Identify the performance bottleneck for G(1, 3)

[utensil]

I've just noticed that the test CI is slow due to G(1, 3) Graded identities, particularly for A4, which takes 32m44.7s for no good reason. Tested with branch https://github.com/pygae/GAlgebra.jl/tree/profile_11

  G(1, 3, 0)          |  467            467  34m24.2s
    definition        |   25             25      6.8s
    LA identities     |   12             12      0.0s
    GA identities     |   30             30      9.8s
    Graded identities |  400            400  34m06.2s
      r: 0            |   72             72      0.3s
      r: 1            |   79             79      1.4s
      r: 2            |   82             82      6.3s
      r: 3            |   83             83   1m13.5s
        ArBs s: 0     |   13             13      0.1s
        ArBs s: 1     |   13             13      0.2s
        ArBs s: 2     |   13             13      0.3s
        ArBs s: 3     |   12             12      0.2s
        ArBs s: 4     |   12             12      0.1s
      r: 4            |   84             84  32m44.7s
        ArBs s: 0     |   13             13      0.0s
        ArBs s: 1     |   13             13      0.0s
        ArBs s: 2     |   13             13      0.1s
        ArBs s: 3     |   13             13      0.1s
        ArBs s: 4     |   12             12      0.0s

[utensil]

The slow bit is the tests for A.4.32:

a = V.mv("a", "vector")
a₁₋ᵣ = [V.mv("a_$(i)", "vector") for i in 1:r]

wedge_a₁₋ᵣ = reduce(∧, a₁₋ᵣ)
prod_a₁₋ᵣ = reduce(*, a₁₋ᵣ)

@test wedge_a₁₋ᵣ == prod_a₁₋ᵣ[r]                                                  # A.4.12

A₁₋ᵣ = prod_a₁₋ᵣ

s = 3

Bs = B[s]
# 0.604375 seconds (5 allocations: 96 bytes)
@time AB1 = A₁₋ᵣ * Bs
# 0.976315 seconds (7.27 k allocations: 366.075 KiB, 1.75% compilation time)
@time AB2 = (A₁₋ᵣ)ǂ
# 60.840067 seconds (5 allocations: 96 bytes)
@time A_Bs_Aǂ = AB1 * AB2
# 283.460948 seconds (22 allocations: 704 bytes)
@time @test A_Bs_Aǂ == A_Bs_Aǂ[s]                                         # A.4.32

I've also tried G(4), almost the same time, which means it's not triggered by metric.

[utensil]

Complete stat by https://github.com/pygae/GAlgebra.jl/actions/runs/5081830873/jobs/9130739582 of 7ac49b0

  G(1, 3, 0)          |  467            467  35m01.8s
    definition        |   25             25      7.0s
    LA identities     |   12             12      0.0s
    GA identities     |   30             30      9.9s
    Graded identities |  400            400  34m43.5s
      r: 0            |   72             72      0.3s
        ArBs s: 0     |   12             12      0.0s
        ArBs s: 1     |   12             12      0.1s
        ArBs s: 2     |   12             12      0.1s
        ArBs s: 3     |   12             12      0.1s
        ArBs s: 4     |   12             12      0.0s
      r: 1            |   79             79      1.4s
        s: 1          |    1              1      0.0s
        s: 1          |    1              1      0.1s
        s: 1          |    1              1      0.2s
        s: 1          |    1              1      0.1s
        s: 1          |    1              1      0.0s
        ArBs s: 0     |   13             13      0.1s
        ArBs s: 1     |   12             12      0.2s
        ArBs s: 2     |   12             12      0.3s
        ArBs s: 3     |   12             12      0.2s
        ArBs s: 4     |   12             12      0.0s
      r: 2            |   82             82      6.4s
        s: 2          |    1              1      0.2s
        s: 2          |    1              1      1.2s
        s: 2          |    1              1      2.0s
        s: 2          |    1              1      1.3s
        s: 2          |    1              1      0.2s
        ArBs s: 0     |   13             13      0.1s
        ArBs s: 1     |   13             13      0.3s
        ArBs s: 2     |   12             12      0.5s
        ArBs s: 3     |   12             12      0.3s
        ArBs s: 4     |   12             12      0.1s
      r: 3            |   83             83   1m14.3s
        s: 3          |    1              1      2.2s
        s: 3          |    1              1     16.6s
        s: 3          |    1              1     35.3s
        s: 3          |    1              1     16.7s
        s: 3          |    1              1      2.2s
        ArBs s: 0     |   13             13      0.1s
        ArBs s: 1     |   13             13      0.2s
        ArBs s: 2     |   13             13      0.3s
        ArBs s: 3     |   12             12      0.2s
        ArBs s: 4     |   12             12      0.1s
      r: 4            |   84             84  33m21.1s
        s: 4          |    1              1     32.0s
        s: 4          |    1              1   6m05.0s
        s: 4          |    1              1  20m10.1s
        s: 4          |    1              1   6m01.0s
        s: 4          |    1              1     31.8s
        ArBs s: 0     |   13             13      0.0s
        ArBs s: 1     |   13             13      0.1s
        ArBs s: 2     |   13             13      0.1s
        ArBs s: 3     |   13             13      0.1s
        ArBs s: 4     |   12             12      0.0s

compared to G(3):

  G(3, 0, 0)          |  379       1    380     29.2s
    definition        |   34             34      3.1s
    LA identities     |   12             12      0.0s
    GA identities     |   52       1     53     17.1s
    Graded identities |  281            281      8.9s
      r: 0            |   64             64      0.3s
        ArBs s: 0     |   13             13      0.0s
        ArBs s: 1     |   13             13      0.1s
        ArBs s: 2     |   13             13      0.1s
        ArBs s: 3     |   13             13      0.0s
      r: 1            |   70             70      0.9s
        s: 1          |    1              1      0.0s
        s: 1          |    1              1      0.0s
        s: 1          |    1              1      0.0s
        s: 1          |    1              1      0.0s
        ArBs s: 0     |   14             14      0.1s
        ArBs s: 1     |   13             13      0.3s
        ArBs s: 2     |   13             13      0.3s
        ArBs s: 3     |   13             13      0.1s
      r: 2            |   73             73      1.5s
        s: 2          |    1              1      0.1s
        s: 2          |    1              1      0.3s
        s: 2          |    1              1      0.3s
        s: 2          |    1              1      0.1s
        ArBs s: 0     |   14             14      0.1s
        ArBs s: 1     |   14             14      0.3s
        ArBs s: 2     |   13             13      0.3s
        ArBs s: 3     |   13             13      0.1s
      r: 3            |   74             74      6.1s
        s: 3          |    1              1      0.4s
        s: 3          |    1              1      2.5s
        s: 3          |    1              1      2.5s
        s: 3          |    1              1      0.4s
        ArBs s: 0     |   14             14      0.0s
        ArBs s: 1     |   14             14      0.1s
        ArBs s: 2     |   14             14      0.1s
        ArBs s: 3     |   13             13      0.0s