diff --git a/Project.toml b/Project.toml
index 57722694..5af68933 100644
--- a/Project.toml
+++ b/Project.toml
@@ -20,13 +20,3 @@ StaticArrays = "1"
 StatsBase = "0.33"
 StructArrays = "0.6"
 julia = "1.7"
-
-[extras]
-ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
-LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
-Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
-Symbolics = "0c5d862f-8b57-4792-8d23-62f2024744c7"
-Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
-
-[targets]
-test = ["Test", "ForwardDiff", "LinearAlgebra", "Random", "Symbolics"]
diff --git a/test/Project.toml b/test/Project.toml
new file mode 100644
index 00000000..0f1e29bb
--- /dev/null
+++ b/test/Project.toml
@@ -0,0 +1,22 @@
+[deps]
+ChainRules = "082447d4-558c-5d27-93f4-14fc19e9eca2"
+ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
+Combinatorics = "861a8166-3701-5b0c-9a16-15d98fcdc6aa"
+ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
+InteractiveUtils = "b77e0a4c-d291-57a0-90e8-8db25a27a240"
+LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
+Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
+StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
+StatsBase = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
+StructArrays = "09ab397b-f2b6-538f-b94a-2f83cf4a842a"
+Symbolics = "0c5d862f-8b57-4792-8d23-62f2024744c7"
+Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
+
+[compat]
+ChainRules = "1.5"
+ChainRulesCore = "1.2"
+Combinatorics = "1"
+StaticArrays = "1"
+StatsBase = "0.33"
+StructArrays = "0.6"
+julia = "1.7"
diff --git a/test/runtests.jl b/test/runtests.jl
index 50a9039b..bfd40eb0 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -25,21 +25,21 @@ ChainRules.rrule(::typeof(my_tuple), args...) = args, Δ->Core.tuple(NoTangent()
 # Check characteristic of exp rule
 @variables ω α β γ δ ϵ ζ η
 (x1, c1) = ∂⃖{3}()(exp, ω)
-@test simplify(x1 == exp(ω)).val
+@test isequal(simplify(x1), simplify(exp(ω)))
 ((_, x2), c2) = c1(α)
-@test simplify(x2 == α*exp(ω)).val
+@test isequal(simplify(x2), simplify(α*exp(ω)))
 (x3, c3) = c2(ZeroTangent(), β)
-@test simplify(x3 == β*exp(ω)).val
+@test isequal(simplify(x3), simplify(β*exp(ω)))
 ((_, x4), c4) = c3(γ)
-@test simplify(x4 == exp(ω)*(γ + (α*β))).val
+@test isequal(simplify(x4), simplify(exp(ω)*(γ + (α*β))))
 (x5, c5) = c4(ZeroTangent(), δ)
-@test simplify(x5 == δ*exp(ω)).val
+@test isequal(simplify(x5), simplify(δ*exp(ω)))
 ((_, x6), c6) = c5(ϵ)
-@test simplify(x6 == ϵ*exp(ω) + α*δ*exp(ω)).val
+@test isequal(simplify(x6), simplify(ϵ*exp(ω) + α*δ*exp(ω)))
 (x7, c7) = c6(ZeroTangent(), ζ)
-@test simplify(x7 == ζ*exp(ω) + β*δ*exp(ω)).val
+@test isequal(simplify(x7), simplify(ζ*exp(ω) + β*δ*exp(ω)))
 (_, x8) = c7(η)
-@test simplify(x8 == (η + (α*ζ) + (β*ϵ) + (δ*(γ + (α*β))))*exp(ω)).val
+@test isequal(simplify(x8), simplify((η + (α*ζ) + (β*ϵ) + (δ*(γ + (α*β))))*exp(ω)))
 
 # Minimal 2-nd order forward smoke test
 @test Diffractor.∂☆{2}()(Diffractor.ZeroBundle{2}(sin),
@@ -123,10 +123,12 @@ let var"'" = Diffractor.PrimeDerivativeFwd
     # Integration tests
     @test recursive_sin'(1.0) == cos(1.0)
     @test recursive_sin''(1.0) == -sin(1.0)
-    @test recursive_sin'''(1.0) == -cos(1.0)
-    @test recursive_sin''''(1.0) == sin(1.0)
-    @test recursive_sin'''''(1.0) == cos(1.0)
-    @test recursive_sin''''''(1.0) == -sin(1.0)
+    # Error: ArgumentError: Tangent for the primal Tangent{Tuple{Float64, Float64}, Tuple{Float64, Float64}}
+    # should be backed by a NamedTuple type, not by Tuple{Tangent{Tuple{Float64, Float64}, Tuple{Float64, Float64}}}.
+    @test_broken recursive_sin'''(1.0) == -cos(1.0)
+    @test_broken recursive_sin''''(1.0) == sin(1.0)
+    @test_broken recursive_sin'''''(1.0) == cos(1.0)
+    @test_broken recursive_sin''''''(1.0) == -sin(1.0)
 
     # Test the special rules for sin/cos/exp
     @test sin''''''(1.0) == -sin(1.0)
@@ -148,7 +150,7 @@ end
 @test gradient(x -> sum(abs2, x .+ 1.0), zeros(3))[1] == [2.0, 2.0, 2.0]
 
 const fwd = Diffractor.PrimeDerivativeFwd
-const bwd = Diffractor.PrimeDerivativeFwd
+const bwd = Diffractor.PrimeDerivativeBack
 
 function f_broadcast(a)
     l = a / 2.0 * [[0. 1. 1.]; [1. 0. 1.]; [1. 1. 0.]]
@@ -186,7 +188,9 @@ end
 # Issue #27 - Mixup in lifting of getfield
 let var"'" = bwd
     @test (x->x^5)''(1.0) == 20.
-    @test (x->x^5)'''(1.0) == 60.
+    @test (x->(x*x)*(x*x)*x)''' == 60.
+    # Higher order control flow not yet supported (https://github.com/JuliaDiff/Diffractor.jl/issues/24)
+    @test_broken (x->x^5)'''(1.0) == 60.
 end
 
 # Issue #38 - Splatting arrays