ForwardDiff on ODE with callback crashes

[hersle]

Differentiate an ODE that uses a callback to terminate when x = 2:

using ModelingToolkit, OrdinaryDiffEq
using ModelingToolkit: t_nounits as t, D_nounits as D

@variables x(t)
@mtkbuild sys = System([D(x) ~ x], t)
callback = ContinuousCallback((u, t, integrator) -> u[1] - 2.0, terminate!)
prob = ODEProblem(sys, [x => NaN], (0.0, 10.0); callback)

function t_when_x_is_2(x0)
    newprob = remake(prob; u0 = [sys.x => x0])
    sol = solve(newprob)
    return sol[t][end]
end

ForwardDiff.derivative(t_when_x_is_2, 1.0)

This errors with

ERROR: MethodError: no method matching Float64(::ForwardDiff.Dual{ForwardDiff.Tag{typeof(t_when_x_is_2), Float64}, Float64, 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.Log4π)
   @ IrrationalConstants ~/.julia/packages/IrrationalConstants/lWTip/src/macro.jl:131
  ...

Stacktrace:
  [1] copysign(x::Float64, y::ForwardDiff.Dual{ForwardDiff.Tag{typeof(t_when_x_is_2), Float64}, Float64, 1})
    @ Base ./floatfuncs.jl:8
  [2] solve(::IntervalNonlinearProblem{…}, ::DiffEqBase.InternalITP; maxiters::Int64, kwargs::@Kwargs{…})
    @ DiffEqBase ~/.julia/packages/DiffEqBase/Rfwzp/src/internal_itp.jl:61
  [3] solve
    @ ~/.julia/packages/DiffEqBase/Rfwzp/src/internal_itp.jl:29 [inlined]
  [4] #bisection#20
    @ ~/.julia/packages/DiffEqBase/Rfwzp/src/callbacks.jl:366 [inlined]
  [5] bisection
    @ ~/.julia/packages/DiffEqBase/Rfwzp/src/callbacks.jl:362 [inlined]
  [6] find_callback_time(integrator::OrdinaryDiffEqCore.ODEIntegrator{…}, callback::ContinuousCallback{…}, counter::Int64)
    @ DiffEqBase ~/.julia/packages/DiffEqBase/Rfwzp/src/callbacks.jl:434
  [7] macro expansion
    @ ~/.julia/packages/DiffEqBase/Rfwzp/src/callbacks.jl:130 [inlined]
  [8] find_first_continuous_callback
    @ ~/.julia/packages/DiffEqBase/Rfwzp/src/callbacks.jl:125 [inlined]
  [9] find_first_continuous_callback
    @ ~/.julia/packages/DiffEqBase/Rfwzp/src/callbacks.jl:123 [inlined]
 [10] handle_callbacks!
    @ ~/.julia/packages/OrdinaryDiffEqCore/TUQ8i/src/integrators/integrator_utils.jl:379 [inlined]
 [11] _loopfooter!(integrator::OrdinaryDiffEqCore.ODEIntegrator{…})
    @ OrdinaryDiffEqCore ~/.julia/packages/OrdinaryDiffEqCore/TUQ8i/src/integrators/integrator_utils.jl:284
 [12] loopfooter!
    @ ~/.julia/packages/OrdinaryDiffEqCore/TUQ8i/src/integrators/integrator_utils.jl:248 [inlined]
 [13] solve!(integrator::OrdinaryDiffEqCore.ODEIntegrator{…})
    @ OrdinaryDiffEqCore ~/.julia/packages/OrdinaryDiffEqCore/TUQ8i/src/solve.jl:611
 [14] #__solve#62
    @ ~/.julia/packages/OrdinaryDiffEqCore/TUQ8i/src/solve.jl:7 [inlined]
 [15] __solve
    @ ~/.julia/packages/OrdinaryDiffEqCore/TUQ8i/src/solve.jl:1 [inlined]
 [16] #__solve#3
    @ ~/.julia/packages/OrdinaryDiffEqDefault/ydhv7/src/default_alg.jl:48 [inlined]
 [17] __solve
    @ ~/.julia/packages/OrdinaryDiffEqDefault/ydhv7/src/default_alg.jl:47 [inlined]
 [18] #__solve#54
    @ ~/.julia/packages/DiffEqBase/Rfwzp/src/solve.jl:896 [inlined]
 [19] __solve
    @ ~/.julia/packages/DiffEqBase/Rfwzp/src/solve.jl:887 [inlined]
 [20] solve_call(::ODEProblem{…}; merge_callbacks::Bool, kwargshandle::Nothing, kwargs::@Kwargs{})
    @ DiffEqBase ~/.julia/packages/DiffEqBase/Rfwzp/src/solve.jl:127
 [21] solve_call
    @ ~/.julia/packages/DiffEqBase/Rfwzp/src/solve.jl:84 [inlined]
 [22] #solve_up#40
    @ ~/.julia/packages/DiffEqBase/Rfwzp/src/solve.jl:665 [inlined]
 [23] solve_up
    @ ~/.julia/packages/DiffEqBase/Rfwzp/src/solve.jl:658 [inlined]
 [24] #solve#38
    @ ~/.julia/packages/DiffEqBase/Rfwzp/src/solve.jl:553 [inlined]
 [25] solve(::ODEProblem{Vector{…}, Tuple{…}, true, MTKParameters{…}, ODEFunction{…}, @Kwargs{…}, SciMLBase.StandardODEProblem})
    @ DiffEqBase ~/.julia/packages/DiffEqBase/Rfwzp/src/solve.jl:543
 [26] t_when_x_is_2(x0::ForwardDiff.Dual{ForwardDiff.Tag{typeof(t_when_x_is_2), Float64}, Float64, 1})
    @ Main ./REPL[65]:11
 [27] derivative(f::typeof(t_when_x_is_2), x::Float64)
    @ ForwardDiff ~/.julia/packages/ForwardDiff/Or6Qh/src/derivative.jl:14
 [28] top-level scope
    @ REPL[65]:15
Some type information was truncated. Use `show(err)` to see complete types.

[hersle]

I realized this seems to be an issue with OrdinaryDiffEq and not ModelingToolkit, so I am closing this and opened SciML/OrdinaryDiffEq.jl#2867.