Index: lib/Analysis/ValueTracking.cpp
===================================================================
--- lib/Analysis/ValueTracking.cpp
+++ lib/Analysis/ValueTracking.cpp
@@ -2817,10 +2817,13 @@
     default:
       break;
     case Intrinsic::maxnum:
-      return cannotBeOrderedLessThanZeroImpl(I->getOperand(0), TLI, SignBitOnly,
-                                             Depth + 1) ||
-             cannotBeOrderedLessThanZeroImpl(I->getOperand(1), TLI, SignBitOnly,
-                                             Depth + 1);
+      return (isKnownNeverNaN(I->getOperand(0)) &&
+              cannotBeOrderedLessThanZeroImpl(I->getOperand(0), TLI,
+                                              SignBitOnly, Depth + 1)) ||
+             (isKnownNeverNaN(I->getOperand(1)) &&
+              cannotBeOrderedLessThanZeroImpl(I->getOperand(1), TLI,
+                                              SignBitOnly, Depth + 1));
+
     case Intrinsic::minnum:
       return cannotBeOrderedLessThanZeroImpl(I->getOperand(0), TLI, SignBitOnly,
                                              Depth + 1) &&
Index: test/Transforms/InstSimplify/floating-point-compare.ll
===================================================================
--- test/Transforms/InstSimplify/floating-point-compare.ll
+++ test/Transforms/InstSimplify/floating-point-compare.ll
@@ -266,13 +266,15 @@
   ret i1 %uge
 }
 
-; FIXME: This is wrong.
 ; PR37776: https://bugs.llvm.org/show_bug.cgi?id=37776
 ; exp() may return nan, leaving %1 as the unknown result, so we can't simplify.
 
 define i1 @orderedLessZeroMaxNum(float, float) {
 ; CHECK-LABEL: @orderedLessZeroMaxNum(
-; CHECK-NEXT:    ret i1 true
+; CHECK-NEXT:    [[A:%.*]] = call float @llvm.exp.f32(float [[TMP0:%.*]])
+; CHECK-NEXT:    [[B:%.*]] = call float @llvm.maxnum.f32(float [[A]], float [[TMP1:%.*]])
+; CHECK-NEXT:    [[UGE:%.*]] = fcmp uge float [[B]], 0.000000e+00
+; CHECK-NEXT:    ret i1 [[UGE]]
 ;
   %a = call float @llvm.exp.f32(float %0)
   %b = call float @llvm.maxnum.f32(float %a, float %1)