Hessian-tracing over ForwardDiff is broken

[gdalle]

See this comment by @Vaibhavdixit02: JuliaDiff/DifferentiationInterface.jl#165 (review)

I think that's because we don't know how to take Tracers of Dual numbers or something of the sort

[adrhill]

When called with prepare_hessian SparsityConnectivityTracer choice throws

ERROR: MethodError: no method matching dual_definition_retval(::Val{…}, ::SparseConnectivityTracer.Tracer, ::Float64, ::ForwardDiff.Partials{…})

This might be due to ForwardDiff defining dual_definition_retval for Real but Tracer being a Number:
https://github.com/JuliaDiff/ForwardDiff.jl/blob/1907196ba50e3eb337860301ece3ec37d0582257/src/dual.jl#L199-L204

How about adding a ForwardDiff extension with a dual_definition_retval method for Tracer?

[gdalle]

Yeah that seems like the wisest course of action. And add the appropriate tests (no idea what these are)

[adrhill]

Is this still a desired feature now that we have HessianTracer #24?

[gdalle]

Nope