Make non-lazy the default?

[ChrisRackauckas]

SciML/OrdinaryDiffEq.jl#418

[ChrisRackauckas]

using DifferentialEquations, DiffEqDevTools, Plots, ODEInterfaceDiffEq, ODE
# 2D Linear ODE
f = (du,u,p,t) -> begin
  for i in 1:length(u)
    du[i] = 1.01*u[i]
  end
end
function (::typeof(f))(::Type{Val{:analytic}},u₀,p,t)
  @. u₀*exp(1.01*t)
end
tspan = (0.0,10.0)
prob = ODEProblem(f,rand(100,100),tspan)

abstols = (1/10) .^ (3:13)
reltols = (1/10) .^ (0:10);

setups = [Dict(:alg=>Vern7())
          Dict(:alg=>Vern7(lazy=false))
          Dict(:alg=>Vern9())
          Dict(:alg=>Vern9(lazy=false))]
wp = WorkPrecisionSet(prob,abstols,reltols,setups;save_everystep=false)

for i in 1:length(wp)
  println(wp[i])
end

Name: Vern7
Times: [0.00196151, 0.00233463, 0.00251639, 0.00320673, 0.00383201, 0.00486687, 0.0060342, 0.0077189,
 0.0102769, 0.0138131, 0.0188274]
Errors: [3.90079, 0.714491, 0.0176868, 0.0123713, 0.00384236, 0.000784381, 0.00011652, 1.46882e-5, 1.
73589e-6, 1.90531e-7, 2.04493e-8]

Name: Vern7
Times: [0.00452478, 0.005845, 0.00645485, 0.00829678, 0.0101863, 0.0135109, 0.0173762, 0.0224715, 0.0
303368, 0.040751, 0.0561816]
Errors: [3.90079, 0.714491, 0.0176868, 0.0123713, 0.00384236, 0.000784381, 0.00011652, 1.46882e-5, 1.
73589e-6, 1.90531e-7, 2.04493e-8]

Name: Vern9
Times: [0.00274411, 0.00393324, 0.00417484, 0.00453326, 0.00516893, 0.00641746, 0.00781036, 0.0087458
2, 0.0107107, 0.0132366, 0.0166486]
Errors: [2.03359, 0.188555, 0.00505698, 0.00214654, 0.000678968, 0.000173599, 3.04662e-5, 4.21087e-6,
 5.91104e-7, 7.35837e-8, 8.75057e-9]

Name: Vern9
Times: [0.00902597, 0.0119615, 0.0136698, 0.0148335, 0.0178316, 0.0225473, 0.027008, 0.0313818, 0.039
4139, 0.0491864, 0.060887]
Errors: [2.03359, 0.188555, 0.00505698, 0.00214654, 0.000678968, 0.000173599, 3.04662e-5, 4.21087e-6,
 5.91104e-7, 7.35837e-8, 8.75057e-9]

That's a pretty big hit, so it should only be done when callbacks are used.