3 argument dot is slower than a matmul and two arg dot

[SobhanMP]

Somewhat counter intuitive:

using LinearAlgebra, StaticArrays, BenchmarkTools

f1(x, A) = dot(x, A * x)
f2(x, A) = dot(x, A, x)
let 
    x = randn(3)
    A = randn(3, 3)
    A = A * A' + 1e-6 * I
    sx = SVector{3}(x...)
    sA = SMatrix{3,3}(A...)
    display(@benchmark(f1($sx, $sA)))
    display(@benchmark(f2($sx, $sA)))
end

BenchmarkTools.Trial: 10000 samples with 1000 evaluations.
 Range (min … max):  2.813 ns … 18.835 ns  ┊ GC (min … max): 0.00% … 0.00%
 Time  (median):     2.817 ns              ┊ GC (median):    0.00%
 Time  (mean ± σ):   2.878 ns ±  0.673 ns  ┊ GC (mean ± σ):  0.00% ± 0.00%

  █   ▅▁                                                     ▁
  █▅▁▁██▄▁▄▁▁▁▁▁▇▁▁▁▁▆▃▁▁▃▃▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▃▄▄▃▆▇▅ █
  2.81 ns      Histogram: log(frequency) by time     3.54 ns <

 Memory estimate: 0 bytes, allocs estimate: 0.
BenchmarkTools.Trial: 10000 samples with 1000 evaluations.
 Range (min … max):  3.815 ns … 54.783 ns  ┊ GC (min … max): 0.00% … 0.00%
 Time  (median):     3.821 ns              ┊ GC (median):    0.00%
 Time  (mean ± σ):   3.931 ns ±  1.141 ns  ┊ GC (mean ± σ):  0.00% ± 0.00%

  █  ▆     ▁                                                 ▁
  █▆▅█▅▇▃▅▇█▃▅▃▅▄▅▁▁▁▄▁▁▁▃▁▁▁▁▁▃▃▁▃▁▃▁▁▁▃▁▁▁▁▃▁▃▃▁▁▁▁▄▁▁▁▁▁▃ █
  3.82 ns      Histogram: log(frequency) by time      5.3 ns <

 Memory estimate: 0 bytes, allocs estimate: 0.

julia> versioninfo()
Julia Version 1.11.1
Commit 8f5b7ca12ad (2024-10-16 10:53 UTC)
Build Info:
 Official https://julialang.org/ release
Platform Info:
 OS: Linux (x86_64-linux-gnu)
 CPU: 16 × 11th Gen Intel(R) Core(TM) i7-11700K @ 3.60GHz
 WORD_SIZE: 64
 LLVM: libLLVM-16.0.6 (ORCJIT, rocketlake)
Threads: 16 default, 0 interactive, 8 GC (on 16 virtual cores)
Environment:
 JULIA_EDITOR = code
 JULIA_NUM_THREADS = 16