diff --git a/llvm/lib/Transforms/InstCombine/InstCombineMulDivRem.cpp b/llvm/lib/Transforms/InstCombine/InstCombineMulDivRem.cpp
--- a/llvm/lib/Transforms/InstCombine/InstCombineMulDivRem.cpp
+++ b/llvm/lib/Transforms/InstCombine/InstCombineMulDivRem.cpp
@@ -544,6 +544,21 @@
       return replaceInstUsesWith(I, Sqrt);
     }
 
+    // The following transforms are done irrespective of the number of uses
+    // for the expression "1.0/sqrt(X)".
+    //  1) 1.0/sqrt(X) * X -> X/sqrt(X)
+    //  2) X * 1.0/sqrt(X) -> X/sqrt(X)
+    // We always expect the backend to reduce X/sqrt(X) to sqrt(X), if it
+    // has the necessary (reassoc) fast-math-flags.
+    if (I.hasNoSignedZeros() &&
+        match(Op0, (m_FDiv(m_SpecificFP(1.0), m_Value(Y)))) &&
+        match(Y, m_Intrinsic<Intrinsic::sqrt>(m_Value(X))) && Op1 == X)
+      return BinaryOperator::CreateFDivFMF(X, Y, &I);
+    if (I.hasNoSignedZeros() &&
+        match(Op1, (m_FDiv(m_SpecificFP(1.0), m_Value(Y)))) &&
+        match(Y, m_Intrinsic<Intrinsic::sqrt>(m_Value(X))) && Op0 == X)
+      return BinaryOperator::CreateFDivFMF(X, Y, &I);
+
     // Like the similar transform in instsimplify, this requires 'nsz' because
     // sqrt(-0.0) = -0.0, and -0.0 * -0.0 does not simplify to -0.0.
     if (I.hasNoNaNs() && I.hasNoSignedZeros() && Op0 == Op1 &&
diff --git a/llvm/test/Transforms/InstCombine/fmul-sqrt.ll b/llvm/test/Transforms/InstCombine/fmul-sqrt.ll
--- a/llvm/test/Transforms/InstCombine/fmul-sqrt.ll
+++ b/llvm/test/Transforms/InstCombine/fmul-sqrt.ll
@@ -103,7 +103,7 @@
 ; CHECK-LABEL: @rsqrt_x_reassociate_extra_use(
 ; CHECK-NEXT:    [[SQRT:%.*]] = call double @llvm.sqrt.f64(double [[X:%.*]])
 ; CHECK-NEXT:    [[RSQRT:%.*]] = fdiv double 1.000000e+00, [[SQRT]]
-; CHECK-NEXT:    [[RES:%.*]] = fmul reassoc nsz double [[RSQRT]], [[X]]
+; CHECK-NEXT:    [[RES:%.*]] = fdiv reassoc nsz double [[X:%.*]], [[SQRT]]
 ; CHECK-NEXT:    store double [[RSQRT]], double* [[P:%.*]], align 8
 ; CHECK-NEXT:    ret double [[RES]]
 ;
@@ -119,7 +119,7 @@
 ; CHECK-NEXT:    [[ADD:%.*]] = fadd fast <2 x float> [[X:%.*]], [[Y:%.*]]
 ; CHECK-NEXT:    [[SQRT:%.*]] = call fast <2 x float> @llvm.sqrt.v2f32(<2 x float> [[ADD]])
 ; CHECK-NEXT:    [[RSQRT:%.*]] = fdiv fast <2 x float> <float 1.000000e+00, float 1.000000e+00>, [[SQRT]]
-; CHECK-NEXT:    [[RES:%.*]] = fmul fast <2 x float> [[ADD]], [[RSQRT]]
+; CHECK-NEXT:    [[RES:%.*]] = fdiv fast <2 x float> [[ADD]], [[SQRT]]
 ; CHECK-NEXT:    store <2 x float> [[RSQRT]], <2 x float>* [[P:%.*]], align 8
 ; CHECK-NEXT:    ret <2 x float> [[RES]]
 ;