diff --git a/llvm/include/llvm/Analysis/ScalarEvolutionExpressions.h b/llvm/include/llvm/Analysis/ScalarEvolutionExpressions.h
index ff24cafbe680..9414c7bb5743 100644
--- a/llvm/include/llvm/Analysis/ScalarEvolutionExpressions.h
+++ b/llvm/include/llvm/Analysis/ScalarEvolutionExpressions.h
@@ -537,14 +537,33 @@ namespace llvm {
     T.visitAll(Root);
   }
 
-  /// Recursively visits a SCEV expression and re-writes it.
+  /// This visitor recursively visits a SCEV expression and re-writes it.
+  /// The result from each visit is cached, so it will return the same
+  /// SCEV for the same input.
   template<typename SC>
   class SCEVRewriteVisitor : public SCEVVisitor<SC, const SCEV *> {
   protected:
     ScalarEvolution &SE;
+    // Memoize the result of each visit so that we only compute once for
+    // the same input SCEV. This is to avoid redundant computations when
+    // a SCEV is referenced by multiple SCEVs. Without memoization, this
+    // visit algorithm would have exponential time complexity in the worst
+    // case, causing the compiler to hang on certain tests.
+    DenseMap<const SCEV *, const SCEV *> RewriteResults;
+
   public:
     SCEVRewriteVisitor(ScalarEvolution &SE) : SE(SE) {}
 
+    const SCEV *visit(const SCEV *S) {
+      auto It = RewriteResults.find(S);
+      if (It != RewriteResults.end())
+        return It->second;
+      auto *Result = SCEVVisitor<SC, const SCEV *>::visit(S);
+      assert(RewriteResults.insert({S, Result}).second &&
+             "Should insert a new entry");
+      return Result;
+    }
+
     const SCEV *visitConstant(const SCEVConstant *Constant) {
       return Constant;
     }
diff --git a/llvm/test/Analysis/ScalarEvolution/pr18606.ll b/llvm/test/Analysis/ScalarEvolution/pr18606.ll
new file mode 100644
index 000000000000..6154a0f7d424
--- /dev/null
+++ b/llvm/test/Analysis/ScalarEvolution/pr18606.ll
@@ -0,0 +1,67 @@
+; RUN: opt -S -indvars < %s | FileCheck %s
+
+; CHECK: @main
+; CHECK: %mul.lcssa5 = phi i32 [ %a.promoted4, %entry ], [ %mul.30, %for.body3 ]
+; CEHCK: %mul = mul nsw i32 %mul.lcssa5, %mul.lcssa5
+; CHECK: %mul.30 = mul nsw i32 %mul.29, %mul.29
+
+target datalayout = "e-m:e-i64:64-f80:128-n8:16:32:64-S128"
+target triple = "x86_64-unknown-linux-gnu"
+
+@a = local_unnamed_addr global i32 0, align 4
+@b = local_unnamed_addr global i32 0, align 4
+
+; Function Attrs: norecurse nounwind uwtable
+define i32 @main() local_unnamed_addr {
+entry:
+  %a.promoted4 = load i32, i32* @a, align 4
+  br label %for.cond1.preheader
+
+for.cond1.preheader:                              ; preds = %entry, %for.body3
+  %mul.lcssa5 = phi i32 [ %a.promoted4, %entry ], [ %mul.30, %for.body3 ]
+  %i.03 = phi i32 [ 0, %entry ], [ %inc5, %for.body3 ]
+  br label %for.body3
+
+for.body3:                                        ; preds = %for.cond1.preheader
+  %mul = mul nsw i32 %mul.lcssa5, %mul.lcssa5
+  %mul.1 = mul nsw i32 %mul, %mul
+  %mul.2 = mul nsw i32 %mul.1, %mul.1
+  %mul.3 = mul nsw i32 %mul.2, %mul.2
+  %mul.4 = mul nsw i32 %mul.3, %mul.3
+  %mul.5 = mul nsw i32 %mul.4, %mul.4
+  %mul.6 = mul nsw i32 %mul.5, %mul.5
+  %mul.7 = mul nsw i32 %mul.6, %mul.6
+  %mul.8 = mul nsw i32 %mul.7, %mul.7
+  %mul.9 = mul nsw i32 %mul.8, %mul.8
+  %mul.10 = mul nsw i32 %mul.9, %mul.9
+  %mul.11 = mul nsw i32 %mul.10, %mul.10
+  %mul.12 = mul nsw i32 %mul.11, %mul.11
+  %mul.13 = mul nsw i32 %mul.12, %mul.12
+  %mul.14 = mul nsw i32 %mul.13, %mul.13
+  %mul.15 = mul nsw i32 %mul.14, %mul.14
+  %mul.16 = mul nsw i32 %mul.15, %mul.15
+  %mul.17 = mul nsw i32 %mul.16, %mul.16
+  %mul.18 = mul nsw i32 %mul.17, %mul.17
+  %mul.19 = mul nsw i32 %mul.18, %mul.18
+  %mul.20 = mul nsw i32 %mul.19, %mul.19
+  %mul.21 = mul nsw i32 %mul.20, %mul.20
+  %mul.22 = mul nsw i32 %mul.21, %mul.21
+  %mul.23 = mul nsw i32 %mul.22, %mul.22
+  %mul.24 = mul nsw i32 %mul.23, %mul.23
+  %mul.25 = mul nsw i32 %mul.24, %mul.24
+  %mul.26 = mul nsw i32 %mul.25, %mul.25
+  %mul.27 = mul nsw i32 %mul.26, %mul.26
+  %mul.28 = mul nsw i32 %mul.27, %mul.27
+  %mul.29 = mul nsw i32 %mul.28, %mul.28
+  %mul.30 = mul nsw i32 %mul.29, %mul.29
+  %inc5 = add nuw nsw i32 %i.03, 1
+  %exitcond = icmp ne i32 %inc5, 10
+  br i1 %exitcond, label %for.cond1.preheader, label %for.end6
+
+for.end6:                                         ; preds = %for.body3
+  %mul.lcssa.lcssa = phi i32 [ %mul.30, %for.body3 ]
+  %inc.lcssa.lcssa = phi i32 [ 31, %for.body3 ]
+  store i32 %mul.lcssa.lcssa, i32* @a, align 4
+  store i32 %inc.lcssa.lcssa, i32* @b, align 4
+  ret i32 0
+}