Update benchmark results

Author: ferrolho

docs/src/benchmarks.md

@@ -1,6 +1,9 @@
 # Benchmarks
 
-To attain maximal performance, it is recommended to pass `-O3`, `--check-bounds=no` as command line flags to `julia`. As of Julia 1.1, maximizing performance for the `dynamics!` algorithm requires either setting the number of BLAS threads to 1 (`using LinearAlgebra; BLAS.set_num_threads(1)`) if using OpenBLAS (the default), or compiling Julia with MKL. See [this issue](https://github.com/JuliaRobotics/RigidBodyDynamics.jl/issues/500) for more information.
+To attain maximal performance, it is recommended to pass `-O3` and `--check-bounds=no` as command line flags to `julia`.
+
+> **Warning**
+> For Julia versions previous to `v1.8`, maximizing performance for the `dynamics!` algorithm requires either setting the number of BLAS threads to 1 (`using LinearAlgebra; BLAS.set_num_threads(1)`) if using OpenBLAS (the default), or compiling Julia with MKL. See [this issue](https://github.com/JuliaRobotics/RigidBodyDynamics.jl/issues/500) for more information.
 
 Run `perf/runbenchmarks.jl` to see benchmark results for the Atlas robot (v5). Results below are for the following scenarios:
 
@@ -9,69 +12,81 @@ Run `perf/runbenchmarks.jl` to see benchmark results for the Atlas robot (v5). R
 3. Do inverse dynamics.
 4. Do forward dynamics.
 
-Note that results on CI builds are **not at all** representative because of code coverage. Results on a reasonably fast laptop at commit [870bea6](https://github.com/JuliaRobotics/RigidBodyDynamics.jl/commit/870bea668d5b11ce0555fa0552592d2c3cb15c54):
+> **Note**
+> Results on CI builds are **not at all** representative because of code coverage.
 
-Output of `versioninfo()`:
+Here are the results on an Apple MacBook Air (M1, 2020) (8GB RAM, 512GB SSD) at commit [b9ef1d](https://github.com/JuliaRobotics/RigidBodyDynamics.jl/commit/b9ef1d6974beff4d4fbe7dffc6dbfa65f71e0132):
 
+Output of `versioninfo()`:
 ```
-Julia Version 1.5.3
-Commit 788b2c77c1 (2020-11-09 13:37 UTC)
+Julia Version 1.8.5
+Commit 17cfb8e65e* (2023-01-08 06:45 UTC)
 Platform Info:
-  OS: macOS (x86_64-apple-darwin18.7.0)
-  CPU: Intel(R) Core(TM) i7-8850H CPU @ 2.60GHz
+  OS: macOS (arm64-apple-darwin22.1.0)
+  CPU: 8 × Apple M1
   WORD_SIZE: 64
   LIBM: libopenlibm
-  LLVM: libLLVM-9.0.1 (ORCJIT, skylake)
+  LLVM: libLLVM-13.0.1 (ORCJIT, apple-m1)
+  Threads: 1 on 4 virtual cores
 ```
 
-Note that this is a different machine than the one that was used for earlier benchmarks.
+> **Note**
+> This is a different machine than the one that was used for earlier benchmarks.
 
-Mass matrix:
-
-```
-  memory estimate:  0 bytes
-  allocs estimate:  0
-  --------------
-  minimum time:     4.415 μs (0.00% GC)
-  median time:      4.579 μs (0.00% GC)
-  mean time:        4.916 μs (0.00% GC)
-  maximum time:     19.794 μs (0.00% GC)
+Mass matrix ([`mass_matrix!`](@ref)):
 ```
+BenchmarkTools.Trial: 10000 samples with 10 evaluations.
+ Range (min … max):  3.796 μs …  6.183 μs  ┊ GC (min … max): 0.00% … 0.00%
+ Time  (median):     3.858 μs              ┊ GC (median):    0.00%
+ Time  (mean ± σ):   3.879 μs ± 93.310 ns  ┊ GC (mean ± σ):  0.00% ± 0.00%
 
-Mass matrix and Jacobian from left hand to right foot:
+    ▁▄▄▆▆██▇█▆▇▄▅▄▂▃▁▃▂▃▃▁▃▁▂ ▁                              ▂
+  ▅█████████████████████████████▇█▇█▇▆▇▅▆▅▆▅▅▆▅▆▄▇▆█▇▅▆▆▇▅▄▄ █
+  3.8 μs       Histogram: log(frequency) by time     4.18 μs <
 
+ Memory estimate: 0 bytes, allocs estimate: 0.
 ```
-  memory estimate:  0 bytes
-  allocs estimate:  0
-  --------------
-  minimum time:     4.860 μs (0.00% GC)
-  median time:      4.982 μs (0.00% GC)
-  mean time:        5.399 μs (0.00% GC)
-  maximum time:     24.712 μs (0.00% GC)
+
+Mass matrix ([`mass_matrix!`](@ref)) and Jacobian ([`geometric_jacobian!`](@ref)) from left hand to right foot:
+```julia
+BenchmarkTools.Trial: 10000 samples with 10 evaluations.
+ Range (min … max):  4.042 μs …   6.763 μs  ┊ GC (min … max): 0.00% … 0.00%
+ Time  (median):     4.167 μs               ┊ GC (median):    0.00%
+ Time  (mean ± σ):   4.187 μs ± 115.303 ns  ┊ GC (mean ± σ):  0.00% ± 0.00%
+
+     ▁▁▂▁▁ ▁▃▄▆▇██▇█▇▆▄▃▃▃▃▁▃▃▃▂▂▁▁                           ▃
+  ▃▅███████████████████████████████▇██▇██▆▇▆▄▆▅▆▇▇██▆██▆▆▅▁▅▄ █
+  4.04 μs      Histogram: log(frequency) by time       4.5 μs <
+
+ Memory estimate: 0 bytes, allocs estimate: 0.
 ```
 
 Note the low additional cost of computing a Jacobian when the mass matrix is already computed. This is because RigidBodyDynamics.jl caches intermediate computation results.
 
-Inverse dynamics:
+Inverse dynamics ([`inverse_dynamics!`](@ref)):
+```julia
+BenchmarkTools.Trial: 10000 samples with 10 evaluations.
+ Range (min … max):  2.700 μs …  5.700 μs  ┊ GC (min … max): 0.00% … 0.00%
+ Time  (median):     2.767 μs              ┊ GC (median):    0.00%
+ Time  (mean ± σ):   2.773 μs ± 79.491 ns  ┊ GC (mean ± σ):  0.00% ± 0.00%
 
-```
-  memory estimate:  0 bytes
-  allocs estimate:  0
-  --------------
-  minimum time:     4.256 μs (0.00% GC)
-  median time:      4.541 μs (0.00% GC)
-  mean time:        4.831 μs (0.00% GC)
-  maximum time:     21.625 μs (0.00% GC)
+              ▁▁█
+  ▂▂▂▂▂▂▃▅▅▆▇█████▇▆▅▄▃▄▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▁▂▂▁▂▂▂▁▂▂▂▂ ▃
+  2.7 μs         Histogram: frequency by time        2.98 μs <
+
+ Memory estimate: 0 bytes, allocs estimate: 0.
 ```
 
-Forward dynamics:
+Forward dynamics ([`dynamics!`](@ref)):
+```julia
+BenchmarkTools.Trial: 10000 samples with 10 evaluations.
+ Range (min … max):  10.554 μs …  23.692 μs  ┊ GC (min … max): 0.00% … 0.00%
+ Time  (median):     10.667 μs               ┊ GC (median):    0.00%
+ Time  (mean ± σ):   10.703 μs ± 212.557 ns  ┊ GC (mean ± σ):  0.00% ± 0.00%
 
-```
-  memory estimate:  0 bytes
-  allocs estimate:  0
-  --------------
-  minimum time:     13.600 μs (0.00% GC)
-  median time:      14.419 μs (0.00% GC)
-  mean time:        16.071 μs (0.00% GC)
-  maximum time:     55.328 μs (0.00% GC)
+        ▃▇█▇▅▂
+  ▁▁▂▂▄███████▇▄▃▂▂▂▁▁▁▁▁▁▁▁▁▁▂▂▂▂▂▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ ▂
+  10.6 μs         Histogram: frequency by time         11.3 μs <
+
+ Memory estimate: 0 bytes, allocs estimate: 0.
 ```