title: Julia DifferentialEquations.jl speed
body: <p>I am trying to test the speed of Julia ODE solvers. I used the Lorenz equation in the tutorial:</p>
  <pre><code>using DifferentialEquations
  using Plots
  function lorenz(t,u,du)
  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
  
  u0 = [1.0;1.0;1.0]
  tspan = (0.0,100.0)
  prob = ODEProblem(lorenz,u0,tspan)
  sol = solve(prob,reltol=1e-8,abstol=1e-8,saveat=collect(0:0.01:100))
  </code></pre>
  <p>Loading the packages took about 25 s in the beginning, and the code ran for 7 s on a windows 10 quad core laptop in Jupyter notebook. I understand that Julia need to precompile packages first, and is that why the loading time was so long?  I found 25 s unbearable. Also, when I ran the solver again using different initial values it took much less time (~1s) to run, and why is that? Is this the typical speed?</p>