diff --git a/base/compiler/optimize.jl b/base/compiler/optimize.jl
index 120fc89754a11..db66e63d407bc 100644
--- a/base/compiler/optimize.jl
+++ b/base/compiler/optimize.jl
@@ -408,7 +408,7 @@ function finish(interp::AbstractInterpreter, opt::OptimizationState,
         # otherwise we might skip throwing errors (issue #20704)
         # TODO: Improve this analysis; if a function is marked @pure we should really
         # only care about certain errors (e.g. method errors and type errors).
-        if length(ir.stmts) < 10
+        if length(ir.stmts) < 15
             proven_pure = true
             for i in 1:length(ir.stmts)
                 node = ir.stmts[i]
@@ -624,7 +624,8 @@ function is_pure_intrinsic_infer(f::IntrinsicFunction)
 end
 
 # whether `f` is effect free if nothrow
-intrinsic_effect_free_if_nothrow(f) = f === Intrinsics.pointerref || is_pure_intrinsic_infer(f)
+intrinsic_effect_free_if_nothrow(f) = f === Intrinsics.pointerref ||
+    f === Intrinsics.have_fma || is_pure_intrinsic_infer(f)
 
 ## Computing the cost of a function body
 
diff --git a/base/compiler/tfuncs.jl b/base/compiler/tfuncs.jl
index 65a86f262d9b3..1967b237ca009 100644
--- a/base/compiler/tfuncs.jl
+++ b/base/compiler/tfuncs.jl
@@ -1815,6 +1815,10 @@ function intrinsic_nothrow(f::IntrinsicFunction, argtypes::Array{Any, 1})
         xty = widenconst(argtypes[2])
         return isconcrete && isprimitivetype(ty) && isprimitivetype(xty)
     end
+    if f === Intrinsics.have_fma
+        ty, isexact, isconcrete = instanceof_tfunc(argtypes[1])
+        return isconcrete && isprimitivetype(ty)
+    end
     # The remaining intrinsics are math/bits/comparison intrinsics. They work on all
     # primitive types of the same type.
     isshift = f === shl_int || f === lshr_int || f === ashr_int
diff --git a/test/compiler/inline.jl b/test/compiler/inline.jl
index a2f6ddc99409a..035c291b4be8f 100644
--- a/test/compiler/inline.jl
+++ b/test/compiler/inline.jl
@@ -880,3 +880,7 @@ end
         @test count(iscall((src,UnionAll)), src.code) == 0
     end
 end
+
+# have_fma elimination inside ^
+f_pow() = ^(2.0, -1.0)
+@test fully_eliminated(f_pow, Tuple{})