julia> using ForwardDiff, StaticArrays

julia> struct TestTag end

julia> struct OuterTestTag end

julia> ForwardDiff.:≺(::Type{TestTag}, ::Type{OuterTestTag}) = true

julia> ForwardDiff.:≺(::Type{OuterTestTag}, ::Type{<:ForwardDiff.Tag}) = true

julia> x = [ForwardDiff.Dual{OuterTestTag}(ForwardDiff.Dual{TestTag}(1.3, 2.1), ForwardDiff.Dual{TestTag}(0.3, -2.4))];

julia> ForwardDiff.derivative(ForwardDiff.value, only(x))
Dual{OuterTestTag}(Dual{TestTag}(0.0,0.0),Dual{TestTag}(0.0,0.0))

julia> ForwardDiff.gradient(x -> ForwardDiff.value(only(x)), x)
ERROR: MethodError: no method matching Float64(::ForwardDiff.Dual{OuterTestTag, ForwardDiff.Dual{TestTag, Float64, 1}, 1})
The type `Float64` exists, but no method is defined for this combination of argument types when trying to construct it.

Closest candidates are:
  (::Type{T})(::Real, ::RoundingMode) where T<:AbstractFloat
   @ Base rounding.jl:265
  (::Type{T})(::T) where T<:Number
   @ Core boot.jl:900
  Float64(::IrrationalConstants.Inv2π)
   @ IrrationalConstants ~/.julia/packages/IrrationalConstants/lWTip/src/macro.jl:131
  ...

Stacktrace:
 [1] convert
   @ ~/.julia/packages/ForwardDiff/Or6Qh/src/dual.jl:467 [inlined]
 [2] setindex!(A::Vector{ForwardDiff.Dual{…}}, x::ForwardDiff.Dual{OuterTestTag, ForwardDiff.Dual{…}, 1}, i::Int64)
   @ Base ./array.jl:987
 [3] extract_gradient!
   @ ~/.julia/packages/ForwardDiff/Or6Qh/src/gradient.jl:69 [inlined]
 [4] vector_mode_gradient
   @ ~/.julia/packages/ForwardDiff/Or6Qh/src/gradient.jl:101 [inlined]
 [5] gradient
   @ ~/.julia/packages/ForwardDiff/Or6Qh/src/gradient.jl:20 [inlined]
 [6] gradient(f::var"#9#10", x::Vector{…}, cfg::ForwardDiff.GradientConfig{…})
   @ ForwardDiff ~/.julia/packages/ForwardDiff/Or6Qh/src/gradient.jl:17
 [7] gradient(f::var"#9#10", x::Vector{ForwardDiff.Dual{OuterTestTag, ForwardDiff.Dual{TestTag, Float64, 1}, 1}})
   @ ForwardDiff ~/.julia/packages/ForwardDiff/Or6Qh/src/gradient.jl:17
 [8] top-level scope
   @ REPL[11]:1
Some type information was truncated. Use `show(err)` to see complete types.

julia> ForwardDiff.gradient(x -> ForwardDiff.value(only(x)), SVector{1}(x))
ERROR: MethodError: no method matching Float64(::ForwardDiff.Dual{OuterTestTag, ForwardDiff.Dual{TestTag, Float64, 1}, 1})
The type `Float64` exists, but no method is defined for this combination of argument types when trying to construct it.

Closest candidates are:
  (::Type{T})(::Real, ::RoundingMode) where T<:AbstractFloat
   @ Base rounding.jl:265
  (::Type{T})(::T) where T<:Number
   @ Core boot.jl:900
  Float64(::IrrationalConstants.Inv2π)
   @ IrrationalConstants ~/.julia/packages/IrrationalConstants/lWTip/src/macro.jl:131
  ...

Stacktrace:
 [1] convert
   @ ~/.julia/packages/ForwardDiff/Or6Qh/src/dual.jl:467 [inlined]
 [2] macro expansion
   @ ~/.julia/packages/StaticArraysCore/7xxEJ/src/StaticArraysCore.jl:88 [inlined]
 [3] convert_ntuple
   @ ~/.julia/packages/StaticArraysCore/7xxEJ/src/StaticArraysCore.jl:84 [inlined]
 [4] SVector{1, ForwardDiff.Dual{TestTag, Float64, 1}}(x::Tuple{ForwardDiff.Dual{OuterTestTag, ForwardDiff.Dual{…}, 1}})
   @ StaticArraysCore ~/.julia/packages/StaticArraysCore/7xxEJ/src/StaticArraysCore.jl:120
 [5] macro expansion
   @ ~/.julia/packages/ForwardDiff/Or6Qh/ext/ForwardDiffStaticArraysExt.jl:51 [inlined]
 [6] extract_gradient
   @ ~/.julia/packages/ForwardDiff/Or6Qh/ext/ForwardDiffStaticArraysExt.jl:46 [inlined]
 [7] vector_mode_gradient
   @ ~/.julia/packages/ForwardDiff/Or6Qh/ext/ForwardDiffStaticArraysExt.jl:57 [inlined]
 [8] gradient(f::var"#13#14", x::SVector{1, ForwardDiff.Dual{OuterTestTag, ForwardDiff.Dual{TestTag, Float64, 1}, 1}})
   @ ForwardDiffStaticArraysExt ~/.julia/packages/ForwardDiff/Or6Qh/ext/ForwardDiffStaticArraysExt.jl:38
 [9] top-level scope
   @ REPL[12]:1
Some type information was truncated. Use `show(err)` to see complete types.

julia> ForwardDiff.jacobian(x -> map(ForwardDiff.value, x), x)
ERROR: MethodError: no method matching Float64(::ForwardDiff.Dual{OuterTestTag, ForwardDiff.Dual{TestTag, Float64, 1}, 1})
The type `Float64` exists, but no method is defined for this combination of argument types when trying to construct it.

Closest candidates are:
  (::Type{T})(::Real, ::RoundingMode) where T<:AbstractFloat
   @ Base rounding.jl:265
  (::Type{T})(::T) where T<:Number
   @ Core boot.jl:900
  Float64(::IrrationalConstants.Inv2π)
   @ IrrationalConstants ~/.julia/packages/IrrationalConstants/lWTip/src/macro.jl:131
  ...

Stacktrace:
  [1] convert
    @ ~/.julia/packages/ForwardDiff/Or6Qh/src/dual.jl:467 [inlined]
  [2] setindex!
    @ ./array.jl:994 [inlined]
  [3] setindex!
    @ ./multidimensional.jl:704 [inlined]
  [4] macro expansion
    @ ./broadcast.jl:973 [inlined]
  [5] macro expansion
    @ ./simdloop.jl:77 [inlined]
  [6] copyto!
    @ ./broadcast.jl:972 [inlined]
  [7] copyto!
    @ ./broadcast.jl:925 [inlined]
  [8] materialize!
    @ ./broadcast.jl:883 [inlined]
  [9] materialize!
    @ ./broadcast.jl:880 [inlined]
 [10] extract_jacobian!(::Type{…}, result::Matrix{…}, ydual::Vector{…}, n::Int64)
    @ ForwardDiff ~/.julia/packages/ForwardDiff/Or6Qh/src/jacobian.jl:100
 [11] vector_mode_jacobian(f::var"#15#16", x::Vector{…}, cfg::ForwardDiff.JacobianConfig{…})
    @ ForwardDiff ~/.julia/packages/ForwardDiff/Or6Qh/src/jacobian.jl:132
 [12] jacobian
    @ ~/.julia/packages/ForwardDiff/Or6Qh/src/jacobian.jl:22 [inlined]
 [13] jacobian(f::var"#15#16", x::Vector{…}, cfg::ForwardDiff.JacobianConfig{…})
    @ ForwardDiff ~/.julia/packages/ForwardDiff/Or6Qh/src/jacobian.jl:19
 [14] jacobian(f::var"#15#16", x::Vector{ForwardDiff.Dual{OuterTestTag, ForwardDiff.Dual{TestTag, Float64, 1}, 1}})
    @ ForwardDiff ~/.julia/packages/ForwardDiff/Or6Qh/src/jacobian.jl:19
 [15] top-level scope
    @ REPL[13]:1
Some type information was truncated. Use `show(err)` to see complete types.

julia> ForwardDiff.jacobian(x -> map(ForwardDiff.value, x), SVector{1}(x))
ERROR: MethodError: no method matching Float64(::ForwardDiff.Dual{OuterTestTag, ForwardDiff.Dual{TestTag, Float64, 1}, 1})
The type `Float64` exists, but no method is defined for this combination of argument types when trying to construct it.

Closest candidates are:
  (::Type{T})(::Real, ::RoundingMode) where T<:AbstractFloat
   @ Base rounding.jl:265
  (::Type{T})(::T) where T<:Number
   @ Core boot.jl:900
  Float64(::IrrationalConstants.Inv2π)
   @ IrrationalConstants ~/.julia/packages/IrrationalConstants/lWTip/src/macro.jl:131
  ...

Stacktrace:
 [1] convert
   @ ~/.julia/packages/ForwardDiff/Or6Qh/src/dual.jl:467 [inlined]
 [2] macro expansion
   @ ~/.julia/packages/StaticArraysCore/7xxEJ/src/StaticArraysCore.jl:88 [inlined]
 [3] convert_ntuple
   @ ~/.julia/packages/StaticArraysCore/7xxEJ/src/StaticArraysCore.jl:84 [inlined]
 [4] SMatrix{1, 1, ForwardDiff.Dual{…}, 1}(x::Tuple{ForwardDiff.Dual{…}})
   @ StaticArraysCore ~/.julia/packages/StaticArraysCore/7xxEJ/src/StaticArraysCore.jl:120
 [5] macro expansion
   @ ~/.julia/packages/ForwardDiff/Or6Qh/ext/ForwardDiffStaticArraysExt.jl:80 [inlined]
 [6] extract_jacobian
   @ ~/.julia/packages/ForwardDiff/Or6Qh/ext/ForwardDiffStaticArraysExt.jl:74 [inlined]
 [7] vector_mode_jacobian
   @ ~/.julia/packages/ForwardDiff/Or6Qh/ext/ForwardDiffStaticArraysExt.jl:86 [inlined]
 [8] jacobian(f::var"#19#20", x::SVector{1, ForwardDiff.Dual{OuterTestTag, ForwardDiff.Dual{TestTag, Float64, 1}, 1}})
   @ ForwardDiffStaticArraysExt ~/.julia/packages/ForwardDiff/Or6Qh/ext/ForwardDiffStaticArraysExt.jl:66
 [9] top-level scope
   @ REPL[14]:1
Some type information was truncated. Use `show(err)` to see complete types.