Benchmarks

a = rand(Vec{3})
A = rand(SecondOrderTensor{3})
S = rand(SymmetricSecondOrderTensor{3})
B = rand(Tensor{Tuple{3,3,3}})
AA = rand(FourthOrderTensor{3})
SS = rand(SymmetricFourthOrderTensor{3})

Operation	`Tensor`	`Array`	speed-up
Single contraction
`a ⋅ a`	2.785 ns	9.577 ns	×3.4
`A ⋅ a`	3.095 ns	62.944 ns	×20.3
`S ⋅ a`	3.095 ns	62.974 ns	×20.3
Double contraction
`A ⊡ A`	3.406 ns	12.095 ns	×3.6
`S ⊡ S`	3.406 ns	11.112 ns	×3.3
`B ⊡ A`	5.419 ns	134.883 ns	×24.9
`AA ⊡ A`	7.732 ns	145.162 ns	×18.8
`SS ⊡ S`	4.087 ns	150.219 ns	×36.8
Tensor product
`a ⊗ a`	3.406 ns	39.265 ns	×11.5
Cross product
`a × a`	3.406 ns	39.265 ns	×11.5
Determinant
`det(A)`	3.396 ns	191.000 ns	×56.2
`det(S)`	3.406 ns	191.278 ns	×56.2
Inverse
`inv(A)`	5.801 ns	488.241 ns	×84.2
`inv(S)`	4.889 ns	493.082 ns	×100.9
`inv(AA)`	906.158 ns	1.540 μs	×1.7
`inv(SS)`	325.468 ns	1.543 μs	×4.7

The benchmarks are generated by runbenchmarks.jl on the following system:

julia> versioninfo()
Julia Version 1.10.2
Commit bd47eca2c8a (2024-03-01 10:14 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: Linux (x86_64-linux-gnu)
  CPU: 4 × AMD EPYC 7763 64-Core Processor
  WORD_SIZE: 64
  LIBM: libopenlibm
  LLVM: libLLVM-15.0.7 (ORCJIT, znver3)
Threads: 1 default, 0 interactive, 1 GC (on 4 virtual cores)