# Strange Memory Allocations with DifferentialEquations

Hello,

I’m observing very strange and large memory allocations while solving a standard ODE and evaluating it at given times. However, after the first benchmark, if (and only if!) I recompile the integrated function these allocations disappear.

``````using BenchmarkTools
import DifferentialEquations: Vern9, ODEProblem, solve
``````

The function I’m integrating is:

``````
@inbounds function dyn_twobody!(du::Vector{Float64}, u::Vector{Float64},
GM::Float64, t::Float64)

r = (u[1]*u[1] + u[2]*u[2] + u[3]*u[3])^1.5

du[1] = u[4]
du[2] = u[5]
du[3] = u[6]
du[4] = -GM*u[1]/r
du[5] = -GM*u[2]/r
du[6] = -GM*u[3]/r

nothing
end
``````

while `test` is the function that evaluates the solution at the given times:

``````
function test(x::Vector{Float64}, tms::Vector{Float64})

GM_MOON = 4.902780137400001e3;
user_prob = ODEProblem(dyn_twobody!, x, [0., 86400], GM_MOON)

user_sol = solve(user_prob, Vern9(), abstol=1e-10, reltol=1e-9, saveat=tms, save_everystep=false).u

return user_sol
end
``````

Calling it with:

``````x =  [50500., 232., 32321., -1.2, 0.01, 0.3];
tms = collect(LinRange(0., 86400., 86400));

@benchmark test(\$x, \$tms)
``````

yields:

``````BenchmarkTools.Trial: 30 samples with 1 evaluation.
Range (min … max):  129.553 ms … 535.830 ms  ┊ GC (min … max): 11.32% … 74.42%
Time  (median):     151.338 ms               ┊ GC (median):    14.82%
Time  (mean ± σ):   167.691 ms ±  71.469 ms  ┊ GC (mean ± σ):  21.46% ± 11.46%

██
▆▇██▆▁▆▁▆▄▄▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▄ ▁
130 ms           Histogram: frequency by time          536 ms <

Memory estimate: 304.61 MiB, allocs estimate: 432505.
``````

If i recompile `dyn_twobody!` the new benchmark is:

``````BenchmarkTools.Trial: 81 samples with 1 evaluation.
Range (min … max):  49.294 ms … 106.972 ms  ┊ GC (min … max): 0.00% … 0.00%
Time  (median):     59.441 ms               ┊ GC (median):    0.00%
Time  (mean ± σ):   62.334 ms ±  12.016 ms  ┊ GC (mean ± σ):  2.41% ± 4.19%

█ ▁    ▁▁    ▃
█▆█▇▄▇▇██▇▆▇▇█▁▇▆▆▆▆▄▆▆▆▄▄▁▁▄▁▁▆▆▁▁▁▄▁▁▁▁▁▁▁▆▁▁▄▁▄▄▁▁▁▁▁▁▁▁▄ ▁
49.3 ms         Histogram: frequency by time         98.8 ms <

Memory estimate: 17.22 MiB, allocs estimate: 173311.
``````

Any idea what’s happening with my code? I see the Garbage Collector is taking quite a lot of time

Seems like something in the inlinling heuristics? I’ll try and get a compiler person to take a look. Can you open an issue?

Hello and thanks for answering, actually I had already opened the very same issue here: Strange Memory Allocations with saveat · Issue #880 · SciML/DifferentialEquations.jl · GitHub

I plan to further investigate it as soon as I have more time. In the meantime, couldn’t it be associated to some wrong type inference in the dense functions of DE.jl? Because, irrespective of the function I’m integrating, I always get the same behavior

Maybe type inference, or maybe it’s just inlining heuristics. @aviatesk mentioned that it could just be because when running the function building with a different cache you could get different inference and inlining behavior. So maybe one spot just needs `@inline` and it goes away? It’s hard to tell.