diff --git a/mlir/include/mlir/Analysis/Presburger/IntegerRelation.h b/mlir/include/mlir/Analysis/Presburger/IntegerRelation.h
--- a/mlir/include/mlir/Analysis/Presburger/IntegerRelation.h
+++ b/mlir/include/mlir/Analysis/Presburger/IntegerRelation.h
@@ -133,6 +133,11 @@
   /// (see IntegerRelation::findIntegerSample()).
   bool isEqual(const IntegerRelation &other) const;
 
+  /// Return whether `this` and `other` are equal. The equality check is
+  /// performed in a plain manner, by comparing if all the equalities and
+  /// inequalities in `this` and `other` IntegerRelations are the same.
+  bool isPlainEqual(const IntegerRelation &other) const;
+
   /// Return whether this is a subset of the given IntegerRelation. This is
   /// integer-exact and somewhat expensive, since it uses the integer emptiness
   /// check (see IntegerRelation::findIntegerSample()).
diff --git a/mlir/include/mlir/Analysis/Presburger/PresburgerRelation.h b/mlir/include/mlir/Analysis/Presburger/PresburgerRelation.h
--- a/mlir/include/mlir/Analysis/Presburger/PresburgerRelation.h
+++ b/mlir/include/mlir/Analysis/Presburger/PresburgerRelation.h
@@ -138,6 +138,10 @@
   /// otherwise.
   bool isPlainUniverse() const;
 
+  /// Return true if the set is obviously to be equal with the other set,
+  /// directly comparing whether each internal disjunct is the same
+  bool isPlainEqual(const PresburgerRelation &set) const;
+
   /// Return true if the set is consist of a single disjunct, without any local
   /// variables, false otherwise.
   bool isConvexNoLocals() const;
diff --git a/mlir/lib/Analysis/Presburger/IntegerRelation.cpp b/mlir/lib/Analysis/Presburger/IntegerRelation.cpp
--- a/mlir/lib/Analysis/Presburger/IntegerRelation.cpp
+++ b/mlir/lib/Analysis/Presburger/IntegerRelation.cpp
@@ -80,6 +80,33 @@
   return PresburgerRelation(*this).isEqual(PresburgerRelation(other));
 }
 
+/// The equality check is performed by comparing the number of equalities and
+/// inequalities in `this` and `other` IntegerRelations, and then comparing the
+/// coefficients of each corresponding equality and inequality.
+bool IntegerRelation::isPlainEqual(const IntegerRelation &other) const {
+  if (!space.isCompatible(other.getSpace()))
+    return false;
+  if (getNumEqualities() != other.getNumEqualities())
+    return false;
+  if (getNumInequalities() != other.getNumInequalities())
+    return false;
+
+  unsigned int cols = getNumCols();
+  for (unsigned int i = 0, eqs = getNumEqualities(); i < eqs; ++i) {
+    for (unsigned int j = 0; j < cols; ++j) {
+      if (atEq(i, j) != other.atEq(i, j))
+        return false;
+    }
+  }
+  for (unsigned int i = 0, ineqs = getNumInequalities(); i < ineqs; ++i) {
+    for (unsigned int j = 0; j < cols; ++j) {
+      if (atIneq(i, j) != other.atIneq(i, j))
+        return false;
+    }
+  }
+  return true;
+}
+
 bool IntegerRelation::isSubsetOf(const IntegerRelation &other) const {
   assert(space.isCompatible(other.getSpace()) && "Spaces must be compatible.");
   return PresburgerRelation(*this).isSubsetOf(PresburgerRelation(other));
diff --git a/mlir/lib/Analysis/Presburger/PresburgerRelation.cpp b/mlir/lib/Analysis/Presburger/PresburgerRelation.cpp
--- a/mlir/lib/Analysis/Presburger/PresburgerRelation.cpp
+++ b/mlir/lib/Analysis/Presburger/PresburgerRelation.cpp
@@ -53,9 +53,28 @@
 /// Mutate this set, turning it into the union of this set and the given set.
 ///
 /// This is accomplished by simply adding all the disjuncts of the given set
-/// to this set.
+/// to this set, except for cases where it's obvious that no processing is
+/// needed for.
 void PresburgerRelation::unionInPlace(const PresburgerRelation &set) {
   assert(space.isCompatible(set.getSpace()) && "Spaces should match");
+
+  if (isPlainEqual(set))
+    return;
+
+  if (isPlainEmpty()) {
+    disjuncts = set.disjuncts;
+    return;
+  }
+  if (set.isPlainEmpty())
+    return;
+
+  if (isPlainUniverse())
+    return;
+  if (set.isPlainUniverse()) {
+    disjuncts = set.disjuncts;
+    return;
+  }
+
   for (const IntegerRelation &disjunct : set.disjuncts)
     unionInPlace(disjunct);
 }
@@ -484,6 +503,13 @@
 PresburgerRelation::subtract(const PresburgerRelation &set) const {
   assert(space.isCompatible(set.getSpace()) && "Spaces should match");
   PresburgerRelation result(getSpace());
+
+  // If we know that the two sets are clearly equal, we can simply return the
+  // empty set
+  if (isPlainEqual(set)) {
+    return result;
+  }
+
   // We compute (U_i t_i) \ (U_i set_i) as U_i (t_i \ V_i set_i).
   for (const IntegerRelation &disjunct : disjuncts)
     result.unionInPlace(getSetDifference(disjunct, set));
@@ -503,6 +529,26 @@
   return this->isSubsetOf(set) && set.isSubsetOf(*this);
 }
 
+/// Check if this PresburgerRelation is equal to another given
+/// PresburgerRelation. Two PresburgerRelations are considered equal if they
+/// have the same space, and each disjunct in this PresburgerRelation is equal
+/// to the corresponding disjunct in the other PresburgerRelation.
+bool PresburgerRelation::isPlainEqual(const PresburgerRelation &set) const {
+  if (!space.isCompatible(set.getSpace()))
+    return false;
+
+  if (getNumDisjuncts() != set.getNumDisjuncts())
+    return false;
+
+  // Compare each disjunct in this PresburgerRelation with the corresponding
+  // disjunct in the other PresburgerRelation.
+  for (unsigned int i = 0, n = getNumDisjuncts(); i < n; ++i) {
+    if (!getDisjunct(i).isPlainEqual(set.getDisjunct(i)))
+      return false;
+  }
+  return true;
+}
+
 /// Return true if the Presburger relation represents the universe set, false
 /// otherwise. It is a simple check that only check if the relation has at least
 /// one unconstrained disjunct, indicating the absence of constraints or