Less time to compute overlap

[Leticia-maria]

julia> @time overlap(basis, mol)
  0.000214 seconds (730 allocations: 57.672 KiB)
9×9 Matrix{Float64}:
  1.0           0.417217      4.7553e-22    0.0       -2.24549e-23   0.193855   0.193845   0.193845   0.193849
  0.417217      1.21286      -1.33492e-21   0.0        1.13493e-22   0.859163   0.859146   0.859146   0.859154
  4.7553e-22   -1.33492e-21   1.0           0.0       -4.14649e-43  -0.0939536  0.361208   0.167531  -0.434825
  0.0           0.0           0.0           1.0        0.0           0.41387    0.117069  -0.388952  -0.14202
 -2.24549e-23   1.13493e-22  -4.14649e-43   0.0        1.0          -0.295301   0.350927  -0.296608   0.240999
  0.193855      0.859163     -0.0939536     0.41387   -0.295301      1.0        0.5271     0.527089   0.527123
  0.193845      0.859146      0.361208      0.117069   0.350927      0.5271     1.0        0.527093   0.527093
  0.193845      0.859146      0.167531     -0.388952  -0.296608      0.527089   0.527093   1.0        0.527113
  0.193849      0.859154     -0.434825     -0.14202    0.240999      0.527123   0.527093   0.527113   1.0

julia> using BenchmarkTools

julia> @benchmark overlap(basis, mol)
BenchmarkTools.Trial: 10000 samples with 1 evaluation.
 Range (min … max):  111.042 μs …  21.491 ms  ┊ GC (min … max): 0.00% … 99.29%
 Time  (median):     120.208 μs               ┊ GC (median):    0.00%
 Time  (mean ± σ):   124.477 μs ± 241.769 μs  ┊ GC (mean ± σ):  2.96% ±  1.70%

               ▁  ▂▄▇█▇█▄▅▃▁
  ▁▁▁▂▁▂▃▃▄▆▇███▆▇███████████▆▅▅▄▄▄▃▃▃▃▂▂▂▂▂▂▂▂▂▂▂▁▁▁▁▁▁▁▁▁▁▁▁▁ ▃
  111 μs           Histogram: frequency by time          138 μs <

 Memory estimate: 57.67 KiB, allocs estimate: 730.

[Leticia-maria]

By adding new doublefactorial() factorial, I have:

julia> @benchmark overlap(basis, mol)
BenchmarkTools.Trial: 10000 samples with 1 evaluation.
 Range (min … max):  103.875 μs …  35.961 ms  ┊ GC (min … max): 0.00% … 99.57%
 Time  (median):     108.583 μs               ┊ GC (median):    0.00%
 Time  (mean ± σ):   113.875 μs ± 372.782 μs  ┊ GC (mean ± σ):  4.04% ±  1.40%

             ▂▃▆▅▇▇█▇▆▆▅▃
  ▂▄▆▇█▇▅▃▃▄▇█████████████▇▅▆▅▅▅▆▅▄▅▄▄▄▃▃▃▃▃▃▃▃▂▃▃▂▂▂▂▂▂▂▁▂▂▁▁▂ ▄
  104 μs           Histogram: frequency by time          119 μs <

 Memory estimate: 57.67 KiB, allocs estimate: 730.

[Leticia-maria]

old overlap

julia> @benchmark overlap_2(basis, mol)
BenchmarkTools.Trial: 10000 samples with 1 evaluation.
 Range (min … max):  122.417 μs …  21.263 ms  ┊ GC (min … max): 0.00% … 99.24%
 Time  (median):     128.125 μs               ┊ GC (median):    0.00%
 Time  (mean ± σ):   131.677 μs ± 252.757 μs  ┊ GC (mean ± σ):  2.65% ±  1.40%

            ▁▁   ▁▃▁▄▂▄▃▅▇▅█▅▇▇▅▄▂▃▁
  ▁▁▁▂▃▅▆▇█▇██▆██████████████████████▇▆▅▅▄▄▃▃▃▃▂▂▂▂▂▂▁▂▂▂▁▁▁▁▁▁ ▄
  122 μs           Histogram: frequency by time          137 μs <

 Memory estimate: 57.67 KiB, allocs estimate: 730.