using IntervalArithmetic invalidates a lot of code from ModelingToolkit.jl

[jaakkor2]

In my system, IntervalArithmetic.jl is pulled in when using GLMakie.jl.

(@v1.10) pkg> why IntervalArithmetic
  GLMakie → Makie → DelaunayTriangulation → ExactPredicates → IntervalArithmetic
  IntervalArithmetic

Taking the example from https://github.com/SciML/ModelingToolkit.jl front page (README.md) and omitting the plotting part, and naming it MTKdemo.jl

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

@parameters σ ρ β
@variables x(t) y(t) z(t)

eqs = [D(D(x)) ~ σ * (y - x),
    D(y) ~ x * (ρ - z) - y,
    D(z) ~ x * y - β * z]

@mtkbuild sys = ODESystem(eqs, t)

u0 = [D(x) => 2.0,
    x => 1.0,
    y => 0.0,
    z => 0.0]

p = [σ => 28.0,
    ρ => 10.0,
    β => 8 / 3]

tspan = (0.0, 100.0)
prob = ODEProblem(sys, u0, tspan, p, jac = true)
sol = solve(prob)
nothing

Then a lot of code from the example above needs to recompiled after using IntervalArithmetic

julia> @time include("MTKdemo.jl")
 13.122820 seconds (25.34 M allocations: 1.698 GiB, 7.29% gc time, 63.39% compilation time: <1% of which was recompilation)

julia> @time include("MTKdemo.jl")
  0.019970 seconds (154.13 k allocations: 8.521 MiB, 0.00% compilation time)

julia> @time using IntervalArithmetic
  0.071065 seconds (79.87 k allocations: 4.100 MiB)

julia> @time include("MTKdemo.jl")
 11.524903 seconds (19.34 M allocations: 1.292 GiB, 2.09% gc time, 99.71% compilation time: 93% of which was recompilation)

julia> @time include("MTKdemo.jl")
  0.020549 seconds (153.11 k allocations: 8.454 MiB, 0.00% compilation time)

(@v1.10) pkg> st
  [d1acc4aa] IntervalArithmetic v0.22.31
  [961ee093] ModelingToolkit v9.76.0
  [50262376] OrdinaryDiffEqDefault v1.3.0

Julia v1.10.9.

Earlier I opened an issue at lairez/ExactPredicates.jl#27, but looks like the invalidations are coming from IntervalArithmetic.jl.

[OlivierHnt]

Thank you for opening this issue. Could this be due to our use of @eval?

Edit: actually, reading the discussion at lairez/ExactPredicates.jl#27, it seems that this is due to our overloading of similar.