diff --git a/src/adtypes_interface.jl b/src/adtypes_interface.jl
index b373477..3e8618b 100644
--- a/src/adtypes_interface.jl
+++ b/src/adtypes_interface.jl
@@ -19,7 +19,10 @@ For local sparsity patterns at a specific input point, use [`TracerLocalSparsity
 ```jldoctest
 julia> using SparseConnectivityTracer
 
-julia> jacobian_sparsity(diff, rand(4), TracerSparsityDetector())
+julia> detector = TracerSparsityDetector()
+TracerSparsityDetector()
+
+julia> jacobian_sparsity(diff, rand(4), detector)
 3×4 SparseArrays.SparseMatrixCSC{Bool, Int64} with 6 stored entries:
  1  1  ⋅  ⋅
  ⋅  1  1  ⋅
@@ -29,7 +32,7 @@ julia> jacobian_sparsity(diff, rand(4), TracerSparsityDetector())
 ```jldoctest
 julia> f(x) = x[1] + x[2]*x[3] + 1/x[4];
 
-julia> hessian_sparsity(f, rand(4), TracerSparsityDetector())
+julia> hessian_sparsity(f, rand(4), detector)
 4×4 SparseArrays.SparseMatrixCSC{Bool, Int64} with 3 stored entries:
  ⋅  ⋅  ⋅  ⋅
  ⋅  ⋅  1  ⋅
@@ -78,23 +81,24 @@ Local sparsity patterns are less convervative than global patterns and need to b
 ```jldoctest
 julia> using SparseConnectivityTracer
 
-julia> method = TracerLocalSparsityDetector();
+julia> detector = TracerLocalSparsityDetector()
+TracerLocalSparsityDetector()
 
 julia> f(x) = x[1] * x[2]; # J_f = [x[2], x[1]]
 
-julia> jacobian_sparsity(f, [1, 0], method)
+julia> jacobian_sparsity(f, [1, 0], detector)
 1×2 SparseArrays.SparseMatrixCSC{Bool, Int64} with 1 stored entry:
  ⋅  1
 
-julia> jacobian_sparsity(f, [0, 1], method)
+julia> jacobian_sparsity(f, [0, 1], detector)
 1×2 SparseArrays.SparseMatrixCSC{Bool, Int64} with 1 stored entry:
  1  ⋅
 
-julia> jacobian_sparsity(f, [0, 0], method)
+julia> jacobian_sparsity(f, [0, 0], detector)
 1×2 SparseArrays.SparseMatrixCSC{Bool, Int64} with 0 stored entries:
  ⋅  ⋅
 
-julia> jacobian_sparsity(f, [1, 1], method)
+julia> jacobian_sparsity(f, [1, 1], detector)
 1×2 SparseArrays.SparseMatrixCSC{Bool, Int64} with 2 stored entries:
  1  1
 ```