code: def _try_isolate_lhs(
      expr: sympy.Basic, thing: sympy.Basic, floordiv_inequality: bool
  ) -> sympy.Basic:
      e = expr
      op = type(expr)
  
      if isinstance(e, sympy.Rel):
          # Move any constants in the left-hand side to the right-hand side.
          lhs_not_thing = (
              sum([a for a in e.lhs.args if not a.has(thing)])
              if isinstance(e.lhs, sympy.Add)
              else 0
          )
          e = op(expr.lhs - lhs_not_thing, expr.rhs - lhs_not_thing)  # type: ignore[attr-defined]
  
      # Divide both sides by the factors that don't contain thing.
      if isinstance(e, sympy.Rel) and isinstance(e.lhs, sympy.Mul):
          lhs, rhs = e.args
          other = sympy.Mul(*[a for a in lhs.args if not a.has(thing)])
  
          # If we can't tell whether 'other' is negative or positive, we do nothing.
          # That is because we don't know whether we have mirror the operation or not.
          if not (
              isinstance(e, INEQUALITY_TYPES)
              and other.is_negative is None
          ):
              # Divide both sides by 'other'.
              lhs = lhs / other
              rhs = rhs / other
  
              # If 'e' is an inequality and 'other' is negative, we have to
              # mirror the expression.
              if isinstance(e, INEQUALITY_TYPES) and other.is_negative:
                  op = mirror_rel_op(op)  # type: ignore[assignment]
  
              assert op is not None
              e = op(lhs, rhs)
  
      ################################################################################
      # left-hand side is FloorDiv
      ################################################################################
      #
      # Given the expression: a // b op c
      # where 'op' is a relational operation, these rules only work if:
      #   - b > 0
      #   - c is an integer
      if (
          floordiv_inequality
          and isinstance(e, sympy.Rel)
          and isinstance(e.lhs, FloorDiv)
          and e.lhs.divisor.is_positive
          and e.rhs.is_integer
      ):
          # a // b == expr
          # => a >= (b * expr) and a < (b * (expr + 1))
          if isinstance(expr, sympy.Eq):
              numerator, denominator = e.lhs.args
              return sympy.And(
                  sympy.Ge(numerator, (e.rhs * denominator)),  # type: ignore[arg-type]
                  sympy.Lt(numerator, ((e.rhs + 1) * denominator)),  # type: ignore[arg-type]
              )
          # a // b != expr
          # => a < (b * expr) or a >= (b * (expr + 1))
          if isinstance(expr, sympy.Ne):
              numerator, denominator = e.lhs.args
              return sympy.Or(
                  sympy.Lt(numerator, (e.rhs * denominator)),  # type: ignore[arg-type]
                  sympy.Ge(numerator, ((e.rhs + 1) * denominator)),  # type: ignore[arg-type]
              )
          # The transformations below only work if b is positive.
          # Note: we only have this information for constants.
          # a // b > expr  => a >= b * (expr + 1)
          # a // b >= expr => a >= b * expr
          if isinstance(expr, (sympy.Gt, sympy.Ge)):
              quotient = e.rhs if isinstance(expr, sympy.Ge) else (e.rhs + 1)  # type: ignore[arg-type]
              return sympy.Ge(e.lhs.args[0], (quotient * e.lhs.args[1]))  # type: ignore[arg-type]
          # a // b < expr  => a < b * expr
          # a // b <= expr => a < b * (expr + 1)
          if isinstance(expr, (sympy.Lt, sympy.Le)):
              quotient = e.rhs if isinstance(expr, sympy.Lt) else (e.rhs + 1)  # type: ignore[arg-type]
              return sympy.Lt(e.lhs.args[0], (quotient * e.lhs.args[1]))  # type: ignore[arg-type]
  
      return e
  
imports: import logging
  from typing import Dict, Optional, Tuple, Type
  import sympy
  from torch.utils._sympy.functions import FloorDiv
label_desc: Use image node_id 3 for calling a global function with example usage: _try_isolate_lhs(expr, thing, floordiv_inequality) and returns: e, sympy, sympy, sympy, sympy