Index: lib/Transforms/InstCombine/InstCombineMulDivRem.cpp
===================================================================
--- lib/Transforms/InstCombine/InstCombineMulDivRem.cpp
+++ lib/Transforms/InstCombine/InstCombineMulDivRem.cpp
@@ -507,6 +507,22 @@
       return replaceInstUsesWith(I, Sqrt);
     }
 
+    // exp(X) * exp(Y) -> exp(X + Y)
+    if (match(Op0, m_OneUse(m_Intrinsic<Intrinsic::exp>(m_Value(X)))) &&
+        match(Op1, m_OneUse(m_Intrinsic<Intrinsic::exp>(m_Value(Y))))) {
+      Value *XY = Builder.CreateFAddFMF(X, Y, &I);
+      Value *Exp = Builder.CreateIntrinsic(Intrinsic::exp, { XY }, &I);
+      return replaceInstUsesWith(I, Exp);
+    }
+
+    // exp2(X) * exp2(Y) -> exp2(X + Y)
+    if (match(Op0, m_OneUse(m_Intrinsic<Intrinsic::exp2>(m_Value(X)))) &&
+        match(Op1, m_OneUse(m_Intrinsic<Intrinsic::exp2>(m_Value(Y))))) {
+      Value *XY = Builder.CreateFAddFMF(X, Y, &I);
+      Value *Exp2 = Builder.CreateIntrinsic(Intrinsic::exp2, { XY }, &I);
+      return replaceInstUsesWith(I, Exp2);
+    }
+
     // (X*Y) * X => (X*X) * Y where Y != X
     //  The purpose is two-fold:
     //   1) to form a power expression (of X).
Index: test/Transforms/InstCombine/fmul-exp.ll
===================================================================
--- /dev/null
+++ test/Transforms/InstCombine/fmul-exp.ll
@@ -0,0 +1,67 @@
+; NOTE: Assertions have been autogenerated by utils/update_test_checks.py
+; RUN: opt -S -instcombine < %s | FileCheck %s
+
+declare double @llvm.exp.f64(double) nounwind readnone speculatable
+declare void @use(double)
+
+; exp(a) * exp(b) no math flags
+define double @exp_a_exp_b(double %a, double %b) {
+; CHECK-LABEL: @exp_a_exp_b(
+; CHECK-NEXT:    [[TMP1:%.*]] = call double @llvm.exp.f64(double [[A:%.*]])
+; CHECK-NEXT:    [[TMP2:%.*]] = call double @llvm.exp.f64(double [[B:%.*]])
+; CHECK-NEXT:    [[MUL:%.*]] = fmul double [[TMP1]], [[TMP2]]
+; CHECK-NEXT:    ret double [[MUL]]
+;
+  %1 = call double @llvm.exp.f64(double %a)
+  %2 = call double @llvm.exp.f64(double %b)
+  %mul = fmul double %1, %2
+  ret double %mul
+}
+
+; exp(a) * exp(b) fast-math, multiple uses
+define double @exp_a_exp_b_multiple_uses(double %a, double %b) {
+; CHECK-LABEL: @exp_a_exp_b_multiple_uses(
+; CHECK-NEXT:    [[TMP1:%.*]] = call fast double @llvm.exp.f64(double [[A:%.*]])
+; CHECK-NEXT:    [[TMP2:%.*]] = call fast double @llvm.exp.f64(double [[B:%.*]])
+; CHECK-NEXT:    [[MUL:%.*]] = fmul fast double [[TMP1]], [[TMP2]]
+; CHECK-NEXT:    call void @use(double [[TMP2]])
+; CHECK-NEXT:    ret double [[MUL]]
+;
+  %1 = call fast double @llvm.exp.f64(double %a)
+  %2 = call fast double @llvm.exp.f64(double %b)
+  %mul = fmul fast double %1, %2
+  call void @use(double %2)
+  ret double %mul
+}
+
+; exp(a) * exp(b) => exp(a+b) with fast-math
+define double @exp_a_exp_b_fast(double %a, double %b) {
+; CHECK-LABEL: @exp_a_exp_b_fast(
+; CHECK-NEXT:    [[TMP1:%.*]] = fadd fast double [[A:%.*]], [[B:%.*]]
+; CHECK-NEXT:    [[TMP2:%.*]] = call fast double @llvm.exp.f64(double [[TMP1]])
+; CHECK-NEXT:    ret double [[TMP2]]
+;
+  %1 = call fast double @llvm.exp.f64(double %a)
+  %2 = call fast double @llvm.exp.f64(double %b)
+  %mul = fmul fast double %1, %2
+  ret double %mul
+}
+
+; exp(a) * exp(b) * exp(c) * exp(d) => exp(a+b+c+d) with fast-math
+define double @exp_a_exp_b_exp_c_exp_d_fast(double %a, double %b, double %c, double %d) {
+; CHECK-LABEL: @exp_a_exp_b_exp_c_exp_d_fast(
+; CHECK-NEXT:    [[TMP1:%.*]] = fadd fast double [[A:%.*]], [[B:%.*]]
+; CHECK-NEXT:    [[TMP2:%.*]] = fadd fast double [[TMP1]], [[C:%.*]]
+; CHECK-NEXT:    [[TMP3:%.*]] = fadd fast double [[TMP2]], [[D:%.*]]
+; CHECK-NEXT:    [[TMP4:%.*]] = call fast double @llvm.exp.f64(double [[TMP3]])
+; CHECK-NEXT:    ret double [[TMP4]]
+;
+  %1 = call fast double @llvm.exp.f64(double %a)
+  %2 = call fast double @llvm.exp.f64(double %b)
+  %mul = fmul fast double %1, %2
+  %3 = call fast double @llvm.exp.f64(double %c)
+  %mul1 = fmul fast double %mul, %3
+  %4 = call fast double @llvm.exp.f64(double %d)
+  %mul2 = fmul fast double %mul1, %4
+  ret double %mul2
+}
\ No newline at end of file
Index: test/Transforms/InstCombine/fmul-exp2.ll
===================================================================
--- /dev/null
+++ test/Transforms/InstCombine/fmul-exp2.ll
@@ -0,0 +1,67 @@
+; NOTE: Assertions have been autogenerated by utils/update_test_checks.py
+; RUN: opt -S -instcombine < %s | FileCheck %s
+
+declare double @llvm.exp2.f64(double) nounwind readnone speculatable
+declare void @use(double)
+
+; exp2(a) * exp2(b) no math flags
+define double @exp2_a_exp2_b(double %a, double %b) {
+; CHECK-LABEL: @exp2_a_exp2_b(
+; CHECK-NEXT:    [[TMP1:%.*]] = call double @llvm.exp2.f64(double [[A:%.*]])
+; CHECK-NEXT:    [[TMP2:%.*]] = call double @llvm.exp2.f64(double [[B:%.*]])
+; CHECK-NEXT:    [[MUL:%.*]] = fmul double [[TMP1]], [[TMP2]]
+; CHECK-NEXT:    ret double [[MUL]]
+;
+  %1 = call double @llvm.exp2.f64(double %a)
+  %2 = call double @llvm.exp2.f64(double %b)
+  %mul = fmul double %1, %2
+  ret double %mul
+}
+
+; exp2(a) * exp2(b) fast-math, multiple uses
+define double @exp2_a_exp2_b_multiple_uses(double %a, double %b) {
+; CHECK-LABEL: @exp2_a_exp2_b_multiple_uses(
+; CHECK-NEXT:    [[TMP1:%.*]] = call fast double @llvm.exp2.f64(double [[A:%.*]])
+; CHECK-NEXT:    [[TMP2:%.*]] = call fast double @llvm.exp2.f64(double [[B:%.*]])
+; CHECK-NEXT:    [[MUL:%.*]] = fmul fast double [[TMP1]], [[TMP2]]
+; CHECK-NEXT:    call void @use(double [[TMP2]])
+; CHECK-NEXT:    ret double [[MUL]]
+;
+  %1 = call fast double @llvm.exp2.f64(double %a)
+  %2 = call fast double @llvm.exp2.f64(double %b)
+  %mul = fmul fast double %1, %2
+  call void @use(double %2)
+  ret double %mul
+}
+
+; exp2(a) * exp2(b) => exp2(a+b) with fast-math
+define double @exp2_a_exp2_b_fast(double %a, double %b) {
+; CHECK-LABEL: @exp2_a_exp2_b_fast(
+; CHECK-NEXT:    [[TMP1:%.*]] = fadd fast double [[A:%.*]], [[B:%.*]]
+; CHECK-NEXT:    [[TMP2:%.*]] = call fast double @llvm.exp2.f64(double [[TMP1]])
+; CHECK-NEXT:    ret double [[TMP2]]
+;
+  %1 = call fast double @llvm.exp2.f64(double %a)
+  %2 = call fast double @llvm.exp2.f64(double %b)
+  %mul = fmul fast double %1, %2
+  ret double %mul
+}
+
+; exp2(a) * exp2(b) * exp2(c) * exp2(d) => exp2(a+b+c+d) with fast-math
+define double @exp2_a_exp2_b_exp2_c_exp2_d(double %a, double %b, double %c, double %d) {
+; CHECK-LABEL: @exp2_a_exp2_b_exp2_c_exp2_d(
+; CHECK-NEXT:    [[TMP1:%.*]] = fadd fast double [[A:%.*]], [[B:%.*]]
+; CHECK-NEXT:    [[TMP2:%.*]] = fadd fast double [[TMP1]], [[C:%.*]]
+; CHECK-NEXT:    [[TMP3:%.*]] = fadd fast double [[TMP2]], [[D:%.*]]
+; CHECK-NEXT:    [[TMP4:%.*]] = call fast double @llvm.exp2.f64(double [[TMP3]])
+; CHECK-NEXT:    ret double [[TMP4]]
+;
+  %1 = call fast double @llvm.exp2.f64(double %a)
+  %2 = call fast double @llvm.exp2.f64(double %b)
+  %mul = fmul fast double %1, %2
+  %3 = call fast double @llvm.exp2.f64(double %c)
+  %mul1 = fmul fast double %mul, %3
+  %4 = call fast double @llvm.exp2.f64(double %d)
+  %mul2 = fmul fast double %mul1, %4
+  ret double %mul2
+}
\ No newline at end of file