Index: lib/Transforms/InstCombine/InstCombineCalls.cpp
===================================================================
--- lib/Transforms/InstCombine/InstCombineCalls.cpp
+++ lib/Transforms/InstCombine/InstCombineCalls.cpp
@@ -2114,6 +2114,54 @@
 
     break;
   }
+  case Intrinsic::exp: {
+    if (II->isFast()) {
+      Value *SrcSrc = nullptr;
+      Value *Src = II->getArgOperand(0);
+      // exp(log(x)) -> x
+      if (match(Src, m_Intrinsic<Intrinsic::log>(m_Value(SrcSrc)))) {
+        return replaceInstUsesWith(CI, SrcSrc);
+      }
+    }
+
+    break;
+  }
+  case Intrinsic::exp2: {
+    if (II->isFast()) {
+      Value *SrcSrc = nullptr;
+      Value *Src = II->getArgOperand(0);
+      // exp2(log2(x)) -> x
+      if (match(Src, m_Intrinsic<Intrinsic::log2>(m_Value(SrcSrc)))) {
+        return replaceInstUsesWith(CI, SrcSrc);
+      }
+    }
+
+    break;
+  }
+  case Intrinsic::log: {
+    if (II->isFast()) {
+      Value *SrcSrc = nullptr;
+      Value *Src = II->getArgOperand(0);
+      // log(exp(x)) -> x
+      if (match(Src, m_Intrinsic<Intrinsic::exp>(m_Value(SrcSrc)))) {
+        return replaceInstUsesWith(CI, SrcSrc);
+      }
+    }
+
+    break;
+  }
+  case Intrinsic::log2: {
+    if (II->isFast()) {
+      Value *SrcSrc = nullptr;
+      Value *Src = II->getArgOperand(0);
+      // log2(exp2(x)) -> x
+      if (match(Src, m_Intrinsic<Intrinsic::exp2>(m_Value(SrcSrc)))) {
+        return replaceInstUsesWith(CI, SrcSrc);
+      }
+    }
+
+    break;
+  }
   case Intrinsic::ppc_altivec_lvx:
   case Intrinsic::ppc_altivec_lvxl:
     // Turn PPC lvx -> load if the pointer is known aligned.
Index: test/Transforms/InstCombine/exp-intrinsic.ll
===================================================================
--- /dev/null
+++ test/Transforms/InstCombine/exp-intrinsic.ll
@@ -0,0 +1,46 @@
+; RUN: opt < %s -instcombine -S | FileCheck %s
+
+declare double @llvm.exp.f64(double)
+declare double @llvm.log.f64(double)
+
+; CHECK-LABEL: @exp_log(
+; CHECK-NEXT: %1 = call double @llvm.log.f64(double %a)
+; CHECK-NEXT: %2 = call double @llvm.exp.f64(double %1)
+; CHECK-NEXT: ret double %2
+define double @exp_log(double %a) {
+  %1 = call double @llvm.log.f64(double %a)
+  %2 = call double @llvm.exp.f64(double %1)
+  ret double %2
+}
+
+; CHECK-LABEL: @exp_log_fast(
+; CHECK-NEXT: ret double %a
+define double @exp_log_fast(double %a) {
+  %1 = call fast double @llvm.log.f64(double %a)
+  %2 = call fast double @llvm.exp.f64(double %1)
+  ret double %2
+}
+
+; CHECK-LABEL: @exp_log_exp_log(
+; CHECK-NEXT: %1 = call double @llvm.log.f64(double %a)
+; CHECK-NEXT: %2 = call double @llvm.exp.f64(double %1)
+; CHECK-NEXT: %3 = call double @llvm.log.f64(double %2)
+; CHECK-NEXT: %4 = call double @llvm.exp.f64(double %3)
+; CHECK-NEXT: ret double %4
+define double @exp_log_exp_log(double %a) {
+  %1 = call double @llvm.log.f64(double %a)
+  %2 = call double @llvm.exp.f64(double %1)
+  %3 = call double @llvm.log.f64(double %2)
+  %4 = call double @llvm.exp.f64(double %3)
+  ret double %4
+}
+
+; CHECK-LABEL: @exp_log_exp_log_fast(
+; CHECK-NEXT: ret double %a
+define double @exp_log_exp_log_fast(double %a) {
+  %1 = call fast double @llvm.log.f64(double %a)
+  %2 = call fast double @llvm.exp.f64(double %1)
+  %3 = call fast double @llvm.log.f64(double %2)
+  %4 = call fast double @llvm.exp.f64(double %3)
+  ret double %4
+}
\ No newline at end of file
Index: test/Transforms/InstCombine/exp2-intrinsic.ll
===================================================================
--- /dev/null
+++ test/Transforms/InstCombine/exp2-intrinsic.ll
@@ -0,0 +1,46 @@
+; RUN: opt < %s -instcombine -S | FileCheck %s
+
+declare double @llvm.exp2.f64(double)
+declare double @llvm.log2.f64(double)
+
+; CHECK-LABEL: @exp2_log2(
+; CHECK-NEXT: %1 = call double @llvm.log2.f64(double %a)
+; CHECK-NEXT: %2 = call double @llvm.exp2.f64(double %1)
+; CHECK-NEXT: ret double %2
+define double @exp2_log2(double %a) {
+  %1 = call double @llvm.log2.f64(double %a)
+  %2 = call double @llvm.exp2.f64(double %1)
+  ret double %2
+}
+
+; CHECK-LABEL: @exp2_log2_fast(
+; CHECK-NEXT: ret double %a
+define double @exp2_log2_fast(double %a) {
+  %1 = call fast double @llvm.log2.f64(double %a)
+  %2 = call fast double @llvm.exp2.f64(double %1)
+  ret double %2
+}
+
+; CHECK-LABEL: @exp2_log2_exp2_log2(
+; CHECK-NEXT: %1 = call double @llvm.log2.f64(double %a)
+; CHECK-NEXT: %2 = call double @llvm.exp2.f64(double %1)
+; CHECK-NEXT: %3 = call double @llvm.log2.f64(double %2)
+; CHECK-NEXT: %4 = call double @llvm.exp2.f64(double %3)
+; CHECK-NEXT: ret double %4
+define double @exp2_log2_exp2_log2(double %a) {
+  %1 = call double @llvm.log2.f64(double %a)
+  %2 = call double @llvm.exp2.f64(double %1)
+  %3 = call double @llvm.log2.f64(double %2)
+  %4 = call double @llvm.exp2.f64(double %3)
+  ret double %4
+}
+
+; CHECK-LABEL: @exp2_log2_exp2_log2_fast(
+; CHECK-NEXT: ret double %a
+define double @exp2_log2_exp2_log2_fast(double %a) {
+  %1 = call fast double @llvm.log2.f64(double %a)
+  %2 = call fast double @llvm.exp2.f64(double %1)
+  %3 = call fast double @llvm.log2.f64(double %2)
+  %4 = call fast double @llvm.exp2.f64(double %3)
+  ret double %4
+}
\ No newline at end of file
Index: test/Transforms/InstCombine/log-intrinsic.ll
===================================================================
--- /dev/null
+++ test/Transforms/InstCombine/log-intrinsic.ll
@@ -0,0 +1,46 @@
+; RUN: opt < %s -instcombine -S | FileCheck %s
+
+declare double @llvm.log.f64(double)
+declare double @llvm.exp.f64(double)
+
+; CHECK-LABEL: @log_exp(
+; CHECK-NEXT: %1 = call double @llvm.exp.f64(double %a)
+; CHECK-NEXT: %2 = call double @llvm.log.f64(double %1)
+; CHECK-NEXT: ret double %2
+define double @log_exp(double %a) {
+  %1 = call double @llvm.exp.f64(double %a)
+  %2 = call double @llvm.log.f64(double %1)
+  ret double %2
+}
+
+; CHECK-LABEL: @log_exp_fast(
+; CHECK-NEXT: ret double %a
+define double @log_exp_fast(double %a) {
+  %1 = call fast double @llvm.exp.f64(double %a)
+  %2 = call fast double @llvm.log.f64(double %1)
+  ret double %2
+}
+
+; CHECK-LABEL: @log_exp_log_exp(
+; CHECK-NEXT: %1 = call double @llvm.exp.f64(double %a)
+; CHECK-NEXT: %2 = call double @llvm.log.f64(double %1)
+; CHECK-NEXT: %3 = call double @llvm.exp.f64(double %2)
+; CHECK-NEXT: %4 = call double @llvm.log.f64(double %3)
+; CHECK-NEXT: ret double %4
+define double @log_exp_log_exp(double %a) {
+  %1 = call double @llvm.exp.f64(double %a)
+  %2 = call double @llvm.log.f64(double %1)
+  %3 = call double @llvm.exp.f64(double %2)
+  %4 = call double @llvm.log.f64(double %3)
+  ret double %4
+}
+
+; CHECK-LABEL: @log_exp_log_exp_fast(
+; CHECK-NEXT: ret double %a
+define double @log_exp_log_exp_fast(double %a) {
+  %1 = call fast double @llvm.exp.f64(double %a)
+  %2 = call fast double @llvm.log.f64(double %1)
+  %3 = call fast double @llvm.exp.f64(double %2)
+  %4 = call fast double @llvm.log.f64(double %3)
+  ret double %4
+}
\ No newline at end of file
Index: test/Transforms/InstCombine/log2-intrinsic.ll
===================================================================
--- /dev/null
+++ test/Transforms/InstCombine/log2-intrinsic.ll
@@ -0,0 +1,46 @@
+; RUN: opt < %s -instcombine -S | FileCheck %s
+
+declare double @llvm.log2.f64(double)
+declare double @llvm.exp2.f64(double)
+
+; CHECK-LABEL: @log2_exp2(
+; CHECK-NEXT: %1 = call double @llvm.exp2.f64(double %a)
+; CHECK-NEXT: %2 = call double @llvm.log2.f64(double %1)
+; CHECK-NEXT: ret double %2
+define double @log2_exp2(double %a) {
+  %1 = call double @llvm.exp2.f64(double %a)
+  %2 = call double @llvm.log2.f64(double %1)
+  ret double %2
+}
+
+; CHECK-LABEL: @log2_exp2_fast(
+; CHECK-NEXT: ret double %a
+define double @log2_exp2_fast(double %a) {
+  %1 = call fast double @llvm.exp2.f64(double %a)
+  %2 = call fast double @llvm.log2.f64(double %1)
+  ret double %2
+}
+
+; CHECK-LABEL: @log2_exp2_log2_exp2(
+; CHECK-NEXT: %1 = call double @llvm.exp2.f64(double %a)
+; CHECK-NEXT: %2 = call double @llvm.log2.f64(double %1)
+; CHECK-NEXT: %3 = call double @llvm.exp2.f64(double %2)
+; CHECK-NEXT: %4 = call double @llvm.log2.f64(double %3)
+; CHECK-NEXT: ret double %4
+define double @log2_exp2_log2_exp2(double %a) {
+  %1 = call double @llvm.exp2.f64(double %a)
+  %2 = call double @llvm.log2.f64(double %1)
+  %3 = call double @llvm.exp2.f64(double %2)
+  %4 = call double @llvm.log2.f64(double %3)
+  ret double %4
+}
+
+; CHECK-LABEL: @log2_exp2_log2_exp2_fast(
+; CHECK-NEXT: ret double %a
+define double @log2_exp2_log2_exp2_fast(double %a) {
+  %1 = call fast double @llvm.exp2.f64(double %a)
+  %2 = call fast double @llvm.log2.f64(double %1)
+  %3 = call fast double @llvm.exp2.f64(double %2)
+  %4 = call fast double @llvm.log2.f64(double %3)
+  ret double %4
+}
\ No newline at end of file