Stabilize doctests

docs/Project.toml

@@ -1,5 +1,7 @@
 [deps]
 Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4"
+ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
+LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 Markdown = "d6f4376e-aef5-505a-96c1-9c027394607a"
 
 [compat]

src/with_ladj.jl

@@ -17,6 +17,8 @@ For `(y, ladj) = with_logabsdet_jacobian(f, x)`, the following must hold true:
 # Examples
 
 ```jldoctest a
+using ChangesOfVariables
+
 foo(x) = inv(exp(-x) + 1)
 
 function ChangesOfVariables.with_logabsdet_jacobian(::typeof(foo), x)
@@ -28,29 +30,33 @@ end
 x = 4.2
 y, ladj_y = with_logabsdet_jacobian(foo, x)
 
+using LinearAlgebra, ForwardDiff
+y == foo(x), ladj_y ≈ log(abs(ForwardDiff.derivative(foo, x)))
+
 # output
 
-(0.9852259683067269, -4.229768509343836)
+(true, true)
 ```
 
 ```jldoctest a
-X = [3, 7, 5]
+X = rand(10)
 broadcasted_foo = Base.Fix1(broadcast, foo)
 Y, ladj_Y = with_logabsdet_jacobian(broadcasted_foo, X)
+Y == broadcasted_foo(X), ladj_Y ≈ logabsdet(ForwardDiff.jacobian(broadcasted_foo, X))[1]
 
 # output
 
-([0.9525741268224334, 0.9990889488055994, 0.9933071490757153], -15.112428333033268)
+(true, true)
 ```
 
 ```jldoctest a
 # Requires Julia >= v1.6:
 z, ladj_z = with_logabsdet_jacobian(log ∘ foo, x)
-z == log(foo(x)) && ladj_z == ladj_y + with_logabsdet_jacobian(log, y)[2]
+z == log(foo(x)), ladj_z == ladj_y + with_logabsdet_jacobian(log, y)[2]
 
 # output
 
-true
+(true, true)
 ```
 
 Implementations of with_logabsdet_jacobian can be tested (as a