ForwardDiff is broken for differently sized inputs

[torfjelde]

julia> using AbstractDifferentiation, ForwardDiff

julia> AD = AbstractDifferentiation
AbstractDifferentiation

julia> ad = AD.ForwardDiffBackend()
AbstractDifferentiation.ForwardDiffBackend{Nothing}()

julia> AD.jacobian(ad, (x, y) -> sum(x .+ y), randn(2), randn(1)) # (!!!) Result should not be tuple of inputs!
(1.0, 2.0)

Environment

julia> versioninfo()
Julia Version 1.8.0
Commit 5544a0fab76 (2022-08-17 13:38 UTC)
Platform Info:
  OS: Linux (x86_64-linux-gnu)
  CPU: 12 × Intel(R) Core(TM) i7-10710U CPU @ 1.10GHz
  WORD_SIZE: 64
  LIBM: libopenlibm
  LLVM: libLLVM-13.0.1 (ORCJIT, skylake)
  Threads: 1 on 12 virtual cores

(jl_z9VwJo) pkg> st
Status `/tmp/jl_z9VwJo/Project.toml`
  [c29ec348] AbstractDifferentiation v0.4.3
  [f6369f11] ForwardDiff v0.10.32

(jl_z9VwJo) pkg> st --manifest
Status `/tmp/jl_z9VwJo/Manifest.toml`
  [c29ec348] AbstractDifferentiation v0.4.3
  [d360d2e6] ChainRulesCore v1.15.6
  [9e997f8a] ChangesOfVariables v0.1.4
  [bbf7d656] CommonSubexpressions v0.3.0
  [34da2185] Compat v4.3.0
  [163ba53b] DiffResults v1.1.0
  [b552c78f] DiffRules v1.11.1
  [ffbed154] DocStringExtensions v0.9.1
  [e2ba6199] ExprTools v0.1.8
  [f6369f11] ForwardDiff v0.10.32
  [3587e190] InverseFunctions v0.1.8
  [92d709cd] IrrationalConstants v0.1.1
  [692b3bcd] JLLWrappers v1.4.1
  [2ab3a3ac] LogExpFunctions v0.3.18
  [1914dd2f] MacroTools v0.5.10
  [77ba4419] NaNMath v1.0.1
  [21216c6a] Preferences v1.3.0
  [ae029012] Requires v1.3.0
  [276daf66] SpecialFunctions v2.1.7
  [90137ffa] StaticArrays v1.5.9
  [1e83bf80] StaticArraysCore v1.4.0
  [efe28fd5] OpenSpecFun_jll v0.5.5+0
  [0dad84c5] ArgTools v1.1.1
  [56f22d72] Artifacts
  [2a0f44e3] Base64
  [ade2ca70] Dates
  [f43a241f] Downloads v1.6.0
  [7b1f6079] FileWatching
  [b77e0a4c] InteractiveUtils
  [b27032c2] LibCURL v0.6.3
  [76f85450] LibGit2
  [8f399da3] Libdl
  [37e2e46d] LinearAlgebra
  [56ddb016] Logging
  [d6f4376e] Markdown
  [ca575930] NetworkOptions v1.2.0
  [44cfe95a] Pkg v1.8.0
  [de0858da] Printf
  [3fa0cd96] REPL
  [9a3f8284] Random
  [ea8e919c] SHA v0.7.0
  [9e88b42a] Serialization
  [6462fe0b] Sockets
  [2f01184e] SparseArrays
  [10745b16] Statistics
  [fa267f1f] TOML v1.0.0
  [a4e569a6] Tar v1.10.0
  [8dfed614] Test
  [cf7118a7] UUIDs
  [4ec0a83e] Unicode
  [e66e0078] CompilerSupportLibraries_jll v0.5.2+0
  [deac9b47] LibCURL_jll v7.84.0+0
  [29816b5a] LibSSH2_jll v1.10.2+0
  [c8ffd9c3] MbedTLS_jll v2.28.0+0
  [14a3606d] MozillaCACerts_jll v2022.2.1
  [4536629a] OpenBLAS_jll v0.3.20+0
  [05823500] OpenLibm_jll v0.8.1+0
  [83775a58] Zlib_jll v1.2.12+3
  [8e850b90] libblastrampoline_jll v5.1.1+0
  [8e850ede] nghttp2_jll v1.48.0+0
  [3f19e933] p7zip_jll v17.4.0+0