fix: replace MissingBackendError with error hint

DifferentiationInterface/src/DifferentiationInterface.jl

@@ -41,7 +41,6 @@ include("utils/traits.jl")
 include("utils/basis.jl")
 include("utils/batchsize.jl")
 include("utils/check.jl")
-include("utils/exceptions.jl")
 include("utils/printing.jl")
 include("utils/context.jl")
 include("utils/linalg.jl")
@@ -123,4 +122,6 @@ export AutoSparse
 
 @public inner, outer
 
+include("init.jl")
+
 end # module

DifferentiationInterface/src/first_order/pullback.jl

@@ -145,18 +145,6 @@ function _prepare_pullback_aux(
     return PushforwardPullbackPrep(pushforward_prep)
 end
 
-function _prepare_pullback_aux(
-    ::PullbackFast, f, backend::AbstractADType, x, ty::NTuple, contexts::Vararg{Context}
-)
-    throw(MissingBackendError(backend))
-end
-
-function _prepare_pullback_aux(
-    ::PullbackFast, f!, y, backend::AbstractADType, x, ty::NTuple, contexts::Vararg{Context}
-)
-    throw(MissingBackendError(backend))
-end
-
 ## One argument
 
 function _pullback_via_pushforward(

DifferentiationInterface/src/first_order/pushforward.jl

@@ -146,24 +146,6 @@ function _prepare_pushforward_aux(
     return PullbackPushforwardPrep(pullback_prep)
 end
 
-function _prepare_pushforward_aux(
-    ::PushforwardFast, f, backend::AbstractADType, x, tx::NTuple, contexts::Vararg{Context}
-)
-    throw(MissingBackendError(backend))
-end
-
-function _prepare_pushforward_aux(
-    ::PushforwardFast,
-    f!,
-    y,
-    backend::AbstractADType,
-    x,
-    tx::NTuple,
-    contexts::Vararg{Context},
-)
-    throw(MissingBackendError(backend))
-end
-
 ## One argument
 
 function _pushforward_via_pullback(

DifferentiationInterface/src/init.jl

@@ -0,0 +1,13 @@
+function __init__()
+    Base.Experimental.register_error_hint(MethodError) do io, exc, argtypes, kwargs
+        if exc.f in (_prepare_pushforward_aux, _prepare_pullback_aux)
+            B = first(T for T in argtypes if T <: AbstractADType)
+            printstyled(
+                io,
+                "\n\nThe autodiff backend package you want to use may not be loaded. Please run the following command and try again:";
+                bold=true,
+            )
+            printstyled(io, "\n\n\timport $(package_name(B))"; color=:cyan, bold=true)
+        end
+    end
+end

DifferentiationInterface/src/utils/printing.jl

@@ -1,19 +1,24 @@
-function package_name(b::AbstractADType)
-    s = string(b)
+package_name(b::AbstractADType) = package_name(typeof(b))
+
+function package_name(::Type{B}) where {B<:AbstractADType}
+    s = string(B)
     s = chopprefix(s, "ADTypes.")
     s = chopprefix(s, "Auto")
-    k = findfirst('(', s)
-    isnothing(k) && throw(ArgumentError("Cannot parse backend into package"))
-    return s[begin:(k - 1)]
+    k = findfirst('{', s)
+    if isnothing(k)
+        return s
+    else
+        return s[begin:(k - 1)]
+    end
 end
 
-function package_name(b::SecondOrder)
-    p1 = package_name(outer(b))
-    p2 = package_name(inner(b))
+function package_name(::Type{SecondOrder{O,I}}) where {O,I}
+    p1 = package_name(O)
+    p2 = package_name(I)
     return p1 == p2 ? p1 : "$p1, $p2"
 end
 
-package_name(b::AutoSparse) = package_name(dense_ad(b))
+package_name(::Type{<:AutoSparse{D}}) where {D} = package_name(D)
 
 function document_preparation(operator_name::AbstractString; same_point=false)
     if same_point