ContinuousCallback with u[1]^3 doesn't find correct event time

[frankschae]

When replacing the condition of the ContinuousCallback used in the bouncing/free falling ball example https://diffeq.sciml.ai/stable/features/callback_functions/#Example-1:-Bouncing-Ball by u[1]^3=0, one expects to get the same event time t for both callbacks. However, one finds:

• t=3.194 for u[1]=0
• t=3.146 for u[1]^3=0.

MWE:

using OrdinaryDiffEq
condition(u,t,integrator) = u[1] # Event when event_f(u,t) == 0
condition2(u,t,integrator) = u[1]^3 # Event when event_f(u,t) == 0
function affect!(integrator)
  # for simplicity the callback doesn't do anything, except saving the state
  integrator.u[2] += zero(integrator.u[2]) #-integrator.p[2]*integrator.u[2] 
end
cb = ContinuousCallback(condition,affect!,save_positions=(true,true))
cb2 = ContinuousCallback(condition2,affect!,save_positions=(true,true))
function fiip(du,u,p,t)
  du[1] = u[2]
  du[2] = -p[1]
end
abstol=1e-4
reltol=1e-4
u0 = [50.0,0.0]
tspan = (0.0,5.0)
p = [9.8, 0.8]
prob = ODEProblem(fiip,u0,tspan,p)
sol1 = solve(prob,Tsit5(),callback=cb, abstol=abstol,reltol=reltol,
            save_everystep=true,save_start=true)
sol2 = solve(prob,Tsit5(),callback=cb2, abstol=abstol,reltol=reltol,
        save_everystep=true,save_start=true)
sol1.t != sol2.t

when dt_max=0.1 is set, the second callback results in an error:

ERROR: Double callback crossing floating pointer reducer errored. Report this issue.
Stacktrace: Stacktrace:
  [1] error(s::String)
    @ Base ./error.jl:33
  [2] find_callback_time(integrator::OrdinaryDiffEq.ODEIntegrator{Tsit5, true, Vector{Float64}, Nothing, Float64, Vector{Float64}, Float64, Float64, Float64, Vector{Vector{Float64}}, ODESolution{Float64, 2, Vector{Vector{Float64}}, Nothing, Nothing, Vector{Float64}, Vector{Vector{Vector{Float64}}}, ODEProblem{Vector{Float64}, Tuple{Float64, Float64}, true, Vector{Float64}, ODEFunction{true, typeof(fiip), LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing}, Base.Iterators.Pairs{Union{}, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}, SciMLBase.StandardODEProblem}, Tsit5, OrdinaryDiffEq.InterpolationData{ODEFunction{true, typeof(fiip), LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing}, Vector{Vector{Float64}}, Vector{Float64}, Vector{Vector{Vector{Float64}}}, OrdinaryDiffEq.Tsit5Cache{Vector{Float64}, Vector{Float64}, Vector{Float64}, OrdinaryDiffEq.Tsit5ConstantCache{Float64, Float64}}}, DiffEqBase.DEStats}, ODEFunction{true, typeof(fiip), LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing}, OrdinaryDiffEq.Tsit5Cache{Vector{Float64}, Vector{Float64}, Vector{Float64}, OrdinaryDiffEq.Tsit5ConstantCache{Float64, Float64}}, OrdinaryDiffEq.DEOptions{Float64, Float64, Float64, Float64, PIController{Float64}, typeof(DiffEqBase.ODE_DEFAULT_NORM), typeof(LinearAlgebra.opnorm), Nothing, CallbackSet{Tuple{ContinuousCallback{typeof(condition2), typeof(affect!), typeof(affect!), typeof(DiffEqBase.INITIALIZE_DEFAULT), typeof(DiffEqBase.FINALIZE_DEFAULT), Float64, Int64, Nothing, Int64}}, Tuple{}}, typeof(DiffEqBase.ODE_DEFAULT_ISOUTOFDOMAIN), typeof(DiffEqBase.ODE_DEFAULT_PROG_MESSAGE), typeof(DiffEqBase.ODE_DEFAULT_UNSTABLE_CHECK), DataStructures.BinaryMinHeap{Float64}, DataStructures.BinaryMinHeap{Float64}, Nothing, Nothing, Int64, Tuple{}, Tuple{}, Tuple{}}, Vector{Float64}, Float64, Nothing, OrdinaryDiffEq.DefaultInit}, callback::ContinuousCallback{typeof(condition2), typeof(affect!), typeof(affect!), typeof(DiffEqBase.INITIALIZE_DEFAULT), typeof(DiffEqBase.FINALIZE_DEFAULT), Float64, Int64, Nothing, Int64}, counter::Int64)
    @ DiffEqBase ~/.julia/packages/DiffEqBase/lULzQ/src/callbacks.jl:697
  [3] find_first_continuous_callback
    @ ~/.julia/packages/DiffEqBase/lULzQ/src/callbacks.jl:459 [inlined]
  [4] handle_callbacks!
    @ ~/.julia/packages/OrdinaryDiffEq/2ZBfC/src/integrators/integrator_utils.jl:249 [inlined]
  [5] _loopfooter!(integrator::OrdinaryDiffEq.ODEIntegrator{Tsit5, true, Vector{Float64}, Nothing, Float64, Vector{Float64}, Float64, Float64, Float64, Vector{Vector{Float64}}, ODESolution{Float64, 2, Vector{Vector{Float64}}, Nothing, Nothing, Vector{Float64}, Vector{Vector{Vector{Float64}}}, ODEProblem{Vector{Float64}, Tuple{Float64, Float64}, true, Vector{Float64}, ODEFunction{true, typeof(fiip), LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing}, Base.Iterators.Pairs{Union{}, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}, SciMLBase.StandardODEProblem}, Tsit5, OrdinaryDiffEq.InterpolationData{ODEFunction{true, typeof(fiip), LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing}, Vector{Vector{Float64}}, Vector{Float64}, Vector{Vector{Vector{Float64}}}, OrdinaryDiffEq.Tsit5Cache{Vector{Float64}, Vector{Float64}, Vector{Float64}, OrdinaryDiffEq.Tsit5ConstantCache{Float64, Float64}}}, DiffEqBase.DEStats}, ODEFunction{true, typeof(fiip), LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing}, OrdinaryDiffEq.Tsit5Cache{Vector{Float64}, Vector{Float64}, Vector{Float64}, OrdinaryDiffEq.Tsit5ConstantCache{Float64, Float64}}, OrdinaryDiffEq.DEOptions{Float64, Float64, Float64, Float64, PIController{Float64}, typeof(DiffEqBase.ODE_DEFAULT_NORM), typeof(LinearAlgebra.opnorm), Nothing, CallbackSet{Tuple{ContinuousCallback{typeof(condition2), typeof(affect!), typeof(affect!), typeof(DiffEqBase.INITIALIZE_DEFAULT), typeof(DiffEqBase.FINALIZE_DEFAULT), Float64, Int64, Nothing, Int64}}, Tuple{}}, typeof(DiffEqBase.ODE_DEFAULT_ISOUTOFDOMAIN), typeof(DiffEqBase.ODE_DEFAULT_PROG_MESSAGE), typeof(DiffEqBase.ODE_DEFAULT_UNSTABLE_CHECK), DataStructures.BinaryMinHeap{Float64}, DataStructures.BinaryMinHeap{Float64}, Nothing, Nothing, Int64, Tuple{}, Tuple{}, Tuple{}}, Vector{Float64}, Float64, Nothing, OrdinaryDiffEq.DefaultInit})
    @ OrdinaryDiffEq ~/.julia/packages/OrdinaryDiffEq/2ZBfC/src/integrators/integrator_utils.jl:204
  [6] loopfooter!
    @ ~/.julia/packages/OrdinaryDiffEq/2ZBfC/src/integrators/integrator_utils.jl:168 [inlined]
  [7] solve!(integrator::OrdinaryDiffEq.ODEIntegrator{Tsit5, true, Vector{Float64}, Nothing, Float64, Vector{Float64}, Float64, Float64, Float64, Vector{Vector{Float64}}, ODESolution{Float64, 2, Vector{Vector{Float64}}, Nothing, Nothing, Vector{Float64}, Vector{Vector{Vector{Float64}}}, ODEProblem{Vector{Float64}, Tuple{Float64, Float64}, true, Vector{Float64}, ODEFunction{true, typeof(fiip), LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing}, Base.Iterators.Pairs{Union{}, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}, SciMLBase.StandardODEProblem}, Tsit5, OrdinaryDiffEq.InterpolationData{ODEFunction{true, typeof(fiip), LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing}, Vector{Vector{Float64}}, Vector{Float64}, Vector{Vector{Vector{Float64}}}, OrdinaryDiffEq.Tsit5Cache{Vector{Float64}, Vector{Float64}, Vector{Float64}, OrdinaryDiffEq.Tsit5ConstantCache{Float64, Float64}}}, DiffEqBase.DEStats}, ODEFunction{true, typeof(fiip), LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing}, OrdinaryDiffEq.Tsit5Cache{Vector{Float64}, Vector{Float64}, Vector{Float64}, OrdinaryDiffEq.Tsit5ConstantCache{Float64, Float64}}, OrdinaryDiffEq.DEOptions{Float64, Float64, Float64, Float64, PIController{Float64}, typeof(DiffEqBase.ODE_DEFAULT_NORM), typeof(LinearAlgebra.opnorm), Nothing, CallbackSet{Tuple{ContinuousCallback{typeof(condition2), typeof(affect!), typeof(affect!), typeof(DiffEqBase.INITIALIZE_DEFAULT), typeof(DiffEqBase.FINALIZE_DEFAULT), Float64, Int64, Nothing, Int64}}, Tuple{}}, typeof(DiffEqBase.ODE_DEFAULT_ISOUTOFDOMAIN), typeof(DiffEqBase.ODE_DEFAULT_PROG_MESSAGE), typeof(DiffEqBase.ODE_DEFAULT_UNSTABLE_CHECK), DataStructures.BinaryMinHeap{Float64}, DataStructures.BinaryMinHeap{Float64}, Nothing, Nothing, Int64, Tuple{}, Tuple{}, Tuple{}}, Vector{Float64}, Float64, Nothing, OrdinaryDiffEq.DefaultInit})
    @ OrdinaryDiffEq ~/.julia/packages/OrdinaryDiffEq/2ZBfC/src/solve.jl:478
  [8] #__solve#404
    @ ~/.julia/packages/OrdinaryDiffEq/2ZBfC/src/solve.jl:5 [inlined]
  [9] #solve_call#56
    @ ~/.julia/packages/DiffEqBase/lULzQ/src/solve.jl:61 [inlined]
 [10] solve_up(prob::ODEProblem{Vector{Float64}, Tuple{Float64, Float64}, true, Vector{Float64}, ODEFunction{true, typeof(fiip), LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing}, Base.Iterators.Pairs{Union{}, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}, SciMLBase.StandardODEProblem}, sensealg::Nothing, u0::Vector{Float64}, p::Vector{Float64}, args::Tsit5; kwargs::Base.Iterators.Pairs{Symbol, Any, NTuple{6, Symbol}, NamedTuple{(:callback, :abstol, :reltol, :save_everystep, :save_start, :dtmax), Tuple{ContinuousCallback{typeof(condition2), typeof(affect!), typeof(affect!), typeof(DiffEqBase.INITIALIZE_DEFAULT), typeof(DiffEqBase.FINALIZE_DEFAULT), Float64, Int64, Nothing, Int64}, Float64, Float64, Bool, Bool, Float64}}})
    @ DiffEqBase ~/.julia/packages/DiffEqBase/lULzQ/src/solve.jl:82
 [11] #solve#57
    @ ~/.julia/packages/DiffEqBase/lULzQ/src/solve.jl:70 [inlined]
 [12] top-level scope
    @ none:1

The final zero_func(Θ) in https://github.com/SciML/DiffEqBase.jl/blob/master/src/callbacks.jl#L700 looks relatively stable:

@show Θ
Θ1 = Θ+100eps(Θ)
Θ2 = Θ-100eps(Θ)
@show ODE_DEFAULT_NORM(zero_func(Θ),Θ)
@show ODE_DEFAULT_NORM(zero_func(Θ1),Θ1)
@show ODE_DEFAULT_NORM(zero_func(Θ2),Θ2)

Θ = 3.142840820939239
ODE_DEFAULT_NORM(zero_func(Θ), Θ) = 4.09986205491231
ODE_DEFAULT_NORM(zero_func(Θ1), Θ1) = 4.099862054901799
ODE_DEFAULT_NORM(zero_func(Θ2), Θ2) = 4.099862054922821
integrator.t = 3.142840820939239

[DaniGlez]

It's possible this was fixed a while ago (maybe in #917 or a different one), since both problems now detect almost the same crossing time (there's a bit of precision loss, but much smaller and likely due to loss of absolute precision with the cubic power) and I'm not seeing the Double callback crossing floating pointer reducer errored. Report this issue error reported with the dtmax setting.