diff --git a/Project.toml b/Project.toml
index 390d81b..37a0a82 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,6 +1,6 @@
 name = "ChangesOfVariables"
 uuid = "9e997f8a-9a97-42d5-a9f1-ce6bfc15e2c0"
-version = "0.1.9"
+version = "0.1.10"
 
 [deps]
 InverseFunctions = "3587e190-3f89-42d0-90ee-14403ec27112"
diff --git a/README.md b/README.md
index 61289d4..3e09ca5 100644
--- a/README.md
+++ b/README.md
@@ -3,7 +3,7 @@
 [![Documentation for stable version](https://img.shields.io/badge/docs-stable-blue.svg)](https://JuliaMath.github.io/ChangesOfVariables.jl/stable)
 [![Documentation for development version](https://img.shields.io/badge/docs-dev-blue.svg)](https://JuliaMath.github.io/ChangesOfVariables.jl/dev)
 [![License](http://img.shields.io/badge/license-MIT-brightgreen.svg?style=flat)](LICENSE.md)
-[![Build Status](https://github.com/JuliaMath/ChangesOfVariables.jl/workflows/CI/badge.svg?branch=master)](https://github.com/JuliaMath/ChangesOfVariables.jl/actions?query=workflow%3ACI)
+[![Build Status](https://github.com/JuliaMath/ChangesOfVariables.jl/workflows/CI/badge.svg)](https://github.com/JuliaMath/ChangesOfVariables.jl/actions?query=workflow%3ACI)
 [![Codecov](https://codecov.io/gh/JuliaMath/ChangesOfVariables.jl/branch/master/graph/badge.svg)](https://codecov.io/gh/JuliaMath/ChangesOfVariables.jl)
 
 
diff --git a/src/with_ladj.jl b/src/with_ladj.jl
index 52ec48d..2fcb4ce 100644
--- a/src/with_ladj.jl
+++ b/src/with_ladj.jl
@@ -80,24 +80,34 @@ export with_logabsdet_jacobian
     struct NoLogAbsDetJacobian{F,T}
 
 An instance `NoLogAbsDetJacobian{F,T}()` signifies that `with_logabsdet_jacobian(::F, ::T)` is not defined.
+
+Constructors:
+```julia
+NoLogAbsDetJacobian(f, x)
+NoLogAbsDetJacobian{F,T}()
+```
 """
 struct NoLogAbsDetJacobian{F,T} end
 export NoLogAbsDetJacobian
 
-with_logabsdet_jacobian(::F, ::T) where {F,T} = NoLogAbsDetJacobian{F,T}()
+@inline NoLogAbsDetJacobian(::F, ::T) where {F,T} = NoLogAbsDetJacobian{F,T}()
+@inline NoLogAbsDetJacobian(::Type{F}, ::T) where {F,T} = NoLogAbsDetJacobian{Type{F},T}()
+@inline NoLogAbsDetJacobian(::F, ::Type{T}) where {F,T} = NoLogAbsDetJacobian{F,Type{T}}()
+@inline NoLogAbsDetJacobian(::Type{F}, ::Type{T}) where {F,T} = NoLogAbsDetJacobian{Type{F},Type{T}}()
 
+with_logabsdet_jacobian(f, x) = NoLogAbsDetJacobian(f, x)
 
 
 @static if VERSION >= v"1.6"
     function with_logabsdet_jacobian(f::Base.ComposedFunction, x)
         y_ladj_inner = with_logabsdet_jacobian(f.inner, x)
         if y_ladj_inner isa NoLogAbsDetJacobian
-            NoLogAbsDetJacobian{typeof(f),typeof(x)}()
+            NoLogAbsDetJacobian(f, x)
         else
             y_inner, ladj_inner = y_ladj_inner
             y_ladj_outer = with_logabsdet_jacobian(f.outer, y_inner)
             if y_ladj_outer isa NoLogAbsDetJacobian
-                NoLogAbsDetJacobian{typeof(f),typeof(x)}()
+                NoLogAbsDetJacobian(f, x)
             else
                 y, ladj_outer = y_ladj_outer
                 (y, ladj_inner + ladj_outer)
@@ -107,6 +117,10 @@ with_logabsdet_jacobian(::F, ::T) where {F,T} = NoLogAbsDetJacobian{F,T}()
 end
 
 
+function _with_ladj_on_mapped(@nospecialize(map_or_bc::F), y_with_ladj::NoLogAbsDetJacobian) where {F<:Union{typeof(map),typeof(broadcast)}}
+    return y_with_ladj
+end
+
 function _with_ladj_on_mapped(map_or_bc::F, y_with_ladj::Tuple{Any,Real})  where {F<:Union{typeof(map),typeof(broadcast)}}
     return y_with_ladj
 end
diff --git a/test/getjacobian.jl b/test/getjacobian.jl
index 4766d8a..ff4c480 100644
--- a/test/getjacobian.jl
+++ b/test/getjacobian.jl
@@ -1,5 +1,7 @@
 # This file is a part of ChangesOfVariables.jl, licensed under the MIT License (MIT).
 
+if !isdefined(Main, :getjacobian)
+
 import ForwardDiff
 
 torv_and_back(V::AbstractVector{<:Real}) = V, identity
@@ -33,4 +35,11 @@ function getjacobian(f, x)
     ForwardDiff.jacobian(vf, V)
 end
 
+end # !isdefined(Main, :getjacobian)
+
+
+if !isdefined(Main, :foo)
+
 foo(x) = inv(exp(-x) + 1)
+
+end # !isdefined(Main, :foo)
diff --git a/test/test_with_ladj.jl b/test/test_with_ladj.jl
index 5db91c1..ff307f7 100644
--- a/test/test_with_ladj.jl
+++ b/test/test_with_ladj.jl
@@ -18,11 +18,20 @@ include("getjacobian.jl")
         _bc_func(f) = Base.Fix1(broadcast, f)
     end
 
-    @test with_logabsdet_jacobian(sum, rand(5)) == NoLogAbsDetJacobian{typeof(sum),Vector{Float64}}()
-    @test with_logabsdet_jacobian(sum ∘ log, 5.0f0) == NoLogAbsDetJacobian{typeof(sum ∘ log),Float32}()
-    @test with_logabsdet_jacobian(log ∘ sum, 5.0f0) == NoLogAbsDetJacobian{typeof(log ∘ sum),Float32}()
+    @test with_logabsdet_jacobian(sum, rand(5)) === NoLogAbsDetJacobian(sum, rand(5))
+    @test with_logabsdet_jacobian(log ∘ sum, 5.0f0) === NoLogAbsDetJacobian(log ∘ sum, 5.0f0)
     @test_throws MethodError _, _ = with_logabsdet_jacobian(sum, rand(5))
 
+    @test with_logabsdet_jacobian(sin, 4.9) === NoLogAbsDetJacobian{typeof(sin), Float64}()
+    @test with_logabsdet_jacobian(String, 4.9) === NoLogAbsDetJacobian{Type{String}, Float64}()
+    @test with_logabsdet_jacobian(String, Float64) === NoLogAbsDetJacobian{Type{String}, Type{Float64}}()
+    @test with_logabsdet_jacobian(sin, Float64) === NoLogAbsDetJacobian{typeof(sin), Type{Float64}}()
+
+    @test with_logabsdet_jacobian(sin ∘ log, 4.9) === NoLogAbsDetJacobian{typeof(sin ∘ log), Float64}()
+    @test with_logabsdet_jacobian(log ∘ sin, 4.9) === NoLogAbsDetJacobian{typeof(log ∘ sin), Float64}()
+
+    @test with_logabsdet_jacobian(Base.Fix1(broadcast, sin), 4.9) === NoLogAbsDetJacobian{typeof(sin), Float64}()
+
     function ChangesOfVariables.with_logabsdet_jacobian(::typeof(foo), x)
         y = foo(x)
         ladj = -x + 2 * log(y)