Handle Slow Precompilation + Reduce Runtime Dispatches

[avik-pal]

Fixes #148

[github-actions]

Benchmark Results

	master	eeddc71...	t[master]/t[eeddc71...]
Simple Pendulum/IIP/MultipleShooting(10, Tsit5; grid_coarsening = false)	1.82 ± 0.042 ms	1.83 ± 0.057 ms	0.994
Simple Pendulum/IIP/MultipleShooting(10, Tsit5; grid_coarsening = true)	3.33 ± 0.056 ms	3.4 ± 0.1 ms	0.98
Simple Pendulum/IIP/MultipleShooting(100, Tsit5; grid_coarsening = false)	0.0521 ± 0.0034 s	0.054 ± 0.0043 s	0.964
Simple Pendulum/IIP/MultipleShooting(100, Tsit5; grid_coarsening = true)	1.12 ± 0.0017 s	1.14 ± 0.015 s	0.981
Simple Pendulum/IIP/Shooting(Tsit5())	0.177 ± 0.0052 ms	0.233 ± 0.0053 ms	0.761
Simple Pendulum/OOP/MultipleShooting(10, Tsit5; grid_coarsening = false)	4.19 ± 0.2 ms	4.44 ± 0.31 ms	0.944
Simple Pendulum/OOP/MultipleShooting(10, Tsit5; grid_coarsening = true)	7.39 ± 4.1 ms	7.87 ± 5.3 ms	0.938
Simple Pendulum/OOP/MultipleShooting(100, Tsit5; grid_coarsening = false)	0.125 ± 0.0014 s	0.145 ± 0.0026 s	0.864
Simple Pendulum/OOP/MultipleShooting(100, Tsit5; grid_coarsening = true)	4.78 ± 0.02 s	4.87 ± 0.003 s	0.98
Simple Pendulum/OOP/Shooting(Tsit5())	0.701 ± 0.024 ms	0.838 ± 0.055 ms	0.836
time_to_load	8.04 ± 0.034 s	8.08 ± 0.06 s	0.996

Benchmark Plots

A plot of the benchmark results have been uploaded as an artifact to the workflow run for this PR.
Go to "Actions"->"Benchmark a pull request"->[the most recent run]->"Artifacts" (at the bottom).

[avik-pal]

I might end up splitting this PR into multiple smaller ones for easier review but for now I am aggregating all the fixes that need to go in

[avik-pal]

using SnoopCompile, JET
using BoundaryValueDiffEq, LinearAlgebra, LinearSolve, OrdinaryDiffEq, Test

tspan = (0.0, 100.0)
u0 = [0.0, 1.0]

# Inplace
function f1!(du, u, p, t)
    du[1] = u[2]
    du[2] = -u[1]
    return nothing
end

function bc1!(resid, sol, p, t)
    t₀, t₁ = first(t), last(t)
    resid[1] = sol(t₀)[1]
    resid[2] = sol(t₁)[1] - 1
    return nothing
end

bvp1 = BVProblem(BVPFunction{true}(f1!, bc1!), u0, tspan)

sol = solve(bvp1, Shooting(Tsit5()); abstol = 1e-13, reltol = 1e-13,
    odesolve_kwargs = (; abstol = 1e-6, reltol = 1e-3))

tinf = let bvp = bvp1
    solve(bvp, Shooting(Tsit5()); abstol = 1e-13, reltol = 1e-13,
        odesolve_kwargs = (; abstol = 1e-6, reltol = 1e-3))
    @snoopi_deep solve(bvp, Shooting(Tsit5()); abstol = 1e-13, reltol = 1e-13,
        odesolve_kwargs = (; abstol = 1e-6, reltol = 1e-3))
end

# InferenceTimingNode: 0.065630/0.065630 on Core.Compiler.Timings.ROOT() with 0 direct children <-- This PR
# InferenceTimingNode: 0.126995/0.126995 on Core.Compiler.Timings.ROOT() with 0 direct children <-- Current Release