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Avoid RecursiveFactorization except on simple number types #722

Merged
merged 1 commit into from
Dec 13, 2021
Merged

Avoid RecursiveFactorization except on simple number types #722

merged 1 commit into from
Dec 13, 2021

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ChrisRackauckas
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@ChrisRackauckas ChrisRackauckas commented Dec 13, 2021 •
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using OrdinaryDiffEq, SnoopCompile, ForwardDiff

lorenz = (du,u,p,t) -> begin
        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;0.0;0.0]; tspan = (0.0,100.0);
prob = ODEProblem(lorenz,u0,tspan); alg = Rodas5();
tinf = @snoopi_deep ForwardDiff.gradient(u0 -> sum(solve(ODEProblem(lorenz,u0,tspan),alg)), u0)

Before:

InferenceTimingNode: 1.720146/12.692469 on Core.Compiler.Timings.ROOT() with 32 direct children

After:

InferenceTimingNode: 1.243689/4.828318 on Core.Compiler.Timings.ROOT() with 33 direct children

@chriselrod
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chriselrod commented Dec 13, 2021 •
edited
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RecursiveFactorization seems worse at large sizes? @YingboMa

julia> using BenchmarkTools, RecursiveFactorization, ForwardDiff, LinearAlgrebra

julia> for i in 12:12:144
           @show i
           A = ForwardDiff.Dual.([randn(i,i) for _ in 1:9]...); B = similar(A);
           println("RecursiveFactorization:")
           display(@benchmark RecursiveFactorization.lu!(copyto!($B,$A)))
           println("Generic:")
           display(@benchmark LinearAlgebra.lu!(copyto!($B,$A)))
           println()
       end
i = 12
RecursiveFactorization:
BenchmarkTools.Trial: 10000 samples with 10 evaluations.
 Range (min … max):  1.572 μs …   5.131 μs  ┊ GC (min … max): 0.00% … 0.00%
 Time  (median):     1.591 μs               ┊ GC (median):    0.00%
 Time  (mean ± σ):   1.642 μs ± 113.170 ns  ┊ GC (mean ± σ):  0.00% ± 0.00%

  ▅██▆▂            ▅▇▆▅▄▃▂        ▂▂▁▁                        ▂
  █████▇▇▇▅▃▄▄▄▁▁▃█████████▇▆▆▄▆▆██████▇▆▆▃▄▅▃▄▄▄▅▅▃▃▃▄▅▃▃▁▁▃ █
  1.57 μs      Histogram: log(frequency) by time      1.93 μs <

 Memory estimate: 176 bytes, allocs estimate: 1.
Generic:
BenchmarkTools.Trial: 10000 samples with 10 evaluations.
 Range (min … max):  1.640 μs …   5.133 μs  ┊ GC (min … max): 0.00% … 0.00%
 Time  (median):     1.662 μs               ┊ GC (median):    0.00%
 Time  (mean ± σ):   1.713 μs ± 107.547 ns  ┊ GC (mean ± σ):  0.00% ± 0.00%

    █▅
  ▂███▆▃▂▂▂▂▂▂▂▂▂▂▂▂▂▂▄▇█▆▅▄▃▂▂▂▂▂▂▂▂▂▂▂▃▃▂▂▂▂▂▂▂▂▂▁▂▁▂▁▂▂▂▂▂ ▃
  1.64 μs         Histogram: frequency by time        1.96 μs <

 Memory estimate: 176 bytes, allocs estimate: 1.

i = 24
RecursiveFactorization:
BenchmarkTools.Trial: 10000 samples with 1 evaluation.
 Range (min … max):  11.616 μs …  46.104 μs  ┊ GC (min … max): 0.00% … 0.00%
 Time  (median):     11.716 μs               ┊ GC (median):    0.00%
 Time  (mean ± σ):   11.833 μs ± 803.628 ns  ┊ GC (mean ± σ):  0.00% ± 0.00%

   ▅██▆▂▁                           ▂▂▁                        ▂
  ███████▇▅▁▄▅▁▄▄▃▃▃▄▃▁▁▁▁▁▁▁▁▁▁▁▁▁████████▇▇▅▅▆▄▃▃▁▅▄▄▅▄▅▃▄▃▄ █
  11.6 μs       Histogram: log(frequency) by time      13.5 μs <

 Memory estimate: 272 bytes, allocs estimate: 1.
Generic:
BenchmarkTools.Trial: 10000 samples with 1 evaluation.
 Range (min … max):  11.889 μs …  40.791 μs  ┊ GC (min … max): 0.00% … 0.00%
 Time  (median):     11.980 μs               ┊ GC (median):    0.00%
 Time  (mean ± σ):   12.118 μs ± 953.985 ns  ┊ GC (mean ± σ):  0.00% ± 0.00%

  ▂▆█▇▄                           ▁▁▂▁▁                        ▂
  ██████▆▅▄▁▃▁▃▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▃▇██████▇▇▆▆▅▅▆▅▄▃▄▄▅▄▃▅▃▃▄▁▆▅ █
  11.9 μs       Histogram: log(frequency) by time      13.9 μs <

 Memory estimate: 272 bytes, allocs estimate: 1.

i = 36
RecursiveFactorization:
BenchmarkTools.Trial: 10000 samples with 1 evaluation.
 Range (min … max):  37.911 μs … 97.809 μs  ┊ GC (min … max): 0.00% … 0.00%
 Time  (median):     38.171 μs              ┊ GC (median):    0.00%
 Time  (mean ± σ):   38.402 μs ±  1.438 μs  ┊ GC (mean ± σ):  0.00% ± 0.00%

  ▇█▂  ▁▄▃▁                                                   ▁
  ███▅▁██████▇▇▆▄▅▅▄▃▁▁▁▁▁▁▁▁▁▁▁▄▁▄▄▃▁▁▁▃▃▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▄▇ █
  37.9 μs      Histogram: log(frequency) by time      49.4 μs <

 Memory estimate: 368 bytes, allocs estimate: 1.
Generic:
BenchmarkTools.Trial: 10000 samples with 1 evaluation.
 Range (min … max):  38.736 μs … 95.261 μs  ┊ GC (min … max): 0.00% … 0.00%
 Time  (median):     38.976 μs              ┊ GC (median):    0.00%
 Time  (mean ± σ):   39.201 μs ±  1.350 μs  ┊ GC (mean ± σ):  0.00% ± 0.00%

  ▇█▁  ▁▄▂                                                    ▁
  ███▄▃███████▇▅▅▆▃▃▁▅▃▃▁▁▁▁▁▃▁▃▃▄▄▃▃▁▃▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▅ █
  38.7 μs      Histogram: log(frequency) by time        50 μs <

 Memory estimate: 368 bytes, allocs estimate: 1.

i = 48
RecursiveFactorization:
BenchmarkTools.Trial: 10000 samples with 1 evaluation.
 Range (min … max):  85.114 μs … 167.962 μs  ┊ GC (min … max): 0.00% … 0.00%
 Time  (median):     85.706 μs               ┊ GC (median):    0.00%
 Time  (mean ± σ):   86.237 μs ±   2.429 μs  ┊ GC (mean ± σ):  0.00% ± 0.00%

  ▇▆██▄▂▃▃▄▃▂▂▁                                            ▂▂▂ ▂
  ███████████████▇▆▆▆▅▄▅▁▄▃▄▃▁▁▁▁▁▁▁▁▁▁▃▁▁▁▁▃▁▃▁▁▁▁▁▁▁▁▁▃▄████ █
  85.1 μs       Histogram: log(frequency) by time      97.2 μs <

 Memory estimate: 496 bytes, allocs estimate: 1.
Generic:
BenchmarkTools.Trial: 10000 samples with 1 evaluation.
 Range (min … max):  86.563 μs … 152.116 μs  ┊ GC (min … max): 0.00% … 0.00%
 Time  (median):     87.065 μs               ┊ GC (median):    0.00%
 Time  (mean ± σ):   87.629 μs ±   2.680 μs  ┊ GC (mean ± σ):  0.00% ± 0.00%

  ▂▅█▄   ▃▄▁  ▁▁                                             ▂ ▁
  ████▅▆████████▇▇▆▆▆▆▄▅▅▄▃▄▁▃▃▁▁▃▁▁▃▁▄▁▃▁▄▁▁▁▃▃▁▁▃▁▃▁▁▁▁▁▄▆██ █
  86.6 μs       Histogram: log(frequency) by time      98.4 μs <

 Memory estimate: 496 bytes, allocs estimate: 1.

i = 60
RecursiveFactorization:
BenchmarkTools.Trial: 10000 samples with 1 evaluation.
 Range (min … max):  162.841 μs … 241.807 μs  ┊ GC (min … max): 0.00% … 0.00%
 Time  (median):     164.033 μs               ┊ GC (median):    0.00%
 Time  (mean ± σ):   164.581 μs ±   2.854 μs  ┊ GC (mean ± σ):  0.00% ± 0.00%

  ▁▆▇▁▄█▇▄▂▁▄▄▃▂▂▂▁                                       ▁▁▁▂▂ ▂
  ██████████████████▇▇▇▆▅▄▁▅▄▁▃▃▃▃▁▄▁▁▃▁▁▁▁▁▃▁▁▁▁▃▁▁▁▁▃▁▃▇█████ █
  163 μs        Histogram: log(frequency) by time        176 μs <

 Memory estimate: 576 bytes, allocs estimate: 1.
Generic:
BenchmarkTools.Trial: 10000 samples with 1 evaluation.
 Range (min … max):  164.795 μs … 242.450 μs  ┊ GC (min … max): 0.00% … 0.00%
 Time  (median):     165.997 μs               ┊ GC (median):    0.00%
 Time  (mean ± σ):   166.703 μs ±   2.622 μs  ┊ GC (mean ± σ):  0.00% ± 0.00%

  ▁▂▄▄▆█▇▁▁▂▄▄▂▂▃▂                                         ▁▁▂▂ ▂
  █████████████████▇██▆▅▄▄▄▄▃▅▄▁▁▁▄▁▁▁▁▁▁▁▁▁▃▁▁▁▃▁▁▁▁▁▁▃▁▅▇████ █
  165 μs        Histogram: log(frequency) by time        178 μs <

 Memory estimate: 576 bytes, allocs estimate: 1.

i = 72
RecursiveFactorization:
BenchmarkTools.Trial: 10000 samples with 1 evaluation.
 Range (min … max):  277.741 μs … 354.358 μs  ┊ GC (min … max): 0.00% … 0.00%
 Time  (median):     279.339 μs               ┊ GC (median):    0.00%
 Time  (mean ± σ):   280.107 μs ±   3.347 μs  ┊ GC (mean ± σ):  0.00% ± 0.00%

   █▁   ▅█
  ▄██▄▃▃██▆▄▃▄▄▃▃▃▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▁▂▁▂▂▁▁▁▁▂▁▁▁▁▁▁▂▂▂▃▂▂▂▃▃▃▂▂▂ ▃
  278 μs           Histogram: frequency by time          292 μs <

 Memory estimate: 672 bytes, allocs estimate: 1.
Generic:
BenchmarkTools.Trial: 10000 samples with 1 evaluation.
 Range (min … max):  280.720 μs … 358.809 μs  ┊ GC (min … max): 0.00% … 0.00%
 Time  (median):     282.281 μs               ┊ GC (median):    0.00%
 Time  (mean ± σ):   283.444 μs ±   3.266 μs  ┊ GC (mean ± σ):  0.00% ± 0.00%

   ▃▃ ▂▇█▆▄▃▄▅▄▄▃▂▁▁▁▁                                 ▁▄▃▁     ▂
  █████████████████████▆▅▅▆▄▃▅▃▃▃▄▄▄▃▃▃▁▁▄▁▁▁▁▁▁▁▁▄▆▇▇▆████▇▇██ █
  281 μs        Histogram: log(frequency) by time        295 μs <

 Memory estimate: 672 bytes, allocs estimate: 1.

i = 84
RecursiveFactorization:
BenchmarkTools.Trial: 10000 samples with 1 evaluation.
 Range (min … max):  434.599 μs … 520.429 μs  ┊ GC (min … max): 0.00% … 0.00%
 Time  (median):     437.904 μs               ┊ GC (median):    0.00%
 Time  (mean ± σ):   439.082 μs ±   4.263 μs  ┊ GC (mean ± σ):  0.00% ± 0.00%

       ▃  ▁▅▅██▂
  ▁▄▆▅███▆███████▅▆▅▅▅▃▂▂▂▂▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▂▂▂▂▂▂▃▃▂▂▂▂▁▁▁▁ ▃
  435 μs           Histogram: frequency by time          452 μs <

 Memory estimate: 816 bytes, allocs estimate: 1.
Generic:
BenchmarkTools.Trial: 10000 samples with 1 evaluation.
 Range (min … max):  439.360 μs … 596.009 μs  ┊ GC (min … max): 0.00% … 0.00%
 Time  (median):     442.078 μs               ┊ GC (median):    0.00%
 Time  (mean ± σ):   444.222 μs ±   5.427 μs  ┊ GC (mean ± σ):  0.00% ± 0.00%

  ▁▃▃▂▁▆██▆▅▄▆▆▅▄▃▃▂▁                   ▁▄▅▄▂▁▂▂▂▁              ▂
  ███████████████████▇▇▇▇▅▃▅▅▁▄▄▃▁▁▃▆██▇█████████████▇▅▅▆▅▃▁▁▄▃ █
  439 μs        Histogram: log(frequency) by time        460 μs <

 Memory estimate: 816 bytes, allocs estimate: 1.

i = 96
RecursiveFactorization:
BenchmarkTools.Trial: 7609 samples with 1 evaluation.
 Range (min … max):  646.730 μs … 731.978 μs  ┊ GC (min … max): 0.00% … 0.00%
 Time  (median):     650.949 μs               ┊ GC (median):    0.00%
 Time  (mean ± σ):   653.262 μs ±   5.974 μs  ┊ GC (mean ± σ):  0.00% ± 0.00%

    ▂    ▃█▇▁
  ▃███▄▄▅████▅▆▇▆▄▃▃▃▂▂▂▂▂▂▂▂▃▃▄▄▃▄▄▅▄▄▃▃▃▃▃▂▂▂▂▁▂▂▁▂▁▂▂▂▂▂▂▂▂▂ ▃
  647 μs           Histogram: frequency by time          673 μs <

 Memory estimate: 896 bytes, allocs estimate: 1.
Generic:
BenchmarkTools.Trial: 7558 samples with 1 evaluation.
 Range (min … max):  650.726 μs … 762.345 μs  ┊ GC (min … max): 0.00% … 0.00%
 Time  (median):     655.038 μs               ┊ GC (median):    0.00%
 Time  (mean ± σ):   657.642 μs ±   5.787 μs  ┊ GC (mean ± σ):  0.00% ± 0.00%

         ▇█▂
  ▂▃▃▃▂▃▆███▅▅▇▆▅▄▃▃▂▂▂▂▂▂▂▂▂▂▂▂▂▂▃▅▅▃▃▃▃▃▃▂▂▂▂▂▂▁▂▁▂▂▂▂▂▂▂▂▂▂▂ ▃
  651 μs           Histogram: frequency by time          678 μs <

 Memory estimate: 896 bytes, allocs estimate: 1.

i = 108
RecursiveFactorization:
BenchmarkTools.Trial: 5368 samples with 1 evaluation.
 Range (min … max):  917.617 μs … 1.291 ms  ┊ GC (min … max): 0.00% … 0.00%
 Time  (median):     924.505 μs             ┊ GC (median):    0.00%
 Time  (mean ± σ):   927.544 μs ± 9.961 μs  ┊ GC (mean ± σ):  0.00% ± 0.00%

     ▁▂    ▃▆█▃
  ▂▅▇███▅▆█████▇▆██▆▃▃▂▂▂▂▂▃▄▄▄▄▅▅▇▆▅▄▃▃▃▂▂▁▁▁▁▁▁▁▂▂▂▂▂▂▂▂▂▂▁ ▃
  918 μs          Histogram: frequency by time         948 μs <

 Memory estimate: 1008 bytes, allocs estimate: 1.
Generic:
BenchmarkTools.Trial: 5336 samples with 1 evaluation.
 Range (min … max):  922.993 μs … 1.024 ms  ┊ GC (min … max): 0.00% … 0.00%
 Time  (median):     930.210 μs             ┊ GC (median):    0.00%
 Time  (mean ± σ):   933.049 μs ± 7.063 μs  ┊ GC (mean ± σ):  0.00% ± 0.00%

          ▂█▆  ▁▁
  ▂▂▂▃▂▂▂▄███▇▅███▅▄▃▃▂▂▂▂▂▂▂▂▂▃▅▆▅▄▃▄▄▄▃▃▂▂▂▂▂▁▂▂▂▂▂▂▃▃▃▂▂▃▂ ▃
  923 μs          Histogram: frequency by time         954 μs <

 Memory estimate: 1008 bytes, allocs estimate: 1.

i = 120
RecursiveFactorization:
BenchmarkTools.Trial: 2305 samples with 1 evaluation.
 Range (min … max):  2.123 ms …  2.443 ms  ┊ GC (min … max): 0.00% … 0.00%
 Time  (median):     2.163 ms              ┊ GC (median):    0.00%
 Time  (mean ± σ):   2.165 ms ± 18.189 μs  ┊ GC (mean ± σ):  0.00% ± 0.00%

                 ▃▄▂▄▅▅▇█▇▇▆█▇▅▆▄▄▁▃▃▁
  ▂▁▂▂▃▂▃▃▃▃▄▅▇▆▇█████████████████████▇██▆▆▅▆▅▄▄▃▄▄▃▃▃▃▃▃▂▃▂ ▅
  2.12 ms        Histogram: frequency by time        2.21 ms <

 Memory estimate: 15.78 KiB, allocs estimate: 14.
Generic:
BenchmarkTools.Trial: 3424 samples with 1 evaluation.
 Range (min … max):  1.438 ms …  2.019 ms  ┊ GC (min … max): 0.00% … 0.00%
 Time  (median):     1.453 ms              ┊ GC (median):    0.00%
 Time  (mean ± σ):   1.456 ms ± 15.187 μs  ┊ GC (mean ± σ):  0.00% ± 0.00%

           ▃▂▆▅▅█▅▆▃▄▂▁▁
  ▁▁▁▂▂▄▅▇███████████████▇▇▆▇▆▇▅▄▅▄▃▄▃▄▃▃▃▂▃▃▂▂▂▂▂▂▂▂▂▁▂▁▂▁▁ ▄
  1.44 ms        Histogram: frequency by time        1.49 ms <

 Memory estimate: 1.06 KiB, allocs estimate: 1.

i = 132
RecursiveFactorization:
BenchmarkTools.Trial: 1750 samples with 1 evaluation.
 Range (min … max):  2.813 ms …  3.204 ms  ┊ GC (min … max): 0.00% … 0.00%
 Time  (median):     2.850 ms              ┊ GC (median):    0.00%
 Time  (mean ± σ):   2.853 ms ± 19.074 μs  ┊ GC (mean ± σ):  0.00% ± 0.00%

               ▃▃▃▄▃▆▇█▆▇▆▄▅▅▅▃▄▃▁
  ▂▁▁▂▂▃▃▃▄▅▅▇██████████████████████▆▆▆▅▆▄▄▄▃▄▃▄▃▃▃▃▃▃▂▂▂▂▃▂ ▅
  2.81 ms        Histogram: frequency by time         2.9 ms <

 Memory estimate: 17.03 KiB, allocs estimate: 14.
Generic:
BenchmarkTools.Trial: 2542 samples with 1 evaluation.
 Range (min … max):  1.931 ms …  2.717 ms  ┊ GC (min … max): 0.00% … 0.00%
 Time  (median):     1.960 ms              ┊ GC (median):    0.00%
 Time  (mean ± σ):   1.963 ms ± 27.273 μs  ┊ GC (mean ± σ):  0.00% ± 0.00%

             ▁▁▃▃▃▄▆█▇▆▆▄▆▂▂▃▃▁▂
  ▂▁▁▁▃▃▃▃▄▆▆██████████████████████▇▅▆▅▅▅▄▄▄▄▄▄▃▄▃▃▃▂▃▂▃▂▂▂▂ ▅
  1.93 ms        Histogram: frequency by time         210 ms <

 Memory estimate: 1.14 KiB, allocs estimate: 1.

i = 144
RecursiveFactorization:
BenchmarkTools.Trial: 1328 samples with 1 evaluation.
 Range (min … max):  3.726 ms …  4.059 ms  ┊ GC (min … max): 0.00% … 0.00%
 Time  (median):     3.758 ms              ┊ GC (median):    0.00%
 Time  (mean ± σ):   3.762 ms ± 20.361 μs  ┊ GC (mean ± σ):  0.00% ± 0.00%

           ▁ ▄▂▆▅▄▄▇█▃▅▄▃ ▁
  ▃▂▃▄▃▃▄▇▇█▇████████████████▆▇▇▇▇▅▇▆▄▅▅▄▄▃▃▄▃▃▃▂▄▃▂▃▂▃▂▂▃▁▃ ▄
  3.73 ms        Histogram: frequency by time        3.82 ms <

 Memory estimate: 18.42 KiB, allocs estimate: 14.
Generic:
BenchmarkTools.Trial: 1899 samples with 1 evaluation.
 Range (min … max):  2.595 ms …  2.773 ms  ┊ GC (min … max): 0.00% … 0.00%
 Time  (median):     2.627 ms              ┊ GC (median):    0.00%
 Time  (mean ± σ):   2.629 ms ± 16.579 μs  ┊ GC (mean ± σ):  0.00% ± 0.00%

             ▁ ▁▅▄▃▃▅▄▄▆█▅▅▃▅▆▃▁▁▁  ▁
  ▂▂▂▂▂▃▅▇▅█▇██████████████████████▇█▆▅▅▅▇▄▃▄▄▅▃▄▄▃▃▃▂▂▂▂▂▂▂ ▄
  2.6 ms         Histogram: frequency by time        2.67 ms <

 Memory estimate: 1.22 KiB, allocs estimate: 1.

It's interesting that the distribution is often bimodal. I suspect that is the result of GC?

@chriselrod
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RecursiveFactorization continues to do worse at larger sizes:

julia> for i in 168:24:504
           @show i
           A = ForwardDiff.Dual.([randn(i,i) for _ in 1:9]...); B = similar(A);
           println("RecursiveFactorization:")
           display(@benchmark RecursiveFactorization.lu!(copyto!($B,$A)))
           println("Generic:")
           display(@benchmark LinearAlgebra.lu!(copyto!($B,$A)))
           println()
       end
i = 168
RecursiveFactorization:
BenchmarkTools.Trial: 866 samples with 1 evaluation.
 Range (min … max):  5.731 ms …  6.186 ms  ┊ GC (min … max): 0.00% … 0.00%
 Time  (median):     5.767 ms              ┊ GC (median):    0.00%
 Time  (mean ± σ):   5.772 ms ± 26.164 μs  ┊ GC (mean ± σ):  0.00% ± 0.00%

          ▁▁ ▂▃▄▃▆█▆▆▄▃▂  ▂
  ▃▁▃▃▃▅█▇██▇██████████████▇▇▇▆▆▆▅▆▅▅▅▅▄▄▄▂▃▃▃▃▄▃▃▁▃▃▂▃▁▁▂▂▃ ▄
  5.73 ms        Histogram: frequency by time        5.84 ms <

 Memory estimate: 23.80 KiB, allocs estimate: 18.
Generic:
BenchmarkTools.Trial: 1097 samples with 1 evaluation.
 Range (min … max):  4.484 ms …  4.760 ms  ┊ GC (min … max): 0.00% … 0.00%
 Time  (median):     4.553 ms              ┊ GC (median):    0.00%
 Time  (mean ± σ):   4.555 ms ± 28.297 μs  ┊ GC (mean ± σ):  0.00% ± 0.00%

               ▁   ▂▂▃▂▂▄▇▄▃█▂▃▄▃
  ▂▂▂▁▃▂▃▃▄▄▄▆▅██▅███████████████████▇█▇▆▅▆▄▅▄▅▃▃▃▃▂▃▃▃▂▂▂▂▂ ▄
  4.48 ms        Histogram: frequency by time        4.64 ms <

 Memory estimate: 1.45 KiB, allocs estimate: 1.

i = 192
RecursiveFactorization:
BenchmarkTools.Trial: 541 samples with 1 evaluation.
 Range (min … max):  9.156 ms …  9.727 ms  ┊ GC (min … max): 0.00% … 0.00%
 Time  (median):     9.241 ms              ┊ GC (median):    0.00%
 Time  (mean ± σ):   9.251 ms ± 55.196 μs  ┊ GC (mean ± σ):  0.00% ± 0.00%

          ▁▁▃▄▄▇▄▄█▆▆█▃▁▄
  ▂▂▂▃▃▃▇▇████████████████▆▇▆▆▇▆▆▃▅▂▆▆▅▄▃▃▂▃▃▃▂▅▂▂▁▂▁▁▁▂▁▂▁▃ ▄
  9.16 ms        Histogram: frequency by time        9.43 ms <

 Memory estimate: 26.91 KiB, allocs estimate: 18.
Generic:
BenchmarkTools.Trial: 709 samples with 1 evaluation.
 Range (min … max):  6.955 ms …  7.168 ms  ┊ GC (min … max): 0.00% … 0.00%
 Time  (median):     7.049 ms              ┊ GC (median):    0.00%
 Time  (mean ± σ):   7.050 ms ± 32.179 μs  ┊ GC (mean ± σ):  0.00% ± 0.00%

                     ▂▁▃ ▂ ▂▆▅▅▄▇▅▅▃█▆▃▅▂▁▅ ▃▂
  ▂▁▁▁▁▃▂▂▄▃▃▇▅▃▅▇▆▅▇███▆█▇████████████████▆██▄█▄▆▅▅▅▄▄▃▄▃▂▄ ▅
  6.96 ms        Histogram: frequency by time        7.13 ms <

 Memory estimate: 1.59 KiB, allocs estimate: 1.

i = 216
RecursiveFactorization:
BenchmarkTools.Trial: 394 samples with 1 evaluation.
 Range (min … max):  12.598 ms … 13.249 ms  ┊ GC (min … max): 0.00% … 0.00%
 Time  (median):     12.700 ms              ┊ GC (median):    0.00%
 Time  (mean ± σ):   12.714 ms ± 71.379 μs  ┊ GC (mean ± σ):  0.00% ± 0.00%

         ▂▂▂▃█▇▆█▅█▆▃▁▁
  ▂▁▂▂▄▃▇██████████████▅▇▅▅▃▂▆▁▂▃▃▁▁▂▁▂▃▃▃▁▃▃▂▂▁▂▁▁▁▂▂▁▂▂▁▂▁▂ ▃
  12.6 ms         Histogram: frequency by time          13 ms <

 Memory estimate: 33.48 KiB, allocs estimate: 23.
Generic:
BenchmarkTools.Trial: 485 samples with 1 evaluation.
 Range (min … max):  10.209 ms … 10.920 ms  ┊ GC (min … max): 0.00% … 0.00%
 Time  (median):     10.303 ms              ┊ GC (median):    0.00%
 Time  (mean ± σ):   10.309 ms ± 47.010 μs  ┊ GC (mean ± σ):  0.00% ± 0.00%

                  ▂▁▂▁    █▇▅▅▇▃▄ ▂ ▅▁ ▁
  ▃▁▁▁▁▃▃▃▄▄▄▅▅▆▅▇████▆██▆███████▆████▇█▆▇▆▇▄▆▅▆▆▄▄▃▃▄▄▃▃▄▅▁▄ ▄
  10.2 ms         Histogram: frequency by time        10.4 ms <

 Memory estimate: 1.77 KiB, allocs estimate: 1.

i = 240
RecursiveFactorization:
BenchmarkTools.Trial: 282 samples with 1 evaluation.
 Range (min … max):  17.638 ms … 18.148 ms  ┊ GC (min … max): 0.00% … 0.00%
 Time  (median):     17.735 ms              ┊ GC (median):    0.00%
 Time  (mean ± σ):   17.751 ms ± 71.965 μs  ┊ GC (mean ± σ):  0.00% ± 0.00%

       ▃  ▃▆▃▆▄▁▄▅█▂▂▃
  ▄▃▄▅▃█▅▇████████████████▄▄▇▅▆▅▄▅▄▃▅▄▄▄▆▄▄▃▃▃▄▁▁▁▁▃▁▃▁▁▁▃▁▁▄ ▄
  17.6 ms         Histogram: frequency by time          18 ms <

 Memory estimate: 36.94 KiB, allocs estimate: 23.
Generic:
BenchmarkTools.Trial: 346 samples with 1 evaluation.
 Range (min … max):  14.290 ms … 14.684 ms  ┊ GC (min … max): 0.00% … 0.00%
 Time  (median):     14.443 ms              ┊ GC (median):    0.00%
 Time  (mean ± σ):   14.444 ms ± 64.187 μs  ┊ GC (mean ± σ):  0.00% ± 0.00%

               ▁       ▂▄▄▁▂▃▃▄▂▅▂▄▁ ██ ▃  ▄▁
  ▄▁▄▃▁▄▃▆▄▆▄▄▄██▆▇▇▇███████████████▆████▆▅██▆▇▆▅▄█▅▇▄▆▃▃▆▅▃▅ ▅
  14.3 ms         Histogram: frequency by time        14.6 ms <

 Memory estimate: 1.98 KiB, allocs estimate: 1.

i = 264
RecursiveFactorization:
BenchmarkTools.Trial: 206 samples with 1 evaluation.
 Range (min … max):  24.069 ms …  25.076 ms  ┊ GC (min … max): 0.00% … 0.00%
 Time  (median):     24.259 ms               ┊ GC (median):    0.00%
 Time  (mean ± σ):   24.299 ms ± 153.273 μs  ┊ GC (mean ± σ):  0.00% ± 0.00%

      ▂   ▁ ▄▇██▁▁▁  ▂▂     ▁ ▁▁▂
  ▆▄▄▄█▆▆███████████▃██▆█▄▇▆█▃████▄▆▃▁▆▃▄▁▆▇▁▇▃▃▄▁▁▆▁▄▁▁▃▃▁▁▃▃ ▄
  24.1 ms         Histogram: frequency by time         24.7 ms <

 Memory estimate: 41.09 KiB, allocs estimate: 25.
Generic:
BenchmarkTools.Trial: 256 samples with 1 evaluation.
 Range (min … max):  19.268 ms …  19.905 ms  ┊ GC (min … max): 0.00% … 0.00%
 Time  (median):     19.601 ms               ┊ GC (median):    0.00%
 Time  (mean ± σ):   19.598 ms ± 113.983 μs  ┊ GC (mean ± σ):  0.00% ± 0.00%

                       ▂▅  ▃  ▄  ▂▃▅ ▂▃ ▄▅█      ▅ ▄
  ▃▁▁▁▁▁▁▁▁▃▃▃▅▃▆█▄▄▄▅▆██▆██▇▇█▇▆██████▇███▇▇▅▆█▇███▄▅▇▆▁▃▃▄▁▇ ▄
  19.3 ms         Histogram: frequency by time         19.8 ms <

 Memory estimate: 2.19 KiB, allocs estimate: 1.

i = 288
RecursiveFactorization:
BenchmarkTools.Trial: 149 samples with 1 evaluation.
 Range (min … max):  33.142 ms …  34.622 ms  ┊ GC (min … max): 0.00% … 0.00%
 Time  (median):     33.630 ms               ┊ GC (median):    0.00%
 Time  (mean ± σ):   33.635 ms ± 215.801 μs  ┊ GC (mean ± σ):  0.00% ± 0.00%

             ▂ ▂  ▂     ▂▆ ▂ ▆█▂▆ ▄  ▂ ▄ ▆  ▂
  ▄▁▁▁▁▄▁▁▄▄██▆████▄███▄██▄█████████████▆█▆██▆▆██▆▄██▄▆▁▄▁▁▁▄▆ ▄
  33.1 ms         Histogram: frequency by time         34.1 ms <

 Memory estimate: 48.25 KiB, allocs estimate: 30.
Generic:
BenchmarkTools.Trial: 194 samples with 1 evaluation.
 Range (min … max):  25.469 ms …  26.329 ms  ┊ GC (min … max): 0.00% … 0.00%
 Time  (median):     25.818 ms               ┊ GC (median):    0.00%
 Time  (mean ± σ):   25.824 ms ± 172.614 μs  ┊ GC (mean ± σ):  0.00% ± 0.00%

           ▃ ▄▁▃▃▁▁▄ ▁▁ █▁▁▁▃▁  ▃▁▄  ▆ ▁▁▁▄▄   ▁▁▄▁▁
  ▆▁▆▁▆▁▆▄▁█▇███████▇██▆██████▇▇███▇▄█▆█████▆▇▄█████▇▇▆▄▁▄▄▁▁▆ ▄
  25.5 ms         Histogram: frequency by time         26.2 ms <

 Memory estimate: 2.38 KiB, allocs estimate: 1.

i = 312
RecursiveFactorization:
BenchmarkTools.Trial: 122 samples with 1 evaluation.
 Range (min … max):  40.617 ms …  41.665 ms  ┊ GC (min … max): 0.00% … 0.00%
 Time  (median):     41.004 ms               ┊ GC (median):    0.00%
 Time  (mean ± σ):   41.009 ms ± 200.696 μs  ┊ GC (mean ± σ):  0.00% ± 0.00%

           ▆ ▁ ▁ ▃▃▁██ █ ▃▆▆▁▆▃▁▃▃▁          ▁
  ▄▇▇▇▁▄▁▇▁█▇█▇█▇█████▄█▄██████████▇▇▄▇▇▇▁▁▇▄█▄▄▁▁▄▄▁▁▄▁▁▁▁▁▁▄ ▄
  40.6 ms         Histogram: frequency by time         41.6 ms <

 Memory estimate: 51.84 KiB, allocs estimate: 30.
Generic:
BenchmarkTools.Trial: 150 samples with 1 evaluation.
 Range (min … max):  32.912 ms …  34.709 ms  ┊ GC (min … max): 0.00% … 0.00%
 Time  (median):     33.542 ms               ┊ GC (median):    0.00%
 Time  (mean ± σ):   33.525 ms ± 283.494 μs  ┊ GC (mean ± σ):  0.00% ± 0.00%

               ▂▂▄   ▂▂▄   █ ▄ ▂ ▄▂ ▂▄▄▄▄▄▄▂ ▂  ▄
  ▄▄▆▄▄▄▄▁▄▁▄▄▄███▄▄▆███▆▆▄█▆█▆█▆██████████████▆█▆▄▄▁▆▄▁▄▄▄▁▁▆ ▄
  32.9 ms         Histogram: frequency by time         34.1 ms <

 Memory estimate: 2.56 KiB, allocs estimate: 1.

i = 336
RecursiveFactorization:
BenchmarkTools.Trial: 97 samples with 1 evaluation.
 Range (min … max):  51.195 ms …  54.155 ms  ┊ GC (min … max): 0.00% … 0.00%
 Time  (median):     51.500 ms               ┊ GC (median):    0.00%
 Time  (mean ± σ):   51.643 ms ± 504.153 μs  ┊ GC (mean ± σ):  0.00% ± 0.00%

     ▄▃█▆
  ▆▆█████▇▇▆██▃▅▁▄▄▁▃▃▁▁▁▁▃▁▁▁▁▃▁▃▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▃▁▁▁▁▁▃ ▁
  51.2 ms         Histogram: frequency by time         54.1 ms <

 Memory estimate: 55.41 KiB, allocs estimate: 30.
Generic:
BenchmarkTools.Trial: 118 samples with 1 evaluation.
 Range (min … max):  41.714 ms …  44.782 ms  ┊ GC (min … max): 0.00% … 0.00%
 Time  (median):     42.414 ms               ┊ GC (median):    0.00%
 Time  (mean ± σ):   42.440 ms ± 416.749 μs  ┊ GC (mean ± σ):  0.00% ± 0.00%

       ▄   ▆█▃▃▁ ▁▄ ▃ ▁▄▆  ▃▄
  ▄▁▁▆▁█▁▆▆█████▄██▄█▇███▇▆██▇▆▆▇▁▄▆▆▆▁▄▄▁▄▄▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▄ ▄
  41.7 ms         Histogram: frequency by time         43.9 ms <

 Memory estimate: 2.75 KiB, allocs estimate: 1.

i = 360
RecursiveFactorization:
BenchmarkTools.Trial: 78 samples with 1 evaluation.
 Range (min … max):  64.140 ms …  69.442 ms  ┊ GC (min … max): 0.00% … 0.00%
 Time  (median):     64.542 ms               ┊ GC (median):    0.00%
 Time  (mean ± σ):   64.803 ms ± 853.327 μs  ┊ GC (mean ± σ):  0.00% ± 0.00%

     ▅▅▃█ ▃   ▂ ▅
  ▇▅█████▅█▇▇▁█▄█▅▄▁▄▁▁▁▄▁▁▁▁▄▁▁▁▁▁▁▁▁▄▁▁▁▁▁▄▁▁▁▁▁▁▁▁▄▁▁▁▄▁▁▄▄ ▁
  64.1 ms         Histogram: frequency by time         67.3 ms <

 Memory estimate: 63.12 KiB, allocs estimate: 36.
Generic:
BenchmarkTools.Trial: 95 samples with 1 evaluation.
 Range (min … max):  51.808 ms …  56.556 ms  ┊ GC (min … max): 0.00% … 0.00%
 Time  (median):     53.020 ms               ┊ GC (median):    0.00%
 Time  (mean ± σ):   53.114 ms ± 899.077 μs  ┊ GC (mean ± σ):  0.00% ± 0.00%

  ▁    ▄    ▁   █  ▁█▁ ▁▁   ▁
  █▄▄▄▆█▇▄▆▇█▆▄▄█▇▇███▄██▆▄▄█▁▁▄▁▄▄▄▄▄▄▄▄▄▁▁▁▁▄▄▄▁▁▁▁▄▁▁▁▁▁▁▁▄ ▁
  51.8 ms         Histogram: frequency by time           56 ms <

 Memory estimate: 2.94 KiB, allocs estimate: 1.

i = 384
RecursiveFactorization:
BenchmarkTools.Trial: 59 samples with 1 evaluation.
 Range (min … max):  83.964 ms … 92.575 ms  ┊ GC (min … max): 0.00% … 0.00%
 Time  (median):     84.602 ms              ┊ GC (median):    0.00%
 Time  (mean ± σ):   85.407 ms ±  2.127 ms  ┊ GC (mean ± σ):  0.00% ± 0.00%

  ▂ █ ▇
  █▆█▇█▇▆▇▃▃▅▁▁▁▁▁▁▁▁▁▁▃▁▁▁▃▁▁▃▁▃▁▁▁▃▁▁▁▁▁▁▁▁▃▁▁▁▁▁▁▁▁▃▁▃▁▁▁▃ ▁
  84 ms           Histogram: frequency by time        92.1 ms <

 Memory estimate: 68.58 KiB, allocs estimate: 39.
Generic:
BenchmarkTools.Trial: 82 samples with 1 evaluation.
 Range (min … max):  60.014 ms …  62.082 ms  ┊ GC (min … max): 0.00% … 0.00%
 Time  (median):     61.102 ms               ┊ GC (median):    0.00%
 Time  (mean ± σ):   61.091 ms ± 414.833 μs  ┊ GC (mean ± σ):  0.00% ± 0.00%

                              ▂▂   █ ▂▅   ▅▅      █   ▂
  ▅▁▁▁▅▁▁▅▅▁▁▅█▅▁▁▁▅▅▅▅▅▅▁▁█▅▅██▅███▅████▅███▁▅██▅█▁▅▁██▅█▁▅█▅ ▁
  60 ms           Histogram: frequency by time         61.8 ms <

 Memory estimate: 3.12 KiB, allocs estimate: 1.

i = 408
RecursiveFactorization:
BenchmarkTools.Trial: 54 samples with 1 evaluation.
 Range (min … max):  93.414 ms …  95.268 ms  ┊ GC (min … max): 0.00% … 0.00%
 Time  (median):     93.858 ms               ┊ GC (median):    0.00%
 Time  (mean ± σ):   94.007 ms ± 451.799 μs  ┊ GC (mean ± σ):  0.00% ± 0.00%

      ▂  █   █         ▂                 ▂
  ▅▅▅▁██▁██▅██▅▁▅█▁▅▁▅▁█▅▅█▅▅▅▁▁▁▁▁▁▁▁▅▅▅█▁▅▁▅▁█▅▁▅▁▁▁▁▁▅▁▁▁▁▅ ▁
  93.4 ms         Histogram: frequency by time           95 ms <

 Memory estimate: 72.38 KiB, allocs estimate: 39.
Generic:
BenchmarkTools.Trial: 68 samples with 1 evaluation.
 Range (min … max):  72.788 ms …  75.219 ms  ┊ GC (min … max): 0.00% … 0.00%
 Time  (median):     74.003 ms               ┊ GC (median):    0.00%
 Time  (mean ± σ):   74.030 ms ± 537.652 μs  ┊ GC (mean ± σ):  0.00% ± 0.00%

                        ▂     ▅▅  ▂         █  ▂
  █▁▁▁▁▁▅▁▁▅▅▅▅▅▅▁▅▁▅▅█▅█▅▁▅▅▅██▅▅█▅▁▅▅█▅█▅▁█████▅▁▁██▁█▅▁▁▁▁▅ ▁
  72.8 ms         Histogram: frequency by time           75 ms <

 Memory estimate: 3.31 KiB, allocs estimate: 1.

i = 432
RecursiveFactorization:
BenchmarkTools.Trial: 45 samples with 1 evaluation.
 Range (min … max):  112.522 ms … 113.863 ms  ┊ GC (min … max): 0.00% … 0.00%
 Time  (median):     112.999 ms               ┊ GC (median):    0.00%
 Time  (mean ± σ):   113.038 ms ± 251.410 μs  ┊ GC (mean ± σ):  0.00% ± 0.00%

           ▁   ▁▁▄ ▄  ▁█▄█      ▄   ▁
  ▆▁▁▁▁▁▁▆▁█▆▁▁███▆█▆▁████▆▁▁▆▆▁█▆▆▁█▁▆▁▁▁▆▁▁▁▆▁▁▁▁▁▆▁▁▁▁▁▁▁▁▁▆ ▁
  113 ms           Histogram: frequency by time          114 ms <

 Memory estimate: 77.50 KiB, allocs estimate: 39.
Generic:
BenchmarkTools.Trial: 57 samples with 1 evaluation.
 Range (min … max):  86.836 ms …  89.692 ms  ┊ GC (min … max): 0.00% … 0.00%
 Time  (median):     88.482 ms               ┊ GC (median):    0.00%
 Time  (mean ± σ):   88.438 ms ± 592.800 μs  ┊ GC (mean ± σ):  0.00% ± 0.00%

                              ▅     ▂▅ █ ▂    ▂    ▂
  ▅▁▁▁▁▁▁▁▅▅▁▁▁▅▅▁▁▁▁▅▁█▅▅▅▁█▁█▅█▅▁▁██▅███▁▅▁▁█▅█▁██▁▅▁▁▁▅▅▅▁▅ ▁
  86.8 ms         Histogram: frequency by time         89.5 ms <

 Memory estimate: 3.50 KiB, allocs estimate: 1.

i = 456
RecursiveFactorization:
BenchmarkTools.Trial: 37 samples with 1 evaluation.
 Range (min … max):  135.696 ms … 137.304 ms  ┊ GC (min … max): 0.00% … 0.00%
 Time  (median):     136.045 ms               ┊ GC (median):    0.00%
 Time  (mean ± σ):   136.114 ms ± 324.938 μs  ┊ GC (mean ± σ):  0.00% ± 0.00%

  ▃   ▃ ▃▃█ ▃ ▃█  ▃ ▃ ▃                ▃
  █▇▁▁█▇███▇█▁██▁▁█▇█▇█▇▁▁▁▇▇▁▁▁▇▁▇▁▁▁▁█▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▇ ▁
  136 ms           Histogram: frequency by time          137 ms <

 Memory estimate: 80.72 KiB, allocs estimate: 40.
Generic:
BenchmarkTools.Trial: 48 samples with 1 evaluation.
 Range (min … max):  103.839 ms … 106.750 ms  ┊ GC (min … max): 0.00% … 0.00%
 Time  (median):     105.004 ms               ┊ GC (median):    0.00%
 Time  (mean ± σ):   105.037 ms ± 640.019 μs  ┊ GC (mean ± σ):  0.00% ± 0.00%

  ▃           █  ▃█  ▃▃▃  █    ▃▃    ▃▃ ▃ █
  █▁▇▁▇▁▇▁▁▁▇▁█▇▁██▁▇███▇▁█▇▇▁▇██▁▇▁▁██▇█▁█▁▁▁▇▇▁▁▇▁▁▁▁▁▁▁▁▁▁▁▇ ▁
  104 ms           Histogram: frequency by time          107 ms <

 Memory estimate: 3.69 KiB, allocs estimate: 1.

i = 480
RecursiveFactorization:
BenchmarkTools.Trial: 32 samples with 1 evaluation.
 Range (min … max):  158.583 ms … 161.430 ms  ┊ GC (min … max): 0.00% … 0.00%
 Time  (median):     158.980 ms               ┊ GC (median):    0.00%
 Time  (mean ± σ):   159.118 ms ± 582.721 μs  ┊ GC (mean ± σ):  0.00% ± 0.00%

  █▃█ ▃▃  █▃    ▃   ▃
  ███▇██▇▇██▁▇▇▁█▇▁▇█▁▁▁▁▇▁▁▇▁▁▁▁▁▁▁▁▁▁▇▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▇ ▁
  159 ms           Histogram: frequency by time          161 ms <

 Memory estimate: 91.03 KiB, allocs estimate: 48.
Generic:
BenchmarkTools.Trial: 41 samples with 1 evaluation.
 Range (min … max):  121.945 ms … 124.500 ms  ┊ GC (min … max): 0.00% … 0.00%
 Time  (median):     123.559 ms               ┊ GC (median):    0.00%
 Time  (mean ± σ):   123.520 ms ± 508.894 μs  ┊ GC (mean ± σ):  0.00% ± 0.00%

                             █    ▂          ▅
  ▅▁▁▁▁▁▁▁▁▁▁▅▁▁▁▁▁▁▁▁▁▁▁▅▅▁▁█▅▅▅▁██▁▁█▁███▅▅█▅▁▁▅█▅▁▅▅▁▁▁▁▁▅▅▅ ▁
  122 ms           Histogram: frequency by time          125 ms <

 Memory estimate: 3.88 KiB, allocs estimate: 1.

i = 504
RecursiveFactorization:
BenchmarkTools.Trial: 28 samples with 1 evaluation.
 Range (min … max):  180.187 ms … 182.071 ms  ┊ GC (min … max): 0.00% … 0.00%
 Time  (median):     180.897 ms               ┊ GC (median):    0.00%
 Time  (mean ± σ):   180.904 ms ± 426.190 μs  ┊ GC (mean ± σ):  0.00% ± 0.00%

  ▁  ▁  ▁█    ▁▁█ ▁ ▁▁ █  █ █ █▁▁▁ ▁  ▁        ▁ ▁            ▁
  █▁▁█▁▁██▁▁▁▁███▁█▁██▁█▁▁█▁█▁████▁█▁▁█▁▁▁▁▁▁▁▁█▁█▁▁▁▁▁▁▁▁▁▁▁▁█ ▁
  180 ms           Histogram: frequency by time          182 ms <

 Memory estimate: 96.86 KiB, allocs estimate: 51.
Generic:
BenchmarkTools.Trial: 35 samples with 1 evaluation.
 Range (min … max):  142.253 ms … 145.542 ms  ┊ GC (min … max): 0.00% … 0.00%
 Time  (median):     143.214 ms               ┊ GC (median):    0.00%
 Time  (mean ± σ):   143.344 ms ± 711.690 μs  ┊ GC (mean ± σ):  0.00% ± 0.00%

      ▃▃  ▃    ▃█  ▃      ▃ ▃     ▃▃
  ▇▁▇▁██▁▁█▁▇▁▇██▇▇█▁▁▁▇▁▇█▇█▁▇▁▇▁██▁▁▁▁▁▁▇▁▁▇▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▇ ▁
  142 ms           Histogram: frequency by time          146 ms <

 Memory estimate: 4.06 KiB, allocs estimate: 1.

@ChrisRackauckas
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Screenshot 2021-12-13 110317

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black is ForwardDiff.jl. ForwardDiff.jl is unable to cache compiles because of tags, so if you precompiled for a given tag those would be gone otherwise we can't do anything else about it
11:04
teal is all mapreduce stacks, I don't know why mapreduce is so bad
11:05
green is logging, I don't know why logging is so specialized to types? That seems fixable
11:05
brown can be fixed on the DiffEq side if we aren't lazy.

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the three browns

Chris Rackauckas:headphones: 11:06 AM
@inline @muladd function calculate_residuals(ũ::Number, u₀::Number, u₁::Number,
α, ρ, internalnorm,t)
@fastmath ũ / (α + max(internalnorm(u₀,t), internalnorm(u₁,t)) * ρ)
end

1 reply
Today at 11:09 AMView thread

Chris Rackauckas:headphones: 11:06 AM
@fastmax div is not precompiled in the Base system image.
11:07
right next to it
11:07
@inline function mul!(C::AbstractArray, s::Number, X::AbstractArray, alpha::Number, beta::Number)
if axes(C) == axes(X)
C .= (s .* X) .*ₛ alpha .+ C .ₛ beta
else
generic_mul!(C, s, X, MulAddMul(alpha, beta))
end
return C
end
@inline function mul!(C::AbstractArray, X::AbstractArray, s::Number, alpha::Number, beta::Number)
if axes(C) == axes(X)
C .= (X . s) .*ₛ alpha .+ C .*ₛ beta
else
generic_mul!(C, X, s, MulAddMul(alpha, beta))
end
return C
end
11:08
those take a substantial amount of time (that's the big stack on the right most brown one). If we make a dispatch for array that has no broadcasting then that would chop out that whole stack.
11:09
The Brown on the left is
function DiffEqBase.remake(thing::Union{OrdinaryDiffEqAdaptiveImplicitAlgorithm{CS,AD,FDT},
OrdinaryDiffEqImplicitAlgorithm{CS,AD,FDT},
DAEAlgorithm{CS,AD,FDT}}; kwargs...) where {CS, AD, FDT}
T = SciMLBase.remaker_of(thing)
T(; chunk_size=Val{CS}(),autodiff=Val{AD}(),SciMLBase.struct_as_namedtuple(thing)...,kwargs...)
end
11:09
that doesn't precompile in DiffEq. 🤷 I might be too lazy for that.

@ChrisRackauckas ChrisRackauckas mentioned this pull request Dec 13, 2021
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@ChrisRackauckas ChrisRackauckas merged commit e22ae54 into master Dec 13, 2021
@ChrisRackauckas ChrisRackauckas deleted the rf_duals branch December 13, 2021 17:10
@ChrisRackauckas ChrisRackauckas mentioned this pull request Dec 14, 2021
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