diff --git a/src/UnifyDuplicateLets.cpp b/src/UnifyDuplicateLets.cpp
index 5f6e120d6e76..fe163ae20778 100644
--- a/src/UnifyDuplicateLets.cpp
+++ b/src/UnifyDuplicateLets.cpp
@@ -1,6 +1,7 @@
 #include "UnifyDuplicateLets.h"
 #include "IREquality.h"
 #include "IRMutator.h"
+#include "Simplify.h"
 #include <map>
 
 namespace Halide {
@@ -14,31 +15,32 @@ namespace {
 class UnifyDuplicateLets : public IRMutator {
     using IRMutator::visit;
 
-    map<Expr, string, IRDeepCompare> scope;
-    map<string, string> rewrites;
-    string producing;
+    // Map from Exprs to a Variable in the let name that first introduced that
+    // Expr.
+    map<Expr, Expr, IRDeepCompare> scope;
+
+    // Map from Vars to the Expr they should be replaced with.
+    map<string, Expr> rewrites;
 
 public:
     using IRMutator::mutate;
 
     Expr mutate(const Expr &e) override {
-        if (e.defined()) {
-            map<Expr, string, IRDeepCompare>::iterator iter = scope.find(e);
-            if (iter != scope.end()) {
-                return Variable::make(e.type(), iter->second);
-            } else {
-                return IRMutator::mutate(e);
-            }
-        } else {
-            return Expr();
+        Expr new_e = IRMutator::mutate(e);
+
+        if (auto iter = scope.find(new_e);
+            iter != scope.end()) {
+            return iter->second;
         }
+
+        return new_e;
     }
 
 protected:
     Expr visit(const Variable *op) override {
-        map<string, string>::iterator iter = rewrites.find(op->name);
+        auto iter = rewrites.find(op->name);
         if (iter != rewrites.end()) {
-            return Variable::make(op->type, iter->second);
+            return iter->second;
         } else {
             return op;
         }
@@ -56,36 +58,41 @@ class UnifyDuplicateLets : public IRMutator {
         return IRMutator::visit(op);
     }
 
-    Stmt visit(const ProducerConsumer *op) override {
-        if (op->is_producer) {
-            string old_producing = producing;
-            producing = op->name;
-            Stmt stmt = IRMutator::visit(op);
-            producing = old_producing;
-            return stmt;
-        } else {
-            return IRMutator::visit(op);
-        }
-    }
-
     template<typename LetStmtOrLet>
     auto visit_let(const LetStmtOrLet *op) -> decltype(op->body) {
         is_impure = false;
         Expr value = mutate(op->value);
+        Expr simplified = simplify(value);
         auto body = op->body;
 
         bool should_pop = false;
         bool should_erase = false;
 
         if (!is_impure) {
-            map<Expr, string, IRDeepCompare>::iterator iter = scope.find(value);
-            if (iter == scope.end()) {
-                scope[value] = op->name;
-                should_pop = true;
-            } else {
-                value = Variable::make(value.type(), iter->second);
-                rewrites[op->name] = iter->second;
+            if (simplified.as<Variable>() ||
+                simplified.as<IntImm>()) {
+                // The RHS collapsed to just a Var or a constant, so uses of
+                // this should be rewritten to that value and we should drop
+                // this let. The LetStmts at this point in lowering that we're
+                // trying to remove are generally bounds inference expressions,
+                // so it's not worth checking for other types of constant.
+                rewrites[op->name] = simplified;
                 should_erase = true;
+            } else {
+                Expr var = Variable::make(value.type(), op->name);
+
+                // The mutate implementation above checks Exprs
+                // post-mutation but without simplification, so we should
+                // put the unsimplified version of the Expr into the scope.
+                auto [it, inserted] = scope.emplace(value, std::move(var));
+
+                if (inserted) {
+                    should_pop = true;
+                } else {
+                    // We have the same RHS as some earlier Let
+                    should_erase = true;
+                    rewrites[op->name] = it->second;
+                }
             }
         }
 
@@ -96,12 +103,14 @@ class UnifyDuplicateLets : public IRMutator {
         }
         if (should_erase) {
             rewrites.erase(op->name);
+            // We no longer need this let.
+            return body;
         }
 
-        if (value.same_as(op->value) && body.same_as(op->body)) {
+        if (simplified.same_as(op->value) && body.same_as(op->body)) {
             return op;
         } else {
-            return LetStmtOrLet::make(op->name, value, body);
+            return LetStmtOrLet::make(op->name, simplified, body);
         }
     }