diff --git a/pyopencl/array.py b/pyopencl/array.py
index b6f52abe2e2e4df72d395beaaaf6c0527f0bcc9f..f3dd5e74d467ac175f2c8fcbfa448057ddd19807 100644
--- a/pyopencl/array.py
+++ b/pyopencl/array.py
@@ -32,7 +32,7 @@ import builtins
 from dataclasses import dataclass
 from functools import reduce
 from numbers import Number
-from typing import Any, Dict, Hashable, List, Optional, Tuple, Union
+from typing import Any, Dict, List, Optional, Tuple, Union
 from warnings import warn
 
 import numpy as np
@@ -58,20 +58,14 @@ else:
     _SVMPointer_or_nothing = ()
 
 
-_NUMPY_PRE_2 = np.__version__.startswith("1.")
-
-
 # {{{ _get_common_dtype
 
-_COMMON_DTYPE_CACHE: Dict[Tuple[Hashable, ...], np.dtype] = {}
-
-
 class DoubleDowncastWarning(UserWarning):
     pass
 
 
 _DOUBLE_DOWNCAST_WARNING = (
-        "The operation you requested would result in a double-precisision "
+        "The operation you requested would result in a double-precision "
         "quantity according to numpy semantics. Since your device does not "
         "support double precision, a single-precision quantity is being returned.")
 
@@ -81,78 +75,9 @@ def _get_common_dtype(obj1, obj2, queue):
         raise ValueError("PyOpenCL array has no queue; call .with_queue() to "
                 "add one in order to be able to perform operations")
 
-    allow_double = has_double_support(queue.device)
-    cache_key = None
-    o1_is_array = isinstance(obj1, Array)
-    o2_is_array = isinstance(obj2, Array)
-
-    if o1_is_array and o2_is_array:
-        o1_dtype = obj1.dtype
-        o2_dtype = obj2.dtype
-        cache_key = (obj1.dtype, obj2.dtype, allow_double)
-    else:
-        o1_dtype = getattr(obj1, "dtype", type(obj1))
-        o2_dtype = getattr(obj2, "dtype", type(obj2))
-
-        o1_is_integral = np.issubdtype(o1_dtype, np.integer)
-        o2_is_integral = np.issubdtype(o1_dtype, np.integer)
-
-        o1_key = obj1 if o1_is_integral and not o1_is_array else o1_dtype
-        o2_key = obj2 if o2_is_integral and not o2_is_array else o2_dtype
+    result = np.result_type(obj1, obj2)
 
-        cache_key = (o1_key, o2_key, o1_is_array, o2_is_array, allow_double)
-
-    try:
-        return _COMMON_DTYPE_CACHE[cache_key]
-    except KeyError:
-        pass
-
-    # Numpy's behavior around integers is a bit bizarre, and definitely value-
-    # and not just type-sensitive when it comes to scalars.  We'll just do our
-    # best to emulate it.
-    #
-    # Some samples that are true as of numpy 1.23.1.
-    #
-    # >>> a = np.zeros(1, dtype=np.int16)
-    # >>> (a + 123123123312).dtype
-    # dtype('int64')
-    # >>> (a + 12312).dtype
-    # dtype('int16')
-    # >>> (a + 12312444).dtype
-    # dtype('int32')
-    # >>> (a + np.int32(12312444)).dtype
-    # dtype('int32')
-    # >>> (a + np.int32(1234)).dtype
-    # dtype('int16')
-    #
-    # Note that np.find_common_type, while appealing, won't be able to tell
-    # the full story.
-
-    if (_NUMPY_PRE_2
-            and not (o1_is_array and o2_is_array)
-            and o1_is_integral and o2_is_integral):
-        if o1_is_array:
-            obj1 = np.zeros(1, dtype=o1_dtype)
-        if o2_is_array:
-            obj2 = np.zeros(1, dtype=o2_dtype)
-
-        result = (obj1 + obj2).dtype
-    else:
-        array_types = []
-        scalars = []
-
-        if o1_is_array:
-            array_types.append(o1_dtype)
-        else:
-            scalars.append(obj1)
-        if o2_is_array:
-            array_types.append(o2_dtype)
-        else:
-            scalars.append(obj2)
-
-        result = np.result_type(*array_types, *scalars)
-
-    if not allow_double:
+    if not has_double_support(queue.device):
         if result == np.float64:
             result = np.dtype(np.float32)
             warn(_DOUBLE_DOWNCAST_WARNING, DoubleDowncastWarning, stacklevel=3)
@@ -160,9 +85,6 @@ def _get_common_dtype(obj1, obj2, queue):
             result = np.dtype(np.complex64)
             warn(_DOUBLE_DOWNCAST_WARNING, DoubleDowncastWarning, stacklevel=3)
 
-    if cache_key is not None:
-        _COMMON_DTYPE_CACHE[cache_key] = result
-
     return result
 
 # }}}