need to be saved
      saved: List[SavedAttribute] = []
  
      if ".sizes()" in formula or "->sizes()" in formula:
          raise RuntimeError(
              ".sizes() is not supported in derivative formulas. Instead, please use the SymInt version,"
              + f".sym_sizes(), which returned a c10::SymIntArrayRef. formula={formula}"
          )
      if re.search(r"\.size\([-]?\d+\)", formula) or re.search(
          r"->size\([-]?\d+\)", formula
      ):
          raise RuntimeError(
              ".size(int) is not supported in derivative formulas. Instead, please use the SymInt version,"
              + f".sym_size(int), which returned a c10::SymIntArrayRef. formula={formula}"
          )
      if ".strides()" in formula or "->strides()" in formula:
          raise RuntimeError(
              ".strides() is not supported in derivative formulas. Instead, please use the SymInt version,"
              + f".sym_strides(), which returned a c10::SymIntArrayRef. formula={formula}"
          )
      for nctype in nctypes:
          name = (
              nctype.name.name
              if isinstance(nctype.name, SpecialArgName)
              else nctype.name
          )
          # First search the formula for expressions which can be evaluated
          # when the autograd Function is created to avoid saving variables
          for regex, info in REPLACEMENTS:
  
              def repl(m: Match[str]) -> str:
                  suffix: str = (
                      info["suffix"](m)
                      if callable(info["suffix"])
                      else info["suffix"]
                  )
                  expr: str = (
                      info["expr"](name)
                      if "expr" in info
                      else m.group(0)
                  )
                  saved.append(
                      SavedAttribute(
                          nctype=info["nctype"](name + suffix),
                          expr=expr,
                      )
                  )
                  if "res" in info:
                      replacement: str = info["res"](name)
                      return replacement
                  return name + suffix
  
              formula = re.sub(regex.format(name), repl, formula)
  
          # c10::optional<std::string> types stored in Backward nodes must be
          # converted to c10::optional<c10::string_view> before being passed into
          # the backward function
          if nctype.type == OptionalCType(BaseCType(stringT)):
              formula = re.sub(
                  rf"\b{name}\b",
                  f"{name}.has_value() ? c10::optional<c10::string_view>({name}.value()) : c10::nullopt",
                  formula,
              )
  
          # Find any variables which remain in the formula and save them
          if re.search(IDENT_REGEX.format(name), formula):
              saved.append(
                  SavedAttribute(
                      nctype=nctype,
                      expr=name,
                  )
              )
  
      return formula, tuple(saved)
  
imports: import re
  from collections import defaultdict
  from typing import Any, Counter, Dict, List, Match, Optional, Sequence, Set, Tuple
  import yaml
  from torchgen.api import cpp
  from torchgen.api.autograd import Derivative, DifferentiabilityInfo, ForwardDerivative, SavedAttribute
  from torchgen.api.types import BaseCType, Binding, boolT, CppSignatureGroup, layoutT, longT, NamedCType, OptionalCType, scalarTypeT, SpecialArgName, stringT, symIntArrayRefT, SymIntT, tensorGeometryT, tensorOptionsT, typeAndSizeT, VectorCType
  from torchgen.context import with_native_function
  from torchgen.gen import get_grouped_by_view_native_functions, parse_native_yaml
  from torchgen.model import AUTOGRAD_KEYS, FunctionSchema, NativeFunction, NativeFunctionsViewGroup, OperatorName, SchemaKind, Type, Variant
  from torchgen.utils import concatMap, IDENT_REGEX, split_name_params
  from torchgen.yaml_utils import YamlLoader
label_desc: Use image node_id 10 for calling a global function with example usage: saved_variables(formula, nctypes, var_names) and returns: formula,  tuple, str, name, str, name, str, unknown, replacement