code: def uop(
      self,
      uop: UOps,
      dtype: Optional[DType] = None,
      vin: Tuple[UOp, ...] = tuple(),
      arg: Any = None,
      cachable=True,
      insert_before=None,
      simplify=True,
  ) -> UOp:  # noqa: E501
      if uop == UOps.ALU:
          if arg in UnaryOps:
              assert (
                  dtype == vin[0].dtype
              ), f"{arg} dtype mismatch {dtype=} != {vin[0].dtype=}"
          elif arg in (BinaryOps.CMPLT, BinaryOps.CMPEQ):
              assert (
                  dtype == dtypes.bool
              ), f"{arg} output dtype mismatch {dtype=} != {dtypes.bool}"
              assert (
                  vin[0].dtype == vin[1].dtype
              ), f"{arg} dtype mismatch {dtype=} != {vin[0].dtype=} != {vin[1].dtype=}"
          elif arg in BinaryOps:
              assert (
                  dtype == vin[0].dtype == vin[1].dtype
              ), f"{arg} dtype mismatch {dtype=} != {vin[0].dtype=} != {vin[1].dtype=}"
          elif arg == TernaryOps.WHERE:
              assert (
                  vin[0].dtype == dtypes.bool
              ), f"{arg} selector dtype mismatch {vin[0].dtype=} != {dtypes.bool}"
              assert (
                  dtype == vin[1].dtype == vin[2].dtype
              ), f"{arg} choice dtype mismatch {dtype=} != {vin[1].dtype=} != {vin[2].dtype=}"
  
      if simplify:
          if uop == UOps.PHI and len(vin) == 2:
              return vin[1]  # a phi without loops is a noop
          if uop == UOps.GEP and vin[0].uop == UOps.CONST:
              return self.const(vin[0].arg, dtype, insert_before)
          if (
              uop == UOps.CAST
              and all(x.uop == UOps.CONST for x in vin)
              and all_same([x.arg for x in vin])
          ):
              return self.const(vin[0].arg, dtype, insert_before)
          if uop == UOps.ALU:
              # rewrites. NOTE: the rewritten NEG op is still around...
              if (
                  arg == BinaryOps.ADD
                  and vin[1].uop == UOps.ALU
                  and vin[1].arg == UnaryOps.NEG
              ):
                  return self.uop(
                      UOps.ALU,
                      dtype,
                      (vin[0], vin[1].vin[0]),
                      BinaryOps.SUB,
                      cachable,
                      insert_before,
                  )
              # constant folding
              if arg == UnaryOps.NEG and vin[0].uop == UOps.CONST:
                  return self.const(-vin[0].arg, dtype, insert_before)
              if arg == TernaryOps.WHERE and vin[1] == vin[2]:
                  return vin[
                      1
                  ]  # a conditional with the same results either way is a noop
              # zero folding
              for x in [0, 1]:
                  if (
                      arg == BinaryOps.ADD
                      and vin[x].uop == UOps.CONST
                      and vin[x].arg == 0.0
                  ):
                      return vin[1 - x]
                  if (
                      arg == BinaryOps.MUL
                      and vin[x].uop == UOps.CONST
                      and vin[x].arg == 1.0
                  ):
                      return vin[1 - x]
                  if (
                      arg == BinaryOps.MUL
                      and vin[x].uop == UOps.CONST
                      and vin[x].arg == 0.0
                  ):
                      return vin[x]
              if (
                  arg == BinaryOps.SUB
                  and vin[1].uop == UOps.CONST
                  and vin[1].arg == 0.0
              ):
                  return vin[0]
              if (
                  arg == BinaryOps.DIV
                  and vin[1].uop == UOps.CONST
                  and vin[1].arg == 1.0
              ):
                  return vin[0]
  
      key = (uop, dtype, vin, arg)
      if insert_before is None:
          insert_before = len(self.uops)
      # check if the cached expr is valid with the given insert place.
      if (
          cachable
          and (expr := self.saved_exprs.get(key, None)) is not None
          and self.uops.index(expr) <= insert_before
      ):
          return expr
      ret = UOp(uop, dtype, vin, arg)
      self.uops.insert(insert_before, ret)
      if cachable:
          self.saved_exprs[key] = ret
      return ret
  
imports: from __future__ import annotations
  from typing import List, Tuple, Any, Optional, cast, DefaultDict, Dict, Union, Sequence, Final, Set, Iterator
  import itertools, math, functools
  from collections import defaultdict
  from enum import Enum, auto
  from dataclasses import dataclass
  from tinygrad.dtype import ImageDType, dtypes, DType, PtrDType
  from tinygrad.helpers import colored, DEBUG, prod, getenv, all_same, to_function_name, flatten
  from tinygrad.ops import LazyOp, UnaryOps, BinaryOps, TernaryOps, ReduceOps, ConstBuffer, MemBuffer, BufferOps, get_lazyop_info
  from tinygrad.shape.shapetracker import ShapeTracker
  from tinygrad.shape.symbolic import Variable, NumNode, Node, SumNode, MulNode, DivNode, ModNode, LtNode, AndNode
  from tinygrad.codegen.kernel import LocalBuffer, Kernel
  from tinygrad.features.image import to_image_idx
label_desc: Use image node_id 9 for calling the Linearizer obj's underlying member method code with example usage: obj.uop(uop, dtype, vin, arg, cachable, insert_before, simplify) and returns: ret, expr, vin, self, self, self, self, vin, vin, vin, vin, vin, vin