diff --git a/llvm/lib/Transforms/InstCombine/InstCombineAndOrXor.cpp b/llvm/lib/Transforms/InstCombine/InstCombineAndOrXor.cpp
--- a/llvm/lib/Transforms/InstCombine/InstCombineAndOrXor.cpp
+++ b/llvm/lib/Transforms/InstCombine/InstCombineAndOrXor.cpp
@@ -1351,6 +1351,14 @@
     unsigned FCmpCodeL = getFCmpCode(PredL);
     unsigned FCmpCodeR = getFCmpCode(PredR);
     unsigned NewPred = IsAnd ? FCmpCodeL & FCmpCodeR : FCmpCodeL | FCmpCodeR;
+
+    // Intersect the fast math flags.
+    // TODO: We can union the fast math flags.
+    IRBuilder<>::FastMathFlagGuard FMFG(Builder);
+    FastMathFlags FMF = LHS->getFastMathFlags();
+    FMF &= RHS->getFastMathFlags();
+    Builder.setFastMathFlags(FMF);
+
     return getFCmpValue(NewPred, LHS0, LHS1, Builder);
   }
 
diff --git a/llvm/test/Transforms/InstCombine/and-fcmp.ll b/llvm/test/Transforms/InstCombine/and-fcmp.ll
--- a/llvm/test/Transforms/InstCombine/and-fcmp.ll
+++ b/llvm/test/Transforms/InstCombine/and-fcmp.ll
@@ -3120,3 +3120,47 @@
   %retval = select i1 %cmp, i1 %cmp1, i1 false
   ret i1 %retval
 }
+
+define i1 @intersect_fmf_1(double %a, double %b) {
+; CHECK-LABEL: @intersect_fmf_1(
+; CHECK-NEXT:    [[TMP1:%.*]] = fcmp fast oeq double [[A:%.*]], [[B:%.*]]
+; CHECK-NEXT:    ret i1 [[TMP1]]
+;
+  %cmp = fcmp fast ole double %a, %b
+  %cmp1 = fcmp fast oge double %a, %b
+  %retval = and i1 %cmp, %cmp1
+  ret i1 %retval
+}
+
+define i1 @intersect_fmf_2(double %a, double %b) {
+; CHECK-LABEL: @intersect_fmf_2(
+; CHECK-NEXT:    [[TMP1:%.*]] = fcmp oeq double [[A:%.*]], [[B:%.*]]
+; CHECK-NEXT:    ret i1 [[TMP1]]
+;
+  %cmp = fcmp fast ole double %a, %b
+  %cmp1 = fcmp oge double %a, %b
+  %retval = and i1 %cmp, %cmp1
+  ret i1 %retval
+}
+
+define i1 @intersect_fmf_3(double %a, double %b) {
+; CHECK-LABEL: @intersect_fmf_3(
+; CHECK-NEXT:    [[TMP1:%.*]] = fcmp oeq double [[A:%.*]], [[B:%.*]]
+; CHECK-NEXT:    ret i1 [[TMP1]]
+;
+  %cmp = fcmp ole double %a, %b
+  %cmp1 = fcmp fast oge double %a, %b
+  %retval = and i1 %cmp, %cmp1
+  ret i1 %retval
+}
+
+define i1 @intersect_fmf_4(double %a, double %b) {
+; CHECK-LABEL: @intersect_fmf_4(
+; CHECK-NEXT:    [[TMP1:%.*]] = fcmp oeq double [[A:%.*]], [[B:%.*]]
+; CHECK-NEXT:    ret i1 [[TMP1]]
+;
+  %cmp = fcmp ninf ole double %a, %b
+  %cmp1 = fcmp nnan oge double %a, %b
+  %retval = and i1 %cmp, %cmp1
+  ret i1 %retval
+}
diff --git a/llvm/test/Transforms/InstCombine/or-fcmp.ll b/llvm/test/Transforms/InstCombine/or-fcmp.ll
--- a/llvm/test/Transforms/InstCombine/or-fcmp.ll
+++ b/llvm/test/Transforms/InstCombine/or-fcmp.ll
@@ -3072,3 +3072,47 @@
   %retval = select i1 %cmp, i1 true, i1 %cmp1
   ret i1 %retval
 }
+
+define i1 @intersect_fmf_1(double %a, double %b) {
+; CHECK-LABEL: @intersect_fmf_1(
+; CHECK-NEXT:    [[TMP1:%.*]] = fcmp fast one double [[A:%.*]], [[B:%.*]]
+; CHECK-NEXT:    ret i1 [[TMP1]]
+;
+  %cmp = fcmp fast olt double %a, %b
+  %cmp1 = fcmp fast ogt double %a, %b
+  %retval = or i1 %cmp, %cmp1
+  ret i1 %retval
+}
+
+define i1 @intersect_fmf_2(double %a, double %b) {
+; CHECK-LABEL: @intersect_fmf_2(
+; CHECK-NEXT:    [[TMP1:%.*]] = fcmp one double [[A:%.*]], [[B:%.*]]
+; CHECK-NEXT:    ret i1 [[TMP1]]
+;
+  %cmp = fcmp fast olt double %a, %b
+  %cmp1 = fcmp ogt double %a, %b
+  %retval = or i1 %cmp, %cmp1
+  ret i1 %retval
+}
+
+define i1 @intersect_fmf_3(double %a, double %b) {
+; CHECK-LABEL: @intersect_fmf_3(
+; CHECK-NEXT:    [[TMP1:%.*]] = fcmp one double [[A:%.*]], [[B:%.*]]
+; CHECK-NEXT:    ret i1 [[TMP1]]
+;
+  %cmp = fcmp olt double %a, %b
+  %cmp1 = fcmp fast ogt double %a, %b
+  %retval = or i1 %cmp, %cmp1
+  ret i1 %retval
+}
+
+define i1 @intersect_fmf_4(double %a, double %b) {
+; CHECK-LABEL: @intersect_fmf_4(
+; CHECK-NEXT:    [[TMP1:%.*]] = fcmp one double [[A:%.*]], [[B:%.*]]
+; CHECK-NEXT:    ret i1 [[TMP1]]
+;
+  %cmp = fcmp ninf olt double %a, %b
+  %cmp1 = fcmp nnan ogt double %a, %b
+  %retval = or i1 %cmp, %cmp1
+  ret i1 %retval
+}