diff --git a/lib/Analysis/InstructionSimplify.cpp b/lib/Analysis/InstructionSimplify.cpp
index 3028f17a526..e7ef6ffd8ad 100644
--- a/lib/Analysis/InstructionSimplify.cpp
+++ b/lib/Analysis/InstructionSimplify.cpp
@@ -1873,7 +1873,7 @@ static Value *SimplifyICmpInst(unsigned Predicate, Value *LHS, Value *RHS,
   CmpInst::Predicate P = CmpInst::BAD_ICMP_PREDICATE;
   CmpInst::Predicate EqP; // Chosen so that "A == max/min(A,B)" iff "A EqP B".
 
-  // Signed max/min.
+  // Signed variants on "max(a,b)>=a -> true".
   if (match(LHS, m_SMax(m_Value(A), m_Value(B))) && (A == RHS || B == RHS)) {
     if (A != RHS) std::swap(A, B); // smax(A, B) pred A.
     EqP = CmpInst::ICMP_SGE; // "A == smax(A, B)" iff "A sge B".
@@ -1929,7 +1929,7 @@ static Value *SimplifyICmpInst(unsigned Predicate, Value *LHS, Value *RHS,
     }
   }
 
-  // Unsigned max/min.
+  // Unsigned variants on "max(a,b)>=a -> true".
   P = CmpInst::BAD_ICMP_PREDICATE;
   if (match(LHS, m_UMax(m_Value(A), m_Value(B))) && (A == RHS || B == RHS)) {
     if (A != RHS) std::swap(A, B); // umax(A, B) pred A.
@@ -1986,6 +1986,50 @@ static Value *SimplifyICmpInst(unsigned Predicate, Value *LHS, Value *RHS,
     }
   }
 
+  // Variants on "max(x,y) >= min(x,z)".
+  Value *C, *D;
+  if (match(LHS, m_SMax(m_Value(A), m_Value(B))) &&
+      match(RHS, m_SMin(m_Value(C), m_Value(D))) &&
+      (A == C || A == D || B == C || B == D)) {
+    // max(x, ?) pred min(x, ?).
+    if (Pred == CmpInst::ICMP_SGE)
+      // Always true.
+      return Constant::getAllOnesValue(ITy);
+    if (Pred == CmpInst::ICMP_SLT)
+      // Always false.
+      return Constant::getNullValue(ITy);
+  } else if (match(LHS, m_SMin(m_Value(A), m_Value(B))) &&
+             match(RHS, m_SMax(m_Value(C), m_Value(D))) &&
+             (A == C || A == D || B == C || B == D)) {
+    // min(x, ?) pred max(x, ?).
+    if (Pred == CmpInst::ICMP_SLE)
+      // Always true.
+      return Constant::getAllOnesValue(ITy);
+    if (Pred == CmpInst::ICMP_SGT)
+      // Always false.
+      return Constant::getNullValue(ITy);
+  } else if (match(LHS, m_UMax(m_Value(A), m_Value(B))) &&
+             match(RHS, m_UMin(m_Value(C), m_Value(D))) &&
+             (A == C || A == D || B == C || B == D)) {
+    // max(x, ?) pred min(x, ?).
+    if (Pred == CmpInst::ICMP_UGE)
+      // Always true.
+      return Constant::getAllOnesValue(ITy);
+    if (Pred == CmpInst::ICMP_ULT)
+      // Always false.
+      return Constant::getNullValue(ITy);
+  } else if (match(LHS, m_UMin(m_Value(A), m_Value(B))) &&
+             match(RHS, m_UMax(m_Value(C), m_Value(D))) &&
+             (A == C || A == D || B == C || B == D)) {
+    // min(x, ?) pred max(x, ?).
+    if (Pred == CmpInst::ICMP_ULE)
+      // Always true.
+      return Constant::getAllOnesValue(ITy);
+    if (Pred == CmpInst::ICMP_UGT)
+      // Always false.
+      return Constant::getNullValue(ITy);
+  }
+
   // If the comparison is with the result of a select instruction, check whether
   // comparing with either branch of the select always yields the same value.
   if (isa<SelectInst>(LHS) || isa<SelectInst>(RHS))
diff --git a/test/Transforms/InstSimplify/maxmin.ll b/test/Transforms/InstSimplify/maxmin.ll
index 6d9225921c2..707422cc01b 100644
--- a/test/Transforms/InstSimplify/maxmin.ll
+++ b/test/Transforms/InstSimplify/maxmin.ll
@@ -143,3 +143,91 @@ define i1 @min8(i32 %x, i32 %y) {
   ret i1 %r
 ; CHECK: ret i1 true
 }
+
+define i1 @maxmin1(i32 %x, i32 %y, i32 %z) {
+; CHECK: @maxmin1
+  %c1 = icmp sge i32 %x, %y
+  %max = select i1 %c1, i32 %x, i32 %y
+  %c2 = icmp sge i32 %x, %z
+  %min = select i1 %c2, i32 %z, i32 %x
+  %c = icmp sge i32 %max, %min
+  ret i1 %c
+; CHECK: ret i1 true
+}
+
+define i1 @maxmin2(i32 %x, i32 %y, i32 %z) {
+; CHECK: @maxmin2
+  %c1 = icmp sge i32 %x, %y
+  %max = select i1 %c1, i32 %x, i32 %y
+  %c2 = icmp sge i32 %x, %z
+  %min = select i1 %c2, i32 %z, i32 %x
+  %c = icmp sgt i32 %min, %max
+  ret i1 %c
+; CHECK: ret i1 false
+}
+
+define i1 @maxmin3(i32 %x, i32 %y, i32 %z) {
+; CHECK: @maxmin3
+  %c1 = icmp sge i32 %x, %y
+  %max = select i1 %c1, i32 %x, i32 %y
+  %c2 = icmp sge i32 %x, %z
+  %min = select i1 %c2, i32 %z, i32 %x
+  %c = icmp sle i32 %min, %max
+  ret i1 %c
+; CHECK: ret i1 true
+}
+
+define i1 @maxmin4(i32 %x, i32 %y, i32 %z) {
+; CHECK: @maxmin4
+  %c1 = icmp sge i32 %x, %y
+  %max = select i1 %c1, i32 %x, i32 %y
+  %c2 = icmp sge i32 %x, %z
+  %min = select i1 %c2, i32 %z, i32 %x
+  %c = icmp slt i32 %max, %min
+  ret i1 %c
+; CHECK: ret i1 false
+}
+
+define i1 @maxmin5(i32 %x, i32 %y, i32 %z) {
+; CHECK: @maxmin5
+  %c1 = icmp uge i32 %x, %y
+  %max = select i1 %c1, i32 %x, i32 %y
+  %c2 = icmp uge i32 %x, %z
+  %min = select i1 %c2, i32 %z, i32 %x
+  %c = icmp uge i32 %max, %min
+  ret i1 %c
+; CHECK: ret i1 true
+}
+
+define i1 @maxmin6(i32 %x, i32 %y, i32 %z) {
+; CHECK: @maxmin6
+  %c1 = icmp uge i32 %x, %y
+  %max = select i1 %c1, i32 %x, i32 %y
+  %c2 = icmp uge i32 %x, %z
+  %min = select i1 %c2, i32 %z, i32 %x
+  %c = icmp ugt i32 %min, %max
+  ret i1 %c
+; CHECK: ret i1 false
+}
+
+define i1 @maxmin7(i32 %x, i32 %y, i32 %z) {
+; CHECK: @maxmin7
+  %c1 = icmp uge i32 %x, %y
+  %max = select i1 %c1, i32 %x, i32 %y
+  %c2 = icmp uge i32 %x, %z
+  %min = select i1 %c2, i32 %z, i32 %x
+  %c = icmp ule i32 %min, %max
+  ret i1 %c
+; CHECK: ret i1 true
+}
+
+define i1 @maxmin8(i32 %x, i32 %y, i32 %z) {
+; CHECK: @maxmin8
+  %c1 = icmp uge i32 %x, %y
+  %max = select i1 %c1, i32 %x, i32 %y
+  %c2 = icmp uge i32 %x, %z
+  %min = select i1 %c2, i32 %z, i32 %x
+  %c = icmp ult i32 %max, %min
+  ret i1 %c
+; CHECK: ret i1 false
+}