diff --git a/src/rules.jl b/src/rules.jl
index d1ca0a2..45104aa 100644
--- a/src/rules.jl
+++ b/src/rules.jl
@@ -244,6 +244,8 @@ _abs_deriv(x) = signbit(x) ? -one(x) : one(x)
 @define_diffrule LogExpFunctions.log1mexp(x) = :(-exp($x - LogExpFunctions.log1mexp($x)))
 @define_diffrule LogExpFunctions.log2mexp(x) = :(-exp($x - LogExpFunctions.log2mexp($x)))
 @define_diffrule LogExpFunctions.logexpm1(x) = :(exp($x - LogExpFunctions.logexpm1($x)))
+@define_diffrule LogExpFunctions.log1pmx(x) = :(-$x / (1 + $x))
+@define_diffrule LogExpFunctions.logmxp1(x) = :((1 - $x) / $x)
 
 # binary
 @define_diffrule LogExpFunctions.xlogy(x, y) = :(log($y)), :($x / $y)
diff --git a/test/runtests.jl b/test/runtests.jl
index 6618a36..ba687a9 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -27,7 +27,7 @@ non_diffeable_arg_functions = [(:Base, :rem2pi, 2), (:Base, :ldexp, 2), (:Base,
                     goo = if $(f in (:asec, :acsc, :asecd, :acscd, :acosh, :acoth))
                         # avoid singularities with finite differencing
                         rand($T) + $T(1.5)
-                    elseif $(f in (:log, :airyaix, :airyaiprimex))
+                    elseif $(f in (:log, :airyaix, :airyaiprimex, :logmxp1))
                         # avoid singularities with finite differencing
                         rand($T) + $T(0.5)
                     elseif $(f === :log1mexp)
@@ -40,7 +40,13 @@ non_diffeable_arg_functions = [(:Base, :rem2pi, 2), (:Base, :ldexp, 2), (:Base,
                     # We're happy with types with the correct promotion behavior, e.g.
                     # it's fine to return `1` as a derivative despite input being `Float64`.
                     @test promote_type(typeof($deriv), $T) === $T
-                    @test $deriv ≈ finitediff($M.$f, goo) rtol=1e-2 atol=1e-3
+                    if $(f in (:log1pmx, :logmxp1)) && $T == Float32
+                        # These two functions currently don't have fallbacks for `Real`
+                        # arguments, nor optimized implementations for `Float32`
+                        @test_throws MethodError finitediff($M.$f, goo)
+                    else
+                        @test $deriv ≈ finitediff($M.$f, goo) rtol=1e-2 atol=1e-3     
+                    end
                     # test for 2pi functions
                     if $(f === :mod2pi)
                         goo = 4 * pi