MWE now works:

```julia
using Enzyme, OrdinaryDiffEq, StaticArrays

Enzyme.EnzymeCore.EnzymeRules.inactive_type(::Type{SciMLBase.DEStats}) = true
Enzyme.EnzymeCore.EnzymeRules.inactive(::typeof(OrdinaryDiffEq.increment_nf!), args...) = true
Enzyme.EnzymeCore.EnzymeRules.inactive(::typeof(OrdinaryDiffEq.increment_nf_from_initdt!), args...) = true
Enzyme.EnzymeCore.EnzymeRules.inactive(::typeof(OrdinaryDiffEq.fixed_t_for_floatingpoint_error!), args...) = true
Enzyme.EnzymeCore.EnzymeRules.inactive(::typeof(OrdinaryDiffEq.increment_accept!), args...) = true
Enzyme.EnzymeCore.EnzymeRules.inactive(::typeof(OrdinaryDiffEq.increment_reject!), args...) = true
Enzyme.EnzymeCore.EnzymeRules.inactive(::typeof(DiffEqBase.fastpow), args...) = true
Enzyme.EnzymeCore.EnzymeRules.inactive(::typeof(OrdinaryDiffEq.increment_nf_perform_step!), args...) = true
Enzyme.EnzymeCore.EnzymeRules.inactive(::typeof(OrdinaryDiffEq.check_error!), args...) = true
Enzyme.EnzymeCore.EnzymeRules.inactive(::typeof(OrdinaryDiffEq.log_step!), args...) = true

function lorenz!(du, u, p, t)
    du[1] = 10.0(u[2] - u[1])
    du[2] = u[1] * (28.0 - u[3]) - u[2]
    du[3] = u[1] * u[2] - (8 / 3) * u[3]
end

const _saveat =  SA[0.0,0.25,0.5,0.75,1.0,1.25,1.5,1.75,2.0,2.25,2.5,2.75,3.0]

function f(y::Array{Float64}, u0::Array{Float64})
    tspan = (0.0, 3.0)
    prob = ODEProblem{true, SciMLBase.FullSpecialize}(lorenz!, u0, tspan)
    sol = DiffEqBase.solve(prob, Tsit5(), saveat = _saveat, sensealg = DiffEqBase.SensitivityADPassThrough())
    y .= sol[1,:]
    return nothing
end;
u0 = [1.0; 0.0; 0.0]
d_u0 = zeros(3)
y  = zeros(13)
dy = zeros(13)

Enzyme.autodiff(Reverse, f,  Duplicated(y, dy), Duplicated(u0, d_u0));
```

Core issues to finish this:

1. I shouldn't have to pull all of the logging out to a separate function, but there seems to be a bug in enzyme with int inactivity EnzymeAD/Enzyme.jl#1636
2. `saveat` has issues because it uses Julia ranges, which can have a floating point fix issue EnzymeAD/Enzyme.jl#274
3. adding the zero(u), zero(u) is required because Enzyme does not seem to support non-fully initialized types (@wsmoses is that known?) and segfaults when trying to use the uninitialized memory. So making the inner constructor not use undef is and easy fix to that. But that's not memory optimal. It would take a bit of a refactor to make it memory optimal, but it's no big deal and it's probably something that improves the package anyways.