docstr: self._simplify_with_ranges() can be expensive, cache its results
code: def make_simplify_with_ranges_cache(
      self,
  ) -> Callable[[Expr, VarRanges], Expr]:
      """
      self._simplify_with_ranges() can be expensive, cache its results
      """
      cache: Dict[Tuple[Any, ...], Expr] = dict()
      replacement_count = len(self.replacements)
  
      def simplify_with_ranges(
          expr: Expr, var_ranges: VarRanges
      ) -> Expr:
          nonlocal replacement_count
          if replacement_count != len(self.replacements):
              # new replacements invalidates cached results
              cache.clear()
              replacement_count = len(self.replacements)
          key = (expr, *var_ranges.items())
          result = cache.get(key, None)
          if result is None:
              result = self._simplify_with_ranges(expr, var_ranges)
              cache[key] = result
          return result
  
      return simplify_with_ranges
  
imports: import functools
  import itertools
  import logging
  from typing import Any, Callable, Dict, Iterable, List, Optional, Set, Tuple, Union
  import sympy
  from sympy import Expr
  from torch.fx.experimental.symbolic_shapes import ShapeEnv
  from torch.utils._sympy.functions import FloorDiv, ModularIndexing
  from torch.utils._sympy.value_ranges import bound_sympy
  from .utils import sympy_subs, sympy_symbol, VarRanges
  from .virtualized import V
label_desc: Use image node_id 3 for calling the SizeVarAllocator obj's underlying member method code with example usage: obj.make_simplify_with_ranges_cache() and returns: simplify_with_ranges, result