Compare 2x2 matrix multiplication methods in Julia

mult.jl

using BenchmarkTools. LinearAlgebra
function naive_mul!(C,A,B)
    C[1,1] = A[1,1] * B[1,1] + A[1,2] * B[2,1]
    C[1,2] = A[1,1] * B[1,2] + A[1,2] * B[2,2]
    C[2,1] = A[2,1] * B[1,1] + A[2,2] * B[2,1]
    C[2,2] = A[2,1] * B[1,2] + A[2,2] * B[2,2]
    return nothing
end 

function strassen_mul!(C,A,B)
    M1 = (A[1,1] + A[2,2]) * (B[1,1] + B[2,2])
    M2 = (A[2,1] + A[2,2]) * B[1,1]
    M3 = A[1,1] * (B[1,2] - B[2,2])
    M4 = A[2,2] * (B[2,1] - B[1,1])
    M5 = (A[1,1] + A[1,2]) * B[2,2]
    M6 = (A[2,1] - A[1,1]) * (B[1,1] + B[1,2])
    M7 = (A[1,2] - A[2,2]) * (B[2,1] + B[2,2])
    C[1,1] = M1 + M4 - M5 + M7 
    C[1,2] = M3 + M5 
    C[2,1] = M2 + M4 
    C[2,2] = M1 - M2 + M3 + M6 
    return nothing 
end

A = rand(2,2)
B = rand(2,2)
C = zeros(2,2)
@benchmark mul!($C,$A,$B) 
# BenchmarkTools.Trial: 
#   memory estimate:  0 bytes
#   allocs estimate:  0
#   --------------
#   minimum time:     16.749 ns (0.00% GC)
#   median time:      17.271 ns (0.00% GC)
#   mean time:        17.642 ns (0.00% GC)
#   maximum time:     46.273 ns (0.00% GC)
#   --------------
#   samples:          10000
#   evals/sample:     998
@benchmark naive_mul!($C,$A,$B)
# BenchmarkTools.Trial: 
#   memory estimate:  0 bytes
#   allocs estimate:  0
#   --------------
#   minimum time:     12.518 ns (0.00% GC)
#   median time:      12.635 ns (0.00% GC)
#   mean time:        12.886 ns (0.00% GC)
#   maximum time:     52.074 ns (0.00% GC)
#   --------------
#   samples:          10000
#   evals/sample:     999
@benchmark strassen_mul!($C,$A,$B)
# BenchmarkTools.Trial: 
#   memory estimate:  0 bytes
#   allocs estimate:  0
#   --------------
#   minimum time:     14.810 ns (0.00% GC)
#   median time:      14.869 ns (0.00% GC)
#   mean time:        15.177 ns (0.00% GC)
#   maximum time:     47.266 ns (0.00% GC)
#   --------------
#   samples:          10000
#   evals/sample:     998