diff --git a/src/rules.jl b/src/rules.jl
index e2dd233..c32e6dd 100644
--- a/src/rules.jl
+++ b/src/rules.jl
@@ -96,6 +96,8 @@ _abs_deriv(x) = signbit(x) ? -one(x) : one(x)
 # trinary #
 #---------#
 
+@define_diffrule Base.hypot(x, y, z) = :( $x / hypot($x, $y, $z) ), :( $y / hypot($x, $y, $z) ), :( $z / hypot($x, $y, $z) )
+
 #=
 
 @define_diffrule Base.muladd(x, y, z) = :($y), :($x), :(one($z))
diff --git a/test/runtests.jl b/test/runtests.jl
index 92b0866..5f91905 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -88,23 +88,32 @@ non_diffeable_arg_functions = [(:Base, :rem2pi, 2), (:Base, :ldexp, 2), (:Base,
                 end
             end
         elseif arity == 3
-            #=
             @test DiffRules.hasdiffrule(M, f, 3)
             derivs = DiffRules.diffrule(M, f, :foo, :bar, :goo)
             @eval begin
-                foo, bar, goo = randn(3)
-                dx, dy, dz = $(derivs[1]), $(derivs[2]), $(derivs[3])
-                if !(isnan(dx))
-                    @test isapprox(dx, finitediff(x -> $M.$f(x, bar, goo), foo), rtol=0.05)
-                end
-                if !(isnan(dy))
-                    @test isapprox(dy, finitediff(y -> $M.$f(foo, y, goo), bar), rtol=0.05)
-                end
-                if !(isnan(dz))
-                    @test isapprox(dz, finitediff(z -> $M.$f(foo, bar, z), goo), rtol=0.05)
+                let
+                    foo, bar, goo = rand($T), rand($T), rand($T)
+                    dx, dy, dz = $(derivs[1]), $(derivs[2]), $(derivs[3])
+                    if !(isnan(dx))
+                        @test dx ≈ finitediff(z -> $M.$f(z, bar, goo), foo) rtol=1e-2
+
+                        # Check type, if applicable.
+                        @test promote_type(typeof(real(dx)), $T) === $T
+                    end
+                    if !(isnan(dy))
+                        @test dy ≈ finitediff(z -> $M.$f(foo, z, goo), bar) rtol=1e-2
+
+                        # Check type, if applicable.
+                        @test promote_type(typeof(real(dy)), $T) === $T
+                    end
+                    if !(isnan(dz))
+                        @test dz ≈ finitediff(z -> $M.$f(foo, bar, z), goo) rtol=1e-2
+
+                        # Check type, if applicable.
+                        @test promote_type(typeof(real(dz)), $T) === $T
+                    end
                 end
             end
-            =#
         end
     end
 end