diff --git a/llvm/lib/Analysis/ValueTracking.cpp b/llvm/lib/Analysis/ValueTracking.cpp
--- a/llvm/lib/Analysis/ValueTracking.cpp
+++ b/llvm/lib/Analysis/ValueTracking.cpp
@@ -2887,6 +2887,15 @@
       return XKnown.isNonZero() ||
              isKnownNonZero(I->getOperand(0), DemandedElts, Depth, Q);
 
+    // If there exists any subset of X (sX) and subset of Y (sY) s.t sX * sY is
+    // non-zero, then X * Y is non-zero. We can find sX and sY by just taking
+    // the the lowest known One of X and Y. If they are non-zero, the result
+    // must be non-zero. We can check if LSB(X) * LSB(Y) != 0 by doing
+    // X.CountLeadingZeros + Y.CountLeadingZeros < BitWidth.
+    if ((XKnown.countMaxTrailingZeros() + YKnown.countMaxTrailingZeros()) <
+        BitWidth)
+      return true;
+
     return KnownBits::mul(XKnown, YKnown).isNonZero();
   }
   case Instruction::Select:
diff --git a/llvm/test/Analysis/ValueTracking/known-non-zero.ll b/llvm/test/Analysis/ValueTracking/known-non-zero.ll
--- a/llvm/test/Analysis/ValueTracking/known-non-zero.ll
+++ b/llvm/test/Analysis/ValueTracking/known-non-zero.ll
@@ -1099,11 +1099,7 @@
 
 define i1 @mul_nonzero_contains_nonzero_mul(i8 %x, i8 %y) {
 ; CHECK-LABEL: @mul_nonzero_contains_nonzero_mul(
-; CHECK-NEXT:    [[XX:%.*]] = or i8 [[X:%.*]], 16
-; CHECK-NEXT:    [[YY:%.*]] = or i8 [[Y:%.*]], 8
-; CHECK-NEXT:    [[XY:%.*]] = mul i8 [[XX]], [[YY]]
-; CHECK-NEXT:    [[NZ:%.*]] = icmp ne i8 [[XY]], 0
-; CHECK-NEXT:    ret i1 [[NZ]]
+; CHECK-NEXT:    ret i1 true
 ;
   %xx = or i8 %x, 16
   %yy = or i8 %y, 8