Index: llvm/lib/Transforms/Utils/SimplifyLibCalls.cpp
===================================================================
--- llvm/lib/Transforms/Utils/SimplifyLibCalls.cpp
+++ llvm/lib/Transforms/Utils/SimplifyLibCalls.cpp
@@ -1204,7 +1204,8 @@
   return nullptr;
 }
 
-/// Use sqrt() for pow(x, +/-0.5) and cbrt() for pow(x, +/-0.333...).
+/// Use sqrt() for pow(x, +/-0.5) and pow(x, +/-0.25) and
+/// cbrt() for pow(x, +/-0.333...).
 Value *LibCallSimplifier::replacePowWithRoot(CallInst *Pow, IRBuilder<> &B) {
   Value *Root, *Base = Pow->getArgOperand(0), *Expo = Pow->getArgOperand(1);
   AttributeList Attrs = Pow->getCalledFunction()->getAttributes();
@@ -1217,21 +1218,25 @@
 
   const double OneThird = (Ty->getTypeID() == Type::FloatTyID)
                           ? (1.0f / 3.0f) : (1.0 / 3.0);
-  bool isHalf  (ExpoF->isExactlyValue(0.5) || ExpoF->isExactlyValue(-0.5)),
-       isThird (ExpoF->isExactlyValue(OneThird) ||
-                ExpoF->isExactlyValue(-OneThird));
-  if (!isHalf && !isThird)
+  bool isHalf    (ExpoF->isExactlyValue(0.5) || ExpoF->isExactlyValue(-0.5)),
+       isThird   (ExpoF->isExactlyValue(OneThird) ||
+                  ExpoF->isExactlyValue(-OneThird)),
+       isQuarter (ExpoF->isExactlyValue(0.25) || ExpoF->isExactlyValue(-0.25));
+  if (!isHalf && !isThird && !isQuarter)
     return nullptr;
 
-  // Expand pow(x, +/-0.5) to sqrt().
-  if (isHalf) {
-    // If errno is never set, then use the intrinsic for sqrt().
+  // Expand pow(x, +/-0.5) to sqrt() and pow(x, +/-0.25) to sqrt(sqrt()).
+  if (isHalf || isQuarter) {
     if (Pow->hasFnAttr(Attribute::ReadNone)) {
       Function *SqrtFn = Intrinsic::getDeclaration(Mod, Intrinsic::sqrt, Ty);
       Root = B.CreateCall(SqrtFn, Base, "sqrt");
+      if (isQuarter)
+        Root = B.CreateCall(SqrtFn, Root, "sqrt");
     }
-    // Otherwise, use the libcall for sqrt().
-    else if (hasUnaryFloatFn(TLI, Ty,
+    // Otherwise, use the libcall for sqrt(), but only when the exponent is 0.5,
+    // since using the libcall back to back doesn't seem to be a good idea.
+    else if (!isQuarter &&
+             hasUnaryFloatFn(TLI, Ty,
                              LibFunc_sqrt, LibFunc_sqrtf, LibFunc_sqrtl))
       // TODO: We also should check that the target can in fact lower the sqrt()
       // libcall.  We currently have no way to ask this question, so we ask if
Index: llvm/test/Transforms/InstCombine/pow-sqrt.ll
===================================================================
--- llvm/test/Transforms/InstCombine/pow-sqrt.ll
+++ llvm/test/Transforms/InstCombine/pow-sqrt.ll
@@ -1,4 +1,3 @@
-; NOTE: Assertions have been autogenerated by utils/update_test_checks.py
 ; RUN: opt < %s -instcombine -S | FileCheck %s
 
 define float @powf_intrinsic_half_fast(float %x) {
@@ -10,6 +9,16 @@
   ret float %pow
 }
 
+define double @pow_intrinsic_quarter_fast(double %x) {
+; CHECK-LABEL: @pow_intrinsic_quarter_fast(
+; CHECK-NEXT:    [[SQRT:%.*]] = call fast double @llvm.sqrt.f64(double %x)
+; CHECK-NEXT:    [[SQRT1:%.*]] = call fast double @llvm.sqrt.f64(double [[SQRT]])
+; CHECK-NEXT:    ret double [[SQRT1]]
+;
+  %pow = call fast double @llvm.pow.f64(double %x, double 2.5e-01)
+  ret double %pow
+}
+
 define <2 x double> @pow_intrinsic_half_approx(<2 x double> %x) {
 ; CHECK-LABEL: @pow_intrinsic_half_approx(
 ; CHECK-NEXT:    [[SQRT:%.*]] = call afn <2 x double> @llvm.sqrt.v2f64(<2 x double> %x)
@@ -22,6 +31,19 @@
   ret <2 x double> %pow
 }
 
+define <2 x float> @powf_intrinsic_quarter_approx(<2 x float> %x) {
+; CHECK-LABEL: @powf_intrinsic_quarter_approx(
+; CHECK-NEXT:    [[SQRT:%.*]] = call afn <2 x float> @llvm.sqrt.v2f32(<2 x float> %x)
+; CHECK-NEXT:    [[SQRT1:%.*]] = call afn <2 x float> @llvm.sqrt.v2f32(<2 x float> [[SQRT]])
+; CHECK-NEXT:    [[TMP1:%.*]] = call afn <2 x float> @llvm.fabs.v2f32(<2 x float> [[SQRT1]])
+; CHECK-NEXT:    [[TMP2:%.*]] = fcmp afn oeq <2 x float> %x, <float 0xFFF0000000000000, float 0xFFF0000000000000>
+; CHECK-NEXT:    [[TMP3:%.*]] = select <2 x i1> [[TMP2]], <2 x float> <float 0x7FF0000000000000, float 0x7FF0000000000000>, <2 x float> [[TMP1]]
+; CHECK-NEXT:    ret <2 x float> [[TMP3]]
+;
+  %pow = call afn <2 x float> @llvm.pow.v2f32(<2 x float> %x, <2 x float> <float 2.5e-01, float 2.5e-01>)
+  ret <2 x float> %pow
+}
+
 define float @powf_libcall_half_ninf(float %x) {
 ; CHECK-LABEL: @powf_libcall_half_ninf(
 ; CHECK-NEXT:    [[SQRTF:%.*]] = call ninf float @sqrtf(float %x)
@@ -32,16 +54,36 @@
   ret float %pow
 }
 
+define double @pow_libcall_quarter_ninf(double %x) {
+; CHECK-LABEL: @pow_libcall_quarter_ninf(
+; CHECK-NEXT:    [[POW:%.*]] = call ninf double @pow(double %x, double 2.500000e-01)
+; CHECK-NEXT:    ret double [[POW]]
+;
+  %pow = call ninf double @pow(double %x, double 2.5e-01)
+  ret double %pow
+}
+
 define <2 x double> @pow_intrinsic_neghalf_fast(<2 x double> %x) {
 ; CHECK-LABEL: @pow_intrinsic_neghalf_fast(
-; CHECK-NEXT:    [[SQRT:%.*]] = call fast <2 x double> @llvm.sqrt.v2f64(<2 x double> [[X:%.*]])
-; CHECK-NEXT:    [[RECP:%.*]] = fdiv fast <2 x double> <double 1.000000e+00, double 1.000000e+00>, [[SQRT]]
-; CHECK-NEXT:    ret <2 x double> [[RECP]]
+; CHECK-NEXT:    [[SQRT:%.*]] = call fast <2 x double> @llvm.sqrt.v2f64(<2 x double> %x)
+; CHECK-NEXT:    [[TMP1:%.*]] = fdiv fast <2 x double> <double 1.000000e+00, double 1.000000e+00>, [[SQRT]]
+; CHECK-NEXT:    ret <2 x double> [[TMP1]]
 ;
   %pow = call fast <2 x double> @llvm.pow.v2f64(<2 x double> %x, <2 x double> <double -5.0e-01, double -5.0e-01>)
   ret <2 x double> %pow
 }
 
+define <4 x float> @powf_intrinsic_negquarter_fast(<4 x float> %x) {
+; CHECK-LABEL: @powf_intrinsic_negquarter_fast(
+; CHECK-NEXT:    [[SQRT:%.*]] = call fast <4 x float> @llvm.sqrt.v4f32(<4 x float> %x)
+; CHECK-NEXT:    [[SQRT1:%.*]] = call fast <4 x float> @llvm.sqrt.v4f32(<4 x float> [[SQRT]])
+; CHECK-NEXT:    [[TMP1:%.*]] = fdiv fast <4 x float> <float 1.000000e+00, float 1.000000e+00, float 1.000000e+00, float 1.000000e+00>, [[SQRT1]]
+; CHECK-NEXT:    ret <4 x float> [[TMP1]]
+;
+  %pow = call fast <4 x float> @llvm.pow.v4f32(<4 x float> %x, <4 x float> <float -2.5e-01, float -2.5e-01, float -2.5e-01, float -2.5e-01>)
+  ret <4 x float> %pow
+}
+
 define <2 x float> @powf_intrinsic_neghalf_ninf(<2 x float> %x) {
 ; CHECK-LABEL: @powf_intrinsic_neghalf_ninf(
 ; CHECK-NEXT:    [[SQRT:%.*]] = call ninf <2 x float> @llvm.sqrt.v2f32(<2 x float> %x)
@@ -53,6 +95,18 @@
   ret <2 x float> %pow
 }
 
+define <2 x double> @pow_intrinsic_negquarter_ninf(<2 x double> %x) {
+; CHECK-LABEL: @pow_intrinsic_negquarter_ninf(
+; CHECK-NEXT:    [[SQRT:%.*]] = call ninf <2 x double> @llvm.sqrt.v2f64(<2 x double> %x)
+; CHECK-NEXT:    [[SQRT1:%.*]] = call ninf <2 x double> @llvm.sqrt.v2f64(<2 x double> [[SQRT]])
+; CHECK-NEXT:    [[TMP1:%.*]] = call ninf <2 x double> @llvm.fabs.v2f64(<2 x double> [[SQRT1]])
+; CHECK-NEXT:    [[TMP2:%.*]] = fdiv ninf <2 x double> <double 1.000000e+00, double 1.000000e+00>, [[TMP1]]
+; CHECK-NEXT:    ret <2 x double> [[TMP2]]
+;
+  %pow = call ninf <2 x double> @llvm.pow.v2f64(<2 x double> %x, <2 x double> <double -2.5e-01, double-2.5e-01>)
+  ret <2 x double> %pow
+}
+
 define float @powf_libcall_neghalf_approx(float %x) {
 ; CHECK-LABEL: @powf_libcall_neghalf_approx(
 ; CHECK-NEXT:    [[SQRTF:%.*]] = call afn float @sqrtf(float %x)
@@ -66,6 +120,15 @@
   ret float %pow
 }
 
+define double @pow_libcall_negquarter_approx(double %x) {
+; CHECK-LABEL: @pow_libcall_negquarter_approx(
+; CHECK-NEXT:    [[POW:%.*]] = call afn double @pow(double %x, double -2.500000e-01)
+; CHECK-NEXT:    ret double [[POW]]
+;
+  %pow = call afn double @pow(double %x, double -2.5e-01)
+  ret double %pow
+}
+
 define double @pow_libcall_neghalf_fast(double %x) {
 ; CHECK-LABEL: @pow_libcall_neghalf_fast(
 ; CHECK-NEXT:    [[SQRT:%.*]] = call fast double @sqrt(double %x)
@@ -76,6 +139,15 @@
   ret double %pow
 }
 
+define float @powf_libcall_negquarter_fast(float %x) {
+; CHECK-LABEL: @powf_libcall_negquarter_fast(
+; CHECK-NEXT:    [[POW:%.*]] = call fast float @powf(float %x, float -2.500000e-01)
+; CHECK-NEXT:    ret float [[POW]]
+;
+  %pow = call fast float @powf(float %x, float -2.5e-01)
+  ret float %pow
+}
+
 declare double @llvm.pow.f64(double, double) #0
 declare float @llvm.pow.f32(float, float) #0
 declare <2 x double> @llvm.pow.v2f64(<2 x double>, <2 x double>) #0
@@ -85,3 +157,4 @@
 declare float @powf(float, float)
 
 attributes #0 = { nounwind readnone speculatable }
+attributes #1 = { nounwind readnone }