diff --git a/loopy/array_buffer_map.py b/loopy/array_buffer_map.py
index 0be16ce5b3d9b7af477f7ee849d0dbe8e6b90c7c..72fca8a4a17a183251c877e41b033539e2f00c85 100644
--- a/loopy/array_buffer_map.py
+++ b/loopy/array_buffer_map.py
@@ -28,7 +28,7 @@ from islpy import dim_type
 from loopy.symbolic import (get_dependencies, SubstitutionMapper)
 from pymbolic.mapper.substitutor import make_subst_func
 
-from pytools import Record
+from pytools import Record, memoize_method
 from pymbolic import var
 
 
@@ -64,7 +64,7 @@ def to_parameters_or_project_out(param_inames, set_inames, set):
 
 # {{{ construct storage->sweep map
 
-def build_per_access_storage_to_domain_map(accdesc, domain,
+def build_per_access_storage_to_domain_map(storage_axis_exprs, domain,
         storage_axis_names,
         prime_sweep_inames):
 
@@ -91,7 +91,7 @@ def build_per_access_storage_to_domain_map(accdesc, domain,
 
     from loopy.symbolic import aff_from_expr
 
-    for saxis, sa_expr in zip(storage_axis_names, accdesc.storage_axis_exprs):
+    for saxis, sa_expr in zip(storage_axis_names, storage_axis_exprs):
         cns = isl.Constraint.equality_from_aff(
                 aff_from_expr(set_space,
                     var(saxis+"'") - prime_sweep_inames(sa_expr)))
@@ -138,7 +138,7 @@ def build_global_storage_to_sweep_map(kernel, access_descriptors,
     # build footprint
     for accdesc in access_descriptors:
         stor2sweep = build_per_access_storage_to_domain_map(
-                accdesc, domain_dup_sweep,
+                accdesc.storage_axis_exprs, domain_dup_sweep,
                 storage_axis_names,
                 prime_sweep_inames)
 
@@ -336,6 +336,11 @@ class ArrayToBufferMap(object):
             return convexify(domain)
 
     def is_access_descriptor_in_footprint(self, accdesc):
+        return self._is_access_descriptor_in_footprint_inner(
+                tuple(accdesc.storage_axis_exprs))
+
+    @memoize_method
+    def _is_access_descriptor_in_footprint_inner(self, storage_axis_exprs):
         # Make all inames except the sweep parameters. (The footprint may depend on
         # those.) (I.e. only leave sweep inames as out parameters.)
 
@@ -347,7 +352,7 @@ class ArrayToBufferMap(object):
                 set(global_s2s_par_dom.get_var_names(dim_type.param))
                 & self.kernel.all_inames())
 
-        for arg in accdesc.storage_axis_exprs:
+        for arg in storage_axis_exprs:
             arg_inames.update(get_dependencies(arg))
         arg_inames = frozenset(arg_inames)
 
@@ -363,7 +368,8 @@ class ArrayToBufferMap(object):
                 usage_domain = usage_domain.set_dim_name(
                         dim_type.set, i, iname+"'")
 
-        stor2sweep = build_per_access_storage_to_domain_map(accdesc,
+        stor2sweep = build_per_access_storage_to_domain_map(
+                storage_axis_exprs,
                 usage_domain, self.storage_axis_names,
                 self.prime_sweep_inames)