diff --git a/llvm/include/llvm/Analysis/ScalarEvolution.h b/llvm/include/llvm/Analysis/ScalarEvolution.h
--- a/llvm/include/llvm/Analysis/ScalarEvolution.h
+++ b/llvm/include/llvm/Analysis/ScalarEvolution.h
@@ -744,6 +744,8 @@
     Exact,
     /// A constant which provides an upper bound on the exact trip count.
     ConstantMaximum,
+    /// An expression which provides an upper bound on the exact trip count.
+    SymbolicMaximum,
   };
 
   /// Return the number of times the backedge executes before the given exit
@@ -780,12 +782,15 @@
   /// SCEVCouldNotCompute object.
   const SCEV *getConstantMaxBackedgeTakenCount(const Loop *L) {
     return getBackedgeTakenCount(L, ConstantMaximum);
-  } 
+  }
 
-  /// Return a symbolic upper bound for the backedge taken count of the loop.
-  /// This is more general than getConstantMaxBackedgeTakenCount as it returns
-  /// an arbitrary expression as opposed to only constants.
-  const SCEV* computeMaxBackedgeTakenCount(const Loop *L);
+  /// When successful, this returns a SCEV that is greater than or equal
+  /// to (i.e. a "conservative over-approximation") of the value returend by
+  /// getBackedgeTakenCount.  If such a value cannot be computed, it returns the
+  /// SCEVCouldNotCompute object.
+  const SCEV *getSymbolicMaxBackedgeTakenCount(const Loop *L) {
+    return getBackedgeTakenCount(L, SymbolicMaximum);
+  }
 
   /// Return true if the backedge taken count is either the value returned by
   /// getConstantMaxBackedgeTakenCount or zero.
@@ -1317,23 +1322,24 @@
     /// never have more than one computable exit.
     SmallVector<ExitNotTakenInfo, 1> ExitNotTaken;
 
-    /// Expression indicating the least maximum backedge-taken count of the loop
-    /// that is known, or a SCEVCouldNotCompute. This expression is only valid
-    /// if the redicates associated with all loop exits are true.
+    /// Expression indicating the least constant maximum backedge-taken count of
+    /// the loop that is known, or a SCEVCouldNotCompute. This expression is
+    /// only valid if the redicates associated with all loop exits are true.
     const SCEV *ConstantMax;
 
     /// Indicating if \c ExitNotTaken has an element for every exiting block in
     /// the loop.
     bool IsComplete;
 
+    /// Expression indicating the least maximum backedge-taken count of the loop
+    /// that is known, or a SCEVCouldNotCompute. Lazily computed on first query.
+    const SCEV *SymbolicMax = nullptr;
+
     /// True iff the backedge is taken either exactly Max or zero times.
     bool MaxOrZero = false;
 
-    /// \name Helper projection functions on \c ConstantMaxAndComplete.
-    /// @{
     bool isComplete() const { return IsComplete; }
     const SCEV *getConstantMax() const { return ConstantMax; }
-    /// @}
 
   public:
     BackedgeTakenInfo() : ConstantMax(nullptr), IsComplete(false) {}
@@ -1391,6 +1397,9 @@
     const SCEV *getConstantMax(const BasicBlock *ExitingBlock,
                                ScalarEvolution *SE) const;
 
+    /// Get the symbolic max backedge taken count for the loop.
+    const SCEV *getSymbolicMax(const Loop *L, ScalarEvolution *SE);
+
     /// Return true if the number of times this backedge is taken is either the
     /// value returned by getConstantMax or zero.
     bool isConstantMaxOrZero(ScalarEvolution *SE) const;
@@ -1543,7 +1552,7 @@
   /// Return the BackedgeTakenInfo for the given loop, lazily computing new
   /// values if the loop hasn't been analyzed yet. The returned result is
   /// guaranteed not to be predicated.
-  const BackedgeTakenInfo &getBackedgeTakenInfo(const Loop *L);
+  BackedgeTakenInfo &getBackedgeTakenInfo(const Loop *L);
 
   /// Similar to getBackedgeTakenInfo, but will add predicates as required
   /// with the purpose of returning complete information.
@@ -1576,6 +1585,11 @@
                                      bool ExitIfTrue, bool ControlsExit,
                                      bool AllowPredicates = false);
 
+  /// Return a symbolic upper bound for the backedge taken count of the loop.
+  /// This is more general than getConstantMaxBackedgeTakenCount as it returns
+  /// an arbitrary expression as opposed to only constants.
+  const SCEV *computeSymbolicMaxBackedgeTakenCount(const Loop *L);
+
   // Helper functions for computeExitLimitFromCond to avoid exponential time
   // complexity.
 
diff --git a/llvm/lib/Analysis/ScalarEvolution.cpp b/llvm/lib/Analysis/ScalarEvolution.cpp
--- a/llvm/lib/Analysis/ScalarEvolution.cpp
+++ b/llvm/lib/Analysis/ScalarEvolution.cpp
@@ -6508,6 +6508,7 @@
                                           ExitCountKind Kind) {
   switch (Kind) {
   case Exact:
+  case SymbolicMaximum:
     return getBackedgeTakenInfo(L).getExact(ExitingBlock, this);
   case ConstantMaximum:
     return getBackedgeTakenInfo(L).getConstantMax(ExitingBlock, this);
@@ -6528,6 +6529,8 @@
     return getBackedgeTakenInfo(L).getExact(L, this);
   case ConstantMaximum:
     return getBackedgeTakenInfo(L).getConstantMax(this);
+  case SymbolicMaximum:
+    return getBackedgeTakenInfo(L).getSymbolicMax(L, this);
   };
   llvm_unreachable("Invalid ExitCountKind!");
 }
@@ -6563,7 +6566,7 @@
   return PredicatedBackedgeTakenCounts.find(L)->second = std::move(Result);
 }
 
-const ScalarEvolution::BackedgeTakenInfo &
+ScalarEvolution::BackedgeTakenInfo &
 ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
   // Initially insert an invalid entry for this loop. If the insertion
   // succeeds, proceed to actually compute a backedge-taken count and
@@ -6850,7 +6853,7 @@
   return SE->getCouldNotCompute();
 }
 
-/// getMax - Get the max backedge taken count for the loop.
+/// getConstantMax - Get the constant max backedge taken count for the loop.
 const SCEV *
 ScalarEvolution::BackedgeTakenInfo::getConstantMax(ScalarEvolution *SE) const {
   auto PredicateNotAlwaysTrue = [](const ExitNotTakenInfo &ENT) {
@@ -6866,6 +6869,14 @@
   return getConstantMax();
 }
 
+const SCEV *
+ScalarEvolution::BackedgeTakenInfo::getSymbolicMax(const Loop *L,
+                                                   ScalarEvolution *SE) {
+  if (!SymbolicMax)
+    SymbolicMax = SE->computeSymbolicMaxBackedgeTakenCount(L);
+  return SymbolicMax;
+}
+
 bool ScalarEvolution::BackedgeTakenInfo::isConstantMaxOrZero(
     ScalarEvolution *SE) const {
   auto PredicateNotAlwaysTrue = [](const ExitNotTakenInfo &ENT) {
@@ -12714,7 +12725,8 @@
   return false;
 }
 
-const SCEV* ScalarEvolution::computeMaxBackedgeTakenCount(const Loop *L) {
+const SCEV *
+ScalarEvolution::computeSymbolicMaxBackedgeTakenCount(const Loop *L) {
   SmallVector<BasicBlock*, 16> ExitingBlocks;
   L->getExitingBlocks(ExitingBlocks);
 
diff --git a/llvm/lib/Transforms/Scalar/IndVarSimplify.cpp b/llvm/lib/Transforms/Scalar/IndVarSimplify.cpp
--- a/llvm/lib/Transforms/Scalar/IndVarSimplify.cpp
+++ b/llvm/lib/Transforms/Scalar/IndVarSimplify.cpp
@@ -2372,7 +2372,7 @@
     return false;
 
   // Get a symbolic upper bound on the loop backedge taken count.
-  const SCEV *MaxExitCount = SE->computeMaxBackedgeTakenCount(L);
+  const SCEV *MaxExitCount = SE->getSymbolicMaxBackedgeTakenCount(L);
   if (isa<SCEVCouldNotCompute>(MaxExitCount))
     return false;