diff --git a/grudge/symbolic/mappers/__init__.py b/grudge/symbolic/mappers/__init__.py
index 288cc30cf..22137d85b 100644
--- a/grudge/symbolic/mappers/__init__.py
+++ b/grudge/symbolic/mappers/__init__.py
@@ -32,6 +32,7 @@
 import pymbolic.mapper.constant_converter
 import pymbolic.mapper.flop_counter
 from pymbolic.mapper import CSECachingMapperMixin
+from pymbolic.mapper.equality import EqualityMapper as EqualityMapperBase
 
 from grudge import sym
 import grudge.dof_desc as dof_desc
@@ -1295,4 +1296,46 @@ def map_common_subexpression(self, expr):
 # }}}
 
 
+# {{{ equality
+
+class EqualityMapper(EqualityMapperBase):
+    def map_ones(self, expr, other) -> bool:
+        return expr.dd == other.dd
+
+    def map_grudge_variable(self, expr, other) -> bool:
+        return (
+                expr.name == other.name
+                and expr.dd == other.dd)
+
+    def map_node_coordinate_component(self, expr, other) -> bool:
+        return (
+                expr.axis == other.axis
+                and expr.dd == other.dd)
+
+    def map_operator_binding(self, expr, other) -> bool:
+        return (
+                self.rec(expr.op, other.op)
+                and self.rec(expr.field, other.field))
+
+    def map_ref_diff(self, expr, other) -> bool:
+        return (
+                expr.rst_axis == other.rst_axis
+                and expr.dd_in == other.dd_in
+                and expr.dd_out == other.dd_out)
+
+    map_ref_stiffness_t = map_ref_diff
+
+    def map_elementwise_linear(self, expr, other) -> bool:
+        return (
+                expr.dd_in == other.dd_in
+                and expr.dd_out == other.dd_out)
+
+    map_ref_mass = map_elementwise_linear
+    map_ref_inverse_mass = map_elementwise_linear
+    map_face_mass_operator = map_elementwise_linear
+    map_ref_face_mass_operator = map_elementwise_linear
+    map_projection = map_elementwise_linear
+
+# }}}
+
 # vim: foldmethod=marker
diff --git a/grudge/symbolic/operators.py b/grudge/symbolic/operators.py
index 031ec60e0..09e2d811e 100644
--- a/grudge/symbolic/operators.py
+++ b/grudge/symbolic/operators.py
@@ -139,6 +139,11 @@ def __getinitargs__(self):
     def make_stringifier(self, originating_stringifier=None):
         from grudge.symbolic.mappers import StringifyMapper
         return StringifyMapper()
+
+    def make_equality_mapper(self):
+        from grudge.symbolic.mappers import EqualityMapper
+        return EqualityMapper()
+
 # }}}
 
 
diff --git a/grudge/symbolic/primitives.py b/grudge/symbolic/primitives.py
index d95bc657b..77a152bae 100644
--- a/grudge/symbolic/primitives.py
+++ b/grudge/symbolic/primitives.py
@@ -42,6 +42,10 @@ def make_stringifier(self, originating_stringifier=None):
         from grudge.symbolic.mappers import StringifyMapper
         return StringifyMapper()
 
+    def make_equality_mapper(self):
+        from grudge.symbolic.mappers import EqualityMapper
+        return EqualityMapper()
+
 
 __doc__ = """
 
diff --git a/requirements.txt b/requirements.txt
index 2107e5aeb..9f9551855 100644
--- a/requirements.txt
+++ b/requirements.txt
@@ -1,10 +1,10 @@
 numpy
 mpi4py
 git+https://github.com/inducer/pytools.git#egg=pytools
-git+https://github.com/inducer/pymbolic.git#egg=pymbolic
+git+https://github.com/alexfikl/pymbolic.git@equality-mapper#egg=pymbolic
 git+https://github.com/inducer/islpy.git#egg=islpy
 git+https://github.com/inducer/pyopencl.git#egg=pyopencl
-git+https://github.com/inducer/loopy.git#egg=loopy
+git+https://github.com/alexfikl/loopy.git@equality-mapper#egg=loopy
 git+https://github.com/inducer/dagrt.git#egg=dagrt
 git+https://github.com/inducer/leap.git#egg=leap
 git+https://github.com/inducer/meshpy.git#egg=meshpy
@@ -14,7 +14,7 @@ git+https://github.com/inducer/meshmode.git#egg=meshmode
 git+https://github.com/inducer/pyvisfile.git#egg=pyvisfile
 git+https://github.com/inducer/pymetis.git#egg=pymetis
 git+https://github.com/illinois-ceesd/logpyle.git#egg=logpyle
-git+https://github.com/inducer/pytato.git#egg=pytato
+git+https://github.com/alexfikl/pytato.git@equality-mapper#egg=pytato
 
 # for test_wave_dt_estimate
 sympy
diff --git a/test/test_mpi_communication.py b/test/test_mpi_communication.py
index 8e053f6fd..b436e74ee 100644
--- a/test/test_mpi_communication.py
+++ b/test/test_mpi_communication.py
@@ -100,6 +100,7 @@ def run_test_with_mpi_inner():
 
 # {{{ func_comparison
 
+@pytest.mark.mpi
 @pytest.mark.parametrize("actx_class", DISTRIBUTED_ACTXS)
 @pytest.mark.parametrize("num_ranks", [2])
 def test_func_comparison_mpi(actx_class, num_ranks):
@@ -177,6 +178,7 @@ def hopefully_zero():
 
 # {{{ wave operator
 
+@pytest.mark.mpi
 @pytest.mark.parametrize("actx_class", DISTRIBUTED_ACTXS)
 @pytest.mark.parametrize("num_ranks", [2])
 def test_mpi_wave_op(actx_class, num_ranks):