# Performance overhead observed variables ModelingToolkit
**URL:** https://discourse.julialang.org/t/performance-overhead-observed-variables-modelingtoolkit/64164
**Category:** Modelling & Simulations
**Tags:** question, modelingtoolkit
**Created:** [July 6, 2021, 5:33pm UTC](https://discourse.julialang.org/t/performance-overhead-observed-variables-modelingtoolkit/64164 "2021-07-06T17:33:49Z")
**Posts on this page:** 2
**Page:** 1
### Author:  [@Elmo](https://discourse.julialang.org/u/Elmo)
#### Post date: [July 6, 2021, 5:33pm UTC](https://discourse.julialang.org/t/performance-overhead-observed-variables-modelingtoolkit/64164/1 "2021-07-06T17:33:49Z")
Hi all, I am using ModelingToolkit to simulate a system and noticed that there seems to be a serious performance cost associated with using the nice observed variables functionality of ModelingToolkit. Here is a minimal working example of what I mean.
Problem setup:
```julia
using DifferentialEquations, ModelingToolkit, BenchmarkTools
@parameters t σ ρ β
@variables x(t) y(t) z(t) v_x(t) v_y(t) v_z(t)
D = Differential(t)
eqs = [
v_x ~ σ *(y - x),
v_y ~ x * (ρ - z) - y,
v_z ~ x*y - β * z,
D(x) ~ v_x,
D(y) ~ v_y,
D(z) ~ v_z
]
sys = ODESystem(eqs)
sys = structural_simplify(sys) # get rid of v_x, v_y, v_z
ps = Dict(σ => 10.0, ρ => 28.0, β => 2.66)
u0 = Dict(x => 1.0, y => 0.5, z => 0.8)
tspan = (0.0,1.0)
prob = ODEProblem(sys, u0, tspan, ps)
sol = solve(prob, saveat=[0.1]) # more saveat locations makes everything worse
```
Then when using the observed variables:
```julia
f(sol) = sol[x][end] * sol[v_x][end] + sol[y][end] * sol[v_y][end] + sol[z][end] * sol[v_z][end]
@benchmark f(sol)
julia> @benchmark f(sol)
BechmarkTools.Trial: 10000 samples with 1 evaluations.
Range (min … max): 38.800 μs … 10.927 ms ┊ GC (min … max): 0.00% … 98.40%
Time (median): 46.200 μs ┊ GC (median): 0.00%
Time (mean ± σ): 54.137 μs ± 149.940 μs ┊ GC (mean ± σ): 3.79% ± 1.40%
▆▆██▇▇▆▆▅▄▄▃▃▄▃▂▂▁ ▁▁▁ ▂
████████████████████▇▇█████████▇▇▇▇▇▇▇█▇▇▇▇▅▇▇▆▆▆▅▆▆▅▅▅▅▄▅▃▆ █
38.8 μs Histogram: log(frequency) by time 133 μs <
Memory estimate: 17.22 KiB, allocs estimate: 235.
```
Versus when not using them:
```julia
vec = [sol[x][end], sol[y][end], sol[z][end], sol[v_x][end], sol[v_y][end], sol[v_z][end]]
g(vec) = vec[1] * vec[4] + vec[2] * vec[5] + vec[3] * vec[6]
@benchmark g(vec)
julia> @benchmark g(vec)
BechmarkTools.Trial: 10000 samples with 979 evaluations.
Range (min … max): 27.681 ns … 12.044 μs ┊ GC (min … max): 0.00% … 99.43%
Time (median): 39.122 ns ┊ GC (median): 0.00%
Time (mean ± σ): 48.855 ns ± 123.743 ns ┊ GC (mean ± σ): 2.45% ± 0.99%
▇▆▃▅██▅▄▃▂▃▅▄▃▂▁▁▂▂▂▂▂▁ ▁▁▁ ▂
█████████████████████████████████▇▇▇█▇▇▇▇▇▆▆▆▆▆▅▆▅▆▆▄▂▄▅▆▄▆▅ █
27.7 ns Histogram: log(frequency) by time 164 ns <
Memory estimate: 16 bytes, allocs estimate: 1.
```
Is there a better way to access observed variables that get eliminated through `structural_simplify`? This overhead becomes a problem when using ensemble simulations… Or am I doing something silly?
---
### Author:  [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)
#### Post date: [July 6, 2021, 9:43pm UTC](https://discourse.julialang.org/t/performance-overhead-observed-variables-modelingtoolkit/64164/2 "2021-07-06T21:43:51Z")
Open an issue. We should be able to fix this.